diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_internal.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_internal.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..bc44e0ce5bba2d3d194807c107abd5592b3f0694 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_internal.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_ufunc_config.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_ufunc_config.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f854e15dcb99ac4a3d4f236125c1db06e32f4d45 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/_ufunc_config.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/einsumfunc.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/einsumfunc.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..5e0fcadc8f2c29715680fe93f6b07d767e382328 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/einsumfunc.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/function_base.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/function_base.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..5760d223b4fa24039488299258ef00365ed60d4b Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/function_base.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/multiarray.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/multiarray.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..39300944c6ef1ee6d4cc590bde046eb6727c3a7c Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/multiarray.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numeric.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numeric.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..2ad647905b76800ec1564200b465c2638e094199 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numeric.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numerictypes.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numerictypes.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..cb3b9313693a8dc4801ddab29d437f7847360f83 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/numerictypes.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/overrides.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/overrides.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ebd1adaf098b4f66551827cf39284577e3900169 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/overrides.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/printoptions.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/printoptions.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..44af7734f88e9f320cc52182fdc544f72613c20f Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/__pycache__/printoptions.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.c b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.c new file mode 100644 index 0000000000000000000000000000000000000000..c1a152704fa18c79f928b8fa6644f362579383f1 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.c @@ -0,0 +1,376 @@ + +/* These pointers will be stored in the C-object for use in other + extension modules +*/ + +void *PyArray_API[] = { + (void *) PyArray_GetNDArrayCVersion, + NULL, + (void *) &PyArray_Type, + (void *) &PyArrayDescr_Type, + NULL, + (void *) &PyArrayIter_Type, + (void *) &PyArrayMultiIter_Type, + (int *) &NPY_NUMUSERTYPES, + (void *) &PyBoolArrType_Type, + (void *) &_PyArrayScalar_BoolValues, + (void *) &PyGenericArrType_Type, + (void *) &PyNumberArrType_Type, + (void *) &PyIntegerArrType_Type, + (void *) &PySignedIntegerArrType_Type, + (void *) &PyUnsignedIntegerArrType_Type, + (void *) &PyInexactArrType_Type, + (void *) &PyFloatingArrType_Type, + (void *) &PyComplexFloatingArrType_Type, + (void *) &PyFlexibleArrType_Type, + (void *) &PyCharacterArrType_Type, + (void *) &PyByteArrType_Type, + (void *) &PyShortArrType_Type, + (void *) &PyIntArrType_Type, + (void *) &PyLongArrType_Type, + (void *) &PyLongLongArrType_Type, + (void *) &PyUByteArrType_Type, + (void *) &PyUShortArrType_Type, + (void *) &PyUIntArrType_Type, + (void *) &PyULongArrType_Type, + (void *) &PyULongLongArrType_Type, + (void *) &PyFloatArrType_Type, + (void *) &PyDoubleArrType_Type, + (void *) &PyLongDoubleArrType_Type, + (void *) &PyCFloatArrType_Type, + (void *) &PyCDoubleArrType_Type, + (void *) &PyCLongDoubleArrType_Type, + (void *) &PyObjectArrType_Type, + (void *) &PyStringArrType_Type, + (void *) &PyUnicodeArrType_Type, + (void *) &PyVoidArrType_Type, + NULL, + NULL, + (void *) PyArray_INCREF, + (void *) PyArray_XDECREF, + (void *) PyArray_SetStringFunction, + (void *) PyArray_DescrFromType, + (void *) PyArray_TypeObjectFromType, + (void *) PyArray_Zero, + (void *) PyArray_One, + (void *) PyArray_CastToType, + (void *) PyArray_CopyInto, + (void *) PyArray_CopyAnyInto, + (void *) PyArray_CanCastSafely, + (void *) PyArray_CanCastTo, + (void *) PyArray_ObjectType, + (void *) PyArray_DescrFromObject, + (void *) PyArray_ConvertToCommonType, + (void *) PyArray_DescrFromScalar, + (void *) PyArray_DescrFromTypeObject, + (void *) PyArray_Size, + (void *) PyArray_Scalar, + (void *) PyArray_FromScalar, + (void *) PyArray_ScalarAsCtype, + (void *) PyArray_CastScalarToCtype, + (void *) PyArray_CastScalarDirect, + (void *) PyArray_Pack, + NULL, + NULL, + NULL, + (void *) PyArray_FromAny, + (void *) PyArray_EnsureArray, + (void *) PyArray_EnsureAnyArray, + (void *) PyArray_FromFile, + (void *) PyArray_FromString, + (void *) PyArray_FromBuffer, + (void *) PyArray_FromIter, + (void *) PyArray_Return, + (void *) PyArray_GetField, + (void *) PyArray_SetField, + (void *) PyArray_Byteswap, + (void *) PyArray_Resize, + NULL, + NULL, + NULL, + (void *) PyArray_CopyObject, + (void *) PyArray_NewCopy, + (void *) PyArray_ToList, + (void *) PyArray_ToString, + (void *) PyArray_ToFile, + (void *) PyArray_Dump, + (void *) PyArray_Dumps, + (void *) PyArray_ValidType, + (void *) PyArray_UpdateFlags, + (void *) PyArray_New, + (void *) PyArray_NewFromDescr, + (void *) PyArray_DescrNew, + (void *) PyArray_DescrNewFromType, + (void *) PyArray_GetPriority, + (void *) PyArray_IterNew, + (void *) PyArray_MultiIterNew, + (void *) PyArray_PyIntAsInt, + (void *) PyArray_PyIntAsIntp, + (void *) PyArray_Broadcast, + NULL, + (void *) PyArray_FillWithScalar, + (void *) PyArray_CheckStrides, + (void *) PyArray_DescrNewByteorder, + (void *) PyArray_IterAllButAxis, + (void *) PyArray_CheckFromAny, + (void *) PyArray_FromArray, + (void *) PyArray_FromInterface, + (void *) PyArray_FromStructInterface, + (void *) PyArray_FromArrayAttr, + (void *) PyArray_ScalarKind, + (void *) PyArray_CanCoerceScalar, + NULL, + (void *) PyArray_CanCastScalar, + NULL, + (void *) PyArray_RemoveSmallest, + (void *) PyArray_ElementStrides, + (void *) PyArray_Item_INCREF, + (void *) PyArray_Item_XDECREF, + NULL, + (void *) PyArray_Transpose, + (void *) PyArray_TakeFrom, + (void *) PyArray_PutTo, + (void *) PyArray_PutMask, + (void *) PyArray_Repeat, + (void *) PyArray_Choose, + (void *) PyArray_Sort, + (void *) PyArray_ArgSort, + (void *) PyArray_SearchSorted, + (void *) PyArray_ArgMax, + (void *) PyArray_ArgMin, + (void *) PyArray_Reshape, + (void *) PyArray_Newshape, + (void *) PyArray_Squeeze, + (void *) PyArray_View, + (void *) PyArray_SwapAxes, + (void *) PyArray_Max, + (void *) PyArray_Min, + (void *) PyArray_Ptp, + (void *) PyArray_Mean, + (void *) PyArray_Trace, + (void *) PyArray_Diagonal, + (void *) PyArray_Clip, + (void *) PyArray_Conjugate, + (void *) PyArray_Nonzero, + (void *) PyArray_Std, + (void *) PyArray_Sum, + (void *) PyArray_CumSum, + (void *) PyArray_Prod, + (void *) PyArray_CumProd, + (void *) PyArray_All, + (void *) PyArray_Any, + (void *) PyArray_Compress, + (void *) PyArray_Flatten, + (void *) PyArray_Ravel, + (void *) PyArray_MultiplyList, + (void *) PyArray_MultiplyIntList, + (void *) PyArray_GetPtr, + (void *) PyArray_CompareLists, + (void *) PyArray_AsCArray, + NULL, + NULL, + (void *) PyArray_Free, + (void *) PyArray_Converter, + (void *) PyArray_IntpFromSequence, + (void *) PyArray_Concatenate, + (void *) PyArray_InnerProduct, + (void *) PyArray_MatrixProduct, + NULL, + (void *) PyArray_Correlate, + NULL, + (void *) PyArray_DescrConverter, + (void *) PyArray_DescrConverter2, + (void *) PyArray_IntpConverter, + (void *) PyArray_BufferConverter, + (void *) PyArray_AxisConverter, + (void *) PyArray_BoolConverter, + (void *) PyArray_ByteorderConverter, + (void *) PyArray_OrderConverter, + (void *) PyArray_EquivTypes, + (void *) PyArray_Zeros, + (void *) PyArray_Empty, + (void *) PyArray_Where, + (void *) PyArray_Arange, + (void *) PyArray_ArangeObj, + (void *) PyArray_SortkindConverter, + (void *) PyArray_LexSort, + (void *) PyArray_Round, + (void *) PyArray_EquivTypenums, + (void *) PyArray_RegisterDataType, + (void *) PyArray_RegisterCastFunc, + (void *) PyArray_RegisterCanCast, + (void *) PyArray_InitArrFuncs, + (void *) PyArray_IntTupleFromIntp, + NULL, + (void *) PyArray_ClipmodeConverter, + (void *) PyArray_OutputConverter, + (void *) PyArray_BroadcastToShape, + NULL, + NULL, + (void *) PyArray_DescrAlignConverter, + (void *) PyArray_DescrAlignConverter2, + (void *) PyArray_SearchsideConverter, + (void *) PyArray_CheckAxis, + (void *) PyArray_OverflowMultiplyList, + NULL, + (void *) PyArray_MultiIterFromObjects, + (void *) PyArray_GetEndianness, + (void *) PyArray_GetNDArrayCFeatureVersion, + (void *) PyArray_Correlate2, + (void *) PyArray_NeighborhoodIterNew, + (void *) &PyTimeIntegerArrType_Type, + (void *) &PyDatetimeArrType_Type, + (void *) &PyTimedeltaArrType_Type, + (void *) &PyHalfArrType_Type, + (void *) &NpyIter_Type, + NULL, + NULL, + NULL, + NULL, + NULL, + (void *) NpyIter_New, + (void *) NpyIter_MultiNew, + (void *) NpyIter_AdvancedNew, + (void *) NpyIter_Copy, + (void *) NpyIter_Deallocate, + (void *) NpyIter_HasDelayedBufAlloc, + (void *) NpyIter_HasExternalLoop, + (void *) NpyIter_EnableExternalLoop, + (void *) NpyIter_GetInnerStrideArray, + (void *) NpyIter_GetInnerLoopSizePtr, + (void *) NpyIter_Reset, + (void *) NpyIter_ResetBasePointers, + (void *) NpyIter_ResetToIterIndexRange, + (void *) NpyIter_GetNDim, + (void *) NpyIter_GetNOp, + (void *) NpyIter_GetIterNext, + (void *) NpyIter_GetIterSize, + (void *) NpyIter_GetIterIndexRange, + (void *) NpyIter_GetIterIndex, + (void *) NpyIter_GotoIterIndex, + (void *) NpyIter_HasMultiIndex, + (void *) NpyIter_GetShape, + (void *) NpyIter_GetGetMultiIndex, + (void *) NpyIter_GotoMultiIndex, + (void *) NpyIter_RemoveMultiIndex, + (void *) NpyIter_HasIndex, + (void *) NpyIter_IsBuffered, + (void *) NpyIter_IsGrowInner, + (void *) NpyIter_GetBufferSize, + (void *) NpyIter_GetIndexPtr, + (void *) NpyIter_GotoIndex, + (void *) NpyIter_GetDataPtrArray, + (void *) NpyIter_GetDescrArray, + (void *) NpyIter_GetOperandArray, + (void *) NpyIter_GetIterView, + (void *) NpyIter_GetReadFlags, + (void *) NpyIter_GetWriteFlags, + (void *) NpyIter_DebugPrint, + (void *) NpyIter_IterationNeedsAPI, + (void *) NpyIter_GetInnerFixedStrideArray, + (void *) NpyIter_RemoveAxis, + (void *) NpyIter_GetAxisStrideArray, + (void *) NpyIter_RequiresBuffering, + (void *) NpyIter_GetInitialDataPtrArray, + (void *) NpyIter_CreateCompatibleStrides, + (void *) PyArray_CastingConverter, + (void *) PyArray_CountNonzero, + (void *) PyArray_PromoteTypes, + (void *) PyArray_MinScalarType, + (void *) PyArray_ResultType, + (void *) PyArray_CanCastArrayTo, + (void *) PyArray_CanCastTypeTo, + (void *) PyArray_EinsteinSum, + (void *) PyArray_NewLikeArray, + NULL, + (void *) PyArray_ConvertClipmodeSequence, + (void *) PyArray_MatrixProduct2, + (void *) NpyIter_IsFirstVisit, + (void *) PyArray_SetBaseObject, + (void *) PyArray_CreateSortedStridePerm, + (void *) PyArray_RemoveAxesInPlace, + (void *) PyArray_DebugPrint, + (void *) PyArray_FailUnlessWriteable, + (void *) PyArray_SetUpdateIfCopyBase, + (void *) PyDataMem_NEW, + (void *) PyDataMem_FREE, + (void *) PyDataMem_RENEW, + NULL, + (NPY_CASTING *) &NPY_DEFAULT_ASSIGN_CASTING, + NULL, + NULL, + NULL, + (void *) PyArray_Partition, + (void *) PyArray_ArgPartition, + (void *) PyArray_SelectkindConverter, + (void *) PyDataMem_NEW_ZEROED, + (void *) PyArray_CheckAnyScalarExact, + NULL, + (void *) PyArray_ResolveWritebackIfCopy, + (void *) PyArray_SetWritebackIfCopyBase, + (void *) PyDataMem_SetHandler, + (void *) PyDataMem_GetHandler, + (PyObject* *) &PyDataMem_DefaultHandler, + (void *) NpyDatetime_ConvertDatetime64ToDatetimeStruct, + (void *) NpyDatetime_ConvertDatetimeStructToDatetime64, + (void *) NpyDatetime_ConvertPyDateTimeToDatetimeStruct, + (void *) NpyDatetime_GetDatetimeISO8601StrLen, + (void *) NpyDatetime_MakeISO8601Datetime, + (void *) NpyDatetime_ParseISO8601Datetime, + (void *) NpyString_load, + (void *) NpyString_pack, + (void *) NpyString_pack_null, + (void *) NpyString_acquire_allocator, + (void *) NpyString_acquire_allocators, + (void *) NpyString_release_allocator, + (void *) NpyString_release_allocators, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + NULL, + (void *) PyArray_GetDefaultDescr, + (void *) PyArrayInitDTypeMeta_FromSpec, + (void *) PyArray_CommonDType, + (void *) PyArray_PromoteDTypeSequence, + (void *) _PyDataType_GetArrFuncs, + NULL, + NULL, + NULL +}; diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.h new file mode 100644 index 0000000000000000000000000000000000000000..cfc3628aa53e41f22d81877df31d40020519bebf --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__multiarray_api.h @@ -0,0 +1,1613 @@ + +#if defined(_MULTIARRAYMODULE) || defined(WITH_CPYCHECKER_STEALS_REFERENCE_TO_ARG_ATTRIBUTE) + +typedef struct { + PyObject_HEAD + npy_bool obval; +} PyBoolScalarObject; + +extern NPY_NO_EXPORT PyTypeObject PyArrayNeighborhoodIter_Type; +extern NPY_NO_EXPORT PyBoolScalarObject _PyArrayScalar_BoolValues[2]; + +NPY_NO_EXPORT unsigned int PyArray_GetNDArrayCVersion \ + (void); +extern NPY_NO_EXPORT PyTypeObject PyArray_Type; + +extern NPY_NO_EXPORT PyArray_DTypeMeta PyArrayDescr_TypeFull; +#define PyArrayDescr_Type (*(PyTypeObject *)(&PyArrayDescr_TypeFull)) + +extern NPY_NO_EXPORT PyTypeObject PyArrayIter_Type; + +extern NPY_NO_EXPORT PyTypeObject PyArrayMultiIter_Type; + +extern NPY_NO_EXPORT int NPY_NUMUSERTYPES; + +extern NPY_NO_EXPORT PyTypeObject PyBoolArrType_Type; + +extern NPY_NO_EXPORT PyBoolScalarObject _PyArrayScalar_BoolValues[2]; + +extern NPY_NO_EXPORT PyTypeObject PyGenericArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyNumberArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyIntegerArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PySignedIntegerArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUnsignedIntegerArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyInexactArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyFloatingArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyComplexFloatingArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyFlexibleArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyCharacterArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyByteArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyShortArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyIntArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyLongArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyLongLongArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUByteArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUShortArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUIntArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyULongArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyULongLongArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyFloatArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyDoubleArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyLongDoubleArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyCFloatArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyCDoubleArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyCLongDoubleArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyObjectArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyStringArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUnicodeArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyVoidArrType_Type; + +NPY_NO_EXPORT int PyArray_INCREF \ + (PyArrayObject *); +NPY_NO_EXPORT int PyArray_XDECREF \ + (PyArrayObject *); +NPY_NO_EXPORT void PyArray_SetStringFunction \ + (PyObject *, int); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrFromType \ + (int); +NPY_NO_EXPORT PyObject * PyArray_TypeObjectFromType \ + (int); +NPY_NO_EXPORT char * PyArray_Zero \ + (PyArrayObject *); +NPY_NO_EXPORT char * PyArray_One \ + (PyArrayObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_CastToType \ + (PyArrayObject *, PyArray_Descr *, int); +NPY_NO_EXPORT int PyArray_CopyInto \ + (PyArrayObject *, PyArrayObject *); +NPY_NO_EXPORT int PyArray_CopyAnyInto \ + (PyArrayObject *, PyArrayObject *); +NPY_NO_EXPORT int PyArray_CanCastSafely \ + (int, int); +NPY_NO_EXPORT npy_bool PyArray_CanCastTo \ + (PyArray_Descr *, PyArray_Descr *); +NPY_NO_EXPORT int PyArray_ObjectType \ + (PyObject *, int); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrFromObject \ + (PyObject *, PyArray_Descr *); +NPY_NO_EXPORT PyArrayObject ** PyArray_ConvertToCommonType \ + (PyObject *, int *); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrFromScalar \ + (PyObject *); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrFromTypeObject \ + (PyObject *); +NPY_NO_EXPORT npy_intp PyArray_Size \ + (PyObject *); +NPY_NO_EXPORT PyObject * PyArray_Scalar \ + (void *, PyArray_Descr *, PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromScalar \ + (PyObject *, PyArray_Descr *); +NPY_NO_EXPORT void PyArray_ScalarAsCtype \ + (PyObject *, void *); +NPY_NO_EXPORT int PyArray_CastScalarToCtype \ + (PyObject *, void *, PyArray_Descr *); +NPY_NO_EXPORT int PyArray_CastScalarDirect \ + (PyObject *, PyArray_Descr *, void *, int); +NPY_NO_EXPORT int PyArray_Pack \ + (PyArray_Descr *, void *, PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromAny \ + (PyObject *, PyArray_Descr *, int, int, int, PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_EnsureArray \ + (PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_EnsureAnyArray \ + (PyObject *); +NPY_NO_EXPORT PyObject * PyArray_FromFile \ + (FILE *, PyArray_Descr *, npy_intp, char *); +NPY_NO_EXPORT PyObject * PyArray_FromString \ + (char *, npy_intp, PyArray_Descr *, npy_intp, char *); +NPY_NO_EXPORT PyObject * PyArray_FromBuffer \ + (PyObject *, PyArray_Descr *, npy_intp, npy_intp); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromIter \ + (PyObject *, PyArray_Descr *, npy_intp); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(1) PyObject * PyArray_Return \ + (PyArrayObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_GetField \ + (PyArrayObject *, PyArray_Descr *, int); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetField \ + (PyArrayObject *, PyArray_Descr *, int, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_Byteswap \ + (PyArrayObject *, npy_bool); +NPY_NO_EXPORT PyObject * PyArray_Resize \ + (PyArrayObject *, PyArray_Dims *, int, NPY_ORDER NPY_UNUSED(order)); +NPY_NO_EXPORT int PyArray_CopyObject \ + (PyArrayObject *, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_NewCopy \ + (PyArrayObject *, NPY_ORDER); +NPY_NO_EXPORT PyObject * PyArray_ToList \ + (PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_ToString \ + (PyArrayObject *, NPY_ORDER); +NPY_NO_EXPORT int PyArray_ToFile \ + (PyArrayObject *, FILE *, char *, char *); +NPY_NO_EXPORT int PyArray_Dump \ + (PyObject *, PyObject *, int); +NPY_NO_EXPORT PyObject * PyArray_Dumps \ + (PyObject *, int); +NPY_NO_EXPORT int PyArray_ValidType \ + (int); +NPY_NO_EXPORT void PyArray_UpdateFlags \ + (PyArrayObject *, int); +NPY_NO_EXPORT PyObject * PyArray_New \ + (PyTypeObject *, int, npy_intp const *, int, npy_intp const *, void *, int, int, PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_NewFromDescr \ + (PyTypeObject *, PyArray_Descr *, int, npy_intp const *, npy_intp const *, void *, int, PyObject *); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrNew \ + (PyArray_Descr *); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrNewFromType \ + (int); +NPY_NO_EXPORT double PyArray_GetPriority \ + (PyObject *, double); +NPY_NO_EXPORT PyObject * PyArray_IterNew \ + (PyObject *); +NPY_NO_EXPORT PyObject* PyArray_MultiIterNew \ + (int, ...); +NPY_NO_EXPORT int PyArray_PyIntAsInt \ + (PyObject *); +NPY_NO_EXPORT npy_intp PyArray_PyIntAsIntp \ + (PyObject *); +NPY_NO_EXPORT int PyArray_Broadcast \ + (PyArrayMultiIterObject *); +NPY_NO_EXPORT int PyArray_FillWithScalar \ + (PyArrayObject *, PyObject *); +NPY_NO_EXPORT npy_bool PyArray_CheckStrides \ + (int, int, npy_intp, npy_intp, npy_intp const *, npy_intp const *); +NPY_NO_EXPORT PyArray_Descr * PyArray_DescrNewByteorder \ + (PyArray_Descr *, char); +NPY_NO_EXPORT PyObject * PyArray_IterAllButAxis \ + (PyObject *, int *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_CheckFromAny \ + (PyObject *, PyArray_Descr *, int, int, int, PyObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_FromArray \ + (PyArrayObject *, PyArray_Descr *, int); +NPY_NO_EXPORT PyObject * PyArray_FromInterface \ + (PyObject *); +NPY_NO_EXPORT PyObject * PyArray_FromStructInterface \ + (PyObject *); +NPY_NO_EXPORT PyObject * PyArray_FromArrayAttr \ + (PyObject *, PyArray_Descr *, PyObject *); +NPY_NO_EXPORT NPY_SCALARKIND PyArray_ScalarKind \ + (int, PyArrayObject **); +NPY_NO_EXPORT int PyArray_CanCoerceScalar \ + (int, int, NPY_SCALARKIND); +NPY_NO_EXPORT npy_bool PyArray_CanCastScalar \ + (PyTypeObject *, PyTypeObject *); +NPY_NO_EXPORT int PyArray_RemoveSmallest \ + (PyArrayMultiIterObject *); +NPY_NO_EXPORT int PyArray_ElementStrides \ + (PyObject *); +NPY_NO_EXPORT void PyArray_Item_INCREF \ + (char *, PyArray_Descr *); +NPY_NO_EXPORT void PyArray_Item_XDECREF \ + (char *, PyArray_Descr *); +NPY_NO_EXPORT PyObject * PyArray_Transpose \ + (PyArrayObject *, PyArray_Dims *); +NPY_NO_EXPORT PyObject * PyArray_TakeFrom \ + (PyArrayObject *, PyObject *, int, PyArrayObject *, NPY_CLIPMODE); +NPY_NO_EXPORT PyObject * PyArray_PutTo \ + (PyArrayObject *, PyObject*, PyObject *, NPY_CLIPMODE); +NPY_NO_EXPORT PyObject * PyArray_PutMask \ + (PyArrayObject *, PyObject*, PyObject*); +NPY_NO_EXPORT PyObject * PyArray_Repeat \ + (PyArrayObject *, PyObject *, int); +NPY_NO_EXPORT PyObject * PyArray_Choose \ + (PyArrayObject *, PyObject *, PyArrayObject *, NPY_CLIPMODE); +NPY_NO_EXPORT int PyArray_Sort \ + (PyArrayObject *, int, NPY_SORTKIND); +NPY_NO_EXPORT PyObject * PyArray_ArgSort \ + (PyArrayObject *, int, NPY_SORTKIND); +NPY_NO_EXPORT PyObject * PyArray_SearchSorted \ + (PyArrayObject *, PyObject *, NPY_SEARCHSIDE, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_ArgMax \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_ArgMin \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Reshape \ + (PyArrayObject *, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_Newshape \ + (PyArrayObject *, PyArray_Dims *, NPY_ORDER); +NPY_NO_EXPORT PyObject * PyArray_Squeeze \ + (PyArrayObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) PyObject * PyArray_View \ + (PyArrayObject *, PyArray_Descr *, PyTypeObject *); +NPY_NO_EXPORT PyObject * PyArray_SwapAxes \ + (PyArrayObject *, int, int); +NPY_NO_EXPORT PyObject * PyArray_Max \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Min \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Ptp \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Mean \ + (PyArrayObject *, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Trace \ + (PyArrayObject *, int, int, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Diagonal \ + (PyArrayObject *, int, int, int); +NPY_NO_EXPORT PyObject * PyArray_Clip \ + (PyArrayObject *, PyObject *, PyObject *, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Conjugate \ + (PyArrayObject *, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Nonzero \ + (PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Std \ + (PyArrayObject *, int, int, PyArrayObject *, int); +NPY_NO_EXPORT PyObject * PyArray_Sum \ + (PyArrayObject *, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_CumSum \ + (PyArrayObject *, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Prod \ + (PyArrayObject *, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_CumProd \ + (PyArrayObject *, int, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_All \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Any \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Compress \ + (PyArrayObject *, PyObject *, int, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyArray_Flatten \ + (PyArrayObject *, NPY_ORDER); +NPY_NO_EXPORT PyObject * PyArray_Ravel \ + (PyArrayObject *, NPY_ORDER); +NPY_NO_EXPORT npy_intp PyArray_MultiplyList \ + (npy_intp const *, int); +NPY_NO_EXPORT int PyArray_MultiplyIntList \ + (int const *, int); +NPY_NO_EXPORT void * PyArray_GetPtr \ + (PyArrayObject *, npy_intp const*); +NPY_NO_EXPORT int PyArray_CompareLists \ + (npy_intp const *, npy_intp const *, int); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(5) int PyArray_AsCArray \ + (PyObject **, void *, npy_intp *, int, PyArray_Descr*); +NPY_NO_EXPORT int PyArray_Free \ + (PyObject *, void *); +NPY_NO_EXPORT int PyArray_Converter \ + (PyObject *, PyObject **); +NPY_NO_EXPORT int PyArray_IntpFromSequence \ + (PyObject *, npy_intp *, int); +NPY_NO_EXPORT PyObject * PyArray_Concatenate \ + (PyObject *, int); +NPY_NO_EXPORT PyObject * PyArray_InnerProduct \ + (PyObject *, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_MatrixProduct \ + (PyObject *, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_Correlate \ + (PyObject *, PyObject *, int); +NPY_NO_EXPORT int PyArray_DescrConverter \ + (PyObject *, PyArray_Descr **); +NPY_NO_EXPORT int PyArray_DescrConverter2 \ + (PyObject *, PyArray_Descr **); +NPY_NO_EXPORT int PyArray_IntpConverter \ + (PyObject *, PyArray_Dims *); +NPY_NO_EXPORT int PyArray_BufferConverter \ + (PyObject *, PyArray_Chunk *); +NPY_NO_EXPORT int PyArray_AxisConverter \ + (PyObject *, int *); +NPY_NO_EXPORT int PyArray_BoolConverter \ + (PyObject *, npy_bool *); +NPY_NO_EXPORT int PyArray_ByteorderConverter \ + (PyObject *, char *); +NPY_NO_EXPORT int PyArray_OrderConverter \ + (PyObject *, NPY_ORDER *); +NPY_NO_EXPORT unsigned char PyArray_EquivTypes \ + (PyArray_Descr *, PyArray_Descr *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_Zeros \ + (int, npy_intp const *, PyArray_Descr *, int); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_Empty \ + (int, npy_intp const *, PyArray_Descr *, int); +NPY_NO_EXPORT PyObject * PyArray_Where \ + (PyObject *, PyObject *, PyObject *); +NPY_NO_EXPORT PyObject * PyArray_Arange \ + (double, double, double, int); +NPY_NO_EXPORT PyObject * PyArray_ArangeObj \ + (PyObject *, PyObject *, PyObject *, PyArray_Descr *); +NPY_NO_EXPORT int PyArray_SortkindConverter \ + (PyObject *, NPY_SORTKIND *); +NPY_NO_EXPORT PyObject * PyArray_LexSort \ + (PyObject *, int); +NPY_NO_EXPORT PyObject * PyArray_Round \ + (PyArrayObject *, int, PyArrayObject *); +NPY_NO_EXPORT unsigned char PyArray_EquivTypenums \ + (int, int); +NPY_NO_EXPORT int PyArray_RegisterDataType \ + (PyArray_DescrProto *); +NPY_NO_EXPORT int PyArray_RegisterCastFunc \ + (PyArray_Descr *, int, PyArray_VectorUnaryFunc *); +NPY_NO_EXPORT int PyArray_RegisterCanCast \ + (PyArray_Descr *, int, NPY_SCALARKIND); +NPY_NO_EXPORT void PyArray_InitArrFuncs \ + (PyArray_ArrFuncs *); +NPY_NO_EXPORT PyObject * PyArray_IntTupleFromIntp \ + (int, npy_intp const *); +NPY_NO_EXPORT int PyArray_ClipmodeConverter \ + (PyObject *, NPY_CLIPMODE *); +NPY_NO_EXPORT int PyArray_OutputConverter \ + (PyObject *, PyArrayObject **); +NPY_NO_EXPORT PyObject * PyArray_BroadcastToShape \ + (PyObject *, npy_intp *, int); +NPY_NO_EXPORT int PyArray_DescrAlignConverter \ + (PyObject *, PyArray_Descr **); +NPY_NO_EXPORT int PyArray_DescrAlignConverter2 \ + (PyObject *, PyArray_Descr **); +NPY_NO_EXPORT int PyArray_SearchsideConverter \ + (PyObject *, void *); +NPY_NO_EXPORT PyObject * PyArray_CheckAxis \ + (PyArrayObject *, int *, int); +NPY_NO_EXPORT npy_intp PyArray_OverflowMultiplyList \ + (npy_intp const *, int); +NPY_NO_EXPORT PyObject* PyArray_MultiIterFromObjects \ + (PyObject **, int, int, ...); +NPY_NO_EXPORT int PyArray_GetEndianness \ + (void); +NPY_NO_EXPORT unsigned int PyArray_GetNDArrayCFeatureVersion \ + (void); +NPY_NO_EXPORT PyObject * PyArray_Correlate2 \ + (PyObject *, PyObject *, int); +NPY_NO_EXPORT PyObject* PyArray_NeighborhoodIterNew \ + (PyArrayIterObject *, const npy_intp *, int, PyArrayObject*); +extern NPY_NO_EXPORT PyTypeObject PyTimeIntegerArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyDatetimeArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyTimedeltaArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject PyHalfArrType_Type; + +extern NPY_NO_EXPORT PyTypeObject NpyIter_Type; + +NPY_NO_EXPORT NpyIter * NpyIter_New \ + (PyArrayObject *, npy_uint32, NPY_ORDER, NPY_CASTING, PyArray_Descr*); +NPY_NO_EXPORT NpyIter * NpyIter_MultiNew \ + (int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **); +NPY_NO_EXPORT NpyIter * NpyIter_AdvancedNew \ + (int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **, int, int **, npy_intp *, npy_intp); +NPY_NO_EXPORT NpyIter * NpyIter_Copy \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_Deallocate \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_HasDelayedBufAlloc \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_HasExternalLoop \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_EnableExternalLoop \ + (NpyIter *); +NPY_NO_EXPORT npy_intp * NpyIter_GetInnerStrideArray \ + (NpyIter *); +NPY_NO_EXPORT npy_intp * NpyIter_GetInnerLoopSizePtr \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_Reset \ + (NpyIter *, char **); +NPY_NO_EXPORT int NpyIter_ResetBasePointers \ + (NpyIter *, char **, char **); +NPY_NO_EXPORT int NpyIter_ResetToIterIndexRange \ + (NpyIter *, npy_intp, npy_intp, char **); +NPY_NO_EXPORT int NpyIter_GetNDim \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_GetNOp \ + (NpyIter *); +NPY_NO_EXPORT NpyIter_IterNextFunc * NpyIter_GetIterNext \ + (NpyIter *, char **); +NPY_NO_EXPORT npy_intp NpyIter_GetIterSize \ + (NpyIter *); +NPY_NO_EXPORT void NpyIter_GetIterIndexRange \ + (NpyIter *, npy_intp *, npy_intp *); +NPY_NO_EXPORT npy_intp NpyIter_GetIterIndex \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_GotoIterIndex \ + (NpyIter *, npy_intp); +NPY_NO_EXPORT npy_bool NpyIter_HasMultiIndex \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_GetShape \ + (NpyIter *, npy_intp *); +NPY_NO_EXPORT NpyIter_GetMultiIndexFunc * NpyIter_GetGetMultiIndex \ + (NpyIter *, char **); +NPY_NO_EXPORT int NpyIter_GotoMultiIndex \ + (NpyIter *, npy_intp const *); +NPY_NO_EXPORT int NpyIter_RemoveMultiIndex \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_HasIndex \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_IsBuffered \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_IsGrowInner \ + (NpyIter *); +NPY_NO_EXPORT npy_intp NpyIter_GetBufferSize \ + (NpyIter *); +NPY_NO_EXPORT npy_intp * NpyIter_GetIndexPtr \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_GotoIndex \ + (NpyIter *, npy_intp); +NPY_NO_EXPORT char ** NpyIter_GetDataPtrArray \ + (NpyIter *); +NPY_NO_EXPORT PyArray_Descr ** NpyIter_GetDescrArray \ + (NpyIter *); +NPY_NO_EXPORT PyArrayObject ** NpyIter_GetOperandArray \ + (NpyIter *); +NPY_NO_EXPORT PyArrayObject * NpyIter_GetIterView \ + (NpyIter *, npy_intp); +NPY_NO_EXPORT void NpyIter_GetReadFlags \ + (NpyIter *, char *); +NPY_NO_EXPORT void NpyIter_GetWriteFlags \ + (NpyIter *, char *); +NPY_NO_EXPORT void NpyIter_DebugPrint \ + (NpyIter *); +NPY_NO_EXPORT npy_bool NpyIter_IterationNeedsAPI \ + (NpyIter *); +NPY_NO_EXPORT void NpyIter_GetInnerFixedStrideArray \ + (NpyIter *, npy_intp *); +NPY_NO_EXPORT int NpyIter_RemoveAxis \ + (NpyIter *, int); +NPY_NO_EXPORT npy_intp * NpyIter_GetAxisStrideArray \ + (NpyIter *, int); +NPY_NO_EXPORT npy_bool NpyIter_RequiresBuffering \ + (NpyIter *); +NPY_NO_EXPORT char ** NpyIter_GetInitialDataPtrArray \ + (NpyIter *); +NPY_NO_EXPORT int NpyIter_CreateCompatibleStrides \ + (NpyIter *, npy_intp, npy_intp *); +NPY_NO_EXPORT int PyArray_CastingConverter \ + (PyObject *, NPY_CASTING *); +NPY_NO_EXPORT npy_intp PyArray_CountNonzero \ + (PyArrayObject *); +NPY_NO_EXPORT PyArray_Descr * PyArray_PromoteTypes \ + (PyArray_Descr *, PyArray_Descr *); +NPY_NO_EXPORT PyArray_Descr * PyArray_MinScalarType \ + (PyArrayObject *); +NPY_NO_EXPORT PyArray_Descr * PyArray_ResultType \ + (npy_intp, PyArrayObject *arrs[], npy_intp, PyArray_Descr *descrs[]); +NPY_NO_EXPORT npy_bool PyArray_CanCastArrayTo \ + (PyArrayObject *, PyArray_Descr *, NPY_CASTING); +NPY_NO_EXPORT npy_bool PyArray_CanCastTypeTo \ + (PyArray_Descr *, PyArray_Descr *, NPY_CASTING); +NPY_NO_EXPORT PyArrayObject * PyArray_EinsteinSum \ + (char *, npy_intp, PyArrayObject **, PyArray_Descr *, NPY_ORDER, NPY_CASTING, PyArrayObject *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(3) PyObject * PyArray_NewLikeArray \ + (PyArrayObject *, NPY_ORDER, PyArray_Descr *, int); +NPY_NO_EXPORT int PyArray_ConvertClipmodeSequence \ + (PyObject *, NPY_CLIPMODE *, int); +NPY_NO_EXPORT PyObject * PyArray_MatrixProduct2 \ + (PyObject *, PyObject *, PyArrayObject*); +NPY_NO_EXPORT npy_bool NpyIter_IsFirstVisit \ + (NpyIter *, int); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetBaseObject \ + (PyArrayObject *, PyObject *); +NPY_NO_EXPORT void PyArray_CreateSortedStridePerm \ + (int, npy_intp const *, npy_stride_sort_item *); +NPY_NO_EXPORT void PyArray_RemoveAxesInPlace \ + (PyArrayObject *, const npy_bool *); +NPY_NO_EXPORT void PyArray_DebugPrint \ + (PyArrayObject *); +NPY_NO_EXPORT int PyArray_FailUnlessWriteable \ + (PyArrayObject *, const char *); +NPY_NO_EXPORT NPY_STEALS_REF_TO_ARG(2) int PyArray_SetUpdateIfCopyBase \ + (PyArrayObject *, PyArrayObject *); +NPY_NO_EXPORT void * PyDataMem_NEW \ + (size_t); +NPY_NO_EXPORT void PyDataMem_FREE \ + (void *); +NPY_NO_EXPORT void * PyDataMem_RENEW \ + (void *, size_t); +extern NPY_NO_EXPORT NPY_CASTING NPY_DEFAULT_ASSIGN_CASTING; + +NPY_NO_EXPORT int PyArray_Partition \ + (PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND); +NPY_NO_EXPORT PyObject * PyArray_ArgPartition \ + (PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND); +NPY_NO_EXPORT int PyArray_SelectkindConverter \ + (PyObject *, NPY_SELECTKIND *); +NPY_NO_EXPORT void * PyDataMem_NEW_ZEROED \ + (size_t, size_t); +NPY_NO_EXPORT int PyArray_CheckAnyScalarExact \ + (PyObject *); +NPY_NO_EXPORT int PyArray_ResolveWritebackIfCopy \ + (PyArrayObject *); +NPY_NO_EXPORT int PyArray_SetWritebackIfCopyBase \ + (PyArrayObject *, PyArrayObject *); +NPY_NO_EXPORT PyObject * PyDataMem_SetHandler \ + (PyObject *); +NPY_NO_EXPORT PyObject * PyDataMem_GetHandler \ + (void); +extern NPY_NO_EXPORT PyObject* PyDataMem_DefaultHandler; + +NPY_NO_EXPORT int NpyDatetime_ConvertDatetime64ToDatetimeStruct \ + (PyArray_DatetimeMetaData *, npy_datetime, npy_datetimestruct *); +NPY_NO_EXPORT int NpyDatetime_ConvertDatetimeStructToDatetime64 \ + (PyArray_DatetimeMetaData *, const npy_datetimestruct *, npy_datetime *); +NPY_NO_EXPORT int NpyDatetime_ConvertPyDateTimeToDatetimeStruct \ + (PyObject *, npy_datetimestruct *, NPY_DATETIMEUNIT *, int); +NPY_NO_EXPORT int NpyDatetime_GetDatetimeISO8601StrLen \ + (int, NPY_DATETIMEUNIT); +NPY_NO_EXPORT int NpyDatetime_MakeISO8601Datetime \ + (npy_datetimestruct *, char *, npy_intp, int, int, NPY_DATETIMEUNIT, int, NPY_CASTING); +NPY_NO_EXPORT int NpyDatetime_ParseISO8601Datetime \ + (char const *, Py_ssize_t, NPY_DATETIMEUNIT, NPY_CASTING, npy_datetimestruct *, NPY_DATETIMEUNIT *, npy_bool *); +NPY_NO_EXPORT int NpyString_load \ + (npy_string_allocator *, const npy_packed_static_string *, npy_static_string *); +NPY_NO_EXPORT int NpyString_pack \ + (npy_string_allocator *, npy_packed_static_string *, const char *, size_t); +NPY_NO_EXPORT int NpyString_pack_null \ + (npy_string_allocator *, npy_packed_static_string *); +NPY_NO_EXPORT npy_string_allocator * NpyString_acquire_allocator \ + (const PyArray_StringDTypeObject *); +NPY_NO_EXPORT void NpyString_acquire_allocators \ + (size_t, PyArray_Descr *const descrs[], npy_string_allocator *allocators[]); +NPY_NO_EXPORT void NpyString_release_allocator \ + (npy_string_allocator *); +NPY_NO_EXPORT void NpyString_release_allocators \ + (size_t, npy_string_allocator *allocators[]); +NPY_NO_EXPORT PyArray_Descr * PyArray_GetDefaultDescr \ + (PyArray_DTypeMeta *); +NPY_NO_EXPORT int PyArrayInitDTypeMeta_FromSpec \ + (PyArray_DTypeMeta *, PyArrayDTypeMeta_Spec *); +NPY_NO_EXPORT PyArray_DTypeMeta * PyArray_CommonDType \ + (PyArray_DTypeMeta *, PyArray_DTypeMeta *); +NPY_NO_EXPORT PyArray_DTypeMeta * PyArray_PromoteDTypeSequence \ + (npy_intp, PyArray_DTypeMeta **); +NPY_NO_EXPORT PyArray_ArrFuncs * _PyDataType_GetArrFuncs \ + (const PyArray_Descr *); + +#else + +#if defined(PY_ARRAY_UNIQUE_SYMBOL) + #define PyArray_API PY_ARRAY_UNIQUE_SYMBOL + #define _NPY_VERSION_CONCAT_HELPER2(x, y) x ## y + #define _NPY_VERSION_CONCAT_HELPER(arg) \ + _NPY_VERSION_CONCAT_HELPER2(arg, PyArray_RUNTIME_VERSION) + #define PyArray_RUNTIME_VERSION \ + _NPY_VERSION_CONCAT_HELPER(PY_ARRAY_UNIQUE_SYMBOL) +#endif + +/* By default do not export API in an .so (was never the case on windows) */ +#ifndef NPY_API_SYMBOL_ATTRIBUTE + #define NPY_API_SYMBOL_ATTRIBUTE NPY_VISIBILITY_HIDDEN +#endif + +#if defined(NO_IMPORT) || defined(NO_IMPORT_ARRAY) +extern NPY_API_SYMBOL_ATTRIBUTE void **PyArray_API; +extern NPY_API_SYMBOL_ATTRIBUTE int PyArray_RUNTIME_VERSION; +#else +#if defined(PY_ARRAY_UNIQUE_SYMBOL) +NPY_API_SYMBOL_ATTRIBUTE void **PyArray_API; +NPY_API_SYMBOL_ATTRIBUTE int PyArray_RUNTIME_VERSION; +#else +static void **PyArray_API = NULL; +static int PyArray_RUNTIME_VERSION = 0; +#endif +#endif + +#define PyArray_GetNDArrayCVersion \ + (*(unsigned int (*)(void)) \ + PyArray_API[0]) +#define PyArray_Type (*(PyTypeObject *)PyArray_API[2]) +#define PyArrayDescr_Type (*(PyTypeObject *)PyArray_API[3]) +#define PyArrayIter_Type (*(PyTypeObject *)PyArray_API[5]) +#define PyArrayMultiIter_Type (*(PyTypeObject *)PyArray_API[6]) +#define NPY_NUMUSERTYPES (*(int *)PyArray_API[7]) +#define PyBoolArrType_Type (*(PyTypeObject *)PyArray_API[8]) +#define _PyArrayScalar_BoolValues ((PyBoolScalarObject *)PyArray_API[9]) +#define PyGenericArrType_Type (*(PyTypeObject *)PyArray_API[10]) +#define PyNumberArrType_Type (*(PyTypeObject *)PyArray_API[11]) +#define PyIntegerArrType_Type (*(PyTypeObject *)PyArray_API[12]) +#define PySignedIntegerArrType_Type (*(PyTypeObject *)PyArray_API[13]) +#define PyUnsignedIntegerArrType_Type (*(PyTypeObject *)PyArray_API[14]) +#define PyInexactArrType_Type (*(PyTypeObject *)PyArray_API[15]) +#define PyFloatingArrType_Type (*(PyTypeObject *)PyArray_API[16]) +#define PyComplexFloatingArrType_Type (*(PyTypeObject *)PyArray_API[17]) +#define PyFlexibleArrType_Type (*(PyTypeObject *)PyArray_API[18]) +#define PyCharacterArrType_Type (*(PyTypeObject *)PyArray_API[19]) +#define PyByteArrType_Type (*(PyTypeObject *)PyArray_API[20]) +#define PyShortArrType_Type (*(PyTypeObject *)PyArray_API[21]) +#define PyIntArrType_Type (*(PyTypeObject *)PyArray_API[22]) +#define PyLongArrType_Type (*(PyTypeObject *)PyArray_API[23]) +#define PyLongLongArrType_Type (*(PyTypeObject *)PyArray_API[24]) +#define PyUByteArrType_Type (*(PyTypeObject *)PyArray_API[25]) +#define PyUShortArrType_Type (*(PyTypeObject *)PyArray_API[26]) +#define PyUIntArrType_Type (*(PyTypeObject *)PyArray_API[27]) +#define PyULongArrType_Type (*(PyTypeObject *)PyArray_API[28]) +#define PyULongLongArrType_Type (*(PyTypeObject *)PyArray_API[29]) +#define PyFloatArrType_Type (*(PyTypeObject *)PyArray_API[30]) +#define PyDoubleArrType_Type (*(PyTypeObject *)PyArray_API[31]) +#define PyLongDoubleArrType_Type (*(PyTypeObject *)PyArray_API[32]) +#define PyCFloatArrType_Type (*(PyTypeObject *)PyArray_API[33]) +#define PyCDoubleArrType_Type (*(PyTypeObject *)PyArray_API[34]) +#define PyCLongDoubleArrType_Type (*(PyTypeObject *)PyArray_API[35]) +#define PyObjectArrType_Type (*(PyTypeObject *)PyArray_API[36]) +#define PyStringArrType_Type (*(PyTypeObject *)PyArray_API[37]) +#define PyUnicodeArrType_Type (*(PyTypeObject *)PyArray_API[38]) +#define PyVoidArrType_Type (*(PyTypeObject *)PyArray_API[39]) +#define PyArray_INCREF \ + (*(int (*)(PyArrayObject *)) \ + PyArray_API[42]) +#define PyArray_XDECREF \ + (*(int (*)(PyArrayObject *)) \ + PyArray_API[43]) +#define PyArray_SetStringFunction \ + (*(void (*)(PyObject *, int)) \ + PyArray_API[44]) +#define PyArray_DescrFromType \ + (*(PyArray_Descr * (*)(int)) \ + PyArray_API[45]) +#define PyArray_TypeObjectFromType \ + (*(PyObject * (*)(int)) \ + PyArray_API[46]) +#define PyArray_Zero \ + (*(char * (*)(PyArrayObject *)) \ + PyArray_API[47]) +#define PyArray_One \ + (*(char * (*)(PyArrayObject *)) \ + PyArray_API[48]) +#define PyArray_CastToType \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \ + PyArray_API[49]) +#define PyArray_CopyInto \ + (*(int (*)(PyArrayObject *, PyArrayObject *)) \ + PyArray_API[50]) +#define PyArray_CopyAnyInto \ + (*(int (*)(PyArrayObject *, PyArrayObject *)) \ + PyArray_API[51]) +#define PyArray_CanCastSafely \ + (*(int (*)(int, int)) \ + PyArray_API[52]) +#define PyArray_CanCastTo \ + (*(npy_bool (*)(PyArray_Descr *, PyArray_Descr *)) \ + PyArray_API[53]) +#define PyArray_ObjectType \ + (*(int (*)(PyObject *, int)) \ + PyArray_API[54]) +#define PyArray_DescrFromObject \ + (*(PyArray_Descr * (*)(PyObject *, PyArray_Descr *)) \ + PyArray_API[55]) +#define PyArray_ConvertToCommonType \ + (*(PyArrayObject ** (*)(PyObject *, int *)) \ + PyArray_API[56]) +#define PyArray_DescrFromScalar \ + (*(PyArray_Descr * (*)(PyObject *)) \ + PyArray_API[57]) +#define PyArray_DescrFromTypeObject \ + (*(PyArray_Descr * (*)(PyObject *)) \ + PyArray_API[58]) +#define PyArray_Size \ + (*(npy_intp (*)(PyObject *)) \ + PyArray_API[59]) +#define PyArray_Scalar \ + (*(PyObject * (*)(void *, PyArray_Descr *, PyObject *)) \ + PyArray_API[60]) +#define PyArray_FromScalar \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *)) \ + PyArray_API[61]) +#define PyArray_ScalarAsCtype \ + (*(void (*)(PyObject *, void *)) \ + PyArray_API[62]) +#define PyArray_CastScalarToCtype \ + (*(int (*)(PyObject *, void *, PyArray_Descr *)) \ + PyArray_API[63]) +#define PyArray_CastScalarDirect \ + (*(int (*)(PyObject *, PyArray_Descr *, void *, int)) \ + PyArray_API[64]) + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyArray_Pack \ + (*(int (*)(PyArray_Descr *, void *, PyObject *)) \ + PyArray_API[65]) +#endif +#define PyArray_FromAny \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *, int, int, int, PyObject *)) \ + PyArray_API[69]) +#define PyArray_EnsureArray \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[70]) +#define PyArray_EnsureAnyArray \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[71]) +#define PyArray_FromFile \ + (*(PyObject * (*)(FILE *, PyArray_Descr *, npy_intp, char *)) \ + PyArray_API[72]) +#define PyArray_FromString \ + (*(PyObject * (*)(char *, npy_intp, PyArray_Descr *, npy_intp, char *)) \ + PyArray_API[73]) +#define PyArray_FromBuffer \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *, npy_intp, npy_intp)) \ + PyArray_API[74]) +#define PyArray_FromIter \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *, npy_intp)) \ + PyArray_API[75]) +#define PyArray_Return \ + (*(PyObject * (*)(PyArrayObject *)) \ + PyArray_API[76]) +#define PyArray_GetField \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \ + PyArray_API[77]) +#define PyArray_SetField \ + (*(int (*)(PyArrayObject *, PyArray_Descr *, int, PyObject *)) \ + PyArray_API[78]) +#define PyArray_Byteswap \ + (*(PyObject * (*)(PyArrayObject *, npy_bool)) \ + PyArray_API[79]) +#define PyArray_Resize \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *, int, NPY_ORDER NPY_UNUSED(order))) \ + PyArray_API[80]) +#define PyArray_CopyObject \ + (*(int (*)(PyArrayObject *, PyObject *)) \ + PyArray_API[84]) +#define PyArray_NewCopy \ + (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \ + PyArray_API[85]) +#define PyArray_ToList \ + (*(PyObject * (*)(PyArrayObject *)) \ + PyArray_API[86]) +#define PyArray_ToString \ + (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \ + PyArray_API[87]) +#define PyArray_ToFile \ + (*(int (*)(PyArrayObject *, FILE *, char *, char *)) \ + PyArray_API[88]) +#define PyArray_Dump \ + (*(int (*)(PyObject *, PyObject *, int)) \ + PyArray_API[89]) +#define PyArray_Dumps \ + (*(PyObject * (*)(PyObject *, int)) \ + PyArray_API[90]) +#define PyArray_ValidType \ + (*(int (*)(int)) \ + PyArray_API[91]) +#define PyArray_UpdateFlags \ + (*(void (*)(PyArrayObject *, int)) \ + PyArray_API[92]) +#define PyArray_New \ + (*(PyObject * (*)(PyTypeObject *, int, npy_intp const *, int, npy_intp const *, void *, int, int, PyObject *)) \ + PyArray_API[93]) +#define PyArray_NewFromDescr \ + (*(PyObject * (*)(PyTypeObject *, PyArray_Descr *, int, npy_intp const *, npy_intp const *, void *, int, PyObject *)) \ + PyArray_API[94]) +#define PyArray_DescrNew \ + (*(PyArray_Descr * (*)(PyArray_Descr *)) \ + PyArray_API[95]) +#define PyArray_DescrNewFromType \ + (*(PyArray_Descr * (*)(int)) \ + PyArray_API[96]) +#define PyArray_GetPriority \ + (*(double (*)(PyObject *, double)) \ + PyArray_API[97]) +#define PyArray_IterNew \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[98]) +#define PyArray_MultiIterNew \ + (*(PyObject* (*)(int, ...)) \ + PyArray_API[99]) +#define PyArray_PyIntAsInt \ + (*(int (*)(PyObject *)) \ + PyArray_API[100]) +#define PyArray_PyIntAsIntp \ + (*(npy_intp (*)(PyObject *)) \ + PyArray_API[101]) +#define PyArray_Broadcast \ + (*(int (*)(PyArrayMultiIterObject *)) \ + PyArray_API[102]) +#define PyArray_FillWithScalar \ + (*(int (*)(PyArrayObject *, PyObject *)) \ + PyArray_API[104]) +#define PyArray_CheckStrides \ + (*(npy_bool (*)(int, int, npy_intp, npy_intp, npy_intp const *, npy_intp const *)) \ + PyArray_API[105]) +#define PyArray_DescrNewByteorder \ + (*(PyArray_Descr * (*)(PyArray_Descr *, char)) \ + PyArray_API[106]) +#define PyArray_IterAllButAxis \ + (*(PyObject * (*)(PyObject *, int *)) \ + PyArray_API[107]) +#define PyArray_CheckFromAny \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *, int, int, int, PyObject *)) \ + PyArray_API[108]) +#define PyArray_FromArray \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, int)) \ + PyArray_API[109]) +#define PyArray_FromInterface \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[110]) +#define PyArray_FromStructInterface \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[111]) +#define PyArray_FromArrayAttr \ + (*(PyObject * (*)(PyObject *, PyArray_Descr *, PyObject *)) \ + PyArray_API[112]) +#define PyArray_ScalarKind \ + (*(NPY_SCALARKIND (*)(int, PyArrayObject **)) \ + PyArray_API[113]) +#define PyArray_CanCoerceScalar \ + (*(int (*)(int, int, NPY_SCALARKIND)) \ + PyArray_API[114]) +#define PyArray_CanCastScalar \ + (*(npy_bool (*)(PyTypeObject *, PyTypeObject *)) \ + PyArray_API[116]) +#define PyArray_RemoveSmallest \ + (*(int (*)(PyArrayMultiIterObject *)) \ + PyArray_API[118]) +#define PyArray_ElementStrides \ + (*(int (*)(PyObject *)) \ + PyArray_API[119]) +#define PyArray_Item_INCREF \ + (*(void (*)(char *, PyArray_Descr *)) \ + PyArray_API[120]) +#define PyArray_Item_XDECREF \ + (*(void (*)(char *, PyArray_Descr *)) \ + PyArray_API[121]) +#define PyArray_Transpose \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *)) \ + PyArray_API[123]) +#define PyArray_TakeFrom \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, int, PyArrayObject *, NPY_CLIPMODE)) \ + PyArray_API[124]) +#define PyArray_PutTo \ + (*(PyObject * (*)(PyArrayObject *, PyObject*, PyObject *, NPY_CLIPMODE)) \ + PyArray_API[125]) +#define PyArray_PutMask \ + (*(PyObject * (*)(PyArrayObject *, PyObject*, PyObject*)) \ + PyArray_API[126]) +#define PyArray_Repeat \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, int)) \ + PyArray_API[127]) +#define PyArray_Choose \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, PyArrayObject *, NPY_CLIPMODE)) \ + PyArray_API[128]) +#define PyArray_Sort \ + (*(int (*)(PyArrayObject *, int, NPY_SORTKIND)) \ + PyArray_API[129]) +#define PyArray_ArgSort \ + (*(PyObject * (*)(PyArrayObject *, int, NPY_SORTKIND)) \ + PyArray_API[130]) +#define PyArray_SearchSorted \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, NPY_SEARCHSIDE, PyObject *)) \ + PyArray_API[131]) +#define PyArray_ArgMax \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[132]) +#define PyArray_ArgMin \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[133]) +#define PyArray_Reshape \ + (*(PyObject * (*)(PyArrayObject *, PyObject *)) \ + PyArray_API[134]) +#define PyArray_Newshape \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Dims *, NPY_ORDER)) \ + PyArray_API[135]) +#define PyArray_Squeeze \ + (*(PyObject * (*)(PyArrayObject *)) \ + PyArray_API[136]) +#define PyArray_View \ + (*(PyObject * (*)(PyArrayObject *, PyArray_Descr *, PyTypeObject *)) \ + PyArray_API[137]) +#define PyArray_SwapAxes \ + (*(PyObject * (*)(PyArrayObject *, int, int)) \ + PyArray_API[138]) +#define PyArray_Max \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[139]) +#define PyArray_Min \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[140]) +#define PyArray_Ptp \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[141]) +#define PyArray_Mean \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \ + PyArray_API[142]) +#define PyArray_Trace \ + (*(PyObject * (*)(PyArrayObject *, int, int, int, int, PyArrayObject *)) \ + PyArray_API[143]) +#define PyArray_Diagonal \ + (*(PyObject * (*)(PyArrayObject *, int, int, int)) \ + PyArray_API[144]) +#define PyArray_Clip \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, PyObject *, PyArrayObject *)) \ + PyArray_API[145]) +#define PyArray_Conjugate \ + (*(PyObject * (*)(PyArrayObject *, PyArrayObject *)) \ + PyArray_API[146]) +#define PyArray_Nonzero \ + (*(PyObject * (*)(PyArrayObject *)) \ + PyArray_API[147]) +#define PyArray_Std \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *, int)) \ + PyArray_API[148]) +#define PyArray_Sum \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \ + PyArray_API[149]) +#define PyArray_CumSum \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \ + PyArray_API[150]) +#define PyArray_Prod \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \ + PyArray_API[151]) +#define PyArray_CumProd \ + (*(PyObject * (*)(PyArrayObject *, int, int, PyArrayObject *)) \ + PyArray_API[152]) +#define PyArray_All \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[153]) +#define PyArray_Any \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[154]) +#define PyArray_Compress \ + (*(PyObject * (*)(PyArrayObject *, PyObject *, int, PyArrayObject *)) \ + PyArray_API[155]) +#define PyArray_Flatten \ + (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \ + PyArray_API[156]) +#define PyArray_Ravel \ + (*(PyObject * (*)(PyArrayObject *, NPY_ORDER)) \ + PyArray_API[157]) +#define PyArray_MultiplyList \ + (*(npy_intp (*)(npy_intp const *, int)) \ + PyArray_API[158]) +#define PyArray_MultiplyIntList \ + (*(int (*)(int const *, int)) \ + PyArray_API[159]) +#define PyArray_GetPtr \ + (*(void * (*)(PyArrayObject *, npy_intp const*)) \ + PyArray_API[160]) +#define PyArray_CompareLists \ + (*(int (*)(npy_intp const *, npy_intp const *, int)) \ + PyArray_API[161]) +#define PyArray_AsCArray \ + (*(int (*)(PyObject **, void *, npy_intp *, int, PyArray_Descr*)) \ + PyArray_API[162]) +#define PyArray_Free \ + (*(int (*)(PyObject *, void *)) \ + PyArray_API[165]) +#define PyArray_Converter \ + (*(int (*)(PyObject *, PyObject **)) \ + PyArray_API[166]) +#define PyArray_IntpFromSequence \ + (*(int (*)(PyObject *, npy_intp *, int)) \ + PyArray_API[167]) +#define PyArray_Concatenate \ + (*(PyObject * (*)(PyObject *, int)) \ + PyArray_API[168]) +#define PyArray_InnerProduct \ + (*(PyObject * (*)(PyObject *, PyObject *)) \ + PyArray_API[169]) +#define PyArray_MatrixProduct \ + (*(PyObject * (*)(PyObject *, PyObject *)) \ + PyArray_API[170]) +#define PyArray_Correlate \ + (*(PyObject * (*)(PyObject *, PyObject *, int)) \ + PyArray_API[172]) +#define PyArray_DescrConverter \ + (*(int (*)(PyObject *, PyArray_Descr **)) \ + PyArray_API[174]) +#define PyArray_DescrConverter2 \ + (*(int (*)(PyObject *, PyArray_Descr **)) \ + PyArray_API[175]) +#define PyArray_IntpConverter \ + (*(int (*)(PyObject *, PyArray_Dims *)) \ + PyArray_API[176]) +#define PyArray_BufferConverter \ + (*(int (*)(PyObject *, PyArray_Chunk *)) \ + PyArray_API[177]) +#define PyArray_AxisConverter \ + (*(int (*)(PyObject *, int *)) \ + PyArray_API[178]) +#define PyArray_BoolConverter \ + (*(int (*)(PyObject *, npy_bool *)) \ + PyArray_API[179]) +#define PyArray_ByteorderConverter \ + (*(int (*)(PyObject *, char *)) \ + PyArray_API[180]) +#define PyArray_OrderConverter \ + (*(int (*)(PyObject *, NPY_ORDER *)) \ + PyArray_API[181]) +#define PyArray_EquivTypes \ + (*(unsigned char (*)(PyArray_Descr *, PyArray_Descr *)) \ + PyArray_API[182]) +#define PyArray_Zeros \ + (*(PyObject * (*)(int, npy_intp const *, PyArray_Descr *, int)) \ + PyArray_API[183]) +#define PyArray_Empty \ + (*(PyObject * (*)(int, npy_intp const *, PyArray_Descr *, int)) \ + PyArray_API[184]) +#define PyArray_Where \ + (*(PyObject * (*)(PyObject *, PyObject *, PyObject *)) \ + PyArray_API[185]) +#define PyArray_Arange \ + (*(PyObject * (*)(double, double, double, int)) \ + PyArray_API[186]) +#define PyArray_ArangeObj \ + (*(PyObject * (*)(PyObject *, PyObject *, PyObject *, PyArray_Descr *)) \ + PyArray_API[187]) +#define PyArray_SortkindConverter \ + (*(int (*)(PyObject *, NPY_SORTKIND *)) \ + PyArray_API[188]) +#define PyArray_LexSort \ + (*(PyObject * (*)(PyObject *, int)) \ + PyArray_API[189]) +#define PyArray_Round \ + (*(PyObject * (*)(PyArrayObject *, int, PyArrayObject *)) \ + PyArray_API[190]) +#define PyArray_EquivTypenums \ + (*(unsigned char (*)(int, int)) \ + PyArray_API[191]) +#define PyArray_RegisterDataType \ + (*(int (*)(PyArray_DescrProto *)) \ + PyArray_API[192]) +#define PyArray_RegisterCastFunc \ + (*(int (*)(PyArray_Descr *, int, PyArray_VectorUnaryFunc *)) \ + PyArray_API[193]) +#define PyArray_RegisterCanCast \ + (*(int (*)(PyArray_Descr *, int, NPY_SCALARKIND)) \ + PyArray_API[194]) +#define PyArray_InitArrFuncs \ + (*(void (*)(PyArray_ArrFuncs *)) \ + PyArray_API[195]) +#define PyArray_IntTupleFromIntp \ + (*(PyObject * (*)(int, npy_intp const *)) \ + PyArray_API[196]) +#define PyArray_ClipmodeConverter \ + (*(int (*)(PyObject *, NPY_CLIPMODE *)) \ + PyArray_API[198]) +#define PyArray_OutputConverter \ + (*(int (*)(PyObject *, PyArrayObject **)) \ + PyArray_API[199]) +#define PyArray_BroadcastToShape \ + (*(PyObject * (*)(PyObject *, npy_intp *, int)) \ + PyArray_API[200]) +#define PyArray_DescrAlignConverter \ + (*(int (*)(PyObject *, PyArray_Descr **)) \ + PyArray_API[203]) +#define PyArray_DescrAlignConverter2 \ + (*(int (*)(PyObject *, PyArray_Descr **)) \ + PyArray_API[204]) +#define PyArray_SearchsideConverter \ + (*(int (*)(PyObject *, void *)) \ + PyArray_API[205]) +#define PyArray_CheckAxis \ + (*(PyObject * (*)(PyArrayObject *, int *, int)) \ + PyArray_API[206]) +#define PyArray_OverflowMultiplyList \ + (*(npy_intp (*)(npy_intp const *, int)) \ + PyArray_API[207]) +#define PyArray_MultiIterFromObjects \ + (*(PyObject* (*)(PyObject **, int, int, ...)) \ + PyArray_API[209]) +#define PyArray_GetEndianness \ + (*(int (*)(void)) \ + PyArray_API[210]) +#define PyArray_GetNDArrayCFeatureVersion \ + (*(unsigned int (*)(void)) \ + PyArray_API[211]) +#define PyArray_Correlate2 \ + (*(PyObject * (*)(PyObject *, PyObject *, int)) \ + PyArray_API[212]) +#define PyArray_NeighborhoodIterNew \ + (*(PyObject* (*)(PyArrayIterObject *, const npy_intp *, int, PyArrayObject*)) \ + PyArray_API[213]) +#define PyTimeIntegerArrType_Type (*(PyTypeObject *)PyArray_API[214]) +#define PyDatetimeArrType_Type (*(PyTypeObject *)PyArray_API[215]) +#define PyTimedeltaArrType_Type (*(PyTypeObject *)PyArray_API[216]) +#define PyHalfArrType_Type (*(PyTypeObject *)PyArray_API[217]) +#define NpyIter_Type (*(PyTypeObject *)PyArray_API[218]) +#define NpyIter_New \ + (*(NpyIter * (*)(PyArrayObject *, npy_uint32, NPY_ORDER, NPY_CASTING, PyArray_Descr*)) \ + PyArray_API[224]) +#define NpyIter_MultiNew \ + (*(NpyIter * (*)(int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **)) \ + PyArray_API[225]) +#define NpyIter_AdvancedNew \ + (*(NpyIter * (*)(int, PyArrayObject **, npy_uint32, NPY_ORDER, NPY_CASTING, npy_uint32 *, PyArray_Descr **, int, int **, npy_intp *, npy_intp)) \ + PyArray_API[226]) +#define NpyIter_Copy \ + (*(NpyIter * (*)(NpyIter *)) \ + PyArray_API[227]) +#define NpyIter_Deallocate \ + (*(int (*)(NpyIter *)) \ + PyArray_API[228]) +#define NpyIter_HasDelayedBufAlloc \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[229]) +#define NpyIter_HasExternalLoop \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[230]) +#define NpyIter_EnableExternalLoop \ + (*(int (*)(NpyIter *)) \ + PyArray_API[231]) +#define NpyIter_GetInnerStrideArray \ + (*(npy_intp * (*)(NpyIter *)) \ + PyArray_API[232]) +#define NpyIter_GetInnerLoopSizePtr \ + (*(npy_intp * (*)(NpyIter *)) \ + PyArray_API[233]) +#define NpyIter_Reset \ + (*(int (*)(NpyIter *, char **)) \ + PyArray_API[234]) +#define NpyIter_ResetBasePointers \ + (*(int (*)(NpyIter *, char **, char **)) \ + PyArray_API[235]) +#define NpyIter_ResetToIterIndexRange \ + (*(int (*)(NpyIter *, npy_intp, npy_intp, char **)) \ + PyArray_API[236]) +#define NpyIter_GetNDim \ + (*(int (*)(NpyIter *)) \ + PyArray_API[237]) +#define NpyIter_GetNOp \ + (*(int (*)(NpyIter *)) \ + PyArray_API[238]) +#define NpyIter_GetIterNext \ + (*(NpyIter_IterNextFunc * (*)(NpyIter *, char **)) \ + PyArray_API[239]) +#define NpyIter_GetIterSize \ + (*(npy_intp (*)(NpyIter *)) \ + PyArray_API[240]) +#define NpyIter_GetIterIndexRange \ + (*(void (*)(NpyIter *, npy_intp *, npy_intp *)) \ + PyArray_API[241]) +#define NpyIter_GetIterIndex \ + (*(npy_intp (*)(NpyIter *)) \ + PyArray_API[242]) +#define NpyIter_GotoIterIndex \ + (*(int (*)(NpyIter *, npy_intp)) \ + PyArray_API[243]) +#define NpyIter_HasMultiIndex \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[244]) +#define NpyIter_GetShape \ + (*(int (*)(NpyIter *, npy_intp *)) \ + PyArray_API[245]) +#define NpyIter_GetGetMultiIndex \ + (*(NpyIter_GetMultiIndexFunc * (*)(NpyIter *, char **)) \ + PyArray_API[246]) +#define NpyIter_GotoMultiIndex \ + (*(int (*)(NpyIter *, npy_intp const *)) \ + PyArray_API[247]) +#define NpyIter_RemoveMultiIndex \ + (*(int (*)(NpyIter *)) \ + PyArray_API[248]) +#define NpyIter_HasIndex \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[249]) +#define NpyIter_IsBuffered \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[250]) +#define NpyIter_IsGrowInner \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[251]) +#define NpyIter_GetBufferSize \ + (*(npy_intp (*)(NpyIter *)) \ + PyArray_API[252]) +#define NpyIter_GetIndexPtr \ + (*(npy_intp * (*)(NpyIter *)) \ + PyArray_API[253]) +#define NpyIter_GotoIndex \ + (*(int (*)(NpyIter *, npy_intp)) \ + PyArray_API[254]) +#define NpyIter_GetDataPtrArray \ + (*(char ** (*)(NpyIter *)) \ + PyArray_API[255]) +#define NpyIter_GetDescrArray \ + (*(PyArray_Descr ** (*)(NpyIter *)) \ + PyArray_API[256]) +#define NpyIter_GetOperandArray \ + (*(PyArrayObject ** (*)(NpyIter *)) \ + PyArray_API[257]) +#define NpyIter_GetIterView \ + (*(PyArrayObject * (*)(NpyIter *, npy_intp)) \ + PyArray_API[258]) +#define NpyIter_GetReadFlags \ + (*(void (*)(NpyIter *, char *)) \ + PyArray_API[259]) +#define NpyIter_GetWriteFlags \ + (*(void (*)(NpyIter *, char *)) \ + PyArray_API[260]) +#define NpyIter_DebugPrint \ + (*(void (*)(NpyIter *)) \ + PyArray_API[261]) +#define NpyIter_IterationNeedsAPI \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[262]) +#define NpyIter_GetInnerFixedStrideArray \ + (*(void (*)(NpyIter *, npy_intp *)) \ + PyArray_API[263]) +#define NpyIter_RemoveAxis \ + (*(int (*)(NpyIter *, int)) \ + PyArray_API[264]) +#define NpyIter_GetAxisStrideArray \ + (*(npy_intp * (*)(NpyIter *, int)) \ + PyArray_API[265]) +#define NpyIter_RequiresBuffering \ + (*(npy_bool (*)(NpyIter *)) \ + PyArray_API[266]) +#define NpyIter_GetInitialDataPtrArray \ + (*(char ** (*)(NpyIter *)) \ + PyArray_API[267]) +#define NpyIter_CreateCompatibleStrides \ + (*(int (*)(NpyIter *, npy_intp, npy_intp *)) \ + PyArray_API[268]) +#define PyArray_CastingConverter \ + (*(int (*)(PyObject *, NPY_CASTING *)) \ + PyArray_API[269]) +#define PyArray_CountNonzero \ + (*(npy_intp (*)(PyArrayObject *)) \ + PyArray_API[270]) +#define PyArray_PromoteTypes \ + (*(PyArray_Descr * (*)(PyArray_Descr *, PyArray_Descr *)) \ + PyArray_API[271]) +#define PyArray_MinScalarType \ + (*(PyArray_Descr * (*)(PyArrayObject *)) \ + PyArray_API[272]) +#define PyArray_ResultType \ + (*(PyArray_Descr * (*)(npy_intp, PyArrayObject *arrs[], npy_intp, PyArray_Descr *descrs[])) \ + PyArray_API[273]) +#define PyArray_CanCastArrayTo \ + (*(npy_bool (*)(PyArrayObject *, PyArray_Descr *, NPY_CASTING)) \ + PyArray_API[274]) +#define PyArray_CanCastTypeTo \ + (*(npy_bool (*)(PyArray_Descr *, PyArray_Descr *, NPY_CASTING)) \ + PyArray_API[275]) +#define PyArray_EinsteinSum \ + (*(PyArrayObject * (*)(char *, npy_intp, PyArrayObject **, PyArray_Descr *, NPY_ORDER, NPY_CASTING, PyArrayObject *)) \ + PyArray_API[276]) +#define PyArray_NewLikeArray \ + (*(PyObject * (*)(PyArrayObject *, NPY_ORDER, PyArray_Descr *, int)) \ + PyArray_API[277]) +#define PyArray_ConvertClipmodeSequence \ + (*(int (*)(PyObject *, NPY_CLIPMODE *, int)) \ + PyArray_API[279]) +#define PyArray_MatrixProduct2 \ + (*(PyObject * (*)(PyObject *, PyObject *, PyArrayObject*)) \ + PyArray_API[280]) +#define NpyIter_IsFirstVisit \ + (*(npy_bool (*)(NpyIter *, int)) \ + PyArray_API[281]) +#define PyArray_SetBaseObject \ + (*(int (*)(PyArrayObject *, PyObject *)) \ + PyArray_API[282]) +#define PyArray_CreateSortedStridePerm \ + (*(void (*)(int, npy_intp const *, npy_stride_sort_item *)) \ + PyArray_API[283]) +#define PyArray_RemoveAxesInPlace \ + (*(void (*)(PyArrayObject *, const npy_bool *)) \ + PyArray_API[284]) +#define PyArray_DebugPrint \ + (*(void (*)(PyArrayObject *)) \ + PyArray_API[285]) +#define PyArray_FailUnlessWriteable \ + (*(int (*)(PyArrayObject *, const char *)) \ + PyArray_API[286]) +#define PyArray_SetUpdateIfCopyBase \ + (*(int (*)(PyArrayObject *, PyArrayObject *)) \ + PyArray_API[287]) +#define PyDataMem_NEW \ + (*(void * (*)(size_t)) \ + PyArray_API[288]) +#define PyDataMem_FREE \ + (*(void (*)(void *)) \ + PyArray_API[289]) +#define PyDataMem_RENEW \ + (*(void * (*)(void *, size_t)) \ + PyArray_API[290]) +#define NPY_DEFAULT_ASSIGN_CASTING (*(NPY_CASTING *)PyArray_API[292]) +#define PyArray_Partition \ + (*(int (*)(PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND)) \ + PyArray_API[296]) +#define PyArray_ArgPartition \ + (*(PyObject * (*)(PyArrayObject *, PyArrayObject *, int, NPY_SELECTKIND)) \ + PyArray_API[297]) +#define PyArray_SelectkindConverter \ + (*(int (*)(PyObject *, NPY_SELECTKIND *)) \ + PyArray_API[298]) +#define PyDataMem_NEW_ZEROED \ + (*(void * (*)(size_t, size_t)) \ + PyArray_API[299]) +#define PyArray_CheckAnyScalarExact \ + (*(int (*)(PyObject *)) \ + PyArray_API[300]) +#define PyArray_ResolveWritebackIfCopy \ + (*(int (*)(PyArrayObject *)) \ + PyArray_API[302]) +#define PyArray_SetWritebackIfCopyBase \ + (*(int (*)(PyArrayObject *, PyArrayObject *)) \ + PyArray_API[303]) + +#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION +#define PyDataMem_SetHandler \ + (*(PyObject * (*)(PyObject *)) \ + PyArray_API[304]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_1_22_API_VERSION +#define PyDataMem_GetHandler \ + (*(PyObject * (*)(void)) \ + PyArray_API[305]) +#endif +#define PyDataMem_DefaultHandler (*(PyObject* *)PyArray_API[306]) + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_ConvertDatetime64ToDatetimeStruct \ + (*(int (*)(PyArray_DatetimeMetaData *, npy_datetime, npy_datetimestruct *)) \ + PyArray_API[307]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_ConvertDatetimeStructToDatetime64 \ + (*(int (*)(PyArray_DatetimeMetaData *, const npy_datetimestruct *, npy_datetime *)) \ + PyArray_API[308]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_ConvertPyDateTimeToDatetimeStruct \ + (*(int (*)(PyObject *, npy_datetimestruct *, NPY_DATETIMEUNIT *, int)) \ + PyArray_API[309]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_GetDatetimeISO8601StrLen \ + (*(int (*)(int, NPY_DATETIMEUNIT)) \ + PyArray_API[310]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_MakeISO8601Datetime \ + (*(int (*)(npy_datetimestruct *, char *, npy_intp, int, int, NPY_DATETIMEUNIT, int, NPY_CASTING)) \ + PyArray_API[311]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyDatetime_ParseISO8601Datetime \ + (*(int (*)(char const *, Py_ssize_t, NPY_DATETIMEUNIT, NPY_CASTING, npy_datetimestruct *, NPY_DATETIMEUNIT *, npy_bool *)) \ + PyArray_API[312]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_load \ + (*(int (*)(npy_string_allocator *, const npy_packed_static_string *, npy_static_string *)) \ + PyArray_API[313]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_pack \ + (*(int (*)(npy_string_allocator *, npy_packed_static_string *, const char *, size_t)) \ + PyArray_API[314]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_pack_null \ + (*(int (*)(npy_string_allocator *, npy_packed_static_string *)) \ + PyArray_API[315]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_acquire_allocator \ + (*(npy_string_allocator * (*)(const PyArray_StringDTypeObject *)) \ + PyArray_API[316]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_acquire_allocators \ + (*(void (*)(size_t, PyArray_Descr *const descrs[], npy_string_allocator *allocators[])) \ + PyArray_API[317]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_release_allocator \ + (*(void (*)(npy_string_allocator *)) \ + PyArray_API[318]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define NpyString_release_allocators \ + (*(void (*)(size_t, npy_string_allocator *allocators[])) \ + PyArray_API[319]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyArray_GetDefaultDescr \ + (*(PyArray_Descr * (*)(PyArray_DTypeMeta *)) \ + PyArray_API[361]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyArrayInitDTypeMeta_FromSpec \ + (*(int (*)(PyArray_DTypeMeta *, PyArrayDTypeMeta_Spec *)) \ + PyArray_API[362]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyArray_CommonDType \ + (*(PyArray_DTypeMeta * (*)(PyArray_DTypeMeta *, PyArray_DTypeMeta *)) \ + PyArray_API[363]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyArray_PromoteDTypeSequence \ + (*(PyArray_DTypeMeta * (*)(npy_intp, PyArray_DTypeMeta **)) \ + PyArray_API[364]) +#endif +#define _PyDataType_GetArrFuncs \ + (*(PyArray_ArrFuncs * (*)(const PyArray_Descr *)) \ + PyArray_API[365]) + +/* + * The DType classes are inconvenient for the Python generation so exposed + * manually in the header below (may be moved). + */ +#include "numpy/_public_dtype_api_table.h" + +#if !defined(NO_IMPORT_ARRAY) && !defined(NO_IMPORT) +static int +_import_array(void) +{ + int st; + PyObject *numpy = PyImport_ImportModule("numpy._core._multiarray_umath"); + if (numpy == NULL && PyErr_ExceptionMatches(PyExc_ModuleNotFoundError)) { + PyErr_Clear(); + numpy = PyImport_ImportModule("numpy.core._multiarray_umath"); + } + + if (numpy == NULL) { + return -1; + } + + PyObject *c_api = PyObject_GetAttrString(numpy, "_ARRAY_API"); + Py_DECREF(numpy); + if (c_api == NULL) { + return -1; + } + + if (!PyCapsule_CheckExact(c_api)) { + PyErr_SetString(PyExc_RuntimeError, "_ARRAY_API is not PyCapsule object"); + Py_DECREF(c_api); + return -1; + } + PyArray_API = (void **)PyCapsule_GetPointer(c_api, NULL); + Py_DECREF(c_api); + if (PyArray_API == NULL) { + PyErr_SetString(PyExc_RuntimeError, "_ARRAY_API is NULL pointer"); + return -1; + } + + /* + * On exceedingly few platforms these sizes may not match, in which case + * We do not support older NumPy versions at all. + */ + if (sizeof(Py_ssize_t) != sizeof(Py_intptr_t) && + PyArray_RUNTIME_VERSION < NPY_2_0_API_VERSION) { + PyErr_Format(PyExc_RuntimeError, + "module compiled against NumPy 2.0 but running on NumPy 1.x. " + "Unfortunately, this is not supported on niche platforms where " + "`sizeof(size_t) != sizeof(inptr_t)`."); + } + /* + * Perform runtime check of C API version. As of now NumPy 2.0 is ABI + * backwards compatible (in the exposed feature subset!) for all practical + * purposes. + */ + if (NPY_VERSION < PyArray_GetNDArrayCVersion()) { + PyErr_Format(PyExc_RuntimeError, "module compiled against "\ + "ABI version 0x%x but this version of numpy is 0x%x", \ + (int) NPY_VERSION, (int) PyArray_GetNDArrayCVersion()); + return -1; + } + PyArray_RUNTIME_VERSION = (int)PyArray_GetNDArrayCFeatureVersion(); + if (NPY_FEATURE_VERSION > PyArray_RUNTIME_VERSION) { + PyErr_Format(PyExc_RuntimeError, + "module was compiled against NumPy C-API version 0x%x " + "(NumPy " NPY_FEATURE_VERSION_STRING ") " + "but the running NumPy has C-API version 0x%x. " + "Check the section C-API incompatibility at the " + "Troubleshooting ImportError section at " + "https://numpy.org/devdocs/user/troubleshooting-importerror.html" + "#c-api-incompatibility " + "for indications on how to solve this problem.", + (int)NPY_FEATURE_VERSION, PyArray_RUNTIME_VERSION); + return -1; + } + + /* + * Perform runtime check of endianness and check it matches the one set by + * the headers (npy_endian.h) as a safeguard + */ + st = PyArray_GetEndianness(); + if (st == NPY_CPU_UNKNOWN_ENDIAN) { + PyErr_SetString(PyExc_RuntimeError, + "FATAL: module compiled as unknown endian"); + return -1; + } +#if NPY_BYTE_ORDER == NPY_BIG_ENDIAN + if (st != NPY_CPU_BIG) { + PyErr_SetString(PyExc_RuntimeError, + "FATAL: module compiled as big endian, but " + "detected different endianness at runtime"); + return -1; + } +#elif NPY_BYTE_ORDER == NPY_LITTLE_ENDIAN + if (st != NPY_CPU_LITTLE) { + PyErr_SetString(PyExc_RuntimeError, + "FATAL: module compiled as little endian, but " + "detected different endianness at runtime"); + return -1; + } +#endif + + return 0; +} + +#define import_array() { \ + if (_import_array() < 0) { \ + PyErr_Print(); \ + PyErr_SetString( \ + PyExc_ImportError, \ + "numpy._core.multiarray failed to import" \ + ); \ + return NULL; \ + } \ +} + +#define import_array1(ret) { \ + if (_import_array() < 0) { \ + PyErr_Print(); \ + PyErr_SetString( \ + PyExc_ImportError, \ + "numpy._core.multiarray failed to import" \ + ); \ + return ret; \ + } \ +} + +#define import_array2(msg, ret) { \ + if (_import_array() < 0) { \ + PyErr_Print(); \ + PyErr_SetString(PyExc_ImportError, msg); \ + return ret; \ + } \ +} + +#endif + +#endif diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.c b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.c new file mode 100644 index 0000000000000000000000000000000000000000..10fcbc4553989057667a90ce9d587deefc13f5f1 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.c @@ -0,0 +1,54 @@ + +/* These pointers will be stored in the C-object for use in other + extension modules +*/ + +void *PyUFunc_API[] = { + (void *) &PyUFunc_Type, + (void *) PyUFunc_FromFuncAndData, + (void *) PyUFunc_RegisterLoopForType, + NULL, + (void *) PyUFunc_f_f_As_d_d, + (void *) PyUFunc_d_d, + (void *) PyUFunc_f_f, + (void *) PyUFunc_g_g, + (void *) PyUFunc_F_F_As_D_D, + (void *) PyUFunc_F_F, + (void *) PyUFunc_D_D, + (void *) PyUFunc_G_G, + (void *) PyUFunc_O_O, + (void *) PyUFunc_ff_f_As_dd_d, + (void *) PyUFunc_ff_f, + (void *) PyUFunc_dd_d, + (void *) PyUFunc_gg_g, + (void *) PyUFunc_FF_F_As_DD_D, + (void *) PyUFunc_DD_D, + (void *) PyUFunc_FF_F, + (void *) PyUFunc_GG_G, + (void *) PyUFunc_OO_O, + (void *) PyUFunc_O_O_method, + (void *) PyUFunc_OO_O_method, + (void *) PyUFunc_On_Om, + NULL, + NULL, + (void *) PyUFunc_clearfperr, + (void *) PyUFunc_getfperr, + NULL, + (void *) PyUFunc_ReplaceLoopBySignature, + (void *) PyUFunc_FromFuncAndDataAndSignature, + NULL, + (void *) PyUFunc_e_e, + (void *) PyUFunc_e_e_As_f_f, + (void *) PyUFunc_e_e_As_d_d, + (void *) PyUFunc_ee_e, + (void *) PyUFunc_ee_e_As_ff_f, + (void *) PyUFunc_ee_e_As_dd_d, + (void *) PyUFunc_DefaultTypeResolver, + (void *) PyUFunc_ValidateCasting, + (void *) PyUFunc_RegisterLoopForDescr, + (void *) PyUFunc_FromFuncAndDataAndSignatureAndIdentity, + (void *) PyUFunc_AddLoopFromSpec, + (void *) PyUFunc_AddPromoter, + (void *) PyUFunc_AddWrappingLoop, + (void *) PyUFunc_GiveFloatingpointErrors +}; diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.h new file mode 100644 index 0000000000000000000000000000000000000000..df7ded10b548d495338dc368d727cf77ff70740a --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/__ufunc_api.h @@ -0,0 +1,340 @@ + +#ifdef _UMATHMODULE + +extern NPY_NO_EXPORT PyTypeObject PyUFunc_Type; + +extern NPY_NO_EXPORT PyTypeObject PyUFunc_Type; + +NPY_NO_EXPORT PyObject * PyUFunc_FromFuncAndData \ + (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int); +NPY_NO_EXPORT int PyUFunc_RegisterLoopForType \ + (PyUFuncObject *, int, PyUFuncGenericFunction, const int *, void *); +NPY_NO_EXPORT void PyUFunc_f_f_As_d_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_d_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_f_f \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_g_g \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_F_F_As_D_D \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_F_F \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_D_D \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_G_G \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_O_O \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_ff_f_As_dd_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_ff_f \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_dd_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_gg_g \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_FF_F_As_DD_D \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_DD_D \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_FF_F \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_GG_G \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_OO_O \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_O_O_method \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_OO_O_method \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_On_Om \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_clearfperr \ + (void); +NPY_NO_EXPORT int PyUFunc_getfperr \ + (void); +NPY_NO_EXPORT int PyUFunc_ReplaceLoopBySignature \ + (PyUFuncObject *, PyUFuncGenericFunction, const int *, PyUFuncGenericFunction *); +NPY_NO_EXPORT PyObject * PyUFunc_FromFuncAndDataAndSignature \ + (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int, const char *); +NPY_NO_EXPORT void PyUFunc_e_e \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_e_e_As_f_f \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_e_e_As_d_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_ee_e \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_ee_e_As_ff_f \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT void PyUFunc_ee_e_As_dd_d \ + (char **, npy_intp const *, npy_intp const *, void *); +NPY_NO_EXPORT int PyUFunc_DefaultTypeResolver \ + (PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyObject *, PyArray_Descr **); +NPY_NO_EXPORT int PyUFunc_ValidateCasting \ + (PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyArray_Descr *const *); +NPY_NO_EXPORT int PyUFunc_RegisterLoopForDescr \ + (PyUFuncObject *, PyArray_Descr *, PyUFuncGenericFunction, PyArray_Descr **, void *); +NPY_NO_EXPORT PyObject * PyUFunc_FromFuncAndDataAndSignatureAndIdentity \ + (PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, const int, const char *, PyObject *); +NPY_NO_EXPORT int PyUFunc_AddLoopFromSpec \ + (PyObject *, PyArrayMethod_Spec *); +NPY_NO_EXPORT int PyUFunc_AddPromoter \ + (PyObject *, PyObject *, PyObject *); +NPY_NO_EXPORT int PyUFunc_AddWrappingLoop \ + (PyObject *, PyArray_DTypeMeta *new_dtypes[], PyArray_DTypeMeta *wrapped_dtypes[], PyArrayMethod_TranslateGivenDescriptors *, PyArrayMethod_TranslateLoopDescriptors *); +NPY_NO_EXPORT int PyUFunc_GiveFloatingpointErrors \ + (const char *, int); + +#else + +#if defined(PY_UFUNC_UNIQUE_SYMBOL) +#define PyUFunc_API PY_UFUNC_UNIQUE_SYMBOL +#endif + +/* By default do not export API in an .so (was never the case on windows) */ +#ifndef NPY_API_SYMBOL_ATTRIBUTE + #define NPY_API_SYMBOL_ATTRIBUTE NPY_VISIBILITY_HIDDEN +#endif + +#if defined(NO_IMPORT) || defined(NO_IMPORT_UFUNC) +extern NPY_API_SYMBOL_ATTRIBUTE void **PyUFunc_API; +#else +#if defined(PY_UFUNC_UNIQUE_SYMBOL) +NPY_API_SYMBOL_ATTRIBUTE void **PyUFunc_API; +#else +static void **PyUFunc_API=NULL; +#endif +#endif + +#define PyUFunc_Type (*(PyTypeObject *)PyUFunc_API[0]) +#define PyUFunc_FromFuncAndData \ + (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int)) \ + PyUFunc_API[1]) +#define PyUFunc_RegisterLoopForType \ + (*(int (*)(PyUFuncObject *, int, PyUFuncGenericFunction, const int *, void *)) \ + PyUFunc_API[2]) +#define PyUFunc_f_f_As_d_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[4]) +#define PyUFunc_d_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[5]) +#define PyUFunc_f_f \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[6]) +#define PyUFunc_g_g \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[7]) +#define PyUFunc_F_F_As_D_D \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[8]) +#define PyUFunc_F_F \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[9]) +#define PyUFunc_D_D \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[10]) +#define PyUFunc_G_G \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[11]) +#define PyUFunc_O_O \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[12]) +#define PyUFunc_ff_f_As_dd_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[13]) +#define PyUFunc_ff_f \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[14]) +#define PyUFunc_dd_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[15]) +#define PyUFunc_gg_g \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[16]) +#define PyUFunc_FF_F_As_DD_D \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[17]) +#define PyUFunc_DD_D \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[18]) +#define PyUFunc_FF_F \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[19]) +#define PyUFunc_GG_G \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[20]) +#define PyUFunc_OO_O \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[21]) +#define PyUFunc_O_O_method \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[22]) +#define PyUFunc_OO_O_method \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[23]) +#define PyUFunc_On_Om \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[24]) +#define PyUFunc_clearfperr \ + (*(void (*)(void)) \ + PyUFunc_API[27]) +#define PyUFunc_getfperr \ + (*(int (*)(void)) \ + PyUFunc_API[28]) +#define PyUFunc_ReplaceLoopBySignature \ + (*(int (*)(PyUFuncObject *, PyUFuncGenericFunction, const int *, PyUFuncGenericFunction *)) \ + PyUFunc_API[30]) +#define PyUFunc_FromFuncAndDataAndSignature \ + (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, int, const char *)) \ + PyUFunc_API[31]) +#define PyUFunc_e_e \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[33]) +#define PyUFunc_e_e_As_f_f \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[34]) +#define PyUFunc_e_e_As_d_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[35]) +#define PyUFunc_ee_e \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[36]) +#define PyUFunc_ee_e_As_ff_f \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[37]) +#define PyUFunc_ee_e_As_dd_d \ + (*(void (*)(char **, npy_intp const *, npy_intp const *, void *)) \ + PyUFunc_API[38]) +#define PyUFunc_DefaultTypeResolver \ + (*(int (*)(PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyObject *, PyArray_Descr **)) \ + PyUFunc_API[39]) +#define PyUFunc_ValidateCasting \ + (*(int (*)(PyUFuncObject *, NPY_CASTING, PyArrayObject **, PyArray_Descr *const *)) \ + PyUFunc_API[40]) +#define PyUFunc_RegisterLoopForDescr \ + (*(int (*)(PyUFuncObject *, PyArray_Descr *, PyUFuncGenericFunction, PyArray_Descr **, void *)) \ + PyUFunc_API[41]) + +#if NPY_FEATURE_VERSION >= NPY_1_16_API_VERSION +#define PyUFunc_FromFuncAndDataAndSignatureAndIdentity \ + (*(PyObject * (*)(PyUFuncGenericFunction *, void *const *, const char *, int, int, int, int, const char *, const char *, const int, const char *, PyObject *)) \ + PyUFunc_API[42]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyUFunc_AddLoopFromSpec \ + (*(int (*)(PyObject *, PyArrayMethod_Spec *)) \ + PyUFunc_API[43]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyUFunc_AddPromoter \ + (*(int (*)(PyObject *, PyObject *, PyObject *)) \ + PyUFunc_API[44]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyUFunc_AddWrappingLoop \ + (*(int (*)(PyObject *, PyArray_DTypeMeta *new_dtypes[], PyArray_DTypeMeta *wrapped_dtypes[], PyArrayMethod_TranslateGivenDescriptors *, PyArrayMethod_TranslateLoopDescriptors *)) \ + PyUFunc_API[45]) +#endif + +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION +#define PyUFunc_GiveFloatingpointErrors \ + (*(int (*)(const char *, int)) \ + PyUFunc_API[46]) +#endif + +static inline int +_import_umath(void) +{ + PyObject *numpy = PyImport_ImportModule("numpy._core._multiarray_umath"); + if (numpy == NULL && PyErr_ExceptionMatches(PyExc_ModuleNotFoundError)) { + PyErr_Clear(); + numpy = PyImport_ImportModule("numpy.core._multiarray_umath"); + } + + if (numpy == NULL) { + PyErr_SetString(PyExc_ImportError, + "_multiarray_umath failed to import"); + return -1; + } + + PyObject *c_api = PyObject_GetAttrString(numpy, "_UFUNC_API"); + Py_DECREF(numpy); + if (c_api == NULL) { + PyErr_SetString(PyExc_AttributeError, "_UFUNC_API not found"); + return -1; + } + + if (!PyCapsule_CheckExact(c_api)) { + PyErr_SetString(PyExc_RuntimeError, "_UFUNC_API is not PyCapsule object"); + Py_DECREF(c_api); + return -1; + } + PyUFunc_API = (void **)PyCapsule_GetPointer(c_api, NULL); + Py_DECREF(c_api); + if (PyUFunc_API == NULL) { + PyErr_SetString(PyExc_RuntimeError, "_UFUNC_API is NULL pointer"); + return -1; + } + return 0; +} + +#define import_umath() \ + do {\ + UFUNC_NOFPE\ + if (_import_umath() < 0) {\ + PyErr_Print();\ + PyErr_SetString(PyExc_ImportError,\ + "numpy._core.umath failed to import");\ + return NULL;\ + }\ + } while(0) + +#define import_umath1(ret) \ + do {\ + UFUNC_NOFPE\ + if (_import_umath() < 0) {\ + PyErr_Print();\ + PyErr_SetString(PyExc_ImportError,\ + "numpy._core.umath failed to import");\ + return ret;\ + }\ + } while(0) + +#define import_umath2(ret, msg) \ + do {\ + UFUNC_NOFPE\ + if (_import_umath() < 0) {\ + PyErr_Print();\ + PyErr_SetString(PyExc_ImportError, msg);\ + return ret;\ + }\ + } while(0) + +#define import_ufunc() \ + do {\ + UFUNC_NOFPE\ + if (_import_umath() < 0) {\ + PyErr_Print();\ + PyErr_SetString(PyExc_ImportError,\ + "numpy._core.umath failed to import");\ + }\ + } while(0) + + +static inline int +PyUFunc_ImportUFuncAPI() +{ + if (NPY_UNLIKELY(PyUFunc_API == NULL)) { + import_umath1(-1); + } + return 0; +} + +#endif diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h new file mode 100644 index 0000000000000000000000000000000000000000..51f39054062762c39b3df4f689b74060e97036c0 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/_public_dtype_api_table.h @@ -0,0 +1,86 @@ +/* + * Public exposure of the DType Classes. These are tricky to expose + * via the Python API, so they are exposed through this header for now. + * + * These definitions are only relevant for the public API and we reserve + * the slots 320-360 in the API table generation for this (currently). + * + * TODO: This file should be consolidated with the API table generation + * (although not sure the current generation is worth preserving). + */ +#ifndef NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_ +#define NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_ + +#if !(defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD) + +/* All of these require NumPy 2.0 support */ +#if NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION + +/* + * The type of the DType metaclass + */ +#define PyArrayDTypeMeta_Type (*(PyTypeObject *)(PyArray_API + 320)[0]) +/* + * NumPy's builtin DTypes: + */ +#define PyArray_BoolDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[1]) +/* Integers */ +#define PyArray_ByteDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[2]) +#define PyArray_UByteDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[3]) +#define PyArray_ShortDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[4]) +#define PyArray_UShortDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[5]) +#define PyArray_IntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[6]) +#define PyArray_UIntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[7]) +#define PyArray_LongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[8]) +#define PyArray_ULongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[9]) +#define PyArray_LongLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[10]) +#define PyArray_ULongLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[11]) +/* Integer aliases */ +#define PyArray_Int8DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[12]) +#define PyArray_UInt8DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[13]) +#define PyArray_Int16DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[14]) +#define PyArray_UInt16DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[15]) +#define PyArray_Int32DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[16]) +#define PyArray_UInt32DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[17]) +#define PyArray_Int64DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[18]) +#define PyArray_UInt64DType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[19]) +#define PyArray_IntpDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[20]) +#define PyArray_UIntpDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[21]) +/* Floats */ +#define PyArray_HalfDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[22]) +#define PyArray_FloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[23]) +#define PyArray_DoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[24]) +#define PyArray_LongDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[25]) +/* Complex */ +#define PyArray_CFloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[26]) +#define PyArray_CDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[27]) +#define PyArray_CLongDoubleDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[28]) +/* String/Bytes */ +#define PyArray_BytesDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[29]) +#define PyArray_UnicodeDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[30]) +/* Datetime/Timedelta */ +#define PyArray_DatetimeDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[31]) +#define PyArray_TimedeltaDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[32]) +/* Object/Void */ +#define PyArray_ObjectDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[33]) +#define PyArray_VoidDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[34]) +/* Python types (used as markers for scalars) */ +#define PyArray_PyLongDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[35]) +#define PyArray_PyFloatDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[36]) +#define PyArray_PyComplexDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[37]) +/* Default integer type */ +#define PyArray_DefaultIntDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[38]) +/* New non-legacy DTypes follow in the order they were added */ +#define PyArray_StringDType (*(PyArray_DTypeMeta *)(PyArray_API + 320)[39]) + +/* NOTE: offset 40 is free */ + +/* Need to start with a larger offset again for the abstract classes: */ +#define PyArray_IntAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[366]) +#define PyArray_FloatAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[367]) +#define PyArray_ComplexAbstractDType (*(PyArray_DTypeMeta *)PyArray_API[368]) + +#endif /* NPY_FEATURE_VERSION >= NPY_2_0_API_VERSION */ + +#endif /* NPY_INTERNAL_BUILD */ +#endif /* NUMPY_CORE_INCLUDE_NUMPY__PUBLIC_DTYPE_API_TABLE_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/arrayscalars.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/arrayscalars.h new file mode 100644 index 0000000000000000000000000000000000000000..ff048061f70abda097606b6247e32234d4eacf29 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/arrayscalars.h @@ -0,0 +1,196 @@ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_ + +#ifndef _MULTIARRAYMODULE +typedef struct { + PyObject_HEAD + npy_bool obval; +} PyBoolScalarObject; +#endif + + +typedef struct { + PyObject_HEAD + signed char obval; +} PyByteScalarObject; + + +typedef struct { + PyObject_HEAD + short obval; +} PyShortScalarObject; + + +typedef struct { + PyObject_HEAD + int obval; +} PyIntScalarObject; + + +typedef struct { + PyObject_HEAD + long obval; +} PyLongScalarObject; + + +typedef struct { + PyObject_HEAD + npy_longlong obval; +} PyLongLongScalarObject; + + +typedef struct { + PyObject_HEAD + unsigned char obval; +} PyUByteScalarObject; + + +typedef struct { + PyObject_HEAD + unsigned short obval; +} PyUShortScalarObject; + + +typedef struct { + PyObject_HEAD + unsigned int obval; +} PyUIntScalarObject; + + +typedef struct { + PyObject_HEAD + unsigned long obval; +} PyULongScalarObject; + + +typedef struct { + PyObject_HEAD + npy_ulonglong obval; +} PyULongLongScalarObject; + + +typedef struct { + PyObject_HEAD + npy_half obval; +} PyHalfScalarObject; + + +typedef struct { + PyObject_HEAD + float obval; +} PyFloatScalarObject; + + +typedef struct { + PyObject_HEAD + double obval; +} PyDoubleScalarObject; + + +typedef struct { + PyObject_HEAD + npy_longdouble obval; +} PyLongDoubleScalarObject; + + +typedef struct { + PyObject_HEAD + npy_cfloat obval; +} PyCFloatScalarObject; + + +typedef struct { + PyObject_HEAD + npy_cdouble obval; +} PyCDoubleScalarObject; + + +typedef struct { + PyObject_HEAD + npy_clongdouble obval; +} PyCLongDoubleScalarObject; + + +typedef struct { + PyObject_HEAD + PyObject * obval; +} PyObjectScalarObject; + +typedef struct { + PyObject_HEAD + npy_datetime obval; + PyArray_DatetimeMetaData obmeta; +} PyDatetimeScalarObject; + +typedef struct { + PyObject_HEAD + npy_timedelta obval; + PyArray_DatetimeMetaData obmeta; +} PyTimedeltaScalarObject; + + +typedef struct { + PyObject_HEAD + char obval; +} PyScalarObject; + +#define PyStringScalarObject PyBytesObject +#ifndef Py_LIMITED_API +typedef struct { + /* note that the PyObject_HEAD macro lives right here */ + PyUnicodeObject base; + Py_UCS4 *obval; + #if NPY_FEATURE_VERSION >= NPY_1_20_API_VERSION + char *buffer_fmt; + #endif +} PyUnicodeScalarObject; +#endif + + +typedef struct { + PyObject_VAR_HEAD + char *obval; +#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD + /* Internally use the subclass to allow accessing names/fields */ + _PyArray_LegacyDescr *descr; +#else + PyArray_Descr *descr; +#endif + int flags; + PyObject *base; + #if NPY_FEATURE_VERSION >= NPY_1_20_API_VERSION + void *_buffer_info; /* private buffer info, tagged to allow warning */ + #endif +} PyVoidScalarObject; + +/* Macros + PyScalarObject + PyArrType_Type + are defined in ndarrayobject.h +*/ + +#define PyArrayScalar_False ((PyObject *)(&(_PyArrayScalar_BoolValues[0]))) +#define PyArrayScalar_True ((PyObject *)(&(_PyArrayScalar_BoolValues[1]))) +#define PyArrayScalar_FromLong(i) \ + ((PyObject *)(&(_PyArrayScalar_BoolValues[((i)!=0)]))) +#define PyArrayScalar_RETURN_BOOL_FROM_LONG(i) \ + return Py_INCREF(PyArrayScalar_FromLong(i)), \ + PyArrayScalar_FromLong(i) +#define PyArrayScalar_RETURN_FALSE \ + return Py_INCREF(PyArrayScalar_False), \ + PyArrayScalar_False +#define PyArrayScalar_RETURN_TRUE \ + return Py_INCREF(PyArrayScalar_True), \ + PyArrayScalar_True + +#define PyArrayScalar_New(cls) \ + Py##cls##ArrType_Type.tp_alloc(&Py##cls##ArrType_Type, 0) +#ifndef Py_LIMITED_API +/* For the limited API, use PyArray_ScalarAsCtype instead */ +#define PyArrayScalar_VAL(obj, cls) \ + ((Py##cls##ScalarObject *)obj)->obval +#define PyArrayScalar_ASSIGN(obj, cls, val) \ + PyArrayScalar_VAL(obj, cls) = val +#endif + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_ARRAYSCALARS_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_1_7_deprecated_api.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_1_7_deprecated_api.h new file mode 100644 index 0000000000000000000000000000000000000000..be53cded488dd373072ab798fd7c25a5041e20ad --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_1_7_deprecated_api.h @@ -0,0 +1,112 @@ +#ifndef NPY_DEPRECATED_INCLUDES +#error "Should never include npy_*_*_deprecated_api directly." +#endif + +#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_1_7_DEPRECATED_API_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_NPY_1_7_DEPRECATED_API_H_ + +/* Emit a warning if the user did not specifically request the old API */ +#ifndef NPY_NO_DEPRECATED_API +#if defined(_WIN32) +#define _WARN___STR2__(x) #x +#define _WARN___STR1__(x) _WARN___STR2__(x) +#define _WARN___LOC__ __FILE__ "(" _WARN___STR1__(__LINE__) ") : Warning Msg: " +#pragma message(_WARN___LOC__"Using deprecated NumPy API, disable it with " \ + "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION") +#else +#warning "Using deprecated NumPy API, disable it with " \ + "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" +#endif +#endif + +/* + * This header exists to collect all dangerous/deprecated NumPy API + * as of NumPy 1.7. + * + * This is an attempt to remove bad API, the proliferation of macros, + * and namespace pollution currently produced by the NumPy headers. + */ + +/* These array flags are deprecated as of NumPy 1.7 */ +#define NPY_CONTIGUOUS NPY_ARRAY_C_CONTIGUOUS +#define NPY_FORTRAN NPY_ARRAY_F_CONTIGUOUS + +/* + * The consistent NPY_ARRAY_* names which don't pollute the NPY_* + * namespace were added in NumPy 1.7. + * + * These versions of the carray flags are deprecated, but + * probably should only be removed after two releases instead of one. + */ +#define NPY_C_CONTIGUOUS NPY_ARRAY_C_CONTIGUOUS +#define NPY_F_CONTIGUOUS NPY_ARRAY_F_CONTIGUOUS +#define NPY_OWNDATA NPY_ARRAY_OWNDATA +#define NPY_FORCECAST NPY_ARRAY_FORCECAST +#define NPY_ENSURECOPY NPY_ARRAY_ENSURECOPY +#define NPY_ENSUREARRAY NPY_ARRAY_ENSUREARRAY +#define NPY_ELEMENTSTRIDES NPY_ARRAY_ELEMENTSTRIDES +#define NPY_ALIGNED NPY_ARRAY_ALIGNED +#define NPY_NOTSWAPPED NPY_ARRAY_NOTSWAPPED +#define NPY_WRITEABLE NPY_ARRAY_WRITEABLE +#define NPY_BEHAVED NPY_ARRAY_BEHAVED +#define NPY_BEHAVED_NS NPY_ARRAY_BEHAVED_NS +#define NPY_CARRAY NPY_ARRAY_CARRAY +#define NPY_CARRAY_RO NPY_ARRAY_CARRAY_RO +#define NPY_FARRAY NPY_ARRAY_FARRAY +#define NPY_FARRAY_RO NPY_ARRAY_FARRAY_RO +#define NPY_DEFAULT NPY_ARRAY_DEFAULT +#define NPY_IN_ARRAY NPY_ARRAY_IN_ARRAY +#define NPY_OUT_ARRAY NPY_ARRAY_OUT_ARRAY +#define NPY_INOUT_ARRAY NPY_ARRAY_INOUT_ARRAY +#define NPY_IN_FARRAY NPY_ARRAY_IN_FARRAY +#define NPY_OUT_FARRAY NPY_ARRAY_OUT_FARRAY +#define NPY_INOUT_FARRAY NPY_ARRAY_INOUT_FARRAY +#define NPY_UPDATE_ALL NPY_ARRAY_UPDATE_ALL + +/* This way of accessing the default type is deprecated as of NumPy 1.7 */ +#define PyArray_DEFAULT NPY_DEFAULT_TYPE + +/* + * Deprecated as of NumPy 1.7, this kind of shortcut doesn't + * belong in the public API. + */ +#define NPY_AO PyArrayObject + +/* + * Deprecated as of NumPy 1.7, an all-lowercase macro doesn't + * belong in the public API. + */ +#define fortran fortran_ + +/* + * Deprecated as of NumPy 1.7, as it is a namespace-polluting + * macro. + */ +#define FORTRAN_IF PyArray_FORTRAN_IF + +/* Deprecated as of NumPy 1.7, datetime64 uses c_metadata instead */ +#define NPY_METADATA_DTSTR "__timeunit__" + +/* + * Deprecated as of NumPy 1.7. + * The reasoning: + * - These are for datetime, but there's no datetime "namespace". + * - They just turn NPY_STR_ into "", which is just + * making something simple be indirected. + */ +#define NPY_STR_Y "Y" +#define NPY_STR_M "M" +#define NPY_STR_W "W" +#define NPY_STR_D "D" +#define NPY_STR_h "h" +#define NPY_STR_m "m" +#define NPY_STR_s "s" +#define NPY_STR_ms "ms" +#define NPY_STR_us "us" +#define NPY_STR_ns "ns" +#define NPY_STR_ps "ps" +#define NPY_STR_fs "fs" +#define NPY_STR_as "as" + + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_NPY_1_7_DEPRECATED_API_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_3kcompat.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_3kcompat.h new file mode 100644 index 0000000000000000000000000000000000000000..c2bf74faf09d9df0df07f23e7d8b8550fe79ba5f --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_3kcompat.h @@ -0,0 +1,374 @@ +/* + * This is a convenience header file providing compatibility utilities + * for supporting different minor versions of Python 3. + * It was originally used to support the transition from Python 2, + * hence the "3k" naming. + * + * If you want to use this for your own projects, it's recommended to make a + * copy of it. We don't provide backwards compatibility guarantees. + */ + +#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_ + +#include +#include + +#include "npy_common.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/* Python13 removes _PyLong_AsInt */ +static inline int +Npy__PyLong_AsInt(PyObject *obj) +{ + int overflow; + long result = PyLong_AsLongAndOverflow(obj, &overflow); + + /* INT_MAX and INT_MIN are defined in Python.h */ + if (overflow || result > INT_MAX || result < INT_MIN) { + /* XXX: could be cute and give a different + message for overflow == -1 */ + PyErr_SetString(PyExc_OverflowError, + "Python int too large to convert to C int"); + return -1; + } + return (int)result; +} + +#if defined _MSC_VER && _MSC_VER >= 1900 + +#include + +/* + * Macros to protect CRT calls against instant termination when passed an + * invalid parameter (https://bugs.python.org/issue23524). + */ +extern _invalid_parameter_handler _Py_silent_invalid_parameter_handler; +#define NPY_BEGIN_SUPPRESS_IPH { _invalid_parameter_handler _Py_old_handler = \ + _set_thread_local_invalid_parameter_handler(_Py_silent_invalid_parameter_handler); +#define NPY_END_SUPPRESS_IPH _set_thread_local_invalid_parameter_handler(_Py_old_handler); } + +#else + +#define NPY_BEGIN_SUPPRESS_IPH +#define NPY_END_SUPPRESS_IPH + +#endif /* _MSC_VER >= 1900 */ + +/* + * PyFile_* compatibility + */ + +/* + * Get a FILE* handle to the file represented by the Python object + */ +static inline FILE* +npy_PyFile_Dup2(PyObject *file, char *mode, npy_off_t *orig_pos) +{ + int fd, fd2, unbuf; + Py_ssize_t fd2_tmp; + PyObject *ret, *os, *io, *io_raw; + npy_off_t pos; + FILE *handle; + + /* Flush first to ensure things end up in the file in the correct order */ + ret = PyObject_CallMethod(file, "flush", ""); + if (ret == NULL) { + return NULL; + } + Py_DECREF(ret); + fd = PyObject_AsFileDescriptor(file); + if (fd == -1) { + return NULL; + } + + /* + * The handle needs to be dup'd because we have to call fclose + * at the end + */ + os = PyImport_ImportModule("os"); + if (os == NULL) { + return NULL; + } + ret = PyObject_CallMethod(os, "dup", "i", fd); + Py_DECREF(os); + if (ret == NULL) { + return NULL; + } + fd2_tmp = PyNumber_AsSsize_t(ret, PyExc_IOError); + Py_DECREF(ret); + if (fd2_tmp == -1 && PyErr_Occurred()) { + return NULL; + } + if (fd2_tmp < INT_MIN || fd2_tmp > INT_MAX) { + PyErr_SetString(PyExc_IOError, + "Getting an 'int' from os.dup() failed"); + return NULL; + } + fd2 = (int)fd2_tmp; + + /* Convert to FILE* handle */ +#ifdef _WIN32 + NPY_BEGIN_SUPPRESS_IPH + handle = _fdopen(fd2, mode); + NPY_END_SUPPRESS_IPH +#else + handle = fdopen(fd2, mode); +#endif + if (handle == NULL) { + PyErr_SetString(PyExc_IOError, + "Getting a FILE* from a Python file object via " + "_fdopen failed. If you built NumPy, you probably " + "linked with the wrong debug/release runtime"); + return NULL; + } + + /* Record the original raw file handle position */ + *orig_pos = npy_ftell(handle); + if (*orig_pos == -1) { + /* The io module is needed to determine if buffering is used */ + io = PyImport_ImportModule("io"); + if (io == NULL) { + fclose(handle); + return NULL; + } + /* File object instances of RawIOBase are unbuffered */ + io_raw = PyObject_GetAttrString(io, "RawIOBase"); + Py_DECREF(io); + if (io_raw == NULL) { + fclose(handle); + return NULL; + } + unbuf = PyObject_IsInstance(file, io_raw); + Py_DECREF(io_raw); + if (unbuf == 1) { + /* Succeed if the IO is unbuffered */ + return handle; + } + else { + PyErr_SetString(PyExc_IOError, "obtaining file position failed"); + fclose(handle); + return NULL; + } + } + + /* Seek raw handle to the Python-side position */ + ret = PyObject_CallMethod(file, "tell", ""); + if (ret == NULL) { + fclose(handle); + return NULL; + } + pos = PyLong_AsLongLong(ret); + Py_DECREF(ret); + if (PyErr_Occurred()) { + fclose(handle); + return NULL; + } + if (npy_fseek(handle, pos, SEEK_SET) == -1) { + PyErr_SetString(PyExc_IOError, "seeking file failed"); + fclose(handle); + return NULL; + } + return handle; +} + +/* + * Close the dup-ed file handle, and seek the Python one to the current position + */ +static inline int +npy_PyFile_DupClose2(PyObject *file, FILE* handle, npy_off_t orig_pos) +{ + int fd, unbuf; + PyObject *ret, *io, *io_raw; + npy_off_t position; + + position = npy_ftell(handle); + + /* Close the FILE* handle */ + fclose(handle); + + /* + * Restore original file handle position, in order to not confuse + * Python-side data structures + */ + fd = PyObject_AsFileDescriptor(file); + if (fd == -1) { + return -1; + } + + if (npy_lseek(fd, orig_pos, SEEK_SET) == -1) { + + /* The io module is needed to determine if buffering is used */ + io = PyImport_ImportModule("io"); + if (io == NULL) { + return -1; + } + /* File object instances of RawIOBase are unbuffered */ + io_raw = PyObject_GetAttrString(io, "RawIOBase"); + Py_DECREF(io); + if (io_raw == NULL) { + return -1; + } + unbuf = PyObject_IsInstance(file, io_raw); + Py_DECREF(io_raw); + if (unbuf == 1) { + /* Succeed if the IO is unbuffered */ + return 0; + } + else { + PyErr_SetString(PyExc_IOError, "seeking file failed"); + return -1; + } + } + + if (position == -1) { + PyErr_SetString(PyExc_IOError, "obtaining file position failed"); + return -1; + } + + /* Seek Python-side handle to the FILE* handle position */ + ret = PyObject_CallMethod(file, "seek", NPY_OFF_T_PYFMT "i", position, 0); + if (ret == NULL) { + return -1; + } + Py_DECREF(ret); + return 0; +} + +static inline PyObject* +npy_PyFile_OpenFile(PyObject *filename, const char *mode) +{ + PyObject *open; + open = PyDict_GetItemString(PyEval_GetBuiltins(), "open"); + if (open == NULL) { + return NULL; + } + return PyObject_CallFunction(open, "Os", filename, mode); +} + +static inline int +npy_PyFile_CloseFile(PyObject *file) +{ + PyObject *ret; + + ret = PyObject_CallMethod(file, "close", NULL); + if (ret == NULL) { + return -1; + } + Py_DECREF(ret); + return 0; +} + +/* This is a copy of _PyErr_ChainExceptions, which + * is no longer exported from Python3.12 + */ +static inline void +npy_PyErr_ChainExceptions(PyObject *exc, PyObject *val, PyObject *tb) +{ + if (exc == NULL) + return; + + if (PyErr_Occurred()) { + PyObject *exc2, *val2, *tb2; + PyErr_Fetch(&exc2, &val2, &tb2); + PyErr_NormalizeException(&exc, &val, &tb); + if (tb != NULL) { + PyException_SetTraceback(val, tb); + Py_DECREF(tb); + } + Py_DECREF(exc); + PyErr_NormalizeException(&exc2, &val2, &tb2); + PyException_SetContext(val2, val); + PyErr_Restore(exc2, val2, tb2); + } + else { + PyErr_Restore(exc, val, tb); + } +} + +/* This is a copy of _PyErr_ChainExceptions, with: + * __cause__ used instead of __context__ + */ +static inline void +npy_PyErr_ChainExceptionsCause(PyObject *exc, PyObject *val, PyObject *tb) +{ + if (exc == NULL) + return; + + if (PyErr_Occurred()) { + PyObject *exc2, *val2, *tb2; + PyErr_Fetch(&exc2, &val2, &tb2); + PyErr_NormalizeException(&exc, &val, &tb); + if (tb != NULL) { + PyException_SetTraceback(val, tb); + Py_DECREF(tb); + } + Py_DECREF(exc); + PyErr_NormalizeException(&exc2, &val2, &tb2); + PyException_SetCause(val2, val); + PyErr_Restore(exc2, val2, tb2); + } + else { + PyErr_Restore(exc, val, tb); + } +} + +/* + * PyCObject functions adapted to PyCapsules. + * + * The main job here is to get rid of the improved error handling + * of PyCapsules. It's a shame... + */ +static inline PyObject * +NpyCapsule_FromVoidPtr(void *ptr, void (*dtor)(PyObject *)) +{ + PyObject *ret = PyCapsule_New(ptr, NULL, dtor); + if (ret == NULL) { + PyErr_Clear(); + } + return ret; +} + +static inline PyObject * +NpyCapsule_FromVoidPtrAndDesc(void *ptr, void* context, void (*dtor)(PyObject *)) +{ + PyObject *ret = NpyCapsule_FromVoidPtr(ptr, dtor); + if (ret != NULL && PyCapsule_SetContext(ret, context) != 0) { + PyErr_Clear(); + Py_DECREF(ret); + ret = NULL; + } + return ret; +} + +static inline void * +NpyCapsule_AsVoidPtr(PyObject *obj) +{ + void *ret = PyCapsule_GetPointer(obj, NULL); + if (ret == NULL) { + PyErr_Clear(); + } + return ret; +} + +static inline void * +NpyCapsule_GetDesc(PyObject *obj) +{ + return PyCapsule_GetContext(obj); +} + +static inline int +NpyCapsule_Check(PyObject *ptr) +{ + return PyCapsule_CheckExact(ptr); +} + +#ifdef __cplusplus +} +#endif + + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_NPY_3KCOMPAT_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_cpu.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_cpu.h new file mode 100644 index 0000000000000000000000000000000000000000..15f9f12931c82f0be8bfe6e32903754c5915485d --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/npy_cpu.h @@ -0,0 +1,134 @@ +/* + * This set (target) cpu specific macros: + * - Possible values: + * NPY_CPU_X86 + * NPY_CPU_AMD64 + * NPY_CPU_PPC + * NPY_CPU_PPC64 + * NPY_CPU_PPC64LE + * NPY_CPU_SPARC + * NPY_CPU_S390 + * NPY_CPU_IA64 + * NPY_CPU_HPPA + * NPY_CPU_ALPHA + * NPY_CPU_ARMEL + * NPY_CPU_ARMEB + * NPY_CPU_SH_LE + * NPY_CPU_SH_BE + * NPY_CPU_ARCEL + * NPY_CPU_ARCEB + * NPY_CPU_RISCV64 + * NPY_CPU_RISCV32 + * NPY_CPU_LOONGARCH + * NPY_CPU_WASM + */ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_ + +#include "numpyconfig.h" + +#if defined( __i386__ ) || defined(i386) || defined(_M_IX86) + /* + * __i386__ is defined by gcc and Intel compiler on Linux, + * _M_IX86 by VS compiler, + * i386 by Sun compilers on opensolaris at least + */ + #define NPY_CPU_X86 +#elif defined(__x86_64__) || defined(__amd64__) || defined(__x86_64) || defined(_M_AMD64) + /* + * both __x86_64__ and __amd64__ are defined by gcc + * __x86_64 defined by sun compiler on opensolaris at least + * _M_AMD64 defined by MS compiler + */ + #define NPY_CPU_AMD64 +#elif defined(__powerpc64__) && defined(__LITTLE_ENDIAN__) + #define NPY_CPU_PPC64LE +#elif defined(__powerpc64__) && defined(__BIG_ENDIAN__) + #define NPY_CPU_PPC64 +#elif defined(__ppc__) || defined(__powerpc__) || defined(_ARCH_PPC) + /* + * __ppc__ is defined by gcc, I remember having seen __powerpc__ once, + * but can't find it ATM + * _ARCH_PPC is used by at least gcc on AIX + * As __powerpc__ and _ARCH_PPC are also defined by PPC64 check + * for those specifically first before defaulting to ppc + */ + #define NPY_CPU_PPC +#elif defined(__sparc__) || defined(__sparc) + /* __sparc__ is defined by gcc and Forte (e.g. Sun) compilers */ + #define NPY_CPU_SPARC +#elif defined(__s390__) + #define NPY_CPU_S390 +#elif defined(__ia64) + #define NPY_CPU_IA64 +#elif defined(__hppa) + #define NPY_CPU_HPPA +#elif defined(__alpha__) + #define NPY_CPU_ALPHA +#elif defined(__arm__) || defined(__aarch64__) || defined(_M_ARM64) + /* _M_ARM64 is defined in MSVC for ARM64 compilation on Windows */ + #if defined(__ARMEB__) || defined(__AARCH64EB__) + #if defined(__ARM_32BIT_STATE) + #define NPY_CPU_ARMEB_AARCH32 + #elif defined(__ARM_64BIT_STATE) + #define NPY_CPU_ARMEB_AARCH64 + #else + #define NPY_CPU_ARMEB + #endif + #elif defined(__ARMEL__) || defined(__AARCH64EL__) || defined(_M_ARM64) + #if defined(__ARM_32BIT_STATE) + #define NPY_CPU_ARMEL_AARCH32 + #elif defined(__ARM_64BIT_STATE) || defined(_M_ARM64) || defined(__AARCH64EL__) + #define NPY_CPU_ARMEL_AARCH64 + #else + #define NPY_CPU_ARMEL + #endif + #else + # error Unknown ARM CPU, please report this to numpy maintainers with \ + information about your platform (OS, CPU and compiler) + #endif +#elif defined(__sh__) && defined(__LITTLE_ENDIAN__) + #define NPY_CPU_SH_LE +#elif defined(__sh__) && defined(__BIG_ENDIAN__) + #define NPY_CPU_SH_BE +#elif defined(__MIPSEL__) + #define NPY_CPU_MIPSEL +#elif defined(__MIPSEB__) + #define NPY_CPU_MIPSEB +#elif defined(__or1k__) + #define NPY_CPU_OR1K +#elif defined(__mc68000__) + #define NPY_CPU_M68K +#elif defined(__arc__) && defined(__LITTLE_ENDIAN__) + #define NPY_CPU_ARCEL +#elif defined(__arc__) && defined(__BIG_ENDIAN__) + #define NPY_CPU_ARCEB +#elif defined(__riscv) + #if __riscv_xlen == 64 + #define NPY_CPU_RISCV64 + #elif __riscv_xlen == 32 + #define NPY_CPU_RISCV32 + #endif +#elif defined(__loongarch__) + #define NPY_CPU_LOONGARCH +#elif defined(__EMSCRIPTEN__) + /* __EMSCRIPTEN__ is defined by emscripten: an LLVM-to-Web compiler */ + #define NPY_CPU_WASM +#else + #error Unknown CPU, please report this to numpy maintainers with \ + information about your platform (OS, CPU and compiler) +#endif + +/* + * Except for the following architectures, memory access is limited to the natural + * alignment of data types otherwise it may lead to bus error or performance regression. + * For more details about unaligned access, see https://www.kernel.org/doc/Documentation/unaligned-memory-access.txt. +*/ +#if defined(NPY_CPU_X86) || defined(NPY_CPU_AMD64) || defined(__aarch64__) || defined(__powerpc64__) + #define NPY_ALIGNMENT_REQUIRED 0 +#endif +#ifndef NPY_ALIGNMENT_REQUIRED + #define NPY_ALIGNMENT_REQUIRED 1 +#endif + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_NPY_CPU_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/numpyconfig.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/numpyconfig.h new file mode 100644 index 0000000000000000000000000000000000000000..46ecade41ada08fad4c1ae389cc4e9b6e902de24 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/numpyconfig.h @@ -0,0 +1,178 @@ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_ + +#include "_numpyconfig.h" + +/* + * On Mac OS X, because there is only one configuration stage for all the archs + * in universal builds, any macro which depends on the arch needs to be + * hardcoded. + * + * Note that distutils/pip will attempt a universal2 build when Python itself + * is built as universal2, hence this hardcoding is needed even if we do not + * support universal2 wheels anymore (see gh-22796). + * This code block can be removed after we have dropped the setup.py based + * build completely. + */ +#ifdef __APPLE__ + #undef NPY_SIZEOF_LONG + + #ifdef __LP64__ + #define NPY_SIZEOF_LONG 8 + #else + #define NPY_SIZEOF_LONG 4 + #endif + + #undef NPY_SIZEOF_LONGDOUBLE + #undef NPY_SIZEOF_COMPLEX_LONGDOUBLE + #ifdef HAVE_LDOUBLE_IEEE_DOUBLE_LE + #undef HAVE_LDOUBLE_IEEE_DOUBLE_LE + #endif + #ifdef HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE + #undef HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE + #endif + + #if defined(__arm64__) + #define NPY_SIZEOF_LONGDOUBLE 8 + #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 16 + #define HAVE_LDOUBLE_IEEE_DOUBLE_LE 1 + #elif defined(__x86_64) + #define NPY_SIZEOF_LONGDOUBLE 16 + #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 32 + #define HAVE_LDOUBLE_INTEL_EXTENDED_16_BYTES_LE 1 + #elif defined (__i386) + #define NPY_SIZEOF_LONGDOUBLE 12 + #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 24 + #elif defined(__ppc__) || defined (__ppc64__) + #define NPY_SIZEOF_LONGDOUBLE 16 + #define NPY_SIZEOF_COMPLEX_LONGDOUBLE 32 + #else + #error "unknown architecture" + #endif +#endif + + +/** + * To help with both NPY_TARGET_VERSION and the NPY_NO_DEPRECATED_API macro, + * we include API version numbers for specific versions of NumPy. + * To exclude all API that was deprecated as of 1.7, add the following before + * #including any NumPy headers: + * #define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION + * The same is true for NPY_TARGET_VERSION, although NumPy will default to + * a backwards compatible build anyway. + */ +#define NPY_1_7_API_VERSION 0x00000007 +#define NPY_1_8_API_VERSION 0x00000008 +#define NPY_1_9_API_VERSION 0x00000009 +#define NPY_1_10_API_VERSION 0x0000000a +#define NPY_1_11_API_VERSION 0x0000000a +#define NPY_1_12_API_VERSION 0x0000000a +#define NPY_1_13_API_VERSION 0x0000000b +#define NPY_1_14_API_VERSION 0x0000000c +#define NPY_1_15_API_VERSION 0x0000000c +#define NPY_1_16_API_VERSION 0x0000000d +#define NPY_1_17_API_VERSION 0x0000000d +#define NPY_1_18_API_VERSION 0x0000000d +#define NPY_1_19_API_VERSION 0x0000000d +#define NPY_1_20_API_VERSION 0x0000000e +#define NPY_1_21_API_VERSION 0x0000000e +#define NPY_1_22_API_VERSION 0x0000000f +#define NPY_1_23_API_VERSION 0x00000010 +#define NPY_1_24_API_VERSION 0x00000010 +#define NPY_1_25_API_VERSION 0x00000011 +#define NPY_2_0_API_VERSION 0x00000012 +#define NPY_2_1_API_VERSION 0x00000013 + + +/* + * Binary compatibility version number. This number is increased + * whenever the C-API is changed such that binary compatibility is + * broken, i.e. whenever a recompile of extension modules is needed. + */ +#define NPY_VERSION NPY_ABI_VERSION + +/* + * Minor API version we are compiling to be compatible with. The version + * Number is always increased when the API changes via: `NPY_API_VERSION` + * (and should maybe just track the NumPy version). + * + * If we have an internal build, we always target the current version of + * course. + * + * For downstream users, we default to an older version to provide them with + * maximum compatibility by default. Downstream can choose to extend that + * default, or narrow it down if they wish to use newer API. If you adjust + * this, consider the Python version support (example for 1.25.x): + * + * NumPy 1.25.x supports Python: 3.9 3.10 3.11 (3.12) + * NumPy 1.19.x supports Python: 3.6 3.7 3.8 3.9 + * NumPy 1.17.x supports Python: 3.5 3.6 3.7 3.8 + * NumPy 1.15.x supports Python: ... 3.6 3.7 + * + * Users of the stable ABI may wish to target the last Python that is not + * end of life. This would be 3.8 at NumPy 1.25 release time. + * 1.17 as default was the choice of oldest-support-numpy at the time and + * has in practice no limit (compared to 1.19). Even earlier becomes legacy. + */ +#if defined(NPY_INTERNAL_BUILD) && NPY_INTERNAL_BUILD + /* NumPy internal build, always use current version. */ + #define NPY_FEATURE_VERSION NPY_API_VERSION +#elif defined(NPY_TARGET_VERSION) && NPY_TARGET_VERSION + /* user provided a target version, use it */ + #define NPY_FEATURE_VERSION NPY_TARGET_VERSION +#else + /* Use the default (increase when dropping Python 3.10 support) */ + #define NPY_FEATURE_VERSION NPY_1_21_API_VERSION +#endif + +/* Sanity check the (requested) feature version */ +#if NPY_FEATURE_VERSION > NPY_API_VERSION + #error "NPY_TARGET_VERSION higher than NumPy headers!" +#elif NPY_FEATURE_VERSION < NPY_1_15_API_VERSION + /* No support for irrelevant old targets, no need for error, but warn. */ + #ifndef _MSC_VER + #warning "Requested NumPy target lower than supported NumPy 1.15." + #else + #define _WARN___STR2__(x) #x + #define _WARN___STR1__(x) _WARN___STR2__(x) + #define _WARN___LOC__ __FILE__ "(" _WARN___STR1__(__LINE__) ") : Warning Msg: " + #pragma message(_WARN___LOC__"Requested NumPy target lower than supported NumPy 1.15.") + #endif +#endif + +/* + * We define a human readable translation to the Python version of NumPy + * for error messages (and also to allow grepping the binaries for conda). + */ +#if NPY_FEATURE_VERSION == NPY_1_7_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.7" +#elif NPY_FEATURE_VERSION == NPY_1_8_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.8" +#elif NPY_FEATURE_VERSION == NPY_1_9_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.9" +#elif NPY_FEATURE_VERSION == NPY_1_10_API_VERSION /* also 1.11, 1.12 */ + #define NPY_FEATURE_VERSION_STRING "1.10" +#elif NPY_FEATURE_VERSION == NPY_1_13_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.13" +#elif NPY_FEATURE_VERSION == NPY_1_14_API_VERSION /* also 1.15 */ + #define NPY_FEATURE_VERSION_STRING "1.14" +#elif NPY_FEATURE_VERSION == NPY_1_16_API_VERSION /* also 1.17, 1.18, 1.19 */ + #define NPY_FEATURE_VERSION_STRING "1.16" +#elif NPY_FEATURE_VERSION == NPY_1_20_API_VERSION /* also 1.21 */ + #define NPY_FEATURE_VERSION_STRING "1.20" +#elif NPY_FEATURE_VERSION == NPY_1_22_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.22" +#elif NPY_FEATURE_VERSION == NPY_1_23_API_VERSION /* also 1.24 */ + #define NPY_FEATURE_VERSION_STRING "1.23" +#elif NPY_FEATURE_VERSION == NPY_1_25_API_VERSION + #define NPY_FEATURE_VERSION_STRING "1.25" +#elif NPY_FEATURE_VERSION == NPY_2_0_API_VERSION + #define NPY_FEATURE_VERSION_STRING "2.0" +#elif NPY_FEATURE_VERSION == NPY_2_1_API_VERSION + #define NPY_FEATURE_VERSION_STRING "2.1" +#else + #error "Missing version string define for new NumPy version." +#endif + + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_NPY_NUMPYCONFIG_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/bitgen.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/bitgen.h new file mode 100644 index 0000000000000000000000000000000000000000..162dd5c5753079eb1d76efa7fc8a3847c2ad6602 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/bitgen.h @@ -0,0 +1,20 @@ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_ + +#pragma once +#include +#include +#include + +/* Must match the declaration in numpy/random/.pxd */ + +typedef struct bitgen { + void *state; + uint64_t (*next_uint64)(void *st); + uint32_t (*next_uint32)(void *st); + double (*next_double)(void *st); + uint64_t (*next_raw)(void *st); +} bitgen_t; + + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_RANDOM_BITGEN_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/distributions.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/distributions.h new file mode 100644 index 0000000000000000000000000000000000000000..e7fa4bd00d43430eb1da23bd577688d8733bb6e8 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/random/distributions.h @@ -0,0 +1,209 @@ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_ + +#ifdef __cplusplus +extern "C" { +#endif + +#include +#include "numpy/npy_common.h" +#include +#include +#include + +#include "numpy/npy_math.h" +#include "numpy/random/bitgen.h" + +/* + * RAND_INT_TYPE is used to share integer generators with RandomState which + * used long in place of int64_t. If changing a distribution that uses + * RAND_INT_TYPE, then the original unmodified copy must be retained for + * use in RandomState by copying to the legacy distributions source file. + */ +#ifdef NP_RANDOM_LEGACY +#define RAND_INT_TYPE long +#define RAND_INT_MAX LONG_MAX +#else +#define RAND_INT_TYPE int64_t +#define RAND_INT_MAX INT64_MAX +#endif + +#ifdef _MSC_VER +#define DECLDIR __declspec(dllexport) +#else +#define DECLDIR extern +#endif + +#ifndef MIN +#define MIN(x, y) (((x) < (y)) ? x : y) +#define MAX(x, y) (((x) > (y)) ? x : y) +#endif + +#ifndef M_PI +#define M_PI 3.14159265358979323846264338328 +#endif + +typedef struct s_binomial_t { + int has_binomial; /* !=0: following parameters initialized for binomial */ + double psave; + RAND_INT_TYPE nsave; + double r; + double q; + double fm; + RAND_INT_TYPE m; + double p1; + double xm; + double xl; + double xr; + double c; + double laml; + double lamr; + double p2; + double p3; + double p4; +} binomial_t; + +DECLDIR float random_standard_uniform_f(bitgen_t *bitgen_state); +DECLDIR double random_standard_uniform(bitgen_t *bitgen_state); +DECLDIR void random_standard_uniform_fill(bitgen_t *, npy_intp, double *); +DECLDIR void random_standard_uniform_fill_f(bitgen_t *, npy_intp, float *); + +DECLDIR int64_t random_positive_int64(bitgen_t *bitgen_state); +DECLDIR int32_t random_positive_int32(bitgen_t *bitgen_state); +DECLDIR int64_t random_positive_int(bitgen_t *bitgen_state); +DECLDIR uint64_t random_uint(bitgen_t *bitgen_state); + +DECLDIR double random_standard_exponential(bitgen_t *bitgen_state); +DECLDIR float random_standard_exponential_f(bitgen_t *bitgen_state); +DECLDIR void random_standard_exponential_fill(bitgen_t *, npy_intp, double *); +DECLDIR void random_standard_exponential_fill_f(bitgen_t *, npy_intp, float *); +DECLDIR void random_standard_exponential_inv_fill(bitgen_t *, npy_intp, double *); +DECLDIR void random_standard_exponential_inv_fill_f(bitgen_t *, npy_intp, float *); + +DECLDIR double random_standard_normal(bitgen_t *bitgen_state); +DECLDIR float random_standard_normal_f(bitgen_t *bitgen_state); +DECLDIR void random_standard_normal_fill(bitgen_t *, npy_intp, double *); +DECLDIR void random_standard_normal_fill_f(bitgen_t *, npy_intp, float *); +DECLDIR double random_standard_gamma(bitgen_t *bitgen_state, double shape); +DECLDIR float random_standard_gamma_f(bitgen_t *bitgen_state, float shape); + +DECLDIR double random_normal(bitgen_t *bitgen_state, double loc, double scale); + +DECLDIR double random_gamma(bitgen_t *bitgen_state, double shape, double scale); +DECLDIR float random_gamma_f(bitgen_t *bitgen_state, float shape, float scale); + +DECLDIR double random_exponential(bitgen_t *bitgen_state, double scale); +DECLDIR double random_uniform(bitgen_t *bitgen_state, double lower, double range); +DECLDIR double random_beta(bitgen_t *bitgen_state, double a, double b); +DECLDIR double random_chisquare(bitgen_t *bitgen_state, double df); +DECLDIR double random_f(bitgen_t *bitgen_state, double dfnum, double dfden); +DECLDIR double random_standard_cauchy(bitgen_t *bitgen_state); +DECLDIR double random_pareto(bitgen_t *bitgen_state, double a); +DECLDIR double random_weibull(bitgen_t *bitgen_state, double a); +DECLDIR double random_power(bitgen_t *bitgen_state, double a); +DECLDIR double random_laplace(bitgen_t *bitgen_state, double loc, double scale); +DECLDIR double random_gumbel(bitgen_t *bitgen_state, double loc, double scale); +DECLDIR double random_logistic(bitgen_t *bitgen_state, double loc, double scale); +DECLDIR double random_lognormal(bitgen_t *bitgen_state, double mean, double sigma); +DECLDIR double random_rayleigh(bitgen_t *bitgen_state, double mode); +DECLDIR double random_standard_t(bitgen_t *bitgen_state, double df); +DECLDIR double random_noncentral_chisquare(bitgen_t *bitgen_state, double df, + double nonc); +DECLDIR double random_noncentral_f(bitgen_t *bitgen_state, double dfnum, + double dfden, double nonc); +DECLDIR double random_wald(bitgen_t *bitgen_state, double mean, double scale); +DECLDIR double random_vonmises(bitgen_t *bitgen_state, double mu, double kappa); +DECLDIR double random_triangular(bitgen_t *bitgen_state, double left, double mode, + double right); + +DECLDIR RAND_INT_TYPE random_poisson(bitgen_t *bitgen_state, double lam); +DECLDIR RAND_INT_TYPE random_negative_binomial(bitgen_t *bitgen_state, double n, + double p); + +DECLDIR int64_t random_binomial(bitgen_t *bitgen_state, double p, + int64_t n, binomial_t *binomial); + +DECLDIR int64_t random_logseries(bitgen_t *bitgen_state, double p); +DECLDIR int64_t random_geometric(bitgen_t *bitgen_state, double p); +DECLDIR RAND_INT_TYPE random_geometric_search(bitgen_t *bitgen_state, double p); +DECLDIR RAND_INT_TYPE random_zipf(bitgen_t *bitgen_state, double a); +DECLDIR int64_t random_hypergeometric(bitgen_t *bitgen_state, + int64_t good, int64_t bad, int64_t sample); +DECLDIR uint64_t random_interval(bitgen_t *bitgen_state, uint64_t max); + +/* Generate random uint64 numbers in closed interval [off, off + rng]. */ +DECLDIR uint64_t random_bounded_uint64(bitgen_t *bitgen_state, uint64_t off, + uint64_t rng, uint64_t mask, + bool use_masked); + +/* Generate random uint32 numbers in closed interval [off, off + rng]. */ +DECLDIR uint32_t random_buffered_bounded_uint32(bitgen_t *bitgen_state, + uint32_t off, uint32_t rng, + uint32_t mask, bool use_masked, + int *bcnt, uint32_t *buf); +DECLDIR uint16_t random_buffered_bounded_uint16(bitgen_t *bitgen_state, + uint16_t off, uint16_t rng, + uint16_t mask, bool use_masked, + int *bcnt, uint32_t *buf); +DECLDIR uint8_t random_buffered_bounded_uint8(bitgen_t *bitgen_state, uint8_t off, + uint8_t rng, uint8_t mask, + bool use_masked, int *bcnt, + uint32_t *buf); +DECLDIR npy_bool random_buffered_bounded_bool(bitgen_t *bitgen_state, npy_bool off, + npy_bool rng, npy_bool mask, + bool use_masked, int *bcnt, + uint32_t *buf); + +DECLDIR void random_bounded_uint64_fill(bitgen_t *bitgen_state, uint64_t off, + uint64_t rng, npy_intp cnt, + bool use_masked, uint64_t *out); +DECLDIR void random_bounded_uint32_fill(bitgen_t *bitgen_state, uint32_t off, + uint32_t rng, npy_intp cnt, + bool use_masked, uint32_t *out); +DECLDIR void random_bounded_uint16_fill(bitgen_t *bitgen_state, uint16_t off, + uint16_t rng, npy_intp cnt, + bool use_masked, uint16_t *out); +DECLDIR void random_bounded_uint8_fill(bitgen_t *bitgen_state, uint8_t off, + uint8_t rng, npy_intp cnt, + bool use_masked, uint8_t *out); +DECLDIR void random_bounded_bool_fill(bitgen_t *bitgen_state, npy_bool off, + npy_bool rng, npy_intp cnt, + bool use_masked, npy_bool *out); + +DECLDIR void random_multinomial(bitgen_t *bitgen_state, RAND_INT_TYPE n, RAND_INT_TYPE *mnix, + double *pix, npy_intp d, binomial_t *binomial); + +/* multivariate hypergeometric, "count" method */ +DECLDIR int random_multivariate_hypergeometric_count(bitgen_t *bitgen_state, + int64_t total, + size_t num_colors, int64_t *colors, + int64_t nsample, + size_t num_variates, int64_t *variates); + +/* multivariate hypergeometric, "marginals" method */ +DECLDIR void random_multivariate_hypergeometric_marginals(bitgen_t *bitgen_state, + int64_t total, + size_t num_colors, int64_t *colors, + int64_t nsample, + size_t num_variates, int64_t *variates); + +/* Common to legacy-distributions.c and distributions.c but not exported */ + +RAND_INT_TYPE random_binomial_btpe(bitgen_t *bitgen_state, + RAND_INT_TYPE n, + double p, + binomial_t *binomial); +RAND_INT_TYPE random_binomial_inversion(bitgen_t *bitgen_state, + RAND_INT_TYPE n, + double p, + binomial_t *binomial); +double random_loggam(double x); +static inline double next_double(bitgen_t *bitgen_state) { + return bitgen_state->next_double(bitgen_state->state); +} + +#ifdef __cplusplus +} +#endif + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_RANDOM_DISTRIBUTIONS_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/utils.h b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/utils.h new file mode 100644 index 0000000000000000000000000000000000000000..97f06092e54050baf3c2fc4372429cbd110429e8 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/include/numpy/utils.h @@ -0,0 +1,37 @@ +#ifndef NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_ +#define NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_ + +#ifndef __COMP_NPY_UNUSED + #if defined(__GNUC__) + #define __COMP_NPY_UNUSED __attribute__ ((__unused__)) + #elif defined(__ICC) + #define __COMP_NPY_UNUSED __attribute__ ((__unused__)) + #elif defined(__clang__) + #define __COMP_NPY_UNUSED __attribute__ ((unused)) + #else + #define __COMP_NPY_UNUSED + #endif +#endif + +#if defined(__GNUC__) || defined(__ICC) || defined(__clang__) + #define NPY_DECL_ALIGNED(x) __attribute__ ((aligned (x))) +#elif defined(_MSC_VER) + #define NPY_DECL_ALIGNED(x) __declspec(align(x)) +#else + #define NPY_DECL_ALIGNED(x) +#endif + +/* Use this to tag a variable as not used. It will remove unused variable + * warning on support platforms (see __COM_NPY_UNUSED) and mangle the variable + * to avoid accidental use */ +#define NPY_UNUSED(x) __NPY_UNUSED_TAGGED ## x __COMP_NPY_UNUSED +#define NPY_EXPAND(x) x + +#define NPY_STRINGIFY(x) #x +#define NPY_TOSTRING(x) NPY_STRINGIFY(x) + +#define NPY_CAT__(a, b) a ## b +#define NPY_CAT_(a, b) NPY_CAT__(a, b) +#define NPY_CAT(a, b) NPY_CAT_(a, b) + +#endif /* NUMPY_CORE_INCLUDE_NUMPY_UTILS_H_ */ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/__pycache__/test_array_coercion.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/_core/tests/__pycache__/test_array_coercion.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..66087c5e53c648d3a31b782ee8c8209274f4a49d Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/tests/__pycache__/test_array_coercion.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/astype_copy.pkl b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/astype_copy.pkl new file mode 100644 index 0000000000000000000000000000000000000000..45694ae001c4a103365ff9fd5ae2da0dba3c11f6 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/astype_copy.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9564b309cbf3441ff0a6e4468fddaca46230fab34f15c77d87025a455bdf59d9 +size 716 diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/recarray_from_file.fits b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/recarray_from_file.fits new file mode 100644 index 0000000000000000000000000000000000000000..ca48ee85153645a7510e201d574e9b119c089dce Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/recarray_from_file.fits differ diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv new file mode 100644 index 0000000000000000000000000000000000000000..82c8595cb4a617eb779c18b3e086d8ceb8d231e0 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-arccos.csv @@ -0,0 +1,1429 @@ +dtype,input,output,ulperrortol +np.float32,0xbddd7f50,0x3fd6eec2,3 +np.float32,0xbe32a20c,0x3fdf8182,3 +np.float32,0xbf607c09,0x4028f84f,3 +np.float32,0x3f25d906,0x3f5db544,3 +np.float32,0x3f01cec8,0x3f84febf,3 +np.float32,0x3f1d5c6e,0x3f68a735,3 +np.float32,0xbf0cab89,0x4009c36d,3 +np.float32,0xbf176b40,0x400d0941,3 +np.float32,0x3f3248b2,0x3f4ce6d4,3 +np.float32,0x3f390b48,0x3f434e0d,3 +np.float32,0xbe261698,0x3fddea43,3 +np.float32,0x3f0e1154,0x3f7b848b,3 +np.float32,0xbf379a3c,0x4017b764,3 +np.float32,0xbeda6f2c,0x4000bd62,3 +np.float32,0xbf6a0c3f,0x402e5d5a,3 +np.float32,0x3ef1d700,0x3f8a17b7,3 +np.float32,0xbf6f4f65,0x4031d30d,3 +np.float32,0x3f2c9eee,0x3f54adfd,3 +np.float32,0x3f3cfb18,0x3f3d8a1e,3 +np.float32,0x3ba80800,0x3fc867d2,3 +np.float32,0x3e723b08,0x3faa7e4d,3 +np.float32,0xbf65820f,0x402bb054,3 +np.float32,0xbee64e7a,0x40026410,3 +np.float32,0x3cb15140,0x3fc64a87,3 +np.float32,0x3f193660,0x3f6ddf2a,3 +np.float32,0xbf0e5b52,0x400a44f7,3 +np.float32,0x3ed55f14,0x3f920a4b,3 +np.float32,0x3dd11a80,0x3fbbf85c,3 +np.float32,0xbf4f5c4b,0x4020f4f9,3 +np.float32,0x3f787532,0x3e792e87,3 +np.float32,0x3f40e6ac,0x3f37a74f,3 +np.float32,0x3f1c1318,0x3f6a47b6,3 +np.float32,0xbe3c48d8,0x3fe0bb70,3 +np.float32,0xbe94d4bc,0x3feed08e,3 +np.float32,0xbe5c3688,0x3fe4ce26,3 +np.float32,0xbf6fe026,0x403239cb,3 +np.float32,0x3ea5983c,0x3f9ee7bf,3 +np.float32,0x3f1471e6,0x3f73c5bb,3 +np.float32,0x3f0e2622,0x3f7b6b87,3 +np.float32,0xbf597180,0x40257ad1,3 +np.float32,0xbeb5321c,0x3ff75d34,3 +np.float32,0x3f5afcd2,0x3f0b6012,3 +np.float32,0xbef2ff88,0x40042e14,3 +np.float32,0xbedc747e,0x400104f5,3 +np.float32,0xbee0c2f4,0x40019dfc,3 +np.float32,0xbf152cd8,0x400c57dc,3 +np.float32,0xbf6cf9e2,0x40303bbe,3 +np.float32,0x3ed9cd74,0x3f90d1a1,3 +np.float32,0xbf754406,0x4036767f,3 +np.float32,0x3f59c5c2,0x3f0db42f,3 +np.float32,0x3f2eefd8,0x3f518684,3 +np.float32,0xbf156bf9,0x400c6b49,3 +np.float32,0xbd550790,0x3fcfb8dc,3 +np.float32,0x3ede58fc,0x3f8f8f77,3 +np.float32,0xbf00ac19,0x40063c4b,3 +np.float32,0x3f4d25ba,0x3f24280e,3 +np.float32,0xbe9568be,0x3feef73c,3 +np.float32,0x3f67d154,0x3ee05547,3 +np.float32,0x3f617226,0x3efcb4f4,3 +np.float32,0xbf3ab41a,0x4018d6cc,3 +np.float32,0xbf3186fe,0x401592cd,3 +np.float32,0x3de3ba50,0x3fbacca9,3 +np.float32,0x3e789f98,0x3fa9ab97,3 +np.float32,0x3f016e08,0x3f8536d8,3 +np.float32,0x3e8b618c,0x3fa5c571,3 +np.float32,0x3eff97bc,0x3f8628a9,3 +np.float32,0xbf6729f0,0x402ca32f,3 +np.float32,0xbebec146,0x3ff9eddc,3 +np.float32,0x3ddb2e60,0x3fbb563a,3 +np.float32,0x3caa8e40,0x3fc66595,3 +np.float32,0xbf5973f2,0x40257bfa,3 +np.float32,0xbdd82c70,0x3fd69916,3 +np.float32,0xbedf4c82,0x400169ef,3 +np.float32,0x3ef8f22c,0x3f881184,3 +np.float32,0xbf1d74d4,0x400eedc9,3 +np.float32,0x3f2e10a6,0x3f52b790,3 +np.float32,0xbf08ecc0,0x4008a628,3 +np.float32,0x3ecb7db4,0x3f94be9f,3 +np.float32,0xbf052ded,0x40078bfc,3 +np.float32,0x3f2ee78a,0x3f5191e4,3 +np.float32,0xbf56f4e1,0x40245194,3 +np.float32,0x3f600a3e,0x3f014a25,3 +np.float32,0x3f3836f8,0x3f44808b,3 +np.float32,0x3ecabfbc,0x3f94f25c,3 +np.float32,0x3c70f500,0x3fc72dec,3 +np.float32,0x3f17c444,0x3f6fabf0,3 +np.float32,0xbf4c22a5,0x401f9a09,3 +np.float32,0xbe4205dc,0x3fe1765a,3 +np.float32,0x3ea49138,0x3f9f2d36,3 +np.float32,0xbece0082,0x3ffe106b,3 +np.float32,0xbe387578,0x3fe03eef,3 +np.float32,0xbf2b6466,0x40137a30,3 +np.float32,0xbe9dadb2,0x3ff12204,3 +np.float32,0xbf56b3f2,0x402433bb,3 +np.float32,0xbdf9b4d8,0x3fd8b51f,3 +np.float32,0x3f58a596,0x3f0fd4b4,3 +np.float32,0xbedf5748,0x40016b6e,3 +np.float32,0x3f446442,0x3f32476f,3 +np.float32,0x3f5be886,0x3f099658,3 +np.float32,0x3ea1e44c,0x3f9fe1de,3 +np.float32,0xbf11e9b8,0x400b585f,3 +np.float32,0xbf231f8f,0x4010befb,3 +np.float32,0xbf4395ea,0x401c2dd0,3 +np.float32,0x3e9e7784,0x3fa0c8a6,3 +np.float32,0xbe255184,0x3fddd14c,3 +np.float32,0x3f70d25e,0x3eb13148,3 +np.float32,0x3f220cdc,0x3f62a722,3 +np.float32,0xbd027bf0,0x3fcd23e7,3 +np.float32,0x3e4ef8b8,0x3faf02d2,3 +np.float32,0xbf76fc6b,0x40380728,3 +np.float32,0xbf57e761,0x4024c1cd,3 +np.float32,0x3ed4fc20,0x3f922580,3 +np.float32,0xbf09b64a,0x4008e1db,3 +np.float32,0x3f21ca62,0x3f62fcf5,3 +np.float32,0xbe55f610,0x3fe40170,3 +np.float32,0xbc0def80,0x3fca2bbb,3 +np.float32,0xbebc8764,0x3ff9547b,3 +np.float32,0x3ec1b200,0x3f9766d1,3 +np.float32,0xbf4ee44e,0x4020c1ee,3 +np.float32,0xbea85852,0x3ff3f22a,3 +np.float32,0xbf195c0c,0x400da3d3,3 +np.float32,0xbf754b5d,0x40367ce8,3 +np.float32,0xbdcbfe50,0x3fd5d52b,3 +np.float32,0xbf1adb87,0x400e1be3,3 +np.float32,0xbf6f8491,0x4031f898,3 +np.float32,0xbf6f9ae7,0x4032086e,3 +np.float32,0xbf52b3f0,0x40226790,3 +np.float32,0xbf698452,0x402e09f4,3 +np.float32,0xbf43dc9a,0x401c493a,3 +np.float32,0xbf165f7f,0x400cb664,3 +np.float32,0x3e635468,0x3fac682f,3 +np.float32,0xbe8cf2b6,0x3fecc28a,3 +np.float32,0x7f7fffff,0x7fc00000,3 +np.float32,0xbf4c6513,0x401fb597,3 +np.float32,0xbf02b8f8,0x4006d47e,3 +np.float32,0x3ed3759c,0x3f9290c8,3 +np.float32,0xbf2a7a5f,0x40132b98,3 +np.float32,0xbae65000,0x3fc9496f,3 +np.float32,0x3f65f5ea,0x3ee8ef07,3 +np.float32,0xbe7712fc,0x3fe84106,3 +np.float32,0xbb9ff700,0x3fc9afd2,3 +np.float32,0x3d8d87a0,0x3fc03592,3 +np.float32,0xbefc921c,0x40058c23,3 +np.float32,0xbf286566,0x401279d8,3 +np.float32,0x3f53857e,0x3f192eaf,3 +np.float32,0xbee9b0f4,0x4002dd90,3 +np.float32,0x3f4041f8,0x3f38a14a,3 +np.float32,0x3f54ea96,0x3f16b02d,3 +np.float32,0x3ea50ef8,0x3f9f0c01,3 +np.float32,0xbeaad2dc,0x3ff49a4a,3 +np.float32,0xbec428c8,0x3ffb636f,3 +np.float32,0xbda46178,0x3fd358c7,3 +np.float32,0xbefacfc4,0x40054b7f,3 +np.float32,0xbf7068f9,0x40329c85,3 +np.float32,0x3f70b850,0x3eb1caa7,3 +np.float32,0x7fa00000,0x7fe00000,3 +np.float32,0x80000000,0x3fc90fdb,3 +np.float32,0x3f68d5c8,0x3edb7cf3,3 +np.float32,0x3d9443d0,0x3fbfc98a,3 +np.float32,0xff7fffff,0x7fc00000,3 +np.float32,0xbeee7ba8,0x40038a5e,3 +np.float32,0xbf0aaaba,0x40092a73,3 +np.float32,0x3f36a4e8,0x3f46c0ee,3 +np.float32,0x3ed268e4,0x3f92da82,3 +np.float32,0xbee6002c,0x4002591b,3 +np.float32,0xbe8f2752,0x3fed5576,3 +np.float32,0x3f525912,0x3f1b40e0,3 +np.float32,0xbe8e151e,0x3fed0e16,3 +np.float32,0x1,0x3fc90fdb,3 +np.float32,0x3ee23b84,0x3f8e7ae1,3 +np.float32,0xbf5961ca,0x40257361,3 +np.float32,0x3f6bbca0,0x3ecd14cd,3 +np.float32,0x3e27b230,0x3fb4014d,3 +np.float32,0xbf183bb8,0x400d49fc,3 +np.float32,0x3f57759c,0x3f120b68,3 +np.float32,0xbd6994c0,0x3fd05d84,3 +np.float32,0xbf1dd684,0x400f0cc8,3 +np.float32,0xbececc1c,0x3ffe480a,3 +np.float32,0xbf48855f,0x401e206d,3 +np.float32,0x3f28c922,0x3f59d382,3 +np.float32,0xbf65c094,0x402bd3b0,3 +np.float32,0x3f657d42,0x3eeb11dd,3 +np.float32,0xbed32d4e,0x3fff7b15,3 +np.float32,0xbf31af02,0x4015a0b1,3 +np.float32,0x3d89eb00,0x3fc06f7f,3 +np.float32,0x3dac2830,0x3fbe4a17,3 +np.float32,0x3f7f7cb6,0x3d81a7df,3 +np.float32,0xbedbb570,0x4000ea82,3 +np.float32,0x3db37830,0x3fbdd4a8,3 +np.float32,0xbf376f48,0x4017a7fd,3 +np.float32,0x3f319f12,0x3f4dd2c9,3 +np.float32,0x7fc00000,0x7fc00000,3 +np.float32,0x3f1b4f70,0x3f6b3e31,3 +np.float32,0x3e33c880,0x3fb278d1,3 +np.float32,0x3f2796e0,0x3f5b69bd,3 +np.float32,0x3f4915d6,0x3f2ad4d0,3 +np.float32,0x3e4db120,0x3faf2ca0,3 +np.float32,0x3ef03dd4,0x3f8a8ba9,3 +np.float32,0x3e96ca88,0x3fa2cbf7,3 +np.float32,0xbeb136ce,0x3ff64d2b,3 +np.float32,0xbf2f3938,0x4014c75e,3 +np.float32,0x3f769dde,0x3e8b0d76,3 +np.float32,0x3f67cec8,0x3ee06148,3 +np.float32,0x3f0a1ade,0x3f80204e,3 +np.float32,0x3e4b9718,0x3faf7144,3 +np.float32,0x3cccb480,0x3fc5dcf3,3 +np.float32,0x3caeb740,0x3fc654f0,3 +np.float32,0x3f684e0e,0x3ede0678,3 +np.float32,0x3f0ba93c,0x3f7e6663,3 +np.float32,0xbf12bbc4,0x400b985e,3 +np.float32,0xbf2a8e1a,0x40133235,3 +np.float32,0x3f42029c,0x3f35f5c5,3 +np.float32,0x3eed1728,0x3f8b6f9c,3 +np.float32,0xbe5779ac,0x3fe432fd,3 +np.float32,0x3f6ed8b8,0x3ebc7e4b,3 +np.float32,0x3eea25b0,0x3f8c43c7,3 +np.float32,0x3f1988a4,0x3f6d786b,3 +np.float32,0xbe751674,0x3fe7ff8a,3 +np.float32,0xbe9f7418,0x3ff1997d,3 +np.float32,0x3dca11d0,0x3fbc6979,3 +np.float32,0x3f795226,0x3e6a6cab,3 +np.float32,0xbea780e0,0x3ff3b926,3 +np.float32,0xbed92770,0x4000901e,3 +np.float32,0xbf3e9f8c,0x401a49f8,3 +np.float32,0x3f0f7054,0x3f79ddb2,3 +np.float32,0x3a99d400,0x3fc8e966,3 +np.float32,0xbef082b0,0x4003d3c6,3 +np.float32,0xbf0d0790,0x4009defb,3 +np.float32,0xbf1649da,0x400cafb4,3 +np.float32,0xbea5aca8,0x3ff33d5c,3 +np.float32,0xbf4e1843,0x40206ba1,3 +np.float32,0xbe3d7d5c,0x3fe0e2ad,3 +np.float32,0xbf0e802d,0x400a500e,3 +np.float32,0xbf0de8f0,0x400a2295,3 +np.float32,0xbf3016ba,0x4015137e,3 +np.float32,0x3f36b1ea,0x3f46ae5d,3 +np.float32,0xbd27f170,0x3fce4fc7,3 +np.float32,0x3e96ec54,0x3fa2c31f,3 +np.float32,0x3eb4dfdc,0x3f9ad87d,3 +np.float32,0x3f5cac6c,0x3f0815cc,3 +np.float32,0xbf0489aa,0x40075bf1,3 +np.float32,0x3df010c0,0x3fba05f5,3 +np.float32,0xbf229f4a,0x4010956a,3 +np.float32,0x3f75e474,0x3e905a99,3 +np.float32,0xbcece6a0,0x3fccc397,3 +np.float32,0xbdb41528,0x3fd454e7,3 +np.float32,0x3ec8b2f8,0x3f958118,3 +np.float32,0x3f5eaa70,0x3f041a1d,3 +np.float32,0xbf32e1cc,0x40160b91,3 +np.float32,0xbe8e6026,0x3fed219c,3 +np.float32,0x3e6b3160,0x3fab65e3,3 +np.float32,0x3e6d7460,0x3fab1b81,3 +np.float32,0xbf13fbde,0x400bfa3b,3 +np.float32,0xbe8235ec,0x3fe9f9e3,3 +np.float32,0x3d71c4a0,0x3fc18096,3 +np.float32,0x3eb769d0,0x3f9a2aa0,3 +np.float32,0xbf68cb3b,0x402d99e4,3 +np.float32,0xbd917610,0x3fd22932,3 +np.float32,0x3d3cba60,0x3fc3297f,3 +np.float32,0xbf383cbe,0x4017f1cc,3 +np.float32,0xbeee96d0,0x40038e34,3 +np.float32,0x3ec89cb4,0x3f958725,3 +np.float32,0x3ebf92d8,0x3f97f95f,3 +np.float32,0x3f30f3da,0x3f4ec021,3 +np.float32,0xbd26b560,0x3fce45e4,3 +np.float32,0xbec0eb12,0x3ffa8330,3 +np.float32,0x3f6d592a,0x3ec4a6c1,3 +np.float32,0x3ea6d39c,0x3f9e9463,3 +np.float32,0x3e884184,0x3fa6951e,3 +np.float32,0x3ea566c4,0x3f9ef4d1,3 +np.float32,0x3f0c8f4c,0x3f7d5380,3 +np.float32,0x3f28e1ba,0x3f59b2cb,3 +np.float32,0x3f798538,0x3e66e1c3,3 +np.float32,0xbe2889b8,0x3fde39b8,3 +np.float32,0x3f3da05e,0x3f3c949c,3 +np.float32,0x3f24d700,0x3f5f073e,3 +np.float32,0xbe5b5768,0x3fe4b198,3 +np.float32,0xbed3b03a,0x3fff9f05,3 +np.float32,0x3e8a1c4c,0x3fa619eb,3 +np.float32,0xbf075d24,0x40083030,3 +np.float32,0x3f765648,0x3e8d1f52,3 +np.float32,0xbf70fc5e,0x403308bb,3 +np.float32,0x3f557ae8,0x3f15ab76,3 +np.float32,0x3f02f7ea,0x3f84521c,3 +np.float32,0x3f7ebbde,0x3dcbc5c5,3 +np.float32,0xbefbdfc6,0x40057285,3 +np.float32,0x3ec687ac,0x3f9617d9,3 +np.float32,0x3e4831c8,0x3fafe01b,3 +np.float32,0x3e25cde0,0x3fb43ea8,3 +np.float32,0x3e4f2ab8,0x3faefc70,3 +np.float32,0x3ea60ae4,0x3f9ec973,3 +np.float32,0xbf1ed55f,0x400f5dde,3 +np.float32,0xbf5ad4aa,0x40262479,3 +np.float32,0x3e8b3594,0x3fa5d0de,3 +np.float32,0x3f3a77aa,0x3f413c80,3 +np.float32,0xbf07512b,0x40082ca9,3 +np.float32,0x3f33d990,0x3f4ab5e5,3 +np.float32,0x3f521556,0x3f1bb78f,3 +np.float32,0xbecf6036,0x3ffe7086,3 +np.float32,0x3db91bd0,0x3fbd7a11,3 +np.float32,0x3ef63a74,0x3f88d839,3 +np.float32,0xbf2f1116,0x4014b99c,3 +np.float32,0xbf17fdc0,0x400d36b9,3 +np.float32,0xbe87df2c,0x3feb7117,3 +np.float32,0x80800000,0x3fc90fdb,3 +np.float32,0x3ee24c1c,0x3f8e7641,3 +np.float32,0x3f688dce,0x3edcd644,3 +np.float32,0xbf0f4e1c,0x400a8e1b,3 +np.float32,0x0,0x3fc90fdb,3 +np.float32,0x3f786eba,0x3e7999d4,3 +np.float32,0xbf404f80,0x401aeca8,3 +np.float32,0xbe9ffb6a,0x3ff1bd18,3 +np.float32,0x3f146bfc,0x3f73ccfd,3 +np.float32,0xbe47d630,0x3fe233ee,3 +np.float32,0xbe95847c,0x3feefe7c,3 +np.float32,0xbf135df0,0x400bc9e5,3 +np.float32,0x3ea19f3c,0x3f9ff411,3 +np.float32,0x3f235e20,0x3f60f247,3 +np.float32,0xbec789ec,0x3ffc4def,3 +np.float32,0x3f04b656,0x3f834db6,3 +np.float32,0x3dfaf440,0x3fb95679,3 +np.float32,0xbe4a7f28,0x3fe28abe,3 +np.float32,0x3ed4850c,0x3f92463b,3 +np.float32,0x3ec4ba5c,0x3f9694dd,3 +np.float32,0xbce24ca0,0x3fcc992b,3 +np.float32,0xbf5b7c6e,0x402675a0,3 +np.float32,0xbea3ce2a,0x3ff2bf04,3 +np.float32,0x3db02c60,0x3fbe0998,3 +np.float32,0x3c47b780,0x3fc78069,3 +np.float32,0x3ed33b20,0x3f92a0d5,3 +np.float32,0xbf4556d7,0x401cdcde,3 +np.float32,0xbe1b6e28,0x3fdc90ec,3 +np.float32,0xbf3289b7,0x4015ecd0,3 +np.float32,0x3df3f240,0x3fb9c76d,3 +np.float32,0x3eefa7d0,0x3f8ab61d,3 +np.float32,0xbe945838,0x3feeb006,3 +np.float32,0xbf0b1386,0x400949a3,3 +np.float32,0x3f77e546,0x3e812cc1,3 +np.float32,0x3e804ba0,0x3fa8a480,3 +np.float32,0x3f43dcea,0x3f331a06,3 +np.float32,0x3eb87450,0x3f99e33c,3 +np.float32,0x3e5f4898,0x3facecea,3 +np.float32,0x3f646640,0x3eeff10e,3 +np.float32,0x3f1aa832,0x3f6c1051,3 +np.float32,0xbebf6bfa,0x3ffa1bdc,3 +np.float32,0xbb77f300,0x3fc98bd4,3 +np.float32,0x3f3587fe,0x3f485645,3 +np.float32,0x3ef85f34,0x3f883b8c,3 +np.float32,0x3f50e584,0x3f1dc82c,3 +np.float32,0x3f1d30a8,0x3f68deb0,3 +np.float32,0x3ee75a78,0x3f8d0c86,3 +np.float32,0x3f2c023a,0x3f5581e1,3 +np.float32,0xbf074e34,0x40082bca,3 +np.float32,0xbead71f0,0x3ff54c6d,3 +np.float32,0xbf39ed88,0x40188e69,3 +np.float32,0x3f5d2fe6,0x3f07118b,3 +np.float32,0xbf1f79f8,0x400f9267,3 +np.float32,0x3e900c58,0x3fa48e99,3 +np.float32,0xbf759cb2,0x4036c47b,3 +np.float32,0x3f63329c,0x3ef5359c,3 +np.float32,0xbf5d6755,0x40276709,3 +np.float32,0x3f2ce31c,0x3f54519a,3 +np.float32,0x7f800000,0x7fc00000,3 +np.float32,0x3f1bf50e,0x3f6a6d9a,3 +np.float32,0x3f258334,0x3f5e25d8,3 +np.float32,0xbf661a3f,0x402c06ac,3 +np.float32,0x3d1654c0,0x3fc45cef,3 +np.float32,0xbef14a36,0x4003f009,3 +np.float32,0xbf356051,0x4016ec3a,3 +np.float32,0x3f6ccc42,0x3ec79193,3 +np.float32,0xbf2fe3d6,0x401501f9,3 +np.float32,0x3deedc80,0x3fba195b,3 +np.float32,0x3f2e5a28,0x3f52533e,3 +np.float32,0x3e6b68b8,0x3fab5ec8,3 +np.float32,0x3e458240,0x3fb037b7,3 +np.float32,0xbf24bab0,0x401144cb,3 +np.float32,0x3f600f4c,0x3f013fb2,3 +np.float32,0x3f021a04,0x3f84d316,3 +np.float32,0x3f741732,0x3e9cc948,3 +np.float32,0x3f0788aa,0x3f81a5b0,3 +np.float32,0x3f28802c,0x3f5a347c,3 +np.float32,0x3c9eb400,0x3fc69500,3 +np.float32,0x3e5d11e8,0x3fad357a,3 +np.float32,0x3d921250,0x3fbfecb9,3 +np.float32,0x3f354866,0x3f48b066,3 +np.float32,0xbf72cf43,0x40346d84,3 +np.float32,0x3eecdbb8,0x3f8b805f,3 +np.float32,0xbee585d0,0x400247fd,3 +np.float32,0x3e3607a8,0x3fb22fc6,3 +np.float32,0xbf0cb7d6,0x4009c71c,3 +np.float32,0xbf56b230,0x402432ec,3 +np.float32,0xbf4ced02,0x401fee29,3 +np.float32,0xbf3a325c,0x4018a776,3 +np.float32,0x3ecae8bc,0x3f94e732,3 +np.float32,0xbe48c7e8,0x3fe252bd,3 +np.float32,0xbe175d7c,0x3fdc0d5b,3 +np.float32,0x3ea78dac,0x3f9e632d,3 +np.float32,0xbe7434a8,0x3fe7e279,3 +np.float32,0x3f1f9e02,0x3f65c7b9,3 +np.float32,0xbe150f2c,0x3fdbc2c2,3 +np.float32,0x3ee13480,0x3f8ec423,3 +np.float32,0x3ecb7d54,0x3f94beb9,3 +np.float32,0x3f1cef42,0x3f693181,3 +np.float32,0xbf1ec06a,0x400f5730,3 +np.float32,0xbe112acc,0x3fdb44e8,3 +np.float32,0xbe77b024,0x3fe85545,3 +np.float32,0x3ec86fe0,0x3f959353,3 +np.float32,0x3f36b326,0x3f46ac9a,3 +np.float32,0x3e581a70,0x3fadd829,3 +np.float32,0xbf032c0c,0x4006f5f9,3 +np.float32,0xbf43b1fd,0x401c38b1,3 +np.float32,0x3f3701b4,0x3f463c5c,3 +np.float32,0x3f1a995a,0x3f6c22f1,3 +np.float32,0xbf05de0b,0x4007bf97,3 +np.float32,0x3d4bd960,0x3fc2b063,3 +np.float32,0x3f0e1618,0x3f7b7ed0,3 +np.float32,0x3edfd420,0x3f8f2628,3 +np.float32,0xbf6662fe,0x402c3047,3 +np.float32,0x3ec0690c,0x3f97bf9b,3 +np.float32,0xbeaf4146,0x3ff5c7a0,3 +np.float32,0x3f5e7764,0x3f04816d,3 +np.float32,0xbedd192c,0x40011bc5,3 +np.float32,0x3eb76350,0x3f9a2c5e,3 +np.float32,0xbed8108c,0x400069a5,3 +np.float32,0xbe59f31c,0x3fe48401,3 +np.float32,0xbea3e1e6,0x3ff2c439,3 +np.float32,0x3e26d1f8,0x3fb41db5,3 +np.float32,0x3f3a0a7c,0x3f41dba5,3 +np.float32,0x3ebae068,0x3f993ce4,3 +np.float32,0x3f2d8e30,0x3f536942,3 +np.float32,0xbe838bbe,0x3fea5247,3 +np.float32,0x3ebe4420,0x3f98538f,3 +np.float32,0xbcc59b80,0x3fcc265c,3 +np.float32,0x3eebb5c8,0x3f8bd334,3 +np.float32,0xbafc3400,0x3fc94ee8,3 +np.float32,0xbf63ddc1,0x402ac683,3 +np.float32,0xbeabdf80,0x3ff4e18f,3 +np.float32,0x3ea863f0,0x3f9e2a78,3 +np.float32,0x3f45b292,0x3f303bc1,3 +np.float32,0xbe68aa60,0x3fe666bf,3 +np.float32,0x3eb9de18,0x3f998239,3 +np.float32,0xbf719d85,0x4033815e,3 +np.float32,0x3edef9a8,0x3f8f62db,3 +np.float32,0xbd7781c0,0x3fd0cd1e,3 +np.float32,0x3f0b3b90,0x3f7ee92a,3 +np.float32,0xbe3eb3b4,0x3fe10a27,3 +np.float32,0xbf31a4c4,0x40159d23,3 +np.float32,0x3e929434,0x3fa3e5b0,3 +np.float32,0xbeb1a90e,0x3ff66b9e,3 +np.float32,0xbeba9b5e,0x3ff8d048,3 +np.float32,0xbf272a84,0x4012119e,3 +np.float32,0x3f1ebbd0,0x3f66e889,3 +np.float32,0x3ed3cdc8,0x3f927893,3 +np.float32,0xbf50dfce,0x40219b58,3 +np.float32,0x3f0c02de,0x3f7dfb62,3 +np.float32,0xbf694de3,0x402de8d2,3 +np.float32,0xbeaeb13e,0x3ff5a14f,3 +np.float32,0xbf61aa7a,0x40299702,3 +np.float32,0xbf13d159,0x400bed35,3 +np.float32,0xbeecd034,0x40034e0b,3 +np.float32,0xbe50c2e8,0x3fe35761,3 +np.float32,0x3f714406,0x3eae8e57,3 +np.float32,0xbf1ca486,0x400eabd8,3 +np.float32,0x3f5858cc,0x3f106497,3 +np.float32,0x3f670288,0x3ee41c84,3 +np.float32,0xbf20bd2c,0x400ff9f5,3 +np.float32,0xbe29afd8,0x3fde5eff,3 +np.float32,0xbf635e6a,0x402a80f3,3 +np.float32,0x3e82b7b0,0x3fa80446,3 +np.float32,0x3e982e7c,0x3fa26ece,3 +np.float32,0x3d9f0e00,0x3fbf1c6a,3 +np.float32,0x3e8299b4,0x3fa80c07,3 +np.float32,0xbf0529c1,0x40078ac3,3 +np.float32,0xbf403b8a,0x401ae519,3 +np.float32,0xbe57e09c,0x3fe44027,3 +np.float32,0x3ea1c8f4,0x3f9fe913,3 +np.float32,0xbe216a94,0x3fdd52d0,3 +np.float32,0x3f59c442,0x3f0db709,3 +np.float32,0xbd636260,0x3fd02bdd,3 +np.float32,0xbdbbc788,0x3fd4d08d,3 +np.float32,0x3dd19560,0x3fbbf0a3,3 +np.float32,0x3f060ad4,0x3f828641,3 +np.float32,0x3b102e00,0x3fc8c7c4,3 +np.float32,0x3f42b3b8,0x3f34e5a6,3 +np.float32,0x3f0255ac,0x3f84b071,3 +np.float32,0xbf014898,0x40066996,3 +np.float32,0x3e004dc0,0x3fb8fb51,3 +np.float32,0xbf594ff8,0x40256af2,3 +np.float32,0x3efafddc,0x3f877b80,3 +np.float32,0xbf5f0780,0x40283899,3 +np.float32,0x3ee95e54,0x3f8c7bcc,3 +np.float32,0x3eba2f0c,0x3f996c80,3 +np.float32,0x3f37721c,0x3f459b68,3 +np.float32,0x3e2be780,0x3fb378bf,3 +np.float32,0x3e550270,0x3fae3d69,3 +np.float32,0x3e0f9500,0x3fb70e0a,3 +np.float32,0xbf51974a,0x4021eaf4,3 +np.float32,0x3f393832,0x3f430d05,3 +np.float32,0x3f3df16a,0x3f3c1bd8,3 +np.float32,0xbd662340,0x3fd041ed,3 +np.float32,0x3f7e8418,0x3ddc9fce,3 +np.float32,0xbf392734,0x40184672,3 +np.float32,0x3ee3b278,0x3f8e124e,3 +np.float32,0x3eed4808,0x3f8b61d2,3 +np.float32,0xbf6fccbd,0x40322beb,3 +np.float32,0x3e3ecdd0,0x3fb1123b,3 +np.float32,0x3f4419e0,0x3f32bb45,3 +np.float32,0x3f595e00,0x3f0e7914,3 +np.float32,0xbe8c1486,0x3fec88c6,3 +np.float32,0xbf800000,0x40490fdb,3 +np.float32,0xbdaf5020,0x3fd4084d,3 +np.float32,0xbf407660,0x401afb63,3 +np.float32,0x3f0c3aa8,0x3f7db8b8,3 +np.float32,0xbcdb5980,0x3fcc7d5b,3 +np.float32,0x3f4738d4,0x3f2dd1ed,3 +np.float32,0x3f4d7064,0x3f23ab14,3 +np.float32,0xbeb1d576,0x3ff67774,3 +np.float32,0xbf507166,0x40216bb3,3 +np.float32,0x3e86484c,0x3fa71813,3 +np.float32,0x3f09123e,0x3f80bd35,3 +np.float32,0xbe9abe0e,0x3ff05cb2,3 +np.float32,0x3f3019dc,0x3f4fed21,3 +np.float32,0xbe99e00e,0x3ff0227d,3 +np.float32,0xbf155ec5,0x400c6739,3 +np.float32,0x3f5857ba,0x3f106698,3 +np.float32,0x3edf619c,0x3f8f45fb,3 +np.float32,0xbf5ab76a,0x40261664,3 +np.float32,0x3e54b5a8,0x3fae4738,3 +np.float32,0xbee92772,0x4002ca40,3 +np.float32,0x3f2fd610,0x3f504a7a,3 +np.float32,0xbf38521c,0x4017f97e,3 +np.float32,0xff800000,0x7fc00000,3 +np.float32,0x3e2da348,0x3fb34077,3 +np.float32,0x3f2f85fa,0x3f50b894,3 +np.float32,0x3e88f9c8,0x3fa66551,3 +np.float32,0xbf61e570,0x4029b648,3 +np.float32,0xbeab362c,0x3ff4b4a1,3 +np.float32,0x3ec6c310,0x3f9607bd,3 +np.float32,0x3f0d7bda,0x3f7c3810,3 +np.float32,0xbeba5d36,0x3ff8bf99,3 +np.float32,0x3f4b0554,0x3f27adda,3 +np.float32,0x3f60f5dc,0x3efebfb3,3 +np.float32,0x3f36ce2c,0x3f468603,3 +np.float32,0xbe70afac,0x3fe76e8e,3 +np.float32,0x3f673350,0x3ee339b5,3 +np.float32,0xbe124cf0,0x3fdb698c,3 +np.float32,0xbf1243dc,0x400b73d0,3 +np.float32,0x3f3c8850,0x3f3e3407,3 +np.float32,0x3ea02f24,0x3fa05500,3 +np.float32,0xbeffed34,0x400607db,3 +np.float32,0x3f5c75c2,0x3f08817c,3 +np.float32,0x3f4b2fbe,0x3f27682d,3 +np.float32,0x3ee47c34,0x3f8dd9f9,3 +np.float32,0x3f50d48c,0x3f1de584,3 +np.float32,0x3f12dc5e,0x3f75b628,3 +np.float32,0xbefe7e4a,0x4005d2f4,3 +np.float32,0xbec2e846,0x3ffb0cbc,3 +np.float32,0xbedc3036,0x4000fb80,3 +np.float32,0xbf48aedc,0x401e311f,3 +np.float32,0x3f6e032e,0x3ec11363,3 +np.float32,0xbf60de15,0x40292b72,3 +np.float32,0x3f06585e,0x3f8258ba,3 +np.float32,0x3ef49b98,0x3f894e66,3 +np.float32,0x3cc5fe00,0x3fc5f7cf,3 +np.float32,0xbf7525c5,0x40365c2c,3 +np.float32,0x3f64f9f8,0x3eed5fb2,3 +np.float32,0x3e8849c0,0x3fa692fb,3 +np.float32,0x3e50c878,0x3faec79e,3 +np.float32,0x3ed61530,0x3f91d831,3 +np.float32,0xbf54872e,0x40233724,3 +np.float32,0xbf52ee7f,0x4022815e,3 +np.float32,0xbe708c24,0x3fe769fc,3 +np.float32,0xbf26fc54,0x40120260,3 +np.float32,0x3f226e8a,0x3f6228db,3 +np.float32,0xbef30406,0x40042eb8,3 +np.float32,0x3f5d996c,0x3f063f5f,3 +np.float32,0xbf425f9c,0x401bb618,3 +np.float32,0x3e4bb260,0x3faf6dc9,3 +np.float32,0xbe52d5a4,0x3fe39b29,3 +np.float32,0xbe169cf0,0x3fdbf505,3 +np.float32,0xbedfc422,0x40017a8e,3 +np.float32,0x3d8ffef0,0x3fc00e05,3 +np.float32,0xbf12bdab,0x400b98f2,3 +np.float32,0x3f295d0a,0x3f590e88,3 +np.float32,0x3f49d8e4,0x3f2998aa,3 +np.float32,0xbef914f4,0x40050c12,3 +np.float32,0xbf4ea2b5,0x4020a61e,3 +np.float32,0xbf3a89e5,0x4018c762,3 +np.float32,0x3e8707b4,0x3fa6e67a,3 +np.float32,0x3ac55400,0x3fc8de86,3 +np.float32,0x800000,0x3fc90fdb,3 +np.float32,0xbeb9762c,0x3ff8819b,3 +np.float32,0xbebbe23c,0x3ff92815,3 +np.float32,0xbf598c88,0x402587a1,3 +np.float32,0x3e95d864,0x3fa30b4a,3 +np.float32,0x3f7f6f40,0x3d882486,3 +np.float32,0xbf53658c,0x4022b604,3 +np.float32,0xbf2a35f2,0x401314ad,3 +np.float32,0x3eb14380,0x3f9bcf28,3 +np.float32,0x3f0e0c64,0x3f7b8a7a,3 +np.float32,0x3d349920,0x3fc36a9a,3 +np.float32,0xbec2092c,0x3ffad071,3 +np.float32,0xbe1d08e8,0x3fdcc4e0,3 +np.float32,0xbf008968,0x40063243,3 +np.float32,0xbefad582,0x40054c51,3 +np.float32,0xbe52d010,0x3fe39a72,3 +np.float32,0x3f4afdac,0x3f27ba6b,3 +np.float32,0x3f6c483c,0x3eca4408,3 +np.float32,0xbef3cb68,0x40044b0c,3 +np.float32,0x3e94687c,0x3fa36b6f,3 +np.float32,0xbf64ae5c,0x402b39bb,3 +np.float32,0xbf0022b4,0x40061497,3 +np.float32,0x80000001,0x3fc90fdb,3 +np.float32,0x3f25bcd0,0x3f5dda4b,3 +np.float32,0x3ed91b40,0x3f9102d7,3 +np.float32,0x3f800000,0x0,3 +np.float32,0xbebc6aca,0x3ff94cca,3 +np.float32,0x3f239e9a,0x3f609e7d,3 +np.float32,0xbf7312be,0x4034a305,3 +np.float32,0x3efd16d0,0x3f86e148,3 +np.float32,0x3f52753a,0x3f1b0f72,3 +np.float32,0xbde58960,0x3fd7702c,3 +np.float32,0x3ef88580,0x3f883099,3 +np.float32,0x3eebaefc,0x3f8bd51e,3 +np.float32,0x3e877d2c,0x3fa6c807,3 +np.float32,0x3f1a0324,0x3f6cdf32,3 +np.float32,0xbedfe20a,0x40017eb6,3 +np.float32,0x3f205a3c,0x3f64d69d,3 +np.float32,0xbeed5b7c,0x400361b0,3 +np.float32,0xbf69ba10,0x402e2ad0,3 +np.float32,0x3c4fe200,0x3fc77014,3 +np.float32,0x3f043310,0x3f839a69,3 +np.float32,0xbeaf359a,0x3ff5c485,3 +np.float32,0x3db3f110,0x3fbdcd12,3 +np.float32,0x3e24af88,0x3fb462ed,3 +np.float32,0xbf34e858,0x4016c1c8,3 +np.float32,0x3f3334f2,0x3f4b9cd0,3 +np.float32,0xbf145882,0x400c16a2,3 +np.float32,0xbf541c38,0x40230748,3 +np.float32,0x3eba7e10,0x3f99574b,3 +np.float32,0xbe34c6e0,0x3fdfc731,3 +np.float32,0xbe957abe,0x3feefbf0,3 +np.float32,0xbf595a59,0x40256fdb,3 +np.float32,0xbdedc7b8,0x3fd7f4f0,3 +np.float32,0xbf627c02,0x402a06a9,3 +np.float32,0x3f339b78,0x3f4b0d18,3 +np.float32,0xbf2df6d2,0x40145929,3 +np.float32,0x3f617726,0x3efc9fd8,3 +np.float32,0xbee3a8fc,0x40020561,3 +np.float32,0x3efe9f68,0x3f867043,3 +np.float32,0xbf2c3e76,0x4013c3ba,3 +np.float32,0xbf218f28,0x40103d84,3 +np.float32,0xbf1ea847,0x400f4f7f,3 +np.float32,0x3ded9160,0x3fba2e31,3 +np.float32,0x3bce1b00,0x3fc841bf,3 +np.float32,0xbe90566e,0x3feda46a,3 +np.float32,0xbf5ea2ba,0x4028056b,3 +np.float32,0x3f538e62,0x3f191ee6,3 +np.float32,0xbf59e054,0x4025af74,3 +np.float32,0xbe8c98ba,0x3fecab24,3 +np.float32,0x3ee7bdb0,0x3f8cf0b7,3 +np.float32,0xbf2eb828,0x40149b2b,3 +np.float32,0xbe5eb904,0x3fe52068,3 +np.float32,0xbf16b422,0x400cd08d,3 +np.float32,0x3f1ab9b4,0x3f6bfa58,3 +np.float32,0x3dc23040,0x3fbce82a,3 +np.float32,0xbf29d9e7,0x4012f5e5,3 +np.float32,0xbf38f30a,0x40183393,3 +np.float32,0x3e88e798,0x3fa66a09,3 +np.float32,0x3f1d07e6,0x3f69124f,3 +np.float32,0xbe1d3d34,0x3fdccb7e,3 +np.float32,0xbf1715be,0x400ceec2,3 +np.float32,0x3f7a0eac,0x3e5d11f7,3 +np.float32,0xbe764924,0x3fe82707,3 +np.float32,0xbf01a1f8,0x4006837c,3 +np.float32,0x3f2be730,0x3f55a661,3 +np.float32,0xbf7bb070,0x403d4ce5,3 +np.float32,0xbd602110,0x3fd011c9,3 +np.float32,0x3f5d080c,0x3f07609d,3 +np.float32,0xbda20400,0x3fd332d1,3 +np.float32,0x3f1c62da,0x3f69e308,3 +np.float32,0xbf2c6916,0x4013d223,3 +np.float32,0xbf44f8fd,0x401cb816,3 +np.float32,0x3f4da392,0x3f235539,3 +np.float32,0x3e9e8aa0,0x3fa0c3a0,3 +np.float32,0x3e9633c4,0x3fa2f366,3 +np.float32,0xbf0422ab,0x40073ddd,3 +np.float32,0x3f518386,0x3f1cb603,3 +np.float32,0x3f24307a,0x3f5fe096,3 +np.float32,0xbdfb4220,0x3fd8ce24,3 +np.float32,0x3f179d28,0x3f6fdc7d,3 +np.float32,0xbecc2df0,0x3ffd911e,3 +np.float32,0x3f3dff0c,0x3f3c0782,3 +np.float32,0xbf58c4d8,0x4025295b,3 +np.float32,0xbdcf8438,0x3fd60dd3,3 +np.float32,0xbeeaf1b2,0x40030aa7,3 +np.float32,0xbf298a28,0x4012db45,3 +np.float32,0x3f6c4dec,0x3eca2678,3 +np.float32,0x3f4d1ac8,0x3f243a59,3 +np.float32,0x3f62cdfa,0x3ef6e8f8,3 +np.float32,0xbee8acce,0x4002b909,3 +np.float32,0xbd5f2af0,0x3fd00a15,3 +np.float32,0x3f5fde8e,0x3f01a453,3 +np.float32,0x3e95233c,0x3fa33aa4,3 +np.float32,0x3ecd2a60,0x3f9449be,3 +np.float32,0x3f10aa86,0x3f78619d,3 +np.float32,0x3f3888e8,0x3f440a70,3 +np.float32,0x3eeb5bfc,0x3f8bec7d,3 +np.float32,0xbe12d654,0x3fdb7ae6,3 +np.float32,0x3eca3110,0x3f951931,3 +np.float32,0xbe2d1b7c,0x3fdece05,3 +np.float32,0xbf29e9db,0x4012fb3a,3 +np.float32,0xbf0c50b8,0x4009a845,3 +np.float32,0xbed9f0e4,0x4000abef,3 +np.float64,0x3fd078ec5ba0f1d8,0x3ff4f7c00595a4d3,1 +np.float64,0xbfdbc39743b7872e,0x400027f85bce43b2,1 +np.float64,0xbfacd2707c39a4e0,0x3ffa08ae1075d766,1 +np.float64,0xbfc956890f32ad14,0x3ffc52308e7285fd,1 +np.float64,0xbf939c2298273840,0x3ff9706d18e6ea6b,1 +np.float64,0xbfe0d7048961ae09,0x4000fff4406bd395,1 +np.float64,0xbfe9d19b86f3a337,0x4004139bc683a69f,1 +np.float64,0x3fd35c7f90a6b900,0x3ff437220e9123f8,1 +np.float64,0x3fdddca171bbb944,0x3ff15da61e61ec08,1 +np.float64,0x3feb300de9f6601c,0x3fe1c6fadb68cdca,1 +np.float64,0xbfef1815327e302a,0x400739808fc6f964,1 +np.float64,0xbfe332d78e6665af,0x4001b6c4ef922f7c,1 +np.float64,0xbfedbf4dfb7b7e9c,0x40061cefed62a58b,1 +np.float64,0xbfd8dcc7e3b1b990,0x3fff84307713c2c3,1 +np.float64,0xbfedaf161c7b5e2c,0x400612027c1b2b25,1 +np.float64,0xbfed9bde897b37bd,0x4006053f05bd7d26,1 +np.float64,0xbfe081ebc26103d8,0x4000e70755eb66e0,1 +np.float64,0xbfe0366f9c606cdf,0x4000d11212f29afd,1 +np.float64,0xbfc7c115212f822c,0x3ffc1e8c9d58f7db,1 +np.float64,0x3fd8dd9a78b1bb34,0x3ff2bf8d0f4c9376,1 +np.float64,0xbfe54eff466a9dfe,0x4002655950b611f4,1 +np.float64,0xbfe4aad987e955b3,0x40022efb19882518,1 +np.float64,0x3f70231ca0204600,0x3ff911d834e7abf4,1 +np.float64,0x3fede01d047bc03a,0x3fd773cecbd8561b,1 +np.float64,0xbfd6a00d48ad401a,0x3ffee9fd7051633f,1 +np.float64,0x3fd44f3d50a89e7c,0x3ff3f74dd0fc9c91,1 +np.float64,0x3fe540f0d0ea81e2,0x3feb055a7c7d43d6,1 +np.float64,0xbf3ba2e200374800,0x3ff923b582650c6c,1 +np.float64,0x3fe93b2d3f72765a,0x3fe532fa15331072,1 +np.float64,0x3fee8ce5a17d19cc,0x3fd35666eefbe336,1 +np.float64,0x3fe55d5f8feabac0,0x3feadf3dcfe251d4,1 +np.float64,0xbfd1d2ede8a3a5dc,0x3ffda600041ac884,1 +np.float64,0xbfee41186e7c8231,0x40067a625cc6f64d,1 +np.float64,0x3fe521a8b9ea4352,0x3feb2f1a6c8084e5,1 +np.float64,0x3fc65378ef2ca6f0,0x3ff653dfe81ee9f2,1 +np.float64,0x3fdaba0fbcb57420,0x3ff23d630995c6ba,1 +np.float64,0xbfe6b7441d6d6e88,0x4002e182539a2994,1 +np.float64,0x3fda00b6dcb4016c,0x3ff2703d516f28e7,1 +np.float64,0xbfe8699f01f0d33e,0x400382326920ea9e,1 +np.float64,0xbfef5889367eb112,0x4007832af5983793,1 +np.float64,0x3fefb57c8aff6afa,0x3fc14700ab38dcef,1 +np.float64,0xbfda0dfdaab41bfc,0x3fffd75b6fd497f6,1 +np.float64,0xbfb059c36620b388,0x3ffa27c528b97a42,1 +np.float64,0xbfdd450ab1ba8a16,0x40005dcac6ab50fd,1 +np.float64,0xbfe54d6156ea9ac2,0x400264ce9f3f0fb9,1 +np.float64,0xbfe076e94760edd2,0x4000e3d1374884da,1 +np.float64,0xbfc063286720c650,0x3ffb2fd1d6bff0ef,1 +np.float64,0xbfe24680f2e48d02,0x40016ddfbb5bcc0e,1 +np.float64,0xbfdc9351d2b926a4,0x400044e3756fb765,1 +np.float64,0x3fefb173d8ff62e8,0x3fc1bd5626f80850,1 +np.float64,0x3fe77c117a6ef822,0x3fe7e57089bad2ec,1 +np.float64,0xbfddbcebf7bb79d8,0x40006eadb60406b3,1 +np.float64,0xbfecf6625ff9ecc5,0x40059e6c6961a6db,1 +np.float64,0x3fdc8950b8b912a0,0x3ff1bcfb2e27795b,1 +np.float64,0xbfeb2fa517765f4a,0x4004b00aee3e6888,1 +np.float64,0x3fd0efc88da1df90,0x3ff4d8f7cbd8248a,1 +np.float64,0xbfe6641a2becc834,0x4002c43362c1bd0f,1 +np.float64,0xbfe28aec0fe515d8,0x400182c91d4df039,1 +np.float64,0xbfd5ede8d0abdbd2,0x3ffeba7baef05ae8,1 +np.float64,0xbfbd99702a3b32e0,0x3ffafca21c1053f1,1 +np.float64,0x3f96f043f82de080,0x3ff8c6384d5eb610,1 +np.float64,0xbfe5badbc9eb75b8,0x400289c8cd5873d1,1 +np.float64,0x3fe5c6bf95eb8d80,0x3fea5093e9a3e43e,1 +np.float64,0x3fb1955486232ab0,0x3ff8086d4c3e71d5,1 +np.float64,0xbfea145f397428be,0x4004302237a35871,1 +np.float64,0xbfdabe685db57cd0,0x400003e2e29725fb,1 +np.float64,0xbfefc79758ff8f2f,0x400831814e23bfc8,1 +np.float64,0x3fd7edb66cafdb6c,0x3ff3006c5123bfaf,1 +np.float64,0xbfeaf7644bf5eec8,0x400495a7963ce4ed,1 +np.float64,0x3fdf838d78bf071c,0x3ff0e527eed73800,1 +np.float64,0xbfd1a0165ba3402c,0x3ffd98c5ab76d375,1 +np.float64,0x3fd75b67a9aeb6d0,0x3ff327c8d80b17cf,1 +np.float64,0x3fc2aa9647255530,0x3ff6ca854b157df1,1 +np.float64,0xbfe0957fd4612b00,0x4000ecbf3932becd,1 +np.float64,0x3fda1792c0b42f24,0x3ff269fbb2360487,1 +np.float64,0x3fd480706ca900e0,0x3ff3ea53a6aa3ae8,1 +np.float64,0xbfd0780ed9a0f01e,0x3ffd4bfd544c7d47,1 +np.float64,0x3feeec0cd77dd81a,0x3fd0a8a241fdb441,1 +np.float64,0x3fcfa933e93f5268,0x3ff5223478621a6b,1 +np.float64,0x3fdad2481fb5a490,0x3ff236b86c6b2b49,1 +np.float64,0x3fe03b129de07626,0x3ff09f21fb868451,1 +np.float64,0xbfc01212cd202424,0x3ffb259a07159ae9,1 +np.float64,0x3febdb912df7b722,0x3fe0768e20dac8c9,1 +np.float64,0xbfbf2148763e4290,0x3ffb154c361ce5bf,1 +np.float64,0xbfb1a7eb1e234fd8,0x3ffa3cb37ac4a176,1 +np.float64,0xbfe26ad1ec64d5a4,0x400178f480ecce8d,1 +np.float64,0x3fe6d1cd1b6da39a,0x3fe8dc20ec4dad3b,1 +np.float64,0xbfede0e53dfbc1ca,0x4006340d3bdd7c97,1 +np.float64,0xbfe8fd1bd9f1fa38,0x4003bc3477f93f40,1 +np.float64,0xbfe329d0f26653a2,0x4001b3f345af5648,1 +np.float64,0xbfe4bb20eee97642,0x40023451404d6d08,1 +np.float64,0x3fb574832e2ae900,0x3ff7ca4bed0c7110,1 +np.float64,0xbfdf3c098fbe7814,0x4000a525bb72d659,1 +np.float64,0x3fa453e6d428a7c0,0x3ff87f512bb9b0c6,1 +np.float64,0x3faaec888435d920,0x3ff84a7d9e4def63,1 +np.float64,0xbfcdc240df3b8480,0x3ffce30ece754e7f,1 +np.float64,0xbf8c3220f0386440,0x3ff95a600ae6e157,1 +np.float64,0x3fe806076c700c0e,0x3fe71784a96c76eb,1 +np.float64,0x3fedf9b0e17bf362,0x3fd6e35fc0a7b6c3,1 +np.float64,0xbfe1b48422636908,0x400141bd8ed251bc,1 +np.float64,0xbfe82e2817705c50,0x40036b5a5556d021,1 +np.float64,0xbfc8ef8ff931df20,0x3ffc450ffae7ce58,1 +np.float64,0xbfe919fa94f233f5,0x4003c7cce4697fe8,1 +np.float64,0xbfc3ace4a72759c8,0x3ffb9a197bb22651,1 +np.float64,0x3fe479f71ee8f3ee,0x3fec0bd2f59097aa,1 +np.float64,0xbfeeb54a967d6a95,0x4006da12c83649c5,1 +np.float64,0x3fe5e74ea8ebce9e,0x3fea2407cef0f08c,1 +np.float64,0x3fb382baf2270570,0x3ff7e98213b921ba,1 +np.float64,0xbfdd86fd3cbb0dfa,0x40006712952ddbcf,1 +np.float64,0xbfd250eb52a4a1d6,0x3ffdc6d56253b1cd,1 +np.float64,0x3fea30c4ed74618a,0x3fe3962deba4f30e,1 +np.float64,0x3fc895963d312b30,0x3ff60a5d52fcbccc,1 +np.float64,0x3fe9cc4f6273989e,0x3fe442740942c80f,1 +np.float64,0xbfe8769f5cf0ed3f,0x4003873b4cb5bfce,1 +np.float64,0xbfe382f3726705e7,0x4001cfeb3204d110,1 +np.float64,0x3fbfe9a9163fd350,0x3ff7220bd2b97c8f,1 +np.float64,0xbfca6162bb34c2c4,0x3ffc743f939358f1,1 +np.float64,0x3fe127a014e24f40,0x3ff0147c4bafbc39,1 +np.float64,0x3fee9cdd2a7d39ba,0x3fd2e9ef45ab122f,1 +np.float64,0x3fa9ffb97c33ff80,0x3ff851e69fa3542c,1 +np.float64,0x3fd378f393a6f1e8,0x3ff42faafa77de56,1 +np.float64,0xbfe4df1e1669be3c,0x400240284df1c321,1 +np.float64,0x3fed0ed79bfa1db0,0x3fdba89060aa96fb,1 +np.float64,0x3fdef2ee52bde5dc,0x3ff10e942244f4f1,1 +np.float64,0xbfdab38f3ab5671e,0x40000264d8d5b49b,1 +np.float64,0x3fbe95a96e3d2b50,0x3ff73774cb59ce2d,1 +np.float64,0xbfe945653af28aca,0x4003d9657bf129c2,1 +np.float64,0xbfb18f3f2a231e80,0x3ffa3b27cba23f50,1 +np.float64,0xbfef50bf22fea17e,0x40077998a850082c,1 +np.float64,0xbfc52b8c212a5718,0x3ffbca8d6560a2da,1 +np.float64,0x7ff8000000000000,0x7ff8000000000000,1 +np.float64,0x3fc1e3a02d23c740,0x3ff6e3a5fcac12a4,1 +np.float64,0xbfeb5e4ea5f6bc9d,0x4004c65abef9426f,1 +np.float64,0xbfe425b132684b62,0x400203c29608b00d,1 +np.float64,0xbfbfa1c19e3f4380,0x3ffb1d6367711158,1 +np.float64,0x3fbba2776e3744f0,0x3ff766f6df586fad,1 +np.float64,0xbfb5d0951e2ba128,0x3ffa7f712480b25e,1 +np.float64,0xbfe949fdab7293fb,0x4003db4530a18507,1 +np.float64,0xbfcf13519b3e26a4,0x3ffd0e6f0a6c38ee,1 +np.float64,0x3f91e6d72823cdc0,0x3ff8da5f08909b6e,1 +np.float64,0x3f78a2e360314600,0x3ff909586727caef,1 +np.float64,0xbfe1ae7e8fe35cfd,0x40013fef082caaa3,1 +np.float64,0x3fe97a6dd1f2f4dc,0x3fe4cb4b99863478,1 +np.float64,0xbfcc1e1e69383c3c,0x3ffcad250a949843,1 +np.float64,0x3faccb797c399700,0x3ff83b8066b49330,1 +np.float64,0x3fe7a2647a6f44c8,0x3fe7acceae6ec425,1 +np.float64,0xbfec3bfcf0f877fa,0x4005366af5a7175b,1 +np.float64,0xbfe2310b94646217,0x400167588fceb228,1 +np.float64,0x3feb167372762ce6,0x3fe1f74c0288fad8,1 +np.float64,0xbfb722b4ee2e4568,0x3ffa94a81b94dfca,1 +np.float64,0x3fc58da9712b1b50,0x3ff66cf8f072aa14,1 +np.float64,0xbfe7fff9d6effff4,0x400359d01b8141de,1 +np.float64,0xbfd56691c5aacd24,0x3ffe9686697797e8,1 +np.float64,0x3fe3ab0557e7560a,0x3fed1593959ef8e8,1 +np.float64,0x3fdd458995ba8b14,0x3ff1883d6f22a322,1 +np.float64,0x3fe7bbed2cef77da,0x3fe786d618094cda,1 +np.float64,0x3fa31a30c4263460,0x3ff88920b936fd79,1 +np.float64,0x8010000000000000,0x3ff921fb54442d18,1 +np.float64,0xbfdc5effbdb8be00,0x40003d95fe0dff11,1 +np.float64,0x3febfdad7e77fb5a,0x3fe030b5297dbbdd,1 +np.float64,0x3fe4f3f3b2e9e7e8,0x3feb6bc59eeb2be2,1 +np.float64,0xbfe44469fd6888d4,0x40020daa5488f97a,1 +np.float64,0xbfe19fddb0e33fbc,0x40013b8c902b167b,1 +np.float64,0x3fa36ad17c26d5a0,0x3ff8869b3e828134,1 +np.float64,0x3fcf23e6c93e47d0,0x3ff5336491a65d1e,1 +np.float64,0xffefffffffffffff,0x7ff8000000000000,1 +np.float64,0xbfe375f4cee6ebea,0x4001cbd2ba42e8b5,1 +np.float64,0xbfaef1215c3de240,0x3ffa19ab02081189,1 +np.float64,0xbfec39c59c78738b,0x4005353dc38e3d78,1 +np.float64,0x7ff4000000000000,0x7ffc000000000000,1 +np.float64,0xbfec09bb7b781377,0x40051c0a5754cb3a,1 +np.float64,0x3fe8301f2870603e,0x3fe6d783c5ef0944,1 +np.float64,0xbfed418c987a8319,0x4005cbae1b8693d1,1 +np.float64,0xbfdc16e7adb82dd0,0x4000338b634eaf03,1 +np.float64,0x3fd5d361bdaba6c4,0x3ff390899300a54c,1 +np.float64,0xbff0000000000000,0x400921fb54442d18,1 +np.float64,0x3fd5946232ab28c4,0x3ff3a14767813f29,1 +np.float64,0x3fe833e5fef067cc,0x3fe6d1be720edf2d,1 +np.float64,0x3fedf746a67bee8e,0x3fd6f127fdcadb7b,1 +np.float64,0x3fd90353d3b206a8,0x3ff2b54f7d369ba9,1 +np.float64,0x3fec4b4b72f89696,0x3fdf1b38d2e93532,1 +np.float64,0xbfe9c67596f38ceb,0x40040ee5f524ce03,1 +np.float64,0x3fd350d91aa6a1b4,0x3ff43a303c0da27f,1 +np.float64,0x3fd062603ba0c4c0,0x3ff4fd9514b935d8,1 +np.float64,0xbfe24c075f64980e,0x40016f8e9f2663b3,1 +np.float64,0x3fdaa546eeb54a8c,0x3ff2431a88fef1d5,1 +np.float64,0x3fe92b8151f25702,0x3fe54c67e005cbf9,1 +np.float64,0xbfe1be8b8a637d17,0x400144c078f67c6e,1 +np.float64,0xbfe468a1d7e8d144,0x40021964b118cbf4,1 +np.float64,0xbfdc6de4fab8dbca,0x40003fa9e27893d8,1 +np.float64,0xbfe3c2788ae784f1,0x4001e407ba3aa956,1 +np.float64,0xbfe2bf1542e57e2a,0x400192d4a9072016,1 +np.float64,0xbfe6982f4c6d305e,0x4002d681b1991bbb,1 +np.float64,0x3fdbceb1c4b79d64,0x3ff1f0f117b9d354,1 +np.float64,0x3fdb3705e7b66e0c,0x3ff21af01ca27ace,1 +np.float64,0x3fe3e6358ee7cc6c,0x3fecca4585053983,1 +np.float64,0xbfe16d6a9a62dad5,0x40012c7988aee247,1 +np.float64,0xbfce66e4413ccdc8,0x3ffcf83b08043a0c,1 +np.float64,0xbfeb6cd46876d9a9,0x4004cd61733bfb79,1 +np.float64,0xbfdb1cdd64b639ba,0x400010e6cf087cb7,1 +np.float64,0xbfe09e4e30e13c9c,0x4000ef5277c47721,1 +np.float64,0xbfee88dd127d11ba,0x4006b3cd443643ac,1 +np.float64,0xbf911e06c8223c00,0x3ff966744064fb05,1 +np.float64,0xbfe8f22bc471e458,0x4003b7d5513af295,1 +np.float64,0x3fe3d7329567ae66,0x3fecdd6c241f83ee,1 +np.float64,0x3fc8a9404b315280,0x3ff607dc175edf3f,1 +np.float64,0x3fe7eb80ad6fd702,0x3fe73f8fdb3e6a6c,1 +np.float64,0x3fef0931e37e1264,0x3fcf7fde80a3c5ab,1 +np.float64,0x3fe2ed3c3fe5da78,0x3fee038334cd1860,1 +np.float64,0x3fe251fdb8e4a3fc,0x3feec26dc636ac31,1 +np.float64,0x3feb239436764728,0x3fe1de9462455da7,1 +np.float64,0xbfe63fd7eeec7fb0,0x4002b78cfa3d2fa6,1 +np.float64,0x3fdd639cb5bac738,0x3ff17fc7d92b3eee,1 +np.float64,0x3fd0a7a13fa14f44,0x3ff4eba95c559c84,1 +np.float64,0x3fe804362d70086c,0x3fe71a44cd91ffa4,1 +np.float64,0xbfe0fecf6e61fd9f,0x40010bac8edbdc4f,1 +np.float64,0x3fcb74acfd36e958,0x3ff5ac84437f1b7c,1 +np.float64,0x3fe55053e1eaa0a8,0x3feaf0bf76304c30,1 +np.float64,0x3fc06b508d20d6a0,0x3ff7131da17f3902,1 +np.float64,0x3fdd78750fbaf0ec,0x3ff179e97fbf7f65,1 +np.float64,0x3fe44cb946689972,0x3fec46859b5da6be,1 +np.float64,0xbfeb165a7ff62cb5,0x4004a41c9cc9589e,1 +np.float64,0x3fe01ffb2b603ff6,0x3ff0aed52bf1c3c1,1 +np.float64,0x3f983c60a83078c0,0x3ff8c107805715ab,1 +np.float64,0x3fd8b5ff13b16c00,0x3ff2ca4a837a476a,1 +np.float64,0x3fc80510a1300a20,0x3ff61cc3b4af470b,1 +np.float64,0xbfd3935b06a726b6,0x3ffe1b3a2066f473,1 +np.float64,0xbfdd4a1f31ba943e,0x40005e81979ed445,1 +np.float64,0xbfa76afdd42ed600,0x3ff9dd63ffba72d2,1 +np.float64,0x3fe7e06d496fc0da,0x3fe7503773566707,1 +np.float64,0xbfea5fbfe874bf80,0x40045106af6c538f,1 +np.float64,0x3fee000c487c0018,0x3fd6bef1f8779d88,1 +np.float64,0xbfb39f4ee2273ea0,0x3ffa5c3f2b3888ab,1 +np.float64,0x3feb9247b0772490,0x3fe1092d2905efce,1 +np.float64,0x3fdaa39b4cb54738,0x3ff243901da0da17,1 +np.float64,0x3fcd5b2b493ab658,0x3ff56e262e65b67d,1 +np.float64,0x3fcf82512f3f04a0,0x3ff52738847c55f2,1 +np.float64,0x3fe2af5e0c655ebc,0x3fee4ffab0c82348,1 +np.float64,0xbfec0055d0f800ac,0x4005172d325933e8,1 +np.float64,0x3fe71da9336e3b52,0x3fe86f2e12f6e303,1 +np.float64,0x3fbefab0723df560,0x3ff731188ac716ec,1 +np.float64,0xbfe11dca28623b94,0x400114d3d4ad370d,1 +np.float64,0x3fbcbda8ca397b50,0x3ff755281078abd4,1 +np.float64,0x3fe687c7126d0f8e,0x3fe945099a7855cc,1 +np.float64,0xbfecde510579bca2,0x400590606e244591,1 +np.float64,0xbfd72de681ae5bce,0x3fff0ff797ad1755,1 +np.float64,0xbfe7c0f7386f81ee,0x40034226e0805309,1 +np.float64,0x3fd8d55619b1aaac,0x3ff2c1cb3267b14e,1 +np.float64,0x3fecd7a2ad79af46,0x3fdcabbffeaa279e,1 +np.float64,0x3fee7fb1a8fcff64,0x3fd3ae620286fe19,1 +np.float64,0xbfc5f3a3592be748,0x3ffbe3ed204d9842,1 +np.float64,0x3fec9e5527793caa,0x3fddb00bc8687e4b,1 +np.float64,0x3fc35dc70f26bb90,0x3ff6b3ded7191e33,1 +np.float64,0x3fda91c07ab52380,0x3ff24878848fec8f,1 +np.float64,0xbfe12cde1fe259bc,0x4001194ab99d5134,1 +np.float64,0xbfd35ab736a6b56e,0x3ffe0c5ce8356d16,1 +np.float64,0x3fc9c94123339280,0x3ff5e3239f3ad795,1 +np.float64,0xbfe72f54926e5ea9,0x40030c95d1d02b56,1 +np.float64,0xbfee283186fc5063,0x40066786bd0feb79,1 +np.float64,0xbfe7b383f56f6708,0x40033d23ef0e903d,1 +np.float64,0x3fd6037327ac06e8,0x3ff383bf2f311ddb,1 +np.float64,0x3fe0e344b561c68a,0x3ff03cd90fd4ba65,1 +np.float64,0xbfef0ff54b7e1feb,0x400730fa5fce381e,1 +np.float64,0x3fd269929da4d324,0x3ff476b230136d32,1 +np.float64,0xbfbc5fb9f638bf70,0x3ffae8e63a4e3234,1 +np.float64,0xbfe2e8bc84e5d179,0x40019fb5874f4310,1 +np.float64,0xbfd7017413ae02e8,0x3fff040d843c1531,1 +np.float64,0x3fefd362fa7fa6c6,0x3fbababc3ddbb21d,1 +np.float64,0x3fecb62ed3f96c5e,0x3fdd44ba77ccff94,1 +np.float64,0xbfb16fad5222df58,0x3ffa392d7f02b522,1 +np.float64,0x3fbcf4abc639e950,0x3ff751b23c40e27f,1 +np.float64,0x3fe128adbce2515c,0x3ff013dc91db04b5,1 +np.float64,0x3fa5dd9d842bbb40,0x3ff87300c88d512f,1 +np.float64,0xbfe61efcaf6c3dfa,0x4002ac27117f87c9,1 +np.float64,0x3feffe1233fffc24,0x3f9638d3796a4954,1 +np.float64,0xbfe78548b66f0a92,0x40032c0447b7bfe2,1 +np.float64,0x3fe7bd38416f7a70,0x3fe784e86d6546b6,1 +np.float64,0x3fe0d6bc5961ad78,0x3ff0443899e747ac,1 +np.float64,0xbfd0bb6e47a176dc,0x3ffd5d6dff390d41,1 +np.float64,0xbfec1d16b8f83a2e,0x40052620378d3b78,1 +np.float64,0x3fe9bbec20f377d8,0x3fe45e167c7a3871,1 +np.float64,0xbfeed81d9dfdb03b,0x4006f9dec2db7310,1 +np.float64,0xbfe1e35179e3c6a3,0x40014fd1b1186ac0,1 +np.float64,0xbfc9c7e605338fcc,0x3ffc60a6bd1a7126,1 +np.float64,0x3feec92810fd9250,0x3fd1afde414ab338,1 +np.float64,0xbfeb9f1d90773e3b,0x4004e606b773f5b0,1 +np.float64,0x3fcbabdf6b3757c0,0x3ff5a573866404af,1 +np.float64,0x3fe9f4e1fff3e9c4,0x3fe3fd7b6712dd7b,1 +np.float64,0xbfe6c0175ded802e,0x4002e4a4dc12f3fe,1 +np.float64,0xbfeefc96f37df92e,0x40071d367cd721ff,1 +np.float64,0xbfeaab58dc7556b2,0x400472ce37e31e50,1 +np.float64,0xbfc62668772c4cd0,0x3ffbea5e6c92010a,1 +np.float64,0x3fafe055fc3fc0a0,0x3ff822ce6502519a,1 +np.float64,0x3fd7b648ffaf6c90,0x3ff30f5a42f11418,1 +np.float64,0xbfe934fe827269fd,0x4003d2b9fed9e6ad,1 +np.float64,0xbfe6d691f2edad24,0x4002eca6a4b1797b,1 +np.float64,0x3fc7e62ced2fcc58,0x3ff620b1f44398b7,1 +np.float64,0xbfc89be9f33137d4,0x3ffc3a67a497f59c,1 +np.float64,0xbfe7793d536ef27a,0x40032794bf14dd64,1 +np.float64,0x3fde55a02dbcab40,0x3ff13b5f82d223e4,1 +np.float64,0xbfc8eabd7b31d57c,0x3ffc4472a81cb6d0,1 +np.float64,0x3fddcb5468bb96a8,0x3ff162899c381f2e,1 +np.float64,0xbfec7554d8f8eaaa,0x40055550e18ec463,1 +np.float64,0x3fd0b6e8b6a16dd0,0x3ff4e7b4781a50e3,1 +np.float64,0x3fedaae01b7b55c0,0x3fd8964916cdf53d,1 +np.float64,0x3fe0870f8a610e20,0x3ff072e7db95c2a2,1 +np.float64,0xbfec3e3ce2787c7a,0x4005379d0f6be873,1 +np.float64,0xbfe65502586caa04,0x4002beecff89147f,1 +np.float64,0xbfe0df39a961be74,0x4001025e36d1c061,1 +np.float64,0xbfb5d8edbe2bb1d8,0x3ffa7ff72b7d6a2b,1 +np.float64,0xbfde89574bbd12ae,0x40008ba4cd74544d,1 +np.float64,0xbfe72938f0ee5272,0x40030a5efd1acb6d,1 +np.float64,0xbfcd500d133aa01c,0x3ffcd462f9104689,1 +np.float64,0x3fe0350766606a0e,0x3ff0a2a3664e2c14,1 +np.float64,0xbfc892fb573125f8,0x3ffc3944641cc69d,1 +np.float64,0xbfba7dc7c634fb90,0x3ffaca9a6a0ffe61,1 +np.float64,0xbfeac94478759289,0x40048068a8b83e45,1 +np.float64,0xbfe8f60c1af1ec18,0x4003b961995b6e51,1 +np.float64,0x3fea1c0817743810,0x3fe3ba28c1643cf7,1 +np.float64,0xbfe42a0fefe85420,0x4002052aadd77f01,1 +np.float64,0x3fd2c61c56a58c38,0x3ff45e84cb9a7fa9,1 +np.float64,0xbfd83fb7cdb07f70,0x3fff59ab4790074c,1 +np.float64,0x3fd95e630fb2bcc8,0x3ff29c8bee1335ad,1 +np.float64,0x3feee88f387dd11e,0x3fd0c3ad3ded4094,1 +np.float64,0x3fe061291160c252,0x3ff0890010199bbc,1 +np.float64,0xbfdc7db3b5b8fb68,0x400041dea3759443,1 +np.float64,0x3fee23b320fc4766,0x3fd5ee73d7aa5c56,1 +np.float64,0xbfdc25c590b84b8c,0x4000359cf98a00b4,1 +np.float64,0xbfd63cbfd2ac7980,0x3ffecf7b9cf99b3c,1 +np.float64,0xbfbeb3c29a3d6788,0x3ffb0e66ecc0fc3b,1 +np.float64,0xbfd2f57fd6a5eb00,0x3ffdf1d7c79e1532,1 +np.float64,0xbfab3eda9c367db0,0x3ff9fc0c875f42e9,1 +np.float64,0xbfe12df1c6e25be4,0x4001199c673e698c,1 +np.float64,0x3fef8ab23a7f1564,0x3fc5aff358c59f1c,1 +np.float64,0x3fe562f50feac5ea,0x3fead7bce205f7d9,1 +np.float64,0x3fdc41adbeb8835c,0x3ff1d0f71341b8f2,1 +np.float64,0x3fe2748967e4e912,0x3fee9837f970ff9e,1 +np.float64,0xbfdaa89d57b5513a,0x400000e3889ba4cf,1 +np.float64,0x3fdf2a137dbe5428,0x3ff0fecfbecbbf86,1 +np.float64,0xbfea1fdcd2f43fba,0x4004351974b32163,1 +np.float64,0xbfe34a93a3e69528,0x4001be323946a3e0,1 +np.float64,0x3fe929bacff25376,0x3fe54f47bd7f4cf2,1 +np.float64,0xbfd667fbd6accff8,0x3ffedb04032b3a1a,1 +np.float64,0xbfeb695796f6d2af,0x4004cbb08ec6f525,1 +np.float64,0x3fd204df2ea409c0,0x3ff490f51e6670f5,1 +np.float64,0xbfd89a2757b1344e,0x3fff722127b988c4,1 +np.float64,0xbfd0787187a0f0e4,0x3ffd4c16dbe94f32,1 +np.float64,0x3fd44239bfa88474,0x3ff3fabbfb24b1fa,1 +np.float64,0xbfeb0b3489f61669,0x40049ee33d811d33,1 +np.float64,0x3fdcf04eaab9e09c,0x3ff1a02a29996c4e,1 +np.float64,0x3fd4c51e4fa98a3c,0x3ff3d8302c68fc9a,1 +np.float64,0x3fd1346645a268cc,0x3ff4c72b4970ecaf,1 +np.float64,0x3fd6a89d09ad513c,0x3ff357af6520afac,1 +np.float64,0xbfba0f469a341e90,0x3ffac3a8f41bed23,1 +np.float64,0xbfe13f8ddce27f1c,0x40011ed557719fd6,1 +np.float64,0x3fd43e5e26a87cbc,0x3ff3fbc040fc30dc,1 +np.float64,0x3fe838125a707024,0x3fe6cb5c987248f3,1 +np.float64,0x3fe128c30c625186,0x3ff013cff238dd1b,1 +np.float64,0xbfcd4718833a8e30,0x3ffcd33c96bde6f9,1 +np.float64,0x3fe43fcd08e87f9a,0x3fec573997456ec1,1 +np.float64,0xbfe9a29104734522,0x4003ffd502a1b57f,1 +np.float64,0xbfe4709d7968e13b,0x40021bfc5cd55af4,1 +np.float64,0x3fd21c3925a43874,0x3ff48adf48556cbb,1 +np.float64,0x3fe9a521b2734a44,0x3fe4844fc054e839,1 +np.float64,0xbfdfa6a912bf4d52,0x4000b4730ad8521e,1 +np.float64,0x3fe3740702e6e80e,0x3fed5b106283b6ed,1 +np.float64,0x3fd0a3aa36a14754,0x3ff4ecb02a5e3f49,1 +np.float64,0x3fdcb903d0b97208,0x3ff1afa5d692c5b9,1 +np.float64,0xbfe7d67839efacf0,0x40034a3146abf6f2,1 +np.float64,0x3f9981c6d8330380,0x3ff8bbf1853d7b90,1 +np.float64,0xbfe9d4191673a832,0x400414a9ab453c5d,1 +np.float64,0x3fef0a1e5c7e143c,0x3fcf70b02a54c415,1 +np.float64,0xbfd996dee6b32dbe,0x3fffb6cf707ad8e4,1 +np.float64,0x3fe19bef17e337de,0x3fef9e70d4fcedae,1 +np.float64,0x3fe34a59716694b2,0x3fed8f6d5cfba474,1 +np.float64,0x3fdf27e27cbe4fc4,0x3ff0ff70500e0c7c,1 +np.float64,0xbfe19df87fe33bf1,0x40013afb401de24c,1 +np.float64,0xbfbdfd97ba3bfb30,0x3ffb02ef8c225e57,1 +np.float64,0xbfe3d3417267a683,0x4001e95ed240b0f8,1 +np.float64,0x3fe566498b6acc94,0x3fead342957d4910,1 +np.float64,0x3ff0000000000000,0x0,1 +np.float64,0x3feb329bd8766538,0x3fe1c2225aafe3b4,1 +np.float64,0xbfc19ca703233950,0x3ffb575b5df057b9,1 +np.float64,0x3fe755027d6eaa04,0x3fe81eb99c262e00,1 +np.float64,0xbfe6c2b8306d8570,0x4002e594199f9eec,1 +np.float64,0x3fd69438e6ad2870,0x3ff35d2275ae891d,1 +np.float64,0x3fda3e7285b47ce4,0x3ff25f5573dd47ae,1 +np.float64,0x3fe7928a166f2514,0x3fe7c4490ef4b9a9,1 +np.float64,0xbfd4eb71b9a9d6e4,0x3ffe75e8ccb74be1,1 +np.float64,0xbfcc3a07f1387410,0x3ffcb0b8af914a5b,1 +np.float64,0xbfe6e80225edd004,0x4002f2e26eae8999,1 +np.float64,0xbfb347728a268ee8,0x3ffa56bd526a12db,1 +np.float64,0x3fe5140ead6a281e,0x3feb4132c9140a1c,1 +np.float64,0xbfc147f125228fe4,0x3ffb4cab18b9050f,1 +np.float64,0xbfcb9145b537228c,0x3ffc9b1b6227a8c9,1 +np.float64,0xbfda84ef4bb509de,0x3ffff7f8a674e17d,1 +np.float64,0x3fd2eb6bbfa5d6d8,0x3ff454c225529d7e,1 +np.float64,0x3fe18c95f1e3192c,0x3fefb0cf0efba75a,1 +np.float64,0x3fe78606efef0c0e,0x3fe7d6c3a092d64c,1 +np.float64,0x3fbad5119a35aa20,0x3ff773dffe3ce660,1 +np.float64,0x3fd0cf5903a19eb4,0x3ff4e15fd21fdb42,1 +np.float64,0xbfd85ce90bb0b9d2,0x3fff618ee848e974,1 +np.float64,0x3fe90e11b9f21c24,0x3fe57be62f606f4a,1 +np.float64,0x3fd7a2040faf4408,0x3ff314ce85457ec2,1 +np.float64,0xbfd73fba69ae7f74,0x3fff14bff3504811,1 +np.float64,0x3fa04b4bd42096a0,0x3ff89f9b52f521a2,1 +np.float64,0xbfd7219ce5ae433a,0x3fff0cac0b45cc18,1 +np.float64,0xbfe0cf4661e19e8d,0x4000fdadb14e3c22,1 +np.float64,0x3fd07469fea0e8d4,0x3ff4f8eaa9b2394a,1 +np.float64,0x3f9b05c5d8360b80,0x3ff8b5e10672db5c,1 +np.float64,0x3fe4c25b916984b8,0x3febad29bd0e25e2,1 +np.float64,0xbfde8b4891bd1692,0x40008beb88d5c409,1 +np.float64,0xbfe199a7efe33350,0x400139b089aee21c,1 +np.float64,0x3fecdad25cf9b5a4,0x3fdc9d062867e8c3,1 +np.float64,0xbfe979b277f2f365,0x4003eedb061e25a4,1 +np.float64,0x3fc8c7311f318e60,0x3ff6040b9aeaad9d,1 +np.float64,0x3fd2b605b8a56c0c,0x3ff462b9a955c224,1 +np.float64,0x3fc073b6ad20e770,0x3ff7120e9f2fd63c,1 +np.float64,0xbfec60ede678c1dc,0x40054a3863e24dc2,1 +np.float64,0x3fe225171be44a2e,0x3feef910dca420ea,1 +np.float64,0xbfd7529762aea52e,0x3fff19d00661f650,1 +np.float64,0xbfd781783daf02f0,0x3fff2667b90be461,1 +np.float64,0x3fe3f6ec6d67edd8,0x3fecb4e814a2e33a,1 +np.float64,0x3fece6702df9cce0,0x3fdc6719d92a50d2,1 +np.float64,0xbfb5c602ce2b8c08,0x3ffa7ec761ba856a,1 +np.float64,0xbfd61f0153ac3e02,0x3ffec78e3b1a6c4d,1 +np.float64,0xbfec3462b2f868c5,0x400532630bbd7050,1 +np.float64,0xbfdd248485ba490a,0x400059391c07c1bb,1 +np.float64,0xbfd424921fa84924,0x3ffe416a85d1dcdf,1 +np.float64,0x3fbb23a932364750,0x3ff76eef79209f7f,1 +np.float64,0x3fca248b0f344918,0x3ff5d77c5c1b4e5e,1 +np.float64,0xbfe69af4a4ed35ea,0x4002d77c2e4fbd4e,1 +np.float64,0x3fdafe3cdcb5fc78,0x3ff22a9be6efbbf2,1 +np.float64,0xbfebba3377f77467,0x4004f3836e1fe71a,1 +np.float64,0xbfe650fae06ca1f6,0x4002bd851406377c,1 +np.float64,0x3fda630007b4c600,0x3ff2554f1832bd94,1 +np.float64,0xbfda8107d9b50210,0x3ffff6e6209659f3,1 +np.float64,0x3fea759a02f4eb34,0x3fe31d1a632c9aae,1 +np.float64,0x3fbf88149e3f1030,0x3ff728313aa12ccb,1 +np.float64,0x3f7196d2a0232e00,0x3ff910647e1914c1,1 +np.float64,0x3feeae51d17d5ca4,0x3fd2709698d31f6f,1 +np.float64,0xbfd73cd663ae79ac,0x3fff13f96300b55a,1 +np.float64,0x3fd4fc5f06a9f8c0,0x3ff3c99359854b97,1 +np.float64,0x3fb29f5d6e253ec0,0x3ff7f7c20e396b20,1 +np.float64,0xbfd757c82aaeaf90,0x3fff1b34c6141e98,1 +np.float64,0x3fc56fd4cf2adfa8,0x3ff670c145122909,1 +np.float64,0x3fc609a2f52c1348,0x3ff65d3ef3cade2c,1 +np.float64,0xbfe1de631163bcc6,0x40014e5528fadb73,1 +np.float64,0xbfe7eb4a726fd695,0x40035202f49d95c4,1 +np.float64,0xbfc9223771324470,0x3ffc4b84d5e263b9,1 +np.float64,0x3fee91a8a87d2352,0x3fd3364befde8de6,1 +np.float64,0x3fbc9784fe392f10,0x3ff7578e29f6a1b2,1 +np.float64,0xbfec627c2c78c4f8,0x40054b0ff2cb9c55,1 +np.float64,0xbfb8b406a6316810,0x3ffaadd97062fb8c,1 +np.float64,0xbfecf98384f9f307,0x4005a043d9110d79,1 +np.float64,0xbfe5834bab6b0698,0x400276f114aebee4,1 +np.float64,0xbfd90f391eb21e72,0x3fff91e26a8f48f3,1 +np.float64,0xbfee288ce2fc511a,0x400667cb09aa04b3,1 +np.float64,0x3fd5aa5e32ab54bc,0x3ff39b7080a52214,1 +np.float64,0xbfee7ef907fcfdf2,0x4006ab96a8eba4c5,1 +np.float64,0x3fd6097973ac12f4,0x3ff3822486978bd1,1 +np.float64,0xbfe02d14b8e05a2a,0x4000ce5be53047b1,1 +np.float64,0xbf9c629a6838c540,0x3ff993897728c3f9,1 +np.float64,0xbfee2024667c4049,0x40066188782fb1f0,1 +np.float64,0xbfa42a88fc285510,0x3ff9c35a4bbce104,1 +np.float64,0x3fa407af5c280f60,0x3ff881b360d8eea1,1 +np.float64,0x3fed0ba42cfa1748,0x3fdbb7d55609175f,1 +np.float64,0xbfdd0b5844ba16b0,0x400055b0bb59ebb2,1 +np.float64,0x3fd88d97e6b11b30,0x3ff2d53c1ecb8f8c,1 +np.float64,0xbfeb7a915ef6f523,0x4004d410812eb84c,1 +np.float64,0xbfb5f979ca2bf2f0,0x3ffa8201d73cd4ca,1 +np.float64,0x3fb3b65dd6276cc0,0x3ff7e64576199505,1 +np.float64,0x3fcd47a7793a8f50,0x3ff570a7b672f160,1 +np.float64,0xbfa41dd30c283ba0,0x3ff9c2f488127eb3,1 +np.float64,0x3fe4b1ea1f6963d4,0x3febc2bed7760427,1 +np.float64,0xbfdd0f81d2ba1f04,0x400056463724b768,1 +np.float64,0x3fd15d93f7a2bb28,0x3ff4bc7a24eacfd7,1 +np.float64,0xbfe3213af8e64276,0x4001b14579dfded3,1 +np.float64,0x3fd90dfbeab21bf8,0x3ff2b26a6c2c3bb3,1 +np.float64,0xbfd02d54bca05aaa,0x3ffd38ab3886b203,1 +np.float64,0x3fc218dcad2431b8,0x3ff6dced56d5b417,1 +np.float64,0x3fea5edf71f4bdbe,0x3fe3455ee09f27e6,1 +np.float64,0x3fa74319042e8640,0x3ff867d224545438,1 +np.float64,0x3fd970ad92b2e15c,0x3ff2979084815dc1,1 +np.float64,0x3fce0a4bf73c1498,0x3ff557a4df32df3e,1 +np.float64,0x3fef5c8e10feb91c,0x3fc99ca0eeaaebe4,1 +np.float64,0xbfedae997ffb5d33,0x400611af18f407ab,1 +np.float64,0xbfbcf07d6239e0f8,0x3ffaf201177a2d36,1 +np.float64,0xbfc3c52541278a4c,0x3ffb9d2af0408e4a,1 +np.float64,0x3fe4ef44e4e9de8a,0x3feb71f7331255e5,1 +np.float64,0xbfccd9f5f539b3ec,0x3ffcc53a99339592,1 +np.float64,0xbfda32c745b4658e,0x3fffe16e8727ef89,1 +np.float64,0xbfef54932a7ea926,0x40077e4605e61ca1,1 +np.float64,0x3fe9d4ae3573a95c,0x3fe4344a069a3fd0,1 +np.float64,0x3fda567e73b4acfc,0x3ff258bd77a663c7,1 +np.float64,0xbfd5bcac5eab7958,0x3ffead6379c19c52,1 +np.float64,0xbfee5e56f97cbcae,0x40069131fc54018d,1 +np.float64,0x3fc2d4413925a880,0x3ff6c54163816298,1 +np.float64,0xbfe9ddf6e873bbee,0x400418d8c722f7c5,1 +np.float64,0x3fdaf2a683b5e54c,0x3ff22dcda599d69c,1 +np.float64,0xbfca69789f34d2f0,0x3ffc7547ff10b1a6,1 +np.float64,0x3fed076f62fa0ede,0x3fdbcbda03c1d72a,1 +np.float64,0xbfcb38326f367064,0x3ffc8fb55dadeae5,1 +np.float64,0x3fe1938705e3270e,0x3fefa88130c5adda,1 +np.float64,0x3feaffae3b75ff5c,0x3fe221e3da537c7e,1 +np.float64,0x3fefc94acb7f9296,0x3fbd9a360ace67b4,1 +np.float64,0xbfe8bddeb0f17bbe,0x4003a316685c767e,1 +np.float64,0x3fbe10fbee3c21f0,0x3ff73fceb10650f5,1 +np.float64,0x3fde9126c1bd224c,0x3ff12a742f734d0a,1 +np.float64,0xbfe9686c91f2d0d9,0x4003e7bc6ee77906,1 +np.float64,0xbfb1ba4892237490,0x3ffa3dda064c2509,1 +np.float64,0xbfe2879100e50f22,0x400181c1a5b16f0f,1 +np.float64,0x3fd1cd40b6a39a80,0x3ff49f70e3064e95,1 +np.float64,0xbfc965869132cb0c,0x3ffc5419f3b43701,1 +np.float64,0x3fea7a6f2874f4de,0x3fe31480fb2dd862,1 +np.float64,0x3fc3bc56892778b0,0x3ff6a7e8fa0e8b0e,1 +np.float64,0x3fec1ed451f83da8,0x3fdfd78e564b8ad7,1 +np.float64,0x3feb77d16df6efa2,0x3fe13d083344e45e,1 +np.float64,0xbfe822e7c67045d0,0x400367104a830cf6,1 +np.float64,0x8000000000000001,0x3ff921fb54442d18,1 +np.float64,0xbfd4900918a92012,0x3ffe5dc0e19737b4,1 +np.float64,0x3fed184187fa3084,0x3fdb7b7a39f234f4,1 +np.float64,0x3fecef846179df08,0x3fdc3cb2228c3682,1 +np.float64,0xbfe2d2aed165a55e,0x400198e21c5b861b,1 +np.float64,0x7ff0000000000000,0x7ff8000000000000,1 +np.float64,0xbfee9409a07d2813,0x4006bd358232d073,1 +np.float64,0xbfecedc2baf9db86,0x4005995df566fc21,1 +np.float64,0x3fe6d857396db0ae,0x3fe8d2cb8794aa99,1 +np.float64,0xbf9a579e7834af40,0x3ff98b5cc8021e1c,1 +np.float64,0x3fc664fefb2cca00,0x3ff651a664ccf8fa,1 +np.float64,0xbfe8a7aa0e714f54,0x40039a5b4df938a0,1 +np.float64,0xbfdf27d380be4fa8,0x4000a241074dbae6,1 +np.float64,0x3fe00ddf55e01bbe,0x3ff0b94eb1ea1851,1 +np.float64,0x3feb47edbff68fdc,0x3fe199822d075959,1 +np.float64,0x3fb4993822293270,0x3ff7d80c838186d0,1 +np.float64,0xbfca2cd1473459a4,0x3ffc6d88c8de3d0d,1 +np.float64,0xbfea7d9c7674fb39,0x40045e4559e9e52d,1 +np.float64,0x3fe0dce425e1b9c8,0x3ff04099cab23289,1 +np.float64,0x3fd6bb7e97ad76fc,0x3ff352a30434499c,1 +np.float64,0x3fd4a4f16da949e4,0x3ff3e0b07432c9aa,1 +np.float64,0x8000000000000000,0x3ff921fb54442d18,1 +np.float64,0x3fe688f5b56d11ec,0x3fe9435f63264375,1 +np.float64,0xbfdf5a427ebeb484,0x4000a97a6c5d4abc,1 +np.float64,0xbfd1f3483fa3e690,0x3ffdae6c8a299383,1 +np.float64,0xbfeac920db759242,0x4004805862be51ec,1 +np.float64,0x3fef5bc711feb78e,0x3fc9ac40fba5b93b,1 +np.float64,0x3fe4bd9e12e97b3c,0x3febb363c787d381,1 +np.float64,0x3fef6a59ab7ed4b4,0x3fc880f1324eafce,1 +np.float64,0x3fc07a362120f470,0x3ff7113cf2c672b3,1 +np.float64,0xbfe4d6dbe2e9adb8,0x40023d6f6bea44b7,1 +np.float64,0xbfec2d6a15785ad4,0x40052eb425cc37a2,1 +np.float64,0x3fc90dae05321b60,0x3ff5fb10015d2934,1 +np.float64,0xbfa9239f74324740,0x3ff9eb2d057068ea,1 +np.float64,0xbfeb4fc8baf69f92,0x4004bf5e17fb08a4,1 +np.float64,0x0,0x3ff921fb54442d18,1 +np.float64,0x3faaf1884c35e320,0x3ff84a5591dbe1f3,1 +np.float64,0xbfed842561fb084b,0x4005f5c0a19116ce,1 +np.float64,0xbfc64850c32c90a0,0x3ffbeeac2ee70f9a,1 +np.float64,0x3fd7d879f5afb0f4,0x3ff306254c453436,1 +np.float64,0xbfdabaa586b5754c,0x4000035e6ac83a2b,1 +np.float64,0xbfebfeefa977fddf,0x4005167446fb9faf,1 +np.float64,0xbfe9383462727069,0x4003d407aa6a1577,1 +np.float64,0x3fe108dfb6e211c0,0x3ff026ac924b281d,1 +np.float64,0xbf85096df02a12c0,0x3ff94c0e60a22ede,1 +np.float64,0xbfe3121cd566243a,0x4001ac8f90db5882,1 +np.float64,0xbfd227f62aa44fec,0x3ffdbc26bb175dcc,1 +np.float64,0x3fd931af2cb26360,0x3ff2a8b62dfe003c,1 +np.float64,0xbfd9b794e3b36f2a,0x3fffbfbc89ec013d,1 +np.float64,0x3fc89b2e6f313660,0x3ff609a6e67f15f2,1 +np.float64,0x3fc0b14a8f216298,0x3ff70a4b6905aad2,1 +np.float64,0xbfeda11a657b4235,0x400608b3f9fff574,1 +np.float64,0xbfed2ee9ec7a5dd4,0x4005c040b7c02390,1 +np.float64,0xbfef7819d8fef034,0x4007ac6bf75cf09d,1 +np.float64,0xbfcc4720fb388e40,0x3ffcb2666a00b336,1 +np.float64,0xbfe05dec4be0bbd8,0x4000dc8a25ca3760,1 +np.float64,0x3fb093416e212680,0x3ff81897b6d8b374,1 +np.float64,0xbfc6ab89332d5714,0x3ffbfb4559d143e7,1 +np.float64,0x3fc51948512a3290,0x3ff67bb9df662c0a,1 +np.float64,0x3fed4d94177a9b28,0x3fda76c92f0c0132,1 +np.float64,0x3fdd195fbeba32c0,0x3ff194a5586dd18e,1 +np.float64,0x3fe3f82799e7f050,0x3fecb354c2faf55c,1 +np.float64,0x3fecac2169f95842,0x3fdd7222296cb7a7,1 +np.float64,0x3fe3d3f36fe7a7e6,0x3fece18f45e30dd7,1 +np.float64,0x3fe31ff63d663fec,0x3fedc46c77d30c6a,1 +np.float64,0xbfe3120c83e62419,0x4001ac8a7c4aa742,1 +np.float64,0x3fe7c1a7976f8350,0x3fe77e4a9307c9f8,1 +np.float64,0x3fe226fe9de44dfe,0x3feef6c0f3cb00fa,1 +np.float64,0x3fd5c933baab9268,0x3ff3933e8a37de42,1 +np.float64,0x3feaa98496f5530a,0x3fe2c003832ebf21,1 +np.float64,0xbfc6f80a2f2df014,0x3ffc04fd54cb1317,1 +np.float64,0x3fde5e18d0bcbc30,0x3ff138f7b32a2ca3,1 +np.float64,0xbfe30c8dd566191c,0x4001aad4af935a78,1 +np.float64,0x3fbe8d196e3d1a30,0x3ff737fec8149ecc,1 +np.float64,0x3feaee6731f5dcce,0x3fe241fa42cce22d,1 +np.float64,0x3fef9cc46cff3988,0x3fc3f17b708dbdbb,1 +np.float64,0xbfdb181bdeb63038,0x4000103ecf405602,1 +np.float64,0xbfc58de0ed2b1bc0,0x3ffbd704c14e15cd,1 +np.float64,0xbfee05d5507c0bab,0x40064e480faba6d8,1 +np.float64,0x3fe27d0ffa64fa20,0x3fee8dc71ef79f2c,1 +np.float64,0xbfe4f7ad4c69ef5a,0x400248456cd09a07,1 +np.float64,0xbfe4843e91e9087d,0x4002225f3e139c84,1 +np.float64,0x3fe7158b9c6e2b18,0x3fe87ae845c5ba96,1 +np.float64,0xbfea64316074c863,0x400452fd2bc23a44,1 +np.float64,0xbfc9f3ae4133e75c,0x3ffc663d482afa42,1 +np.float64,0xbfd5e18513abc30a,0x3ffeb72fc76d7071,1 +np.float64,0xbfd52f6438aa5ec8,0x3ffe87e5b18041e5,1 +np.float64,0xbfea970650f52e0d,0x400469a4a6758154,1 +np.float64,0xbfe44321b7e88644,0x40020d404a2141b1,1 +np.float64,0x3fdf5a39bbbeb474,0x3ff0f10453059dbd,1 +np.float64,0xbfa1d4069423a810,0x3ff9b0a2eacd2ce2,1 +np.float64,0xbfc36d16a326da2c,0x3ffb92077d41d26a,1 +np.float64,0x1,0x3ff921fb54442d18,1 +np.float64,0x3feb232a79764654,0x3fe1df5beeb249d0,1 +np.float64,0xbfed2003d5fa4008,0x4005b737c2727583,1 +np.float64,0x3fd5b093a3ab6128,0x3ff399ca2db1d96d,1 +np.float64,0x3fca692c3d34d258,0x3ff5ceb86b79223e,1 +np.float64,0x3fd6bbdf89ad77c0,0x3ff3528916df652d,1 +np.float64,0xbfefdadd46ffb5bb,0x40085ee735e19f19,1 +np.float64,0x3feb69fb2676d3f6,0x3fe157ee0c15691e,1 +np.float64,0x3fe44c931f689926,0x3fec46b6f5e3f265,1 +np.float64,0xbfc43ddbcb287bb8,0x3ffbac71d268d74d,1 +np.float64,0x3fe6e16d43edc2da,0x3fe8c5cf0f0daa66,1 +np.float64,0x3fe489efc76913e0,0x3febf704ca1ac2a6,1 +np.float64,0xbfe590aadceb2156,0x40027b764205cf78,1 +np.float64,0xbf782e8aa0305d00,0x3ff93a29e81928ab,1 +np.float64,0x3fedcb80cffb9702,0x3fd7e5d1f98a418b,1 +np.float64,0x3fe075858060eb0c,0x3ff07d23ab46b60f,1 +np.float64,0x3fe62a68296c54d0,0x3fe9c77f7068043b,1 +np.float64,0x3feff16a3c7fe2d4,0x3fae8e8a739cc67a,1 +np.float64,0xbfd6ed93e3addb28,0x3ffefebab206fa99,1 +np.float64,0x3fe40d8ccf681b1a,0x3fec97e9cd29966d,1 +np.float64,0x3fd6408210ac8104,0x3ff3737a7d374107,1 +np.float64,0x3fec8023b8f90048,0x3fde35ebfb2b3afd,1 +np.float64,0xbfe13babd4627758,0x40011dae5c07c56b,1 +np.float64,0xbfd2183e61a4307c,0x3ffdb80dd747cfbe,1 +np.float64,0x3feae8eb1d75d1d6,0x3fe24c1f6e42ae77,1 +np.float64,0xbfea559b9c74ab37,0x40044c8e5e123b20,1 +np.float64,0xbfd12c9d57a2593a,0x3ffd7ac6222f561c,1 +np.float64,0x3fe32eb697e65d6e,0x3fedb202693875b6,1 +np.float64,0xbfde0808c3bc1012,0x4000794bd8616ea3,1 +np.float64,0x3fe14958a06292b2,0x3ff0007b40ac648a,1 +np.float64,0x3fe3d388a6e7a712,0x3fece21751a6dd7c,1 +np.float64,0x3fe7ad7897ef5af2,0x3fe79c5b3da302a7,1 +np.float64,0x3fec75527e78eaa4,0x3fde655de0cf0508,1 +np.float64,0x3fea920d4c75241a,0x3fe2ea48f031d908,1 +np.float64,0x7fefffffffffffff,0x7ff8000000000000,1 +np.float64,0xbfc17a68cb22f4d0,0x3ffb530925f41aa0,1 +np.float64,0xbfe1c93166e39263,0x400147f3cb435dec,1 +np.float64,0x3feb97c402f72f88,0x3fe0fe5b561bf869,1 +np.float64,0x3fb58ff5162b1ff0,0x3ff7c8933fa969dc,1 +np.float64,0x3fe68e2beded1c58,0x3fe93c075283703b,1 +np.float64,0xbf94564cc828aca0,0x3ff97355e5ee35db,1 +np.float64,0x3fd31061c9a620c4,0x3ff44b150ec96998,1 +np.float64,0xbfc7d0c89f2fa190,0x3ffc208bf4eddc4d,1 +np.float64,0x3fe5736f1d6ae6de,0x3feac18f84992d1e,1 +np.float64,0x3fdb62e480b6c5c8,0x3ff20ecfdc4afe7c,1 +np.float64,0xbfc417228b282e44,0x3ffba78afea35979,1 +np.float64,0x3f8f5ba1303eb780,0x3ff8e343714630ff,1 +np.float64,0x3fe8e99126f1d322,0x3fe5b6511d4c0798,1 +np.float64,0xbfe2ec08a1e5d812,0x4001a0bb28a85875,1 +np.float64,0x3fea3b46cf74768e,0x3fe383dceaa74296,1 +np.float64,0xbfe008b5ed60116c,0x4000c3d62c275d40,1 +np.float64,0xbfcd9f8a4b3b3f14,0x3ffcde98d6484202,1 +np.float64,0xbfdb5fb112b6bf62,0x40001a22137ef1c9,1 +np.float64,0xbfe9079565f20f2b,0x4003c0670c92e401,1 +np.float64,0xbfce250dc53c4a1c,0x3ffcefc2b3dc3332,1 +np.float64,0x3fe9ba85d373750c,0x3fe4607131b28773,1 +np.float64,0x10000000000000,0x3ff921fb54442d18,1 +np.float64,0xbfeb9ef42c773de8,0x4004e5f239203ad8,1 +np.float64,0xbfd6bf457dad7e8a,0x3ffef2563d87b18d,1 +np.float64,0x3fe4de9aa5e9bd36,0x3feb87f97defb04a,1 +np.float64,0x3fedb4f67cfb69ec,0x3fd8603c465bffac,1 +np.float64,0x3fe7b6d9506f6db2,0x3fe78e670c7bdb67,1 +np.float64,0x3fe071717460e2e2,0x3ff07f84472d9cc5,1 +np.float64,0xbfed2e79dbfa5cf4,0x4005bffc6f9ad24f,1 +np.float64,0x3febb8adc377715c,0x3fe0bcebfbd45900,1 +np.float64,0xbfee2cffd87c5a00,0x40066b20a037c478,1 +np.float64,0x3fef7e358d7efc6c,0x3fc6d0ba71a542a8,1 +np.float64,0xbfef027eef7e04fe,0x400723291cb00a7a,1 +np.float64,0x3fac96da34392dc0,0x3ff83d260a936c6a,1 +np.float64,0x3fe9dba94a73b752,0x3fe428736b94885e,1 +np.float64,0x3fed37581efa6eb0,0x3fdae49dcadf1d90,1 +np.float64,0xbfe6e61037edcc20,0x4002f23031b8d522,1 +np.float64,0xbfdea7204dbd4e40,0x40008fe1f37918b7,1 +np.float64,0x3feb9f8edb773f1e,0x3fe0eef20bd4387b,1 +np.float64,0x3feeb0b6ed7d616e,0x3fd25fb3b7a525d6,1 +np.float64,0xbfd7ce9061af9d20,0x3fff3b25d531aa2b,1 +np.float64,0xbfc806b509300d6c,0x3ffc2768743a8360,1 +np.float64,0xbfa283882c250710,0x3ff9b61fda28914a,1 +np.float64,0x3fdec70050bd8e00,0x3ff11b1d769b578f,1 +np.float64,0xbfc858a44930b148,0x3ffc31d6758b4721,1 +np.float64,0x3fdc321150b86424,0x3ff1d5504c3c91e4,1 +np.float64,0x3fd9416870b282d0,0x3ff2a46f3a850f5b,1 +np.float64,0x3fdd756968baead4,0x3ff17ac510a5573f,1 +np.float64,0xbfedfd632cfbfac6,0x400648345a2f89b0,1 +np.float64,0x3fd6874285ad0e84,0x3ff36098ebff763f,1 +np.float64,0x3fe6daacc9edb55a,0x3fe8cf75fae1e35f,1 +np.float64,0x3fe53f19766a7e32,0x3feb07d0e97cd55b,1 +np.float64,0x3fd13cc36ca27988,0x3ff4c4ff801b1faa,1 +np.float64,0x3fe4f21cbce9e43a,0x3feb6e34a72ef529,1 +np.float64,0xbfc21c1cc9243838,0x3ffb67726394ca89,1 +np.float64,0x3fe947a3f2728f48,0x3fe51eae4660e23c,1 +np.float64,0xbfce78cd653cf19c,0x3ffcfa89194b3f5e,1 +np.float64,0x3fe756f049eeade0,0x3fe81be7f2d399e2,1 +np.float64,0xbfcc727cf138e4f8,0x3ffcb7f547841bb0,1 +np.float64,0xbfc2d8d58f25b1ac,0x3ffb7f496cc72458,1 +np.float64,0xbfcfd0e4653fa1c8,0x3ffd26e1309bc80b,1 +np.float64,0xbfe2126c106424d8,0x40015e0e01db6a4a,1 +np.float64,0x3fe580e4306b01c8,0x3feaaf683ce51aa5,1 +np.float64,0x3fcea8a1b93d5140,0x3ff543456c0d28c7,1 +np.float64,0xfff0000000000000,0x7ff8000000000000,1 +np.float64,0xbfd9d5da72b3abb4,0x3fffc8013113f968,1 +np.float64,0xbfe1fdfcea63fbfa,0x400157def2e4808d,1 +np.float64,0xbfc0022e0720045c,0x3ffb239963e7cbf2,1 diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-cbrt.csv b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-cbrt.csv new file mode 100644 index 0000000000000000000000000000000000000000..ad141cb4f5a297e69f3437014087f3c2aea28147 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-cbrt.csv @@ -0,0 +1,1429 @@ +dtype,input,output,ulperrortol +np.float32,0x3ee7054c,0x3f4459ea,2 +np.float32,0x7d1e2489,0x54095925,2 +np.float32,0x7ee5edf5,0x549b992b,2 +np.float32,0x380607,0x2a425e72,2 +np.float32,0x34a8f3,0x2a3e6603,2 +np.float32,0x3eee2844,0x3f465a45,2 +np.float32,0x59e49c,0x2a638d0a,2 +np.float32,0xbf72c77a,0xbf7b83d4,2 +np.float32,0x7f2517b4,0x54af8bf0,2 +np.float32,0x80068a69,0xa9bdfe8b,2 +np.float32,0xbe8e3578,0xbf270775,2 +np.float32,0xbe4224dc,0xbf131119,2 +np.float32,0xbe0053b8,0xbf001be2,2 +np.float32,0x70e8d,0x29c2ddc5,2 +np.float32,0xff63f7b5,0xd4c37b7f,2 +np.float32,0x3f00bbed,0x3f4b9335,2 +np.float32,0x3f135f4e,0x3f54f5d4,2 +np.float32,0xbe13a488,0xbf063d13,2 +np.float32,0x3f14ec78,0x3f55b478,2 +np.float32,0x7ec35cfb,0x54935fbf,2 +np.float32,0x7d41c589,0x5412f904,2 +np.float32,0x3ef8a16e,0x3f4937f7,2 +np.float32,0x3f5d8464,0x3f73f279,2 +np.float32,0xbeec85ac,0xbf45e5cb,2 +np.float32,0x7f11f722,0x54a87cb1,2 +np.float32,0x8032c085,0xaa3c1219,2 +np.float32,0x80544bac,0xaa5eb9f2,2 +np.float32,0x3e944a10,0x3f296065,2 +np.float32,0xbf29fe50,0xbf5f5796,2 +np.float32,0x7e204d8d,0x545b03d5,2 +np.float32,0xfe1d0254,0xd4598127,2 +np.float32,0x80523129,0xaa5cdba9,2 +np.float32,0x806315fa,0xaa6b0eaf,2 +np.float32,0x3ed3d2a4,0x3f3ec117,2 +np.float32,0x7ee15007,0x549a8cc0,2 +np.float32,0x801ffb5e,0xaa213d4f,2 +np.float32,0x807f9f4a,0xaa7fbf76,2 +np.float32,0xbe45e854,0xbf1402d3,2 +np.float32,0x3d9e2e70,0x3eda0b64,2 +np.float32,0x51f404,0x2a5ca4d7,2 +np.float32,0xbe26a8b0,0xbf0bc54d,2 +np.float32,0x22c99a,0x2a25d2a7,2 +np.float32,0xbf71248b,0xbf7af2d5,2 +np.float32,0x7219fe,0x2a76608e,2 +np.float32,0x7f16fd7d,0x54aa6610,2 +np.float32,0x80716faa,0xaa75e5b9,2 +np.float32,0xbe24f9a4,0xbf0b4c65,2 +np.float32,0x800000,0x2a800000,2 +np.float32,0x80747456,0xaa780f27,2 +np.float32,0x68f9e8,0x2a6fa035,2 +np.float32,0x3f6a297e,0x3f7880d8,2 +np.float32,0x3f28b973,0x3f5ec8f6,2 +np.float32,0x7f58c577,0x54c03a70,2 +np.float32,0x804befcc,0xaa571b4f,2 +np.float32,0x3e2be027,0x3f0d36cf,2 +np.float32,0xfe7e80a4,0xd47f7ff7,2 +np.float32,0xfe9d444a,0xd489181b,2 +np.float32,0x3db3e790,0x3ee399d6,2 +np.float32,0xbf154c3e,0xbf55e23e,2 +np.float32,0x3d1096b7,0x3ea7f4aa,2 +np.float32,0x7fc00000,0x7fc00000,2 +np.float32,0x804e2521,0xaa592c06,2 +np.float32,0xbeda2f00,0xbf40a513,2 +np.float32,0x3f191788,0x3f57ae30,2 +np.float32,0x3ed24ade,0x3f3e4b34,2 +np.float32,0x807fadb4,0xaa7fc917,2 +np.float32,0xbe0a06dc,0xbf034234,2 +np.float32,0x3f250bba,0x3f5d276d,2 +np.float32,0x7e948b00,0x548682c8,2 +np.float32,0xfe65ecdc,0xd476fed2,2 +np.float32,0x6fdbdd,0x2a74c095,2 +np.float32,0x800112de,0xa9500fa6,2 +np.float32,0xfe63225c,0xd475fdee,2 +np.float32,0x7f3d9acd,0x54b7d648,2 +np.float32,0xfc46f480,0xd3bacf87,2 +np.float32,0xfe5deaac,0xd47417ff,2 +np.float32,0x60ce53,0x2a693d93,2 +np.float32,0x6a6e2f,0x2a70ba2c,2 +np.float32,0x7f43f0f1,0x54b9dcd0,2 +np.float32,0xbf6170c9,0xbf756104,2 +np.float32,0xbe5c9f74,0xbf197852,2 +np.float32,0xff1502b0,0xd4a9a693,2 +np.float32,0x8064f6af,0xaa6c886e,2 +np.float32,0xbf380564,0xbf6552e5,2 +np.float32,0xfeb9b7dc,0xd490e85f,2 +np.float32,0x7f34f941,0x54b5010d,2 +np.float32,0xbe9d4ca0,0xbf2cbd5f,2 +np.float32,0x3f6e43d2,0x3f79f240,2 +np.float32,0xbdad0530,0xbee0a8f2,2 +np.float32,0x3da18459,0x3edb9105,2 +np.float32,0xfd968340,0xd42a3808,2 +np.float32,0x3ea03e64,0x3f2dcf96,2 +np.float32,0x801d2f5b,0xaa1c6525,2 +np.float32,0xbf47d92d,0xbf6bb7e9,2 +np.float32,0x55a6b9,0x2a5fe9fb,2 +np.float32,0x77a7c2,0x2a7a4fb8,2 +np.float32,0xfebbc16e,0xd4916f88,2 +np.float32,0x3f5d3d6e,0x3f73d86a,2 +np.float32,0xfccd2b60,0xd3edcacb,2 +np.float32,0xbd026460,0xbea244b0,2 +np.float32,0x3e55bd,0x2a4968e4,2 +np.float32,0xbe7b5708,0xbf20490d,2 +np.float32,0xfe413cf4,0xd469171f,2 +np.float32,0x7710e3,0x2a79e657,2 +np.float32,0xfc932520,0xd3d4d9ca,2 +np.float32,0xbf764a1b,0xbf7cb8aa,2 +np.float32,0x6b1923,0x2a713aca,2 +np.float32,0xfe4dcd04,0xd46e092d,2 +np.float32,0xff3085ac,0xd4b381f8,2 +np.float32,0x3f72c438,0x3f7b82b4,2 +np.float32,0xbf6f0c6e,0xbf7a3852,2 +np.float32,0x801d2b1b,0xaa1c5d8d,2 +np.float32,0x3e9db91e,0x3f2ce50d,2 +np.float32,0x3f684f9d,0x3f77d8c5,2 +np.float32,0x7dc784,0x2a7e82cc,2 +np.float32,0x7d2c88e9,0x540d64f8,2 +np.float32,0x807fb708,0xaa7fcf51,2 +np.float32,0x8003c49a,0xa99e16e0,2 +np.float32,0x3ee4f5b8,0x3f43c3ff,2 +np.float32,0xfe992c5e,0xd487e4ec,2 +np.float32,0x4b4dfa,0x2a568216,2 +np.float32,0x3d374c80,0x3eb5c6a8,2 +np.float32,0xbd3a4700,0xbeb6c15c,2 +np.float32,0xbf13cb80,0xbf5529e5,2 +np.float32,0xbe7306d4,0xbf1e7f91,2 +np.float32,0xbf800000,0xbf800000,2 +np.float32,0xbea42efe,0xbf2f394e,2 +np.float32,0x3e1981d0,0x3f07fe2c,2 +np.float32,0x3f17ea1d,0x3f572047,2 +np.float32,0x7dc1e0,0x2a7e7efe,2 +np.float32,0x80169c08,0xaa0fa320,2 +np.float32,0x3f3e1972,0x3f67d248,2 +np.float32,0xfe5d3c88,0xd473d815,2 +np.float32,0xbf677448,0xbf778aac,2 +np.float32,0x7e799b7d,0x547dd9e4,2 +np.float32,0x3f00bb2c,0x3f4b92cf,2 +np.float32,0xbeb29f9c,0xbf343798,2 +np.float32,0xbd6b7830,0xbec59a86,2 +np.float32,0x807a524a,0xaa7c282a,2 +np.float32,0xbe0a7a04,0xbf0366ab,2 +np.float32,0x80237470,0xaa26e061,2 +np.float32,0x3ccbc0f6,0x3e95744f,2 +np.float32,0x3edec6bc,0x3f41fcb6,2 +np.float32,0x3f635198,0x3f760efa,2 +np.float32,0x800eca4f,0xa9f960d8,2 +np.float32,0x3f800000,0x3f800000,2 +np.float32,0xff4eeb9e,0xd4bd456a,2 +np.float32,0x56f4e,0x29b29e70,2 +np.float32,0xff5383a0,0xd4bea95c,2 +np.float32,0x3f4c3a77,0x3f6d6d94,2 +np.float32,0x3f6c324a,0x3f79388c,2 +np.float32,0xbebdc092,0xbf37e27c,2 +np.float32,0xff258956,0xd4afb42e,2 +np.float32,0xdc78c,0x29f39012,2 +np.float32,0xbf2db06a,0xbf60f2f5,2 +np.float32,0xbe3c5808,0xbf119660,2 +np.float32,0xbf1ba866,0xbf58e0f4,2 +np.float32,0x80377640,0xaa41b79d,2 +np.float32,0x4fdc4d,0x2a5abfea,2 +np.float32,0x7f5e7560,0x54c1e516,2 +np.float32,0xfeb4d3f2,0xd48f9fde,2 +np.float32,0x3f12a622,0x3f549c7d,2 +np.float32,0x7f737ed7,0x54c7d2dc,2 +np.float32,0xa0ddc,0x29db456d,2 +np.float32,0xfe006740,0xd44b6689,2 +np.float32,0x3f17dfd4,0x3f571b6c,2 +np.float32,0x67546e,0x2a6e5dd1,2 +np.float32,0xff0d0f11,0xd4a693e2,2 +np.float32,0xbd170090,0xbeaa6738,2 +np.float32,0x5274a0,0x2a5d1806,2 +np.float32,0x3e154fe0,0x3f06be1a,2 +np.float32,0x7ddb302e,0x5440f0a7,2 +np.float32,0x3f579d10,0x3f71c2af,2 +np.float32,0xff2bc5bb,0xd4b1e20c,2 +np.float32,0xfee8fa6a,0xd49c4872,2 +np.float32,0xbea551b0,0xbf2fa07b,2 +np.float32,0xfeabc75c,0xd48d3004,2 +np.float32,0x7f50a5a8,0x54bdcbd1,2 +np.float32,0x50354b,0x2a5b110d,2 +np.float32,0x7d139f13,0x54063b6b,2 +np.float32,0xbeee1b08,0xbf465699,2 +np.float32,0xfe5e1650,0xd47427fe,2 +np.float32,0x7f7fffff,0x54cb2ff5,2 +np.float32,0xbf52ede8,0xbf6fff35,2 +np.float32,0x804bba81,0xaa56e8f1,2 +np.float32,0x6609e2,0x2a6d5e94,2 +np.float32,0x692621,0x2a6fc1d6,2 +np.float32,0xbf288bb6,0xbf5eb4d3,2 +np.float32,0x804f28c4,0xaa5a1b82,2 +np.float32,0xbdaad2a8,0xbedfb46e,2 +np.float32,0x5e04f8,0x2a66fb13,2 +np.float32,0x804c10da,0xaa573a81,2 +np.float32,0xbe412764,0xbf12d0fd,2 +np.float32,0x801c35cc,0xaa1aa250,2 +np.float32,0x6364d4,0x2a6b4cf9,2 +np.float32,0xbf6d3cea,0xbf79962f,2 +np.float32,0x7e5a9935,0x5472defb,2 +np.float32,0xbe73a38c,0xbf1ea19c,2 +np.float32,0xbd35e950,0xbeb550f2,2 +np.float32,0x46cc16,0x2a5223d6,2 +np.float32,0x3f005288,0x3f4b5b97,2 +np.float32,0x8034e8b7,0xaa3eb2be,2 +np.float32,0xbea775fc,0xbf3061cf,2 +np.float32,0xea0e9,0x29f87751,2 +np.float32,0xbf38faaf,0xbf65b89d,2 +np.float32,0xbedf3184,0xbf421bb0,2 +np.float32,0xbe04250c,0xbf015def,2 +np.float32,0x7f56dae8,0x54bfa901,2 +np.float32,0xfebe3e04,0xd492132e,2 +np.float32,0x3e4dc326,0x3f15f19e,2 +np.float32,0x803da197,0xaa48a621,2 +np.float32,0x7eeb35aa,0x549cc7c6,2 +np.float32,0xfebb3eb6,0xd4914dc0,2 +np.float32,0xfed17478,0xd496d5e2,2 +np.float32,0x80243694,0xaa280ed2,2 +np.float32,0x8017e666,0xaa1251d3,2 +np.float32,0xbf07e942,0xbf4f4a3e,2 +np.float32,0xbf578fa6,0xbf71bdab,2 +np.float32,0x7ed8d80f,0x549896b6,2 +np.float32,0x3f2277ae,0x3f5bff11,2 +np.float32,0x7e6f195b,0x547a3cd4,2 +np.float32,0xbf441559,0xbf6a3a91,2 +np.float32,0x7f1fb427,0x54ad9d8d,2 +np.float32,0x71695f,0x2a75e12d,2 +np.float32,0xbd859588,0xbece19a1,2 +np.float32,0x7f5702fc,0x54bfb4eb,2 +np.float32,0x3f040008,0x3f4d4842,2 +np.float32,0x3de00ca5,0x3ef4df89,2 +np.float32,0x3eeabb03,0x3f45658c,2 +np.float32,0x3dfe5e65,0x3eff7480,2 +np.float32,0x1,0x26a14518,2 +np.float32,0x8065e400,0xaa6d4130,2 +np.float32,0xff50e1bb,0xd4bdde07,2 +np.float32,0xbe88635a,0xbf24b7e9,2 +np.float32,0x3f46bfab,0x3f6b4908,2 +np.float32,0xbd85c3c8,0xbece3168,2 +np.float32,0xbe633f64,0xbf1afdb1,2 +np.float32,0xff2c7706,0xd4b21f2a,2 +np.float32,0xbf02816c,0xbf4c812a,2 +np.float32,0x80653aeb,0xaa6cbdab,2 +np.float32,0x3eef1d10,0x3f469e24,2 +np.float32,0x3d9944bf,0x3ed7c36a,2 +np.float32,0x1b03d4,0x2a186b2b,2 +np.float32,0x3f251b7c,0x3f5d2e76,2 +np.float32,0x3edebab0,0x3f41f937,2 +np.float32,0xfefc2148,0xd4a073ff,2 +np.float32,0x7448ee,0x2a77f051,2 +np.float32,0x3bb8a400,0x3e3637ee,2 +np.float32,0x57df36,0x2a61d527,2 +np.float32,0xfd8b9098,0xd425fccb,2 +np.float32,0x7f67627e,0x54c4744d,2 +np.float32,0x801165d7,0xaa039fba,2 +np.float32,0x53aae5,0x2a5e2bfd,2 +np.float32,0x8014012b,0xaa09e4f1,2 +np.float32,0x3f7a2d53,0x3f7e0b4b,2 +np.float32,0x3f5fb700,0x3f74c052,2 +np.float32,0x7f192a06,0x54ab366c,2 +np.float32,0x3f569611,0x3f71603b,2 +np.float32,0x25e2dc,0x2a2a9b65,2 +np.float32,0x8036465e,0xaa405342,2 +np.float32,0x804118e1,0xaa4c5785,2 +np.float32,0xbef08d3e,0xbf4703e1,2 +np.float32,0x3447e2,0x2a3df0be,2 +np.float32,0xbf2a350b,0xbf5f6f8c,2 +np.float32,0xbec87e3e,0xbf3b4a73,2 +np.float32,0xbe99a4a8,0xbf2b6412,2 +np.float32,0x2ea2ae,0x2a36d77e,2 +np.float32,0xfcb69600,0xd3e4b9e3,2 +np.float32,0x717700,0x2a75eb06,2 +np.float32,0xbf4e81ce,0xbf6e4ecc,2 +np.float32,0xbe2021ac,0xbf09ebee,2 +np.float32,0xfef94eee,0xd49fda31,2 +np.float32,0x8563e,0x29ce0015,2 +np.float32,0x7f5d0ca5,0x54c17c0f,2 +np.float32,0x3f16459a,0x3f56590f,2 +np.float32,0xbe12f7bc,0xbf0608a0,2 +np.float32,0x3f10fd3d,0x3f53ce5f,2 +np.float32,0x3ca5e1b0,0x3e8b8d96,2 +np.float32,0xbe5288e0,0xbf17181f,2 +np.float32,0xbf7360f6,0xbf7bb8c9,2 +np.float32,0x7e989d33,0x5487ba88,2 +np.float32,0x3ea7b5dc,0x3f307839,2 +np.float32,0x7e8da0c9,0x548463f0,2 +np.float32,0xfeaf7888,0xd48e3122,2 +np.float32,0x7d90402d,0x5427d321,2 +np.float32,0x72e309,0x2a76f0ee,2 +np.float32,0xbe1faa34,0xbf09c998,2 +np.float32,0xbf2b1652,0xbf5fd1f4,2 +np.float32,0x8051eb0c,0xaa5c9cca,2 +np.float32,0x7edf02bf,0x549a058e,2 +np.float32,0x7fa00000,0x7fe00000,2 +np.float32,0x3f67f873,0x3f77b9c1,2 +np.float32,0x3f276b63,0x3f5e358c,2 +np.float32,0x7eeb4bf2,0x549cccb9,2 +np.float32,0x3bfa2c,0x2a46d675,2 +np.float32,0x3e133c50,0x3f061d75,2 +np.float32,0x3ca302c0,0x3e8abe4a,2 +np.float32,0x802e152e,0xaa361dd5,2 +np.float32,0x3f504810,0x3f6efd0a,2 +np.float32,0xbf43e0b5,0xbf6a2599,2 +np.float32,0x80800000,0xaa800000,2 +np.float32,0x3f1c0980,0x3f590e03,2 +np.float32,0xbf0084f6,0xbf4b7638,2 +np.float32,0xfee72d32,0xd49be10d,2 +np.float32,0x3f3c00ed,0x3f66f763,2 +np.float32,0x80511e81,0xaa5be492,2 +np.float32,0xfdd1b8a0,0xd43e1f0d,2 +np.float32,0x7d877474,0x54245785,2 +np.float32,0x7f110bfe,0x54a82207,2 +np.float32,0xff800000,0xff800000,2 +np.float32,0x6b6a2,0x29bfa706,2 +np.float32,0xbf5bdfd9,0xbf7357b7,2 +np.float32,0x8025bfa3,0xaa2a6676,2 +np.float32,0x3a3581,0x2a44dd3a,2 +np.float32,0x542c2a,0x2a5e9e2f,2 +np.float32,0xbe1d5650,0xbf091d57,2 +np.float32,0x3e97760d,0x3f2a935e,2 +np.float32,0x7f5dcde2,0x54c1b460,2 +np.float32,0x800bde1e,0xa9e7bbaf,2 +np.float32,0x3e6b9e61,0x3f1cdf07,2 +np.float32,0x7d46c003,0x54143884,2 +np.float32,0x80073fbb,0xa9c49e67,2 +np.float32,0x503c23,0x2a5b1748,2 +np.float32,0x7eb7b070,0x549060c8,2 +np.float32,0xe9d8f,0x29f86456,2 +np.float32,0xbeedd4f0,0xbf464320,2 +np.float32,0x3f40d5d6,0x3f68eda1,2 +np.float32,0xff201f28,0xd4adc44b,2 +np.float32,0xbdf61e98,0xbefca9c7,2 +np.float32,0x3e8a0dc9,0x3f2562e3,2 +np.float32,0xbc0c0c80,0xbe515f61,2 +np.float32,0x2b3c15,0x2a3248e3,2 +np.float32,0x42a7bb,0x2a4df592,2 +np.float32,0x7f337947,0x54b480af,2 +np.float32,0xfec21db4,0xd4930f4b,2 +np.float32,0x7f4fdbf3,0x54bd8e94,2 +np.float32,0x1e2253,0x2a1e1286,2 +np.float32,0x800c4c80,0xa9ea819e,2 +np.float32,0x7e96f5b7,0x54873c88,2 +np.float32,0x7ce4e131,0x53f69ed4,2 +np.float32,0xbead8372,0xbf327b63,2 +np.float32,0x3e15ca7e,0x3f06e2f3,2 +np.float32,0xbf63e17b,0xbf7642da,2 +np.float32,0xff5bdbdb,0xd4c122f9,2 +np.float32,0x3f44411e,0x3f6a4bfd,2 +np.float32,0xfd007da0,0xd40029d2,2 +np.float32,0xbe940168,0xbf2944b7,2 +np.float32,0x80000000,0x80000000,2 +np.float32,0x3d28e356,0x3eb0e1b8,2 +np.float32,0x3eb9fcd8,0x3f36a918,2 +np.float32,0x4f6410,0x2a5a51eb,2 +np.float32,0xbdf18e30,0xbefb1775,2 +np.float32,0x32edbd,0x2a3c49e3,2 +np.float32,0x801f70a5,0xaa2052da,2 +np.float32,0x8045a045,0xaa50f98c,2 +np.float32,0xbdd6cb00,0xbef17412,2 +np.float32,0x3f118f2c,0x3f541557,2 +np.float32,0xbe65c378,0xbf1b8f95,2 +np.float32,0xfd9a9060,0xd42bbb8b,2 +np.float32,0x3f04244f,0x3f4d5b0f,2 +np.float32,0xff05214b,0xd4a3656f,2 +np.float32,0xfe342cd0,0xd463b706,2 +np.float32,0x3f3409a8,0x3f63a836,2 +np.float32,0x80205db2,0xaa21e1e5,2 +np.float32,0xbf37c982,0xbf653a03,2 +np.float32,0x3f36ce8f,0x3f64d17e,2 +np.float32,0x36ffda,0x2a412d61,2 +np.float32,0xff569752,0xd4bf94e6,2 +np.float32,0x802fdb0f,0xaa386c3a,2 +np.float32,0x7ec55a87,0x5493df71,2 +np.float32,0x7f2234c7,0x54ae847e,2 +np.float32,0xbf02df76,0xbf4cb23d,2 +np.float32,0x3d68731a,0x3ec4c156,2 +np.float32,0x8146,0x2921cd8e,2 +np.float32,0x80119364,0xaa041235,2 +np.float32,0xfe6c1c00,0xd47930b5,2 +np.float32,0x8070da44,0xaa757996,2 +np.float32,0xfefbf50c,0xd4a06a9d,2 +np.float32,0xbf01b6a8,0xbf4c170a,2 +np.float32,0x110702,0x2a02aedb,2 +np.float32,0xbf063cd4,0xbf4e6f87,2 +np.float32,0x3f1ff178,0x3f5ad9dd,2 +np.float32,0xbf76dcd4,0xbf7cead0,2 +np.float32,0x80527281,0xaa5d1620,2 +np.float32,0xfea96df8,0xd48c8a7f,2 +np.float32,0x68db02,0x2a6f88b0,2 +np.float32,0x62d971,0x2a6adec7,2 +np.float32,0x3e816fe0,0x3f21df04,2 +np.float32,0x3f586379,0x3f720cc0,2 +np.float32,0x804a3718,0xaa5577ff,2 +np.float32,0x2e2506,0x2a3632b2,2 +np.float32,0x3f297d,0x2a4a4bf3,2 +np.float32,0xbe37aba8,0xbf105f88,2 +np.float32,0xbf18b264,0xbf577ea7,2 +np.float32,0x7f50d02d,0x54bdd8b5,2 +np.float32,0xfee296dc,0xd49ad757,2 +np.float32,0x7ec5137e,0x5493cdb1,2 +np.float32,0x3f4811f4,0x3f6bce3a,2 +np.float32,0xfdff32a0,0xd44af991,2 +np.float32,0x3f6ef140,0x3f7a2ed6,2 +np.float32,0x250838,0x2a2950b5,2 +np.float32,0x25c28e,0x2a2a6ada,2 +np.float32,0xbe875e50,0xbf244e90,2 +np.float32,0x3e3bdff8,0x3f11776a,2 +np.float32,0x3e9fe493,0x3f2daf17,2 +np.float32,0x804d8599,0xaa5897d9,2 +np.float32,0x3f0533da,0x3f4de759,2 +np.float32,0xbe63023c,0xbf1aefc8,2 +np.float32,0x80636e5e,0xaa6b547f,2 +np.float32,0xff112958,0xd4a82d5d,2 +np.float32,0x3e924112,0x3f28991f,2 +np.float32,0xbe996ffc,0xbf2b507a,2 +np.float32,0x802a7cda,0xaa314081,2 +np.float32,0x8022b524,0xaa25b21e,2 +np.float32,0x3f0808c8,0x3f4f5a43,2 +np.float32,0xbef0ec2a,0xbf471e0b,2 +np.float32,0xff4c2345,0xd4bc6b3c,2 +np.float32,0x25ccc8,0x2a2a7a3b,2 +np.float32,0x7f4467d6,0x54ba0260,2 +np.float32,0x7f506539,0x54bdb846,2 +np.float32,0x412ab4,0x2a4c6a2a,2 +np.float32,0x80672c4a,0xaa6e3ef0,2 +np.float32,0xbddfb7f8,0xbef4c0ac,2 +np.float32,0xbf250bb9,0xbf5d276c,2 +np.float32,0x807dca65,0xaa7e84bd,2 +np.float32,0xbf63b8e0,0xbf763438,2 +np.float32,0xbeed1b0c,0xbf460f6b,2 +np.float32,0x8021594f,0xaa238136,2 +np.float32,0xbebc74c8,0xbf377710,2 +np.float32,0x3e9f8e3b,0x3f2d8fce,2 +np.float32,0x7f50ca09,0x54bdd6d8,2 +np.float32,0x805797c1,0xaa6197df,2 +np.float32,0x3de198f9,0x3ef56f98,2 +np.float32,0xf154d,0x29fb0392,2 +np.float32,0xff7fffff,0xd4cb2ff5,2 +np.float32,0xfed22fa8,0xd49702c4,2 +np.float32,0xbf733736,0xbf7baa64,2 +np.float32,0xbf206a8a,0xbf5b1108,2 +np.float32,0xbca49680,0xbe8b3078,2 +np.float32,0xfecba794,0xd4956e1a,2 +np.float32,0x80126582,0xaa061886,2 +np.float32,0xfee5cc82,0xd49b919f,2 +np.float32,0xbf7ad6ae,0xbf7e4491,2 +np.float32,0x7ea88c81,0x548c4c0c,2 +np.float32,0xbf493a0d,0xbf6c4255,2 +np.float32,0xbf06dda0,0xbf4ec1d4,2 +np.float32,0xff3f6e84,0xd4b86cf6,2 +np.float32,0x3e4fe093,0x3f1674b0,2 +np.float32,0x8048ad60,0xaa53fbde,2 +np.float32,0x7ebb7112,0x54915ac5,2 +np.float32,0x5bd191,0x2a652a0d,2 +np.float32,0xfe3121d0,0xd4626cfb,2 +np.float32,0x7e4421c6,0x546a3f83,2 +np.float32,0x19975b,0x2a15b14f,2 +np.float32,0x801c8087,0xaa1b2a64,2 +np.float32,0xfdf6e950,0xd448c0f6,2 +np.float32,0x74e711,0x2a786083,2 +np.float32,0xbf2b2f2e,0xbf5fdccb,2 +np.float32,0x7ed19ece,0x5496e00b,2 +np.float32,0x7f6f8322,0x54c6ba63,2 +np.float32,0x3e90316d,0x3f27cd69,2 +np.float32,0x7ecb42ce,0x54955571,2 +np.float32,0x3f6d49be,0x3f799aaf,2 +np.float32,0x8053d327,0xaa5e4f9a,2 +np.float32,0x7ebd7361,0x5491df3e,2 +np.float32,0xfdb6eed0,0xd435a7aa,2 +np.float32,0x7f3e79f4,0x54b81e4b,2 +np.float32,0xfe83afa6,0xd4813794,2 +np.float32,0x37c443,0x2a421246,2 +np.float32,0xff075a10,0xd4a44cd8,2 +np.float32,0x3ebc5fe0,0x3f377047,2 +np.float32,0x739694,0x2a77714e,2 +np.float32,0xfe832946,0xd4810b91,2 +np.float32,0x7f2638e6,0x54aff235,2 +np.float32,0xfe87f7a6,0xd4829a3f,2 +np.float32,0x3f50f3f8,0x3f6f3eb8,2 +np.float32,0x3eafa3d0,0x3f333548,2 +np.float32,0xbec26ee6,0xbf39626f,2 +np.float32,0x7e6f924f,0x547a66ff,2 +np.float32,0x7f0baa46,0x54a606f8,2 +np.float32,0xbf6dfc49,0xbf79d939,2 +np.float32,0x7f005709,0x54a1699d,2 +np.float32,0x7ee3d7ef,0x549b2057,2 +np.float32,0x803709a4,0xaa4138d7,2 +np.float32,0x3f7bf49a,0x3f7ea509,2 +np.float32,0x509db7,0x2a5b6ff5,2 +np.float32,0x7eb1b0d4,0x548ec9ff,2 +np.float32,0x7eb996ec,0x5490dfce,2 +np.float32,0xbf1fcbaa,0xbf5ac89e,2 +np.float32,0x3e2c9a98,0x3f0d69cc,2 +np.float32,0x3ea77994,0x3f306312,2 +np.float32,0x3f3cbfe4,0x3f67457c,2 +np.float32,0x8422a,0x29cd5a30,2 +np.float32,0xbd974558,0xbed6d264,2 +np.float32,0xfecee77a,0xd496387f,2 +np.float32,0x3f51876b,0x3f6f76f1,2 +np.float32,0x3b1a25,0x2a45ddad,2 +np.float32,0xfe9912f0,0xd487dd67,2 +np.float32,0x3f3ab13d,0x3f666d99,2 +np.float32,0xbf35565a,0xbf64341b,2 +np.float32,0x7d4e84aa,0x54162091,2 +np.float32,0x4c2570,0x2a574dea,2 +np.float32,0x7e82dca6,0x5480f26b,2 +np.float32,0x7f5503e7,0x54bf1c8d,2 +np.float32,0xbeb85034,0xbf361c59,2 +np.float32,0x80460a69,0xaa516387,2 +np.float32,0x805fbbab,0xaa68602c,2 +np.float32,0x7d4b4c1b,0x541557b8,2 +np.float32,0xbefa9a0a,0xbf49bfbc,2 +np.float32,0x3dbd233f,0x3ee76e09,2 +np.float32,0x58b6df,0x2a628d50,2 +np.float32,0xfcdcc180,0xd3f3aad9,2 +np.float32,0x423a37,0x2a4d8487,2 +np.float32,0xbed8b32a,0xbf403507,2 +np.float32,0x3f68e85d,0x3f780f0b,2 +np.float32,0x7ee13c4b,0x549a883d,2 +np.float32,0xff2ed4c5,0xd4b2eec1,2 +np.float32,0xbf54dadc,0xbf70b99a,2 +np.float32,0x3f78b0af,0x3f7d8a32,2 +np.float32,0x3f377372,0x3f651635,2 +np.float32,0xfdaa6178,0xd43166bc,2 +np.float32,0x8060c337,0xaa6934a6,2 +np.float32,0x7ec752c2,0x54945cf6,2 +np.float32,0xbd01a760,0xbea1f624,2 +np.float32,0x6f6599,0x2a746a35,2 +np.float32,0x3f6315b0,0x3f75f95b,2 +np.float32,0x7f2baf32,0x54b1da44,2 +np.float32,0x3e400353,0x3f1286d8,2 +np.float32,0x40d3bf,0x2a4c0f15,2 +np.float32,0x7f733aca,0x54c7c03d,2 +np.float32,0x7e5c5407,0x5473828b,2 +np.float32,0x80191703,0xaa14b56a,2 +np.float32,0xbf4fc144,0xbf6ec970,2 +np.float32,0xbf1137a7,0xbf53eacd,2 +np.float32,0x80575410,0xaa615db3,2 +np.float32,0xbd0911d0,0xbea4fe07,2 +np.float32,0x3e98534a,0x3f2ae643,2 +np.float32,0x3f3b089a,0x3f669185,2 +np.float32,0x4fc752,0x2a5aacc1,2 +np.float32,0xbef44ddc,0xbf480b6e,2 +np.float32,0x80464217,0xaa519af4,2 +np.float32,0x80445fae,0xaa4fb6de,2 +np.float32,0x80771cf4,0xaa79eec8,2 +np.float32,0xfd9182e8,0xd4284fed,2 +np.float32,0xff0a5d16,0xd4a58288,2 +np.float32,0x3f33e169,0x3f63973e,2 +np.float32,0x8021a247,0xaa23f820,2 +np.float32,0xbf362522,0xbf648ab8,2 +np.float32,0x3f457cd7,0x3f6ac95e,2 +np.float32,0xbcadf400,0xbe8dc7e2,2 +np.float32,0x80237210,0xaa26dca7,2 +np.float32,0xbf1293c9,0xbf54939f,2 +np.float32,0xbc5e73c0,0xbe744a37,2 +np.float32,0x3c03f980,0x3e4d44df,2 +np.float32,0x7da46f,0x2a7e6b20,2 +np.float32,0x5d4570,0x2a665dd0,2 +np.float32,0x3e93fbac,0x3f294287,2 +np.float32,0x7e6808fd,0x5477bfa4,2 +np.float32,0xff5aa9a6,0xd4c0c925,2 +np.float32,0xbf5206ba,0xbf6fa767,2 +np.float32,0xbf6e513e,0xbf79f6f1,2 +np.float32,0x3ed01c0f,0x3f3da20f,2 +np.float32,0xff47d93d,0xd4bb1704,2 +np.float32,0x7f466cfd,0x54baa514,2 +np.float32,0x665e10,0x2a6d9fc8,2 +np.float32,0x804d0629,0xaa5820e8,2 +np.float32,0x7e0beaa0,0x54514e7e,2 +np.float32,0xbf7fcb6c,0xbf7fee78,2 +np.float32,0x3f6c5b03,0x3f7946dd,2 +np.float32,0x3e941504,0x3f294c30,2 +np.float32,0xbf2749ad,0xbf5e26a1,2 +np.float32,0xfec2a00a,0xd493302d,2 +np.float32,0x3f15a358,0x3f560bce,2 +np.float32,0x3f15c4e7,0x3f561bcd,2 +np.float32,0xfedc8692,0xd499728c,2 +np.float32,0x7e8f6902,0x5484f180,2 +np.float32,0x7f663d62,0x54c42136,2 +np.float32,0x8027ea62,0xaa2d99b4,2 +np.float32,0x3f3d093d,0x3f67636d,2 +np.float32,0x7f118c33,0x54a85382,2 +np.float32,0x803e866a,0xaa499d43,2 +np.float32,0x80053632,0xa9b02407,2 +np.float32,0xbf36dd66,0xbf64d7af,2 +np.float32,0xbf560358,0xbf71292b,2 +np.float32,0x139a8,0x29596bc0,2 +np.float32,0xbe04f75c,0xbf01a26c,2 +np.float32,0xfe1c3268,0xd45920fa,2 +np.float32,0x7ec77f72,0x5494680c,2 +np.float32,0xbedde724,0xbf41bbba,2 +np.float32,0x3e81dbe0,0x3f220bfd,2 +np.float32,0x800373ac,0xa99989d4,2 +np.float32,0x3f7f859a,0x3f7fd72d,2 +np.float32,0x3eb9dc7e,0x3f369e80,2 +np.float32,0xff5f8eb7,0xd4c236b1,2 +np.float32,0xff1c03cb,0xd4ac44ac,2 +np.float32,0x18cfe1,0x2a14285b,2 +np.float32,0x7f21b075,0x54ae54fd,2 +np.float32,0xff490bd8,0xd4bb7680,2 +np.float32,0xbf15dc22,0xbf5626de,2 +np.float32,0xfe1d5a10,0xd459a9a3,2 +np.float32,0x750544,0x2a7875e4,2 +np.float32,0x8023d5df,0xaa2778b3,2 +np.float32,0x3e42aa08,0x3f1332b2,2 +np.float32,0x3ecaa751,0x3f3bf60d,2 +np.float32,0x0,0x0,2 +np.float32,0x80416da6,0xaa4cb011,2 +np.float32,0x3f4ea9ae,0x3f6e5e22,2 +np.float32,0x2113f4,0x2a230f8e,2 +np.float32,0x3f35c2e6,0x3f64619a,2 +np.float32,0xbf50db8a,0xbf6f3564,2 +np.float32,0xff4d5cea,0xd4bccb8a,2 +np.float32,0x7ee54420,0x549b72d2,2 +np.float32,0x64ee68,0x2a6c81f7,2 +np.float32,0x5330da,0x2a5dbfc2,2 +np.float32,0x80047f88,0xa9a7b467,2 +np.float32,0xbda01078,0xbedae800,2 +np.float32,0xfe96d05a,0xd487315f,2 +np.float32,0x8003cc10,0xa99e7ef4,2 +np.float32,0x8007b4ac,0xa9c8aa3d,2 +np.float32,0x5d4bcf,0x2a66630e,2 +np.float32,0xfdd0c0b0,0xd43dd403,2 +np.float32,0xbf7a1d82,0xbf7e05f0,2 +np.float32,0x74ca33,0x2a784c0f,2 +np.float32,0x804f45e5,0xaa5a3640,2 +np.float32,0x7e6d16aa,0x547988c4,2 +np.float32,0x807d5762,0xaa7e3714,2 +np.float32,0xfecf93d0,0xd4966229,2 +np.float32,0xfecbd25c,0xd4957890,2 +np.float32,0xff7db31c,0xd4ca93b0,2 +np.float32,0x3dac9e18,0x3ee07c4a,2 +np.float32,0xbf4b2d28,0xbf6d0509,2 +np.float32,0xbd4f4c50,0xbebd62e0,2 +np.float32,0xbd2eac40,0xbeb2e0ee,2 +np.float32,0x3d01b69b,0x3ea1fc7b,2 +np.float32,0x7ec63902,0x549416ed,2 +np.float32,0xfcc47700,0xd3ea616d,2 +np.float32,0xbf5ddec2,0xbf7413a1,2 +np.float32,0xff6a6110,0xd4c54c52,2 +np.float32,0xfdfae2a0,0xd449d335,2 +np.float32,0x7e54868c,0x547099cd,2 +np.float32,0x802b5b88,0xaa327413,2 +np.float32,0x80440e72,0xaa4f647a,2 +np.float32,0x3e313c94,0x3f0eaad5,2 +np.float32,0x3ebb492a,0x3f3715a2,2 +np.float32,0xbef56286,0xbf4856d5,2 +np.float32,0x3f0154ba,0x3f4be3a0,2 +np.float32,0xff2df86c,0xd4b2a376,2 +np.float32,0x3ef6a850,0x3f48af57,2 +np.float32,0x3d8d33e1,0x3ed1f22d,2 +np.float32,0x4dd9b9,0x2a58e615,2 +np.float32,0x7f1caf83,0x54ac83c9,2 +np.float32,0xbf7286b3,0xbf7b6d73,2 +np.float32,0x80064f88,0xa9bbbd9f,2 +np.float32,0xbf1f55fa,0xbf5a92db,2 +np.float32,0x546a81,0x2a5ed516,2 +np.float32,0xbe912880,0xbf282d0a,2 +np.float32,0x5df587,0x2a66ee6e,2 +np.float32,0x801f706c,0xaa205279,2 +np.float32,0x58cb6d,0x2a629ece,2 +np.float32,0xfe754f8c,0xd47c62da,2 +np.float32,0xbefb6f4c,0xbf49f8e7,2 +np.float32,0x80000001,0xa6a14518,2 +np.float32,0xbf067837,0xbf4e8df4,2 +np.float32,0x3e8e715c,0x3f271ee4,2 +np.float32,0x8009de9b,0xa9d9ebc8,2 +np.float32,0xbf371ff1,0xbf64f36e,2 +np.float32,0x7f5ce661,0x54c170e4,2 +np.float32,0x3f3c47d1,0x3f671467,2 +np.float32,0xfea5e5a6,0xd48b8eb2,2 +np.float32,0xff62b17f,0xd4c31e15,2 +np.float32,0xff315932,0xd4b3c98f,2 +np.float32,0xbf1c3ca8,0xbf5925b9,2 +np.float32,0x7f800000,0x7f800000,2 +np.float32,0xfdf20868,0xd4476c3b,2 +np.float32,0x5b790e,0x2a64e052,2 +np.float32,0x3f5ddf4e,0x3f7413d4,2 +np.float32,0x7f1a3182,0x54ab9861,2 +np.float32,0x3f4b906e,0x3f6d2b9d,2 +np.float32,0x7ebac760,0x54912edb,2 +np.float32,0x7f626d3f,0x54c30a7e,2 +np.float32,0x3e27b058,0x3f0c0edc,2 +np.float32,0x8041e69c,0xaa4d2de8,2 +np.float32,0x3f42cee0,0x3f69b84a,2 +np.float32,0x7ec5fe83,0x5494085b,2 +np.float32,0x9d3e6,0x29d99cde,2 +np.float32,0x3edc50c0,0x3f41452d,2 +np.float32,0xbf2c463a,0xbf60562c,2 +np.float32,0x800bfa33,0xa9e871e8,2 +np.float32,0x7c9f2c,0x2a7dba4d,2 +np.float32,0x7f2ef9fd,0x54b2fb73,2 +np.float32,0x80741847,0xaa77cdb9,2 +np.float32,0x7e9c462a,0x5488ce1b,2 +np.float32,0x3ea47ec1,0x3f2f55a9,2 +np.float32,0x7f311c43,0x54b3b4f5,2 +np.float32,0x3d8f4c73,0x3ed2facd,2 +np.float32,0x806d7bd2,0xaa7301ef,2 +np.float32,0xbf633d24,0xbf760799,2 +np.float32,0xff4f9a3f,0xd4bd7a99,2 +np.float32,0x3f6021ca,0x3f74e73d,2 +np.float32,0x7e447015,0x546a5eac,2 +np.float32,0x6bff3c,0x2a71e711,2 +np.float32,0xe9c9f,0x29f85f06,2 +np.float32,0x8009fe14,0xa9dad277,2 +np.float32,0x807cf79c,0xaa7df644,2 +np.float32,0xff440e1b,0xd4b9e608,2 +np.float32,0xbddf9a50,0xbef4b5db,2 +np.float32,0x7f3b1c39,0x54b706fc,2 +np.float32,0x3c7471a0,0x3e7c16a7,2 +np.float32,0x8065b02b,0xaa6d18ee,2 +np.float32,0x7f63a3b2,0x54c36379,2 +np.float32,0xbe9c9d92,0xbf2c7d33,2 +np.float32,0x3d93aad3,0x3ed51a2e,2 +np.float32,0xbf41b040,0xbf694571,2 +np.float32,0x80396b9e,0xaa43f899,2 +np.float64,0x800fa025695f404b,0xaaa4000ff64bb00c,2 +np.float64,0xbfecc00198f98003,0xbfeee0b623fbd94b,2 +np.float64,0x7f9eeb60b03dd6c0,0x55291bf8554bb303,2 +np.float64,0x3fba74485634e890,0x3fde08710bdb148d,2 +np.float64,0xbfdd9a75193b34ea,0xbfe8bf711660a2f5,2 +np.float64,0xbfcf92e17a3f25c4,0xbfe4119eda6f3773,2 +np.float64,0xbfe359e2ba66b3c6,0xbfeb0f7ae97ea142,2 +np.float64,0x20791a5640f24,0x2a9441f13d262bed,2 +np.float64,0x3fe455fbfae8abf8,0x3feb830d63e1022c,2 +np.float64,0xbd112b7b7a226,0x2aa238c097ec269a,2 +np.float64,0x93349ba126694,0x2aa0c363cd74465a,2 +np.float64,0x20300cd440602,0x2a9432b4f4081209,2 +np.float64,0x3fdcfae677b9f5cc,0x3fe892a9ee56fe8d,2 +np.float64,0xbfefaae3f7bf55c8,0xbfefe388066132c4,2 +np.float64,0x1a7d6eb634faf,0x2a92ed9851d29ab5,2 +np.float64,0x7fd5308d39aa6119,0x553be444e30326c6,2 +np.float64,0xff811c7390223900,0xd5205cb404952fa7,2 +np.float64,0x80083d24aff07a4a,0xaaa0285cf764d898,2 +np.float64,0x800633810ccc6703,0xaa9d65341419586b,2 +np.float64,0x800ff456223fe8ac,0xaaa423bbcc24dff1,2 +np.float64,0x7fde5c99aebcb932,0x553f71be7d6d9daa,2 +np.float64,0x3fed961c4b3b2c39,0x3fef2ca146270cac,2 +np.float64,0x7fe744d30c6e89a5,0x554220a4cdc78e62,2 +np.float64,0x3fd8f527c7b1ea50,0x3fe76101085be1cb,2 +np.float64,0xbfc96a14b232d428,0xbfe2ab1a8962606c,2 +np.float64,0xffe85f540cf0bea7,0xd54268dff964519a,2 +np.float64,0x800e3be0fe7c77c2,0xaaa3634efd7f020b,2 +np.float64,0x3feb90d032f721a0,0x3fee72a4579e8b12,2 +np.float64,0xffe05674aaa0ace9,0xd5401c9e3fb4abcf,2 +np.float64,0x3fefc2e32c3f85c6,0x3fefeb940924bf42,2 +np.float64,0xbfecfd89e9f9fb14,0xbfeef6addf73ee49,2 +np.float64,0xf5862717eb0c5,0x2aa3e1428780382d,2 +np.float64,0xffc3003b32260078,0xd53558f92202dcdb,2 +np.float64,0x3feb4c152c36982a,0x3fee5940f7da0825,2 +np.float64,0x3fe7147b002e28f6,0x3fecb2948f46d1e3,2 +np.float64,0x7fe00ad9b4a015b2,0x5540039d15e1da54,2 +np.float64,0x8010000000000000,0xaaa428a2f98d728b,2 +np.float64,0xbfd3a41bfea74838,0xbfe595ab45b1be91,2 +np.float64,0x7fdbfd6e5537fadc,0x553e9a6e1107b8d0,2 +np.float64,0x800151d9d9a2a3b4,0xaa918cd8fb63f40f,2 +np.float64,0x7fe6828401ad0507,0x5541eda05dcd1fcf,2 +np.float64,0x3fdae1e7a1b5c3d0,0x3fe7f711e72ecc35,2 +np.float64,0x7fdf4936133e926b,0x553fc29c8d5edea3,2 +np.float64,0x80079de12d4f3bc3,0xaa9f7b06a9286da4,2 +np.float64,0x3fe1261cade24c39,0x3fe9fe09488e417a,2 +np.float64,0xbfc20dce21241b9c,0xbfe0a842fb207a28,2 +np.float64,0x3fe3285dfa2650bc,0x3feaf85215f59ef9,2 +np.float64,0x7fe42b93aea85726,0x554148c3c3bb35e3,2 +np.float64,0xffe6c74e7f6d8e9c,0xd541ffd13fa36dbd,2 +np.float64,0x3fe73ea139ee7d42,0x3fecc402242ab7d3,2 +np.float64,0xffbd4b46be3a9690,0xd53392de917c72e4,2 +np.float64,0x800caed8df395db2,0xaaa2a811a02e6be4,2 +np.float64,0x800aacdb6c9559b7,0xaaa19d6fbc8feebf,2 +np.float64,0x839fb4eb073f7,0x2aa0264b98327c12,2 +np.float64,0xffd0157ba9a02af8,0xd5397157a11c0d05,2 +np.float64,0x7fddc8ff173b91fd,0x553f3e7663fb2ac7,2 +np.float64,0x67b365facf66d,0x2a9dd4d838b0d853,2 +np.float64,0xffe12e7fc7225cff,0xd5406272a83a8e1b,2 +np.float64,0x7fea5b19a034b632,0x5542e567658b3e36,2 +np.float64,0x124989d824932,0x2a90ba8dc7a39532,2 +np.float64,0xffe12ef098225de0,0xd54062968450a078,2 +np.float64,0x3fea2f44a3f45e8a,0x3fedee3c461f4716,2 +np.float64,0x3fe6b033e66d6068,0x3fec88c8035e06b1,2 +np.float64,0x3fe928a2ccf25146,0x3fed88d4cde7a700,2 +np.float64,0x3feead27e97d5a50,0x3fef8d7537d82e60,2 +np.float64,0x8003ab80b6875702,0xaa98adfedd7715a9,2 +np.float64,0x45a405828b481,0x2a9a1fa99a4eff1e,2 +np.float64,0x8002ddebad85bbd8,0xaa96babfda4e0031,2 +np.float64,0x3fc278c32824f186,0x3fe0c8e7c979fbd5,2 +np.float64,0x2e10fffc5c221,0x2a96c30a766d06fa,2 +np.float64,0xffd6ba8c2ead7518,0xd53c8d1d92bc2788,2 +np.float64,0xbfeb5ec3a036bd87,0xbfee602bbf0a0d01,2 +np.float64,0x3fed5bd58f7ab7ab,0x3fef181bf591a4a7,2 +np.float64,0x7feb5274a5b6a4e8,0x55431fcf81876218,2 +np.float64,0xaf8fd6cf5f1fb,0x2aa1c6edbb1e2aaf,2 +np.float64,0x7fece718f179ce31,0x55437c74efb90933,2 +np.float64,0xbfa3c42d0c278860,0xbfd5a16407c77e73,2 +np.float64,0x800b5cff0576b9fe,0xaaa1fc4ecb0dec4f,2 +np.float64,0x800be89ae557d136,0xaaa244d115fc0963,2 +np.float64,0x800d2578f5ba4af2,0xaaa2e18a3a3fc134,2 +np.float64,0x80090ff93e321ff3,0xaaa0add578e3cc3c,2 +np.float64,0x28c5a240518c,0x2a81587cccd7e202,2 +np.float64,0x7fec066929780cd1,0x55434971435d1069,2 +np.float64,0x7fc84d4d15309a99,0x55372c204515694f,2 +np.float64,0xffe070a75de0e14e,0xd54025365046dad2,2 +np.float64,0x7fe5b27cc36b64f9,0x5541b5b822f0b6ca,2 +np.float64,0x3fdea35ac8bd46b6,0x3fe9086a0fb792c2,2 +np.float64,0xbfe79996f7af332e,0xbfece9571d37a5b3,2 +np.float64,0xffdfb47f943f6900,0xd53fe6c14c3366db,2 +np.float64,0xc015cf63802ba,0x2aa2517164d075f4,2 +np.float64,0x7feba98948375312,0x5543340b5b1f1181,2 +np.float64,0x8008678e6550cf1d,0xaaa043e7cea90da5,2 +np.float64,0x3fb11b92fa223726,0x3fd9f8b53be4d90b,2 +np.float64,0x7fc9b18cf0336319,0x55379b42da882047,2 +np.float64,0xbfe5043e736a087d,0xbfebd0c67db7a8e3,2 +np.float64,0x7fde88546a3d10a8,0x553f80cfe5bcf5fe,2 +np.float64,0x8006a6c82dcd4d91,0xaa9e171d182ba049,2 +np.float64,0xbfa0f707ac21ee10,0xbfd48e5d3faa1699,2 +np.float64,0xbfe7716bffaee2d8,0xbfecd8e6abfb8964,2 +np.float64,0x9511ccab2a23a,0x2aa0d56d748f0313,2 +np.float64,0x8003ddb9b847bb74,0xaa991ca06fd9d308,2 +np.float64,0x80030710fac60e23,0xaa9725845ac95fe8,2 +np.float64,0xffece5bbaeb9cb76,0xd5437c2670f894f4,2 +np.float64,0x3fd9be5c72b37cb9,0x3fe79f2e932a5708,2 +np.float64,0x1f050cca3e0a3,0x2a93f36499fe5228,2 +np.float64,0x3fd5422becaa8458,0x3fe6295d6150df58,2 +np.float64,0xffd72c050e2e580a,0xd53cbc52d73b495f,2 +np.float64,0xbfe66d5235ecdaa4,0xbfec6ca27e60bf23,2 +np.float64,0x17ac49a42f58a,0x2a923b5b757087a0,2 +np.float64,0xffd39edc40273db8,0xd53b2f7bb99b96bf,2 +np.float64,0x7fde6cf009bcd9df,0x553f77614eb30d75,2 +np.float64,0x80042b4c3fa85699,0xaa99c05fbdd057db,2 +np.float64,0xbfde5547f8bcaa90,0xbfe8f3147d67a940,2 +np.float64,0xbfdd02f9bf3a05f4,0xbfe894f2048aa3fe,2 +np.float64,0xbfa20ec82c241d90,0xbfd4fd02ee55aac7,2 +np.float64,0x8002f670f8c5ece3,0xaa96fad7e53dd479,2 +np.float64,0x80059f24d7eb3e4a,0xaa9c7312dae0d7bc,2 +np.float64,0x7fe6ae7423ad5ce7,0x5541f9430be53062,2 +np.float64,0xe135ea79c26be,0x2aa350d8f8c526e1,2 +np.float64,0x3fec188ce4f8311a,0x3feea44d21c23f68,2 +np.float64,0x800355688286aad2,0xaa97e6ca51eb8357,2 +np.float64,0xa2d6530b45acb,0x2aa15635bbd366e8,2 +np.float64,0x600e0150c01c1,0x2a9d1456ea6c239c,2 +np.float64,0x8009c30863338611,0xaaa118f94b188bcf,2 +np.float64,0x3fe7e4c0dfefc982,0x3fed07e8480b8c07,2 +np.float64,0xbfddac6407bb58c8,0xbfe8c46f63a50225,2 +np.float64,0xbc85e977790bd,0x2aa2344636ed713d,2 +np.float64,0xfff0000000000000,0xfff0000000000000,2 +np.float64,0xffcd1570303a2ae0,0xd5389a27d5148701,2 +np.float64,0xbf937334d026e660,0xbfd113762e4e29a7,2 +np.float64,0x3fdbfdaa9b37fb55,0x3fe84a425fdff7df,2 +np.float64,0xffc10800f5221000,0xd5349535ffe12030,2 +np.float64,0xaf40f3755e81f,0x2aa1c443af16cd27,2 +np.float64,0x800f7da34f7efb47,0xaaa3f14bf25fc89f,2 +np.float64,0xffe4a60125a94c02,0xd5416b764a294128,2 +np.float64,0xbf8e25aa903c4b40,0xbfcf5ebc275b4789,2 +np.float64,0x3fca681bbb34d038,0x3fe2e882bcaee320,2 +np.float64,0xbfd0f3c9c1a1e794,0xbfe48d0df7b47572,2 +np.float64,0xffeb99b49d373368,0xd5433060dc641910,2 +np.float64,0x3fe554fb916aa9f8,0x3febf437cf30bd67,2 +np.float64,0x80079518d0af2a32,0xaa9f6ee87044745a,2 +np.float64,0x5e01a8a0bc036,0x2a9cdf0badf222c3,2 +np.float64,0xbfea9831b3f53064,0xbfee1601ee953ab3,2 +np.float64,0xbfc369d1a826d3a4,0xbfe110b675c311e0,2 +np.float64,0xa82e640d505cd,0x2aa1863d4e523b9c,2 +np.float64,0x3fe506d70a2a0dae,0x3febd1eba3aa83fa,2 +np.float64,0xcbacba7197598,0x2aa2adeb9927f1f2,2 +np.float64,0xc112d6038225b,0x2aa25978f12038b0,2 +np.float64,0xffa7f5f44c2febf0,0xd52d0ede02d4e18b,2 +np.float64,0x8006f218e34de433,0xaa9e870cf373b4eb,2 +np.float64,0xffe6d9a5d06db34b,0xd54204a4adc608c7,2 +np.float64,0x7fe717210eae2e41,0x554214bf3e2b5228,2 +np.float64,0xbfdd4b45cdba968c,0xbfe8a94c7f225f8e,2 +np.float64,0x883356571066b,0x2aa055ab0b2a8833,2 +np.float64,0x3fe307fc02a60ff8,0x3feae9175053288f,2 +np.float64,0x3fefa985f77f530c,0x3fefe31289446615,2 +np.float64,0x8005698a98aad316,0xaa9c17814ff7d630,2 +np.float64,0x3fea77333c74ee66,0x3fee098ba70e10fd,2 +np.float64,0xbfd1d00b0023a016,0xbfe4e497fd1cbea1,2 +np.float64,0x80009b0c39813619,0xaa8b130a6909cc3f,2 +np.float64,0x3fdbeb896fb7d714,0x3fe84502ba5437f8,2 +np.float64,0x3fb6e7e3562dcfc7,0x3fdca00d35c389ad,2 +np.float64,0xb2d46ebf65a8e,0x2aa1e2fe158d0838,2 +np.float64,0xbfd5453266aa8a64,0xbfe62a6a74c8ef6e,2 +np.float64,0x7fe993aa07732753,0x5542b5438bf31cb7,2 +np.float64,0xbfda5a098cb4b414,0xbfe7ce6d4d606203,2 +np.float64,0xbfe40c3ce068187a,0xbfeb61a32c57a6d0,2 +np.float64,0x3fcf17671d3e2ed0,0x3fe3f753170ab686,2 +np.float64,0xbfe4f814b6e9f02a,0xbfebcb67c60b7b08,2 +np.float64,0x800efedf59fdfdbf,0xaaa3ba4ed44ad45a,2 +np.float64,0x800420b556e8416b,0xaa99aa7fb14edeab,2 +np.float64,0xbf6e4ae6403c9600,0xbfc3cb2b29923989,2 +np.float64,0x3fda5c760a34b8ec,0x3fe7cf2821c52391,2 +np.float64,0x7f898faac0331f55,0x5522b44a01408188,2 +np.float64,0x3fd55af4b7aab5e9,0x3fe631f6d19503b3,2 +np.float64,0xbfa30a255c261450,0xbfd55caf0826361d,2 +np.float64,0x7fdfb801343f7001,0x553fe7ee50b9199a,2 +np.float64,0x7fa89ee91c313dd1,0x552d528ca2a4d659,2 +np.float64,0xffea72921d34e524,0xd542eb01af2e470d,2 +np.float64,0x3feddf0f33fbbe1e,0x3fef462b67fc0a91,2 +np.float64,0x3fe36700b566ce01,0x3feb1596caa8eff7,2 +np.float64,0x7fe6284a25ac5093,0x5541d58be3956601,2 +np.float64,0xffda16f7c8b42df0,0xd53de4f722485205,2 +np.float64,0x7f9355b94026ab72,0x552578cdeb41d2ca,2 +np.float64,0xffd3a9b022275360,0xd53b347b02dcea21,2 +np.float64,0x3fcb7f4f4a36fe9f,0x3fe32a40e9f6c1aa,2 +np.float64,0x7fdb958836372b0f,0x553e746103f92111,2 +np.float64,0x3fd37761c0a6eec4,0x3fe5853c5654027e,2 +np.float64,0x3fe449f1a2e893e4,0x3feb7d9e4eacc356,2 +np.float64,0x80077dfbef0efbf9,0xaa9f4ed788d2fadd,2 +np.float64,0x4823aa7890476,0x2a9a6eb4b653bad5,2 +np.float64,0xbfede01a373bc034,0xbfef468895fbcd29,2 +np.float64,0xbfe2bac5f125758c,0xbfeac4811c4dd66f,2 +np.float64,0x3fec10373af8206e,0x3feea14529e0f178,2 +np.float64,0x3fe305e30ca60bc6,0x3feae81a2f9d0302,2 +np.float64,0xa9668c5f52cd2,0x2aa1910e3a8f2113,2 +np.float64,0xbfd98b1717b3162e,0xbfe78f75995335d2,2 +np.float64,0x800fa649c35f4c94,0xaaa402ae79026a8f,2 +np.float64,0xbfb07dacf620fb58,0xbfd9a7d33d93a30f,2 +np.float64,0x80015812f382b027,0xaa91a843e9c85c0e,2 +np.float64,0x3fc687d96c2d0fb3,0x3fe1ef0ac16319c5,2 +np.float64,0xbfecad2ecd795a5e,0xbfeed9f786697af0,2 +np.float64,0x1608c1242c119,0x2a91cd11e9b4ccd2,2 +np.float64,0x6df775e8dbeef,0x2a9e6ba8c71130eb,2 +np.float64,0xffe96e9332b2dd26,0xd542ac342d06299b,2 +np.float64,0x7fecb6a3b8396d46,0x5543718af8162472,2 +np.float64,0x800d379f893a6f3f,0xaaa2ea36bbcb9308,2 +np.float64,0x3f924cdb202499b6,0x3fd0bb90af8d1f79,2 +np.float64,0x0,0x0,2 +np.float64,0x7feaf3b365f5e766,0x5543099a160e2427,2 +np.float64,0x3fea169ed0742d3e,0x3fede4d526e404f8,2 +np.float64,0x7feaf5f2f775ebe5,0x55430a2196c5f35a,2 +np.float64,0xbfc80d4429301a88,0xbfe2541f2ddd3334,2 +np.float64,0xffc75203b32ea408,0xd536db2837068689,2 +np.float64,0xffed2850e63a50a1,0xd5438b1217b72b8a,2 +np.float64,0x7fc16b0e7f22d61c,0x5534bcd0bfddb6f0,2 +np.float64,0x7feee8ed09fdd1d9,0x5543ed5b3ca483ab,2 +np.float64,0x7fb6c7ee662d8fdc,0x5531fffb5d46dafb,2 +np.float64,0x3fd77cebf8aef9d8,0x3fe6e9242e2bd29d,2 +np.float64,0x3f81c33f70238680,0x3fca4c7f3c9848f7,2 +np.float64,0x3fd59fea92ab3fd5,0x3fe649c1558cadd5,2 +np.float64,0xffeba82d4bf7505a,0xd54333bad387f7bd,2 +np.float64,0xffd37630e1a6ec62,0xd53b1ca62818c670,2 +np.float64,0xffec2c1e70b8583c,0xd5435213dcd27c22,2 +np.float64,0x7fec206971f840d2,0x55434f6660a8ae41,2 +np.float64,0x3fed2964adba52c9,0x3fef0642fe72e894,2 +np.float64,0xffd08e30d6211c62,0xd539b060e0ae02da,2 +np.float64,0x3e5f976c7cbf4,0x2a992e6ff991a122,2 +np.float64,0xffe6eee761adddce,0xd5420a393c67182f,2 +np.float64,0xbfe8ec9a31f1d934,0xbfed714426f58147,2 +np.float64,0x7fefffffffffffff,0x554428a2f98d728b,2 +np.float64,0x3fb3ae8b2c275d16,0x3fdb36b81b18a546,2 +np.float64,0x800f73df4dfee7bf,0xaaa3ed1a3e2cf49c,2 +np.float64,0xffd0c8873b21910e,0xd539ce6a3eab5dfd,2 +np.float64,0x3facd6c49439ad80,0x3fd8886f46335df1,2 +np.float64,0x3935859c726b2,0x2a98775f6438dbb1,2 +np.float64,0x7feed879fbfdb0f3,0x5543e9d1ac239469,2 +np.float64,0xbfe84dd990f09bb3,0xbfed323af09543b1,2 +np.float64,0xbfe767cc5a6ecf98,0xbfecd4f39aedbacb,2 +np.float64,0xffd8bd91d5b17b24,0xd53d5eb3734a2609,2 +np.float64,0xbfe13edeb2a27dbe,0xbfea0a856f0b9656,2 +np.float64,0xd933dd53b267c,0x2aa3158784e428c9,2 +np.float64,0xbfef6fef987edfdf,0xbfefcfb1c160462b,2 +np.float64,0x8009eeda4893ddb5,0xaaa13268a41045b1,2 +np.float64,0xab48c7a156919,0x2aa1a1a9c124c87d,2 +np.float64,0xa997931d532f3,0x2aa192bfe5b7bbb4,2 +np.float64,0xffe39ce8b1e739d1,0xd5411fa1c5c2cbd8,2 +np.float64,0x7e7ac2f6fcf59,0x2a9fdf6f263a9e9f,2 +np.float64,0xbfee1e35a6fc3c6b,0xbfef5c25d32b4047,2 +np.float64,0xffe5589c626ab138,0xd5419d220cc9a6da,2 +np.float64,0x7fe12509bf224a12,0x55405f7036dc5932,2 +np.float64,0xa6f15ba94de2c,0x2aa17b3367b1fc1b,2 +np.float64,0x3fca8adbfa3515b8,0x3fe2f0ca775749e5,2 +np.float64,0xbfcb03aa21360754,0xbfe30d5b90ca41f7,2 +np.float64,0x3fefafb2da7f5f66,0x3fefe5251aead4e7,2 +np.float64,0xffd90a59d23214b4,0xd53d7cf63a644f0e,2 +np.float64,0x3fba499988349333,0x3fddf84154fab7e5,2 +np.float64,0x800a76a0bc54ed42,0xaaa17f68cf67f2fa,2 +np.float64,0x3fea33d15bb467a3,0x3fedeff7f445b2ff,2 +np.float64,0x8005d9b0726bb362,0xaa9cd48624afeca9,2 +np.float64,0x7febf42e9a77e85c,0x55434541d8073376,2 +np.float64,0xbfedfc4469bbf889,0xbfef505989f7ee7d,2 +np.float64,0x8001211f1422423f,0xaa90a9889d865349,2 +np.float64,0x800e852f7fdd0a5f,0xaaa3845f11917f8e,2 +np.float64,0xffefd613c87fac27,0xd5441fd17ec669b4,2 +np.float64,0x7fed2a74543a54e8,0x55438b8c637da8b8,2 +np.float64,0xb83d50ff707aa,0x2aa210b4fc11e4b2,2 +np.float64,0x10000000000000,0x2aa428a2f98d728b,2 +np.float64,0x474ad9208e97,0x2a84e5a31530368a,2 +np.float64,0xffd0c5498ea18a94,0xd539ccc0e5cb425e,2 +np.float64,0x8001a8e9c82351d4,0xaa92f1aee6ca5b7c,2 +np.float64,0xd28db1e5a51b6,0x2aa2e328c0788f4a,2 +np.float64,0x3bf734ac77ee7,0x2a98da65c014b761,2 +np.float64,0x3fe56e17c96adc30,0x3febff2b6b829b7a,2 +np.float64,0x7783113eef063,0x2a9f46c3f09eb42c,2 +np.float64,0x3fd69d4e42ad3a9d,0x3fe69f83a21679f4,2 +np.float64,0x3fd34f4841a69e90,0x3fe5766b3c771616,2 +np.float64,0x3febb49895b76931,0x3fee7fcb603416c9,2 +np.float64,0x7fe8d6cb55f1ad96,0x554286c3b3bf4313,2 +np.float64,0xbfe67c6ba36cf8d8,0xbfec730218f2e284,2 +np.float64,0xffef9d97723f3b2e,0xd54413e38b6c29be,2 +np.float64,0x12d8cd2a25b1b,0x2a90e5ccd37b8563,2 +np.float64,0x81fe019103fc0,0x2aa01524155e73c5,2 +np.float64,0x7fe95d546f72baa8,0x5542a7fabfd425ff,2 +np.float64,0x800e742f1f9ce85e,0xaaa37cbe09e1f874,2 +np.float64,0xffd96bd3a732d7a8,0xd53da3086071264a,2 +np.float64,0x4ef2691e9de4e,0x2a9b3d316047fd6d,2 +np.float64,0x1a91684c3522e,0x2a92f25913c213de,2 +np.float64,0x3d5151b87aa2b,0x2a9909dbd9a44a84,2 +np.float64,0x800d9049435b2093,0xaaa31424e32d94a2,2 +np.float64,0xffe5b25fcc2b64bf,0xd541b5b0416b40b5,2 +np.float64,0xffe0eb784c21d6f0,0xd5404d083c3d6bc6,2 +np.float64,0x8007ceefbf0f9de0,0xaa9fbe0d739368b4,2 +np.float64,0xb78529416f0b,0x2a8ca3b29b5b3f18,2 +np.float64,0x7fba61130034c225,0x5532e6d4ca0f2918,2 +np.float64,0x3fba8d67ae351acf,0x3fde11efd6239b09,2 +np.float64,0x3fe7f24c576fe498,0x3fed0d63947a854d,2 +np.float64,0x2bb58dec576b3,0x2a965de7fca12aff,2 +np.float64,0xbfe86ceec4f0d9de,0xbfed3ea7f1d084e2,2 +np.float64,0x7fd1a7f7bca34fee,0x553a3f01b67fad2a,2 +np.float64,0x3fd9a43acfb34874,0x3fe7972dc5d8dfd6,2 +np.float64,0x7fd9861acdb30c35,0x553dad3b1bbb3b4d,2 +np.float64,0xffecc0c388398186,0xd54373d3b903deec,2 +np.float64,0x3fa6f86e9c2df0e0,0x3fd6bdbe40fcf710,2 +np.float64,0x800ddd99815bbb33,0xaaa33820d2f889bb,2 +np.float64,0x7fe087089b610e10,0x55402c868348a6d3,2 +np.float64,0x3fdf43d249be87a5,0x3fe933d29fbf7c23,2 +np.float64,0x7fe4f734c7a9ee69,0x5541822e56c40725,2 +np.float64,0x3feb39a9d3b67354,0x3fee526bf1f69f0e,2 +np.float64,0x3fe61454a0ec28a9,0x3fec46d7c36f7566,2 +np.float64,0xbfeafaa0a375f541,0xbfee3af2e49d457a,2 +np.float64,0x3fda7378e1b4e6f0,0x3fe7d613a3f92c40,2 +np.float64,0xe3e31c5fc7c64,0x2aa3645c12e26171,2 +np.float64,0xbfe97a556df2f4ab,0xbfeda8aa84cf3544,2 +np.float64,0xff612f9c80225f00,0xd514a51e5a2a8a97,2 +np.float64,0x800c51c8a0f8a391,0xaaa279fe7d40b50b,2 +np.float64,0xffd6f9d2312df3a4,0xd53ca783a5f8d110,2 +np.float64,0xbfead48bd7f5a918,0xbfee2cb2f89c5e57,2 +np.float64,0x800f5949e89eb294,0xaaa3e1a67a10cfef,2 +np.float64,0x800faf292b7f5e52,0xaaa40675e0c96cfd,2 +np.float64,0xbfedc238453b8470,0xbfef3c179d2d0209,2 +np.float64,0x3feb0443c5760888,0x3fee3e8bf29089c2,2 +np.float64,0xb26f69e164ded,0x2aa1df9f3dd7d765,2 +np.float64,0x3fcacdc053359b80,0x3fe300a67765b667,2 +np.float64,0x3fe8b274647164e8,0x3fed5a4cd4da8155,2 +np.float64,0x291e6782523ce,0x2a95ea7ac1b13a68,2 +np.float64,0xbfc4fc094e29f814,0xbfe1838671fc8513,2 +np.float64,0x3fbf1301f23e2600,0x3fdfb03a6f13e597,2 +np.float64,0xffeb36554ab66caa,0xd543193d8181e4f9,2 +np.float64,0xbfd969a52db2d34a,0xbfe78528ae61f16d,2 +np.float64,0x800cccd04d3999a1,0xaaa2b6b7a2d2d2d6,2 +np.float64,0x808eb4cb011d7,0x2aa005effecb2b4a,2 +np.float64,0x7fe839b3f9b07367,0x55425f61e344cd6d,2 +np.float64,0xbfeb25b6ed764b6e,0xbfee4b0234fee365,2 +np.float64,0xffefffffffffffff,0xd54428a2f98d728b,2 +np.float64,0xbfe01305da60260c,0xbfe9700b784af7e9,2 +np.float64,0xffcbf36b0a37e6d8,0xd538474b1d74ffe1,2 +np.float64,0xffaeebe3e83dd7c0,0xd52fa2e8dabf7209,2 +np.float64,0xbfd9913bf0b32278,0xbfe7915907aab13c,2 +np.float64,0xbfe7d125d9efa24c,0xbfecfff563177706,2 +np.float64,0xbfee98d23cbd31a4,0xbfef867ae393e446,2 +np.float64,0x3fe30efb67e61df6,0x3feaec6344633d11,2 +np.float64,0x1,0x2990000000000000,2 +np.float64,0x7fd5524fd3aaa49f,0x553bf30d18ab877e,2 +np.float64,0xc98b403f93168,0x2aa29d2fadb13c07,2 +np.float64,0xffe57080046ae100,0xd541a3b1b687360e,2 +np.float64,0x7fe20bade5e4175b,0x5540a79b94294f40,2 +np.float64,0x3fe155400a22aa80,0x3fea15c45f5b5837,2 +np.float64,0x7fe428dc8f6851b8,0x554147fd2ce93cc1,2 +np.float64,0xffefb77eb67f6efc,0xd544195dcaff4980,2 +np.float64,0x3fe49e733b293ce6,0x3feba394b833452a,2 +np.float64,0x38e01e3e71c05,0x2a986b2c955bad21,2 +np.float64,0x7fe735eb376e6bd5,0x55421cc51290d92d,2 +np.float64,0xbfd81d8644b03b0c,0xbfe71ce6d6fbd51a,2 +np.float64,0x8009a32325134647,0xaaa10645d0e6b0d7,2 +np.float64,0x56031ab8ac064,0x2a9c074be40b1f80,2 +np.float64,0xff8989aa30331340,0xd522b2d319a0ac6e,2 +np.float64,0xbfd6c183082d8306,0xbfe6ab8ffb3a8293,2 +np.float64,0x7ff8000000000000,0x7ff8000000000000,2 +np.float64,0xbfe17b68b1e2f6d2,0xbfea28dac8e0c457,2 +np.float64,0x3fbb50e42236a1c8,0x3fde5b090d51e3bd,2 +np.float64,0xffc2bb7cbf2576f8,0xd5353f1b3571c17f,2 +np.float64,0xbfe7576bca6eaed8,0xbfecce388241f47c,2 +np.float64,0x3fe7b52b04ef6a56,0x3fecf495bef99e7e,2 +np.float64,0xffe5511af82aa236,0xd5419b11524e8350,2 +np.float64,0xbfe66d5edf2cdabe,0xbfec6ca7d7b5be8c,2 +np.float64,0xc84a0ba790942,0x2aa29346f16a2cb4,2 +np.float64,0x6db5e7a0db6be,0x2a9e659c0e8244a0,2 +np.float64,0x7fef8f7b647f1ef6,0x554410e67af75d27,2 +np.float64,0xbfe2b4ada7e5695c,0xbfeac1997ec5a064,2 +np.float64,0xbfe99372e03326e6,0xbfedb2662b287543,2 +np.float64,0x3fa45d352428ba6a,0x3fd5d8a895423abb,2 +np.float64,0x3fa029695c2052d3,0x3fd439f858998886,2 +np.float64,0xffe0a9bd3261537a,0xd54037d0cd8bfcda,2 +np.float64,0xbfef83e09a7f07c1,0xbfefd66a4070ce73,2 +np.float64,0x7fee3dcc31fc7b97,0x5543c8503869407e,2 +np.float64,0xffbd16f1603a2de0,0xd533872fa5be978b,2 +np.float64,0xbfe8173141b02e62,0xbfed1c478614c6f4,2 +np.float64,0xbfef57aa277eaf54,0xbfefc77fdab27771,2 +np.float64,0x7fe883a02f31073f,0x554271ff0e3208da,2 +np.float64,0xe3adb63bc75b7,0x2aa362d833d0e41c,2 +np.float64,0x8001c430bac38862,0xaa93575026d26510,2 +np.float64,0x12fb347225f67,0x2a90f00eb9edb3fe,2 +np.float64,0x3fe53f83cbaa7f08,0x3febead40de452c2,2 +np.float64,0xbfe7f67227efece4,0xbfed0f10e32ad220,2 +np.float64,0xb8c5b45d718b7,0x2aa2152912cda86d,2 +np.float64,0x3fd23bb734a4776e,0x3fe50e5d3008c095,2 +np.float64,0x8001fd558ee3faac,0xaa941faa1f7ed450,2 +np.float64,0xffe6bbeda9ed77db,0xd541fcd185a63afa,2 +np.float64,0x4361d79086c3c,0x2a99d692237c30b7,2 +np.float64,0xbfd012f004a025e0,0xbfe43093e290fd0d,2 +np.float64,0xffe1d8850423b10a,0xd54097cf79d8d01e,2 +np.float64,0x3fccf4df7939e9bf,0x3fe37f8cf8be6436,2 +np.float64,0x8000546bc6c0a8d8,0xaa861bb3588556f2,2 +np.float64,0xbfecb4d6ba7969ae,0xbfeedcb6239135fe,2 +np.float64,0xbfaeb425cc3d6850,0xbfd90cfc103bb896,2 +np.float64,0x800ec037ec7d8070,0xaaa39eae8bde9774,2 +np.float64,0xbfeeaf863dfd5f0c,0xbfef8e4514772a8a,2 +np.float64,0xffec67c6c4b8cf8d,0xd5435fad89f900cf,2 +np.float64,0x3fda4498da348932,0x3fe7c7f6b3f84048,2 +np.float64,0xbfd05fd3dea0bfa8,0xbfe4509265a9b65f,2 +np.float64,0x3fe42cc713a8598e,0x3feb706ba9cd533c,2 +np.float64,0xec22d4d7d845b,0x2aa39f8cccb9711c,2 +np.float64,0x7fda30606c3460c0,0x553deea865065196,2 +np.float64,0xbfd58cba8bab1976,0xbfe64327ce32d611,2 +np.float64,0xadd521c75baa4,0x2aa1b7efce201a98,2 +np.float64,0x7fed43c1027a8781,0x55439131832b6429,2 +np.float64,0x800bee278fb7dc4f,0xaaa247a71e776db4,2 +np.float64,0xbfe9be5dd2737cbc,0xbfedc2f9501755b0,2 +np.float64,0x8003f4854447e90b,0xaa994d9b5372b13b,2 +np.float64,0xbfe5d0f867eba1f1,0xbfec29f8dd8b33a4,2 +np.float64,0x3fd79102d5af2206,0x3fe6efaa7a1efddb,2 +np.float64,0xbfeae783c835cf08,0xbfee33cdb4a44e81,2 +np.float64,0x3fcf1713e83e2e28,0x3fe3f7414753ddfb,2 +np.float64,0xffe5ab3cff2b567a,0xd541b3bf0213274a,2 +np.float64,0x7fe0fc65d8a1f8cb,0x554052761ac96386,2 +np.float64,0x7e81292efd026,0x2a9fdff8c01ae86f,2 +np.float64,0x80091176039222ec,0xaaa0aebf0565dfa6,2 +np.float64,0x800d2bf5ab5a57ec,0xaaa2e4a4c31e7e29,2 +np.float64,0xffd1912ea923225e,0xd53a33b2856726ab,2 +np.float64,0x800869918ed0d323,0xaaa0453408e1295d,2 +np.float64,0xffba0898fa341130,0xd532d19b202a9646,2 +np.float64,0xbfe09fac29613f58,0xbfe9b9687b5811a1,2 +np.float64,0xbfbd4ae82e3a95d0,0xbfdf1220f6f0fdfa,2 +np.float64,0xffea11d27bb423a4,0xd542d3d3e1522474,2 +np.float64,0xbfe6b05705ad60ae,0xbfec88d6bcab2683,2 +np.float64,0x3fe624a3f2ec4948,0x3fec4dcc78ddf871,2 +np.float64,0x53483018a6907,0x2a9bba8f92006b69,2 +np.float64,0xbfec0a6eeb7814de,0xbfee9f2a741248d7,2 +np.float64,0x3fe8c8ce6371919d,0x3fed63250c643482,2 +np.float64,0xbfe26b0ef964d61e,0xbfea9e511db83437,2 +np.float64,0xffa0408784208110,0xd52987f62c369ae9,2 +np.float64,0xffc153abc322a758,0xd534b384b5c5fe63,2 +np.float64,0xbfbdce88a63b9d10,0xbfdf4065ef0b01d4,2 +np.float64,0xffed4a4136fa9482,0xd54392a450f8b0af,2 +np.float64,0x8007aa18748f5432,0xaa9f8bd2226d4299,2 +np.float64,0xbfdab4d3e8b569a8,0xbfe7e9a5402540e5,2 +np.float64,0x7fe68914f92d1229,0x5541ef5e78fa35de,2 +np.float64,0x800a538bb1b4a718,0xaaa16bc487711295,2 +np.float64,0xffe02edbc8605db7,0xd5400f8f713df890,2 +np.float64,0xffe8968053712d00,0xd54276b9cc7f460a,2 +np.float64,0x800a4ce211d499c5,0xaaa1680491deb40c,2 +np.float64,0x3f988080f8310102,0x3fd2713691e99329,2 +np.float64,0xf64e42a7ec9c9,0x2aa3e6a7af780878,2 +np.float64,0xff73cc7100279900,0xd51b4478c3409618,2 +np.float64,0x71e6722ce3ccf,0x2a9ec76ddf296ce0,2 +np.float64,0x8006ca16ab0d942e,0xaa9e4bfd862af570,2 +np.float64,0x8000000000000000,0x8000000000000000,2 +np.float64,0xbfed373e02ba6e7c,0xbfef0b2b7bb767b3,2 +np.float64,0xa6cb0f694d962,0x2aa179dd16b0242b,2 +np.float64,0x7fec14626cf828c4,0x55434ca55b7c85d5,2 +np.float64,0x3fcda404513b4808,0x3fe3a68e8d977752,2 +np.float64,0xbfeb94995f772933,0xbfee74091d288b81,2 +np.float64,0x3fce2299a13c4530,0x3fe3c2603f28d23b,2 +np.float64,0xffd07f4534a0fe8a,0xd539a8a6ebc5a603,2 +np.float64,0x7fdb1c651e3638c9,0x553e478a6385c86b,2 +np.float64,0x3fec758336f8eb06,0x3feec5f3b92c8b28,2 +np.float64,0x796fc87cf2dfa,0x2a9f7184a4ad8c49,2 +np.float64,0x3fef9ba866ff3750,0x3fefde6a446fc2cd,2 +np.float64,0x964d26c72c9a5,0x2aa0e143f1820179,2 +np.float64,0xbfef6af750bed5ef,0xbfefce04870a97bd,2 +np.float64,0x3fe2f3961aa5e72c,0x3feadf769321a3ff,2 +np.float64,0xbfd6b706e9ad6e0e,0xbfe6a8141c5c3b5d,2 +np.float64,0x7fe0ecc40a21d987,0x55404d72c2b46a82,2 +np.float64,0xbfe560d19deac1a3,0xbfebf962681a42a4,2 +np.float64,0xbfea37170ab46e2e,0xbfedf136ee9df02b,2 +np.float64,0xbfebf78947b7ef12,0xbfee9847ef160257,2 +np.float64,0x800551f8312aa3f1,0xaa9bee7d3aa5491b,2 +np.float64,0xffed2513897a4a26,0xd5438a58c4ae28ec,2 +np.float64,0x7fd962d75cb2c5ae,0x553d9f8a0c2016f3,2 +np.float64,0x3fefdd8512bfbb0a,0x3feff47d8da7424d,2 +np.float64,0xbfefa5b43bff4b68,0xbfefe1ca42867af0,2 +np.float64,0xbfc8a2853531450c,0xbfe279bb7b965729,2 +np.float64,0x800c8843bc391088,0xaaa2951344e7b29b,2 +np.float64,0x7fe22587bae44b0e,0x5540af8bb58cfe86,2 +np.float64,0xbfe159fae822b3f6,0xbfea182394eafd8d,2 +np.float64,0xbfe6fdfd50edfbfa,0xbfeca93f2a3597d0,2 +np.float64,0xbfe5cd5afaeb9ab6,0xbfec286a8ce0470f,2 +np.float64,0xbfc84bb97f309774,0xbfe263ef0f8f1f6e,2 +np.float64,0x7fd9c1e548b383ca,0x553dc4556874ecb9,2 +np.float64,0x7fda43d33bb487a5,0x553df60f61532fc0,2 +np.float64,0xbfe774bd25eee97a,0xbfecda42e8578c1f,2 +np.float64,0x800df1f5ab9be3ec,0xaaa34184712e69db,2 +np.float64,0xbff0000000000000,0xbff0000000000000,2 +np.float64,0x3fe14ec21b629d84,0x3fea128244215713,2 +np.float64,0x7fc1ce7843239cf0,0x5534e3fa8285b7b8,2 +np.float64,0xbfe922b204724564,0xbfed86818687d649,2 +np.float64,0x3fc58924fb2b1248,0x3fe1aa715ff6ebbf,2 +np.float64,0x8008b637e4d16c70,0xaaa0760b53abcf46,2 +np.float64,0xffbf55bd4c3eab78,0xd53404a23091a842,2 +np.float64,0x9f6b4a753ed6a,0x2aa136ef9fef9596,2 +np.float64,0xbfd11da7f8a23b50,0xbfe49deb493710d8,2 +np.float64,0x800a2f07fcd45e10,0xaaa157237c98b4f6,2 +np.float64,0x3fdd4defa4ba9bdf,0x3fe8aa0bcf895f4f,2 +np.float64,0x7fe9b0ab05f36155,0x5542bc5335414473,2 +np.float64,0x3fe89c97de313930,0x3fed51a1189b8982,2 +np.float64,0x3fdd45c8773a8b91,0x3fe8a7c2096fbf5a,2 +np.float64,0xbfeb6f64daf6deca,0xbfee665167ef43ad,2 +np.float64,0xffdf9da1c4bf3b44,0xd53fdf141944a983,2 +np.float64,0x3fde092ed0bc125c,0x3fe8de25bfbfc2db,2 +np.float64,0xbfcb21f96b3643f4,0xbfe3147904c258cf,2 +np.float64,0x800c9c934f993927,0xaaa29f17c43f021b,2 +np.float64,0x9b91814d37230,0x2aa11329e59bf6b0,2 +np.float64,0x3fe28a7e0b6514fc,0x3feaad6d23e2eadd,2 +np.float64,0xffecf38395f9e706,0xd5437f3ee1cd61e4,2 +np.float64,0x3fcade92a935bd25,0x3fe3049f4c1da1d0,2 +np.float64,0x800ab25d95d564bc,0xaaa1a076d7c66e04,2 +np.float64,0xffc0989e1e21313c,0xd53467f3b8158298,2 +np.float64,0x3fd81523eeb02a48,0x3fe71a38d2da8a82,2 +np.float64,0x7fe5b9dd402b73ba,0x5541b7b9b8631010,2 +np.float64,0x2c160d94582c3,0x2a966e51b503a3d1,2 +np.float64,0x2c416ffa5882f,0x2a9675aaef8b29c4,2 +np.float64,0x7fefe2ff01bfc5fd,0x55442289faf22b86,2 +np.float64,0xbfd469bf5d28d37e,0xbfe5dd239ffdc7eb,2 +np.float64,0xbfdd56f3eabaade8,0xbfe8ac93244ca17b,2 +np.float64,0xbfe057b89160af71,0xbfe9941557340bb3,2 +np.float64,0x800c50e140b8a1c3,0xaaa2798ace9097ee,2 +np.float64,0xbfda5a8984b4b514,0xbfe7ce93d65a56b0,2 +np.float64,0xbfcd6458323ac8b0,0xbfe39872514127bf,2 +np.float64,0x3fefb1f5ebff63ec,0x3fefe5e761b49b89,2 +np.float64,0x3fea3abc1df47578,0x3fedf29a1c997863,2 +np.float64,0x7fcb4a528e3694a4,0x553815f169667213,2 +np.float64,0x8c77da7b18efc,0x2aa080e52bdedb54,2 +np.float64,0x800e5dde4c5cbbbd,0xaaa372b16fd8b1ad,2 +np.float64,0x3fd2976038a52ec0,0x3fe5316b4f79fdbc,2 +np.float64,0x69413a0ed2828,0x2a9dfacd9cb44286,2 +np.float64,0xbfebbac0bdb77582,0xbfee820d9288b631,2 +np.float64,0x1a12aa7c34256,0x2a92d407e073bbfe,2 +np.float64,0xbfc41a27c3283450,0xbfe143c8665b0d3c,2 +np.float64,0xffe4faa41369f548,0xd54183230e0ce613,2 +np.float64,0xbfdeae81f23d5d04,0xbfe90b734bf35b68,2 +np.float64,0x3fc984ba58330975,0x3fe2b19e9052008e,2 +np.float64,0x7fe6e51b8d2dca36,0x554207a74ae2bb39,2 +np.float64,0x80081a58a81034b2,0xaaa0117d4aff11c8,2 +np.float64,0x7fde3fddfe3c7fbb,0x553f67d0082acc67,2 +np.float64,0x3fac7c999038f933,0x3fd86ec2f5dc3aa4,2 +np.float64,0x7fa26b4c4c24d698,0x552a9e6ea8545c18,2 +np.float64,0x3fdacd06e6b59a0e,0x3fe7f0dc0e8f9c6d,2 +np.float64,0x80064b62cbec96c6,0xaa9d8ac0506fdd05,2 +np.float64,0xb858116170b1,0x2a8caea703d9ccc8,2 +np.float64,0xbfe8d94ccef1b29a,0xbfed69a8782cbf3d,2 +np.float64,0x8005607d6a6ac0fc,0xaa9c07cf8620b037,2 +np.float64,0xbfe66a52daacd4a6,0xbfec6b5e403e6864,2 +np.float64,0x7fc398c2e0273185,0x5535918245894606,2 +np.float64,0x74b2d7dce965c,0x2a9f077020defdbc,2 +np.float64,0x7fe8f7a4d9b1ef49,0x55428eeae210e8eb,2 +np.float64,0x80027deddc84fbdc,0xaa95b11ff9089745,2 +np.float64,0xffeba2a94e774552,0xd5433273f6568902,2 +np.float64,0x80002f8259405f05,0xaa8240b68d7b9dc4,2 +np.float64,0xbfdf0d84883e1b0a,0xbfe92532c69c5802,2 +np.float64,0xbfcdfa7b6b3bf4f8,0xbfe3b997a84d0914,2 +np.float64,0x800c18b04e183161,0xaaa25d46d60b15c6,2 +np.float64,0xffeaf1e37c35e3c6,0xd543092cd929ac19,2 +np.float64,0xbfc5aa07752b5410,0xbfe1b36ab5ec741f,2 +np.float64,0x3fe5c491d1eb8924,0x3fec24a1c3f6a178,2 +np.float64,0xbfeb736937f6e6d2,0xbfee67cd296e6fa9,2 +np.float64,0xffec3d5718787aad,0xd5435602e1a2cc43,2 +np.float64,0x7fe71e1da86e3c3a,0x55421691ead882cb,2 +np.float64,0x3fdd6ed0c93adda2,0x3fe8b341d066c43c,2 +np.float64,0x7fbe3d7a203c7af3,0x5533c83e53283430,2 +np.float64,0x3fdc20cb56384197,0x3fe854676360aba9,2 +np.float64,0xb7a1ac636f436,0x2aa20b9d40d66e78,2 +np.float64,0x3fb1491bb8229237,0x3fda0fabad1738ee,2 +np.float64,0xbfdf9c0ce73f381a,0xbfe94b716dbe35ee,2 +np.float64,0xbfbd4f0ad23a9e18,0xbfdf1397329a2dce,2 +np.float64,0xbfe4e0caac69c196,0xbfebc119b8a181cd,2 +np.float64,0x5753641aaea6d,0x2a9c2ba3e92b0cd2,2 +np.float64,0x72bb814ae5771,0x2a9eda92fada66de,2 +np.float64,0x57ed8f5aafdb3,0x2a9c3c2e1d42e609,2 +np.float64,0xffec33359c38666a,0xd54353b2acd0daf1,2 +np.float64,0x3fa5fe6e8c2bfce0,0x3fd66a0b3bf2720a,2 +np.float64,0xffe2dc8d7ca5b91a,0xd540e6ebc097d601,2 +np.float64,0x7fd99d260eb33a4b,0x553db626c9c75f78,2 +np.float64,0xbfe2dd73e425bae8,0xbfead4fc4b93a727,2 +np.float64,0xdcd4a583b9a95,0x2aa33094c9a17ad7,2 +np.float64,0x7fb0af6422215ec7,0x553039a606e8e64f,2 +np.float64,0x7fdfab6227bf56c3,0x553fe3b26164aeda,2 +np.float64,0x1e4d265e3c9a6,0x2a93cba8a1a8ae6d,2 +np.float64,0xbfdc7d097238fa12,0xbfe86ee2f24fd473,2 +np.float64,0x7fe5d35d29eba6b9,0x5541bea5878bce2b,2 +np.float64,0xffcb886a903710d4,0xd53828281710aab5,2 +np.float64,0xffe058c7ffe0b190,0xd5401d61e9a7cbcf,2 +np.float64,0x3ff0000000000000,0x3ff0000000000000,2 +np.float64,0xffd5b1c1132b6382,0xd53c1c839c098340,2 +np.float64,0x3fe2e7956725cf2b,0x3fead9c907b9d041,2 +np.float64,0x800a8ee293951dc6,0xaaa18ce3f079f118,2 +np.float64,0x7febcd3085b79a60,0x55433c47e1f822ad,2 +np.float64,0x3feb0e14cd761c2a,0x3fee423542102546,2 +np.float64,0x3fb45e6d0628bcda,0x3fdb86db67d0c992,2 +np.float64,0x7fa836e740306dce,0x552d2907cb8118b2,2 +np.float64,0x3fd15ba25b22b745,0x3fe4b6b018409d78,2 +np.float64,0xbfb59980ce2b3300,0xbfdc1206274cb51d,2 +np.float64,0x3fdef1b87fbde371,0x3fe91dafc62124a1,2 +np.float64,0x7fed37a4337a6f47,0x55438e7e0b50ae37,2 +np.float64,0xffe6c87633ad90ec,0xd542001f216ab448,2 +np.float64,0x8008d2548ab1a4a9,0xaaa087ad272d8e17,2 +np.float64,0xbfd1d6744da3ace8,0xbfe4e71965adda74,2 +np.float64,0xbfb27f751224fee8,0xbfdaa82132775406,2 +np.float64,0x3fe2b336ae65666d,0x3feac0e6b13ec2d2,2 +np.float64,0xffc6bac2262d7584,0xd536a951a2eecb49,2 +np.float64,0x7fdb661321b6cc25,0x553e62dfd7fcd3f3,2 +np.float64,0xffe83567d5706acf,0xd5425e4bb5027568,2 +np.float64,0xbf7f0693e03e0d00,0xbfc9235314d53f82,2 +np.float64,0x3feb32b218766564,0x3fee4fd5847f3722,2 +np.float64,0x3fec25d33df84ba6,0x3feea91fcd4aebab,2 +np.float64,0x7fe17abecb22f57d,0x55407a8ba661207c,2 +np.float64,0xbfe5674b1eeace96,0xbfebfc351708dc70,2 +np.float64,0xbfe51a2d2f6a345a,0xbfebda702c9d302a,2 +np.float64,0x3fec05584af80ab0,0x3fee9d502a7bf54d,2 +np.float64,0xffda8871dcb510e4,0xd53e10105f0365b5,2 +np.float64,0xbfc279c31824f388,0xbfe0c9354d871484,2 +np.float64,0x1cbed61e397dc,0x2a937364712cd518,2 +np.float64,0x800787d198af0fa4,0xaa9f5c847affa1d2,2 +np.float64,0x80079f6d65af3edc,0xaa9f7d2863368bbd,2 +np.float64,0xb942f1e97285e,0x2aa2193e0c513b7f,2 +np.float64,0x7fe9078263320f04,0x554292d85dee2c18,2 +np.float64,0xbfe4de0761a9bc0f,0xbfebbfe04116b829,2 +np.float64,0xbfdbe6f3fc37cde8,0xbfe843aea59a0749,2 +np.float64,0xffcb6c0de136d81c,0xd5381fd9c525b813,2 +np.float64,0x9b6bda9336d7c,0x2aa111c924c35386,2 +np.float64,0x3fe17eece422fdda,0x3fea2a9bacd78607,2 +np.float64,0xd8011c49b0024,0x2aa30c87574fc0c6,2 +np.float64,0xbfc0a08b3f214118,0xbfe034d48f0d8dc0,2 +np.float64,0x3fd60adb1eac15b8,0x3fe66e42e4e7e6b5,2 +np.float64,0x80011d68ea023ad3,0xaa909733befbb962,2 +np.float64,0xffb35ac32426b588,0xd5310c4be1c37270,2 +np.float64,0x3fee8b56c9bd16ae,0x3fef81d8d15f6939,2 +np.float64,0x3fdc10a45e382149,0x3fe84fbe4cf11e68,2 +np.float64,0xbfc85dc45e30bb88,0xbfe2687b5518abde,2 +np.float64,0x3fd53b85212a770a,0x3fe6270d6d920d0f,2 +np.float64,0x800fc158927f82b1,0xaaa40e303239586f,2 +np.float64,0x11af5e98235ed,0x2a908b04a790083f,2 +np.float64,0xbfe2a097afe54130,0xbfeab80269eece99,2 +np.float64,0xbfd74ac588ae958c,0xbfe6d8ca3828d0b8,2 +np.float64,0xffea18ab2ef43156,0xd542d579ab31df1e,2 +np.float64,0xbfecda7058f9b4e1,0xbfeeea29c33b7913,2 +np.float64,0x3fc4ac56ed2958b0,0x3fe16d3e2bd7806d,2 +np.float64,0x3feccc898cb99913,0x3feee531f217dcfa,2 +np.float64,0xffeb3a64c5b674c9,0xd5431a30a41f0905,2 +np.float64,0x3fe5a7ee212b4fdc,0x3fec1844af9076fc,2 +np.float64,0x80080fdb52301fb7,0xaaa00a8b4274db67,2 +np.float64,0x800b3e7e47d67cfd,0xaaa1ec2876959852,2 +np.float64,0x80063fb8ee2c7f73,0xaa9d7875c9f20d6f,2 +np.float64,0x7fdacf80d0b59f01,0x553e2acede4c62a8,2 +np.float64,0x401e9b24803d4,0x2a996a0a75d0e093,2 +np.float64,0x3fe6c29505ed852a,0x3fec907a6d8c10af,2 +np.float64,0x8005c04ee2cb809f,0xaa9caa9813faef46,2 +np.float64,0xbfe1360f21e26c1e,0xbfea06155d6985b6,2 +np.float64,0xffc70606682e0c0c,0xd536c239b9d4be0a,2 +np.float64,0x800e639afefcc736,0xaaa37547d0229a26,2 +np.float64,0x3fe5589290aab125,0x3febf5c925c4e6db,2 +np.float64,0x8003b59330276b27,0xaa98c47e44524335,2 +np.float64,0x800d67ec22dacfd8,0xaaa301251b6a730a,2 +np.float64,0x7fdaeb5025b5d69f,0x553e35397dfe87eb,2 +np.float64,0x3fdae32a24b5c654,0x3fe7f771bc108f6c,2 +np.float64,0xffe6c1fc93ad83f8,0xd541fe6a6a716756,2 +np.float64,0xbfd7b9c1d32f7384,0xbfe6fcdae563d638,2 +np.float64,0x800e1bea06fc37d4,0xaaa354c0bf61449c,2 +np.float64,0xbfd78f097aaf1e12,0xbfe6ef068329bdf4,2 +np.float64,0x7fea6a400874d47f,0x5542e905978ad722,2 +np.float64,0x8008b4377cb1686f,0xaaa074c87eee29f9,2 +np.float64,0x8002f3fb8d45e7f8,0xaa96f47ac539b614,2 +np.float64,0xbfcf2b3fd13e5680,0xbfe3fb91c0cc66ad,2 +np.float64,0xffecca2f5279945e,0xd54375f361075927,2 +np.float64,0x7ff0000000000000,0x7ff0000000000000,2 +np.float64,0x7f84d5a5a029ab4a,0x552178d1d4e8640e,2 +np.float64,0x3fea8a4b64351497,0x3fee10c332440eb2,2 +np.float64,0x800fe01ac1dfc036,0xaaa41b34d91a4bee,2 +np.float64,0x3fc0b3d8872167b1,0x3fe03b178d354f8d,2 +np.float64,0x5ee8b0acbdd17,0x2a9cf69f2e317729,2 +np.float64,0x8006ef0407adde09,0xaa9e82888f3dd83e,2 +np.float64,0x7fdbb08a07b76113,0x553e7e4e35b938b9,2 +np.float64,0x49663f9c92cc9,0x2a9a95e0affe5108,2 +np.float64,0x7fd9b87e79b370fc,0x553dc0b5cff3dc7d,2 +np.float64,0xbfd86ae657b0d5cc,0xbfe73584d02bdd2b,2 +np.float64,0x3fd4d4a13729a942,0x3fe6030a962aaaf8,2 +np.float64,0x7fcc246bcb3848d7,0x5538557309449bba,2 +np.float64,0xbfdc86a7d5b90d50,0xbfe871a2983c2a29,2 +np.float64,0xd2a6e995a54dd,0x2aa2e3e9c0fdd6c0,2 +np.float64,0x3f92eb447825d680,0x3fd0eb4fd2ba16d2,2 +np.float64,0x800d4001697a8003,0xaaa2ee358661b75c,2 +np.float64,0x3fd3705fd1a6e0c0,0x3fe582a6f321d7d6,2 +np.float64,0xbfcfdf51533fbea4,0xbfe421c3bdd9f2a3,2 +np.float64,0x3fe268e87964d1d1,0x3fea9d47e08aad8a,2 +np.float64,0x24b8901e49713,0x2a951adeefe7b31b,2 +np.float64,0x3fedb35d687b66bb,0x3fef36e440850bf8,2 +np.float64,0x3fb7ab5cbe2f56c0,0x3fdcf097380721c6,2 +np.float64,0x3f8c4eaa10389d54,0x3fceb7ecb605b73b,2 +np.float64,0xbfed831ed6fb063e,0xbfef25f462a336f1,2 +np.float64,0x7fd8c52112318a41,0x553d61b0ee609f58,2 +np.float64,0xbfe71c4ff76e38a0,0xbfecb5d32e789771,2 +np.float64,0xbfe35fb7b166bf70,0xbfeb12328e75ee6b,2 +np.float64,0x458e1a3a8b1c4,0x2a9a1cebadc81342,2 +np.float64,0x8003c1b3ad478368,0xaa98df5ed060b28c,2 +np.float64,0x7ff4000000000000,0x7ffc000000000000,2 +np.float64,0x7fe17098c162e131,0x5540775a9a3a104f,2 +np.float64,0xbfd95cb71732b96e,0xbfe7812acf7ea511,2 +np.float64,0x8000000000000001,0xa990000000000000,2 +np.float64,0xbfde0e7d9ebc1cfc,0xbfe8df9ca9e49a5b,2 +np.float64,0xffef4f67143e9ecd,0xd5440348a6a2f231,2 +np.float64,0x7fe37d23c826fa47,0x5541165de17caa03,2 +np.float64,0xbfcc0e5f85381cc0,0xbfe34b44b0deefe9,2 +np.float64,0x3fe858f1c470b1e4,0x3fed36ab90557d89,2 +np.float64,0x800e857278fd0ae5,0xaaa3847d13220545,2 +np.float64,0x3febd31a66f7a635,0x3fee8af90e66b043,2 +np.float64,0x7fd3fde1b127fbc2,0x553b5b186a49b968,2 +np.float64,0x3fd3dabb8b27b577,0x3fe5a99b446bed26,2 +np.float64,0xffeb4500f1768a01,0xd5431cab828e254a,2 +np.float64,0xffccca8fc6399520,0xd53884f8b505e79e,2 +np.float64,0xffeee9406b7dd280,0xd543ed6d27a1a899,2 +np.float64,0xffecdde0f0f9bbc1,0xd5437a6258b14092,2 +np.float64,0xe6b54005cd6a8,0x2aa378c25938dfda,2 +np.float64,0x7fe610f1022c21e1,0x5541cf460b972925,2 +np.float64,0xbfe5a170ec6b42e2,0xbfec1576081e3232,2 diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv new file mode 100644 index 0000000000000000000000000000000000000000..4e0a63e8e2c5061d6a158f9347a6085e5e8c4ffa --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-exp2.csv @@ -0,0 +1,1429 @@ +dtype,input,output,ulperrortol +np.float32,0xbdfe94b0,0x3f6adda6,2 +np.float32,0x3f20f8f8,0x3fc5ec69,2 +np.float32,0x7040b5,0x3f800000,2 +np.float32,0x30ec5,0x3f800000,2 +np.float32,0x3eb63070,0x3fa3ce29,2 +np.float32,0xff4dda3d,0x0,2 +np.float32,0x805b832f,0x3f800000,2 +np.float32,0x3e883fb7,0x3f99ed8c,2 +np.float32,0x3f14d71f,0x3fbf8708,2 +np.float32,0xff7b1e55,0x0,2 +np.float32,0xbf691ac6,0x3f082fa2,2 +np.float32,0x7ee3e6ab,0x7f800000,2 +np.float32,0xbec6e2b4,0x3f439248,2 +np.float32,0xbf5f5ec2,0x3f0bd2c0,2 +np.float32,0x8025cc2c,0x3f800000,2 +np.float32,0x7e0d7672,0x7f800000,2 +np.float32,0xff4bbc5c,0x0,2 +np.float32,0xbd94fb30,0x3f73696b,2 +np.float32,0x6cc079,0x3f800000,2 +np.float32,0x803cf080,0x3f800000,2 +np.float32,0x71d418,0x3f800000,2 +np.float32,0xbf24a442,0x3f23ec1e,2 +np.float32,0xbe6c9510,0x3f5a1e1d,2 +np.float32,0xbe8fb284,0x3f52be38,2 +np.float32,0x7ea64754,0x7f800000,2 +np.float32,0x7fc00000,0x7fc00000,2 +np.float32,0x80620cfd,0x3f800000,2 +np.float32,0x3f3e20e8,0x3fd62e72,2 +np.float32,0x3f384600,0x3fd2d00e,2 +np.float32,0xff362150,0x0,2 +np.float32,0xbf349fa8,0x3f1cfaef,2 +np.float32,0xbf776cf2,0x3f0301a6,2 +np.float32,0x8021fc60,0x3f800000,2 +np.float32,0xbdb75280,0x3f70995c,2 +np.float32,0x7e9363a6,0x7f800000,2 +np.float32,0x7e728422,0x7f800000,2 +np.float32,0xfe91edc2,0x0,2 +np.float32,0x3f5f438c,0x3fea491d,2 +np.float32,0x3f2afae9,0x3fcb5c1f,2 +np.float32,0xbef8e766,0x3f36c448,2 +np.float32,0xba522c00,0x3f7fdb97,2 +np.float32,0xff18ee8c,0x0,2 +np.float32,0xbee8c5f4,0x3f3acd44,2 +np.float32,0x3e790448,0x3f97802c,2 +np.float32,0x3e8c9541,0x3f9ad571,2 +np.float32,0xbf03fa9f,0x3f331460,2 +np.float32,0x801ee053,0x3f800000,2 +np.float32,0xbf773230,0x3f03167f,2 +np.float32,0x356fd9,0x3f800000,2 +np.float32,0x8009cd88,0x3f800000,2 +np.float32,0x7f2bac51,0x7f800000,2 +np.float32,0x4d9eeb,0x3f800000,2 +np.float32,0x3133,0x3f800000,2 +np.float32,0x7f4290e0,0x7f800000,2 +np.float32,0xbf5e6523,0x3f0c3161,2 +np.float32,0x3f19182e,0x3fc1bf10,2 +np.float32,0x7e1248bb,0x7f800000,2 +np.float32,0xff5f7aae,0x0,2 +np.float32,0x7e8557b5,0x7f800000,2 +np.float32,0x26fc7f,0x3f800000,2 +np.float32,0x80397d61,0x3f800000,2 +np.float32,0x3cb1825d,0x3f81efe0,2 +np.float32,0x3ed808d0,0x3fab7c45,2 +np.float32,0xbf6f668a,0x3f05e259,2 +np.float32,0x3e3c7802,0x3f916abd,2 +np.float32,0xbd5ac5a0,0x3f76b21b,2 +np.float32,0x805aa6c9,0x3f800000,2 +np.float32,0xbe4d6f68,0x3f5ec3e1,2 +np.float32,0x3f3108b2,0x3fceb87f,2 +np.float32,0x3ec385cc,0x3fa6c9fb,2 +np.float32,0xbe9fc1ce,0x3f4e35e8,2 +np.float32,0x43b68,0x3f800000,2 +np.float32,0x3ef0cdcc,0x3fb15557,2 +np.float32,0x3e3f729b,0x3f91b5e1,2 +np.float32,0x7f52a4df,0x7f800000,2 +np.float32,0xbf56da96,0x3f0f15b9,2 +np.float32,0xbf161d2b,0x3f2a7faf,2 +np.float32,0x3e8df763,0x3f9b1fbe,2 +np.float32,0xff4f0780,0x0,2 +np.float32,0x8048f594,0x3f800000,2 +np.float32,0x3e62bb1d,0x3f953b7e,2 +np.float32,0xfe58e764,0x0,2 +np.float32,0x3dd2c922,0x3f897718,2 +np.float32,0x7fa00000,0x7fe00000,2 +np.float32,0xff07b4b2,0x0,2 +np.float32,0x7f6231a0,0x7f800000,2 +np.float32,0xb8d1d,0x3f800000,2 +np.float32,0x3ee01d24,0x3fad5f16,2 +np.float32,0xbf43f59f,0x3f169869,2 +np.float32,0x801f5257,0x3f800000,2 +np.float32,0x803c15d8,0x3f800000,2 +np.float32,0x3f171a08,0x3fc0b42a,2 +np.float32,0x127aef,0x3f800000,2 +np.float32,0xfd1c6,0x3f800000,2 +np.float32,0x3f1ed13e,0x3fc4c59a,2 +np.float32,0x57fd4f,0x3f800000,2 +np.float32,0x6e8c61,0x3f800000,2 +np.float32,0x804019ab,0x3f800000,2 +np.float32,0x3ef4e5c6,0x3fb251a1,2 +np.float32,0x5044c3,0x3f800000,2 +np.float32,0x3f04460f,0x3fb7204b,2 +np.float32,0x7e326b47,0x7f800000,2 +np.float32,0x800a7e4c,0x3f800000,2 +np.float32,0xbf47ec82,0x3f14fccc,2 +np.float32,0xbedb1b3e,0x3f3e4a4d,2 +np.float32,0x3f741d86,0x3ff7e4b0,2 +np.float32,0xbe249d20,0x3f6501a6,2 +np.float32,0xbf2ea152,0x3f1f8c68,2 +np.float32,0x3ec6dbcc,0x3fa78b3f,2 +np.float32,0x7ebd9bb4,0x7f800000,2 +np.float32,0x3f61b574,0x3febd77a,2 +np.float32,0x3f3dfb2b,0x3fd61891,2 +np.float32,0x3c7d95,0x3f800000,2 +np.float32,0x8071e840,0x3f800000,2 +np.float32,0x15c6fe,0x3f800000,2 +np.float32,0xbf096601,0x3f307893,2 +np.float32,0x7f5c2ef9,0x7f800000,2 +np.float32,0xbe79f750,0x3f582689,2 +np.float32,0x1eb692,0x3f800000,2 +np.float32,0xbd8024f0,0x3f75226d,2 +np.float32,0xbf5a8be8,0x3f0da950,2 +np.float32,0xbf4d28f3,0x3f12e3e1,2 +np.float32,0x7f800000,0x7f800000,2 +np.float32,0xfea8a758,0x0,2 +np.float32,0x8075d2cf,0x3f800000,2 +np.float32,0xfd99af58,0x0,2 +np.float32,0x9e6a,0x3f800000,2 +np.float32,0x2fa19f,0x3f800000,2 +np.float32,0x3e9f4206,0x3f9ecc56,2 +np.float32,0xbee0b666,0x3f3cd9fc,2 +np.float32,0xbec558c4,0x3f43fab1,2 +np.float32,0x7e9a77df,0x7f800000,2 +np.float32,0xff3a9694,0x0,2 +np.float32,0x3f3b3708,0x3fd47f9a,2 +np.float32,0x807cd6d4,0x3f800000,2 +np.float32,0x804aa422,0x3f800000,2 +np.float32,0xfead7a70,0x0,2 +np.float32,0x3f08c610,0x3fb95efe,2 +np.float32,0xff390126,0x0,2 +np.float32,0x5d2d47,0x3f800000,2 +np.float32,0x8006849c,0x3f800000,2 +np.float32,0x654f6e,0x3f800000,2 +np.float32,0xff478a16,0x0,2 +np.float32,0x3f480b0c,0x3fdc024c,2 +np.float32,0xbc3b96c0,0x3f7df9f4,2 +np.float32,0xbcc96460,0x3f7bacb5,2 +np.float32,0x7f349f30,0x7f800000,2 +np.float32,0xbe08fa98,0x3f6954a1,2 +np.float32,0x4f3a13,0x3f800000,2 +np.float32,0x7f6a5ab4,0x7f800000,2 +np.float32,0x7eb85247,0x7f800000,2 +np.float32,0xbf287246,0x3f223e08,2 +np.float32,0x801584d0,0x3f800000,2 +np.float32,0x7ec25371,0x7f800000,2 +np.float32,0x3f002165,0x3fb51552,2 +np.float32,0x3e1108a8,0x3f8d3429,2 +np.float32,0x4f0f88,0x3f800000,2 +np.float32,0x7f67c1ce,0x7f800000,2 +np.float32,0xbf4348f8,0x3f16dedf,2 +np.float32,0xbe292b64,0x3f644d24,2 +np.float32,0xbf2bfa36,0x3f20b2d6,2 +np.float32,0xbf2a6e58,0x3f215f71,2 +np.float32,0x3e97d5d3,0x3f9d35df,2 +np.float32,0x31f597,0x3f800000,2 +np.float32,0x100544,0x3f800000,2 +np.float32,0x10a197,0x3f800000,2 +np.float32,0x3f44df50,0x3fda20d2,2 +np.float32,0x59916d,0x3f800000,2 +np.float32,0x707472,0x3f800000,2 +np.float32,0x8054194e,0x3f800000,2 +np.float32,0x80627b01,0x3f800000,2 +np.float32,0x7f4d5a5b,0x7f800000,2 +np.float32,0xbcecad00,0x3f7aeca5,2 +np.float32,0xff69c541,0x0,2 +np.float32,0xbe164e20,0x3f673c3a,2 +np.float32,0x3dd321de,0x3f897b39,2 +np.float32,0x3c9c4900,0x3f81b431,2 +np.float32,0x7f0efae3,0x7f800000,2 +np.float32,0xbf1b3ee6,0x3f282567,2 +np.float32,0x3ee858ac,0x3faf5083,2 +np.float32,0x3f0e6a39,0x3fbc3965,2 +np.float32,0x7f0c06d8,0x7f800000,2 +np.float32,0x801dd236,0x3f800000,2 +np.float32,0x564245,0x3f800000,2 +np.float32,0x7e99d3ad,0x7f800000,2 +np.float32,0xff3b0164,0x0,2 +np.float32,0x3f386f18,0x3fd2e785,2 +np.float32,0x7f603c39,0x7f800000,2 +np.float32,0x3cbd9b00,0x3f8211f0,2 +np.float32,0x2178e2,0x3f800000,2 +np.float32,0x5db226,0x3f800000,2 +np.float32,0xfec78d62,0x0,2 +np.float32,0x7f40bc1e,0x7f800000,2 +np.float32,0x80325064,0x3f800000,2 +np.float32,0x3f6068dc,0x3feb0377,2 +np.float32,0xfe8b95c6,0x0,2 +np.float32,0xbe496894,0x3f5f5f87,2 +np.float32,0xbf18722a,0x3f296cf4,2 +np.float32,0x332d0e,0x3f800000,2 +np.float32,0x3f6329dc,0x3fecc5c0,2 +np.float32,0x807d1802,0x3f800000,2 +np.float32,0x3e8afcee,0x3f9a7ff1,2 +np.float32,0x26a0a7,0x3f800000,2 +np.float32,0x7f13085d,0x7f800000,2 +np.float32,0x68d547,0x3f800000,2 +np.float32,0x7e9b04ae,0x7f800000,2 +np.float32,0x3f3ecdfe,0x3fd692ea,2 +np.float32,0x805256f4,0x3f800000,2 +np.float32,0x3f312dc8,0x3fcecd42,2 +np.float32,0x23ca15,0x3f800000,2 +np.float32,0x3f53c455,0x3fe31ad6,2 +np.float32,0xbf21186c,0x3f2580fd,2 +np.float32,0x803b9bb1,0x3f800000,2 +np.float32,0xff6ae1fc,0x0,2 +np.float32,0x2103cf,0x3f800000,2 +np.float32,0xbedcec6c,0x3f3dd29d,2 +np.float32,0x7f520afa,0x7f800000,2 +np.float32,0x7e8b44f2,0x7f800000,2 +np.float32,0xfef7f6ce,0x0,2 +np.float32,0xbd5e7c30,0x3f768a6f,2 +np.float32,0xfeb36848,0x0,2 +np.float32,0xff49effb,0x0,2 +np.float32,0xbec207c0,0x3f44dc74,2 +np.float32,0x3e91147f,0x3f9bc77f,2 +np.float32,0xfe784cd4,0x0,2 +np.float32,0xfd1a7250,0x0,2 +np.float32,0xff3b3f48,0x0,2 +np.float32,0x3f685db5,0x3ff0219f,2 +np.float32,0x3f370976,0x3fd21bae,2 +np.float32,0xfed4cc20,0x0,2 +np.float32,0xbf41e337,0x3f17714a,2 +np.float32,0xbf4e8638,0x3f12593a,2 +np.float32,0x3edaf0f1,0x3fac295e,2 +np.float32,0x803cbb4f,0x3f800000,2 +np.float32,0x7f492043,0x7f800000,2 +np.float32,0x2cabcf,0x3f800000,2 +np.float32,0x17f8ac,0x3f800000,2 +np.float32,0x3e846478,0x3f99205a,2 +np.float32,0x76948f,0x3f800000,2 +np.float32,0x1,0x3f800000,2 +np.float32,0x7ea6419e,0x7f800000,2 +np.float32,0xa5315,0x3f800000,2 +np.float32,0xff3a8e32,0x0,2 +np.float32,0xbe5714e8,0x3f5d50b7,2 +np.float32,0xfeadf960,0x0,2 +np.float32,0x3ebbd1a8,0x3fa50efc,2 +np.float32,0x7f31dce7,0x7f800000,2 +np.float32,0x80314999,0x3f800000,2 +np.float32,0x8017f41b,0x3f800000,2 +np.float32,0x7ed6d051,0x7f800000,2 +np.float32,0x7f525688,0x7f800000,2 +np.float32,0x7f7fffff,0x7f800000,2 +np.float32,0x3e8b0461,0x3f9a8180,2 +np.float32,0x3d9fe46e,0x3f871e1f,2 +np.float32,0x5e6d8f,0x3f800000,2 +np.float32,0xbf09ae55,0x3f305608,2 +np.float32,0xfe7028c4,0x0,2 +np.float32,0x7f3ade56,0x7f800000,2 +np.float32,0xff4c9ef9,0x0,2 +np.float32,0x7e3199cf,0x7f800000,2 +np.float32,0x8048652f,0x3f800000,2 +np.float32,0x805e1237,0x3f800000,2 +np.float32,0x189ed8,0x3f800000,2 +np.float32,0xbea7c094,0x3f4bfd98,2 +np.float32,0xbf2f109c,0x3f1f5c5c,2 +np.float32,0xbf0e7f4c,0x3f2e0d2c,2 +np.float32,0x8005981f,0x3f800000,2 +np.float32,0xbf762005,0x3f0377f3,2 +np.float32,0xbf0f60ab,0x3f2da317,2 +np.float32,0xbf4aa3e7,0x3f13e54e,2 +np.float32,0xbf348fd2,0x3f1d01aa,2 +np.float32,0x3e530b50,0x3f93a7fb,2 +np.float32,0xbf0b05a4,0x3f2fb26a,2 +np.float32,0x3eea416c,0x3fafc4aa,2 +np.float32,0x805ad04d,0x3f800000,2 +np.float32,0xbf6328d8,0x3f0a655e,2 +np.float32,0x3f7347b9,0x3ff75558,2 +np.float32,0xfda3ca68,0x0,2 +np.float32,0x80497d21,0x3f800000,2 +np.float32,0x3e740452,0x3f96fd22,2 +np.float32,0x3e528e57,0x3f939b7e,2 +np.float32,0x3e9e19fa,0x3f9e8cbd,2 +np.float32,0x8078060b,0x3f800000,2 +np.float32,0x3f3fea7a,0x3fd73872,2 +np.float32,0xfcfa30a0,0x0,2 +np.float32,0x7f4eb4bf,0x7f800000,2 +np.float32,0x3f712618,0x3ff5e900,2 +np.float32,0xbf668f0e,0x3f0920c6,2 +np.float32,0x3f3001e9,0x3fce259d,2 +np.float32,0xbe9b6fac,0x3f4f6b9c,2 +np.float32,0xbf61fcf3,0x3f0ad5ec,2 +np.float32,0xff08a55c,0x0,2 +np.float32,0x3e805014,0x3f984872,2 +np.float32,0x6ce04c,0x3f800000,2 +np.float32,0x7f7cbc07,0x7f800000,2 +np.float32,0x3c87dc,0x3f800000,2 +np.float32,0x3f2ee498,0x3fcd869a,2 +np.float32,0x4b1116,0x3f800000,2 +np.float32,0x3d382d06,0x3f840d5f,2 +np.float32,0xff7de21e,0x0,2 +np.float32,0x3f2f1d6d,0x3fcda63c,2 +np.float32,0xbf1c1618,0x3f27c38a,2 +np.float32,0xff4264b1,0x0,2 +np.float32,0x8026e5e7,0x3f800000,2 +np.float32,0xbe6fa180,0x3f59ab02,2 +np.float32,0xbe923c02,0x3f52053b,2 +np.float32,0xff3aa453,0x0,2 +np.float32,0x3f77a7ac,0x3ffa47d0,2 +np.float32,0xbed15f36,0x3f40d08a,2 +np.float32,0xa62d,0x3f800000,2 +np.float32,0xbf342038,0x3f1d3123,2 +np.float32,0x7f2f7f80,0x7f800000,2 +np.float32,0x7f2b6fc1,0x7f800000,2 +np.float32,0xff323540,0x0,2 +np.float32,0x3f1a2b6e,0x3fc24faa,2 +np.float32,0x800cc1d2,0x3f800000,2 +np.float32,0xff38fa01,0x0,2 +np.float32,0x80800000,0x3f800000,2 +np.float32,0xbf3d22e0,0x3f196745,2 +np.float32,0x7f40fd62,0x7f800000,2 +np.float32,0x7e1785c7,0x7f800000,2 +np.float32,0x807408c4,0x3f800000,2 +np.float32,0xbf300192,0x3f1ef485,2 +np.float32,0x351e3d,0x3f800000,2 +np.float32,0x7f5ab736,0x7f800000,2 +np.float32,0x2f1696,0x3f800000,2 +np.float32,0x806ac5d7,0x3f800000,2 +np.float32,0x42ec59,0x3f800000,2 +np.float32,0x7f79f52d,0x7f800000,2 +np.float32,0x44ad28,0x3f800000,2 +np.float32,0xbf49dc9c,0x3f143532,2 +np.float32,0x3f6c1f1f,0x3ff295e7,2 +np.float32,0x1589b3,0x3f800000,2 +np.float32,0x3f49b44e,0x3fdd0031,2 +np.float32,0x7f5942c9,0x7f800000,2 +np.float32,0x3f2dab28,0x3fccd877,2 +np.float32,0xff7fffff,0x0,2 +np.float32,0x80578eb2,0x3f800000,2 +np.float32,0x3f39ba67,0x3fd3a50b,2 +np.float32,0x8020340d,0x3f800000,2 +np.float32,0xbf6025b2,0x3f0b8783,2 +np.float32,0x8015ccfe,0x3f800000,2 +np.float32,0x3f6b9762,0x3ff23cd0,2 +np.float32,0xfeeb0c86,0x0,2 +np.float32,0x802779bc,0x3f800000,2 +np.float32,0xbf32bf64,0x3f1dc796,2 +np.float32,0xbf577eb6,0x3f0ed631,2 +np.float32,0x0,0x3f800000,2 +np.float32,0xfe99de6c,0x0,2 +np.float32,0x7a4e53,0x3f800000,2 +np.float32,0x1a15d3,0x3f800000,2 +np.float32,0x8035fe16,0x3f800000,2 +np.float32,0x3e845784,0x3f991dab,2 +np.float32,0x43d688,0x3f800000,2 +np.float32,0xbd447cc0,0x3f77a0b7,2 +np.float32,0x3f83fa,0x3f800000,2 +np.float32,0x3f141df2,0x3fbf2719,2 +np.float32,0x805c586a,0x3f800000,2 +np.float32,0x14c47e,0x3f800000,2 +np.float32,0x3d3bed00,0x3f8422d4,2 +np.float32,0x7f6f4ecd,0x7f800000,2 +np.float32,0x3f0a5e5a,0x3fba2c5c,2 +np.float32,0x523ecf,0x3f800000,2 +np.float32,0xbef4a6e8,0x3f37d262,2 +np.float32,0xff54eb58,0x0,2 +np.float32,0xff3fc875,0x0,2 +np.float32,0x8067c392,0x3f800000,2 +np.float32,0xfedae910,0x0,2 +np.float32,0x80595979,0x3f800000,2 +np.float32,0x3ee87d1d,0x3faf5929,2 +np.float32,0x7f5bad33,0x7f800000,2 +np.float32,0xbf45b868,0x3f15e109,2 +np.float32,0x3ef2277d,0x3fb1a868,2 +np.float32,0x3ca5a950,0x3f81ce8c,2 +np.float32,0x3e70f4e6,0x3f96ad25,2 +np.float32,0xfe3515bc,0x0,2 +np.float32,0xfe4af088,0x0,2 +np.float32,0xff3c78b2,0x0,2 +np.float32,0x7f50f51a,0x7f800000,2 +np.float32,0x3e3a232a,0x3f913009,2 +np.float32,0x7dfec6ff,0x7f800000,2 +np.float32,0x3e1bbaec,0x3f8e3ad6,2 +np.float32,0xbd658fa0,0x3f763ee7,2 +np.float32,0xfe958684,0x0,2 +np.float32,0x503670,0x3f800000,2 +np.float32,0x3f800000,0x40000000,2 +np.float32,0x1bbec6,0x3f800000,2 +np.float32,0xbea7bb7c,0x3f4bff00,2 +np.float32,0xff3a24a2,0x0,2 +np.float32,0xbf416240,0x3f17a635,2 +np.float32,0xbf800000,0x3f000000,2 +np.float32,0xff0c965c,0x0,2 +np.float32,0x80000000,0x3f800000,2 +np.float32,0xbec2c69a,0x3f44a99e,2 +np.float32,0x5b68d4,0x3f800000,2 +np.float32,0xb9a93000,0x3f7ff158,2 +np.float32,0x3d5a0dd8,0x3f84cfbc,2 +np.float32,0xbeaf7a28,0x3f49de4e,2 +np.float32,0x3ee83555,0x3faf4820,2 +np.float32,0xfd320330,0x0,2 +np.float32,0xe1af2,0x3f800000,2 +np.float32,0x7cf28caf,0x7f800000,2 +np.float32,0x80781009,0x3f800000,2 +np.float32,0xbf1e0baf,0x3f26e04d,2 +np.float32,0x7edb05b1,0x7f800000,2 +np.float32,0x3de004,0x3f800000,2 +np.float32,0xff436af6,0x0,2 +np.float32,0x802a9408,0x3f800000,2 +np.float32,0x7ed82205,0x7f800000,2 +np.float32,0x3e3f8212,0x3f91b767,2 +np.float32,0x16a2b2,0x3f800000,2 +np.float32,0xff1e5af3,0x0,2 +np.float32,0xbf1c860c,0x3f2790b7,2 +np.float32,0x3f3bc5da,0x3fd4d1d6,2 +np.float32,0x7f5f7085,0x7f800000,2 +np.float32,0x7f68e409,0x7f800000,2 +np.float32,0x7f4b3388,0x7f800000,2 +np.float32,0x7ecaf440,0x7f800000,2 +np.float32,0x80078785,0x3f800000,2 +np.float32,0x3ebd800d,0x3fa56f45,2 +np.float32,0xbe39a140,0x3f61c58e,2 +np.float32,0x803b587e,0x3f800000,2 +np.float32,0xbeaaa418,0x3f4b31c4,2 +np.float32,0xff7e2b9f,0x0,2 +np.float32,0xff5180a3,0x0,2 +np.float32,0xbf291394,0x3f21f73c,2 +np.float32,0x7f7b9698,0x7f800000,2 +np.float32,0x4218da,0x3f800000,2 +np.float32,0x7f135262,0x7f800000,2 +np.float32,0x804c10e8,0x3f800000,2 +np.float32,0xbf1c2a54,0x3f27ba5a,2 +np.float32,0x7f41fd32,0x7f800000,2 +np.float32,0x3e5cc464,0x3f94a195,2 +np.float32,0xff7a2fa7,0x0,2 +np.float32,0x3e05dc30,0x3f8c23c9,2 +np.float32,0x7f206d99,0x7f800000,2 +np.float32,0xbe9ae520,0x3f4f9287,2 +np.float32,0xfe4f4d58,0x0,2 +np.float32,0xbf44db42,0x3f163ae3,2 +np.float32,0x3f65ac48,0x3fee6300,2 +np.float32,0x3ebfaf36,0x3fa5ecb0,2 +np.float32,0x3f466719,0x3fdb08b0,2 +np.float32,0x80000001,0x3f800000,2 +np.float32,0xff4b3c7b,0x0,2 +np.float32,0x3df44374,0x3f8b0819,2 +np.float32,0xfea4b540,0x0,2 +np.float32,0x7f358e3d,0x7f800000,2 +np.float32,0x801f5e63,0x3f800000,2 +np.float32,0x804ae77e,0x3f800000,2 +np.float32,0xdbb5,0x3f800000,2 +np.float32,0x7f0a7e3b,0x7f800000,2 +np.float32,0xbe4152e4,0x3f609953,2 +np.float32,0x4b9579,0x3f800000,2 +np.float32,0x3ece0bd4,0x3fa92ea5,2 +np.float32,0x7e499d9a,0x7f800000,2 +np.float32,0x80637d8a,0x3f800000,2 +np.float32,0x3e50a425,0x3f936a8b,2 +np.float32,0xbf0e8cb0,0x3f2e06dd,2 +np.float32,0x802763e2,0x3f800000,2 +np.float32,0xff73041b,0x0,2 +np.float32,0xfea466da,0x0,2 +np.float32,0x80064c73,0x3f800000,2 +np.float32,0xbef29222,0x3f385728,2 +np.float32,0x8029c215,0x3f800000,2 +np.float32,0xbd3994e0,0x3f7815d1,2 +np.float32,0xbe6ac9e4,0x3f5a61f3,2 +np.float32,0x804b58b0,0x3f800000,2 +np.float32,0xbdb83be0,0x3f70865c,2 +np.float32,0x7ee18da2,0x7f800000,2 +np.float32,0xfd4ca010,0x0,2 +np.float32,0x807c668b,0x3f800000,2 +np.float32,0xbd40ed90,0x3f77c6e9,2 +np.float32,0x7efc6881,0x7f800000,2 +np.float32,0xfe633bfc,0x0,2 +np.float32,0x803ce363,0x3f800000,2 +np.float32,0x7ecba81e,0x7f800000,2 +np.float32,0xfdcb2378,0x0,2 +np.float32,0xbebc5524,0x3f4662b2,2 +np.float32,0xfaa30000,0x0,2 +np.float32,0x805d451b,0x3f800000,2 +np.float32,0xbee85600,0x3f3ae996,2 +np.float32,0xfefb0a54,0x0,2 +np.float32,0xbdfc6690,0x3f6b0a08,2 +np.float32,0x58a57,0x3f800000,2 +np.float32,0x3b41b7,0x3f800000,2 +np.float32,0x7c99812d,0x7f800000,2 +np.float32,0xbd3ae740,0x3f78079d,2 +np.float32,0xbf4a48a7,0x3f1409dd,2 +np.float32,0xfdeaad58,0x0,2 +np.float32,0xbe9aa65a,0x3f4fa42c,2 +np.float32,0x3f79d78c,0x3ffbc458,2 +np.float32,0x805e7389,0x3f800000,2 +np.float32,0x7ebb3612,0x7f800000,2 +np.float32,0x2e27dc,0x3f800000,2 +np.float32,0x80726dec,0x3f800000,2 +np.float32,0xfe8fb738,0x0,2 +np.float32,0xff1ff3bd,0x0,2 +np.float32,0x7f5264a2,0x7f800000,2 +np.float32,0x3f5a6893,0x3fe739ca,2 +np.float32,0xbec4029c,0x3f44558d,2 +np.float32,0xbef65cfa,0x3f37657e,2 +np.float32,0x63aba1,0x3f800000,2 +np.float32,0xfbb6e200,0x0,2 +np.float32,0xbf3466fc,0x3f1d1307,2 +np.float32,0x3f258844,0x3fc861d7,2 +np.float32,0xbf5f29a7,0x3f0be6dc,2 +np.float32,0x802b51cd,0x3f800000,2 +np.float32,0xbe9094dc,0x3f527dae,2 +np.float32,0xfec2e68c,0x0,2 +np.float32,0x807b38bd,0x3f800000,2 +np.float32,0xbf594662,0x3f0e2663,2 +np.float32,0x7cbcf747,0x7f800000,2 +np.float32,0xbe4b88f0,0x3f5f0d47,2 +np.float32,0x3c53c4,0x3f800000,2 +np.float32,0xbe883562,0x3f54e3f7,2 +np.float32,0xbf1efaf0,0x3f267456,2 +np.float32,0x3e22cd3e,0x3f8ee98b,2 +np.float32,0x80434875,0x3f800000,2 +np.float32,0xbf000b44,0x3f34ff6e,2 +np.float32,0x7f311c3a,0x7f800000,2 +np.float32,0x802f7f3f,0x3f800000,2 +np.float32,0x805155fe,0x3f800000,2 +np.float32,0x7f5d7485,0x7f800000,2 +np.float32,0x80119197,0x3f800000,2 +np.float32,0x3f445b8b,0x3fd9d30d,2 +np.float32,0xbf638eb3,0x3f0a3f38,2 +np.float32,0x402410,0x3f800000,2 +np.float32,0xbc578a40,0x3f7dad1d,2 +np.float32,0xbeecbf8a,0x3f39cc9e,2 +np.float32,0x7f2935a4,0x7f800000,2 +np.float32,0x3f570fea,0x3fe523e2,2 +np.float32,0xbf06bffa,0x3f31bdb6,2 +np.float32,0xbf2afdfd,0x3f2120ba,2 +np.float32,0x7f76f7ab,0x7f800000,2 +np.float32,0xfee2d1e8,0x0,2 +np.float32,0x800b026d,0x3f800000,2 +np.float32,0xff0eda75,0x0,2 +np.float32,0x3d4c,0x3f800000,2 +np.float32,0xbed538a2,0x3f3fcffb,2 +np.float32,0x3f73f4f9,0x3ff7c979,2 +np.float32,0x2aa9fc,0x3f800000,2 +np.float32,0x806a45b3,0x3f800000,2 +np.float32,0xff770d35,0x0,2 +np.float32,0x7e999be3,0x7f800000,2 +np.float32,0x80741128,0x3f800000,2 +np.float32,0xff6aac34,0x0,2 +np.float32,0x470f74,0x3f800000,2 +np.float32,0xff423b7b,0x0,2 +np.float32,0x17dfdd,0x3f800000,2 +np.float32,0x7f029e12,0x7f800000,2 +np.float32,0x803fcb9d,0x3f800000,2 +np.float32,0x3f3dc3,0x3f800000,2 +np.float32,0x7f3a27bc,0x7f800000,2 +np.float32,0x3e473108,0x3f9279ec,2 +np.float32,0x7f4add5d,0x7f800000,2 +np.float32,0xfd9736e0,0x0,2 +np.float32,0x805f1df2,0x3f800000,2 +np.float32,0x6c49c1,0x3f800000,2 +np.float32,0x7ec733c7,0x7f800000,2 +np.float32,0x804c1abf,0x3f800000,2 +np.float32,0x3de2e887,0x3f8a37a5,2 +np.float32,0x3f51630a,0x3fe1a561,2 +np.float32,0x3de686a8,0x3f8a62ff,2 +np.float32,0xbedb3538,0x3f3e439c,2 +np.float32,0xbf3aa892,0x3f1a6f9e,2 +np.float32,0x7ee5fb32,0x7f800000,2 +np.float32,0x7e916c9b,0x7f800000,2 +np.float32,0x3f033f1c,0x3fb69e19,2 +np.float32,0x25324b,0x3f800000,2 +np.float32,0x3f348d1d,0x3fd0b2e2,2 +np.float32,0x3f5797e8,0x3fe57851,2 +np.float32,0xbf69c316,0x3f07f1a0,2 +np.float32,0xbe8b7fb0,0x3f53f1bf,2 +np.float32,0xbdbbc190,0x3f703d00,2 +np.float32,0xff6c4fc0,0x0,2 +np.float32,0x7f29fcbe,0x7f800000,2 +np.float32,0x3f678d19,0x3fef9a23,2 +np.float32,0x73d140,0x3f800000,2 +np.float32,0x3e25bdd2,0x3f8f326b,2 +np.float32,0xbeb775ec,0x3f47b2c6,2 +np.float32,0xff451c4d,0x0,2 +np.float32,0x8072c466,0x3f800000,2 +np.float32,0x3f65e836,0x3fee89b2,2 +np.float32,0x52ca7a,0x3f800000,2 +np.float32,0x62cfed,0x3f800000,2 +np.float32,0xbf583dd0,0x3f0e8c5c,2 +np.float32,0xbf683842,0x3f088342,2 +np.float32,0x3f1a7828,0x3fc2780c,2 +np.float32,0x800ea979,0x3f800000,2 +np.float32,0xbeb9133c,0x3f474328,2 +np.float32,0x3ef09fc7,0x3fb14a4b,2 +np.float32,0x7ebbcb75,0x7f800000,2 +np.float32,0xff316c0e,0x0,2 +np.float32,0x805b84e3,0x3f800000,2 +np.float32,0x3d6a55e0,0x3f852d8a,2 +np.float32,0x3e755788,0x3f971fd1,2 +np.float32,0x3ee7aacb,0x3faf2743,2 +np.float32,0x7f714039,0x7f800000,2 +np.float32,0xff70bad8,0x0,2 +np.float32,0xbe0b74c8,0x3f68f08c,2 +np.float32,0xbf6cb170,0x3f06de86,2 +np.float32,0x7ec1fbff,0x7f800000,2 +np.float32,0x8014b1f6,0x3f800000,2 +np.float32,0xfe8b45fe,0x0,2 +np.float32,0x6e2220,0x3f800000,2 +np.float32,0x3ed1777d,0x3fa9f7ab,2 +np.float32,0xff48e467,0x0,2 +np.float32,0xff76c5aa,0x0,2 +np.float32,0x3e9bd330,0x3f9e0fd7,2 +np.float32,0x3f17de4f,0x3fc11aae,2 +np.float32,0x7eeaa2fd,0x7f800000,2 +np.float32,0xbf572746,0x3f0ef806,2 +np.float32,0x7e235554,0x7f800000,2 +np.float32,0xfe24fc1c,0x0,2 +np.float32,0x7daf71ad,0x7f800000,2 +np.float32,0x800d4a6b,0x3f800000,2 +np.float32,0xbf6fc31d,0x3f05c0ce,2 +np.float32,0x1c4d93,0x3f800000,2 +np.float32,0x7ee9200c,0x7f800000,2 +np.float32,0x3f54b4da,0x3fe3aeec,2 +np.float32,0x2b37b1,0x3f800000,2 +np.float32,0x3f7468bd,0x3ff81731,2 +np.float32,0x3f2850ea,0x3fc9e5f4,2 +np.float32,0xbe0d47ac,0x3f68a6f9,2 +np.float32,0x314877,0x3f800000,2 +np.float32,0x802700c3,0x3f800000,2 +np.float32,0x7e2c915f,0x7f800000,2 +np.float32,0x800d0059,0x3f800000,2 +np.float32,0x3f7f3c25,0x3fff7862,2 +np.float32,0xff735d31,0x0,2 +np.float32,0xff7e339e,0x0,2 +np.float32,0xbef96cf0,0x3f36a340,2 +np.float32,0x3db6ea21,0x3f882cb2,2 +np.float32,0x67cb3d,0x3f800000,2 +np.float32,0x801f349d,0x3f800000,2 +np.float32,0x3f1390ec,0x3fbede29,2 +np.float32,0x7f13644a,0x7f800000,2 +np.float32,0x804a369b,0x3f800000,2 +np.float32,0x80262666,0x3f800000,2 +np.float32,0x7e850fbc,0x7f800000,2 +np.float32,0x18b002,0x3f800000,2 +np.float32,0x8051f1ed,0x3f800000,2 +np.float32,0x3eba48f6,0x3fa4b753,2 +np.float32,0xbf3f4130,0x3f1886a9,2 +np.float32,0xbedac006,0x3f3e61cf,2 +np.float32,0xbf097c70,0x3f306ddc,2 +np.float32,0x4aba6d,0x3f800000,2 +np.float32,0x580078,0x3f800000,2 +np.float32,0x3f64d82e,0x3fedda40,2 +np.float32,0x7f781fd6,0x7f800000,2 +np.float32,0x6aff3d,0x3f800000,2 +np.float32,0xff25e074,0x0,2 +np.float32,0x7ea9ec89,0x7f800000,2 +np.float32,0xbf63b816,0x3f0a2fbb,2 +np.float32,0x133f07,0x3f800000,2 +np.float32,0xff800000,0x0,2 +np.float32,0x8013dde7,0x3f800000,2 +np.float32,0xff770b95,0x0,2 +np.float32,0x806154e8,0x3f800000,2 +np.float32,0x3f1e7bce,0x3fc4981a,2 +np.float32,0xff262c78,0x0,2 +np.float32,0x3f59a652,0x3fe6c04c,2 +np.float32,0x7f220166,0x7f800000,2 +np.float32,0x7eb24939,0x7f800000,2 +np.float32,0xbed58bb0,0x3f3fba6a,2 +np.float32,0x3c2ad000,0x3f80eda7,2 +np.float32,0x2adb2e,0x3f800000,2 +np.float32,0xfe8b213e,0x0,2 +np.float32,0xbf2e0c1e,0x3f1fccea,2 +np.float32,0x7e1716be,0x7f800000,2 +np.float32,0x80184e73,0x3f800000,2 +np.float32,0xbf254743,0x3f23a3d5,2 +np.float32,0x8063a722,0x3f800000,2 +np.float32,0xbe50adf0,0x3f5e46c7,2 +np.float32,0x3f614158,0x3feb8d60,2 +np.float32,0x8014bbc8,0x3f800000,2 +np.float32,0x283bc7,0x3f800000,2 +np.float32,0x3ffb5c,0x3f800000,2 +np.float32,0xfe8de6bc,0x0,2 +np.float32,0xbea6e086,0x3f4c3b82,2 +np.float32,0xfee64b92,0x0,2 +np.float32,0x506c1a,0x3f800000,2 +np.float32,0xff342af8,0x0,2 +np.float32,0x6b6f4c,0x3f800000,2 +np.float32,0xfeb42b1e,0x0,2 +np.float32,0x3e49384a,0x3f92ad71,2 +np.float32,0x152d08,0x3f800000,2 +np.float32,0x804c8f09,0x3f800000,2 +np.float32,0xff5e927d,0x0,2 +np.float32,0x6374da,0x3f800000,2 +np.float32,0x3f48f011,0x3fdc8ae4,2 +np.float32,0xbf446a30,0x3f1668e8,2 +np.float32,0x3ee77073,0x3faf196e,2 +np.float32,0xff4caa40,0x0,2 +np.float32,0x7efc9363,0x7f800000,2 +np.float32,0xbf706dcc,0x3f05830d,2 +np.float32,0xfe29c7e8,0x0,2 +np.float32,0x803cfe58,0x3f800000,2 +np.float32,0x3ec34c7c,0x3fa6bd0a,2 +np.float32,0x3eb85b62,0x3fa44968,2 +np.float32,0xfda1b9d8,0x0,2 +np.float32,0x802932cd,0x3f800000,2 +np.float32,0xbf5cde78,0x3f0cc5fa,2 +np.float32,0x3f31bf44,0x3fcf1ec8,2 +np.float32,0x803a0882,0x3f800000,2 +np.float32,0x800000,0x3f800000,2 +np.float32,0x3f54110e,0x3fe34a08,2 +np.float32,0x80645ea9,0x3f800000,2 +np.float32,0xbd8c1070,0x3f7425c3,2 +np.float32,0x801a006a,0x3f800000,2 +np.float32,0x7f5d161e,0x7f800000,2 +np.float32,0x805b5df3,0x3f800000,2 +np.float32,0xbf71a7c0,0x3f0511be,2 +np.float32,0xbe9a55c0,0x3f4fbad6,2 +np.float64,0xde7e2fd9bcfc6,0x3ff0000000000000,1 +np.float64,0xbfd8cd88eb319b12,0x3fe876349efbfa2b,1 +np.float64,0x3fe4fa13ace9f428,0x3ff933fbb117d196,1 +np.float64,0x475b3d048eb68,0x3ff0000000000000,1 +np.float64,0x7fef39ed07be73d9,0x7ff0000000000000,1 +np.float64,0x80026b84d904d70a,0x3ff0000000000000,1 +np.float64,0xebd60627d7ac1,0x3ff0000000000000,1 +np.float64,0xbfd7cbefdbaf97e0,0x3fe8bad30f6cf8e1,1 +np.float64,0x7fc17c605a22f8c0,0x7ff0000000000000,1 +np.float64,0x8cdac05119b58,0x3ff0000000000000,1 +np.float64,0x3fc45cd60a28b9ac,0x3ff1dd8028ec3f41,1 +np.float64,0x7fef4fce137e9f9b,0x7ff0000000000000,1 +np.float64,0xe5a2b819cb457,0x3ff0000000000000,1 +np.float64,0xe3bcfd4dc77a0,0x3ff0000000000000,1 +np.float64,0x68f0b670d1e17,0x3ff0000000000000,1 +np.float64,0xae69a6455cd35,0x3ff0000000000000,1 +np.float64,0xffe7007a0c6e00f4,0x0,1 +np.float64,0x59fc57a8b3f8c,0x3ff0000000000000,1 +np.float64,0xbfeee429c0bdc854,0x3fe0638fa62bed9f,1 +np.float64,0x80030bb6e206176f,0x3ff0000000000000,1 +np.float64,0x8006967a36ad2cf5,0x3ff0000000000000,1 +np.float64,0x3fe128176a22502f,0x3ff73393301e5dc8,1 +np.float64,0x218de20c431bd,0x3ff0000000000000,1 +np.float64,0x3fe7dbc48aafb789,0x3ffad38989b5955c,1 +np.float64,0xffda1ef411343de8,0x0,1 +np.float64,0xc6b392838d673,0x3ff0000000000000,1 +np.float64,0x7fe6d080c1ada101,0x7ff0000000000000,1 +np.float64,0xbfed36dd67fa6dbb,0x3fe0fec342c4ee89,1 +np.float64,0x3fee2bb6a3fc576e,0x3ffec1c149f1f092,1 +np.float64,0xbfd1f785eb23ef0c,0x3fea576eb01233cb,1 +np.float64,0x7fdad29a1f35a533,0x7ff0000000000000,1 +np.float64,0xffe8928c4fb12518,0x0,1 +np.float64,0x7fb123160022462b,0x7ff0000000000000,1 +np.float64,0x8007ab56cfaf56ae,0x3ff0000000000000,1 +np.float64,0x7fda342d6634685a,0x7ff0000000000000,1 +np.float64,0xbfe3b7e42c676fc8,0x3fe4e05cf8685b8a,1 +np.float64,0xffa708be7c2e1180,0x0,1 +np.float64,0xbfe8ffbece31ff7e,0x3fe29eb84077a34a,1 +np.float64,0xbf91002008220040,0x3fefa245058f05cb,1 +np.float64,0x8000281f0ee0503f,0x3ff0000000000000,1 +np.float64,0x8005617adc2ac2f6,0x3ff0000000000000,1 +np.float64,0x7fa84fec60309fd8,0x7ff0000000000000,1 +np.float64,0x8d00c0231a018,0x3ff0000000000000,1 +np.float64,0xbfdfe52ca63fca5a,0x3fe6a7324cc00d57,1 +np.float64,0x7fcc81073d39020d,0x7ff0000000000000,1 +np.float64,0x800134ff5a6269ff,0x3ff0000000000000,1 +np.float64,0xffc7fff98d2ffff4,0x0,1 +np.float64,0x8000925ce50124bb,0x3ff0000000000000,1 +np.float64,0xffe2530c66a4a618,0x0,1 +np.float64,0x7fc99070673320e0,0x7ff0000000000000,1 +np.float64,0xbfddd5c1f13bab84,0x3fe72a0c80f8df39,1 +np.float64,0x3fe1c220fee38442,0x3ff7817ec66aa55b,1 +np.float64,0x3fb9a1e1043343c2,0x3ff1265e575e6404,1 +np.float64,0xffef72e0833ee5c0,0x0,1 +np.float64,0x3fe710c0416e2181,0x3ffa5e93588aaa69,1 +np.float64,0xbfd8d23cbab1a47a,0x3fe874f5b9d99885,1 +np.float64,0x7fe9628ebd72c51c,0x7ff0000000000000,1 +np.float64,0xdd5fa611babf5,0x3ff0000000000000,1 +np.float64,0x8002bafac86575f6,0x3ff0000000000000,1 +np.float64,0x68acea44d159e,0x3ff0000000000000,1 +np.float64,0xffd776695eaeecd2,0x0,1 +np.float64,0x80059b59bb4b36b4,0x3ff0000000000000,1 +np.float64,0xbdcdd2af7b9bb,0x3ff0000000000000,1 +np.float64,0x8002b432ee856867,0x3ff0000000000000,1 +np.float64,0xcbc72f09978e6,0x3ff0000000000000,1 +np.float64,0xbfee8f4bf6fd1e98,0x3fe081cc0318b170,1 +np.float64,0xffc6e2892d2dc514,0x0,1 +np.float64,0x7feb682e4db6d05c,0x7ff0000000000000,1 +np.float64,0x8004b70a04296e15,0x3ff0000000000000,1 +np.float64,0x42408a4284812,0x3ff0000000000000,1 +np.float64,0xbfe9b8b197f37163,0x3fe254b4c003ce0a,1 +np.float64,0x3fcaadf5f5355bec,0x3ff27ca7876a8d20,1 +np.float64,0xfff0000000000000,0x0,1 +np.float64,0x7fea8376d33506ed,0x7ff0000000000000,1 +np.float64,0xffef73c2d63ee785,0x0,1 +np.float64,0xffe68b2bae2d1657,0x0,1 +np.float64,0x3fd8339cb2306739,0x3ff4cb774d616f90,1 +np.float64,0xbfc6d1db4d2da3b8,0x3fec47bb873a309c,1 +np.float64,0x7fe858016230b002,0x7ff0000000000000,1 +np.float64,0x7fe74cb99d2e9972,0x7ff0000000000000,1 +np.float64,0xffec2e96dc385d2d,0x0,1 +np.float64,0xb762a9876ec55,0x3ff0000000000000,1 +np.float64,0x3feca230c5794462,0x3ffdbfe62a572f52,1 +np.float64,0xbfb5ebad3a2bd758,0x3fee27eed86dcc39,1 +np.float64,0x471c705a8e38f,0x3ff0000000000000,1 +np.float64,0x7fc79bb5cf2f376b,0x7ff0000000000000,1 +np.float64,0xbfe53d6164ea7ac3,0x3fe4331b3beb73bd,1 +np.float64,0xbfe375a3f766eb48,0x3fe4fe67edb516e6,1 +np.float64,0x3fe1c7686ca38ed1,0x3ff7842f04770ba9,1 +np.float64,0x242e74dc485cf,0x3ff0000000000000,1 +np.float64,0x8009c06ab71380d6,0x3ff0000000000000,1 +np.float64,0x3fd08505efa10a0c,0x3ff3227b735b956d,1 +np.float64,0xffe3dfcecda7bf9d,0x0,1 +np.float64,0x8001f079bbc3e0f4,0x3ff0000000000000,1 +np.float64,0x3fddc706b6bb8e0c,0x3ff616d927987363,1 +np.float64,0xbfd151373ea2a26e,0x3fea870ba53ec126,1 +np.float64,0x7fe89533bfb12a66,0x7ff0000000000000,1 +np.float64,0xffed302cbc3a6059,0x0,1 +np.float64,0x3fd871cc28b0e398,0x3ff4d97d58c16ae2,1 +np.float64,0x7fbe9239683d2472,0x7ff0000000000000,1 +np.float64,0x848a445909149,0x3ff0000000000000,1 +np.float64,0x8007b104ce2f620a,0x3ff0000000000000,1 +np.float64,0x7fc2cd6259259ac4,0x7ff0000000000000,1 +np.float64,0xbfeadb640df5b6c8,0x3fe1e2b068de10af,1 +np.float64,0x800033b2f1a06767,0x3ff0000000000000,1 +np.float64,0x7fe54e5b7caa9cb6,0x7ff0000000000000,1 +np.float64,0x4f928f209f26,0x3ff0000000000000,1 +np.float64,0x8003c3dc6f2787ba,0x3ff0000000000000,1 +np.float64,0xbfd55a59daaab4b4,0x3fe9649d57b32b5d,1 +np.float64,0xffe3e2968d67c52c,0x0,1 +np.float64,0x80087434d550e86a,0x3ff0000000000000,1 +np.float64,0xffdde800083bd000,0x0,1 +np.float64,0xffe291f0542523e0,0x0,1 +np.float64,0xbfe1419bc3e28338,0x3fe6051d4f95a34a,1 +np.float64,0x3fd9d00ee1b3a01e,0x3ff5292bb8d5f753,1 +np.float64,0x3fdb720b60b6e417,0x3ff589d133625374,1 +np.float64,0xbfe3e21f0967c43e,0x3fe4cd4d02e3ef9a,1 +np.float64,0x7fd7e27f3dafc4fd,0x7ff0000000000000,1 +np.float64,0x3fd1cc2620a3984c,0x3ff366befbc38e3e,1 +np.float64,0x3fe78d05436f1a0b,0x3ffaa5ee4ea54b79,1 +np.float64,0x7e2acc84fc55a,0x3ff0000000000000,1 +np.float64,0x800ffb861c5ff70c,0x3ff0000000000000,1 +np.float64,0xffb2b0db1a2561b8,0x0,1 +np.float64,0xbfe80c2363701847,0x3fe301fdfe789576,1 +np.float64,0x7fe383c1c3e70783,0x7ff0000000000000,1 +np.float64,0xbfeefc02e6fdf806,0x3fe05b1a8528bf6c,1 +np.float64,0xbfe42c9268285925,0x3fe4abdc14793cb8,1 +np.float64,0x1,0x3ff0000000000000,1 +np.float64,0xa71c7ce94e390,0x3ff0000000000000,1 +np.float64,0x800ed4e6777da9cd,0x3ff0000000000000,1 +np.float64,0x3fde11b35d3c2367,0x3ff628bdc6dd1b78,1 +np.float64,0x3fef3964dbfe72ca,0x3fff777cae357608,1 +np.float64,0x3fefe369b7ffc6d4,0x3fffec357be508a3,1 +np.float64,0xbfdef1855f3de30a,0x3fe6e348c58e3fed,1 +np.float64,0x3fee0e2bc13c1c58,0x3ffeae1909c1b973,1 +np.float64,0xbfd31554ffa62aaa,0x3fea06628b2f048a,1 +np.float64,0x800dc56bcc7b8ad8,0x3ff0000000000000,1 +np.float64,0x7fbba01b8e374036,0x7ff0000000000000,1 +np.float64,0x7fd9737a92b2e6f4,0x7ff0000000000000,1 +np.float64,0x3feeae0fac3d5c1f,0x3fff1913705f1f07,1 +np.float64,0x3fdcc64fcdb98ca0,0x3ff5d9c3e5862972,1 +np.float64,0x3fdad9f83db5b3f0,0x3ff56674e81c1bd1,1 +np.float64,0x32b8797065710,0x3ff0000000000000,1 +np.float64,0x3fd20deae6241bd6,0x3ff37495bc057394,1 +np.float64,0x7fc899f0763133e0,0x7ff0000000000000,1 +np.float64,0x80045805fc08b00d,0x3ff0000000000000,1 +np.float64,0xbfcd8304cb3b0608,0x3feb4611f1eaa30c,1 +np.float64,0x3fd632a2fcac6544,0x3ff4592e1ea14fb0,1 +np.float64,0xffeeb066007d60cb,0x0,1 +np.float64,0x800bb12a42b76255,0x3ff0000000000000,1 +np.float64,0xbfe060fe1760c1fc,0x3fe6714640ab2574,1 +np.float64,0x80067ed737acfdaf,0x3ff0000000000000,1 +np.float64,0x3fd5ec3211abd864,0x3ff449adea82e73e,1 +np.float64,0x7fc4b2fdc22965fb,0x7ff0000000000000,1 +np.float64,0xff656afd002ad600,0x0,1 +np.float64,0xffeadefcdcb5bdf9,0x0,1 +np.float64,0x80052f18610a5e32,0x3ff0000000000000,1 +np.float64,0xbfd5b75c78ab6eb8,0x3fe94b15e0f39194,1 +np.float64,0xa4d3de2b49a7c,0x3ff0000000000000,1 +np.float64,0xbfe321c93de64392,0x3fe524ac7bbee401,1 +np.float64,0x3feb32f5def665ec,0x3ffcd6e4e5f9c271,1 +np.float64,0x7fe6b07e4ced60fc,0x7ff0000000000000,1 +np.float64,0x3fe013bb2de02776,0x3ff6aa4c32ab5ba4,1 +np.float64,0xbfeadd81d375bb04,0x3fe1e1de89b4aebf,1 +np.float64,0xffece7678079cece,0x0,1 +np.float64,0x3fe3d87b8467b0f8,0x3ff897cf22505e4d,1 +np.float64,0xffc4e3a05129c740,0x0,1 +np.float64,0xbfddee6b03bbdcd6,0x3fe723dd83ab49bd,1 +np.float64,0x3fcc4e2672389c4d,0x3ff2a680db769116,1 +np.float64,0x3fd8ed221ab1da44,0x3ff4f569aec8b850,1 +np.float64,0x80000a3538a0146b,0x3ff0000000000000,1 +np.float64,0x8004832eb109065e,0x3ff0000000000000,1 +np.float64,0xffdca83c60395078,0x0,1 +np.float64,0xffef551cda3eaa39,0x0,1 +np.float64,0x800fd95dd65fb2bc,0x3ff0000000000000,1 +np.float64,0x3ff0000000000000,0x4000000000000000,1 +np.float64,0xbfc06f5c4f20deb8,0x3fed466c17305ad8,1 +np.float64,0xbfeb01b5f476036c,0x3fe1d3de0f4211f4,1 +np.float64,0xbfdb2b9284365726,0x3fe7d7b02f790b05,1 +np.float64,0xff76ba83202d7500,0x0,1 +np.float64,0x3fd3f1c59ea7e38c,0x3ff3db96b3a0aaad,1 +np.float64,0x8b99ff6d17340,0x3ff0000000000000,1 +np.float64,0xbfeb383aa0f67075,0x3fe1bedcf2531c08,1 +np.float64,0x3fe321e35fa643c7,0x3ff83749a5d686ee,1 +np.float64,0xbfd863eb2130c7d6,0x3fe8923fcc39bac7,1 +np.float64,0x9e71dd333ce3c,0x3ff0000000000000,1 +np.float64,0x9542962b2a853,0x3ff0000000000000,1 +np.float64,0xba2c963b74593,0x3ff0000000000000,1 +np.float64,0x80019f4d0ca33e9b,0x3ff0000000000000,1 +np.float64,0xffde3e39a73c7c74,0x0,1 +np.float64,0x800258ae02c4b15d,0x3ff0000000000000,1 +np.float64,0xbfd99a535a3334a6,0x3fe8402f3a0662a5,1 +np.float64,0xe6c62143cd8c4,0x3ff0000000000000,1 +np.float64,0x7fbcc828f0399051,0x7ff0000000000000,1 +np.float64,0xbfe42e3596285c6b,0x3fe4ab2066d66071,1 +np.float64,0xffe2ee42d365dc85,0x0,1 +np.float64,0x3fe1f98abea3f315,0x3ff79dc68002a80b,1 +np.float64,0x7fd7225891ae44b0,0x7ff0000000000000,1 +np.float64,0x477177408ee30,0x3ff0000000000000,1 +np.float64,0xbfe16a7e2162d4fc,0x3fe5f1a5c745385d,1 +np.float64,0xbf98aaee283155e0,0x3fef785952e9c089,1 +np.float64,0x7fd7c14a8daf8294,0x7ff0000000000000,1 +np.float64,0xf7e7713defcee,0x3ff0000000000000,1 +np.float64,0x800769aa11aed355,0x3ff0000000000000,1 +np.float64,0xbfed30385e3a6071,0x3fe10135a3bd9ae6,1 +np.float64,0x3fe6dd7205edbae4,0x3ffa4155899efd70,1 +np.float64,0x800d705d26bae0ba,0x3ff0000000000000,1 +np.float64,0xa443ac1f48876,0x3ff0000000000000,1 +np.float64,0xbfec8cfec43919fe,0x3fe13dbf966e6633,1 +np.float64,0x7fd246efaa248dde,0x7ff0000000000000,1 +np.float64,0x800f2ad14afe55a3,0x3ff0000000000000,1 +np.float64,0x800487a894c90f52,0x3ff0000000000000,1 +np.float64,0x80014c4f19e2989f,0x3ff0000000000000,1 +np.float64,0x3fc11f265f223e4d,0x3ff18def05c971e5,1 +np.float64,0xffeb6d565776daac,0x0,1 +np.float64,0x7fd5ca5df8ab94bb,0x7ff0000000000000,1 +np.float64,0xbfe33de4fde67bca,0x3fe517d0e212cd1c,1 +np.float64,0xbfd1c738e5a38e72,0x3fea6539e9491693,1 +np.float64,0xbfec1d8c33b83b18,0x3fe16790fbca0c65,1 +np.float64,0xbfeecb464b7d968d,0x3fe06c67e2aefa55,1 +np.float64,0xbfd621dbf1ac43b8,0x3fe92dfa32d93846,1 +np.float64,0x80069a02860d3406,0x3ff0000000000000,1 +np.float64,0xbfe84f650e309eca,0x3fe2e661300f1975,1 +np.float64,0x7fc1d2cec523a59d,0x7ff0000000000000,1 +np.float64,0x3fd7706d79aee0db,0x3ff49fb033353dfe,1 +np.float64,0xffd94ba458329748,0x0,1 +np.float64,0x7fea98ba1a753173,0x7ff0000000000000,1 +np.float64,0xbfe756ba092ead74,0x3fe34d428d1857bc,1 +np.float64,0xffecfbd836b9f7b0,0x0,1 +np.float64,0x3fd211fbe5a423f8,0x3ff375711a3641e0,1 +np.float64,0x7fee24f7793c49ee,0x7ff0000000000000,1 +np.float64,0x7fe6a098886d4130,0x7ff0000000000000,1 +np.float64,0xbfd4ade909a95bd2,0x3fe99436524db1f4,1 +np.float64,0xbfeb704e6476e09d,0x3fe1a95be4a21bc6,1 +np.float64,0xffefc0f6627f81ec,0x0,1 +np.float64,0x7feff3f896ffe7f0,0x7ff0000000000000,1 +np.float64,0xa3f74edb47eea,0x3ff0000000000000,1 +np.float64,0xbfe0a551cf214aa4,0x3fe65027a7ff42e3,1 +np.float64,0x3fe164b23622c964,0x3ff7521c6225f51d,1 +np.float64,0x7fc258752324b0e9,0x7ff0000000000000,1 +np.float64,0x4739b3348e737,0x3ff0000000000000,1 +np.float64,0xb0392b1d60726,0x3ff0000000000000,1 +np.float64,0x7fe26f42e5e4de85,0x7ff0000000000000,1 +np.float64,0x8004601f87e8c040,0x3ff0000000000000,1 +np.float64,0xffe92ce37b3259c6,0x0,1 +np.float64,0x3fe620da3a6c41b4,0x3ff9d6ee3d005466,1 +np.float64,0x3fd850cfa2b0a1a0,0x3ff4d20bd249d411,1 +np.float64,0xffdcdfdfb5b9bfc0,0x0,1 +np.float64,0x800390297d672054,0x3ff0000000000000,1 +np.float64,0x3fde5864f6bcb0ca,0x3ff639bb9321f5ef,1 +np.float64,0x3fee484cec7c909a,0x3ffed4d2c6274219,1 +np.float64,0x7fe9b9a064b37340,0x7ff0000000000000,1 +np.float64,0xffe50028b8aa0051,0x0,1 +np.float64,0x3fe37774ade6eee9,0x3ff864558498a9a8,1 +np.float64,0x7fef83c724bf078d,0x7ff0000000000000,1 +np.float64,0xbfeb58450fb6b08a,0x3fe1b290556be73d,1 +np.float64,0x7fd7161475ae2c28,0x7ff0000000000000,1 +np.float64,0x3fece09621f9c12c,0x3ffde836a583bbdd,1 +np.float64,0x3fd045790ea08af2,0x3ff31554778fd4e2,1 +np.float64,0xbfe7c7dd6cef8fbb,0x3fe31e2eeda857fc,1 +np.float64,0xffe9632f5372c65e,0x0,1 +np.float64,0x800d4f3a703a9e75,0x3ff0000000000000,1 +np.float64,0xffea880e4df5101c,0x0,1 +np.float64,0xbfeb7edc4ff6fdb8,0x3fe1a3cb5dc33594,1 +np.float64,0xbfcaae4bab355c98,0x3febb1ee65e16b58,1 +np.float64,0xbfde598a19bcb314,0x3fe709145eafaaf8,1 +np.float64,0x3feefb6d78fdf6db,0x3fff4d5c8c68e39a,1 +np.float64,0x13efc75427dfa,0x3ff0000000000000,1 +np.float64,0xffe26f65c064decb,0x0,1 +np.float64,0xbfed5c1addfab836,0x3fe0f1133bd2189a,1 +np.float64,0x7fe7a7cf756f4f9e,0x7ff0000000000000,1 +np.float64,0xffc681702e2d02e0,0x0,1 +np.float64,0x8003d6ab5067ad57,0x3ff0000000000000,1 +np.float64,0xffa695f1342d2be0,0x0,1 +np.float64,0xbfcf8857db3f10b0,0x3feafa14da8c29a4,1 +np.float64,0xbfe8ca06be71940e,0x3fe2b46f6d2c64b4,1 +np.float64,0x3451c74468a3a,0x3ff0000000000000,1 +np.float64,0x3fde47d5f6bc8fac,0x3ff635bf8e024716,1 +np.float64,0xffda159d5db42b3a,0x0,1 +np.float64,0x7fef9fecaa3f3fd8,0x7ff0000000000000,1 +np.float64,0x3fd4e745e3a9ce8c,0x3ff410a9cb6fd8bf,1 +np.float64,0xffef57019b3eae02,0x0,1 +np.float64,0xbfe6604f4f6cc09e,0x3fe3b55de43c626d,1 +np.float64,0xffe066a424a0cd48,0x0,1 +np.float64,0x3fd547de85aa8fbc,0x3ff425b2a7a16675,1 +np.float64,0xffb3c69280278d28,0x0,1 +np.float64,0xffebe0b759f7c16e,0x0,1 +np.float64,0x3fefc84106ff9082,0x3fffd973687337d8,1 +np.float64,0x501c42a4a0389,0x3ff0000000000000,1 +np.float64,0x7feb45d13eb68ba1,0x7ff0000000000000,1 +np.float64,0xbfb16a8c2e22d518,0x3fee86a9c0f9291a,1 +np.float64,0x3be327b877c66,0x3ff0000000000000,1 +np.float64,0x7fe4a58220694b03,0x7ff0000000000000,1 +np.float64,0x3fe0286220a050c4,0x3ff6b472157ab8f2,1 +np.float64,0x3fc9381825327030,0x3ff2575fbea2bf5d,1 +np.float64,0xbfd1af7ee8a35efe,0x3fea6c032cf7e669,1 +np.float64,0xbfea9b0f39b5361e,0x3fe1fbae14b40b4d,1 +np.float64,0x39efe4aa73dfd,0x3ff0000000000000,1 +np.float64,0xffeb06fdc8360dfb,0x0,1 +np.float64,0xbfda481e72b4903c,0x3fe812b4b08d4884,1 +np.float64,0xbfd414ba5ba82974,0x3fe9bec9474bdfe6,1 +np.float64,0x7fe707177b6e0e2e,0x7ff0000000000000,1 +np.float64,0x8000000000000001,0x3ff0000000000000,1 +np.float64,0xbfede6a75bbbcd4f,0x3fe0be874cccd399,1 +np.float64,0x8006cdb577cd9b6c,0x3ff0000000000000,1 +np.float64,0x800051374f20a26f,0x3ff0000000000000,1 +np.float64,0x3fe5cba8c96b9752,0x3ff9a76b3adcc122,1 +np.float64,0xbfee3933487c7267,0x3fe0a0b190f9609a,1 +np.float64,0x3fd574b8d8aae970,0x3ff42f7e83de1af9,1 +np.float64,0xba5db72b74bb7,0x3ff0000000000000,1 +np.float64,0x3fa9bf512c337ea0,0x3ff0914a7f743a94,1 +np.float64,0xffe8cb736c3196e6,0x0,1 +np.float64,0x3761b2f06ec37,0x3ff0000000000000,1 +np.float64,0x8b4d4433169a9,0x3ff0000000000000,1 +np.float64,0x800f0245503e048b,0x3ff0000000000000,1 +np.float64,0x7fb20d54ac241aa8,0x7ff0000000000000,1 +np.float64,0x3fdf26666b3e4ccd,0x3ff66b8995142017,1 +np.float64,0xbfcbf2a83737e550,0x3feb8173a7b9d6b5,1 +np.float64,0x3fd31572a0a62ae5,0x3ff3ac6c94313dcd,1 +np.float64,0x7fb6c2807a2d8500,0x7ff0000000000000,1 +np.float64,0x800799758f2f32ec,0x3ff0000000000000,1 +np.float64,0xe72f1f6bce5e4,0x3ff0000000000000,1 +np.float64,0x3fe0e0f223a1c1e4,0x3ff70fed5b761673,1 +np.float64,0x3fe6d4f133eda9e2,0x3ffa3c8000c169eb,1 +np.float64,0xbfe1ccc3d8639988,0x3fe5c32148bedbda,1 +np.float64,0x3fea71c53574e38a,0x3ffc5f31201fe9be,1 +np.float64,0x9e0323eb3c065,0x3ff0000000000000,1 +np.float64,0x8005cc79a5cb98f4,0x3ff0000000000000,1 +np.float64,0x1dace1f83b59d,0x3ff0000000000000,1 +np.float64,0x10000000000000,0x3ff0000000000000,1 +np.float64,0xbfdef50830bdea10,0x3fe6e269fc17ebef,1 +np.float64,0x8010000000000000,0x3ff0000000000000,1 +np.float64,0xbfdfa82192bf5044,0x3fe6b6313ee0a095,1 +np.float64,0x3fd9398fe2b27320,0x3ff506ca2093c060,1 +np.float64,0x8002721fe664e441,0x3ff0000000000000,1 +np.float64,0x800c04166ad8082d,0x3ff0000000000000,1 +np.float64,0xffec3918b3387230,0x0,1 +np.float64,0x3fec62d5dfb8c5ac,0x3ffd972ea4a54b32,1 +np.float64,0x3fe7e42a0b6fc854,0x3ffad86b0443181d,1 +np.float64,0x3fc0aff5f3215fec,0x3ff1836058d4d210,1 +np.float64,0xbf82ff68a025fec0,0x3fefcb7f06862dce,1 +np.float64,0xae2e35195c5c7,0x3ff0000000000000,1 +np.float64,0x3fece3bddf79c77c,0x3ffdea41fb1ba8fa,1 +np.float64,0xbfa97b947832f730,0x3feeea34ebedbbd2,1 +np.float64,0xbfdfb1b1ce3f6364,0x3fe6b3d72871335c,1 +np.float64,0xbfe61a4f24ac349e,0x3fe3d356bf991b06,1 +np.float64,0x7fe23117a5e4622e,0x7ff0000000000000,1 +np.float64,0x800552a8cccaa552,0x3ff0000000000000,1 +np.float64,0x625b4d0ac4b6a,0x3ff0000000000000,1 +np.float64,0x3f86cf15702d9e00,0x3ff01fbe0381676d,1 +np.float64,0x800d7d1b685afa37,0x3ff0000000000000,1 +np.float64,0x3fe2cb6e40a596dd,0x3ff80a1a562f7fc9,1 +np.float64,0x3fe756eb8e2eadd7,0x3ffa86c638aad07d,1 +np.float64,0x800dc9a5513b934b,0x3ff0000000000000,1 +np.float64,0xbfbbdd118a37ba20,0x3fedacb4624f3cee,1 +np.float64,0x800de01f8efbc03f,0x3ff0000000000000,1 +np.float64,0x800da1a3fe9b4348,0x3ff0000000000000,1 +np.float64,0xbf87d8c7602fb180,0x3fefbe2614998ab6,1 +np.float64,0xbfdfff6141bffec2,0x3fe6a0c54d9f1bc8,1 +np.float64,0xee8fbba5dd1f8,0x3ff0000000000000,1 +np.float64,0x3fe79dc93e6f3b92,0x3ffaaf9d7d955b2c,1 +np.float64,0xffedd4b3d07ba967,0x0,1 +np.float64,0x800905dfc1720bc0,0x3ff0000000000000,1 +np.float64,0x3fd9e483b8b3c907,0x3ff52ddc6c950e7f,1 +np.float64,0xe34ffefdc6a00,0x3ff0000000000000,1 +np.float64,0x2168e62242d1e,0x3ff0000000000000,1 +np.float64,0x800349950e26932b,0x3ff0000000000000,1 +np.float64,0x7fc50da8532a1b50,0x7ff0000000000000,1 +np.float64,0xae1a4d115c34a,0x3ff0000000000000,1 +np.float64,0xa020f0b74041e,0x3ff0000000000000,1 +np.float64,0x3fd2aa2f77a5545f,0x3ff3959f09519a25,1 +np.float64,0x3fbfefc3223fdf86,0x3ff171f3df2d408b,1 +np.float64,0xbfea9fc340b53f86,0x3fe1f9d92b712654,1 +np.float64,0xffe9b920a5337240,0x0,1 +np.float64,0xbfe2eb0265e5d605,0x3fe53dd195782de3,1 +np.float64,0x7fb932c70e32658d,0x7ff0000000000000,1 +np.float64,0x3fda816bfcb502d8,0x3ff551f8d5c84c82,1 +np.float64,0x3fed68cbe9fad198,0x3ffe40f6692d5693,1 +np.float64,0x32df077665be2,0x3ff0000000000000,1 +np.float64,0x7fdc9c2f3539385d,0x7ff0000000000000,1 +np.float64,0x7fe71091a2ee2122,0x7ff0000000000000,1 +np.float64,0xbfe68106c46d020e,0x3fe3a76b56024c2c,1 +np.float64,0xffcf0572823e0ae4,0x0,1 +np.float64,0xbfeeab341fbd5668,0x3fe077d496941cda,1 +np.float64,0x7fe7ada0d2af5b41,0x7ff0000000000000,1 +np.float64,0xffacdef2a439bde0,0x0,1 +np.float64,0x3fe4200f3128401e,0x3ff8be0ddf30fd1e,1 +np.float64,0xffd9022a69320454,0x0,1 +np.float64,0xbfe8e06914f1c0d2,0x3fe2ab5fe7fffb5a,1 +np.float64,0x3fc4b976602972ed,0x3ff1e6786fa7a890,1 +np.float64,0xbfd784c105af0982,0x3fe8cdeb1cdbd57e,1 +np.float64,0x7feb20a20eb64143,0x7ff0000000000000,1 +np.float64,0xbfc87dd83630fbb0,0x3fec067c1e7e6983,1 +np.float64,0x7fe5400cbe6a8018,0x7ff0000000000000,1 +np.float64,0xbfb4a1f5e22943e8,0x3fee42e6c81559a9,1 +np.float64,0x3fe967c575f2cf8a,0x3ffbbd8bc0d5c50d,1 +np.float64,0xbfeb059cf4760b3a,0x3fe1d25c592c4dab,1 +np.float64,0xbfeef536d5bdea6e,0x3fe05d832c15c64a,1 +np.float64,0x3fa90b3f6432167f,0x3ff08d410dd732cc,1 +np.float64,0xbfeaff265e75fe4d,0x3fe1d4db3fb3208d,1 +np.float64,0x6d93d688db27b,0x3ff0000000000000,1 +np.float64,0x800ab9b4ea55736a,0x3ff0000000000000,1 +np.float64,0x3fd444b39d288967,0x3ff3ed749d48d444,1 +np.float64,0xbfd5f2c0d0abe582,0x3fe93ad6124d88e7,1 +np.float64,0x3fea8fd915f51fb2,0x3ffc71b32cb92d60,1 +np.float64,0xbfd23d6491a47aca,0x3fea43875709b0f0,1 +np.float64,0xffe76f75ce6edeeb,0x0,1 +np.float64,0x1f5670da3eacf,0x3ff0000000000000,1 +np.float64,0x8000d89c9621b13a,0x3ff0000000000000,1 +np.float64,0x3fedb51c52bb6a39,0x3ffe732279c228ff,1 +np.float64,0x7f99215ac83242b5,0x7ff0000000000000,1 +np.float64,0x742a6864e854e,0x3ff0000000000000,1 +np.float64,0xbfe02fb340205f66,0x3fe689495f9164e3,1 +np.float64,0x7fef4c12b0fe9824,0x7ff0000000000000,1 +np.float64,0x3fd40e17c2a81c30,0x3ff3e1aee8ed972f,1 +np.float64,0x7fdcd264e939a4c9,0x7ff0000000000000,1 +np.float64,0x3fdb675838b6ceb0,0x3ff587526241c550,1 +np.float64,0x3fdf1a4081be3480,0x3ff66896a18c2385,1 +np.float64,0xbfea5082b874a106,0x3fe218cf8f11be13,1 +np.float64,0xffe1a0ebf7e341d8,0x0,1 +np.float64,0x3fed0a2222ba1444,0x3ffe032ce928ae7d,1 +np.float64,0xffeae036da75c06d,0x0,1 +np.float64,0x5b05fc8ab60c0,0x3ff0000000000000,1 +np.float64,0x7fd8aae5f03155cb,0x7ff0000000000000,1 +np.float64,0xbfd0b4d9fda169b4,0x3feab41e58b6ccb7,1 +np.float64,0xffdcaffa57395ff4,0x0,1 +np.float64,0xbfcbf1455437e28c,0x3feb81a884182c5d,1 +np.float64,0x3f9d6700b83ace01,0x3ff0525657db35d4,1 +np.float64,0x4fd5b0b29fab7,0x3ff0000000000000,1 +np.float64,0x3fe9af2df5b35e5c,0x3ffbe895684df916,1 +np.float64,0x800dfd41f9dbfa84,0x3ff0000000000000,1 +np.float64,0xbf2a30457e546,0x3ff0000000000000,1 +np.float64,0x7fc6be37182d7c6d,0x7ff0000000000000,1 +np.float64,0x800e0f9788dc1f2f,0x3ff0000000000000,1 +np.float64,0x8006890c704d121a,0x3ff0000000000000,1 +np.float64,0xffecb1a7cbb9634f,0x0,1 +np.float64,0xffb35c330426b868,0x0,1 +np.float64,0x7fe8f2ba8a71e574,0x7ff0000000000000,1 +np.float64,0xf3ccff8fe79a0,0x3ff0000000000000,1 +np.float64,0x3fdf19a84e3e3351,0x3ff66871b17474c1,1 +np.float64,0x80049a662d0934cd,0x3ff0000000000000,1 +np.float64,0xdf5bb4bbbeb77,0x3ff0000000000000,1 +np.float64,0x8005eca030cbd941,0x3ff0000000000000,1 +np.float64,0xffe5f239586be472,0x0,1 +np.float64,0xbfc4526a0728a4d4,0x3fecaa52fbf5345e,1 +np.float64,0xbfe8f1ecda31e3da,0x3fe2a44c080848b3,1 +np.float64,0x3feebd32f4bd7a66,0x3fff234788938c3e,1 +np.float64,0xffd6ca04e9ad940a,0x0,1 +np.float64,0x7ff0000000000000,0x7ff0000000000000,1 +np.float64,0xbfd4c560a9a98ac2,0x3fe98db6d97442fc,1 +np.float64,0x8005723471cae46a,0x3ff0000000000000,1 +np.float64,0xbfeb278299764f05,0x3fe1c54b48f8ba4b,1 +np.float64,0x8007907b376f20f7,0x3ff0000000000000,1 +np.float64,0x7fe9c2fd01b385f9,0x7ff0000000000000,1 +np.float64,0x7fdaa37368b546e6,0x7ff0000000000000,1 +np.float64,0xbfe6d0f3786da1e7,0x3fe38582271cada7,1 +np.float64,0xbfea9b77823536ef,0x3fe1fb8575cd1b7d,1 +np.float64,0xbfe90ac38bf21587,0x3fe29a471b47a2e8,1 +np.float64,0xbfe9c51844738a30,0x3fe24fc8de03ea84,1 +np.float64,0x3fe45a9013a8b520,0x3ff8dd7c80f1cf75,1 +np.float64,0xbfe5780551eaf00a,0x3fe419832a6a4c56,1 +np.float64,0xffefffffffffffff,0x0,1 +np.float64,0x7fe3778c84a6ef18,0x7ff0000000000000,1 +np.float64,0xbfdc8a60413914c0,0x3fe77dc55b85028f,1 +np.float64,0xef47ae2fde8f6,0x3ff0000000000000,1 +np.float64,0x8001269fa4c24d40,0x3ff0000000000000,1 +np.float64,0x3fe9d2d39e73a5a7,0x3ffbfe2a66c4148e,1 +np.float64,0xffee61f528fcc3e9,0x0,1 +np.float64,0x3fe8a259ab7144b3,0x3ffb47e797a34bd2,1 +np.float64,0x3f906d610820dac0,0x3ff02dccda8e1a75,1 +np.float64,0x3fe70739f32e0e74,0x3ffa59232f4fcd07,1 +np.float64,0x3fe6b7f5e6ad6fec,0x3ffa2c0cc54f2c16,1 +np.float64,0x95a91a792b524,0x3ff0000000000000,1 +np.float64,0xbfedf6fcf57bedfa,0x3fe0b89bb40081cc,1 +np.float64,0xbfa4d2de9c29a5c0,0x3fef1c485678d657,1 +np.float64,0x3fe130470d22608e,0x3ff737b0be409a38,1 +np.float64,0x3fcf8035423f006b,0x3ff2f9d7c3c6a302,1 +np.float64,0xffe5995a3eab32b4,0x0,1 +np.float64,0xffca68c63034d18c,0x0,1 +np.float64,0xff9d53af903aa760,0x0,1 +np.float64,0x800563f1de6ac7e4,0x3ff0000000000000,1 +np.float64,0x7fce284fa63c509e,0x7ff0000000000000,1 +np.float64,0x7fb2a3959a25472a,0x7ff0000000000000,1 +np.float64,0x7fdbe2652f37c4c9,0x7ff0000000000000,1 +np.float64,0x800d705bbc1ae0b8,0x3ff0000000000000,1 +np.float64,0x7fd9bd2347b37a46,0x7ff0000000000000,1 +np.float64,0x3fcac3c0fb358782,0x3ff27ed62d6c8221,1 +np.float64,0x800110691ec220d3,0x3ff0000000000000,1 +np.float64,0x3fef79a8157ef350,0x3fffa368513eb909,1 +np.float64,0x7fe8bd2f0e317a5d,0x7ff0000000000000,1 +np.float64,0x7fd3040e60a6081c,0x7ff0000000000000,1 +np.float64,0xffea50723234a0e4,0x0,1 +np.float64,0xbfe6220054ac4400,0x3fe3d00961238a93,1 +np.float64,0x3f9eddd8c83dbbc0,0x3ff0567b0c73005a,1 +np.float64,0xbfa4a062c42940c0,0x3fef1e68badde324,1 +np.float64,0xbfd077ad4720ef5a,0x3feac5d577581d07,1 +np.float64,0x7fdfd4b025bfa95f,0x7ff0000000000000,1 +np.float64,0xd00d3cf3a01a8,0x3ff0000000000000,1 +np.float64,0x7fe3010427260207,0x7ff0000000000000,1 +np.float64,0x22ea196645d44,0x3ff0000000000000,1 +np.float64,0x7fd747e8cd2e8fd1,0x7ff0000000000000,1 +np.float64,0xd50665e7aa0cd,0x3ff0000000000000,1 +np.float64,0x7fe1da580ae3b4af,0x7ff0000000000000,1 +np.float64,0xffeb218ecfb6431d,0x0,1 +np.float64,0xbf887d0dd030fa00,0x3fefbc6252c8b354,1 +np.float64,0x3fcaa31067354621,0x3ff27b904c07e07f,1 +np.float64,0x7fe698cc4ded3198,0x7ff0000000000000,1 +np.float64,0x1c40191a38804,0x3ff0000000000000,1 +np.float64,0x80086fd20e30dfa4,0x3ff0000000000000,1 +np.float64,0x7fed34d5eaba69ab,0x7ff0000000000000,1 +np.float64,0xffd00b52622016a4,0x0,1 +np.float64,0x3f80abcdb021579b,0x3ff0172d27945851,1 +np.float64,0x3fe614cfd66c29a0,0x3ff9d031e1839191,1 +np.float64,0x80021d71c8843ae4,0x3ff0000000000000,1 +np.float64,0x800bc2adc657855c,0x3ff0000000000000,1 +np.float64,0x6b9fec1cd73fe,0x3ff0000000000000,1 +np.float64,0xffd9093b5f321276,0x0,1 +np.float64,0x800d3c6c77fa78d9,0x3ff0000000000000,1 +np.float64,0xffe80fc1cbf01f83,0x0,1 +np.float64,0xffbffbaf2a3ff760,0x0,1 +np.float64,0x3fea1ed29eb43da5,0x3ffc2c64ec0e17a3,1 +np.float64,0x7ff4000000000000,0x7ffc000000000000,1 +np.float64,0x3fd944a052328941,0x3ff5094f4c43ecca,1 +np.float64,0x800b1f9416163f29,0x3ff0000000000000,1 +np.float64,0x800f06bf33de0d7e,0x3ff0000000000000,1 +np.float64,0xbfdbf0d226b7e1a4,0x3fe7a4f73793d95b,1 +np.float64,0xffe7306c30ae60d8,0x0,1 +np.float64,0x7fe991accfb32359,0x7ff0000000000000,1 +np.float64,0x3fcc0040d2380082,0x3ff29ea47e4f07d4,1 +np.float64,0x7fefffffffffffff,0x7ff0000000000000,1 +np.float64,0x0,0x3ff0000000000000,1 +np.float64,0x3fe1423f7be2847e,0x3ff740bc1d3b20f8,1 +np.float64,0xbfeae3a3cab5c748,0x3fe1df7e936f8504,1 +np.float64,0x800b2da7d6165b50,0x3ff0000000000000,1 +np.float64,0x800b2404fcd6480a,0x3ff0000000000000,1 +np.float64,0x6fcbcf88df97b,0x3ff0000000000000,1 +np.float64,0xa248c0e14492,0x3ff0000000000000,1 +np.float64,0xffd255776824aaee,0x0,1 +np.float64,0x80057b3effeaf67f,0x3ff0000000000000,1 +np.float64,0x3feb0b07d7761610,0x3ffcbdfe1be5a594,1 +np.float64,0x924e1019249c2,0x3ff0000000000000,1 +np.float64,0x80074307e80e8611,0x3ff0000000000000,1 +np.float64,0xffb207fa46240ff8,0x0,1 +np.float64,0x95ac388d2b587,0x3ff0000000000000,1 +np.float64,0xbff0000000000000,0x3fe0000000000000,1 +np.float64,0x3fd38b6a492716d5,0x3ff3c59f62b5add5,1 +np.float64,0x7fe49362c3e926c5,0x7ff0000000000000,1 +np.float64,0x7fe842889db08510,0x7ff0000000000000,1 +np.float64,0xbfba6003e834c008,0x3fedcb620a2d9856,1 +np.float64,0xffe7e782bd6fcf05,0x0,1 +np.float64,0x7fd9b93d9433727a,0x7ff0000000000000,1 +np.float64,0x7fc8fcb61d31f96b,0x7ff0000000000000,1 +np.float64,0xbfef9be8db3f37d2,0x3fe022d603b81dc2,1 +np.float64,0x6f4fc766de9fa,0x3ff0000000000000,1 +np.float64,0xbfe93016f132602e,0x3fe28b42d782d949,1 +np.float64,0x3fe10e52b8e21ca5,0x3ff726a38b0bb895,1 +np.float64,0x3fbbba0ae6377416,0x3ff13f56084a9da3,1 +np.float64,0x3fe09e42ece13c86,0x3ff6eeb57e775e24,1 +np.float64,0x800942e39fb285c8,0x3ff0000000000000,1 +np.float64,0xffe5964370eb2c86,0x0,1 +np.float64,0x3fde479f32bc8f3e,0x3ff635b2619ba53a,1 +np.float64,0x3fe826e187f04dc3,0x3ffaff52b79c3a08,1 +np.float64,0x3febcbf1eab797e4,0x3ffd37152e5e2598,1 +np.float64,0x3fa0816a202102d4,0x3ff05c8e6a8b00d5,1 +np.float64,0xbd005ccb7a00c,0x3ff0000000000000,1 +np.float64,0x44c12fdc89827,0x3ff0000000000000,1 +np.float64,0xffc8fdffa431fc00,0x0,1 +np.float64,0xffeb4f5a87b69eb4,0x0,1 +np.float64,0xbfb07e7f8420fd00,0x3fee9a32924fe6a0,1 +np.float64,0xbfbd9d1bb63b3a38,0x3fed88ca81e5771c,1 +np.float64,0x8008682a74f0d055,0x3ff0000000000000,1 +np.float64,0x3fdeedbc7b3ddb79,0x3ff65dcb7c55f4dc,1 +np.float64,0x8009e889c613d114,0x3ff0000000000000,1 +np.float64,0x3faea831f43d5064,0x3ff0ad935e890e49,1 +np.float64,0xf0af1703e15e3,0x3ff0000000000000,1 +np.float64,0xffec06c4a5f80d88,0x0,1 +np.float64,0x53a1cc0ca743a,0x3ff0000000000000,1 +np.float64,0x7fd10c9eea22193d,0x7ff0000000000000,1 +np.float64,0xbfd48a6bf0a914d8,0x3fe99e0d109f2bac,1 +np.float64,0x3fd6dfe931adbfd4,0x3ff47f81c2dfc5d3,1 +np.float64,0x3fed20e86b7a41d0,0x3ffe11fecc7bc686,1 +np.float64,0xbfea586818b4b0d0,0x3fe215b7747d5cb8,1 +np.float64,0xbfd4ad3e20295a7c,0x3fe99465ab8c3275,1 +np.float64,0x3fd6619ee4acc33e,0x3ff4638b7b80c08a,1 +np.float64,0x3fdf6fcb63bedf97,0x3ff67d62fd3d560c,1 +np.float64,0x800a9191e7152324,0x3ff0000000000000,1 +np.float64,0x3fd2ff3c0da5fe78,0x3ff3a7b17e892a28,1 +np.float64,0x8003dbf1f327b7e5,0x3ff0000000000000,1 +np.float64,0xffea6b89a934d712,0x0,1 +np.float64,0x7fcfb879043f70f1,0x7ff0000000000000,1 +np.float64,0xea6a84dbd4d51,0x3ff0000000000000,1 +np.float64,0x800ec97a815d92f5,0x3ff0000000000000,1 +np.float64,0xffe304c3a8660987,0x0,1 +np.float64,0xbfefe24dd3ffc49c,0x3fe00a4e065be96d,1 +np.float64,0xffd3cc8c00a79918,0x0,1 +np.float64,0x95be8b7b2b7d2,0x3ff0000000000000,1 +np.float64,0x7fe20570cba40ae1,0x7ff0000000000000,1 +np.float64,0x7f97a06da02f40da,0x7ff0000000000000,1 +np.float64,0xffe702b9522e0572,0x0,1 +np.float64,0x3fada2d8543b45b1,0x3ff0a7adc4201e08,1 +np.float64,0x235e6acc46bce,0x3ff0000000000000,1 +np.float64,0x3fea6bc28ef4d786,0x3ffc5b7fc68fddac,1 +np.float64,0xffdbc9f505b793ea,0x0,1 +np.float64,0xffe98b137ff31626,0x0,1 +np.float64,0x800e26c6721c4d8d,0x3ff0000000000000,1 +np.float64,0x80080de445301bc9,0x3ff0000000000000,1 +np.float64,0x37e504a86fca1,0x3ff0000000000000,1 +np.float64,0x8002f5f60325ebed,0x3ff0000000000000,1 +np.float64,0x5c8772feb90ef,0x3ff0000000000000,1 +np.float64,0xbfe021abb4604358,0x3fe69023a51d22b8,1 +np.float64,0x3fde744f8fbce8a0,0x3ff64074dc84edd7,1 +np.float64,0xbfdd92899f3b2514,0x3fe73aefd9701858,1 +np.float64,0x7fc1ad5c51235ab8,0x7ff0000000000000,1 +np.float64,0xaae2f98955c5f,0x3ff0000000000000,1 +np.float64,0x7f9123d5782247aa,0x7ff0000000000000,1 +np.float64,0xbfe3f8e94b67f1d2,0x3fe4c30ab28e9cb7,1 +np.float64,0x7fdaba8b4cb57516,0x7ff0000000000000,1 +np.float64,0x7fefc85cfeff90b9,0x7ff0000000000000,1 +np.float64,0xffb83b4f523076a0,0x0,1 +np.float64,0xbfe888a68c71114d,0x3fe2ceff17c203d1,1 +np.float64,0x800de1dac4bbc3b6,0x3ff0000000000000,1 +np.float64,0xbfe4f27f09e9e4fe,0x3fe453f9af407eac,1 +np.float64,0xffe3d2713467a4e2,0x0,1 +np.float64,0xbfebaab840375570,0x3fe1931131b98842,1 +np.float64,0x93892a1b27126,0x3ff0000000000000,1 +np.float64,0x1e8e7f983d1d1,0x3ff0000000000000,1 +np.float64,0x3fecc950627992a0,0x3ffdd926f036add0,1 +np.float64,0xbfd41dfb1aa83bf6,0x3fe9bc34ece35b94,1 +np.float64,0x800aebfc6555d7f9,0x3ff0000000000000,1 +np.float64,0x7fe33ba52ca67749,0x7ff0000000000000,1 +np.float64,0xffe57c9b3feaf936,0x0,1 +np.float64,0x3fdd12464fba248c,0x3ff5ebc5598e6bd0,1 +np.float64,0xffe06d7f0fe0dafe,0x0,1 +np.float64,0x800e55b7fe9cab70,0x3ff0000000000000,1 +np.float64,0x3fd33803c8267008,0x3ff3b3cb78b2d642,1 +np.float64,0xe9cab8a1d3957,0x3ff0000000000000,1 +np.float64,0x3fb38ac166271580,0x3ff0de906947c0f0,1 +np.float64,0xbfd67aa552acf54a,0x3fe915cf64a389fd,1 +np.float64,0x1db96daa3b72f,0x3ff0000000000000,1 +np.float64,0xbfee9f08f4fd3e12,0x3fe07c2c615add3c,1 +np.float64,0xf14f6d65e29ee,0x3ff0000000000000,1 +np.float64,0x800bce089e179c12,0x3ff0000000000000,1 +np.float64,0xffc42dcc37285b98,0x0,1 +np.float64,0x7fd5f37063abe6e0,0x7ff0000000000000,1 +np.float64,0xbfd943c2cbb28786,0x3fe856f6452ec753,1 +np.float64,0x8ddfbc091bbf8,0x3ff0000000000000,1 +np.float64,0xbfe153491e22a692,0x3fe5fcb075dbbd5d,1 +np.float64,0xffe7933999ef2672,0x0,1 +np.float64,0x7ff8000000000000,0x7ff8000000000000,1 +np.float64,0x8000000000000000,0x3ff0000000000000,1 +np.float64,0xbfe9154580b22a8b,0x3fe2960bac3a8220,1 +np.float64,0x800dc6dda21b8dbb,0x3ff0000000000000,1 +np.float64,0xbfb26225a824c448,0x3fee7239a457df81,1 +np.float64,0xbfd7b68c83af6d1a,0x3fe8c08e351ab468,1 +np.float64,0xffde01f7213c03ee,0x0,1 +np.float64,0x3fe54cbe0faa997c,0x3ff9614527191d72,1 +np.float64,0xbfd6bec3732d7d86,0x3fe90354909493de,1 +np.float64,0xbfef3c85bd7e790b,0x3fe0444f8c489ca6,1 +np.float64,0x899501b7132a0,0x3ff0000000000000,1 +np.float64,0xbfe17a456462f48b,0x3fe5ea2719a9a84b,1 +np.float64,0xffe34003b8668007,0x0,1 +np.float64,0x7feff6a3633fed46,0x7ff0000000000000,1 +np.float64,0x3fba597ecc34b2fe,0x3ff12ee72e4de474,1 +np.float64,0x4084c7b68109a,0x3ff0000000000000,1 +np.float64,0x3fad23bf4c3a4780,0x3ff0a4d06193ff6d,1 +np.float64,0xffd0fe2707a1fc4e,0x0,1 +np.float64,0xb96cb43f72d97,0x3ff0000000000000,1 +np.float64,0x7fc4d684d829ad09,0x7ff0000000000000,1 +np.float64,0x7fdc349226b86923,0x7ff0000000000000,1 +np.float64,0x7fd82851cd3050a3,0x7ff0000000000000,1 +np.float64,0x800cde0041b9bc01,0x3ff0000000000000,1 +np.float64,0x4e8caa1e9d196,0x3ff0000000000000,1 +np.float64,0xbfed06a6d2fa0d4e,0x3fe1108c3682b05a,1 +np.float64,0xffe8908122312102,0x0,1 +np.float64,0xffe56ed6d9aaddad,0x0,1 +np.float64,0x3fedd6db00fbadb6,0x3ffe896c68c4b26e,1 +np.float64,0x3fde31f9b4bc63f4,0x3ff6307e08f8b6ba,1 +np.float64,0x6bb963c2d772d,0x3ff0000000000000,1 +np.float64,0x787b7142f0f6f,0x3ff0000000000000,1 +np.float64,0x3fe6e4147c6dc829,0x3ffa451bbdece240,1 +np.float64,0x8003857401470ae9,0x3ff0000000000000,1 +np.float64,0xbfeae82c3c75d058,0x3fe1ddbd66e65aab,1 +np.float64,0x7fe174707c62e8e0,0x7ff0000000000000,1 +np.float64,0x80008d2545e11a4b,0x3ff0000000000000,1 +np.float64,0xbfecc2dce17985ba,0x3fe129ad4325985a,1 +np.float64,0xbfe1fa1daf63f43c,0x3fe5adcb0731a44b,1 +np.float64,0x7fcf2530203e4a5f,0x7ff0000000000000,1 +np.float64,0xbfea5cefe874b9e0,0x3fe213f134b61f4a,1 +np.float64,0x800103729f2206e6,0x3ff0000000000000,1 +np.float64,0xbfe8442ff7708860,0x3fe2eaf850faa169,1 +np.float64,0x8006c78e19ed8f1d,0x3ff0000000000000,1 +np.float64,0x3fc259589c24b2b1,0x3ff1abe6a4d28816,1 +np.float64,0xffed02b7b5ba056e,0x0,1 +np.float64,0xbfce0aa4fe3c1548,0x3feb32115d92103e,1 +np.float64,0x7fec06e78bf80dce,0x7ff0000000000000,1 +np.float64,0xbfe0960bbc612c18,0x3fe6578ab29b70d4,1 +np.float64,0x3fee45841cbc8b08,0x3ffed2f6ca808ad3,1 +np.float64,0xbfeb0f8ebef61f1e,0x3fe1ce86003044cd,1 +np.float64,0x8002c357358586af,0x3ff0000000000000,1 +np.float64,0x3fe9aa10cc735422,0x3ffbe57e294ce68b,1 +np.float64,0x800256c0a544ad82,0x3ff0000000000000,1 +np.float64,0x4de6e1449bcdd,0x3ff0000000000000,1 +np.float64,0x65e9bc9ccbd38,0x3ff0000000000000,1 +np.float64,0xbfe53b0fa9aa7620,0x3fe4341f0aa29bbc,1 +np.float64,0xbfcdd94cd13bb298,0x3feb3956acd2e2dd,1 +np.float64,0x8004a49b65a94938,0x3ff0000000000000,1 +np.float64,0x800d3d05deba7a0c,0x3ff0000000000000,1 +np.float64,0x3fe4e05bce69c0b8,0x3ff925f55602a7e0,1 +np.float64,0xffe391e3256723c6,0x0,1 +np.float64,0xbfe92f0f37b25e1e,0x3fe28bacc76ae753,1 +np.float64,0x3f990238d8320472,0x3ff045edd36e2d62,1 +np.float64,0xffed8d15307b1a2a,0x0,1 +np.float64,0x3fee82e01afd05c0,0x3ffefc09e8b9c2b7,1 +np.float64,0xffb2d94b2225b298,0x0,1 diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv new file mode 100644 index 0000000000000000000000000000000000000000..03e76ffc2c222772e872908e147d4347effc1626 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-sin.csv @@ -0,0 +1,1370 @@ +dtype,input,output,ulperrortol +## +ve denormals ## +np.float32,0x004b4716,0x004b4716,2 +np.float32,0x007b2490,0x007b2490,2 +np.float32,0x007c99fa,0x007c99fa,2 +np.float32,0x00734a0c,0x00734a0c,2 +np.float32,0x0070de24,0x0070de24,2 +np.float32,0x007fffff,0x007fffff,2 +np.float32,0x00000001,0x00000001,2 +## -ve denormals ## +np.float32,0x80495d65,0x80495d65,2 +np.float32,0x806894f6,0x806894f6,2 +np.float32,0x80555a76,0x80555a76,2 +np.float32,0x804e1fb8,0x804e1fb8,2 +np.float32,0x80687de9,0x80687de9,2 +np.float32,0x807fffff,0x807fffff,2 +np.float32,0x80000001,0x80000001,2 +## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ## +np.float32,0x00000000,0x00000000,2 +np.float32,0x80000000,0x80000000,2 +np.float32,0x00800000,0x00800000,2 +np.float32,0x80800000,0x80800000,2 +## 1.00f ## +np.float32,0x3f800000,0x3f576aa4,2 +np.float32,0x3f800001,0x3f576aa6,2 +np.float32,0x3f800002,0x3f576aa7,2 +np.float32,0xc090a8b0,0x3f7b4e48,2 +np.float32,0x41ce3184,0x3f192d43,2 +np.float32,0xc1d85848,0xbf7161cb,2 +np.float32,0x402b8820,0x3ee3f29f,2 +np.float32,0x42b4e454,0x3f1d0151,2 +np.float32,0x42a67a60,0x3f7ffa4c,2 +np.float32,0x41d92388,0x3f67beef,2 +np.float32,0x422dd66c,0xbeffb0c1,2 +np.float32,0xc28f5be6,0xbf0bae79,2 +np.float32,0x41ab2674,0x3f0ffe2b,2 +np.float32,0x3f490fdb,0x3f3504f3,2 +np.float32,0xbf490fdb,0xbf3504f3,2 +np.float32,0x3fc90fdb,0x3f800000,2 +np.float32,0xbfc90fdb,0xbf800000,2 +np.float32,0x40490fdb,0xb3bbbd2e,2 +np.float32,0xc0490fdb,0x33bbbd2e,2 +np.float32,0x3fc90fdb,0x3f800000,2 +np.float32,0xbfc90fdb,0xbf800000,2 +np.float32,0x40490fdb,0xb3bbbd2e,2 +np.float32,0xc0490fdb,0x33bbbd2e,2 +np.float32,0x40c90fdb,0x343bbd2e,2 +np.float32,0xc0c90fdb,0xb43bbd2e,2 +np.float32,0x4016cbe4,0x3f3504f3,2 +np.float32,0xc016cbe4,0xbf3504f3,2 +np.float32,0x4096cbe4,0xbf800000,2 +np.float32,0xc096cbe4,0x3f800000,2 +np.float32,0x4116cbe4,0xb2ccde2e,2 +np.float32,0xc116cbe4,0x32ccde2e,2 +np.float32,0x40490fdb,0xb3bbbd2e,2 +np.float32,0xc0490fdb,0x33bbbd2e,2 +np.float32,0x40c90fdb,0x343bbd2e,2 +np.float32,0xc0c90fdb,0xb43bbd2e,2 +np.float32,0x41490fdb,0x34bbbd2e,2 +np.float32,0xc1490fdb,0xb4bbbd2e,2 +np.float32,0x407b53d2,0xbf3504f5,2 +np.float32,0xc07b53d2,0x3f3504f5,2 +np.float32,0x40fb53d2,0x3f800000,2 +np.float32,0xc0fb53d2,0xbf800000,2 +np.float32,0x417b53d2,0xb535563d,2 +np.float32,0xc17b53d2,0x3535563d,2 +np.float32,0x4096cbe4,0xbf800000,2 +np.float32,0xc096cbe4,0x3f800000,2 +np.float32,0x4116cbe4,0xb2ccde2e,2 +np.float32,0xc116cbe4,0x32ccde2e,2 +np.float32,0x4196cbe4,0x334cde2e,2 +np.float32,0xc196cbe4,0xb34cde2e,2 +np.float32,0x40afede0,0xbf3504ef,2 +np.float32,0xc0afede0,0x3f3504ef,2 +np.float32,0x412fede0,0xbf800000,2 +np.float32,0xc12fede0,0x3f800000,2 +np.float32,0x41afede0,0xb5b222c4,2 +np.float32,0xc1afede0,0x35b222c4,2 +np.float32,0x40c90fdb,0x343bbd2e,2 +np.float32,0xc0c90fdb,0xb43bbd2e,2 +np.float32,0x41490fdb,0x34bbbd2e,2 +np.float32,0xc1490fdb,0xb4bbbd2e,2 +np.float32,0x41c90fdb,0x353bbd2e,2 +np.float32,0xc1c90fdb,0xb53bbd2e,2 +np.float32,0x40e231d6,0x3f3504f3,2 +np.float32,0xc0e231d6,0xbf3504f3,2 +np.float32,0x416231d6,0x3f800000,2 +np.float32,0xc16231d6,0xbf800000,2 +np.float32,0x41e231d6,0xb399a6a2,2 +np.float32,0xc1e231d6,0x3399a6a2,2 +np.float32,0x40fb53d2,0x3f800000,2 +np.float32,0xc0fb53d2,0xbf800000,2 +np.float32,0x417b53d2,0xb535563d,2 +np.float32,0xc17b53d2,0x3535563d,2 +np.float32,0x41fb53d2,0x35b5563d,2 +np.float32,0xc1fb53d2,0xb5b5563d,2 +np.float32,0x410a3ae7,0x3f3504eb,2 +np.float32,0xc10a3ae7,0xbf3504eb,2 +np.float32,0x418a3ae7,0xbf800000,2 +np.float32,0xc18a3ae7,0x3f800000,2 +np.float32,0x420a3ae7,0xb6308908,2 +np.float32,0xc20a3ae7,0x36308908,2 +np.float32,0x4116cbe4,0xb2ccde2e,2 +np.float32,0xc116cbe4,0x32ccde2e,2 +np.float32,0x4196cbe4,0x334cde2e,2 +np.float32,0xc196cbe4,0xb34cde2e,2 +np.float32,0x4216cbe4,0x33ccde2e,2 +np.float32,0xc216cbe4,0xb3ccde2e,2 +np.float32,0x41235ce2,0xbf3504f7,2 +np.float32,0xc1235ce2,0x3f3504f7,2 +np.float32,0x41a35ce2,0x3f800000,2 +np.float32,0xc1a35ce2,0xbf800000,2 +np.float32,0x42235ce2,0xb5b889b6,2 +np.float32,0xc2235ce2,0x35b889b6,2 +np.float32,0x412fede0,0xbf800000,2 +np.float32,0xc12fede0,0x3f800000,2 +np.float32,0x41afede0,0xb5b222c4,2 +np.float32,0xc1afede0,0x35b222c4,2 +np.float32,0x422fede0,0x363222c4,2 +np.float32,0xc22fede0,0xb63222c4,2 +np.float32,0x413c7edd,0xbf3504f3,2 +np.float32,0xc13c7edd,0x3f3504f3,2 +np.float32,0x41bc7edd,0xbf800000,2 +np.float32,0xc1bc7edd,0x3f800000,2 +np.float32,0x423c7edd,0xb4000add,2 +np.float32,0xc23c7edd,0x34000add,2 +np.float32,0x41490fdb,0x34bbbd2e,2 +np.float32,0xc1490fdb,0xb4bbbd2e,2 +np.float32,0x41c90fdb,0x353bbd2e,2 +np.float32,0xc1c90fdb,0xb53bbd2e,2 +np.float32,0x42490fdb,0x35bbbd2e,2 +np.float32,0xc2490fdb,0xb5bbbd2e,2 +np.float32,0x4155a0d9,0x3f3504fb,2 +np.float32,0xc155a0d9,0xbf3504fb,2 +np.float32,0x41d5a0d9,0x3f800000,2 +np.float32,0xc1d5a0d9,0xbf800000,2 +np.float32,0x4255a0d9,0xb633bc81,2 +np.float32,0xc255a0d9,0x3633bc81,2 +np.float32,0x416231d6,0x3f800000,2 +np.float32,0xc16231d6,0xbf800000,2 +np.float32,0x41e231d6,0xb399a6a2,2 +np.float32,0xc1e231d6,0x3399a6a2,2 +np.float32,0x426231d6,0x3419a6a2,2 +np.float32,0xc26231d6,0xb419a6a2,2 +np.float32,0x416ec2d4,0x3f3504ef,2 +np.float32,0xc16ec2d4,0xbf3504ef,2 +np.float32,0x41eec2d4,0xbf800000,2 +np.float32,0xc1eec2d4,0x3f800000,2 +np.float32,0x426ec2d4,0xb5bef0a7,2 +np.float32,0xc26ec2d4,0x35bef0a7,2 +np.float32,0x417b53d2,0xb535563d,2 +np.float32,0xc17b53d2,0x3535563d,2 +np.float32,0x41fb53d2,0x35b5563d,2 +np.float32,0xc1fb53d2,0xb5b5563d,2 +np.float32,0x427b53d2,0x3635563d,2 +np.float32,0xc27b53d2,0xb635563d,2 +np.float32,0x4183f268,0xbf3504ff,2 +np.float32,0xc183f268,0x3f3504ff,2 +np.float32,0x4203f268,0x3f800000,2 +np.float32,0xc203f268,0xbf800000,2 +np.float32,0x4283f268,0xb6859a13,2 +np.float32,0xc283f268,0x36859a13,2 +np.float32,0x418a3ae7,0xbf800000,2 +np.float32,0xc18a3ae7,0x3f800000,2 +np.float32,0x420a3ae7,0xb6308908,2 +np.float32,0xc20a3ae7,0x36308908,2 +np.float32,0x428a3ae7,0x36b08908,2 +np.float32,0xc28a3ae7,0xb6b08908,2 +np.float32,0x41908365,0xbf3504f6,2 +np.float32,0xc1908365,0x3f3504f6,2 +np.float32,0x42108365,0xbf800000,2 +np.float32,0xc2108365,0x3f800000,2 +np.float32,0x42908365,0x3592200d,2 +np.float32,0xc2908365,0xb592200d,2 +np.float32,0x4196cbe4,0x334cde2e,2 +np.float32,0xc196cbe4,0xb34cde2e,2 +np.float32,0x4216cbe4,0x33ccde2e,2 +np.float32,0xc216cbe4,0xb3ccde2e,2 +np.float32,0x4296cbe4,0x344cde2e,2 +np.float32,0xc296cbe4,0xb44cde2e,2 +np.float32,0x419d1463,0x3f3504f8,2 +np.float32,0xc19d1463,0xbf3504f8,2 +np.float32,0x421d1463,0x3f800000,2 +np.float32,0xc21d1463,0xbf800000,2 +np.float32,0x429d1463,0xb5c55799,2 +np.float32,0xc29d1463,0x35c55799,2 +np.float32,0x41a35ce2,0x3f800000,2 +np.float32,0xc1a35ce2,0xbf800000,2 +np.float32,0x42235ce2,0xb5b889b6,2 +np.float32,0xc2235ce2,0x35b889b6,2 +np.float32,0x42a35ce2,0x363889b6,2 +np.float32,0xc2a35ce2,0xb63889b6,2 +np.float32,0x41a9a561,0x3f3504e7,2 +np.float32,0xc1a9a561,0xbf3504e7,2 +np.float32,0x4229a561,0xbf800000,2 +np.float32,0xc229a561,0x3f800000,2 +np.float32,0x42a9a561,0xb68733d0,2 +np.float32,0xc2a9a561,0x368733d0,2 +np.float32,0x41afede0,0xb5b222c4,2 +np.float32,0xc1afede0,0x35b222c4,2 +np.float32,0x422fede0,0x363222c4,2 +np.float32,0xc22fede0,0xb63222c4,2 +np.float32,0x42afede0,0x36b222c4,2 +np.float32,0xc2afede0,0xb6b222c4,2 +np.float32,0x41b6365e,0xbf3504f0,2 +np.float32,0xc1b6365e,0x3f3504f0,2 +np.float32,0x4236365e,0x3f800000,2 +np.float32,0xc236365e,0xbf800000,2 +np.float32,0x42b6365e,0x358bb91c,2 +np.float32,0xc2b6365e,0xb58bb91c,2 +np.float32,0x41bc7edd,0xbf800000,2 +np.float32,0xc1bc7edd,0x3f800000,2 +np.float32,0x423c7edd,0xb4000add,2 +np.float32,0xc23c7edd,0x34000add,2 +np.float32,0x42bc7edd,0x34800add,2 +np.float32,0xc2bc7edd,0xb4800add,2 +np.float32,0x41c2c75c,0xbf3504ef,2 +np.float32,0xc1c2c75c,0x3f3504ef,2 +np.float32,0x4242c75c,0xbf800000,2 +np.float32,0xc242c75c,0x3f800000,2 +np.float32,0x42c2c75c,0xb5cbbe8a,2 +np.float32,0xc2c2c75c,0x35cbbe8a,2 +np.float32,0x41c90fdb,0x353bbd2e,2 +np.float32,0xc1c90fdb,0xb53bbd2e,2 +np.float32,0x42490fdb,0x35bbbd2e,2 +np.float32,0xc2490fdb,0xb5bbbd2e,2 +np.float32,0x42c90fdb,0x363bbd2e,2 +np.float32,0xc2c90fdb,0xb63bbd2e,2 +np.float32,0x41cf585a,0x3f3504ff,2 +np.float32,0xc1cf585a,0xbf3504ff,2 +np.float32,0x424f585a,0x3f800000,2 +np.float32,0xc24f585a,0xbf800000,2 +np.float32,0x42cf585a,0xb688cd8c,2 +np.float32,0xc2cf585a,0x3688cd8c,2 +np.float32,0x41d5a0d9,0x3f800000,2 +np.float32,0xc1d5a0d9,0xbf800000,2 +np.float32,0x4255a0d9,0xb633bc81,2 +np.float32,0xc255a0d9,0x3633bc81,2 +np.float32,0x42d5a0d9,0x36b3bc81,2 +np.float32,0xc2d5a0d9,0xb6b3bc81,2 +np.float32,0x41dbe958,0x3f3504e0,2 +np.float32,0xc1dbe958,0xbf3504e0,2 +np.float32,0x425be958,0xbf800000,2 +np.float32,0xc25be958,0x3f800000,2 +np.float32,0x42dbe958,0xb6deab75,2 +np.float32,0xc2dbe958,0x36deab75,2 +np.float32,0x41e231d6,0xb399a6a2,2 +np.float32,0xc1e231d6,0x3399a6a2,2 +np.float32,0x426231d6,0x3419a6a2,2 +np.float32,0xc26231d6,0xb419a6a2,2 +np.float32,0x42e231d6,0x3499a6a2,2 +np.float32,0xc2e231d6,0xb499a6a2,2 +np.float32,0x41e87a55,0xbf3504f8,2 +np.float32,0xc1e87a55,0x3f3504f8,2 +np.float32,0x42687a55,0x3f800000,2 +np.float32,0xc2687a55,0xbf800000,2 +np.float32,0x42e87a55,0xb5d2257b,2 +np.float32,0xc2e87a55,0x35d2257b,2 +np.float32,0x41eec2d4,0xbf800000,2 +np.float32,0xc1eec2d4,0x3f800000,2 +np.float32,0x426ec2d4,0xb5bef0a7,2 +np.float32,0xc26ec2d4,0x35bef0a7,2 +np.float32,0x42eec2d4,0x363ef0a7,2 +np.float32,0xc2eec2d4,0xb63ef0a7,2 +np.float32,0x41f50b53,0xbf3504e7,2 +np.float32,0xc1f50b53,0x3f3504e7,2 +np.float32,0x42750b53,0xbf800000,2 +np.float32,0xc2750b53,0x3f800000,2 +np.float32,0x42f50b53,0xb68a6748,2 +np.float32,0xc2f50b53,0x368a6748,2 +np.float32,0x41fb53d2,0x35b5563d,2 +np.float32,0xc1fb53d2,0xb5b5563d,2 +np.float32,0x427b53d2,0x3635563d,2 +np.float32,0xc27b53d2,0xb635563d,2 +np.float32,0x42fb53d2,0x36b5563d,2 +np.float32,0xc2fb53d2,0xb6b5563d,2 +np.float32,0x4200ce28,0x3f3504f0,2 +np.float32,0xc200ce28,0xbf3504f0,2 +np.float32,0x4280ce28,0x3f800000,2 +np.float32,0xc280ce28,0xbf800000,2 +np.float32,0x4300ce28,0x357dd672,2 +np.float32,0xc300ce28,0xb57dd672,2 +np.float32,0x4203f268,0x3f800000,2 +np.float32,0xc203f268,0xbf800000,2 +np.float32,0x4283f268,0xb6859a13,2 +np.float32,0xc283f268,0x36859a13,2 +np.float32,0x4303f268,0x37059a13,2 +np.float32,0xc303f268,0xb7059a13,2 +np.float32,0x420716a7,0x3f3504ee,2 +np.float32,0xc20716a7,0xbf3504ee,2 +np.float32,0x428716a7,0xbf800000,2 +np.float32,0xc28716a7,0x3f800000,2 +np.float32,0x430716a7,0xb5d88c6d,2 +np.float32,0xc30716a7,0x35d88c6d,2 +np.float32,0x420a3ae7,0xb6308908,2 +np.float32,0xc20a3ae7,0x36308908,2 +np.float32,0x428a3ae7,0x36b08908,2 +np.float32,0xc28a3ae7,0xb6b08908,2 +np.float32,0x430a3ae7,0x37308908,2 +np.float32,0xc30a3ae7,0xb7308908,2 +np.float32,0x420d5f26,0xbf350500,2 +np.float32,0xc20d5f26,0x3f350500,2 +np.float32,0x428d5f26,0x3f800000,2 +np.float32,0xc28d5f26,0xbf800000,2 +np.float32,0x430d5f26,0xb68c0105,2 +np.float32,0xc30d5f26,0x368c0105,2 +np.float32,0x42108365,0xbf800000,2 +np.float32,0xc2108365,0x3f800000,2 +np.float32,0x42908365,0x3592200d,2 +np.float32,0xc2908365,0xb592200d,2 +np.float32,0x43108365,0xb612200d,2 +np.float32,0xc3108365,0x3612200d,2 +np.float32,0x4213a7a5,0xbf3504df,2 +np.float32,0xc213a7a5,0x3f3504df,2 +np.float32,0x4293a7a5,0xbf800000,2 +np.float32,0xc293a7a5,0x3f800000,2 +np.float32,0x4313a7a5,0xb6e1deee,2 +np.float32,0xc313a7a5,0x36e1deee,2 +np.float32,0x4216cbe4,0x33ccde2e,2 +np.float32,0xc216cbe4,0xb3ccde2e,2 +np.float32,0x4296cbe4,0x344cde2e,2 +np.float32,0xc296cbe4,0xb44cde2e,2 +np.float32,0x4316cbe4,0x34ccde2e,2 +np.float32,0xc316cbe4,0xb4ccde2e,2 +np.float32,0x4219f024,0x3f35050f,2 +np.float32,0xc219f024,0xbf35050f,2 +np.float32,0x4299f024,0x3f800000,2 +np.float32,0xc299f024,0xbf800000,2 +np.float32,0x4319f024,0xb71bde6c,2 +np.float32,0xc319f024,0x371bde6c,2 +np.float32,0x421d1463,0x3f800000,2 +np.float32,0xc21d1463,0xbf800000,2 +np.float32,0x429d1463,0xb5c55799,2 +np.float32,0xc29d1463,0x35c55799,2 +np.float32,0x431d1463,0x36455799,2 +np.float32,0xc31d1463,0xb6455799,2 +np.float32,0x422038a3,0x3f3504d0,2 +np.float32,0xc22038a3,0xbf3504d0,2 +np.float32,0x42a038a3,0xbf800000,2 +np.float32,0xc2a038a3,0x3f800000,2 +np.float32,0x432038a3,0xb746cd61,2 +np.float32,0xc32038a3,0x3746cd61,2 +np.float32,0x42235ce2,0xb5b889b6,2 +np.float32,0xc2235ce2,0x35b889b6,2 +np.float32,0x42a35ce2,0x363889b6,2 +np.float32,0xc2a35ce2,0xb63889b6,2 +np.float32,0x43235ce2,0x36b889b6,2 +np.float32,0xc3235ce2,0xb6b889b6,2 +np.float32,0x42268121,0xbf3504f1,2 +np.float32,0xc2268121,0x3f3504f1,2 +np.float32,0x42a68121,0x3f800000,2 +np.float32,0xc2a68121,0xbf800000,2 +np.float32,0x43268121,0x35643aac,2 +np.float32,0xc3268121,0xb5643aac,2 +np.float32,0x4229a561,0xbf800000,2 +np.float32,0xc229a561,0x3f800000,2 +np.float32,0x42a9a561,0xb68733d0,2 +np.float32,0xc2a9a561,0x368733d0,2 +np.float32,0x4329a561,0x370733d0,2 +np.float32,0xc329a561,0xb70733d0,2 +np.float32,0x422cc9a0,0xbf3504ee,2 +np.float32,0xc22cc9a0,0x3f3504ee,2 +np.float32,0x42acc9a0,0xbf800000,2 +np.float32,0xc2acc9a0,0x3f800000,2 +np.float32,0x432cc9a0,0xb5e55a50,2 +np.float32,0xc32cc9a0,0x35e55a50,2 +np.float32,0x422fede0,0x363222c4,2 +np.float32,0xc22fede0,0xb63222c4,2 +np.float32,0x42afede0,0x36b222c4,2 +np.float32,0xc2afede0,0xb6b222c4,2 +np.float32,0x432fede0,0x373222c4,2 +np.float32,0xc32fede0,0xb73222c4,2 +np.float32,0x4233121f,0x3f350500,2 +np.float32,0xc233121f,0xbf350500,2 +np.float32,0x42b3121f,0x3f800000,2 +np.float32,0xc2b3121f,0xbf800000,2 +np.float32,0x4333121f,0xb68f347d,2 +np.float32,0xc333121f,0x368f347d,2 +np.float32,0x4236365e,0x3f800000,2 +np.float32,0xc236365e,0xbf800000,2 +np.float32,0x42b6365e,0x358bb91c,2 +np.float32,0xc2b6365e,0xb58bb91c,2 +np.float32,0x4336365e,0xb60bb91c,2 +np.float32,0xc336365e,0x360bb91c,2 +np.float32,0x42395a9e,0x3f3504df,2 +np.float32,0xc2395a9e,0xbf3504df,2 +np.float32,0x42b95a9e,0xbf800000,2 +np.float32,0xc2b95a9e,0x3f800000,2 +np.float32,0x43395a9e,0xb6e51267,2 +np.float32,0xc3395a9e,0x36e51267,2 +np.float32,0x423c7edd,0xb4000add,2 +np.float32,0xc23c7edd,0x34000add,2 +np.float32,0x42bc7edd,0x34800add,2 +np.float32,0xc2bc7edd,0xb4800add,2 +np.float32,0x433c7edd,0x35000add,2 +np.float32,0xc33c7edd,0xb5000add,2 +np.float32,0x423fa31d,0xbf35050f,2 +np.float32,0xc23fa31d,0x3f35050f,2 +np.float32,0x42bfa31d,0x3f800000,2 +np.float32,0xc2bfa31d,0xbf800000,2 +np.float32,0x433fa31d,0xb71d7828,2 +np.float32,0xc33fa31d,0x371d7828,2 +np.float32,0x4242c75c,0xbf800000,2 +np.float32,0xc242c75c,0x3f800000,2 +np.float32,0x42c2c75c,0xb5cbbe8a,2 +np.float32,0xc2c2c75c,0x35cbbe8a,2 +np.float32,0x4342c75c,0x364bbe8a,2 +np.float32,0xc342c75c,0xb64bbe8a,2 +np.float32,0x4245eb9c,0xbf3504d0,2 +np.float32,0xc245eb9c,0x3f3504d0,2 +np.float32,0x42c5eb9c,0xbf800000,2 +np.float32,0xc2c5eb9c,0x3f800000,2 +np.float32,0x4345eb9c,0xb748671d,2 +np.float32,0xc345eb9c,0x3748671d,2 +np.float32,0x42490fdb,0x35bbbd2e,2 +np.float32,0xc2490fdb,0xb5bbbd2e,2 +np.float32,0x42c90fdb,0x363bbd2e,2 +np.float32,0xc2c90fdb,0xb63bbd2e,2 +np.float32,0x43490fdb,0x36bbbd2e,2 +np.float32,0xc3490fdb,0xb6bbbd2e,2 +np.float32,0x424c341a,0x3f3504f1,2 +np.float32,0xc24c341a,0xbf3504f1,2 +np.float32,0x42cc341a,0x3f800000,2 +np.float32,0xc2cc341a,0xbf800000,2 +np.float32,0x434c341a,0x354a9ee6,2 +np.float32,0xc34c341a,0xb54a9ee6,2 +np.float32,0x424f585a,0x3f800000,2 +np.float32,0xc24f585a,0xbf800000,2 +np.float32,0x42cf585a,0xb688cd8c,2 +np.float32,0xc2cf585a,0x3688cd8c,2 +np.float32,0x434f585a,0x3708cd8c,2 +np.float32,0xc34f585a,0xb708cd8c,2 +np.float32,0x42527c99,0x3f3504ee,2 +np.float32,0xc2527c99,0xbf3504ee,2 +np.float32,0x42d27c99,0xbf800000,2 +np.float32,0xc2d27c99,0x3f800000,2 +np.float32,0x43527c99,0xb5f22833,2 +np.float32,0xc3527c99,0x35f22833,2 +np.float32,0x4255a0d9,0xb633bc81,2 +np.float32,0xc255a0d9,0x3633bc81,2 +np.float32,0x42d5a0d9,0x36b3bc81,2 +np.float32,0xc2d5a0d9,0xb6b3bc81,2 +np.float32,0x4355a0d9,0x3733bc81,2 +np.float32,0xc355a0d9,0xb733bc81,2 +np.float32,0x4258c518,0xbf350500,2 +np.float32,0xc258c518,0x3f350500,2 +np.float32,0x42d8c518,0x3f800000,2 +np.float32,0xc2d8c518,0xbf800000,2 +np.float32,0x4358c518,0xb69267f6,2 +np.float32,0xc358c518,0x369267f6,2 +np.float32,0x425be958,0xbf800000,2 +np.float32,0xc25be958,0x3f800000,2 +np.float32,0x42dbe958,0xb6deab75,2 +np.float32,0xc2dbe958,0x36deab75,2 +np.float32,0x435be958,0x375eab75,2 +np.float32,0xc35be958,0xb75eab75,2 +np.float32,0x425f0d97,0xbf3504df,2 +np.float32,0xc25f0d97,0x3f3504df,2 +np.float32,0x42df0d97,0xbf800000,2 +np.float32,0xc2df0d97,0x3f800000,2 +np.float32,0x435f0d97,0xb6e845e0,2 +np.float32,0xc35f0d97,0x36e845e0,2 +np.float32,0x426231d6,0x3419a6a2,2 +np.float32,0xc26231d6,0xb419a6a2,2 +np.float32,0x42e231d6,0x3499a6a2,2 +np.float32,0xc2e231d6,0xb499a6a2,2 +np.float32,0x436231d6,0x3519a6a2,2 +np.float32,0xc36231d6,0xb519a6a2,2 +np.float32,0x42655616,0x3f35050f,2 +np.float32,0xc2655616,0xbf35050f,2 +np.float32,0x42e55616,0x3f800000,2 +np.float32,0xc2e55616,0xbf800000,2 +np.float32,0x43655616,0xb71f11e5,2 +np.float32,0xc3655616,0x371f11e5,2 +np.float32,0x42687a55,0x3f800000,2 +np.float32,0xc2687a55,0xbf800000,2 +np.float32,0x42e87a55,0xb5d2257b,2 +np.float32,0xc2e87a55,0x35d2257b,2 +np.float32,0x43687a55,0x3652257b,2 +np.float32,0xc3687a55,0xb652257b,2 +np.float32,0x426b9e95,0x3f3504cf,2 +np.float32,0xc26b9e95,0xbf3504cf,2 +np.float32,0x42eb9e95,0xbf800000,2 +np.float32,0xc2eb9e95,0x3f800000,2 +np.float32,0x436b9e95,0xb74a00d9,2 +np.float32,0xc36b9e95,0x374a00d9,2 +np.float32,0x426ec2d4,0xb5bef0a7,2 +np.float32,0xc26ec2d4,0x35bef0a7,2 +np.float32,0x42eec2d4,0x363ef0a7,2 +np.float32,0xc2eec2d4,0xb63ef0a7,2 +np.float32,0x436ec2d4,0x36bef0a7,2 +np.float32,0xc36ec2d4,0xb6bef0a7,2 +np.float32,0x4271e713,0xbf3504f1,2 +np.float32,0xc271e713,0x3f3504f1,2 +np.float32,0x42f1e713,0x3f800000,2 +np.float32,0xc2f1e713,0xbf800000,2 +np.float32,0x4371e713,0x35310321,2 +np.float32,0xc371e713,0xb5310321,2 +np.float32,0x42750b53,0xbf800000,2 +np.float32,0xc2750b53,0x3f800000,2 +np.float32,0x42f50b53,0xb68a6748,2 +np.float32,0xc2f50b53,0x368a6748,2 +np.float32,0x43750b53,0x370a6748,2 +np.float32,0xc3750b53,0xb70a6748,2 +np.float32,0x42782f92,0xbf3504ee,2 +np.float32,0xc2782f92,0x3f3504ee,2 +np.float32,0x42f82f92,0xbf800000,2 +np.float32,0xc2f82f92,0x3f800000,2 +np.float32,0x43782f92,0xb5fef616,2 +np.float32,0xc3782f92,0x35fef616,2 +np.float32,0x427b53d2,0x3635563d,2 +np.float32,0xc27b53d2,0xb635563d,2 +np.float32,0x42fb53d2,0x36b5563d,2 +np.float32,0xc2fb53d2,0xb6b5563d,2 +np.float32,0x437b53d2,0x3735563d,2 +np.float32,0xc37b53d2,0xb735563d,2 +np.float32,0x427e7811,0x3f350500,2 +np.float32,0xc27e7811,0xbf350500,2 +np.float32,0x42fe7811,0x3f800000,2 +np.float32,0xc2fe7811,0xbf800000,2 +np.float32,0x437e7811,0xb6959b6f,2 +np.float32,0xc37e7811,0x36959b6f,2 +np.float32,0x4280ce28,0x3f800000,2 +np.float32,0xc280ce28,0xbf800000,2 +np.float32,0x4300ce28,0x357dd672,2 +np.float32,0xc300ce28,0xb57dd672,2 +np.float32,0x4380ce28,0xb5fdd672,2 +np.float32,0xc380ce28,0x35fdd672,2 +np.float32,0x42826048,0x3f3504de,2 +np.float32,0xc2826048,0xbf3504de,2 +np.float32,0x43026048,0xbf800000,2 +np.float32,0xc3026048,0x3f800000,2 +np.float32,0x43826048,0xb6eb7958,2 +np.float32,0xc3826048,0x36eb7958,2 +np.float32,0x4283f268,0xb6859a13,2 +np.float32,0xc283f268,0x36859a13,2 +np.float32,0x4303f268,0x37059a13,2 +np.float32,0xc303f268,0xb7059a13,2 +np.float32,0x4383f268,0x37859a13,2 +np.float32,0xc383f268,0xb7859a13,2 +np.float32,0x42858487,0xbf3504e2,2 +np.float32,0xc2858487,0x3f3504e2,2 +np.float32,0x43058487,0x3f800000,2 +np.float32,0xc3058487,0xbf800000,2 +np.float32,0x43858487,0x36bea8be,2 +np.float32,0xc3858487,0xb6bea8be,2 +np.float32,0x428716a7,0xbf800000,2 +np.float32,0xc28716a7,0x3f800000,2 +np.float32,0x430716a7,0xb5d88c6d,2 +np.float32,0xc30716a7,0x35d88c6d,2 +np.float32,0x438716a7,0x36588c6d,2 +np.float32,0xc38716a7,0xb6588c6d,2 +np.float32,0x4288a8c7,0xbf3504cf,2 +np.float32,0xc288a8c7,0x3f3504cf,2 +np.float32,0x4308a8c7,0xbf800000,2 +np.float32,0xc308a8c7,0x3f800000,2 +np.float32,0x4388a8c7,0xb74b9a96,2 +np.float32,0xc388a8c7,0x374b9a96,2 +np.float32,0x428a3ae7,0x36b08908,2 +np.float32,0xc28a3ae7,0xb6b08908,2 +np.float32,0x430a3ae7,0x37308908,2 +np.float32,0xc30a3ae7,0xb7308908,2 +np.float32,0x438a3ae7,0x37b08908,2 +np.float32,0xc38a3ae7,0xb7b08908,2 +np.float32,0x428bcd06,0x3f3504f2,2 +np.float32,0xc28bcd06,0xbf3504f2,2 +np.float32,0x430bcd06,0x3f800000,2 +np.float32,0xc30bcd06,0xbf800000,2 +np.float32,0x438bcd06,0x3517675b,2 +np.float32,0xc38bcd06,0xb517675b,2 +np.float32,0x428d5f26,0x3f800000,2 +np.float32,0xc28d5f26,0xbf800000,2 +np.float32,0x430d5f26,0xb68c0105,2 +np.float32,0xc30d5f26,0x368c0105,2 +np.float32,0x438d5f26,0x370c0105,2 +np.float32,0xc38d5f26,0xb70c0105,2 +np.float32,0x428ef146,0x3f3504c0,2 +np.float32,0xc28ef146,0xbf3504c0,2 +np.float32,0x430ef146,0xbf800000,2 +np.float32,0xc30ef146,0x3f800000,2 +np.float32,0x438ef146,0xb790bc40,2 +np.float32,0xc38ef146,0x3790bc40,2 +np.float32,0x42908365,0x3592200d,2 +np.float32,0xc2908365,0xb592200d,2 +np.float32,0x43108365,0xb612200d,2 +np.float32,0xc3108365,0x3612200d,2 +np.float32,0x43908365,0xb692200d,2 +np.float32,0xc3908365,0x3692200d,2 +np.float32,0x42921585,0xbf350501,2 +np.float32,0xc2921585,0x3f350501,2 +np.float32,0x43121585,0x3f800000,2 +np.float32,0xc3121585,0xbf800000,2 +np.float32,0x43921585,0xb698cee8,2 +np.float32,0xc3921585,0x3698cee8,2 +np.float32,0x4293a7a5,0xbf800000,2 +np.float32,0xc293a7a5,0x3f800000,2 +np.float32,0x4313a7a5,0xb6e1deee,2 +np.float32,0xc313a7a5,0x36e1deee,2 +np.float32,0x4393a7a5,0x3761deee,2 +np.float32,0xc393a7a5,0xb761deee,2 +np.float32,0x429539c5,0xbf3504b1,2 +np.float32,0xc29539c5,0x3f3504b1,2 +np.float32,0x431539c5,0xbf800000,2 +np.float32,0xc31539c5,0x3f800000,2 +np.float32,0x439539c5,0xb7bbab34,2 +np.float32,0xc39539c5,0x37bbab34,2 +np.float32,0x4296cbe4,0x344cde2e,2 +np.float32,0xc296cbe4,0xb44cde2e,2 +np.float32,0x4316cbe4,0x34ccde2e,2 +np.float32,0xc316cbe4,0xb4ccde2e,2 +np.float32,0x4396cbe4,0x354cde2e,2 +np.float32,0xc396cbe4,0xb54cde2e,2 +np.float32,0x42985e04,0x3f350510,2 +np.float32,0xc2985e04,0xbf350510,2 +np.float32,0x43185e04,0x3f800000,2 +np.float32,0xc3185e04,0xbf800000,2 +np.float32,0x43985e04,0xb722455d,2 +np.float32,0xc3985e04,0x3722455d,2 +np.float32,0x4299f024,0x3f800000,2 +np.float32,0xc299f024,0xbf800000,2 +np.float32,0x4319f024,0xb71bde6c,2 +np.float32,0xc319f024,0x371bde6c,2 +np.float32,0x4399f024,0x379bde6c,2 +np.float32,0xc399f024,0xb79bde6c,2 +np.float32,0x429b8243,0x3f3504fc,2 +np.float32,0xc29b8243,0xbf3504fc,2 +np.float32,0x431b8243,0xbf800000,2 +np.float32,0xc31b8243,0x3f800000,2 +np.float32,0x439b8243,0x364b2eb8,2 +np.float32,0xc39b8243,0xb64b2eb8,2 +np.float32,0x435b2047,0xbf350525,2 +np.float32,0x42a038a2,0xbf800000,2 +np.float32,0x432038a2,0x3664ca7e,2 +np.float32,0x4345eb9b,0x365e638c,2 +np.float32,0x42c5eb9b,0xbf800000,2 +np.float32,0x42eb9e94,0xbf800000,2 +np.float32,0x4350ea79,0x3f800000,2 +np.float32,0x42dbe957,0x3585522a,2 +np.float32,0x425be957,0xbf800000,2 +np.float32,0x435be957,0xb605522a,2 +np.float32,0x476362a2,0xbd7ff911,2 +np.float32,0x464c99a4,0x3e7f4d41,2 +np.float32,0x4471f73d,0x3e7fe1b0,2 +np.float32,0x445a6752,0x3e7ef367,2 +np.float32,0x474fa400,0x3e7f9fcd,2 +np.float32,0x45c1e72f,0xbe7fc7af,2 +np.float32,0x4558c91d,0x3e7e9f31,2 +np.float32,0x43784f94,0xbdff6654,2 +np.float32,0x466e8500,0xbe7ea0a3,2 +np.float32,0x468e1c25,0x3e7e22fb,2 +np.float32,0x44ea6cfc,0x3dff70c3,2 +np.float32,0x4605126c,0x3e7f89ef,2 +np.float32,0x4788b3c6,0xbb87d853,2 +np.float32,0x4531b042,0x3dffd163,2 +np.float32,0x43f1f71d,0x3dfff387,2 +np.float32,0x462c3fa5,0xbd7fe13d,2 +np.float32,0x441c5354,0xbdff76b4,2 +np.float32,0x44908b69,0x3e7dcf0d,2 +np.float32,0x478813ad,0xbe7e9d80,2 +np.float32,0x441c4351,0x3dff937b,2 +np.float64,0x1,0x1,1 +np.float64,0x8000000000000001,0x8000000000000001,1 +np.float64,0x10000000000000,0x10000000000000,1 +np.float64,0x8010000000000000,0x8010000000000000,1 +np.float64,0x7fefffffffffffff,0x3f7452fc98b34e97,1 +np.float64,0xffefffffffffffff,0xbf7452fc98b34e97,1 +np.float64,0x7ff0000000000000,0xfff8000000000000,1 +np.float64,0xfff0000000000000,0xfff8000000000000,1 +np.float64,0x7ff8000000000000,0x7ff8000000000000,1 +np.float64,0x7ff4000000000000,0x7ffc000000000000,1 +np.float64,0xbfda51b226b4a364,0xbfd9956328ff876c,1 +np.float64,0xbfb4a65aee294cb8,0xbfb4a09fd744f8a5,1 +np.float64,0xbfd73b914fae7722,0xbfd6b9cce55af379,1 +np.float64,0xbfd90c12b4b21826,0xbfd869a3867b51c2,1 +np.float64,0x3fe649bb3d6c9376,0x3fe48778d9b48a21,1 +np.float64,0xbfd5944532ab288a,0xbfd52c30e1951b42,1 +np.float64,0x3fb150c45222a190,0x3fb14d633eb8275d,1 +np.float64,0x3fe4a6ffa9e94e00,0x3fe33f8a95c33299,1 +np.float64,0x3fe8d2157171a42a,0x3fe667d904ac95a6,1 +np.float64,0xbfa889f52c3113f0,0xbfa8878d90a23fa5,1 +np.float64,0x3feb3234bef6646a,0x3fe809d541d9017a,1 +np.float64,0x3fc6de266f2dbc50,0x3fc6bf0ee80a0d86,1 +np.float64,0x3fe8455368f08aa6,0x3fe6028254338ed5,1 +np.float64,0xbfe5576079eaaec1,0xbfe3cb4a8f6bc3f5,1 +np.float64,0xbfe9f822ff73f046,0xbfe7360d7d5cb887,1 +np.float64,0xbfb1960e7e232c20,0xbfb1928438258602,1 +np.float64,0xbfca75938d34eb28,0xbfca4570979bf2fa,1 +np.float64,0x3fd767dd15aecfbc,0x3fd6e33039018bab,1 +np.float64,0xbfe987750ef30eea,0xbfe6e7ed30ce77f0,1 +np.float64,0xbfe87f95a1f0ff2b,0xbfe62ca7e928bb2a,1 +np.float64,0xbfd2465301a48ca6,0xbfd2070245775d76,1 +np.float64,0xbfb1306ed22260e0,0xbfb12d2088eaa4f9,1 +np.float64,0xbfd8089010b01120,0xbfd778f9db77f2f3,1 +np.float64,0x3fbf9cf4ee3f39f0,0x3fbf88674fde1ca2,1 +np.float64,0x3fe6d8468a6db08e,0x3fe4f403f38b7bec,1 +np.float64,0xbfd9e5deefb3cbbe,0xbfd932692c722351,1 +np.float64,0x3fd1584d55a2b09c,0x3fd122253eeecc2e,1 +np.float64,0x3fe857979cf0af30,0x3fe60fc12b5ba8db,1 +np.float64,0x3fe3644149e6c882,0x3fe239f47013cfe6,1 +np.float64,0xbfe22ea62be45d4c,0xbfe13834c17d56fe,1 +np.float64,0xbfe8d93e1df1b27c,0xbfe66cf4ee467fd2,1 +np.float64,0xbfe9c497c9f38930,0xbfe7127417da4204,1 +np.float64,0x3fd6791cecacf238,0x3fd6039ccb5a7fde,1 +np.float64,0xbfc1dc1b1523b838,0xbfc1cd48edd9ae19,1 +np.float64,0xbfc92a8491325508,0xbfc901176e0158a5,1 +np.float64,0x3fa8649b3430c940,0x3fa8623e82d9504f,1 +np.float64,0x3fe0bed6a1617dae,0x3fdffbb307fb1abe,1 +np.float64,0x3febdf7765f7beee,0x3fe87ad01a89b74a,1 +np.float64,0xbfd3a56d46a74ada,0xbfd356cf41bf83cd,1 +np.float64,0x3fd321d824a643b0,0x3fd2d93846a224b3,1 +np.float64,0xbfc6a49fb52d4940,0xbfc686704906e7d3,1 +np.float64,0xbfdd4103c9ba8208,0xbfdc3ef0c03615b4,1 +np.float64,0xbfe0b78a51e16f14,0xbfdfef0d9ffc38b5,1 +np.float64,0xbfdac7a908b58f52,0xbfda0158956ceecf,1 +np.float64,0xbfbfbf12f23f7e28,0xbfbfaa428989258c,1 +np.float64,0xbfd55f5aa2aabeb6,0xbfd4fa39de65f33a,1 +np.float64,0x3fe06969abe0d2d4,0x3fdf6744fafdd9cf,1 +np.float64,0x3fe56ab8be6ad572,0x3fe3da7a1986d543,1 +np.float64,0xbfeefbbec67df77e,0xbfea5d426132f4aa,1 +np.float64,0x3fe6e1f49cedc3ea,0x3fe4fb53f3d8e3d5,1 +np.float64,0x3feceb231c79d646,0x3fe923d3efa55414,1 +np.float64,0xbfd03dd08ea07ba2,0xbfd011549aa1998a,1 +np.float64,0xbfd688327aad1064,0xbfd611c61b56adbe,1 +np.float64,0xbfde3249d8bc6494,0xbfdd16a7237a39d5,1 +np.float64,0x3febd4b65677a96c,0x3fe873e1a401ef03,1 +np.float64,0xbfe46bd2b368d7a6,0xbfe31023c2467749,1 +np.float64,0x3fbf9f5cde3f3ec0,0x3fbf8aca8ec53c45,1 +np.float64,0x3fc20374032406e8,0x3fc1f43f1f2f4d5e,1 +np.float64,0xbfec143b16f82876,0xbfe89caa42582381,1 +np.float64,0xbfd14fa635a29f4c,0xbfd119ced11da669,1 +np.float64,0x3fe25236d4e4a46e,0x3fe156242d644b7a,1 +np.float64,0xbfe4ed793469daf2,0xbfe377a88928fd77,1 +np.float64,0xbfb363572626c6b0,0xbfb35e98d8fe87ae,1 +np.float64,0xbfb389d5aa2713a8,0xbfb384fae55565a7,1 +np.float64,0x3fca6e001934dc00,0x3fca3e0661eaca84,1 +np.float64,0x3fe748f3f76e91e8,0x3fe548ab2168aea6,1 +np.float64,0x3fef150efdfe2a1e,0x3fea6b92d74f60d3,1 +np.float64,0xbfd14b52b1a296a6,0xbfd115a387c0fa93,1 +np.float64,0x3fe3286b5ce650d6,0x3fe208a6469a7527,1 +np.float64,0xbfd57b4f4baaf69e,0xbfd514a12a9f7ab0,1 +np.float64,0xbfef14bd467e297b,0xbfea6b64bbfd42ce,1 +np.float64,0xbfe280bc90650179,0xbfe17d2c49955dba,1 +np.float64,0x3fca8759d7350eb0,0x3fca56d5c17bbc14,1 +np.float64,0xbfdf988f30bf311e,0xbfde53f96f69b05f,1 +np.float64,0x3f6b6eeb4036de00,0x3f6b6ee7e3f86f9a,1 +np.float64,0xbfed560be8faac18,0xbfe9656c5cf973d8,1 +np.float64,0x3fc6102c592c2058,0x3fc5f43efad5396d,1 +np.float64,0xbfdef64ed2bdec9e,0xbfddc4b7fbd45aea,1 +np.float64,0x3fe814acd570295a,0x3fe5df183d543bfe,1 +np.float64,0x3fca21313f344260,0x3fc9f2d47f64fbe2,1 +np.float64,0xbfe89932cc713266,0xbfe63f186a2f60ce,1 +np.float64,0x3fe4ffcff169ffa0,0x3fe386336115ee21,1 +np.float64,0x3fee6964087cd2c8,0x3fea093d31e2c2c5,1 +np.float64,0xbfbeea604e3dd4c0,0xbfbed72734852669,1 +np.float64,0xbfea1954fb7432aa,0xbfe74cdad8720032,1 +np.float64,0x3fea3e1a5ef47c34,0x3fe765ffba65a11d,1 +np.float64,0x3fcedb850b3db708,0x3fce8f39d92f00ba,1 +np.float64,0x3fd3b52d41a76a5c,0x3fd365d22b0003f9,1 +np.float64,0xbfa4108a0c282110,0xbfa40f397fcd844f,1 +np.float64,0x3fd7454c57ae8a98,0x3fd6c2e5542c6c83,1 +np.float64,0xbfeecd3c7a7d9a79,0xbfea42ca943a1695,1 +np.float64,0xbfdddda397bbbb48,0xbfdccb27283d4c4c,1 +np.float64,0x3fe6b52cf76d6a5a,0x3fe4d96ff32925ff,1 +np.float64,0xbfa39a75ec2734f0,0xbfa3993c0da84f87,1 +np.float64,0x3fdd3fe6fdba7fcc,0x3fdc3df12fe9e525,1 +np.float64,0xbfb57a98162af530,0xbfb5742525d5fbe2,1 +np.float64,0xbfd3e166cfa7c2ce,0xbfd38ff2891be9b0,1 +np.float64,0x3fdb6a04f9b6d408,0x3fda955e5018e9dc,1 +np.float64,0x3fe4ab03a4e95608,0x3fe342bfa76e1aa8,1 +np.float64,0xbfe6c8480b6d9090,0xbfe4e7eaa935b3f5,1 +np.float64,0xbdd6b5a17bae,0xbdd6b5a17bae,1 +np.float64,0xd6591979acb23,0xd6591979acb23,1 +np.float64,0x5adbed90b5b7e,0x5adbed90b5b7e,1 +np.float64,0xa664c5314cc99,0xa664c5314cc99,1 +np.float64,0x1727fb162e500,0x1727fb162e500,1 +np.float64,0xdb49a93db6935,0xdb49a93db6935,1 +np.float64,0xb10c958d62193,0xb10c958d62193,1 +np.float64,0xad38276f5a705,0xad38276f5a705,1 +np.float64,0x1d5d0b983aba2,0x1d5d0b983aba2,1 +np.float64,0x915f48e122be9,0x915f48e122be9,1 +np.float64,0x475958ae8eb2c,0x475958ae8eb2c,1 +np.float64,0x3af8406675f09,0x3af8406675f09,1 +np.float64,0x655e88a4cabd2,0x655e88a4cabd2,1 +np.float64,0x40fee8ce81fde,0x40fee8ce81fde,1 +np.float64,0xab83103f57062,0xab83103f57062,1 +np.float64,0x7cf934b8f9f27,0x7cf934b8f9f27,1 +np.float64,0x29f7524853eeb,0x29f7524853eeb,1 +np.float64,0x4a5e954894bd3,0x4a5e954894bd3,1 +np.float64,0x24638f3a48c73,0x24638f3a48c73,1 +np.float64,0xa4f32fc749e66,0xa4f32fc749e66,1 +np.float64,0xf8e92df7f1d26,0xf8e92df7f1d26,1 +np.float64,0x292e9d50525d4,0x292e9d50525d4,1 +np.float64,0xe937e897d26fd,0xe937e897d26fd,1 +np.float64,0xd3bde1d5a77bc,0xd3bde1d5a77bc,1 +np.float64,0xa447ffd548900,0xa447ffd548900,1 +np.float64,0xa3b7b691476f7,0xa3b7b691476f7,1 +np.float64,0x490095c892013,0x490095c892013,1 +np.float64,0xfc853235f90a7,0xfc853235f90a7,1 +np.float64,0x5a8bc082b5179,0x5a8bc082b5179,1 +np.float64,0x1baca45a37595,0x1baca45a37595,1 +np.float64,0x2164120842c83,0x2164120842c83,1 +np.float64,0x66692bdeccd26,0x66692bdeccd26,1 +np.float64,0xf205bdd3e40b8,0xf205bdd3e40b8,1 +np.float64,0x7c3fff98f8801,0x7c3fff98f8801,1 +np.float64,0xccdf10e199bf,0xccdf10e199bf,1 +np.float64,0x92db8e8125b8,0x92db8e8125b8,1 +np.float64,0x5789a8d6af136,0x5789a8d6af136,1 +np.float64,0xbdda869d7bb51,0xbdda869d7bb51,1 +np.float64,0xb665e0596ccbc,0xb665e0596ccbc,1 +np.float64,0x74e6b46ee9cd7,0x74e6b46ee9cd7,1 +np.float64,0x4f39cf7c9e73b,0x4f39cf7c9e73b,1 +np.float64,0xfdbf3907fb7e7,0xfdbf3907fb7e7,1 +np.float64,0xafdef4d55fbdf,0xafdef4d55fbdf,1 +np.float64,0xb49858236930b,0xb49858236930b,1 +np.float64,0x3ebe21d47d7c5,0x3ebe21d47d7c5,1 +np.float64,0x5b620512b6c41,0x5b620512b6c41,1 +np.float64,0x31918cda63232,0x31918cda63232,1 +np.float64,0x68b5741ed16af,0x68b5741ed16af,1 +np.float64,0xa5c09a5b4b814,0xa5c09a5b4b814,1 +np.float64,0x55f51c14abea4,0x55f51c14abea4,1 +np.float64,0xda8a3e41b515,0xda8a3e41b515,1 +np.float64,0x9ea9c8513d539,0x9ea9c8513d539,1 +np.float64,0x7f23b964fe478,0x7f23b964fe478,1 +np.float64,0xf6e08c7bedc12,0xf6e08c7bedc12,1 +np.float64,0x7267aa24e4cf6,0x7267aa24e4cf6,1 +np.float64,0x236bb93a46d78,0x236bb93a46d78,1 +np.float64,0x9a98430b35309,0x9a98430b35309,1 +np.float64,0xbb683fef76d08,0xbb683fef76d08,1 +np.float64,0x1ff0eb6e3fe1e,0x1ff0eb6e3fe1e,1 +np.float64,0xf524038fea481,0xf524038fea481,1 +np.float64,0xd714e449ae29d,0xd714e449ae29d,1 +np.float64,0x4154fd7682aa0,0x4154fd7682aa0,1 +np.float64,0x5b8d2f6cb71a7,0x5b8d2f6cb71a7,1 +np.float64,0xc91aa21d92355,0xc91aa21d92355,1 +np.float64,0xbd94fd117b2a0,0xbd94fd117b2a0,1 +np.float64,0x685b207ad0b65,0x685b207ad0b65,1 +np.float64,0xd2485b05a490c,0xd2485b05a490c,1 +np.float64,0x151ea5e62a3d6,0x151ea5e62a3d6,1 +np.float64,0x2635a7164c6b6,0x2635a7164c6b6,1 +np.float64,0x88ae3b5d115c8,0x88ae3b5d115c8,1 +np.float64,0x8a055a55140ac,0x8a055a55140ac,1 +np.float64,0x756f7694eadef,0x756f7694eadef,1 +np.float64,0x866d74630cdaf,0x866d74630cdaf,1 +np.float64,0x39e44f2873c8b,0x39e44f2873c8b,1 +np.float64,0x2a07ceb6540fb,0x2a07ceb6540fb,1 +np.float64,0xc52b96398a573,0xc52b96398a573,1 +np.float64,0x9546543b2a8cb,0x9546543b2a8cb,1 +np.float64,0x5b995b90b732c,0x5b995b90b732c,1 +np.float64,0x2de10a565bc22,0x2de10a565bc22,1 +np.float64,0x3b06ee94760df,0x3b06ee94760df,1 +np.float64,0xb18e77a5631cf,0xb18e77a5631cf,1 +np.float64,0x3b89ae3a77137,0x3b89ae3a77137,1 +np.float64,0xd9b0b6e5b3617,0xd9b0b6e5b3617,1 +np.float64,0x30b2310861647,0x30b2310861647,1 +np.float64,0x326a3ab464d48,0x326a3ab464d48,1 +np.float64,0x4c18610a9830d,0x4c18610a9830d,1 +np.float64,0x541dea42a83be,0x541dea42a83be,1 +np.float64,0xcd027dbf9a050,0xcd027dbf9a050,1 +np.float64,0x780a0f80f015,0x780a0f80f015,1 +np.float64,0x740ed5b2e81db,0x740ed5b2e81db,1 +np.float64,0xc226814d844d0,0xc226814d844d0,1 +np.float64,0xde958541bd2b1,0xde958541bd2b1,1 +np.float64,0xb563d3296ac7b,0xb563d3296ac7b,1 +np.float64,0x1db3b0b83b677,0x1db3b0b83b677,1 +np.float64,0xa7b0275d4f605,0xa7b0275d4f605,1 +np.float64,0x72f8d038e5f1b,0x72f8d038e5f1b,1 +np.float64,0x860ed1350c1da,0x860ed1350c1da,1 +np.float64,0x79f88262f3f11,0x79f88262f3f11,1 +np.float64,0x8817761f102ef,0x8817761f102ef,1 +np.float64,0xac44784b5888f,0xac44784b5888f,1 +np.float64,0x800fd594241fab28,0x800fd594241fab28,1 +np.float64,0x800ede32f8ddbc66,0x800ede32f8ddbc66,1 +np.float64,0x800de4c1121bc982,0x800de4c1121bc982,1 +np.float64,0x80076ebcddcedd7a,0x80076ebcddcedd7a,1 +np.float64,0x800b3fee06567fdc,0x800b3fee06567fdc,1 +np.float64,0x800b444426b68889,0x800b444426b68889,1 +np.float64,0x800b1c037a563807,0x800b1c037a563807,1 +np.float64,0x8001eb88c2a3d712,0x8001eb88c2a3d712,1 +np.float64,0x80058aae6dab155e,0x80058aae6dab155e,1 +np.float64,0x80083df2d4f07be6,0x80083df2d4f07be6,1 +np.float64,0x800e3b19d97c7634,0x800e3b19d97c7634,1 +np.float64,0x800a71c6f374e38e,0x800a71c6f374e38e,1 +np.float64,0x80048557f1490ab1,0x80048557f1490ab1,1 +np.float64,0x8000a00e6b01401e,0x8000a00e6b01401e,1 +np.float64,0x800766a3e2cecd49,0x800766a3e2cecd49,1 +np.float64,0x80015eb44602bd69,0x80015eb44602bd69,1 +np.float64,0x800bde885a77bd11,0x800bde885a77bd11,1 +np.float64,0x800224c53ea4498b,0x800224c53ea4498b,1 +np.float64,0x80048e8c6a291d1a,0x80048e8c6a291d1a,1 +np.float64,0x800b667e4af6ccfd,0x800b667e4af6ccfd,1 +np.float64,0x800ae3d7e395c7b0,0x800ae3d7e395c7b0,1 +np.float64,0x80086c245550d849,0x80086c245550d849,1 +np.float64,0x800d7d25f6fafa4c,0x800d7d25f6fafa4c,1 +np.float64,0x800f8d9ab0ff1b35,0x800f8d9ab0ff1b35,1 +np.float64,0x800690e949cd21d3,0x800690e949cd21d3,1 +np.float64,0x8003022381060448,0x8003022381060448,1 +np.float64,0x80085e0dad70bc1c,0x80085e0dad70bc1c,1 +np.float64,0x800e2ffc369c5ff9,0x800e2ffc369c5ff9,1 +np.float64,0x800b629b5af6c537,0x800b629b5af6c537,1 +np.float64,0x800fdc964b7fb92d,0x800fdc964b7fb92d,1 +np.float64,0x80036bb4b1c6d76a,0x80036bb4b1c6d76a,1 +np.float64,0x800b382f7f16705f,0x800b382f7f16705f,1 +np.float64,0x800ebac9445d7593,0x800ebac9445d7593,1 +np.float64,0x80015075c3e2a0ec,0x80015075c3e2a0ec,1 +np.float64,0x8002a6ec5ce54dd9,0x8002a6ec5ce54dd9,1 +np.float64,0x8009fab74a93f56f,0x8009fab74a93f56f,1 +np.float64,0x800c94b9ea992974,0x800c94b9ea992974,1 +np.float64,0x800dc2efd75b85e0,0x800dc2efd75b85e0,1 +np.float64,0x800be6400d57cc80,0x800be6400d57cc80,1 +np.float64,0x80021f6858443ed1,0x80021f6858443ed1,1 +np.float64,0x800600e2ac4c01c6,0x800600e2ac4c01c6,1 +np.float64,0x800a2159e6b442b4,0x800a2159e6b442b4,1 +np.float64,0x800c912f4bb9225f,0x800c912f4bb9225f,1 +np.float64,0x800a863a9db50c76,0x800a863a9db50c76,1 +np.float64,0x800ac16851d582d1,0x800ac16851d582d1,1 +np.float64,0x8003f7d32e87efa7,0x8003f7d32e87efa7,1 +np.float64,0x800be4eee3d7c9de,0x800be4eee3d7c9de,1 +np.float64,0x80069ff0ac4d3fe2,0x80069ff0ac4d3fe2,1 +np.float64,0x80061c986d4c3932,0x80061c986d4c3932,1 +np.float64,0x8000737b4de0e6f7,0x8000737b4de0e6f7,1 +np.float64,0x8002066ef7440cdf,0x8002066ef7440cdf,1 +np.float64,0x8001007050c200e1,0x8001007050c200e1,1 +np.float64,0x8008df9fa351bf40,0x8008df9fa351bf40,1 +np.float64,0x800f8394ee5f072a,0x800f8394ee5f072a,1 +np.float64,0x80008e0b01c11c17,0x80008e0b01c11c17,1 +np.float64,0x800f7088ed3ee112,0x800f7088ed3ee112,1 +np.float64,0x800285b86f650b72,0x800285b86f650b72,1 +np.float64,0x8008ec18af51d832,0x8008ec18af51d832,1 +np.float64,0x800da08523bb410a,0x800da08523bb410a,1 +np.float64,0x800de853ca7bd0a8,0x800de853ca7bd0a8,1 +np.float64,0x8008c8aefad1915e,0x8008c8aefad1915e,1 +np.float64,0x80010c39d5821874,0x80010c39d5821874,1 +np.float64,0x8009208349724107,0x8009208349724107,1 +np.float64,0x800783783f0f06f1,0x800783783f0f06f1,1 +np.float64,0x80025caf9984b960,0x80025caf9984b960,1 +np.float64,0x800bc76fa6778ee0,0x800bc76fa6778ee0,1 +np.float64,0x80017e2f89a2fc60,0x80017e2f89a2fc60,1 +np.float64,0x800ef169843de2d3,0x800ef169843de2d3,1 +np.float64,0x80098a5f7db314bf,0x80098a5f7db314bf,1 +np.float64,0x800d646f971ac8df,0x800d646f971ac8df,1 +np.float64,0x800110d1dc6221a4,0x800110d1dc6221a4,1 +np.float64,0x800f8b422a1f1684,0x800f8b422a1f1684,1 +np.float64,0x800785c97dcf0b94,0x800785c97dcf0b94,1 +np.float64,0x800da201283b4403,0x800da201283b4403,1 +np.float64,0x800a117cc7b422fa,0x800a117cc7b422fa,1 +np.float64,0x80024731cfa48e64,0x80024731cfa48e64,1 +np.float64,0x800199d456c333a9,0x800199d456c333a9,1 +np.float64,0x8005f66bab8becd8,0x8005f66bab8becd8,1 +np.float64,0x8008e7227c11ce45,0x8008e7227c11ce45,1 +np.float64,0x8007b66cc42f6cda,0x8007b66cc42f6cda,1 +np.float64,0x800669e6f98cd3cf,0x800669e6f98cd3cf,1 +np.float64,0x800aed917375db23,0x800aed917375db23,1 +np.float64,0x8008b6dd15116dbb,0x8008b6dd15116dbb,1 +np.float64,0x800f49869cfe930d,0x800f49869cfe930d,1 +np.float64,0x800a712661b4e24d,0x800a712661b4e24d,1 +np.float64,0x800944e816f289d1,0x800944e816f289d1,1 +np.float64,0x800eba0f8a1d741f,0x800eba0f8a1d741f,1 +np.float64,0x800cf6ded139edbe,0x800cf6ded139edbe,1 +np.float64,0x80023100c6246202,0x80023100c6246202,1 +np.float64,0x800c5a94add8b52a,0x800c5a94add8b52a,1 +np.float64,0x800adf329b95be66,0x800adf329b95be66,1 +np.float64,0x800af9afc115f360,0x800af9afc115f360,1 +np.float64,0x800d66ce837acd9d,0x800d66ce837acd9d,1 +np.float64,0x8003ffb5e507ff6d,0x8003ffb5e507ff6d,1 +np.float64,0x80027d280024fa51,0x80027d280024fa51,1 +np.float64,0x800fc37e1d1f86fc,0x800fc37e1d1f86fc,1 +np.float64,0x800fc7258b9f8e4b,0x800fc7258b9f8e4b,1 +np.float64,0x8003fb5789e7f6b0,0x8003fb5789e7f6b0,1 +np.float64,0x800eb4e7a13d69cf,0x800eb4e7a13d69cf,1 +np.float64,0x800951850952a30a,0x800951850952a30a,1 +np.float64,0x3fed4071be3a80e3,0x3fe95842074431df,1 +np.float64,0x3f8d2341203a4682,0x3f8d2300b453bd9f,1 +np.float64,0x3fdc8ce332b919c6,0x3fdb9cdf1440c28f,1 +np.float64,0x3fdc69bd84b8d37b,0x3fdb7d25c8166b7b,1 +np.float64,0x3fc4c22ad0298456,0x3fc4aae73e231b4f,1 +np.float64,0x3fea237809f446f0,0x3fe753cc6ca96193,1 +np.float64,0x3fd34cf6462699ed,0x3fd30268909bb47e,1 +np.float64,0x3fafce20643f9c41,0x3fafc8e41a240e35,1 +np.float64,0x3fdc6d416538da83,0x3fdb805262292863,1 +np.float64,0x3fe7d8362aefb06c,0x3fe5b2ce659db7fd,1 +np.float64,0x3fe290087de52011,0x3fe189f9a3eb123d,1 +np.float64,0x3fa62d2bf82c5a58,0x3fa62b65958ca2b8,1 +np.float64,0x3fafd134403fa269,0x3fafcbf670f8a6f3,1 +np.float64,0x3fa224e53c2449ca,0x3fa223ec5de1631b,1 +np.float64,0x3fb67e2c2c2cfc58,0x3fb676c445fb70a0,1 +np.float64,0x3fda358d01346b1a,0x3fd97b9441666eb2,1 +np.float64,0x3fdd30fc4bba61f9,0x3fdc308da423778d,1 +np.float64,0x3fc56e99c52add34,0x3fc5550004492621,1 +np.float64,0x3fe32d08de265a12,0x3fe20c761a73cec2,1 +np.float64,0x3fd46cf932a8d9f2,0x3fd414a7f3db03df,1 +np.float64,0x3fd94cfa2b3299f4,0x3fd8a5961b3e4bdd,1 +np.float64,0x3fed6ea3a6fadd47,0x3fe9745b2f6c9204,1 +np.float64,0x3fe4431d1768863a,0x3fe2ef61d0481de0,1 +np.float64,0x3fe1d8e00ea3b1c0,0x3fe0efab5050ee78,1 +np.float64,0x3fe56f37dcaade70,0x3fe3de00b0f392e0,1 +np.float64,0x3fde919a2dbd2334,0x3fdd6b6d2dcf2396,1 +np.float64,0x3fe251e3d4a4a3c8,0x3fe155de69605d60,1 +np.float64,0x3fe5e0ecc5abc1da,0x3fe436a5de5516cf,1 +np.float64,0x3fcd48780c3a90f0,0x3fcd073fa907ba9b,1 +np.float64,0x3fe4e8149229d029,0x3fe37360801d5b66,1 +np.float64,0x3fb9ef159633de2b,0x3fb9e3bc05a15d1d,1 +np.float64,0x3fc24a3f0424947e,0x3fc23a5432ca0e7c,1 +np.float64,0x3fe55ca196aab943,0x3fe3cf6b3143435a,1 +np.float64,0x3fe184544c2308a9,0x3fe0a7b49fa80aec,1 +np.float64,0x3fe2c76e83658edd,0x3fe1b8355c1ea771,1 +np.float64,0x3fea8d2c4ab51a59,0x3fe79ba85aabc099,1 +np.float64,0x3fd74f98abae9f31,0x3fd6cc85005d0593,1 +np.float64,0x3fec6de9a678dbd3,0x3fe8d59a1d23cdd1,1 +np.float64,0x3fec8a0e50f9141d,0x3fe8e7500f6f6a00,1 +np.float64,0x3fe9de6d08b3bcda,0x3fe7245319508767,1 +np.float64,0x3fe4461fd1688c40,0x3fe2f1cf0b93aba6,1 +np.float64,0x3fde342d9d3c685b,0x3fdd185609d5719d,1 +np.float64,0x3feb413fc8368280,0x3fe813c091d2519a,1 +np.float64,0x3fe64333156c8666,0x3fe48275b9a6a358,1 +np.float64,0x3fe03c65226078ca,0x3fdf18b26786be35,1 +np.float64,0x3fee11054dbc220b,0x3fe9d579a1cfa7ad,1 +np.float64,0x3fbaefccae35df99,0x3fbae314fef7c7ea,1 +np.float64,0x3feed4e3487da9c7,0x3fea4729241c8811,1 +np.float64,0x3fbb655df836cabc,0x3fbb57fcf9a097be,1 +np.float64,0x3fe68b0273ed1605,0x3fe4b96109afdf76,1 +np.float64,0x3fd216bfc3242d80,0x3fd1d957363f6a43,1 +np.float64,0x3fe01328d4a02652,0x3fded083bbf94aba,1 +np.float64,0x3fe3f9a61ae7f34c,0x3fe2b3f701b79028,1 +np.float64,0x3fed4e7cf8fa9cfa,0x3fe960d27084fb40,1 +np.float64,0x3faec08e343d811c,0x3faebbd2aa07ac1f,1 +np.float64,0x3fd2d1bbeea5a378,0x3fd28c9aefcf48ad,1 +np.float64,0x3fd92e941fb25d28,0x3fd889857f88410d,1 +np.float64,0x3fe43decb7e87bd9,0x3fe2eb32b4ee4667,1 +np.float64,0x3fef49cabcfe9395,0x3fea892f9a233f76,1 +np.float64,0x3fe3e96812e7d2d0,0x3fe2a6c6b45dd6ee,1 +np.float64,0x3fd24c0293a49805,0x3fd20c76d54473cb,1 +np.float64,0x3fb43d6b7e287ad7,0x3fb438060772795a,1 +np.float64,0x3fe87bf7d3f0f7f0,0x3fe62a0c47411c62,1 +np.float64,0x3fee82a2e07d0546,0x3fea17e27e752b7b,1 +np.float64,0x3fe40c01bbe81803,0x3fe2c2d9483f44d8,1 +np.float64,0x3fd686ccae2d0d99,0x3fd610763fb61097,1 +np.float64,0x3fe90fcf2af21f9e,0x3fe693c12df59ba9,1 +np.float64,0x3fefb3ce11ff679c,0x3feac3dd4787529d,1 +np.float64,0x3fcec53ff63d8a80,0x3fce79992af00c58,1 +np.float64,0x3fe599dd7bab33bb,0x3fe3ff5da7575d85,1 +np.float64,0x3fe9923b1a732476,0x3fe6ef71d13db456,1 +np.float64,0x3febf76fcef7eee0,0x3fe88a3952e11373,1 +np.float64,0x3fc2cfd128259fa2,0x3fc2be7fd47fd811,1 +np.float64,0x3fe4d37ae269a6f6,0x3fe36300d45e3745,1 +np.float64,0x3fe23aa2e4247546,0x3fe1424e172f756f,1 +np.float64,0x3fe4f0596ca9e0b3,0x3fe379f0c49de7ef,1 +np.float64,0x3fe2e4802fe5c900,0x3fe1d062a8812601,1 +np.float64,0x3fe5989c79eb3139,0x3fe3fe6308552dec,1 +np.float64,0x3fe3c53cb4e78a79,0x3fe28956e573aca4,1 +np.float64,0x3fe6512beeeca258,0x3fe48d2d5ece979f,1 +np.float64,0x3fd8473ddb308e7c,0x3fd7b33e38adc6ad,1 +np.float64,0x3fecd09c9679a139,0x3fe91361fa0c5bcb,1 +np.float64,0x3fc991530e3322a6,0x3fc965e2c514a9e9,1 +np.float64,0x3f6d4508403a8a11,0x3f6d45042b68acc5,1 +np.float64,0x3fea1f198f743e33,0x3fe750ce918d9330,1 +np.float64,0x3fd0a0bb4da14177,0x3fd07100f9c71e1c,1 +np.float64,0x3fd30c45ffa6188c,0x3fd2c499f9961f66,1 +np.float64,0x3fcad98e7c35b31d,0x3fcaa74293cbc52e,1 +np.float64,0x3fec8e4a5eb91c95,0x3fe8e9f898d118db,1 +np.float64,0x3fd19fdb79233fb7,0x3fd1670c00febd24,1 +np.float64,0x3fea9fcbb1f53f97,0x3fe7a836b29c4075,1 +np.float64,0x3fc6d12ea12da25d,0x3fc6b24bd2f89f59,1 +np.float64,0x3fd6af3658ad5e6d,0x3fd636613e08df3f,1 +np.float64,0x3fe31bc385a63787,0x3fe1fe3081621213,1 +np.float64,0x3fc0dbba2221b774,0x3fc0cf42c9313dba,1 +np.float64,0x3fef639ce87ec73a,0x3fea9795454f1036,1 +np.float64,0x3fee5f29dcbcbe54,0x3fea0349b288f355,1 +np.float64,0x3fed46bdb37a8d7b,0x3fe95c199f5aa569,1 +np.float64,0x3fef176afa3e2ed6,0x3fea6ce78b2aa3aa,1 +np.float64,0x3fc841e7683083cf,0x3fc81cccb84848cc,1 +np.float64,0xbfda3ec9a2347d94,0xbfd9840d180e9de3,1 +np.float64,0xbfcd5967ae3ab2d0,0xbfcd17be13142bb9,1 +np.float64,0xbfedf816573bf02d,0xbfe9c6bb06476c60,1 +np.float64,0xbfd0d6e10e21adc2,0xbfd0a54f99d2f3dc,1 +np.float64,0xbfe282df096505be,0xbfe17ef5e2e80760,1 +np.float64,0xbfd77ae6e62ef5ce,0xbfd6f4f6b603ad8a,1 +np.float64,0xbfe37b171aa6f62e,0xbfe24cb4b2d0ade4,1 +np.float64,0xbfef9e5ed9bf3cbe,0xbfeab817b41000bd,1 +np.float64,0xbfe624d6f96c49ae,0xbfe46b1e9c9aff86,1 +np.float64,0xbfefb5da65ff6bb5,0xbfeac4fc9c982772,1 +np.float64,0xbfd29a65d52534cc,0xbfd2579df8ff87b9,1 +np.float64,0xbfd40270172804e0,0xbfd3af6471104aef,1 +np.float64,0xbfb729ee7a2e53e0,0xbfb721d7dbd2705e,1 +np.float64,0xbfb746f1382e8de0,0xbfb73ebc1207f8e3,1 +np.float64,0xbfd3c7e606a78fcc,0xbfd377a8aa1b0dd9,1 +np.float64,0xbfd18c4880231892,0xbfd1543506584ad5,1 +np.float64,0xbfea988080753101,0xbfe7a34cba0d0fa1,1 +np.float64,0xbf877400e02ee800,0xbf8773df47fa7e35,1 +np.float64,0xbfb07e050820fc08,0xbfb07b198d4a52c9,1 +np.float64,0xbfee0a3621fc146c,0xbfe9d1745a05ba77,1 +np.float64,0xbfe78de246ef1bc4,0xbfe57bf2baab91c8,1 +np.float64,0xbfcdbfd3bd3b7fa8,0xbfcd7b728a955a06,1 +np.float64,0xbfe855ea79b0abd5,0xbfe60e8a4a17b921,1 +np.float64,0xbfd86c8e3530d91c,0xbfd7d5e36c918dc1,1 +np.float64,0xbfe4543169e8a863,0xbfe2fd23d42f552e,1 +np.float64,0xbfe41efbf1283df8,0xbfe2d235a2faed1a,1 +np.float64,0xbfd9a55464b34aa8,0xbfd8f7083f7281e5,1 +np.float64,0xbfe5f5078d6bea0f,0xbfe44637d910c270,1 +np.float64,0xbfe6d83e3dedb07c,0xbfe4f3fdadd10552,1 +np.float64,0xbfdb767e70b6ecfc,0xbfdaa0b6c17f3fb1,1 +np.float64,0xbfdfc91b663f9236,0xbfde7eb0dfbeaa26,1 +np.float64,0xbfbfbd18783f7a30,0xbfbfa84bf2fa1c8d,1 +np.float64,0xbfe51199242a2332,0xbfe39447dbe066ae,1 +np.float64,0xbfdbb94814b77290,0xbfdadd63bd796972,1 +np.float64,0xbfd8c6272cb18c4e,0xbfd828f2d9e8607e,1 +np.float64,0xbfce51e0b63ca3c0,0xbfce097ee908083a,1 +np.float64,0xbfe99a177d73342f,0xbfe6f4ec776a57ae,1 +np.float64,0xbfefde2ab0ffbc55,0xbfeadafdcbf54733,1 +np.float64,0xbfcccb5c1c3996b8,0xbfcc8d586a73d126,1 +np.float64,0xbfdf7ddcedbefbba,0xbfde3c749a906de7,1 +np.float64,0xbfef940516ff280a,0xbfeab26429e89f4b,1 +np.float64,0xbfe08009f1e10014,0xbfdf8eab352997eb,1 +np.float64,0xbfe9c02682b3804d,0xbfe70f5fd05f79ee,1 +np.float64,0xbfb3ca1732279430,0xbfb3c50bec5b453a,1 +np.float64,0xbfe368e81926d1d0,0xbfe23dc704d0887c,1 +np.float64,0xbfbd20cc2e3a4198,0xbfbd10b7e6d81c6c,1 +np.float64,0xbfd67ece4d2cfd9c,0xbfd608f527dcc5e7,1 +np.float64,0xbfdc02d1333805a2,0xbfdb20104454b79f,1 +np.float64,0xbfc007a626200f4c,0xbfbff9dc9dc70193,1 +np.float64,0xbfda9e4f8fb53ca0,0xbfd9db8af35dc630,1 +np.float64,0xbfd8173d77302e7a,0xbfd786a0cf3e2914,1 +np.float64,0xbfeb8fcbd0b71f98,0xbfe84734debc10fb,1 +np.float64,0xbfe4bf1cb7697e3a,0xbfe352c891113f29,1 +np.float64,0xbfc18624d5230c48,0xbfc178248e863b64,1 +np.float64,0xbfcf184bac3e3098,0xbfceca3b19be1ebe,1 +np.float64,0xbfd2269c42a44d38,0xbfd1e8920d72b694,1 +np.float64,0xbfe8808526b1010a,0xbfe62d5497292495,1 +np.float64,0xbfe498bd1da9317a,0xbfe334245eadea93,1 +np.float64,0xbfef0855aebe10ab,0xbfea6462f29aeaf9,1 +np.float64,0xbfdeb186c93d630e,0xbfdd87c37943c602,1 +np.float64,0xbfb29fe2ae253fc8,0xbfb29bae3c87efe4,1 +np.float64,0xbfddd9c6c3bbb38e,0xbfdcc7b400bf384b,1 +np.float64,0xbfe3506673e6a0cd,0xbfe2299f26295553,1 +np.float64,0xbfe765957a2ecb2b,0xbfe55e03cf22edab,1 +np.float64,0xbfecc9876c79930f,0xbfe90efaf15b6207,1 +np.float64,0xbfefb37a0a7f66f4,0xbfeac3af3898e7c2,1 +np.float64,0xbfeefa0da7bdf41b,0xbfea5c4cde53c1c3,1 +np.float64,0xbfe6639ee9ecc73e,0xbfe49b4e28a72482,1 +np.float64,0xbfef91a4bb7f2349,0xbfeab114ac9e25dd,1 +np.float64,0xbfc8b392bb316724,0xbfc88c657f4441a3,1 +np.float64,0xbfc88a358231146c,0xbfc863cb900970fe,1 +np.float64,0xbfef25a9d23e4b54,0xbfea74eda432aabe,1 +np.float64,0xbfe6aceea0ed59de,0xbfe4d32e54a3fd01,1 +np.float64,0xbfefe2b3e37fc568,0xbfeadd74f4605835,1 +np.float64,0xbfa9eecb8833dd90,0xbfa9ebf4f4cb2591,1 +np.float64,0xbfd42bad7428575a,0xbfd3d69de8e52d0a,1 +np.float64,0xbfbc366b4a386cd8,0xbfbc27ceee8f3019,1 +np.float64,0xbfd9bca7be337950,0xbfd90c80e6204e57,1 +np.float64,0xbfe8173f53f02e7f,0xbfe5e0f8d8ed329c,1 +np.float64,0xbfce22dbcb3c45b8,0xbfcddbc8159b63af,1 +np.float64,0xbfea2d7ba7345af7,0xbfe75aa62ad5b80a,1 +np.float64,0xbfc08b783e2116f0,0xbfc07faf8d501558,1 +np.float64,0xbfb8c4161c318830,0xbfb8ba33950748ec,1 +np.float64,0xbfddd930bcbbb262,0xbfdcc72dffdf51bb,1 +np.float64,0xbfd108ce8a22119e,0xbfd0d5801e7698bd,1 +np.float64,0xbfd5bd2b5dab7a56,0xbfd552c52c468c76,1 +np.float64,0xbfe7ffe67fefffcd,0xbfe5cfe96e35e6e5,1 +np.float64,0xbfa04ec6bc209d90,0xbfa04e120a2c25cc,1 +np.float64,0xbfef7752cc7eeea6,0xbfeaa28715addc4f,1 +np.float64,0xbfe7083c2eae1078,0xbfe5182bf8ddfc8e,1 +np.float64,0xbfe05dafd0a0bb60,0xbfdf52d397cfe5f6,1 +np.float64,0xbfacb4f2243969e0,0xbfacb118991ea235,1 +np.float64,0xbfc7d47e422fa8fc,0xbfc7b1504714a4fd,1 +np.float64,0xbfbd70b2243ae168,0xbfbd60182efb61de,1 +np.float64,0xbfe930e49cb261c9,0xbfe6ab272b3f9cfc,1 +np.float64,0xbfb5f537e62bea70,0xbfb5ee540dcdc635,1 +np.float64,0xbfbb0c8278361908,0xbfbaffa1f7642a87,1 +np.float64,0xbfe82af2447055e4,0xbfe5ef54ca8db9e8,1 +np.float64,0xbfe92245e6f2448c,0xbfe6a0d32168040b,1 +np.float64,0xbfb799a8522f3350,0xbfb7911a7ada3640,1 +np.float64,0x7faa8290c8350521,0x3fe5916f67209cd6,1 +np.float64,0x7f976597082ecb2d,0x3fcf94dce396bd37,1 +np.float64,0x7fede721237bce41,0x3fe3e7b1575b005f,1 +np.float64,0x7fd5f674d72bece9,0x3fe3210628eba199,1 +np.float64,0x7f9b0f1aa0361e34,0x3feffd34d15d1da7,1 +np.float64,0x7fec48346ab89068,0x3fe93dd84253d9a2,1 +np.float64,0x7f9cac76283958eb,0xbfec4cd999653868,1 +np.float64,0x7fed51ab6bbaa356,0x3fecc27fb5f37bca,1 +np.float64,0x7fded3c116bda781,0xbfda473efee47cf1,1 +np.float64,0x7fd19c48baa33890,0xbfe25700cbfc0326,1 +np.float64,0x7fe5c8f478ab91e8,0xbfee4ab6d84806be,1 +np.float64,0x7fe53c64e46a78c9,0x3fee19c3f227f4e1,1 +np.float64,0x7fc2ad1936255a31,0xbfe56db9b877f807,1 +np.float64,0x7fe2b071b52560e2,0xbfce3990a8d390a9,1 +np.float64,0x7fc93f3217327e63,0xbfd1f6d7ef838d2b,1 +np.float64,0x7fec26df08784dbd,0x3fd5397be41c93d9,1 +np.float64,0x7fcf4770183e8edf,0x3fe6354f5a785016,1 +np.float64,0x7fdc9fcc0bb93f97,0xbfeeeae952e8267d,1 +np.float64,0x7feb21f29c7643e4,0x3fec20122e33f1bf,1 +np.float64,0x7fd0b51273216a24,0x3fefb09f8daba00b,1 +np.float64,0x7fe747a9d76e8f53,0x3feb46a3232842a4,1 +np.float64,0x7fd58885972b110a,0xbfce5ea57c186221,1 +np.float64,0x7fca3ce85c3479d0,0x3fef93a24548e8ca,1 +np.float64,0x7fe1528a46a2a514,0xbfb54bb578d9da91,1 +np.float64,0x7fcc58b21b38b163,0x3feffb5b741ffc2d,1 +np.float64,0x7fdabcaaf5357955,0x3fecbf855db524d1,1 +np.float64,0x7fdd27c6933a4f8c,0xbfef2f41bb80144b,1 +np.float64,0x7fbda4e1be3b49c2,0x3fdb9b33f84f5381,1 +np.float64,0x7fe53363362a66c5,0x3fe4daff3a6a4ed0,1 +np.float64,0x7fe5719d62eae33a,0xbfef761d98f625d5,1 +np.float64,0x7f982ce5a83059ca,0x3fd0b27c3365f0a8,1 +np.float64,0x7fe6db8c42edb718,0x3fe786f4b1fe11a6,1 +np.float64,0x7fe62cca1b2c5993,0x3fd425b6c4c9714a,1 +np.float64,0x7feea88850bd5110,0xbfd7bbb432017175,1 +np.float64,0x7fad6c6ae43ad8d5,0x3fe82e49098bc6de,1 +np.float64,0x7fe70542f02e0a85,0x3fec3017960b4822,1 +np.float64,0x7feaf0bcbb35e178,0xbfc3aac74dd322d5,1 +np.float64,0x7fb5e152fe2bc2a5,0x3fd4b27a4720614c,1 +np.float64,0x7fe456ee5be8addc,0xbfe9e15ab5cff229,1 +np.float64,0x7fd4b53a8d296a74,0xbfefff450f503326,1 +np.float64,0x7fd7149d7a2e293a,0x3fef4ef0a9009096,1 +np.float64,0x7fd43fc5a8a87f8a,0x3fe0c929fee9dce7,1 +np.float64,0x7fef97022aff2e03,0x3fd4ea52a813da20,1 +np.float64,0x7fe035950ae06b29,0x3fef4e125394fb05,1 +np.float64,0x7fecd0548979a0a8,0x3fe89d226244037b,1 +np.float64,0x7fc79b3ac22f3675,0xbfee9c9cf78c8270,1 +np.float64,0x7fd8b8e8263171cf,0x3fe8e24437961db0,1 +np.float64,0x7fc288c23e251183,0xbfbaf8eca50986ca,1 +np.float64,0x7fe436b4b6686d68,0xbfecd661741931c4,1 +np.float64,0x7fcdf99abe3bf334,0x3feaa75c90830b92,1 +np.float64,0x7fd9f9739233f2e6,0xbfebbfcb301b0da5,1 +np.float64,0x7fd6fcbd1b2df979,0xbfccf2c77cb65f56,1 +np.float64,0x7fe242a97b248552,0xbfe5b0f13bcbabc8,1 +np.float64,0x7fe38bf3e06717e7,0x3fbc8fa9004d2668,1 +np.float64,0x7fecd0e8d479a1d1,0xbfe886a6b4f73a4a,1 +np.float64,0x7fe958d60232b1ab,0xbfeb7c4cf0cee2dd,1 +np.float64,0x7f9d492b583a9256,0xbfebe975d00221cb,1 +np.float64,0x7fd6c9983bad932f,0xbfefe817621a31f6,1 +np.float64,0x7fed0d7239fa1ae3,0x3feac7e1b6455b4b,1 +np.float64,0x7fe61dac90ec3b58,0x3fef845b9efe8421,1 +np.float64,0x7f9acd3010359a5f,0xbfe460d376200130,1 +np.float64,0x7fedced9673b9db2,0xbfeeaf23445e1944,1 +np.float64,0x7fd9f271a733e4e2,0xbfd41544535ecb78,1 +np.float64,0x7fe703339bee0666,0x3fef93334626b56c,1 +np.float64,0x7fec7761b7b8eec2,0xbfe6da9179e8e714,1 +np.float64,0x7fdd9fff043b3ffd,0xbfc0761dfb8d94f9,1 +np.float64,0x7fdc10ed17b821d9,0x3fe1481e2a26c77f,1 +np.float64,0x7fe7681e72aed03c,0x3fefff94a6d47c84,1 +np.float64,0x7fe18c29e1e31853,0x3fe86ebd2fd89456,1 +np.float64,0x7fb2fb273c25f64d,0xbfefc136f57e06de,1 +np.float64,0x7fac2bbb90385776,0x3fe25d8e3cdae7e3,1 +np.float64,0x7fed16789efa2cf0,0x3fe94555091fdfd9,1 +np.float64,0x7fd8fe8f7831fd1e,0xbfed58d520361902,1 +np.float64,0x7fa59bde3c2b37bb,0x3fef585391c077ff,1 +np.float64,0x7fda981b53353036,0x3fde02ca08737b5f,1 +np.float64,0x7fd29f388aa53e70,0xbfe04f5499246df2,1 +np.float64,0x7fcd0232513a0464,0xbfd9737f2f565829,1 +np.float64,0x7fe9a881bcf35102,0xbfe079cf285b35dd,1 +np.float64,0x7fdbe399a9b7c732,0x3fe965bc4220f340,1 +np.float64,0x7feb77414af6ee82,0xbfb7df2fcd491f55,1 +np.float64,0x7fa26e86c424dd0d,0xbfea474c3d65b9be,1 +np.float64,0x7feaee869e35dd0c,0xbfd7b333a888cd14,1 +np.float64,0x7fcbd67f6137acfe,0xbfe15a7a15dfcee6,1 +np.float64,0x7fe36991e766d323,0xbfeb288077c4ed9f,1 +np.float64,0x7fdcf4f4fcb9e9e9,0xbfea331ef7a75e7b,1 +np.float64,0x7fbe3445643c688a,0x3fedf21b94ae8e37,1 +np.float64,0x7fd984cfd2b3099f,0x3fc0d3ade71c395e,1 +np.float64,0x7fdec987b23d930e,0x3fe4af5e48f6c26e,1 +np.float64,0x7fde56a9953cad52,0x3fc8e7762cefb8b0,1 +np.float64,0x7fd39fb446273f68,0xbfe6c3443208f44d,1 +np.float64,0x7fc609c1a72c1382,0x3fe884e639571baa,1 +np.float64,0x7fe001be4b20037c,0xbfed0d90cbcb6010,1 +np.float64,0x7fce7ace283cf59b,0xbfd0303792e51f49,1 +np.float64,0x7fe27ba93da4f751,0x3fe548b5ce740d71,1 +np.float64,0x7fcc13c79b38278e,0xbfe2e14f5b64a1e9,1 +np.float64,0x7fc058550620b0a9,0x3fe44bb55ebd0590,1 +np.float64,0x7fa4ba8bf8297517,0x3fee59b39f9d08c4,1 +np.float64,0x7fe50d6872ea1ad0,0xbfea1eaa2d059e13,1 +np.float64,0x7feb7e33b476fc66,0xbfeff28a4424dd3e,1 +np.float64,0x7fe2d7d2a165afa4,0xbfdbaff0ba1ea460,1 +np.float64,0xffd126654b224cca,0xbfef0cd3031fb97c,1 +np.float64,0xffb5f884942bf108,0x3fe0de589bea2e4c,1 +np.float64,0xffe011b4bfe02369,0xbfe805a0edf1e1f2,1 +np.float64,0xffec13eae9b827d5,0x3fb5f30347d78447,1 +np.float64,0xffa6552ae82caa50,0x3fb1ecee60135f2f,1 +np.float64,0xffb62d38b02c5a70,0x3fbd35903148fd12,1 +np.float64,0xffe2c44ea425889d,0xbfd7616547f99a7d,1 +np.float64,0xffea24c61a74498c,0x3fef4a1b15ae9005,1 +np.float64,0xffd23a4ab2a47496,0x3fe933bfaa569ae9,1 +np.float64,0xffc34a073d269410,0xbfeec0f510bb7474,1 +np.float64,0xffeead84cfbd5b09,0x3feb2d635e5a78bd,1 +np.float64,0xffcfd8f3b43fb1e8,0xbfdd59625801771b,1 +np.float64,0xffd3c7f662a78fec,0x3f9cf3209edfbc4e,1 +np.float64,0xffe7b7e4f72f6fca,0xbfefdcff4925632c,1 +np.float64,0xffe48cab05e91956,0x3fe6b41217948423,1 +np.float64,0xffeb6980b336d301,0xbfca5de148f69324,1 +np.float64,0xffe3f15c4aa7e2b8,0xbfeb18efae892081,1 +np.float64,0xffcf290c713e5218,0x3fefe6f1a513ed26,1 +np.float64,0xffd80979b43012f4,0xbfde6c8df91af976,1 +np.float64,0xffc3181e0026303c,0x3fe7448f681def38,1 +np.float64,0xffedfa68f97bf4d1,0xbfeca6efb802d109,1 +np.float64,0xffca0931c0341264,0x3fe31b9f073b08cd,1 +np.float64,0xffe4c44934e98892,0x3feda393a2e8a0f7,1 +np.float64,0xffe65bb56f2cb76a,0xbfeffaf638a4b73e,1 +np.float64,0xffe406a332a80d46,0x3fe8151dadb853c1,1 +np.float64,0xffdb7eae9c36fd5e,0xbfeff89abf5ab16e,1 +np.float64,0xffe245a02da48b40,0x3fef1fb43e85f4b8,1 +np.float64,0xffe2bafa732575f4,0x3fcbab115c6fd86e,1 +np.float64,0xffe8b1eedb7163dd,0x3feff263df6f6b12,1 +np.float64,0xffe6c76c796d8ed8,0xbfe61a8668511293,1 +np.float64,0xffefe327d1ffc64f,0xbfd9b92887a84827,1 +np.float64,0xffa452180c28a430,0xbfa9b9e578a4e52f,1 +np.float64,0xffe9867d0bf30cf9,0xbfca577867588408,1 +np.float64,0xffdfe9b923bfd372,0x3fdab5c15f085c2d,1 +np.float64,0xffed590c6abab218,0xbfd7e7b6c5a120e6,1 +np.float64,0xffeaebcfbab5d79f,0x3fed58be8a9e2c3b,1 +np.float64,0xffe2ba83a8257507,0x3fe6c42a4ac1d4d9,1 +np.float64,0xffe01d5b0ee03ab6,0xbfe5dad6c9247db7,1 +np.float64,0xffe51095d52a212b,0x3fef822cebc32d8e,1 +np.float64,0xffebd7a901b7af51,0xbfe5e63f3e3b1185,1 +np.float64,0xffe4efdcde29dfb9,0xbfe811294dfa758f,1 +np.float64,0xffe3be1aa4a77c35,0x3fdd8dcfcd409bb1,1 +np.float64,0xffbe6f2f763cde60,0x3fd13766e43bd622,1 +np.float64,0xffeed3d80fbda7af,0x3fec10a23c1b7a4a,1 +np.float64,0xffd6ebff37add7fe,0xbfe6177411607c86,1 +np.float64,0xffe85a90f4b0b521,0x3fc09fdd66c8fde9,1 +np.float64,0xffea3d58c2b47ab1,0x3feb5bd4a04b3562,1 +np.float64,0xffef675be6beceb7,0x3fecd840683d1044,1 +np.float64,0xff726a088024d400,0x3feff2b4f47b5214,1 +np.float64,0xffc90856733210ac,0xbfe3c6ffbf6840a5,1 +np.float64,0xffc0b58d9a216b1c,0xbfe10314267d0611,1 +np.float64,0xffee1f3d0abc3e79,0xbfd12ea7efea9067,1 +np.float64,0xffd988c41a331188,0x3febe83802d8a32e,1 +np.float64,0xffe8f1ac9bb1e358,0xbfdbf5fa7e84f2f2,1 +np.float64,0xffe47af279e8f5e4,0x3fef11e339e5fa78,1 +np.float64,0xff9960a7f832c140,0xbfa150363f8ec5b2,1 +np.float64,0xffcac40fa7358820,0xbfec3d5847a3df1d,1 +np.float64,0xffcb024a9d360494,0xbfd060fa31fd6b6a,1 +np.float64,0xffe385ffb3270bff,0xbfee6859e8dcd9e8,1 +np.float64,0xffef62f2c53ec5e5,0x3fe0a71ffddfc718,1 +np.float64,0xffed87ff20fb0ffd,0xbfe661db7c4098e3,1 +np.float64,0xffe369278526d24e,0x3fd64d89a41822fc,1 +np.float64,0xff950288c02a0520,0x3fe1df91d1ad7d5c,1 +np.float64,0xffe70e7c2cee1cf8,0x3fc9fece08df2fd8,1 +np.float64,0xffbaf020b635e040,0xbfc68c43ff9911a7,1 +np.float64,0xffee0120b0fc0240,0x3f9f792e17b490b0,1 +np.float64,0xffe1fa4be7a3f498,0xbfef4b18ab4b319e,1 +np.float64,0xffe61887bf2c310f,0x3fe846714826cb32,1 +np.float64,0xffdc3cf77f3879ee,0x3fe033b948a36125,1 +np.float64,0xffcc2b86f238570c,0xbfefdcceac3f220f,1 +np.float64,0xffe1f030c0a3e061,0x3fef502a808c359a,1 +np.float64,0xffb872c4ee30e588,0x3fef66ed8d3e6175,1 +np.float64,0xffeac8fc617591f8,0xbfe5d8448602aac9,1 +np.float64,0xffe5be16afab7c2d,0x3fee75ccde3cd14d,1 +np.float64,0xffae230ad83c4610,0xbfe49bbe6074d459,1 +np.float64,0xffc8fbeff531f7e0,0x3f77201e0c927f97,1 +np.float64,0xffdc314f48b8629e,0x3fef810dfc5db118,1 +np.float64,0xffec1f8970783f12,0x3fe15567102e042a,1 +np.float64,0xffc6995f902d32c0,0xbfecd5d2eedf342c,1 +np.float64,0xffdc7af76b38f5ee,0xbfd6e754476ab320,1 +np.float64,0xffb30cf8682619f0,0x3fd5ac3dfc4048d0,1 +np.float64,0xffd3a77695a74eee,0xbfefb5d6889e36e9,1 +np.float64,0xffd8b971803172e4,0xbfeb7f62f0b6c70b,1 +np.float64,0xffde4c0234bc9804,0xbfed50ba9e16d5e0,1 +np.float64,0xffb62b3f342c5680,0xbfeabc0de4069b84,1 +np.float64,0xff9af5674035eac0,0xbfed6c198b6b1bd8,1 +np.float64,0xffdfe20cb43fc41a,0x3fb11f8238f66306,1 +np.float64,0xffd2ecd7a0a5d9b0,0xbfec17ef1a62b1e3,1 +np.float64,0xffce60f7863cc1f0,0x3fe6dbcad3e3a006,1 +np.float64,0xffbbb8306a377060,0xbfbfd0fbef485c4c,1 +np.float64,0xffd1b2bd2b23657a,0xbfda3e046d987b99,1 +np.float64,0xffc480f4092901e8,0xbfeeff0427f6897b,1 +np.float64,0xffe6e02d926dc05a,0xbfcd59552778890b,1 +np.float64,0xffd302e5b7a605cc,0xbfee7c08641366b0,1 +np.float64,0xffec2eb92f785d72,0xbfef5c9c7f771050,1 +np.float64,0xffea3e31a9747c62,0xbfc49cd54755faf0,1 +np.float64,0xffce0a4e333c149c,0x3feeb9a6d0db4aee,1 +np.float64,0xffdc520a2db8a414,0x3fefc7b72613dcd0,1 +np.float64,0xffe056b968a0ad72,0xbfe47a9fe1f827fb,1 +np.float64,0xffe5a10f4cab421e,0x3fec2b1f74b73dec,1 diff --git a/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv new file mode 100644 index 0000000000000000000000000000000000000000..9e3ddc60ffa683f01139870d31de5cb61c2cbc2e --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/_core/tests/data/umath-validation-set-tanh.csv @@ -0,0 +1,1429 @@ +dtype,input,output,ulperrortol +np.float32,0xbe26ebb0,0xbe25752f,2 +np.float32,0xbe22ecc0,0xbe219054,2 +np.float32,0x8010a6b3,0x8010a6b3,2 +np.float32,0x3135da,0x3135da,2 +np.float32,0xbe982afc,0xbe93d727,2 +np.float32,0x16a51f,0x16a51f,2 +np.float32,0x491e56,0x491e56,2 +np.float32,0x4bf7ca,0x4bf7ca,2 +np.float32,0x3eebc21c,0x3edc65b2,2 +np.float32,0x80155c94,0x80155c94,2 +np.float32,0x3e14f626,0x3e13eb6a,2 +np.float32,0x801a238f,0x801a238f,2 +np.float32,0xbde33a80,0xbde24cf9,2 +np.float32,0xbef8439c,0xbee67a51,2 +np.float32,0x7f60d0a5,0x3f800000,2 +np.float32,0x190ee3,0x190ee3,2 +np.float32,0x80759113,0x80759113,2 +np.float32,0x800afa9f,0x800afa9f,2 +np.float32,0x7110cf,0x7110cf,2 +np.float32,0x3cf709f0,0x3cf6f6c6,2 +np.float32,0x3ef58da4,0x3ee44fa7,2 +np.float32,0xbf220ff2,0xbf0f662c,2 +np.float32,0xfd888078,0xbf800000,2 +np.float32,0xbe324734,0xbe307f9b,2 +np.float32,0x3eb5cb4f,0x3eae8560,2 +np.float32,0xbf7e7d02,0xbf425493,2 +np.float32,0x3ddcdcf0,0x3ddc02c2,2 +np.float32,0x8026d27a,0x8026d27a,2 +np.float32,0x3d4c0fb1,0x3d4be484,2 +np.float32,0xbf27d2c9,0xbf134d7c,2 +np.float32,0x8029ff80,0x8029ff80,2 +np.float32,0x7f046d2c,0x3f800000,2 +np.float32,0x13f94b,0x13f94b,2 +np.float32,0x7f4ff922,0x3f800000,2 +np.float32,0x3f4ea2ed,0x3f2b03e4,2 +np.float32,0x3e7211f0,0x3e6da8cf,2 +np.float32,0x7f39d0cf,0x3f800000,2 +np.float32,0xfee57fc6,0xbf800000,2 +np.float32,0xff6fb326,0xbf800000,2 +np.float32,0xff800000,0xbf800000,2 +np.float32,0x3f0437a4,0x3ef32fcd,2 +np.float32,0xff546d1e,0xbf800000,2 +np.float32,0x3eb5645b,0x3eae2a5c,2 +np.float32,0x3f08a6e5,0x3ef9ff8f,2 +np.float32,0x80800000,0x80800000,2 +np.float32,0x7f3413da,0x3f800000,2 +np.float32,0xfd760140,0xbf800000,2 +np.float32,0x7f3ad24a,0x3f800000,2 +np.float32,0xbf56e812,0xbf2f7f14,2 +np.float32,0xbece0338,0xbec3920a,2 +np.float32,0xbeede54a,0xbede22ae,2 +np.float32,0x7eaeb215,0x3f800000,2 +np.float32,0x3c213c00,0x3c213aab,2 +np.float32,0x7eaac217,0x3f800000,2 +np.float32,0xbf2f740e,0xbf1851a6,2 +np.float32,0x7f6ca5b8,0x3f800000,2 +np.float32,0xff42ce95,0xbf800000,2 +np.float32,0x802e4189,0x802e4189,2 +np.float32,0x80000001,0x80000001,2 +np.float32,0xbf31f298,0xbf19ebbe,2 +np.float32,0x3dcb0e6c,0x3dca64c1,2 +np.float32,0xbf29599c,0xbf145204,2 +np.float32,0x2e33f2,0x2e33f2,2 +np.float32,0x1c11e7,0x1c11e7,2 +np.float32,0x3f3b188d,0x3f1fa302,2 +np.float32,0x113300,0x113300,2 +np.float32,0x8054589e,0x8054589e,2 +np.float32,0x2a9e69,0x2a9e69,2 +np.float32,0xff513af7,0xbf800000,2 +np.float32,0x7f2e987a,0x3f800000,2 +np.float32,0x807cd426,0x807cd426,2 +np.float32,0x7f0dc4e4,0x3f800000,2 +np.float32,0x7e7c0d56,0x3f800000,2 +np.float32,0x5cb076,0x5cb076,2 +np.float32,0x80576426,0x80576426,2 +np.float32,0xff616222,0xbf800000,2 +np.float32,0xbf7accb5,0xbf40c005,2 +np.float32,0xfe4118c8,0xbf800000,2 +np.float32,0x804b9327,0x804b9327,2 +np.float32,0x3ed2b428,0x3ec79026,2 +np.float32,0x3f4a048f,0x3f286d41,2 +np.float32,0x800000,0x800000,2 +np.float32,0x7efceb9f,0x3f800000,2 +np.float32,0xbf5fe2d3,0xbf34246f,2 +np.float32,0x807e086a,0x807e086a,2 +np.float32,0x7ef5e856,0x3f800000,2 +np.float32,0xfc546f00,0xbf800000,2 +np.float32,0x3a65b890,0x3a65b88c,2 +np.float32,0x800cfa70,0x800cfa70,2 +np.float32,0x80672ea7,0x80672ea7,2 +np.float32,0x3f2bf3f2,0x3f160a12,2 +np.float32,0xbf0ab67e,0xbefd2004,2 +np.float32,0x3f2a0bb4,0x3f14c824,2 +np.float32,0xbeff5374,0xbeec12d7,2 +np.float32,0xbf221b58,0xbf0f6dff,2 +np.float32,0x7cc1f3,0x7cc1f3,2 +np.float32,0x7f234e3c,0x3f800000,2 +np.float32,0x3f60ff10,0x3f34b37d,2 +np.float32,0xbdd957f0,0xbdd887fe,2 +np.float32,0x801ce048,0x801ce048,2 +np.float32,0x7f3a8f76,0x3f800000,2 +np.float32,0xfdd13d08,0xbf800000,2 +np.float32,0x3e9af4a4,0x3e966445,2 +np.float32,0x1e55f3,0x1e55f3,2 +np.float32,0x327905,0x327905,2 +np.float32,0xbf03cf0b,0xbef28dad,2 +np.float32,0x3f0223d3,0x3eeff4f4,2 +np.float32,0xfdd96ff8,0xbf800000,2 +np.float32,0x428db8,0x428db8,2 +np.float32,0xbd74a200,0xbd7457a5,2 +np.float32,0x2a63a3,0x2a63a3,2 +np.float32,0x7e8aa9d7,0x3f800000,2 +np.float32,0x7f50b810,0x3f800000,2 +np.float32,0xbce5ec80,0xbce5dd0d,2 +np.float32,0x54711,0x54711,2 +np.float32,0x8074212a,0x8074212a,2 +np.float32,0xbf13d0ec,0xbf0551b5,2 +np.float32,0x80217f89,0x80217f89,2 +np.float32,0x3f300824,0x3f18b12f,2 +np.float32,0x7d252462,0x3f800000,2 +np.float32,0x807a154c,0x807a154c,2 +np.float32,0x8064d4b9,0x8064d4b9,2 +np.float32,0x804543b4,0x804543b4,2 +np.float32,0x4c269e,0x4c269e,2 +np.float32,0xff39823b,0xbf800000,2 +np.float32,0x3f5040b1,0x3f2be80b,2 +np.float32,0xbf7028c1,0xbf3bfee5,2 +np.float32,0x3e94eb78,0x3e90db93,2 +np.float32,0x3ccc1b40,0x3ccc1071,2 +np.float32,0xbe8796f0,0xbe8481a1,2 +np.float32,0xfc767bc0,0xbf800000,2 +np.float32,0xbdd81ed0,0xbdd75259,2 +np.float32,0xbed31bfc,0xbec7e82d,2 +np.float32,0xbf350a9e,0xbf1be1c6,2 +np.float32,0x33d41f,0x33d41f,2 +np.float32,0x3f73e076,0x3f3db0b5,2 +np.float32,0x3f800000,0x3f42f7d6,2 +np.float32,0xfee27c14,0xbf800000,2 +np.float32,0x7f6e4388,0x3f800000,2 +np.float32,0x4ea19b,0x4ea19b,2 +np.float32,0xff2d75f2,0xbf800000,2 +np.float32,0x7ee225ca,0x3f800000,2 +np.float32,0x3f31cb4b,0x3f19d2a4,2 +np.float32,0x80554a9d,0x80554a9d,2 +np.float32,0x3f4d57fa,0x3f2a4c03,2 +np.float32,0x3eac6a88,0x3ea62e72,2 +np.float32,0x773520,0x773520,2 +np.float32,0x8079c20a,0x8079c20a,2 +np.float32,0xfeb1eb94,0xbf800000,2 +np.float32,0xfe8d81c0,0xbf800000,2 +np.float32,0xfeed6902,0xbf800000,2 +np.float32,0x8066bb65,0x8066bb65,2 +np.float32,0x7f800000,0x3f800000,2 +np.float32,0x1,0x1,2 +np.float32,0x3f2c66a4,0x3f16554a,2 +np.float32,0x3cd231,0x3cd231,2 +np.float32,0x3e932a64,0x3e8f3e0c,2 +np.float32,0xbf3ab1c3,0xbf1f6420,2 +np.float32,0xbc902b20,0xbc902751,2 +np.float32,0x7dac0a5b,0x3f800000,2 +np.float32,0x3f2b7e06,0x3f15bc93,2 +np.float32,0x75de0,0x75de0,2 +np.float32,0x8020b7bc,0x8020b7bc,2 +np.float32,0x3f257cda,0x3f11bb6b,2 +np.float32,0x807480e5,0x807480e5,2 +np.float32,0xfe00d758,0xbf800000,2 +np.float32,0xbd9b54e0,0xbd9b08cd,2 +np.float32,0x4dfbe3,0x4dfbe3,2 +np.float32,0xff645788,0xbf800000,2 +np.float32,0xbe92c80a,0xbe8ee360,2 +np.float32,0x3eb9b400,0x3eb1f77c,2 +np.float32,0xff20b69c,0xbf800000,2 +np.float32,0x623c28,0x623c28,2 +np.float32,0xff235748,0xbf800000,2 +np.float32,0xbf3bbc56,0xbf2006f3,2 +np.float32,0x7e6f78b1,0x3f800000,2 +np.float32,0x7e1584e9,0x3f800000,2 +np.float32,0xff463423,0xbf800000,2 +np.float32,0x8002861e,0x8002861e,2 +np.float32,0xbf0491d8,0xbef3bb6a,2 +np.float32,0x7ea3bc17,0x3f800000,2 +np.float32,0xbedde7ea,0xbed0fb49,2 +np.float32,0xbf4bac48,0xbf295c8b,2 +np.float32,0xff28e276,0xbf800000,2 +np.float32,0x7e8f3bf5,0x3f800000,2 +np.float32,0xbf0a4a73,0xbefc7c9d,2 +np.float32,0x7ec5bd96,0x3f800000,2 +np.float32,0xbf4c22e8,0xbf299f2c,2 +np.float32,0x3e3970a0,0x3e377064,2 +np.float32,0x3ecb1118,0x3ec10c88,2 +np.float32,0xff548a7a,0xbf800000,2 +np.float32,0xfe8ec550,0xbf800000,2 +np.float32,0x3e158985,0x3e147bb2,2 +np.float32,0x7eb79ad7,0x3f800000,2 +np.float32,0xbe811384,0xbe7cd1ab,2 +np.float32,0xbdc4b9e8,0xbdc41f94,2 +np.float32,0xe0fd5,0xe0fd5,2 +np.float32,0x3f2485f2,0x3f11142b,2 +np.float32,0xfdd3c3d8,0xbf800000,2 +np.float32,0xfe8458e6,0xbf800000,2 +np.float32,0x3f06e398,0x3ef74dd8,2 +np.float32,0xff4752cf,0xbf800000,2 +np.float32,0x6998e3,0x6998e3,2 +np.float32,0x626751,0x626751,2 +np.float32,0x806631d6,0x806631d6,2 +np.float32,0xbf0c3cf4,0xbeff6c54,2 +np.float32,0x802860f8,0x802860f8,2 +np.float32,0xff2952cb,0xbf800000,2 +np.float32,0xff31d40b,0xbf800000,2 +np.float32,0x7c389473,0x3f800000,2 +np.float32,0x3dcd2f1b,0x3dcc8010,2 +np.float32,0x3d70c29f,0x3d707bbc,2 +np.float32,0x3f6bd386,0x3f39f979,2 +np.float32,0x1efec9,0x1efec9,2 +np.float32,0x3f675518,0x3f37d338,2 +np.float32,0x5fdbe3,0x5fdbe3,2 +np.float32,0x5d684e,0x5d684e,2 +np.float32,0xbedfe748,0xbed2a4c7,2 +np.float32,0x3f0cb07a,0x3f000cdc,2 +np.float32,0xbf77151e,0xbf3f1f5d,2 +np.float32,0x7f038ea0,0x3f800000,2 +np.float32,0x3ea91be9,0x3ea3376f,2 +np.float32,0xbdf20738,0xbdf0e861,2 +np.float32,0x807ea380,0x807ea380,2 +np.float32,0x2760ca,0x2760ca,2 +np.float32,0x7f20a544,0x3f800000,2 +np.float32,0x76ed83,0x76ed83,2 +np.float32,0x15a441,0x15a441,2 +np.float32,0x74c76d,0x74c76d,2 +np.float32,0xff3d5c2a,0xbf800000,2 +np.float32,0x7f6a76a6,0x3f800000,2 +np.float32,0x3eb87067,0x3eb0dabe,2 +np.float32,0xbf515cfa,0xbf2c83af,2 +np.float32,0xbdececc0,0xbdebdf9d,2 +np.float32,0x7f51b7c2,0x3f800000,2 +np.float32,0x3eb867ac,0x3eb0d30d,2 +np.float32,0xff50fd84,0xbf800000,2 +np.float32,0x806945e9,0x806945e9,2 +np.float32,0x298eed,0x298eed,2 +np.float32,0x441f53,0x441f53,2 +np.float32,0x8066d4b0,0x8066d4b0,2 +np.float32,0x3f6a479c,0x3f393dae,2 +np.float32,0xbf6ce2a7,0xbf3a7921,2 +np.float32,0x8064c3cf,0x8064c3cf,2 +np.float32,0xbf2d8146,0xbf170dfd,2 +np.float32,0x3b0e82,0x3b0e82,2 +np.float32,0xbea97574,0xbea387dc,2 +np.float32,0x67ad15,0x67ad15,2 +np.float32,0xbf68478f,0xbf38485a,2 +np.float32,0xff6f593b,0xbf800000,2 +np.float32,0xbeda26f2,0xbecdd806,2 +np.float32,0xbd216d50,0xbd2157ee,2 +np.float32,0x7a8544db,0x3f800000,2 +np.float32,0x801df20b,0x801df20b,2 +np.float32,0xbe14ba24,0xbe13b0a8,2 +np.float32,0xfdc6d8a8,0xbf800000,2 +np.float32,0x1d6b49,0x1d6b49,2 +np.float32,0x7f5ff1b8,0x3f800000,2 +np.float32,0x3f75e032,0x3f3e9625,2 +np.float32,0x7f2c5687,0x3f800000,2 +np.float32,0x3d95fb6c,0x3d95b6ee,2 +np.float32,0xbea515e4,0xbe9f97c8,2 +np.float32,0x7f2b2cd7,0x3f800000,2 +np.float32,0x3f076f7a,0x3ef8241e,2 +np.float32,0x5178ca,0x5178ca,2 +np.float32,0xbeb5976a,0xbeae5781,2 +np.float32,0x3e3c3563,0x3e3a1e13,2 +np.float32,0xbd208530,0xbd20702a,2 +np.float32,0x3eb03b04,0x3ea995ef,2 +np.float32,0x17fb9c,0x17fb9c,2 +np.float32,0xfca68e40,0xbf800000,2 +np.float32,0xbf5e7433,0xbf336a9f,2 +np.float32,0xff5b8d3d,0xbf800000,2 +np.float32,0x8003121d,0x8003121d,2 +np.float32,0xbe6dd344,0xbe69a3b0,2 +np.float32,0x67cc4,0x67cc4,2 +np.float32,0x9b01d,0x9b01d,2 +np.float32,0x127c13,0x127c13,2 +np.float32,0xfea5e3d6,0xbf800000,2 +np.float32,0xbdf5c610,0xbdf499c1,2 +np.float32,0x3aff4c00,0x3aff4beb,2 +np.float32,0x3b00afd0,0x3b00afc5,2 +np.float32,0x479618,0x479618,2 +np.float32,0x801cbd05,0x801cbd05,2 +np.float32,0x3ec9249f,0x3ebf6579,2 +np.float32,0x3535c4,0x3535c4,2 +np.float32,0xbeb4f662,0xbeadc915,2 +np.float32,0x8006fda6,0x8006fda6,2 +np.float32,0xbf4f3097,0xbf2b5239,2 +np.float32,0xbf3cb9a8,0xbf20a0e9,2 +np.float32,0x32ced0,0x32ced0,2 +np.float32,0x7ea34e76,0x3f800000,2 +np.float32,0x80063046,0x80063046,2 +np.float32,0x80727e8b,0x80727e8b,2 +np.float32,0xfd6b5780,0xbf800000,2 +np.float32,0x80109815,0x80109815,2 +np.float32,0xfdcc8a78,0xbf800000,2 +np.float32,0x81562,0x81562,2 +np.float32,0x803dfacc,0x803dfacc,2 +np.float32,0xbe204318,0xbe1ef75f,2 +np.float32,0xbf745d34,0xbf3de8e2,2 +np.float32,0xff13fdcc,0xbf800000,2 +np.float32,0x7f75ba8c,0x3f800000,2 +np.float32,0x806c04b4,0x806c04b4,2 +np.float32,0x3ec61ca6,0x3ebcc877,2 +np.float32,0xbeaea984,0xbea8301f,2 +np.float32,0xbf4dcd0e,0xbf2a8d34,2 +np.float32,0x802a01d3,0x802a01d3,2 +np.float32,0xbf747be5,0xbf3df6ad,2 +np.float32,0xbf75cbd2,0xbf3e8d0f,2 +np.float32,0x7db86576,0x3f800000,2 +np.float32,0xff49a2c3,0xbf800000,2 +np.float32,0xbedc5314,0xbecfa978,2 +np.float32,0x8078877b,0x8078877b,2 +np.float32,0xbead4824,0xbea6f499,2 +np.float32,0xbf3926e3,0xbf1e716c,2 +np.float32,0x807f4a1c,0x807f4a1c,2 +np.float32,0x7f2cd8fd,0x3f800000,2 +np.float32,0x806cfcca,0x806cfcca,2 +np.float32,0xff1aa048,0xbf800000,2 +np.float32,0x7eb9ea08,0x3f800000,2 +np.float32,0xbf1034bc,0xbf02ab3a,2 +np.float32,0xbd087830,0xbd086b44,2 +np.float32,0x7e071034,0x3f800000,2 +np.float32,0xbefcc9de,0xbeea122f,2 +np.float32,0x80796d7a,0x80796d7a,2 +np.float32,0x33ce46,0x33ce46,2 +np.float32,0x8074a783,0x8074a783,2 +np.float32,0xbe95a56a,0xbe918691,2 +np.float32,0xbf2ff3f4,0xbf18a42d,2 +np.float32,0x1633e9,0x1633e9,2 +np.float32,0x7f0f104b,0x3f800000,2 +np.float32,0xbf800000,0xbf42f7d6,2 +np.float32,0x3d2cd6,0x3d2cd6,2 +np.float32,0xfed43e16,0xbf800000,2 +np.float32,0x3ee6faec,0x3ed87d2c,2 +np.float32,0x3f2c32d0,0x3f163352,2 +np.float32,0xff4290c0,0xbf800000,2 +np.float32,0xbf66500e,0xbf37546a,2 +np.float32,0x7dfb8fe3,0x3f800000,2 +np.float32,0x3f20ba5d,0x3f0e7b16,2 +np.float32,0xff30c7ae,0xbf800000,2 +np.float32,0x1728a4,0x1728a4,2 +np.float32,0x340d82,0x340d82,2 +np.float32,0xff7870b7,0xbf800000,2 +np.float32,0xbeac6ac4,0xbea62ea7,2 +np.float32,0xbef936fc,0xbee73c36,2 +np.float32,0x3ec7e12c,0x3ebe4ef8,2 +np.float32,0x80673488,0x80673488,2 +np.float32,0xfdf14c90,0xbf800000,2 +np.float32,0x3f182568,0x3f08726e,2 +np.float32,0x7ed7dcd0,0x3f800000,2 +np.float32,0x3de4da34,0x3de3e790,2 +np.float32,0xff7fffff,0xbf800000,2 +np.float32,0x4ff90c,0x4ff90c,2 +np.float32,0x3efb0d1c,0x3ee8b1d6,2 +np.float32,0xbf66e952,0xbf379ef4,2 +np.float32,0xba9dc,0xba9dc,2 +np.float32,0xff67c766,0xbf800000,2 +np.float32,0x7f1ffc29,0x3f800000,2 +np.float32,0x3f51c906,0x3f2cbe99,2 +np.float32,0x3f2e5792,0x3f179968,2 +np.float32,0x3ecb9750,0x3ec17fa0,2 +np.float32,0x7f3fcefc,0x3f800000,2 +np.float32,0xbe4e30fc,0xbe4b72f9,2 +np.float32,0x7e9bc4ce,0x3f800000,2 +np.float32,0x7e70aa1f,0x3f800000,2 +np.float32,0x14c6e9,0x14c6e9,2 +np.float32,0xbcf327c0,0xbcf3157a,2 +np.float32,0xff1fd204,0xbf800000,2 +np.float32,0x7d934a03,0x3f800000,2 +np.float32,0x8028bf1e,0x8028bf1e,2 +np.float32,0x7f0800b7,0x3f800000,2 +np.float32,0xfe04825c,0xbf800000,2 +np.float32,0x807210ac,0x807210ac,2 +np.float32,0x3f7faf7c,0x3f42d5fd,2 +np.float32,0x3e04a543,0x3e03e899,2 +np.float32,0x3e98ea15,0x3e94863e,2 +np.float32,0x3d2a2e48,0x3d2a153b,2 +np.float32,0x7fa00000,0x7fe00000,2 +np.float32,0x20a488,0x20a488,2 +np.float32,0x3f6ba86a,0x3f39e51a,2 +np.float32,0x0,0x0,2 +np.float32,0x3e892ddd,0x3e85fcfe,2 +np.float32,0x3e2da627,0x3e2c00e0,2 +np.float32,0xff000a50,0xbf800000,2 +np.float32,0x3eb749f4,0x3eafd739,2 +np.float32,0x8024c0ae,0x8024c0ae,2 +np.float32,0xfc8f3b40,0xbf800000,2 +np.float32,0xbf685fc7,0xbf385405,2 +np.float32,0x3f1510e6,0x3f063a4f,2 +np.float32,0x3f68e8ad,0x3f3895d8,2 +np.float32,0x3dba8608,0x3dba0271,2 +np.float32,0xbf16ea10,0xbf079017,2 +np.float32,0xb3928,0xb3928,2 +np.float32,0xfe447c00,0xbf800000,2 +np.float32,0x3db9cd57,0x3db94b45,2 +np.float32,0x803b66b0,0x803b66b0,2 +np.float32,0x805b5e02,0x805b5e02,2 +np.float32,0x7ec93f61,0x3f800000,2 +np.float32,0x8005a126,0x8005a126,2 +np.float32,0x6d8888,0x6d8888,2 +np.float32,0x3e21b7de,0x3e206314,2 +np.float32,0xbec9c31e,0xbebfedc2,2 +np.float32,0xbea88aa8,0xbea2b4e5,2 +np.float32,0x3d8fc310,0x3d8f86bb,2 +np.float32,0xbf3cc68a,0xbf20a8b8,2 +np.float32,0x432690,0x432690,2 +np.float32,0xbe51d514,0xbe4ef1a3,2 +np.float32,0xbcda6d20,0xbcda5fe1,2 +np.float32,0xfe24e458,0xbf800000,2 +np.float32,0xfedc8c14,0xbf800000,2 +np.float32,0x7f7e9bd4,0x3f800000,2 +np.float32,0x3ebcc880,0x3eb4ab44,2 +np.float32,0xbe0aa490,0xbe09cd44,2 +np.float32,0x3dc9158c,0x3dc870c3,2 +np.float32,0x3e5c319e,0x3e58dc90,2 +np.float32,0x1d4527,0x1d4527,2 +np.float32,0x2dbf5,0x2dbf5,2 +np.float32,0xbf1f121f,0xbf0d5534,2 +np.float32,0x7e3e9ab5,0x3f800000,2 +np.float32,0x7f74b5c1,0x3f800000,2 +np.float32,0xbf6321ba,0xbf35c42b,2 +np.float32,0xbe5c7488,0xbe591c79,2 +np.float32,0x7e7b02cd,0x3f800000,2 +np.float32,0xfe7cbfa4,0xbf800000,2 +np.float32,0xbeace360,0xbea69a86,2 +np.float32,0x7e149b00,0x3f800000,2 +np.float32,0xbf61a700,0xbf35079a,2 +np.float32,0x7eb592a7,0x3f800000,2 +np.float32,0x3f2105e6,0x3f0eaf30,2 +np.float32,0xfd997a88,0xbf800000,2 +np.float32,0xff5d093b,0xbf800000,2 +np.float32,0x63aede,0x63aede,2 +np.float32,0x6907ee,0x6907ee,2 +np.float32,0xbf7578ee,0xbf3e680f,2 +np.float32,0xfea971e8,0xbf800000,2 +np.float32,0x3f21d0f5,0x3f0f3aed,2 +np.float32,0x3a50e2,0x3a50e2,2 +np.float32,0x7f0f5b1e,0x3f800000,2 +np.float32,0x805b9765,0x805b9765,2 +np.float32,0xbe764ab8,0xbe71a664,2 +np.float32,0x3eafac7f,0x3ea91701,2 +np.float32,0x807f4130,0x807f4130,2 +np.float32,0x7c5f31,0x7c5f31,2 +np.float32,0xbdbe0e30,0xbdbd8300,2 +np.float32,0x7ecfe4e0,0x3f800000,2 +np.float32,0xff7cb628,0xbf800000,2 +np.float32,0xff1842bc,0xbf800000,2 +np.float32,0xfd4163c0,0xbf800000,2 +np.float32,0x800e11f7,0x800e11f7,2 +np.float32,0x7f3adec8,0x3f800000,2 +np.float32,0x7f597514,0x3f800000,2 +np.float32,0xbe986e14,0xbe9414a4,2 +np.float32,0x800fa9d7,0x800fa9d7,2 +np.float32,0xff5b79c4,0xbf800000,2 +np.float32,0x80070565,0x80070565,2 +np.float32,0xbee5628e,0xbed72d60,2 +np.float32,0x3f438ef2,0x3f24b3ca,2 +np.float32,0xcda91,0xcda91,2 +np.float32,0x7e64151a,0x3f800000,2 +np.float32,0xbe95d584,0xbe91b2c7,2 +np.float32,0x8022c2a1,0x8022c2a1,2 +np.float32,0x7e7097bf,0x3f800000,2 +np.float32,0x80139035,0x80139035,2 +np.float32,0x804de2cb,0x804de2cb,2 +np.float32,0xfde5d178,0xbf800000,2 +np.float32,0x6d238,0x6d238,2 +np.float32,0x807abedc,0x807abedc,2 +np.float32,0x3f450a12,0x3f259129,2 +np.float32,0x3ef1c120,0x3ee141f2,2 +np.float32,0xfeb64dae,0xbf800000,2 +np.float32,0x8001732c,0x8001732c,2 +np.float32,0x3f76062e,0x3f3ea711,2 +np.float32,0x3eddd550,0x3ed0ebc8,2 +np.float32,0xff5ca1d4,0xbf800000,2 +np.float32,0xbf49dc5e,0xbf285673,2 +np.float32,0x7e9e5438,0x3f800000,2 +np.float32,0x7e83625e,0x3f800000,2 +np.float32,0x3f5dc41c,0x3f3310da,2 +np.float32,0x3f583efa,0x3f30342f,2 +np.float32,0xbe26bf88,0xbe254a2d,2 +np.float32,0xff1e0beb,0xbf800000,2 +np.float32,0xbe2244c8,0xbe20ec86,2 +np.float32,0xff0b1630,0xbf800000,2 +np.float32,0xff338dd6,0xbf800000,2 +np.float32,0x3eafc22c,0x3ea92a51,2 +np.float32,0x800ea07f,0x800ea07f,2 +np.float32,0x3f46f006,0x3f26aa7e,2 +np.float32,0x3e5f57cd,0x3e5bde16,2 +np.float32,0xbf1b2d8e,0xbf0a9a93,2 +np.float32,0xfeacdbe0,0xbf800000,2 +np.float32,0x7e5ea4bc,0x3f800000,2 +np.float32,0xbf51cbe2,0xbf2cc027,2 +np.float32,0x8073644c,0x8073644c,2 +np.float32,0xff2d6bfe,0xbf800000,2 +np.float32,0x3f65f0f6,0x3f37260a,2 +np.float32,0xff4b37a6,0xbf800000,2 +np.float32,0x712df7,0x712df7,2 +np.float32,0x7f71ef17,0x3f800000,2 +np.float32,0x8042245c,0x8042245c,2 +np.float32,0x3e5dde7b,0x3e5a760d,2 +np.float32,0x8069317d,0x8069317d,2 +np.float32,0x807932dd,0x807932dd,2 +np.float32,0x802f847e,0x802f847e,2 +np.float32,0x7e9300,0x7e9300,2 +np.float32,0x8040b4ab,0x8040b4ab,2 +np.float32,0xff76ef8e,0xbf800000,2 +np.float32,0x4aae3a,0x4aae3a,2 +np.float32,0x8058de73,0x8058de73,2 +np.float32,0x7e4d58c0,0x3f800000,2 +np.float32,0x3d811b30,0x3d80ef79,2 +np.float32,0x7ec952cc,0x3f800000,2 +np.float32,0xfe162b1c,0xbf800000,2 +np.float32,0x3f0f1187,0x3f01d367,2 +np.float32,0xbf2f3458,0xbf182878,2 +np.float32,0x5ceb14,0x5ceb14,2 +np.float32,0xbec29476,0xbeb9b939,2 +np.float32,0x3e71f943,0x3e6d9176,2 +np.float32,0x3ededefc,0x3ed1c909,2 +np.float32,0x805df6ac,0x805df6ac,2 +np.float32,0x3e5ae2c8,0x3e579ca8,2 +np.float32,0x3f6ad2c3,0x3f397fdf,2 +np.float32,0x7d5f94d3,0x3f800000,2 +np.float32,0xbeec7fe4,0xbedd0037,2 +np.float32,0x3f645304,0x3f365b0d,2 +np.float32,0xbf69a087,0xbf38edef,2 +np.float32,0x8025102e,0x8025102e,2 +np.float32,0x800db486,0x800db486,2 +np.float32,0x4df6c7,0x4df6c7,2 +np.float32,0x806d8cdd,0x806d8cdd,2 +np.float32,0x7f0c78cc,0x3f800000,2 +np.float32,0x7e1cf70b,0x3f800000,2 +np.float32,0x3e0ae570,0x3e0a0cf7,2 +np.float32,0x80176ef8,0x80176ef8,2 +np.float32,0x3f38b60c,0x3f1e2bbb,2 +np.float32,0x3d3071e0,0x3d3055f5,2 +np.float32,0x3ebfcfdd,0x3eb750a9,2 +np.float32,0xfe2cdec0,0xbf800000,2 +np.float32,0x7eeb2eed,0x3f800000,2 +np.float32,0x8026c904,0x8026c904,2 +np.float32,0xbec79bde,0xbebe133a,2 +np.float32,0xbf7dfab6,0xbf421d47,2 +np.float32,0x805b3cfd,0x805b3cfd,2 +np.float32,0xfdfcfb68,0xbf800000,2 +np.float32,0xbd537ec0,0xbd534eaf,2 +np.float32,0x52ce73,0x52ce73,2 +np.float32,0xfeac6ea6,0xbf800000,2 +np.float32,0x3f2c2990,0x3f162d41,2 +np.float32,0x3e3354e0,0x3e318539,2 +np.float32,0x802db22b,0x802db22b,2 +np.float32,0x7f0faa83,0x3f800000,2 +np.float32,0x7f10e161,0x3f800000,2 +np.float32,0x7f165c60,0x3f800000,2 +np.float32,0xbf5a756f,0xbf315c82,2 +np.float32,0x7f5a4b68,0x3f800000,2 +np.float32,0xbd77fbf0,0xbd77ae7c,2 +np.float32,0x65d83c,0x65d83c,2 +np.float32,0x3e5f28,0x3e5f28,2 +np.float32,0x8040ec92,0x8040ec92,2 +np.float32,0xbf2b41a6,0xbf1594d5,2 +np.float32,0x7f2f88f1,0x3f800000,2 +np.float32,0xfdb64ab8,0xbf800000,2 +np.float32,0xbf7a3ff1,0xbf4082f5,2 +np.float32,0x1948fc,0x1948fc,2 +np.float32,0x802c1039,0x802c1039,2 +np.float32,0x80119274,0x80119274,2 +np.float32,0x7e885d7b,0x3f800000,2 +np.float32,0xfaf6a,0xfaf6a,2 +np.float32,0x3eba28c4,0x3eb25e1d,2 +np.float32,0x3e4df370,0x3e4b37da,2 +np.float32,0xbf19eff6,0xbf09b97d,2 +np.float32,0xbeddd3c6,0xbed0ea7f,2 +np.float32,0xff6fc971,0xbf800000,2 +np.float32,0x7e93de29,0x3f800000,2 +np.float32,0x3eb12332,0x3eaa6485,2 +np.float32,0x3eb7c6e4,0x3eb04563,2 +np.float32,0x4a67ee,0x4a67ee,2 +np.float32,0xff1cafde,0xbf800000,2 +np.float32,0x3f5e2812,0x3f3343da,2 +np.float32,0x3f060e04,0x3ef605d4,2 +np.float32,0x3e9027d8,0x3e8c76a6,2 +np.float32,0xe2d33,0xe2d33,2 +np.float32,0xff4c94fc,0xbf800000,2 +np.float32,0xbf574908,0xbf2fb26b,2 +np.float32,0xbf786c08,0xbf3fb68e,2 +np.float32,0x8011ecab,0x8011ecab,2 +np.float32,0xbf061c6a,0xbef61bfa,2 +np.float32,0x7eea5f9d,0x3f800000,2 +np.float32,0x3ea2e19c,0x3e9d99a5,2 +np.float32,0x8071550c,0x8071550c,2 +np.float32,0x41c70b,0x41c70b,2 +np.float32,0x80291fc8,0x80291fc8,2 +np.float32,0x43b1ec,0x43b1ec,2 +np.float32,0x32f5a,0x32f5a,2 +np.float32,0xbe9310ec,0xbe8f2692,2 +np.float32,0x7f75f6bf,0x3f800000,2 +np.float32,0x3e6642a6,0x3e6274d2,2 +np.float32,0x3ecb88e0,0x3ec1733f,2 +np.float32,0x804011b6,0x804011b6,2 +np.float32,0x80629cca,0x80629cca,2 +np.float32,0x8016b914,0x8016b914,2 +np.float32,0xbdd05fc0,0xbdcfa870,2 +np.float32,0x807b824d,0x807b824d,2 +np.float32,0xfeec2576,0xbf800000,2 +np.float32,0xbf54bf22,0xbf2e584c,2 +np.float32,0xbf185eb0,0xbf089b6b,2 +np.float32,0xfbc09480,0xbf800000,2 +np.float32,0x3f413054,0x3f234e25,2 +np.float32,0x7e9e32b8,0x3f800000,2 +np.float32,0x266296,0x266296,2 +np.float32,0x460284,0x460284,2 +np.float32,0x3eb0b056,0x3ea9fe5a,2 +np.float32,0x1a7be5,0x1a7be5,2 +np.float32,0x7f099895,0x3f800000,2 +np.float32,0x3f3614f0,0x3f1c88ef,2 +np.float32,0x7e757dc2,0x3f800000,2 +np.float32,0x801fc91e,0x801fc91e,2 +np.float32,0x3f5ce37d,0x3f329ddb,2 +np.float32,0x3e664d70,0x3e627f15,2 +np.float32,0xbf38ed78,0xbf1e4dfa,2 +np.float32,0xbf5c563d,0xbf325543,2 +np.float32,0xbe91cc54,0xbe8dfb24,2 +np.float32,0x3d767fbe,0x3d7633ac,2 +np.float32,0xbf6aeb40,0xbf398b7f,2 +np.float32,0x7f40508b,0x3f800000,2 +np.float32,0x2650df,0x2650df,2 +np.float32,0xbe8cea3c,0xbe897628,2 +np.float32,0x80515af8,0x80515af8,2 +np.float32,0x7f423986,0x3f800000,2 +np.float32,0xbdf250e8,0xbdf1310c,2 +np.float32,0xfe89288a,0xbf800000,2 +np.float32,0x397b3b,0x397b3b,2 +np.float32,0x7e5e91b0,0x3f800000,2 +np.float32,0x6866e2,0x6866e2,2 +np.float32,0x7f4d8877,0x3f800000,2 +np.float32,0x3e6c4a21,0x3e682ee3,2 +np.float32,0xfc3d5980,0xbf800000,2 +np.float32,0x7eae2cd0,0x3f800000,2 +np.float32,0xbf241222,0xbf10c579,2 +np.float32,0xfebc02de,0xbf800000,2 +np.float32,0xff6e0645,0xbf800000,2 +np.float32,0x802030b6,0x802030b6,2 +np.float32,0x7ef9a441,0x3f800000,2 +np.float32,0x3fcf9f,0x3fcf9f,2 +np.float32,0xbf0ccf13,0xbf0023cc,2 +np.float32,0xfefee688,0xbf800000,2 +np.float32,0xbf6c8e0c,0xbf3a5160,2 +np.float32,0xfe749c28,0xbf800000,2 +np.float32,0x7f7fffff,0x3f800000,2 +np.float32,0x58c1a0,0x58c1a0,2 +np.float32,0x3f2de0a1,0x3f174c17,2 +np.float32,0xbf5f7138,0xbf33eb03,2 +np.float32,0x3da15270,0x3da0fd3c,2 +np.float32,0x3da66560,0x3da607e4,2 +np.float32,0xbf306f9a,0xbf18f3c6,2 +np.float32,0x3e81a4de,0x3e7de293,2 +np.float32,0xbebb5fb8,0xbeb36f1a,2 +np.float32,0x14bf64,0x14bf64,2 +np.float32,0xbeac46c6,0xbea60e73,2 +np.float32,0xbdcdf210,0xbdcd4111,2 +np.float32,0x3f7e3cd9,0x3f42395e,2 +np.float32,0xbc4be640,0xbc4be38e,2 +np.float32,0xff5f53b4,0xbf800000,2 +np.float32,0xbf1315ae,0xbf04c90b,2 +np.float32,0x80000000,0x80000000,2 +np.float32,0xbf6a4149,0xbf393aaa,2 +np.float32,0x3f66b8ee,0x3f378772,2 +np.float32,0xff29293e,0xbf800000,2 +np.float32,0xbcc989c0,0xbcc97f58,2 +np.float32,0xbd9a1b70,0xbd99d125,2 +np.float32,0xfef353cc,0xbf800000,2 +np.float32,0xbdc30cf0,0xbdc27683,2 +np.float32,0xfdfd6768,0xbf800000,2 +np.float32,0x7ebac44c,0x3f800000,2 +np.float32,0xff453cd6,0xbf800000,2 +np.float32,0x3ef07720,0x3ee03787,2 +np.float32,0x80219c14,0x80219c14,2 +np.float32,0x805553a8,0x805553a8,2 +np.float32,0x80703928,0x80703928,2 +np.float32,0xff16d3a7,0xbf800000,2 +np.float32,0x3f1472bc,0x3f05c77b,2 +np.float32,0x3eeea37a,0x3edebcf9,2 +np.float32,0x3db801e6,0x3db7838d,2 +np.float32,0x800870d2,0x800870d2,2 +np.float32,0xbea1172c,0xbe9bfa32,2 +np.float32,0x3f1f5e7c,0x3f0d8a42,2 +np.float32,0x123cdb,0x123cdb,2 +np.float32,0x7f6e6b06,0x3f800000,2 +np.float32,0x3ed80573,0x3ecc0def,2 +np.float32,0xfea31b82,0xbf800000,2 +np.float32,0x6744e0,0x6744e0,2 +np.float32,0x695e8b,0x695e8b,2 +np.float32,0xbee3888a,0xbed5a67d,2 +np.float32,0x7f64bc2a,0x3f800000,2 +np.float32,0x7f204244,0x3f800000,2 +np.float32,0x7f647102,0x3f800000,2 +np.float32,0x3dd8ebc0,0x3dd81d03,2 +np.float32,0x801e7ab1,0x801e7ab1,2 +np.float32,0x7d034b56,0x3f800000,2 +np.float32,0x7fc00000,0x7fc00000,2 +np.float32,0x80194193,0x80194193,2 +np.float32,0xfe31c8d4,0xbf800000,2 +np.float32,0x7fc0c4,0x7fc0c4,2 +np.float32,0xd95bf,0xd95bf,2 +np.float32,0x7e4f991d,0x3f800000,2 +np.float32,0x7fc563,0x7fc563,2 +np.float32,0xbe3fcccc,0xbe3d968a,2 +np.float32,0xfdaaa1c8,0xbf800000,2 +np.float32,0xbf48e449,0xbf27c949,2 +np.float32,0x3eb6c584,0x3eaf625e,2 +np.float32,0xbea35a74,0xbe9e0702,2 +np.float32,0x3eeab47a,0x3edb89d5,2 +np.float32,0xbed99556,0xbecd5de5,2 +np.float64,0xbfb94a81e0329500,0xbfb935867ba761fe,2 +np.float64,0xbfec132f1678265e,0xbfe6900eb097abc3,2 +np.float64,0x5685ea72ad0be,0x5685ea72ad0be,2 +np.float64,0xbfd74d3169ae9a62,0xbfd652e09b9daf32,2 +np.float64,0xbfe28df53d651bea,0xbfe0b8a7f50ab433,2 +np.float64,0x0,0x0,2 +np.float64,0xbfed912738bb224e,0xbfe749e3732831ae,2 +np.float64,0x7fcc6faed838df5d,0x3ff0000000000000,2 +np.float64,0xbfe95fe9a432bfd3,0xbfe51f6349919910,2 +np.float64,0xbfc4d5900b29ab20,0xbfc4a6f496179b8b,2 +np.float64,0xbfcd6025033ac04c,0xbfccded7b34b49b0,2 +np.float64,0xbfdfa655b43f4cac,0xbfdd4ca1e5bb9db8,2 +np.float64,0xe7ea5c7fcfd4c,0xe7ea5c7fcfd4c,2 +np.float64,0xffa5449ca42a8940,0xbff0000000000000,2 +np.float64,0xffe63294c1ac6529,0xbff0000000000000,2 +np.float64,0x7feb9cbae7f73975,0x3ff0000000000000,2 +np.float64,0x800eb07c3e3d60f9,0x800eb07c3e3d60f9,2 +np.float64,0x3fc95777e932aef0,0x3fc9040391e20c00,2 +np.float64,0x800736052dee6c0b,0x800736052dee6c0b,2 +np.float64,0x3fe9ae4afd335c96,0x3fe54b569bab45c7,2 +np.float64,0x7fee4c94217c9927,0x3ff0000000000000,2 +np.float64,0x80094b594bd296b3,0x80094b594bd296b3,2 +np.float64,0xffe5adbcee6b5b7a,0xbff0000000000000,2 +np.float64,0x3fecb8eab47971d5,0x3fe6e236be6f27e9,2 +np.float64,0x44956914892ae,0x44956914892ae,2 +np.float64,0xbfe3bd18ef677a32,0xbfe190bf1e07200c,2 +np.float64,0x800104e5b46209cc,0x800104e5b46209cc,2 +np.float64,0x8008fbcecf71f79e,0x8008fbcecf71f79e,2 +np.float64,0x800f0a46a0be148d,0x800f0a46a0be148d,2 +np.float64,0x7fe657a0702caf40,0x3ff0000000000000,2 +np.float64,0xffd3ff1a9027fe36,0xbff0000000000000,2 +np.float64,0x3fe78bc87bef1790,0x3fe40d2e63aaf029,2 +np.float64,0x7feeabdc4c7d57b8,0x3ff0000000000000,2 +np.float64,0xbfabd28d8437a520,0xbfabcb8ce03a0e56,2 +np.float64,0xbfddc3a133bb8742,0xbfdbc9fdb2594451,2 +np.float64,0x7fec911565b9222a,0x3ff0000000000000,2 +np.float64,0x71302604e2605,0x71302604e2605,2 +np.float64,0xee919d2bdd234,0xee919d2bdd234,2 +np.float64,0xbfc04fcff3209fa0,0xbfc0395a739a2ce4,2 +np.float64,0xffe4668a36e8cd14,0xbff0000000000000,2 +np.float64,0xbfeeafeebefd5fde,0xbfe7cd5f3d61a3ec,2 +np.float64,0x7fddb34219bb6683,0x3ff0000000000000,2 +np.float64,0xbfd2cac6cba5958e,0xbfd24520abb2ff36,2 +np.float64,0xbfb857e49630afc8,0xbfb8452d5064dec2,2 +np.float64,0x3fd2dbf90b25b7f2,0x3fd254eaf48484c2,2 +np.float64,0x800af65c94f5ecba,0x800af65c94f5ecba,2 +np.float64,0xa0eef4bf41ddf,0xa0eef4bf41ddf,2 +np.float64,0xffd8e0a4adb1c14a,0xbff0000000000000,2 +np.float64,0xffe858f6e870b1ed,0xbff0000000000000,2 +np.float64,0x3f94c2c308298580,0x3f94c208a4bb006d,2 +np.float64,0xffb45f0d7428be18,0xbff0000000000000,2 +np.float64,0x800ed4f43dbda9e9,0x800ed4f43dbda9e9,2 +np.float64,0x8002dd697e85bad4,0x8002dd697e85bad4,2 +np.float64,0x787ceab2f0f9e,0x787ceab2f0f9e,2 +np.float64,0xbfdff5fcc2bfebfa,0xbfdd8b736b128589,2 +np.float64,0x7fdb2b4294365684,0x3ff0000000000000,2 +np.float64,0xffe711e5e92e23cc,0xbff0000000000000,2 +np.float64,0x800b1c93f1163928,0x800b1c93f1163928,2 +np.float64,0x7fc524d2f22a49a5,0x3ff0000000000000,2 +np.float64,0x7fc88013b5310026,0x3ff0000000000000,2 +np.float64,0x3fe1a910c5e35222,0x3fe00fd779ebaa2a,2 +np.float64,0xbfb57ec9ca2afd90,0xbfb571e47ecb9335,2 +np.float64,0x7fd7594b20aeb295,0x3ff0000000000000,2 +np.float64,0x7fba4641ca348c83,0x3ff0000000000000,2 +np.float64,0xffe61393706c2726,0xbff0000000000000,2 +np.float64,0x7fd54f3c7baa9e78,0x3ff0000000000000,2 +np.float64,0xffe65ffb12ecbff6,0xbff0000000000000,2 +np.float64,0xbfba3b0376347608,0xbfba239cbbbd1b11,2 +np.float64,0x800200886d640112,0x800200886d640112,2 +np.float64,0xbfecf0ba4679e174,0xbfe6fd59de44a3ec,2 +np.float64,0xffe5c57e122b8afc,0xbff0000000000000,2 +np.float64,0x7fdaad0143355a02,0x3ff0000000000000,2 +np.float64,0x46ab32c08d567,0x46ab32c08d567,2 +np.float64,0x7ff8000000000000,0x7ff8000000000000,2 +np.float64,0xbfda7980fdb4f302,0xbfd90fa9c8066109,2 +np.float64,0x3fe237703c646ee0,0x3fe07969f8d8805a,2 +np.float64,0x8000e9fcfc21d3fb,0x8000e9fcfc21d3fb,2 +np.float64,0xbfdfe6e958bfcdd2,0xbfdd7f952fe87770,2 +np.float64,0xbd7baf217af8,0xbd7baf217af8,2 +np.float64,0xbfceba9e4b3d753c,0xbfce26e54359869a,2 +np.float64,0xb95a2caf72b46,0xb95a2caf72b46,2 +np.float64,0x3fb407e25a280fc5,0x3fb3fd71e457b628,2 +np.float64,0xa1da09d943b41,0xa1da09d943b41,2 +np.float64,0xbfe9c7271cf38e4e,0xbfe559296b471738,2 +np.float64,0x3fefae6170ff5cc3,0x3fe83c70ba82f0e1,2 +np.float64,0x7fe7375348ae6ea6,0x3ff0000000000000,2 +np.float64,0xffe18c9cc6e31939,0xbff0000000000000,2 +np.float64,0x800483d13a6907a3,0x800483d13a6907a3,2 +np.float64,0x7fe772a18caee542,0x3ff0000000000000,2 +np.float64,0xffefff64e7bffec9,0xbff0000000000000,2 +np.float64,0x7fcffc31113ff861,0x3ff0000000000000,2 +np.float64,0x3fd91e067e323c0d,0x3fd7e70bf365a7b3,2 +np.float64,0xb0a6673d614cd,0xb0a6673d614cd,2 +np.float64,0xffef9a297e3f3452,0xbff0000000000000,2 +np.float64,0xffe87cc15e70f982,0xbff0000000000000,2 +np.float64,0xffefd6ad8e7fad5a,0xbff0000000000000,2 +np.float64,0x7fe3aaa3a8a75546,0x3ff0000000000000,2 +np.float64,0xddab0341bb561,0xddab0341bb561,2 +np.float64,0x3fe996d6d7332dae,0x3fe53e3ed5be2922,2 +np.float64,0x3fdbe66a18b7ccd4,0x3fda41e6053c1512,2 +np.float64,0x8914775d1228f,0x8914775d1228f,2 +np.float64,0x3fe44621d4688c44,0x3fe1ef9c7225f8bd,2 +np.float64,0xffab29a2a4365340,0xbff0000000000000,2 +np.float64,0xffc8d4a0c431a940,0xbff0000000000000,2 +np.float64,0xbfd426e085284dc2,0xbfd382e2a9617b87,2 +np.float64,0xbfd3b0a525a7614a,0xbfd3176856faccf1,2 +np.float64,0x80036dedcb06dbdc,0x80036dedcb06dbdc,2 +np.float64,0x3feb13823b762704,0x3fe60ca3facdb696,2 +np.float64,0x3fd7246b7bae48d8,0x3fd62f08afded155,2 +np.float64,0x1,0x1,2 +np.float64,0x3fe8ade4b9715bc9,0x3fe4b97cc1387d27,2 +np.float64,0x3fdf2dbec53e5b7e,0x3fdcecfeee33de95,2 +np.float64,0x3fe4292bf9685258,0x3fe1dbb5a6704090,2 +np.float64,0xbfd21acbb8243598,0xbfd1a2ff42174cae,2 +np.float64,0xdd0d2d01ba1a6,0xdd0d2d01ba1a6,2 +np.float64,0x3fa3f3d2f427e7a0,0x3fa3f13d6f101555,2 +np.float64,0x7fdabf4aceb57e95,0x3ff0000000000000,2 +np.float64,0xd4d9e39ba9b3d,0xd4d9e39ba9b3d,2 +np.float64,0xffec773396f8ee66,0xbff0000000000000,2 +np.float64,0x3fa88cc79031198f,0x3fa887f7ade722ba,2 +np.float64,0xffe63a92066c7524,0xbff0000000000000,2 +np.float64,0xbfcf514e2e3ea29c,0xbfceb510e99aaa19,2 +np.float64,0x9d78c19d3af18,0x9d78c19d3af18,2 +np.float64,0x7fdd748bfbbae917,0x3ff0000000000000,2 +np.float64,0xffb3594c4626b298,0xbff0000000000000,2 +np.float64,0x80068ce5b32d19cc,0x80068ce5b32d19cc,2 +np.float64,0x3fec63d60e78c7ac,0x3fe6b85536e44217,2 +np.float64,0x80080bad4dd0175b,0x80080bad4dd0175b,2 +np.float64,0xbfec6807baf8d010,0xbfe6ba69740f9687,2 +np.float64,0x7fedbae0bbfb75c0,0x3ff0000000000000,2 +np.float64,0x8001cb7aa3c396f6,0x8001cb7aa3c396f6,2 +np.float64,0x7fe1f1f03563e3df,0x3ff0000000000000,2 +np.float64,0x7fd83d3978307a72,0x3ff0000000000000,2 +np.float64,0xbfc05ffe9d20bffc,0xbfc049464e3f0af2,2 +np.float64,0xfe6e053ffcdc1,0xfe6e053ffcdc1,2 +np.float64,0xbfd3bdf39d277be8,0xbfd32386edf12726,2 +np.float64,0x800f41b27bde8365,0x800f41b27bde8365,2 +np.float64,0xbfe2c98390e59307,0xbfe0e3c9260fe798,2 +np.float64,0xffdd6206bcbac40e,0xbff0000000000000,2 +np.float64,0x67f35ef4cfe6c,0x67f35ef4cfe6c,2 +np.float64,0x800337e02ae66fc1,0x800337e02ae66fc1,2 +np.float64,0x3fe0ff70afe1fee1,0x3fdf1f46434330df,2 +np.float64,0x3fd7e0a1df2fc144,0x3fd6d3f82c8031e4,2 +np.float64,0x8008da5cd1b1b4ba,0x8008da5cd1b1b4ba,2 +np.float64,0x80065ec9e4ccbd95,0x80065ec9e4ccbd95,2 +np.float64,0x3fe1d1e559a3a3cb,0x3fe02e4f146aa1ab,2 +np.float64,0x7feb7d2f0836fa5d,0x3ff0000000000000,2 +np.float64,0xbfcb33ce9736679c,0xbfcaccd431b205bb,2 +np.float64,0x800e6d0adf5cda16,0x800e6d0adf5cda16,2 +np.float64,0x7fe46f272ca8de4d,0x3ff0000000000000,2 +np.float64,0x4fdfc73e9fbfa,0x4fdfc73e9fbfa,2 +np.float64,0x800958a13112b143,0x800958a13112b143,2 +np.float64,0xbfea01f877f403f1,0xbfe579a541594247,2 +np.float64,0xeefaf599ddf5f,0xeefaf599ddf5f,2 +np.float64,0x80038766c5e70ece,0x80038766c5e70ece,2 +np.float64,0x7fd31bc28ba63784,0x3ff0000000000000,2 +np.float64,0xbfe4df77eee9bef0,0xbfe257abe7083b77,2 +np.float64,0x7fe6790c78acf218,0x3ff0000000000000,2 +np.float64,0xffe7c66884af8cd0,0xbff0000000000000,2 +np.float64,0x800115e36f422bc8,0x800115e36f422bc8,2 +np.float64,0x3fc601945d2c0329,0x3fc5cab917bb20bc,2 +np.float64,0x3fd6ac9546ad592b,0x3fd5c55437ec3508,2 +np.float64,0xa7bd59294f7ab,0xa7bd59294f7ab,2 +np.float64,0x8005c26c8b8b84da,0x8005c26c8b8b84da,2 +np.float64,0x8257501704aea,0x8257501704aea,2 +np.float64,0x5b12aae0b6256,0x5b12aae0b6256,2 +np.float64,0x800232fe02c465fd,0x800232fe02c465fd,2 +np.float64,0x800dae28f85b5c52,0x800dae28f85b5c52,2 +np.float64,0x3fdade1ac135bc36,0x3fd964a2000ace25,2 +np.float64,0x3fed72ca04fae594,0x3fe73b9170d809f9,2 +np.float64,0x7fc6397e2b2c72fb,0x3ff0000000000000,2 +np.float64,0x3fe1f5296d23ea53,0x3fe048802d17621e,2 +np.float64,0xffe05544b920aa89,0xbff0000000000000,2 +np.float64,0xbfdb2e1588365c2c,0xbfd9a7e4113c713e,2 +np.float64,0xbfed6a06fa3ad40e,0xbfe7376be60535f8,2 +np.float64,0xbfe31dcaf5e63b96,0xbfe120417c46cac1,2 +np.float64,0xbfb7ed67ae2fdad0,0xbfb7dba14af33b00,2 +np.float64,0xffd32bb7eb265770,0xbff0000000000000,2 +np.float64,0x80039877b04730f0,0x80039877b04730f0,2 +np.float64,0x3f832e5630265cac,0x3f832e316f47f218,2 +np.float64,0xffe7fa7f732ff4fe,0xbff0000000000000,2 +np.float64,0x9649b87f2c937,0x9649b87f2c937,2 +np.float64,0xffaee447183dc890,0xbff0000000000000,2 +np.float64,0x7fe4e02dd869c05b,0x3ff0000000000000,2 +np.float64,0x3fe1d35e7463a6bd,0x3fe02f67bd21e86e,2 +np.float64,0xffe57f40fe2afe82,0xbff0000000000000,2 +np.float64,0xbfea1362b93426c6,0xbfe5833421dba8fc,2 +np.float64,0xffe9c689fe338d13,0xbff0000000000000,2 +np.float64,0xffc592dd102b25bc,0xbff0000000000000,2 +np.float64,0x3fd283c7aba5078f,0x3fd203d61d1398c3,2 +np.float64,0x8001d6820243ad05,0x8001d6820243ad05,2 +np.float64,0x3fe0ad5991e15ab4,0x3fdea14ef0d47fbd,2 +np.float64,0x3fe3916f2ee722de,0x3fe1722684a9ffb1,2 +np.float64,0xffef9e54e03f3ca9,0xbff0000000000000,2 +np.float64,0x7fe864faebb0c9f5,0x3ff0000000000000,2 +np.float64,0xbfed3587c3fa6b10,0xbfe71e7112df8a68,2 +np.float64,0xbfdd9efc643b3df8,0xbfdbac3a16caf208,2 +np.float64,0xbfd5ac08feab5812,0xbfd4e14575a6e41b,2 +np.float64,0xffda90fae6b521f6,0xbff0000000000000,2 +np.float64,0x8001380ecf22701e,0x8001380ecf22701e,2 +np.float64,0x7fed266fa5fa4cde,0x3ff0000000000000,2 +np.float64,0xffec6c0ac3b8d815,0xbff0000000000000,2 +np.float64,0x3fe7de43c32fbc88,0x3fe43ef62821a5a6,2 +np.float64,0x800bf4ffc357ea00,0x800bf4ffc357ea00,2 +np.float64,0x3fe125c975624b93,0x3fdf59b2de3eff5d,2 +np.float64,0x8004714c1028e299,0x8004714c1028e299,2 +np.float64,0x3fef1bfbf5fe37f8,0x3fe7fd2ba1b63c8a,2 +np.float64,0x800cae15c3195c2c,0x800cae15c3195c2c,2 +np.float64,0x7fde708e083ce11b,0x3ff0000000000000,2 +np.float64,0x7fbcee5df639dcbb,0x3ff0000000000000,2 +np.float64,0x800b1467141628cf,0x800b1467141628cf,2 +np.float64,0x3fe525e0d36a4bc2,0x3fe286b6e59e30f5,2 +np.float64,0xffe987f8b8330ff1,0xbff0000000000000,2 +np.float64,0x7e0a8284fc151,0x7e0a8284fc151,2 +np.float64,0x8006f982442df305,0x8006f982442df305,2 +np.float64,0xbfd75a3cb62eb47a,0xbfd65e54cee981c9,2 +np.float64,0x258e91104b1d3,0x258e91104b1d3,2 +np.float64,0xbfecd0056779a00b,0xbfe6ed7ae97fff1b,2 +np.float64,0x7fc3a4f9122749f1,0x3ff0000000000000,2 +np.float64,0x6e2b1024dc563,0x6e2b1024dc563,2 +np.float64,0x800d575ad4daaeb6,0x800d575ad4daaeb6,2 +np.float64,0xbfceafb1073d5f64,0xbfce1c93023d8414,2 +np.float64,0xffe895cb5f312b96,0xbff0000000000000,2 +np.float64,0x7fe7811ed4ef023d,0x3ff0000000000000,2 +np.float64,0xbfd93f952f327f2a,0xbfd803e6b5576b99,2 +np.float64,0xffdd883a3fbb1074,0xbff0000000000000,2 +np.float64,0x7fee5624eefcac49,0x3ff0000000000000,2 +np.float64,0xbfe264bb2624c976,0xbfe09a9b7cc896e7,2 +np.float64,0xffef14b417be2967,0xbff0000000000000,2 +np.float64,0xbfecbd0d94397a1b,0xbfe6e43bef852d9f,2 +np.float64,0xbfe20d9e4ba41b3c,0xbfe05a98e05846d9,2 +np.float64,0x10000000000000,0x10000000000000,2 +np.float64,0x7fefde93f7bfbd27,0x3ff0000000000000,2 +np.float64,0x80076b9e232ed73d,0x80076b9e232ed73d,2 +np.float64,0xbfe80df52c701bea,0xbfe45b754b433792,2 +np.float64,0x7fe3b5a637676b4b,0x3ff0000000000000,2 +np.float64,0x2c81d14c5903b,0x2c81d14c5903b,2 +np.float64,0x80038945c767128c,0x80038945c767128c,2 +np.float64,0xffeebaf544bd75ea,0xbff0000000000000,2 +np.float64,0xffdb1867d2b630d0,0xbff0000000000000,2 +np.float64,0x3fe3376eaee66ede,0x3fe13285579763d8,2 +np.float64,0xffddf65ca43becba,0xbff0000000000000,2 +np.float64,0xffec8e3e04791c7b,0xbff0000000000000,2 +np.float64,0x80064f4bde2c9e98,0x80064f4bde2c9e98,2 +np.float64,0x7fe534a085ea6940,0x3ff0000000000000,2 +np.float64,0xbfcbabe31d3757c8,0xbfcb3f8e70adf7e7,2 +np.float64,0xbfe45ca11e28b942,0xbfe1ff04515ef809,2 +np.float64,0x65f4df02cbe9d,0x65f4df02cbe9d,2 +np.float64,0xb08b0cbb61162,0xb08b0cbb61162,2 +np.float64,0x3feae2e8b975c5d1,0x3fe5f302b5e8eda2,2 +np.float64,0x7fcf277ff93e4eff,0x3ff0000000000000,2 +np.float64,0x80010999c4821334,0x80010999c4821334,2 +np.float64,0xbfd7f65911afecb2,0xbfd6e6e9cd098f8b,2 +np.float64,0x800e0560ec3c0ac2,0x800e0560ec3c0ac2,2 +np.float64,0x7fec4152ba3882a4,0x3ff0000000000000,2 +np.float64,0xbfb5c77cd42b8ef8,0xbfb5ba1336084908,2 +np.float64,0x457ff1b68afff,0x457ff1b68afff,2 +np.float64,0x5323ec56a647e,0x5323ec56a647e,2 +np.float64,0xbfeed16cf8bda2da,0xbfe7dc49fc9ae549,2 +np.float64,0xffe8446106b088c1,0xbff0000000000000,2 +np.float64,0xffb93cd13c3279a0,0xbff0000000000000,2 +np.float64,0x7fe515c2aeea2b84,0x3ff0000000000000,2 +np.float64,0x80099df83f933bf1,0x80099df83f933bf1,2 +np.float64,0x7fb3a375562746ea,0x3ff0000000000000,2 +np.float64,0x7fcd7efa243afdf3,0x3ff0000000000000,2 +np.float64,0xffe40cddb12819bb,0xbff0000000000000,2 +np.float64,0x8008b68eecd16d1e,0x8008b68eecd16d1e,2 +np.float64,0x2aec688055d8e,0x2aec688055d8e,2 +np.float64,0xffe23750bc646ea1,0xbff0000000000000,2 +np.float64,0x5adacf60b5b7,0x5adacf60b5b7,2 +np.float64,0x7fefb29b1cbf6535,0x3ff0000000000000,2 +np.float64,0xbfeadbf90175b7f2,0xbfe5ef55e2194794,2 +np.float64,0xeaad2885d55a5,0xeaad2885d55a5,2 +np.float64,0xffd7939fba2f2740,0xbff0000000000000,2 +np.float64,0x3fd187ea3aa30fd4,0x3fd11af023472386,2 +np.float64,0xbf6eb579c03d6b00,0xbf6eb57052f47019,2 +np.float64,0x3fefb67b3bff6cf6,0x3fe83fe4499969ac,2 +np.float64,0xbfe5183aacea3076,0xbfe27da1aa0b61a0,2 +np.float64,0xbfb83e47a2307c90,0xbfb82bcb0e12db42,2 +np.float64,0x80088849b1b11094,0x80088849b1b11094,2 +np.float64,0x800ceeed7399dddb,0x800ceeed7399dddb,2 +np.float64,0x80097cd90892f9b2,0x80097cd90892f9b2,2 +np.float64,0x7ec73feefd8e9,0x7ec73feefd8e9,2 +np.float64,0x7fe3291de5a6523b,0x3ff0000000000000,2 +np.float64,0xbfd537086daa6e10,0xbfd4787af5f60653,2 +np.float64,0x800e8ed4455d1da9,0x800e8ed4455d1da9,2 +np.float64,0x800ef8d19cbdf1a3,0x800ef8d19cbdf1a3,2 +np.float64,0x800dc4fa3a5b89f5,0x800dc4fa3a5b89f5,2 +np.float64,0xaa8b85cd55171,0xaa8b85cd55171,2 +np.float64,0xffd67a5f40acf4be,0xbff0000000000000,2 +np.float64,0xbfb7496db22e92d8,0xbfb7390a48130861,2 +np.float64,0x3fd86a8e7ab0d51d,0x3fd74bfba0f72616,2 +np.float64,0xffb7f5b7fc2feb70,0xbff0000000000000,2 +np.float64,0xbfea0960a7f412c1,0xbfe57db6d0ff4191,2 +np.float64,0x375f4fc26ebeb,0x375f4fc26ebeb,2 +np.float64,0x800c537e70b8a6fd,0x800c537e70b8a6fd,2 +np.float64,0x800b3f4506d67e8a,0x800b3f4506d67e8a,2 +np.float64,0x7fe61f2d592c3e5a,0x3ff0000000000000,2 +np.float64,0xffefffffffffffff,0xbff0000000000000,2 +np.float64,0x8005d0bb84eba178,0x8005d0bb84eba178,2 +np.float64,0x800c78b0ec18f162,0x800c78b0ec18f162,2 +np.float64,0xbfc42cccfb285998,0xbfc4027392f66b0d,2 +np.float64,0x3fd8fdc73fb1fb8e,0x3fd7cb46f928153f,2 +np.float64,0x800c71754298e2eb,0x800c71754298e2eb,2 +np.float64,0x3fe4aa7a96a954f5,0x3fe233f5d3bc1352,2 +np.float64,0x7fd53841f6aa7083,0x3ff0000000000000,2 +np.float64,0x3fd0a887b8a15110,0x3fd04ac3b9c0d1ca,2 +np.float64,0x8007b8e164cf71c4,0x8007b8e164cf71c4,2 +np.float64,0xbfddc35c66bb86b8,0xbfdbc9c5dddfb014,2 +np.float64,0x6a3756fed46eb,0x6a3756fed46eb,2 +np.float64,0xffd3dcd05527b9a0,0xbff0000000000000,2 +np.float64,0xbfd7dc75632fb8ea,0xbfd6d0538b340a98,2 +np.float64,0x17501f822ea05,0x17501f822ea05,2 +np.float64,0xbfe1f98b99a3f317,0xbfe04bbf8f8b6cb3,2 +np.float64,0x66ea65d2cdd4d,0x66ea65d2cdd4d,2 +np.float64,0xbfd12241e2224484,0xbfd0bc62f46ea5e1,2 +np.float64,0x3fed6e6fb3fadcdf,0x3fe7398249097285,2 +np.float64,0x3fe0b5ebeba16bd8,0x3fdeae84b3000a47,2 +np.float64,0x66d1bce8cda38,0x66d1bce8cda38,2 +np.float64,0x3fdd728db3bae51b,0x3fdb880f28c52713,2 +np.float64,0xffb45dbe5228bb80,0xbff0000000000000,2 +np.float64,0x1ff8990c3ff14,0x1ff8990c3ff14,2 +np.float64,0x800a68e8f294d1d2,0x800a68e8f294d1d2,2 +np.float64,0xbfe4d08b84a9a117,0xbfe24da40bff6be7,2 +np.float64,0x3fe0177f0ee02efe,0x3fddb83c5971df51,2 +np.float64,0xffc56893692ad128,0xbff0000000000000,2 +np.float64,0x51b44f6aa368b,0x51b44f6aa368b,2 +np.float64,0x2258ff4e44b21,0x2258ff4e44b21,2 +np.float64,0x3fe913649e7226c9,0x3fe4f3f119530f53,2 +np.float64,0xffe3767df766ecfc,0xbff0000000000000,2 +np.float64,0xbfe62ae12fec55c2,0xbfe33108f1f22a94,2 +np.float64,0x7fb6a6308e2d4c60,0x3ff0000000000000,2 +np.float64,0xbfe00f2085e01e41,0xbfddab19b6fc77d1,2 +np.float64,0x3fb66447dc2cc890,0x3fb655b4f46844f0,2 +np.float64,0x3fd80238f6b00470,0x3fd6f143be1617d6,2 +np.float64,0xbfd05bfeb3a0b7fe,0xbfd0031ab3455e15,2 +np.float64,0xffc3a50351274a08,0xbff0000000000000,2 +np.float64,0xffd8f4241cb1e848,0xbff0000000000000,2 +np.float64,0xbfca72a88c34e550,0xbfca13ebe85f2aca,2 +np.float64,0x3fd47d683ba8fad0,0x3fd3d13f1176ed8c,2 +np.float64,0x3fb6418e642c831d,0x3fb6333ebe479ff2,2 +np.float64,0x800fde8e023fbd1c,0x800fde8e023fbd1c,2 +np.float64,0x8001fb01e323f605,0x8001fb01e323f605,2 +np.float64,0x3febb21ff9f76440,0x3fe65ed788d52fee,2 +np.float64,0x3fe47553ffe8eaa8,0x3fe20fe01f853603,2 +np.float64,0x7fca20b3f9344167,0x3ff0000000000000,2 +np.float64,0x3fe704f4ec6e09ea,0x3fe3ba7277201805,2 +np.float64,0xf864359df0c87,0xf864359df0c87,2 +np.float64,0x4d96b01c9b2d7,0x4d96b01c9b2d7,2 +np.float64,0x3fe8a09fe9f14140,0x3fe4b1c6a2d2e095,2 +np.float64,0xffc46c61b228d8c4,0xbff0000000000000,2 +np.float64,0x3fe680a837ed0150,0x3fe3679d6eeb6485,2 +np.float64,0xbfecedc20f39db84,0xbfe6fbe9ee978bf6,2 +np.float64,0x3fb2314eae24629d,0x3fb2297ba6d55d2d,2 +np.float64,0x3fe9f0b8e7b3e172,0x3fe57026eae36db3,2 +np.float64,0x80097a132ed2f427,0x80097a132ed2f427,2 +np.float64,0x800ae5a41955cb49,0x800ae5a41955cb49,2 +np.float64,0xbfd7527279aea4e4,0xbfd6577de356e1bd,2 +np.float64,0x3fe27d3e01e4fa7c,0x3fe0ac7dd96f9179,2 +np.float64,0x7fedd8cb01bbb195,0x3ff0000000000000,2 +np.float64,0x78f8695af1f0e,0x78f8695af1f0e,2 +np.float64,0x800d2d0e927a5a1d,0x800d2d0e927a5a1d,2 +np.float64,0xffe74b46fb2e968e,0xbff0000000000000,2 +np.float64,0xbfdd12d4c8ba25aa,0xbfdb39dae49e1c10,2 +np.float64,0xbfd6c14710ad828e,0xbfd5d79ef5a8d921,2 +np.float64,0x921f4e55243ea,0x921f4e55243ea,2 +np.float64,0x800b4e4c80969c99,0x800b4e4c80969c99,2 +np.float64,0x7fe08c6ab7e118d4,0x3ff0000000000000,2 +np.float64,0xbfed290014fa5200,0xbfe71871f7e859ed,2 +np.float64,0x8008c1d5c59183ac,0x8008c1d5c59183ac,2 +np.float64,0x3fd339e68c2673cd,0x3fd2aaff3f165a9d,2 +np.float64,0xbfdd20d8113a41b0,0xbfdb4553ea2cb2fb,2 +np.float64,0x3fe52a25deea544c,0x3fe2898d5bf4442c,2 +np.float64,0x498602d4930c1,0x498602d4930c1,2 +np.float64,0x3fd8c450113188a0,0x3fd799b0b2a6c43c,2 +np.float64,0xbfd72bc2f2ae5786,0xbfd6357e15ba7f70,2 +np.float64,0xbfd076188ea0ec32,0xbfd01b8fce44d1af,2 +np.float64,0x9aace1713559c,0x9aace1713559c,2 +np.float64,0x8008a730e8914e62,0x8008a730e8914e62,2 +np.float64,0x7fe9e9a3d833d347,0x3ff0000000000000,2 +np.float64,0x800d3a0d69da741b,0x800d3a0d69da741b,2 +np.float64,0xbfe3e28a29e7c514,0xbfe1aad7643a2d19,2 +np.float64,0x7fe9894c71331298,0x3ff0000000000000,2 +np.float64,0xbfe7c6acb5ef8d5a,0xbfe430c9e258ce62,2 +np.float64,0xffb5a520a62b4a40,0xbff0000000000000,2 +np.float64,0x7fc02109ae204212,0x3ff0000000000000,2 +np.float64,0xb5c58f196b8b2,0xb5c58f196b8b2,2 +np.float64,0x3feb4ee82e769dd0,0x3fe62bae9a39d8b1,2 +np.float64,0x3fec5c3cf278b87a,0x3fe6b49000f12441,2 +np.float64,0x81f64b8103eca,0x81f64b8103eca,2 +np.float64,0xbfeab00d73f5601b,0xbfe5d7f755ab73d9,2 +np.float64,0x3fd016bf28a02d7e,0x3fcf843ea23bcd3c,2 +np.float64,0xbfa1db617423b6c0,0xbfa1d9872ddeb5a8,2 +np.float64,0x3fe83c879d70790f,0x3fe4771502d8f012,2 +np.float64,0x6b267586d64cf,0x6b267586d64cf,2 +np.float64,0x3fc91b6d3f3236d8,0x3fc8ca3eb4da25a9,2 +np.float64,0x7fd4e3f8f3a9c7f1,0x3ff0000000000000,2 +np.float64,0x800a75899214eb14,0x800a75899214eb14,2 +np.float64,0x7fdb1f2e07b63e5b,0x3ff0000000000000,2 +np.float64,0xffe7805a11ef00b4,0xbff0000000000000,2 +np.float64,0x3fc8e1b88a31c371,0x3fc892af45330818,2 +np.float64,0xbfe809fe447013fc,0xbfe45918f07da4d9,2 +np.float64,0xbfeb9d7f2ab73afe,0xbfe65446bfddc792,2 +np.float64,0x3fb47f0a5c28fe15,0x3fb473db9113e880,2 +np.float64,0x800a17ae3cb42f5d,0x800a17ae3cb42f5d,2 +np.float64,0xf5540945eaa81,0xf5540945eaa81,2 +np.float64,0xbfe577fc26aaeff8,0xbfe2bcfbf2cf69ff,2 +np.float64,0xbfb99b3e06333680,0xbfb98577b88e0515,2 +np.float64,0x7fd9290391b25206,0x3ff0000000000000,2 +np.float64,0x7fe1aa62ffa354c5,0x3ff0000000000000,2 +np.float64,0x7b0189a0f604,0x7b0189a0f604,2 +np.float64,0x3f9000ed602001db,0x3f900097fe168105,2 +np.float64,0x3fd576128d2aec25,0x3fd4b1002c92286f,2 +np.float64,0xffecc98ece79931d,0xbff0000000000000,2 +np.float64,0x800a1736c7f42e6e,0x800a1736c7f42e6e,2 +np.float64,0xbfed947548bb28eb,0xbfe74b71479ae739,2 +np.float64,0xa45c032148b9,0xa45c032148b9,2 +np.float64,0xbfc13d011c227a04,0xbfc1228447de5e9f,2 +np.float64,0xffed8baa6ebb1754,0xbff0000000000000,2 +np.float64,0x800ea2de243d45bc,0x800ea2de243d45bc,2 +np.float64,0x8001396be52272d9,0x8001396be52272d9,2 +np.float64,0xd018d1cda031a,0xd018d1cda031a,2 +np.float64,0x7fe1fece1fe3fd9b,0x3ff0000000000000,2 +np.float64,0x8009ac484c135891,0x8009ac484c135891,2 +np.float64,0x3fc560ad132ac15a,0x3fc52e5a9479f08e,2 +np.float64,0x3fd6f80ebe2df01d,0x3fd607f70ce8e3f4,2 +np.float64,0xbfd3e69e82a7cd3e,0xbfd34887c2a40699,2 +np.float64,0x3fe232d9baa465b3,0x3fe0760a822ada0c,2 +np.float64,0x3fe769bbc6eed378,0x3fe3f872680f6631,2 +np.float64,0xffe63dbd952c7b7a,0xbff0000000000000,2 +np.float64,0x4e0c00da9c181,0x4e0c00da9c181,2 +np.float64,0xffeae4d89735c9b0,0xbff0000000000000,2 +np.float64,0x3fe030bcbb606179,0x3fdddfc66660bfce,2 +np.float64,0x7fe35ca40d66b947,0x3ff0000000000000,2 +np.float64,0xbfd45bd66628b7ac,0xbfd3b2e04bfe7866,2 +np.float64,0x3fd1f0be2323e17c,0x3fd17c1c340d7a48,2 +np.float64,0x3fd7123b6cae2478,0x3fd61f0675aa9ae1,2 +np.float64,0xbfe918a377723147,0xbfe4f6efe66f5714,2 +np.float64,0x7fc400356f28006a,0x3ff0000000000000,2 +np.float64,0x7fd2dead70a5bd5a,0x3ff0000000000000,2 +np.float64,0xffe9c28f81f3851e,0xbff0000000000000,2 +np.float64,0x3fd09b1ec7a1363e,0x3fd03e3894320140,2 +np.float64,0x7fe6e80c646dd018,0x3ff0000000000000,2 +np.float64,0x7fec3760a4786ec0,0x3ff0000000000000,2 +np.float64,0x309eb6ee613d8,0x309eb6ee613d8,2 +np.float64,0x800731cb0ece6397,0x800731cb0ece6397,2 +np.float64,0xbfdb0c553db618aa,0xbfd98b8a4680ee60,2 +np.float64,0x3fd603a52eac074c,0x3fd52f6b53de7455,2 +np.float64,0x9ecb821b3d971,0x9ecb821b3d971,2 +np.float64,0x3feb7d64dc36faca,0x3fe643c2754bb7f4,2 +np.float64,0xffeb94825ef72904,0xbff0000000000000,2 +np.float64,0x24267418484cf,0x24267418484cf,2 +np.float64,0xbfa6b2fbac2d65f0,0xbfa6af2dca5bfa6f,2 +np.float64,0x8010000000000000,0x8010000000000000,2 +np.float64,0xffe6873978ed0e72,0xbff0000000000000,2 +np.float64,0x800447934ba88f27,0x800447934ba88f27,2 +np.float64,0x3fef305f09fe60be,0x3fe806156b8ca47c,2 +np.float64,0xffd441c697a8838e,0xbff0000000000000,2 +np.float64,0xbfa7684f6c2ed0a0,0xbfa764238d34830c,2 +np.float64,0xffb2c976142592f0,0xbff0000000000000,2 +np.float64,0xbfcc9d1585393a2c,0xbfcc25756bcbca1f,2 +np.float64,0xbfd477bb1ba8ef76,0xbfd3cc1d2114e77e,2 +np.float64,0xbfed1559983a2ab3,0xbfe70f03afd994ee,2 +np.float64,0xbfeb51139036a227,0xbfe62ccf56bc7fff,2 +np.float64,0x7d802890fb006,0x7d802890fb006,2 +np.float64,0x800e00af777c015f,0x800e00af777c015f,2 +np.float64,0x800647ce128c8f9d,0x800647ce128c8f9d,2 +np.float64,0x800a26da91d44db6,0x800a26da91d44db6,2 +np.float64,0x3fdc727eddb8e4fe,0x3fdab5fd9db630b3,2 +np.float64,0x7fd06def2ba0dbdd,0x3ff0000000000000,2 +np.float64,0xffe23678c4a46cf1,0xbff0000000000000,2 +np.float64,0xbfe7198e42ee331c,0xbfe3c7326c9c7553,2 +np.float64,0xffae465f3c3c8cc0,0xbff0000000000000,2 +np.float64,0xff9aea7c5035d500,0xbff0000000000000,2 +np.float64,0xbfeae49c0f35c938,0xbfe5f3e9326cb08b,2 +np.float64,0x3f9a16f300342de6,0x3f9a1581212be50f,2 +np.float64,0x8d99e2c31b33d,0x8d99e2c31b33d,2 +np.float64,0xffd58af253ab15e4,0xbff0000000000000,2 +np.float64,0xbfd205cd25a40b9a,0xbfd18f97155f8b25,2 +np.float64,0xbfebe839bbf7d074,0xbfe67a6024e8fefe,2 +np.float64,0xbfe4fb3595a9f66b,0xbfe26a42f99819ea,2 +np.float64,0x800e867c739d0cf9,0x800e867c739d0cf9,2 +np.float64,0x8bc4274f17885,0x8bc4274f17885,2 +np.float64,0xaec8914b5d912,0xaec8914b5d912,2 +np.float64,0x7fd1d64473a3ac88,0x3ff0000000000000,2 +np.float64,0xbfe6d6f69cedaded,0xbfe39dd61bc7e23e,2 +np.float64,0x7fed05039d7a0a06,0x3ff0000000000000,2 +np.float64,0xbfc40eab0f281d58,0xbfc3e50d14b79265,2 +np.float64,0x45179aec8a2f4,0x45179aec8a2f4,2 +np.float64,0xbfe717e362ee2fc7,0xbfe3c62a95b07d13,2 +np.float64,0xbfe5b8df0d6b71be,0xbfe2e76c7ec5013d,2 +np.float64,0x5c67ba6eb8cf8,0x5c67ba6eb8cf8,2 +np.float64,0xbfda72ce4cb4e59c,0xbfd909fdc7ecfe20,2 +np.float64,0x7fdf59a1e2beb343,0x3ff0000000000000,2 +np.float64,0xc4f7897f89ef1,0xc4f7897f89ef1,2 +np.float64,0x8fcd0a351f9a2,0x8fcd0a351f9a2,2 +np.float64,0x3fb161761022c2ec,0x3fb15aa31c464de2,2 +np.float64,0x8008a985be71530c,0x8008a985be71530c,2 +np.float64,0x3fca4ddb5e349bb7,0x3fc9f0a3b60e49c6,2 +np.float64,0x7fcc10a2d9382145,0x3ff0000000000000,2 +np.float64,0x78902b3af1206,0x78902b3af1206,2 +np.float64,0x7fe1e2765f23c4ec,0x3ff0000000000000,2 +np.float64,0xc1d288cf83a51,0xc1d288cf83a51,2 +np.float64,0x7fe8af692bb15ed1,0x3ff0000000000000,2 +np.float64,0x80057d90fb8afb23,0x80057d90fb8afb23,2 +np.float64,0x3fdc136b8fb826d8,0x3fda6749582b2115,2 +np.float64,0x800ec8ea477d91d5,0x800ec8ea477d91d5,2 +np.float64,0x4c0f4796981ea,0x4c0f4796981ea,2 +np.float64,0xec34c4a5d8699,0xec34c4a5d8699,2 +np.float64,0x7fce343dfb3c687b,0x3ff0000000000000,2 +np.float64,0xbfc95a98a332b530,0xbfc90705b2cc2fec,2 +np.float64,0x800d118e1dba231c,0x800d118e1dba231c,2 +np.float64,0x3fd354f310a6a9e8,0x3fd2c3bb90054154,2 +np.float64,0xbfdac0d4fab581aa,0xbfd94bf37424928e,2 +np.float64,0x3fe7f5391fefea72,0x3fe44cb49d51985b,2 +np.float64,0xd4c3c329a9879,0xd4c3c329a9879,2 +np.float64,0x3fc53977692a72f0,0x3fc50835d85c9ed1,2 +np.float64,0xbfd6989538ad312a,0xbfd5b3a2c08511fe,2 +np.float64,0xbfe329f2906653e5,0xbfe128ec1525a1c0,2 +np.float64,0x7ff0000000000000,0x3ff0000000000000,2 +np.float64,0xbfea57c90974af92,0xbfe5a87b04aa3116,2 +np.float64,0x7fdfba94043f7527,0x3ff0000000000000,2 +np.float64,0x3feedabddafdb57c,0x3fe7e06c0661978d,2 +np.float64,0x4bd9f3b697b3f,0x4bd9f3b697b3f,2 +np.float64,0x3fdd15bbfc3a2b78,0x3fdb3c3b8d070f7e,2 +np.float64,0x3fbd89ccd23b13a0,0x3fbd686b825cff80,2 +np.float64,0x7ff4000000000000,0x7ffc000000000000,2 +np.float64,0x3f9baa8928375512,0x3f9ba8d01ddd5300,2 +np.float64,0x4a3ebdf2947d8,0x4a3ebdf2947d8,2 +np.float64,0x3fe698d5c06d31ac,0x3fe376dff48312c8,2 +np.float64,0xffd5323df12a647c,0xbff0000000000000,2 +np.float64,0xffea7f111174fe22,0xbff0000000000000,2 +np.float64,0x3feb4656a9b68cad,0x3fe627392eb2156f,2 +np.float64,0x7fc1260e9c224c1c,0x3ff0000000000000,2 +np.float64,0x80056e45e5eadc8d,0x80056e45e5eadc8d,2 +np.float64,0x7fd0958ef6a12b1d,0x3ff0000000000000,2 +np.float64,0x8001f85664e3f0ae,0x8001f85664e3f0ae,2 +np.float64,0x3fe553853beaa70a,0x3fe2a4f5e7c83558,2 +np.float64,0xbfeb33ce6276679d,0xbfe61d8ec9e5ff8c,2 +np.float64,0xbfd1b24e21a3649c,0xbfd14245df6065e9,2 +np.float64,0x3fe286fc40650df9,0x3fe0b395c8059429,2 +np.float64,0xffed378058fa6f00,0xbff0000000000000,2 +np.float64,0xbfd0c4a2d7a18946,0xbfd06509a434d6a0,2 +np.float64,0xbfea31d581f463ab,0xbfe593d976139f94,2 +np.float64,0xbfe0705c85e0e0b9,0xbfde42efa978eb0c,2 +np.float64,0xe4c4c339c9899,0xe4c4c339c9899,2 +np.float64,0x3fd68befa9ad17df,0x3fd5a870b3f1f83e,2 +np.float64,0x8000000000000001,0x8000000000000001,2 +np.float64,0x3fe294256965284b,0x3fe0bd271e22d86b,2 +np.float64,0x8005327a862a64f6,0x8005327a862a64f6,2 +np.float64,0xbfdb8155ce3702ac,0xbfd9ed9ef97920f8,2 +np.float64,0xbff0000000000000,0xbfe85efab514f394,2 +np.float64,0xffe66988f1ecd312,0xbff0000000000000,2 +np.float64,0x3fb178a85e22f150,0x3fb171b9fbf95f1d,2 +np.float64,0x7f829b900025371f,0x3ff0000000000000,2 +np.float64,0x8000000000000000,0x8000000000000000,2 +np.float64,0x8006cb77f60d96f1,0x8006cb77f60d96f1,2 +np.float64,0x3fe0c5d53aa18baa,0x3fdec7012ab92b42,2 +np.float64,0x77266426ee4cd,0x77266426ee4cd,2 +np.float64,0xbfec95f468392be9,0xbfe6d11428f60136,2 +np.float64,0x3fedbf532dfb7ea6,0x3fe75f8436dd1d58,2 +np.float64,0x8002fadd3f85f5bb,0x8002fadd3f85f5bb,2 +np.float64,0xbfefebaa8d3fd755,0xbfe8566c6aa90fba,2 +np.float64,0xffc7dd2b712fba58,0xbff0000000000000,2 +np.float64,0x7fe5d3a6e8aba74d,0x3ff0000000000000,2 +np.float64,0x2da061525b40d,0x2da061525b40d,2 +np.float64,0x7fcb9b9953373732,0x3ff0000000000000,2 +np.float64,0x2ca2f6fc59460,0x2ca2f6fc59460,2 +np.float64,0xffeb84b05af70960,0xbff0000000000000,2 +np.float64,0xffe551e86c6aa3d0,0xbff0000000000000,2 +np.float64,0xbfdb311311366226,0xbfd9aa6688faafb9,2 +np.float64,0xbfd4f3875629e70e,0xbfd43bcd73534c66,2 +np.float64,0x7fe95666f932accd,0x3ff0000000000000,2 +np.float64,0x3fc73dfb482e7bf7,0x3fc6fd70c20ebf60,2 +np.float64,0x800cd9e40939b3c8,0x800cd9e40939b3c8,2 +np.float64,0x3fb0c9fa422193f0,0x3fb0c3d38879a2ac,2 +np.float64,0xffd59a38372b3470,0xbff0000000000000,2 +np.float64,0x3fa8320ef4306420,0x3fa82d739e937d35,2 +np.float64,0x3fd517f16caa2fe4,0x3fd45c8de1e93b37,2 +np.float64,0xaed921655db24,0xaed921655db24,2 +np.float64,0x93478fb9268f2,0x93478fb9268f2,2 +np.float64,0x1615e28a2c2bd,0x1615e28a2c2bd,2 +np.float64,0xbfead23010f5a460,0xbfe5ea24d5d8f820,2 +np.float64,0x774a6070ee94d,0x774a6070ee94d,2 +np.float64,0x3fdf5874bd3eb0e9,0x3fdd0ef121dd915c,2 +np.float64,0x8004b25f53a964bf,0x8004b25f53a964bf,2 +np.float64,0xbfddacdd2ebb59ba,0xbfdbb78198fab36b,2 +np.float64,0x8008a3acf271475a,0x8008a3acf271475a,2 +np.float64,0xbfdb537c8736a6fa,0xbfd9c741038bb8f0,2 +np.float64,0xbfe56a133f6ad426,0xbfe2b3d5b8d259a1,2 +np.float64,0xffda1db531343b6a,0xbff0000000000000,2 +np.float64,0x3fcbe05f3a37c0be,0x3fcb71a54a64ddfb,2 +np.float64,0x7fe1ccaa7da39954,0x3ff0000000000000,2 +np.float64,0x3faeadd8343d5bb0,0x3faea475608860e6,2 +np.float64,0x3fe662ba1c2cc574,0x3fe354a6176e90df,2 +np.float64,0xffe4d49f4e69a93e,0xbff0000000000000,2 +np.float64,0xbfeadbc424f5b788,0xbfe5ef39dbe66343,2 +np.float64,0x99cf66f1339ed,0x99cf66f1339ed,2 +np.float64,0x33af77a2675f0,0x33af77a2675f0,2 +np.float64,0x7fec7b32ecf8f665,0x3ff0000000000000,2 +np.float64,0xffef3e44993e7c88,0xbff0000000000000,2 +np.float64,0xffe8f8ceac31f19c,0xbff0000000000000,2 +np.float64,0x7fe0d15b6da1a2b6,0x3ff0000000000000,2 +np.float64,0x4ba795c2974f3,0x4ba795c2974f3,2 +np.float64,0x3fe361aa37a6c354,0x3fe15079021d6b15,2 +np.float64,0xffe709714f6e12e2,0xbff0000000000000,2 +np.float64,0xffe7ea6a872fd4d4,0xbff0000000000000,2 +np.float64,0xffdb9441c8b72884,0xbff0000000000000,2 +np.float64,0xffd5e11ae9abc236,0xbff0000000000000,2 +np.float64,0xffe092a08b612540,0xbff0000000000000,2 +np.float64,0x3fe1f27e1ca3e4fc,0x3fe04685b5131207,2 +np.float64,0xbfe71ce1bdee39c4,0xbfe3c940809a7081,2 +np.float64,0xffe8c3aa68318754,0xbff0000000000000,2 +np.float64,0x800d4e2919da9c52,0x800d4e2919da9c52,2 +np.float64,0x7fe6c8bca76d9178,0x3ff0000000000000,2 +np.float64,0x7fced8751e3db0e9,0x3ff0000000000000,2 +np.float64,0xd61d0c8bac3a2,0xd61d0c8bac3a2,2 +np.float64,0x3fec57732938aee6,0x3fe6b22f15f38352,2 +np.float64,0xff9251cc7024a3a0,0xbff0000000000000,2 +np.float64,0xf4a68cb9e94d2,0xf4a68cb9e94d2,2 +np.float64,0x3feed76703bdaece,0x3fe7def0fc9a080c,2 +np.float64,0xbfe8971ff7712e40,0xbfe4ac3eb8ebff07,2 +np.float64,0x3fe4825f682904bf,0x3fe218c1952fe67d,2 +np.float64,0xbfd60f7698ac1eee,0xbfd539f0979b4b0c,2 +np.float64,0x3fcf0845993e1088,0x3fce7032f7180144,2 +np.float64,0x7fc83443f3306887,0x3ff0000000000000,2 +np.float64,0x3fe93123ae726247,0x3fe504e4fc437e89,2 +np.float64,0x3fbf9eb8363f3d70,0x3fbf75cdfa6828d5,2 +np.float64,0xbf8b45e5d0368bc0,0xbf8b457c29dfe1a9,2 +np.float64,0x8006c2853d0d850b,0x8006c2853d0d850b,2 +np.float64,0xffef26e25ffe4dc4,0xbff0000000000000,2 +np.float64,0x7fefffffffffffff,0x3ff0000000000000,2 +np.float64,0xbfde98f2c2bd31e6,0xbfdc761bfab1c4cb,2 +np.float64,0xffb725e6222e4bd0,0xbff0000000000000,2 +np.float64,0x800c63ead5d8c7d6,0x800c63ead5d8c7d6,2 +np.float64,0x3fea087e95f410fd,0x3fe57d3ab440706c,2 +np.float64,0xbfdf9f8a603f3f14,0xbfdd4742d77dfa57,2 +np.float64,0xfff0000000000000,0xbff0000000000000,2 +np.float64,0xbfcdc0841d3b8108,0xbfcd3a401debba9a,2 +np.float64,0x800f0c8f4f7e191f,0x800f0c8f4f7e191f,2 +np.float64,0x800ba6e75fd74dcf,0x800ba6e75fd74dcf,2 +np.float64,0x7fee4927e8bc924f,0x3ff0000000000000,2 +np.float64,0x3fadf141903be283,0x3fade8878d9d3551,2 +np.float64,0x3efb1a267df64,0x3efb1a267df64,2 +np.float64,0xffebf55f22b7eabe,0xbff0000000000000,2 +np.float64,0x7fbe8045663d008a,0x3ff0000000000000,2 +np.float64,0x3fefc0129f7f8026,0x3fe843f8b7d6cf38,2 +np.float64,0xbfe846b420f08d68,0xbfe47d1709e43937,2 +np.float64,0x7fe8e87043f1d0e0,0x3ff0000000000000,2 +np.float64,0x3fcfb718453f6e31,0x3fcf14ecee7b32b4,2 +np.float64,0x7fe4306b71a860d6,0x3ff0000000000000,2 +np.float64,0x7fee08459f7c108a,0x3ff0000000000000,2 +np.float64,0x3fed705165fae0a3,0x3fe73a66369c5700,2 +np.float64,0x7fd0e63f4da1cc7e,0x3ff0000000000000,2 +np.float64,0xffd1a40c2ea34818,0xbff0000000000000,2 +np.float64,0xbfa369795c26d2f0,0xbfa36718218d46b3,2 +np.float64,0xef70b9f5dee17,0xef70b9f5dee17,2 +np.float64,0x3fb50a0a6e2a1410,0x3fb4fdf27724560a,2 +np.float64,0x7fe30a0f6166141e,0x3ff0000000000000,2 +np.float64,0xbfd7b3ca7daf6794,0xbfd6accb81032b2d,2 +np.float64,0x3fc21dceb3243b9d,0x3fc1ff15d5d277a3,2 +np.float64,0x3fe483e445a907c9,0x3fe219ca0e269552,2 +np.float64,0x3fb2b1e2a22563c0,0x3fb2a96554900eaf,2 +np.float64,0x4b1ff6409641,0x4b1ff6409641,2 +np.float64,0xbfd92eabc9b25d58,0xbfd7f55d7776d64e,2 +np.float64,0x8003b8604c8770c1,0x8003b8604c8770c1,2 +np.float64,0x800d20a9df1a4154,0x800d20a9df1a4154,2 +np.float64,0xecf8a535d9f15,0xecf8a535d9f15,2 +np.float64,0x3fe92d15bab25a2b,0x3fe50296aa15ae85,2 +np.float64,0x800239c205a47385,0x800239c205a47385,2 +np.float64,0x3fc48664a9290cc8,0x3fc459d126320ef6,2 +np.float64,0x3fe7620625eec40c,0x3fe3f3bcbee3e8c6,2 +np.float64,0x3fd242ff4ca48600,0x3fd1c81ed7a971c8,2 +np.float64,0xbfe39bafcfa73760,0xbfe17959c7a279db,2 +np.float64,0x7fdcd2567239a4ac,0x3ff0000000000000,2 +np.float64,0x3fe5f2f292ebe5e6,0x3fe30d12f05e2752,2 +np.float64,0x7fda3819d1347033,0x3ff0000000000000,2 +np.float64,0xffca5b4d4334b69c,0xbff0000000000000,2 +np.float64,0xb8a2b7cd71457,0xb8a2b7cd71457,2 +np.float64,0x3fee689603fcd12c,0x3fe7ad4ace26d6dd,2 +np.float64,0x7fe26541a564ca82,0x3ff0000000000000,2 +np.float64,0x3fe6912ee66d225e,0x3fe3720d242c4d82,2 +np.float64,0xffe6580c75ecb018,0xbff0000000000000,2 +np.float64,0x7fe01a3370603466,0x3ff0000000000000,2 +np.float64,0xffe84e3f84b09c7e,0xbff0000000000000,2 +np.float64,0x3ff0000000000000,0x3fe85efab514f394,2 +np.float64,0x3fe214d4266429a8,0x3fe05fec03a3c247,2 +np.float64,0x3fd00aec5da015d8,0x3fcf6e070ad4ad62,2 +np.float64,0x800aac8631f5590d,0x800aac8631f5590d,2 +np.float64,0xbfe7c4f5f76f89ec,0xbfe42fc1c57b4a13,2 +np.float64,0xaf146c7d5e28e,0xaf146c7d5e28e,2 +np.float64,0xbfe57188b66ae312,0xbfe2b8be4615ef75,2 +np.float64,0xffef8cb8e1ff1971,0xbff0000000000000,2 +np.float64,0x8001daf8aa63b5f2,0x8001daf8aa63b5f2,2 +np.float64,0x3fdddcc339bbb986,0x3fdbde5f3783538b,2 +np.float64,0xdd8c92c3bb193,0xdd8c92c3bb193,2 +np.float64,0xbfe861a148f0c342,0xbfe48cf1d228a336,2 +np.float64,0xffe260a32e24c146,0xbff0000000000000,2 +np.float64,0x1f7474b43ee8f,0x1f7474b43ee8f,2 +np.float64,0x3fe81dbd89703b7c,0x3fe464d78df92b7b,2 +np.float64,0x7fed0101177a0201,0x3ff0000000000000,2 +np.float64,0x7fd8b419a8316832,0x3ff0000000000000,2 +np.float64,0x3fe93debccf27bd8,0x3fe50c27727917f0,2 +np.float64,0xe5ead05bcbd5a,0xe5ead05bcbd5a,2 +np.float64,0xbfebbbc4cff7778a,0xbfe663c4ca003bbf,2 +np.float64,0xbfea343eb474687e,0xbfe59529f73ea151,2 +np.float64,0x3fbe74a5963ce94b,0x3fbe50123ed05d8d,2 +np.float64,0x3fd31d3a5d263a75,0x3fd290c026cb38a5,2 +np.float64,0xbfd79908acaf3212,0xbfd695620e31c3c6,2 +np.float64,0xbfc26a350324d46c,0xbfc249f335f3e465,2 +np.float64,0xbfac38d5583871b0,0xbfac31866d12a45e,2 +np.float64,0x3fe40cea672819d5,0x3fe1c83754e72c92,2 +np.float64,0xbfa74770642e8ee0,0xbfa74355fcf67332,2 +np.float64,0x7fc60942d32c1285,0x3ff0000000000000,2 diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.py b/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..b22ade5e28a8cbdfab954a1216af3bf97389d683 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.py @@ -0,0 +1,187 @@ +""" +A sub-package for efficiently dealing with polynomials. + +Within the documentation for this sub-package, a "finite power series," +i.e., a polynomial (also referred to simply as a "series") is represented +by a 1-D numpy array of the polynomial's coefficients, ordered from lowest +order term to highest. For example, array([1,2,3]) represents +``P_0 + 2*P_1 + 3*P_2``, where P_n is the n-th order basis polynomial +applicable to the specific module in question, e.g., `polynomial` (which +"wraps" the "standard" basis) or `chebyshev`. For optimal performance, +all operations on polynomials, including evaluation at an argument, are +implemented as operations on the coefficients. Additional (module-specific) +information can be found in the docstring for the module of interest. + +This package provides *convenience classes* for each of six different kinds +of polynomials: + +======================== ================ +**Name** **Provides** +======================== ================ +`~polynomial.Polynomial` Power series +`~chebyshev.Chebyshev` Chebyshev series +`~legendre.Legendre` Legendre series +`~laguerre.Laguerre` Laguerre series +`~hermite.Hermite` Hermite series +`~hermite_e.HermiteE` HermiteE series +======================== ================ + +These *convenience classes* provide a consistent interface for creating, +manipulating, and fitting data with polynomials of different bases. +The convenience classes are the preferred interface for the `~numpy.polynomial` +package, and are available from the ``numpy.polynomial`` namespace. +This eliminates the need to navigate to the corresponding submodules, e.g. +``np.polynomial.Polynomial`` or ``np.polynomial.Chebyshev`` instead of +``np.polynomial.polynomial.Polynomial`` or +``np.polynomial.chebyshev.Chebyshev``, respectively. +The classes provide a more consistent and concise interface than the +type-specific functions defined in the submodules for each type of polynomial. +For example, to fit a Chebyshev polynomial with degree ``1`` to data given +by arrays ``xdata`` and ``ydata``, the +`~chebyshev.Chebyshev.fit` class method:: + + >>> from numpy.polynomial import Chebyshev + >>> xdata = [1, 2, 3, 4] + >>> ydata = [1, 4, 9, 16] + >>> c = Chebyshev.fit(xdata, ydata, deg=1) + +is preferred over the `chebyshev.chebfit` function from the +``np.polynomial.chebyshev`` module:: + + >>> from numpy.polynomial.chebyshev import chebfit + >>> c = chebfit(xdata, ydata, deg=1) + +See :doc:`routines.polynomials.classes` for more details. + +Convenience Classes +=================== + +The following lists the various constants and methods common to all of +the classes representing the various kinds of polynomials. In the following, +the term ``Poly`` represents any one of the convenience classes (e.g. +`~polynomial.Polynomial`, `~chebyshev.Chebyshev`, `~hermite.Hermite`, etc.) +while the lowercase ``p`` represents an **instance** of a polynomial class. + +Constants +--------- + +- ``Poly.domain`` -- Default domain +- ``Poly.window`` -- Default window +- ``Poly.basis_name`` -- String used to represent the basis +- ``Poly.maxpower`` -- Maximum value ``n`` such that ``p**n`` is allowed +- ``Poly.nickname`` -- String used in printing + +Creation +-------- + +Methods for creating polynomial instances. + +- ``Poly.basis(degree)`` -- Basis polynomial of given degree +- ``Poly.identity()`` -- ``p`` where ``p(x) = x`` for all ``x`` +- ``Poly.fit(x, y, deg)`` -- ``p`` of degree ``deg`` with coefficients + determined by the least-squares fit to the data ``x``, ``y`` +- ``Poly.fromroots(roots)`` -- ``p`` with specified roots +- ``p.copy()`` -- Create a copy of ``p`` + +Conversion +---------- + +Methods for converting a polynomial instance of one kind to another. + +- ``p.cast(Poly)`` -- Convert ``p`` to instance of kind ``Poly`` +- ``p.convert(Poly)`` -- Convert ``p`` to instance of kind ``Poly`` or map + between ``domain`` and ``window`` + +Calculus +-------- +- ``p.deriv()`` -- Take the derivative of ``p`` +- ``p.integ()`` -- Integrate ``p`` + +Validation +---------- +- ``Poly.has_samecoef(p1, p2)`` -- Check if coefficients match +- ``Poly.has_samedomain(p1, p2)`` -- Check if domains match +- ``Poly.has_sametype(p1, p2)`` -- Check if types match +- ``Poly.has_samewindow(p1, p2)`` -- Check if windows match + +Misc +---- +- ``p.linspace()`` -- Return ``x, p(x)`` at equally-spaced points in ``domain`` +- ``p.mapparms()`` -- Return the parameters for the linear mapping between + ``domain`` and ``window``. +- ``p.roots()`` -- Return the roots of ``p``. +- ``p.trim()`` -- Remove trailing coefficients. +- ``p.cutdeg(degree)`` -- Truncate ``p`` to given degree +- ``p.truncate(size)`` -- Truncate ``p`` to given size + +""" +from .polynomial import Polynomial +from .chebyshev import Chebyshev +from .legendre import Legendre +from .hermite import Hermite +from .hermite_e import HermiteE +from .laguerre import Laguerre + +__all__ = [ + "set_default_printstyle", + "polynomial", "Polynomial", + "chebyshev", "Chebyshev", + "legendre", "Legendre", + "hermite", "Hermite", + "hermite_e", "HermiteE", + "laguerre", "Laguerre", +] + + +def set_default_printstyle(style): + """ + Set the default format for the string representation of polynomials. + + Values for ``style`` must be valid inputs to ``__format__``, i.e. 'ascii' + or 'unicode'. + + Parameters + ---------- + style : str + Format string for default printing style. Must be either 'ascii' or + 'unicode'. + + Notes + ----- + The default format depends on the platform: 'unicode' is used on + Unix-based systems and 'ascii' on Windows. This determination is based on + default font support for the unicode superscript and subscript ranges. + + Examples + -------- + >>> p = np.polynomial.Polynomial([1, 2, 3]) + >>> c = np.polynomial.Chebyshev([1, 2, 3]) + >>> np.polynomial.set_default_printstyle('unicode') + >>> print(p) + 1.0 + 2.0·x + 3.0·x² + >>> print(c) + 1.0 + 2.0·T₁(x) + 3.0·T₂(x) + >>> np.polynomial.set_default_printstyle('ascii') + >>> print(p) + 1.0 + 2.0 x + 3.0 x**2 + >>> print(c) + 1.0 + 2.0 T_1(x) + 3.0 T_2(x) + >>> # Formatting supersedes all class/package-level defaults + >>> print(f"{p:unicode}") + 1.0 + 2.0·x + 3.0·x² + """ + if style not in ('unicode', 'ascii'): + raise ValueError( + f"Unsupported format string '{style}'. Valid options are 'ascii' " + f"and 'unicode'" + ) + _use_unicode = True + if style == 'ascii': + _use_unicode = False + from ._polybase import ABCPolyBase + ABCPolyBase._use_unicode = _use_unicode + + +from numpy._pytesttester import PytestTester +test = PytestTester(__name__) +del PytestTester diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.pyi new file mode 100644 index 0000000000000000000000000000000000000000..c5dccfe16dee8889508150ecfe963297f24a5fd0 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/__init__.pyi @@ -0,0 +1,24 @@ +from typing import Final, Literal + +from .polynomial import Polynomial +from .chebyshev import Chebyshev +from .legendre import Legendre +from .hermite import Hermite +from .hermite_e import HermiteE +from .laguerre import Laguerre +from . import polynomial, chebyshev, legendre, hermite, hermite_e, laguerre + +__all__ = [ + "set_default_printstyle", + "polynomial", "Polynomial", + "chebyshev", "Chebyshev", + "legendre", "Legendre", + "hermite", "Hermite", + "hermite_e", "HermiteE", + "laguerre", "Laguerre", +] + +def set_default_printstyle(style: Literal["ascii", "unicode"]) -> None: ... + +from numpy._pytesttester import PytestTester as _PytestTester +test: Final[_PytestTester] diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/_polybase.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/_polybase.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..21d5e0de1f069f0d29e04929e0c470789dd35058 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/_polybase.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/laguerre.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/laguerre.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..81151e6c6e460735b72700c3e0e9f6bc29832e46 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/laguerre.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/polynomial.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/polynomial.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..95373d5ca585c3563cb8d5a63388613a578e0ae4 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/__pycache__/polynomial.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.py b/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.py new file mode 100644 index 0000000000000000000000000000000000000000..1c3d16c6efd7af25ef0cdfc32083802ecce2a92f --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.py @@ -0,0 +1,1197 @@ +""" +Abstract base class for the various polynomial Classes. + +The ABCPolyBase class provides the methods needed to implement the common API +for the various polynomial classes. It operates as a mixin, but uses the +abc module from the stdlib, hence it is only available for Python >= 2.6. + +""" +import os +import abc +import numbers +from typing import Callable + +import numpy as np +from . import polyutils as pu + +__all__ = ['ABCPolyBase'] + +class ABCPolyBase(abc.ABC): + """An abstract base class for immutable series classes. + + ABCPolyBase provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' along with the + methods listed below. + + Parameters + ---------- + coef : array_like + Series coefficients in order of increasing degree, i.e., + ``(1, 2, 3)`` gives ``1*P_0(x) + 2*P_1(x) + 3*P_2(x)``, where + ``P_i`` is the basis polynomials of degree ``i``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is the derived class domain. + window : (2,) array_like, optional + Window, see domain for its use. The default value is the + derived class window. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + Attributes + ---------- + coef : (N,) ndarray + Series coefficients in order of increasing degree. + domain : (2,) ndarray + Domain that is mapped to window. + window : (2,) ndarray + Window that domain is mapped to. + symbol : str + Symbol representing the independent variable. + + Class Attributes + ---------------- + maxpower : int + Maximum power allowed, i.e., the largest number ``n`` such that + ``p(x)**n`` is allowed. This is to limit runaway polynomial size. + domain : (2,) ndarray + Default domain of the class. + window : (2,) ndarray + Default window of the class. + + """ + + # Not hashable + __hash__ = None + + # Opt out of numpy ufuncs and Python ops with ndarray subclasses. + __array_ufunc__ = None + + # Limit runaway size. T_n^m has degree n*m + maxpower = 100 + + # Unicode character mappings for improved __str__ + _superscript_mapping = str.maketrans({ + "0": "⁰", + "1": "¹", + "2": "²", + "3": "³", + "4": "⁴", + "5": "⁵", + "6": "⁶", + "7": "⁷", + "8": "⁸", + "9": "⁹" + }) + _subscript_mapping = str.maketrans({ + "0": "₀", + "1": "₁", + "2": "₂", + "3": "₃", + "4": "₄", + "5": "₅", + "6": "₆", + "7": "₇", + "8": "₈", + "9": "₉" + }) + # Some fonts don't support full unicode character ranges necessary for + # the full set of superscripts and subscripts, including common/default + # fonts in Windows shells/terminals. Therefore, default to ascii-only + # printing on windows. + _use_unicode = not os.name == 'nt' + + @property + def symbol(self): + return self._symbol + + @property + @abc.abstractmethod + def domain(self): + pass + + @property + @abc.abstractmethod + def window(self): + pass + + @property + @abc.abstractmethod + def basis_name(self): + pass + + @staticmethod + @abc.abstractmethod + def _add(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _sub(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _mul(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _div(c1, c2): + pass + + @staticmethod + @abc.abstractmethod + def _pow(c, pow, maxpower=None): + pass + + @staticmethod + @abc.abstractmethod + def _val(x, c): + pass + + @staticmethod + @abc.abstractmethod + def _int(c, m, k, lbnd, scl): + pass + + @staticmethod + @abc.abstractmethod + def _der(c, m, scl): + pass + + @staticmethod + @abc.abstractmethod + def _fit(x, y, deg, rcond, full): + pass + + @staticmethod + @abc.abstractmethod + def _line(off, scl): + pass + + @staticmethod + @abc.abstractmethod + def _roots(c): + pass + + @staticmethod + @abc.abstractmethod + def _fromroots(r): + pass + + def has_samecoef(self, other): + """Check if coefficients match. + + Parameters + ---------- + other : class instance + The other class must have the ``coef`` attribute. + + Returns + ------- + bool : boolean + True if the coefficients are the same, False otherwise. + + """ + if len(self.coef) != len(other.coef): + return False + elif not np.all(self.coef == other.coef): + return False + else: + return True + + def has_samedomain(self, other): + """Check if domains match. + + Parameters + ---------- + other : class instance + The other class must have the ``domain`` attribute. + + Returns + ------- + bool : boolean + True if the domains are the same, False otherwise. + + """ + return np.all(self.domain == other.domain) + + def has_samewindow(self, other): + """Check if windows match. + + Parameters + ---------- + other : class instance + The other class must have the ``window`` attribute. + + Returns + ------- + bool : boolean + True if the windows are the same, False otherwise. + + """ + return np.all(self.window == other.window) + + def has_sametype(self, other): + """Check if types match. + + Parameters + ---------- + other : object + Class instance. + + Returns + ------- + bool : boolean + True if other is same class as self + + """ + return isinstance(other, self.__class__) + + def _get_coefficients(self, other): + """Interpret other as polynomial coefficients. + + The `other` argument is checked to see if it is of the same + class as self with identical domain and window. If so, + return its coefficients, otherwise return `other`. + + Parameters + ---------- + other : anything + Object to be checked. + + Returns + ------- + coef + The coefficients of`other` if it is a compatible instance, + of ABCPolyBase, otherwise `other`. + + Raises + ------ + TypeError + When `other` is an incompatible instance of ABCPolyBase. + + """ + if isinstance(other, ABCPolyBase): + if not isinstance(other, self.__class__): + raise TypeError("Polynomial types differ") + elif not np.all(self.domain == other.domain): + raise TypeError("Domains differ") + elif not np.all(self.window == other.window): + raise TypeError("Windows differ") + elif self.symbol != other.symbol: + raise ValueError("Polynomial symbols differ") + return other.coef + return other + + def __init__(self, coef, domain=None, window=None, symbol='x'): + [coef] = pu.as_series([coef], trim=False) + self.coef = coef + + if domain is not None: + [domain] = pu.as_series([domain], trim=False) + if len(domain) != 2: + raise ValueError("Domain has wrong number of elements.") + self.domain = domain + + if window is not None: + [window] = pu.as_series([window], trim=False) + if len(window) != 2: + raise ValueError("Window has wrong number of elements.") + self.window = window + + # Validation for symbol + try: + if not symbol.isidentifier(): + raise ValueError( + "Symbol string must be a valid Python identifier" + ) + # If a user passes in something other than a string, the above + # results in an AttributeError. Catch this and raise a more + # informative exception + except AttributeError: + raise TypeError("Symbol must be a non-empty string") + + self._symbol = symbol + + def __repr__(self): + coef = repr(self.coef)[6:-1] + domain = repr(self.domain)[6:-1] + window = repr(self.window)[6:-1] + name = self.__class__.__name__ + return (f"{name}({coef}, domain={domain}, window={window}, " + f"symbol='{self.symbol}')") + + def __format__(self, fmt_str): + if fmt_str == '': + return self.__str__() + if fmt_str not in ('ascii', 'unicode'): + raise ValueError( + f"Unsupported format string '{fmt_str}' passed to " + f"{self.__class__}.__format__. Valid options are " + f"'ascii' and 'unicode'" + ) + if fmt_str == 'ascii': + return self._generate_string(self._str_term_ascii) + return self._generate_string(self._str_term_unicode) + + def __str__(self): + if self._use_unicode: + return self._generate_string(self._str_term_unicode) + return self._generate_string(self._str_term_ascii) + + def _generate_string(self, term_method): + """ + Generate the full string representation of the polynomial, using + ``term_method`` to generate each polynomial term. + """ + # Get configuration for line breaks + linewidth = np.get_printoptions().get('linewidth', 75) + if linewidth < 1: + linewidth = 1 + out = pu.format_float(self.coef[0]) + + off, scale = self.mapparms() + + scaled_symbol, needs_parens = self._format_term(pu.format_float, + off, scale) + if needs_parens: + scaled_symbol = '(' + scaled_symbol + ')' + + for i, coef in enumerate(self.coef[1:]): + out += " " + power = str(i + 1) + # Polynomial coefficient + # The coefficient array can be an object array with elements that + # will raise a TypeError with >= 0 (e.g. strings or Python + # complex). In this case, represent the coefficient as-is. + try: + if coef >= 0: + next_term = "+ " + pu.format_float(coef, parens=True) + else: + next_term = "- " + pu.format_float(-coef, parens=True) + except TypeError: + next_term = f"+ {coef}" + # Polynomial term + next_term += term_method(power, scaled_symbol) + # Length of the current line with next term added + line_len = len(out.split('\n')[-1]) + len(next_term) + # If not the last term in the polynomial, it will be two + # characters longer due to the +/- with the next term + if i < len(self.coef[1:]) - 1: + line_len += 2 + # Handle linebreaking + if line_len >= linewidth: + next_term = next_term.replace(" ", "\n", 1) + out += next_term + return out + + @classmethod + def _str_term_unicode(cls, i, arg_str): + """ + String representation of single polynomial term using unicode + characters for superscripts and subscripts. + """ + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis_name, or override " + "_str_term_unicode(cls, i, arg_str)" + ) + return (f"·{cls.basis_name}{i.translate(cls._subscript_mapping)}" + f"({arg_str})") + + @classmethod + def _str_term_ascii(cls, i, arg_str): + """ + String representation of a single polynomial term using ** and _ to + represent superscripts and subscripts, respectively. + """ + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis_name, or override " + "_str_term_ascii(cls, i, arg_str)" + ) + return f" {cls.basis_name}_{i}({arg_str})" + + @classmethod + def _repr_latex_term(cls, i, arg_str, needs_parens): + if cls.basis_name is None: + raise NotImplementedError( + "Subclasses must define either a basis name, or override " + "_repr_latex_term(i, arg_str, needs_parens)") + # since we always add parens, we don't care if the expression needs them + return f"{{{cls.basis_name}}}_{{{i}}}({arg_str})" + + @staticmethod + def _repr_latex_scalar(x, parens=False): + # TODO: we're stuck with disabling math formatting until we handle + # exponents in this function + return r'\text{{{}}}'.format(pu.format_float(x, parens=parens)) + + def _format_term(self, scalar_format: Callable, off: float, scale: float): + """ Format a single term in the expansion """ + if off == 0 and scale == 1: + term = self.symbol + needs_parens = False + elif scale == 1: + term = f"{scalar_format(off)} + {self.symbol}" + needs_parens = True + elif off == 0: + term = f"{scalar_format(scale)}{self.symbol}" + needs_parens = True + else: + term = ( + f"{scalar_format(off)} + " + f"{scalar_format(scale)}{self.symbol}" + ) + needs_parens = True + return term, needs_parens + + def _repr_latex_(self): + # get the scaled argument string to the basis functions + off, scale = self.mapparms() + term, needs_parens = self._format_term(self._repr_latex_scalar, + off, scale) + + mute = r"\color{{LightGray}}{{{}}}".format + + parts = [] + for i, c in enumerate(self.coef): + # prevent duplication of + and - signs + if i == 0: + coef_str = f"{self._repr_latex_scalar(c)}" + elif not isinstance(c, numbers.Real): + coef_str = f" + ({self._repr_latex_scalar(c)})" + elif c >= 0: + coef_str = f" + {self._repr_latex_scalar(c, parens=True)}" + else: + coef_str = f" - {self._repr_latex_scalar(-c, parens=True)}" + + # produce the string for the term + term_str = self._repr_latex_term(i, term, needs_parens) + if term_str == '1': + part = coef_str + else: + part = rf"{coef_str}\,{term_str}" + + if c == 0: + part = mute(part) + + parts.append(part) + + if parts: + body = ''.join(parts) + else: + # in case somehow there are no coefficients at all + body = '0' + + return rf"${self.symbol} \mapsto {body}$" + + + + # Pickle and copy + + def __getstate__(self): + ret = self.__dict__.copy() + ret['coef'] = self.coef.copy() + ret['domain'] = self.domain.copy() + ret['window'] = self.window.copy() + ret['symbol'] = self.symbol + return ret + + def __setstate__(self, dict): + self.__dict__ = dict + + # Call + + def __call__(self, arg): + arg = pu.mapdomain(arg, self.domain, self.window) + return self._val(arg, self.coef) + + def __iter__(self): + return iter(self.coef) + + def __len__(self): + return len(self.coef) + + # Numeric properties. + + def __neg__(self): + return self.__class__( + -self.coef, self.domain, self.window, self.symbol + ) + + def __pos__(self): + return self + + def __add__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._add(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __sub__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._sub(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __mul__(self, other): + othercoef = self._get_coefficients(other) + try: + coef = self._mul(self.coef, othercoef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __truediv__(self, other): + # there is no true divide if the rhs is not a Number, although it + # could return the first n elements of an infinite series. + # It is hard to see where n would come from, though. + if not isinstance(other, numbers.Number) or isinstance(other, bool): + raise TypeError( + f"unsupported types for true division: " + f"'{type(self)}', '{type(other)}'" + ) + return self.__floordiv__(other) + + def __floordiv__(self, other): + res = self.__divmod__(other) + if res is NotImplemented: + return res + return res[0] + + def __mod__(self, other): + res = self.__divmod__(other) + if res is NotImplemented: + return res + return res[1] + + def __divmod__(self, other): + othercoef = self._get_coefficients(other) + try: + quo, rem = self._div(self.coef, othercoef) + except ZeroDivisionError: + raise + except Exception: + return NotImplemented + quo = self.__class__(quo, self.domain, self.window, self.symbol) + rem = self.__class__(rem, self.domain, self.window, self.symbol) + return quo, rem + + def __pow__(self, other): + coef = self._pow(self.coef, other, maxpower=self.maxpower) + res = self.__class__(coef, self.domain, self.window, self.symbol) + return res + + def __radd__(self, other): + try: + coef = self._add(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rsub__(self, other): + try: + coef = self._sub(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rmul__(self, other): + try: + coef = self._mul(other, self.coef) + except Exception: + return NotImplemented + return self.__class__(coef, self.domain, self.window, self.symbol) + + def __rdiv__(self, other): + # set to __floordiv__ /. + return self.__rfloordiv__(other) + + def __rtruediv__(self, other): + # An instance of ABCPolyBase is not considered a + # Number. + return NotImplemented + + def __rfloordiv__(self, other): + res = self.__rdivmod__(other) + if res is NotImplemented: + return res + return res[0] + + def __rmod__(self, other): + res = self.__rdivmod__(other) + if res is NotImplemented: + return res + return res[1] + + def __rdivmod__(self, other): + try: + quo, rem = self._div(other, self.coef) + except ZeroDivisionError: + raise + except Exception: + return NotImplemented + quo = self.__class__(quo, self.domain, self.window, self.symbol) + rem = self.__class__(rem, self.domain, self.window, self.symbol) + return quo, rem + + def __eq__(self, other): + res = (isinstance(other, self.__class__) and + np.all(self.domain == other.domain) and + np.all(self.window == other.window) and + (self.coef.shape == other.coef.shape) and + np.all(self.coef == other.coef) and + (self.symbol == other.symbol)) + return res + + def __ne__(self, other): + return not self.__eq__(other) + + # + # Extra methods. + # + + def copy(self): + """Return a copy. + + Returns + ------- + new_series : series + Copy of self. + + """ + return self.__class__(self.coef, self.domain, self.window, self.symbol) + + def degree(self): + """The degree of the series. + + Returns + ------- + degree : int + Degree of the series, one less than the number of coefficients. + + Examples + -------- + + Create a polynomial object for ``1 + 7*x + 4*x**2``: + + >>> poly = np.polynomial.Polynomial([1, 7, 4]) + >>> print(poly) + 1.0 + 7.0·x + 4.0·x² + >>> poly.degree() + 2 + + Note that this method does not check for non-zero coefficients. + You must trim the polynomial to remove any trailing zeroes: + + >>> poly = np.polynomial.Polynomial([1, 7, 0]) + >>> print(poly) + 1.0 + 7.0·x + 0.0·x² + >>> poly.degree() + 2 + >>> poly.trim().degree() + 1 + + """ + return len(self) - 1 + + def cutdeg(self, deg): + """Truncate series to the given degree. + + Reduce the degree of the series to `deg` by discarding the + high order terms. If `deg` is greater than the current degree a + copy of the current series is returned. This can be useful in least + squares where the coefficients of the high degree terms may be very + small. + + Parameters + ---------- + deg : non-negative int + The series is reduced to degree `deg` by discarding the high + order terms. The value of `deg` must be a non-negative integer. + + Returns + ------- + new_series : series + New instance of series with reduced degree. + + """ + return self.truncate(deg + 1) + + def trim(self, tol=0): + """Remove trailing coefficients + + Remove trailing coefficients until a coefficient is reached whose + absolute value greater than `tol` or the beginning of the series is + reached. If all the coefficients would be removed the series is set + to ``[0]``. A new series instance is returned with the new + coefficients. The current instance remains unchanged. + + Parameters + ---------- + tol : non-negative number. + All trailing coefficients less than `tol` will be removed. + + Returns + ------- + new_series : series + New instance of series with trimmed coefficients. + + """ + coef = pu.trimcoef(self.coef, tol) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def truncate(self, size): + """Truncate series to length `size`. + + Reduce the series to length `size` by discarding the high + degree terms. The value of `size` must be a positive integer. This + can be useful in least squares where the coefficients of the + high degree terms may be very small. + + Parameters + ---------- + size : positive int + The series is reduced to length `size` by discarding the high + degree terms. The value of `size` must be a positive integer. + + Returns + ------- + new_series : series + New instance of series with truncated coefficients. + + """ + isize = int(size) + if isize != size or isize < 1: + raise ValueError("size must be a positive integer") + if isize >= len(self.coef): + coef = self.coef + else: + coef = self.coef[:isize] + return self.__class__(coef, self.domain, self.window, self.symbol) + + def convert(self, domain=None, kind=None, window=None): + """Convert series to a different kind and/or domain and/or window. + + Parameters + ---------- + domain : array_like, optional + The domain of the converted series. If the value is None, + the default domain of `kind` is used. + kind : class, optional + The polynomial series type class to which the current instance + should be converted. If kind is None, then the class of the + current instance is used. + window : array_like, optional + The window of the converted series. If the value is None, + the default window of `kind` is used. + + Returns + ------- + new_series : series + The returned class can be of different type than the current + instance and/or have a different domain and/or different + window. + + Notes + ----- + Conversion between domains and class types can result in + numerically ill defined series. + + """ + if kind is None: + kind = self.__class__ + if domain is None: + domain = kind.domain + if window is None: + window = kind.window + return self(kind.identity(domain, window=window, symbol=self.symbol)) + + def mapparms(self): + """Return the mapping parameters. + + The returned values define a linear map ``off + scl*x`` that is + applied to the input arguments before the series is evaluated. The + map depends on the ``domain`` and ``window``; if the current + ``domain`` is equal to the ``window`` the resulting map is the + identity. If the coefficients of the series instance are to be + used by themselves outside this class, then the linear function + must be substituted for the ``x`` in the standard representation of + the base polynomials. + + Returns + ------- + off, scl : float or complex + The mapping function is defined by ``off + scl*x``. + + Notes + ----- + If the current domain is the interval ``[l1, r1]`` and the window + is ``[l2, r2]``, then the linear mapping function ``L`` is + defined by the equations:: + + L(l1) = l2 + L(r1) = r2 + + """ + return pu.mapparms(self.domain, self.window) + + def integ(self, m=1, k=[], lbnd=None): + """Integrate. + + Return a series instance that is the definite integral of the + current series. + + Parameters + ---------- + m : non-negative int + The number of integrations to perform. + k : array_like + Integration constants. The first constant is applied to the + first integration, the second to the second, and so on. The + list of values must less than or equal to `m` in length and any + missing values are set to zero. + lbnd : Scalar + The lower bound of the definite integral. + + Returns + ------- + new_series : series + A new series representing the integral. The domain is the same + as the domain of the integrated series. + + """ + off, scl = self.mapparms() + if lbnd is None: + lbnd = 0 + else: + lbnd = off + scl*lbnd + coef = self._int(self.coef, m, k, lbnd, 1./scl) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def deriv(self, m=1): + """Differentiate. + + Return a series instance of that is the derivative of the current + series. + + Parameters + ---------- + m : non-negative int + Find the derivative of order `m`. + + Returns + ------- + new_series : series + A new series representing the derivative. The domain is the same + as the domain of the differentiated series. + + """ + off, scl = self.mapparms() + coef = self._der(self.coef, m, scl) + return self.__class__(coef, self.domain, self.window, self.symbol) + + def roots(self): + """Return the roots of the series polynomial. + + Compute the roots for the series. Note that the accuracy of the + roots decreases the further outside the `domain` they lie. + + Returns + ------- + roots : ndarray + Array containing the roots of the series. + + """ + roots = self._roots(self.coef) + return pu.mapdomain(roots, self.window, self.domain) + + def linspace(self, n=100, domain=None): + """Return x, y values at equally spaced points in domain. + + Returns the x, y values at `n` linearly spaced points across the + domain. Here y is the value of the polynomial at the points x. By + default the domain is the same as that of the series instance. + This method is intended mostly as a plotting aid. + + Parameters + ---------- + n : int, optional + Number of point pairs to return. The default value is 100. + domain : {None, array_like}, optional + If not None, the specified domain is used instead of that of + the calling instance. It should be of the form ``[beg,end]``. + The default is None which case the class domain is used. + + Returns + ------- + x, y : ndarray + x is equal to linspace(self.domain[0], self.domain[1], n) and + y is the series evaluated at element of x. + + """ + if domain is None: + domain = self.domain + x = np.linspace(domain[0], domain[1], n) + y = self(x) + return x, y + + @classmethod + def fit(cls, x, y, deg, domain=None, rcond=None, full=False, w=None, + window=None, symbol='x'): + """Least squares fit to data. + + Return a series instance that is the least squares fit to the data + `y` sampled at `x`. The domain of the returned instance can be + specified and this will often result in a superior fit with less + chance of ill conditioning. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) + y-coordinates of the M sample points ``(x[i], y[i])``. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + domain : {None, [beg, end], []}, optional + Domain to use for the returned series. If ``None``, + then a minimal domain that covers the points `x` is chosen. If + ``[]`` the class domain is used. The default value was the + class domain in NumPy 1.4 and ``None`` in later versions. + The ``[]`` option was added in numpy 1.5.0. + rcond : float, optional + Relative condition number of the fit. Singular values smaller + than this relative to the largest singular value will be + ignored. The default value is ``len(x)*eps``, where eps is the + relative precision of the float type, about 2e-16 in most + cases. + full : bool, optional + Switch determining nature of return value. When it is False + (the default) just the coefficients are returned, when True + diagnostic information from the singular value decomposition is + also returned. + w : array_like, shape (M,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have + the same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + window : {[beg, end]}, optional + Window to use for the returned series. The default + value is the default class domain + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + A series that represents the least squares fit to the data and + has the domain and window specified in the call. If the + coefficients for the unscaled and unshifted basis polynomials are + of interest, do ``new_series.convert().coef``. + + [resid, rank, sv, rcond] : list + These values are only returned if ``full == True`` + + - resid -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - sv -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `linalg.lstsq`. + + """ + if domain is None: + domain = pu.getdomain(x) + if domain[0] == domain[1]: + domain[0] -= 1 + domain[1] += 1 + elif type(domain) is list and len(domain) == 0: + domain = cls.domain + + if window is None: + window = cls.window + + xnew = pu.mapdomain(x, domain, window) + res = cls._fit(xnew, y, deg, w=w, rcond=rcond, full=full) + if full: + [coef, status] = res + return ( + cls(coef, domain=domain, window=window, symbol=symbol), status + ) + else: + coef = res + return cls(coef, domain=domain, window=window, symbol=symbol) + + @classmethod + def fromroots(cls, roots, domain=[], window=None, symbol='x'): + """Return series instance that has the specified roots. + + Returns a series representing the product + ``(x - r[0])*(x - r[1])*...*(x - r[n-1])``, where ``r`` is a + list of roots. + + Parameters + ---------- + roots : array_like + List of roots. + domain : {[], None, array_like}, optional + Domain for the resulting series. If None the domain is the + interval from the smallest root to the largest. If [] the + domain is the class domain. The default is []. + window : {None, array_like}, optional + Window for the returned series. If None the class window is + used. The default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + Series with the specified roots. + + """ + [roots] = pu.as_series([roots], trim=False) + if domain is None: + domain = pu.getdomain(roots) + elif type(domain) is list and len(domain) == 0: + domain = cls.domain + + if window is None: + window = cls.window + + deg = len(roots) + off, scl = pu.mapparms(domain, window) + rnew = off + scl*roots + coef = cls._fromroots(rnew) / scl**deg + return cls(coef, domain=domain, window=window, symbol=symbol) + + @classmethod + def identity(cls, domain=None, window=None, symbol='x'): + """Identity function. + + If ``p`` is the returned series, then ``p(x) == x`` for all + values of x. + + Parameters + ---------- + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + Series of representing the identity. + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + off, scl = pu.mapparms(window, domain) + coef = cls._line(off, scl) + return cls(coef, domain, window, symbol) + + @classmethod + def basis(cls, deg, domain=None, window=None, symbol='x'): + """Series basis polynomial of degree `deg`. + + Returns the series representing the basis polynomial of degree `deg`. + + Parameters + ---------- + deg : int + Degree of the basis polynomial for the series. Must be >= 0. + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + symbol : str, optional + Symbol representing the independent variable. Default is 'x'. + + Returns + ------- + new_series : series + A series with the coefficient of the `deg` term set to one and + all others zero. + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + ideg = int(deg) + + if ideg != deg or ideg < 0: + raise ValueError("deg must be non-negative integer") + return cls([0]*ideg + [1], domain, window, symbol) + + @classmethod + def cast(cls, series, domain=None, window=None): + """Convert series to series of this class. + + The `series` is expected to be an instance of some polynomial + series of one of the types supported by by the numpy.polynomial + module, but could be some other class that supports the convert + method. + + Parameters + ---------- + series : series + The series instance to be converted. + domain : {None, array_like}, optional + If given, the array must be of the form ``[beg, end]``, where + ``beg`` and ``end`` are the endpoints of the domain. If None is + given then the class domain is used. The default is None. + window : {None, array_like}, optional + If given, the resulting array must be if the form + ``[beg, end]``, where ``beg`` and ``end`` are the endpoints of + the window. If None is given then the class window is used. The + default is None. + + Returns + ------- + new_series : series + A series of the same kind as the calling class and equal to + `series` when evaluated. + + See Also + -------- + convert : similar instance method + + """ + if domain is None: + domain = cls.domain + if window is None: + window = cls.window + return series.convert(domain, cls, window) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.pyi new file mode 100644 index 0000000000000000000000000000000000000000..ca7ca628d5140c7584ef42a92fb633625ca8a657 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/_polybase.pyi @@ -0,0 +1,287 @@ +import abc +import decimal +import numbers +from collections.abc import Iterator, Mapping, Sequence +from typing import ( + Any, + ClassVar, + Final, + Generic, + Literal, + SupportsIndex, + TypeAlias, + TypeGuard, + overload, +) + +import numpy as np +import numpy.typing as npt +from numpy._typing import ( + _FloatLike_co, + _NumberLike_co, + + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, +) + +from ._polytypes import ( + _AnyInt, + _CoefLike_co, + + _Array2, + _Tuple2, + + _Series, + _CoefSeries, + + _SeriesLikeInt_co, + _SeriesLikeCoef_co, + + _ArrayLikeCoefObject_co, + _ArrayLikeCoef_co, +) + +from typing_extensions import LiteralString, TypeVar + + +__all__: Final[Sequence[str]] = ("ABCPolyBase",) + + +_NameCo = TypeVar("_NameCo", bound=LiteralString | None, covariant=True, default=LiteralString | None) +_Self = TypeVar("_Self") +_Other = TypeVar("_Other", bound=ABCPolyBase) + +_AnyOther: TypeAlias = ABCPolyBase | _CoefLike_co | _SeriesLikeCoef_co +_Hundred: TypeAlias = Literal[100] + + +class ABCPolyBase(Generic[_NameCo], metaclass=abc.ABCMeta): + __hash__: ClassVar[None] # type: ignore[assignment] + __array_ufunc__: ClassVar[None] + + maxpower: ClassVar[_Hundred] + _superscript_mapping: ClassVar[Mapping[int, str]] + _subscript_mapping: ClassVar[Mapping[int, str]] + _use_unicode: ClassVar[bool] + + basis_name: _NameCo + coef: _CoefSeries + domain: _Array2[np.inexact[Any] | np.object_] + window: _Array2[np.inexact[Any] | np.object_] + + _symbol: LiteralString + @property + def symbol(self, /) -> LiteralString: ... + + def __init__( + self, + /, + coef: _SeriesLikeCoef_co, + domain: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> None: ... + + @overload + def __call__(self, /, arg: _Other) -> _Other: ... + # TODO: Once `_ShapeType@ndarray` is covariant and bounded (see #26081), + # additionally include 0-d arrays as input types with scalar return type. + @overload + def __call__( + self, + /, + arg: _FloatLike_co | decimal.Decimal | numbers.Real | np.object_, + ) -> np.float64 | np.complex128: ... + @overload + def __call__( + self, + /, + arg: _NumberLike_co | numbers.Complex, + ) -> np.complex128: ... + @overload + def __call__(self, /, arg: _ArrayLikeFloat_co) -> ( + npt.NDArray[np.float64] + | npt.NDArray[np.complex128] + | npt.NDArray[np.object_] + ): ... + @overload + def __call__( + self, + /, + arg: _ArrayLikeComplex_co, + ) -> npt.NDArray[np.complex128] | npt.NDArray[np.object_]: ... + @overload + def __call__( + self, + /, + arg: _ArrayLikeCoefObject_co, + ) -> npt.NDArray[np.object_]: ... + + def __format__(self, fmt_str: str, /) -> str: ... + def __eq__(self, x: object, /) -> bool: ... + def __ne__(self, x: object, /) -> bool: ... + def __neg__(self: _Self, /) -> _Self: ... + def __pos__(self: _Self, /) -> _Self: ... + def __add__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __sub__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __mul__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __truediv__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __floordiv__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __mod__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __divmod__(self: _Self, x: _AnyOther, /) -> _Tuple2[_Self]: ... + def __pow__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __radd__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rsub__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rmul__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rtruediv__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rfloordiv__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rmod__(self: _Self, x: _AnyOther, /) -> _Self: ... + def __rdivmod__(self: _Self, x: _AnyOther, /) -> _Tuple2[_Self]: ... + def __len__(self, /) -> int: ... + def __iter__(self, /) -> Iterator[np.inexact[Any] | object]: ... + def __getstate__(self, /) -> dict[str, Any]: ... + def __setstate__(self, dict: dict[str, Any], /) -> None: ... + + def has_samecoef(self, /, other: ABCPolyBase) -> bool: ... + def has_samedomain(self, /, other: ABCPolyBase) -> bool: ... + def has_samewindow(self, /, other: ABCPolyBase) -> bool: ... + @overload + def has_sametype(self: _Self, /, other: ABCPolyBase) -> TypeGuard[_Self]: ... + @overload + def has_sametype(self, /, other: object) -> Literal[False]: ... + + def copy(self: _Self, /) -> _Self: ... + def degree(self, /) -> int: ... + def cutdeg(self: _Self, /) -> _Self: ... + def trim(self: _Self, /, tol: _FloatLike_co = ...) -> _Self: ... + def truncate(self: _Self, /, size: _AnyInt) -> _Self: ... + + @overload + def convert( + self, + domain: None | _SeriesLikeCoef_co, + kind: type[_Other], + /, + window: None | _SeriesLikeCoef_co = ..., + ) -> _Other: ... + @overload + def convert( + self, + /, + domain: None | _SeriesLikeCoef_co = ..., + *, + kind: type[_Other], + window: None | _SeriesLikeCoef_co = ..., + ) -> _Other: ... + @overload + def convert( + self: _Self, + /, + domain: None | _SeriesLikeCoef_co = ..., + kind: None | type[_Self] = ..., + window: None | _SeriesLikeCoef_co = ..., + ) -> _Self: ... + + def mapparms(self, /) -> _Tuple2[Any]: ... + + def integ( + self: _Self, /, + m: SupportsIndex = ..., + k: _CoefLike_co | _SeriesLikeCoef_co = ..., + lbnd: None | _CoefLike_co = ..., + ) -> _Self: ... + + def deriv(self: _Self, /, m: SupportsIndex = ...) -> _Self: ... + + def roots(self, /) -> _CoefSeries: ... + + def linspace( + self, /, + n: SupportsIndex = ..., + domain: None | _SeriesLikeCoef_co = ..., + ) -> _Tuple2[_Series[np.float64 | np.complex128]]: ... + + @overload + @classmethod + def fit( + cls: type[_Self], /, + x: _SeriesLikeCoef_co, + y: _SeriesLikeCoef_co, + deg: int | _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co = ..., + rcond: _FloatLike_co = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> _Self: ... + @overload + @classmethod + def fit( + cls: type[_Self], /, + x: _SeriesLikeCoef_co, + y: _SeriesLikeCoef_co, + deg: int | _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co = ..., + rcond: _FloatLike_co = ..., + *, + full: Literal[True], + w: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> tuple[_Self, Sequence[np.inexact[Any] | np.int32]]: ... + @overload + @classmethod + def fit( + cls: type[_Self], + x: _SeriesLikeCoef_co, + y: _SeriesLikeCoef_co, + deg: int | _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co, + rcond: _FloatLike_co, + full: Literal[True], /, + w: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> tuple[_Self, Sequence[np.inexact[Any] | np.int32]]: ... + + @classmethod + def fromroots( + cls: type[_Self], /, + roots: _ArrayLikeCoef_co, + domain: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> _Self: ... + + @classmethod + def identity( + cls: type[_Self], /, + domain: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> _Self: ... + + @classmethod + def basis( + cls: type[_Self], /, + deg: _AnyInt, + domain: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + symbol: str = ..., + ) -> _Self: ... + + @classmethod + def cast( + cls: type[_Self], /, + series: ABCPolyBase, + domain: None | _SeriesLikeCoef_co = ..., + window: None | _SeriesLikeCoef_co = ..., + ) -> _Self: ... + + @classmethod + def _str_term_unicode(cls, /, i: str, arg_str: str) -> str: ... + @staticmethod + def _str_term_ascii(i: str, arg_str: str) -> str: ... + @staticmethod + def _repr_latex_term(i: str, arg_str: str, needs_parens: bool) -> str: ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/_polytypes.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/_polytypes.pyi new file mode 100644 index 0000000000000000000000000000000000000000..b0794eb61831d396c339d54f34dc43c1554657b9 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/_polytypes.pyi @@ -0,0 +1,888 @@ +from collections.abc import Callable, Sequence +from typing import ( + Any, + Literal, + NoReturn, + Protocol, + SupportsIndex, + SupportsInt, + TypeAlias, + overload, + type_check_only, +) + +import numpy as np +import numpy.typing as npt +from numpy._typing import ( + # array-likes + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, + _ArrayLikeNumber_co, + _ArrayLikeObject_co, + _NestedSequence, + _SupportsArray, + + # scalar-likes + _IntLike_co, + _FloatLike_co, + _ComplexLike_co, + _NumberLike_co, +) + +from typing_extensions import LiteralString, TypeVar + + +_T = TypeVar("_T") +_T_contra = TypeVar("_T_contra", contravariant=True) +_Self = TypeVar("_Self") +_SCT = TypeVar("_SCT", bound=np.number[Any] | np.bool | np.object_) + +# compatible with e.g. int, float, complex, Decimal, Fraction, and ABCPolyBase +@type_check_only +class _SupportsCoefOps(Protocol[_T_contra]): + def __eq__(self, x: object, /) -> bool: ... + def __ne__(self, x: object, /) -> bool: ... + + def __neg__(self: _Self, /) -> _Self: ... + def __pos__(self: _Self, /) -> _Self: ... + + def __add__(self: _Self, x: _T_contra, /) -> _Self: ... + def __sub__(self: _Self, x: _T_contra, /) -> _Self: ... + def __mul__(self: _Self, x: _T_contra, /) -> _Self: ... + def __pow__(self: _Self, x: _T_contra, /) -> _Self | float: ... + + def __radd__(self: _Self, x: _T_contra, /) -> _Self: ... + def __rsub__(self: _Self, x: _T_contra, /) -> _Self: ... + def __rmul__(self: _Self, x: _T_contra, /) -> _Self: ... + +_Series: TypeAlias = np.ndarray[tuple[int], np.dtype[_SCT]] + +_FloatSeries: TypeAlias = _Series[np.floating[Any]] +_ComplexSeries: TypeAlias = _Series[np.complexfloating[Any, Any]] +_ObjectSeries: TypeAlias = _Series[np.object_] +_CoefSeries: TypeAlias = _Series[np.inexact[Any] | np.object_] + +_FloatArray: TypeAlias = npt.NDArray[np.floating[Any]] +_ComplexArray: TypeAlias = npt.NDArray[np.complexfloating[Any, Any]] +_ObjectArray: TypeAlias = npt.NDArray[np.object_] +_CoefArray: TypeAlias = npt.NDArray[np.inexact[Any] | np.object_] + +_Tuple2: TypeAlias = tuple[_T, _T] +_Array1: TypeAlias = np.ndarray[tuple[Literal[1]], np.dtype[_SCT]] +_Array2: TypeAlias = np.ndarray[tuple[Literal[2]], np.dtype[_SCT]] + +_AnyInt: TypeAlias = SupportsInt | SupportsIndex + +_CoefObjectLike_co: TypeAlias = np.object_ | _SupportsCoefOps[Any] +_CoefLike_co: TypeAlias = _NumberLike_co | _CoefObjectLike_co + +# The term "series" is used here to refer to 1-d arrays of numeric scalars. +_SeriesLikeBool_co: TypeAlias = ( + _SupportsArray[np.dtype[np.bool]] + | Sequence[bool | np.bool] +) +_SeriesLikeInt_co: TypeAlias = ( + _SupportsArray[np.dtype[np.integer[Any] | np.bool]] + | Sequence[_IntLike_co] +) +_SeriesLikeFloat_co: TypeAlias = ( + _SupportsArray[np.dtype[np.floating[Any] | np.integer[Any] | np.bool]] + | Sequence[_FloatLike_co] +) +_SeriesLikeComplex_co: TypeAlias = ( + _SupportsArray[np.dtype[np.inexact[Any] | np.integer[Any] | np.bool]] + | Sequence[_ComplexLike_co] +) +_SeriesLikeObject_co: TypeAlias = ( + _SupportsArray[np.dtype[np.object_]] + | Sequence[_CoefObjectLike_co] +) +_SeriesLikeCoef_co: TypeAlias = ( + _SupportsArray[np.dtype[np.number[Any] | np.bool | np.object_]] + | Sequence[_CoefLike_co] +) + +_ArrayLikeCoefObject_co: TypeAlias = ( + _CoefObjectLike_co + | _SeriesLikeObject_co + | _NestedSequence[_SeriesLikeObject_co] +) +_ArrayLikeCoef_co: TypeAlias = ( + npt.NDArray[np.number[Any] | np.bool | np.object_] + | _ArrayLikeNumber_co + | _ArrayLikeCoefObject_co +) + +_Name_co = TypeVar("_Name_co", bound=LiteralString, covariant=True, default=LiteralString) + +@type_check_only +class _Named(Protocol[_Name_co]): + @property + def __name__(self, /) -> _Name_co: ... + +_Line: TypeAlias = np.ndarray[tuple[Literal[1, 2]], np.dtype[_SCT]] + +@type_check_only +class _FuncLine(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__(self, /, off: _SCT, scl: _SCT) -> _Line[_SCT]: ... + @overload + def __call__(self, /, off: int, scl: int) -> _Line[np.int_] : ... + @overload + def __call__(self, /, off: float, scl: float) -> _Line[np.float64]: ... + @overload + def __call__( + self, + /, + off: complex, + scl: complex, + ) -> _Line[np.complex128]: ... + @overload + def __call__( + self, + /, + off: _SupportsCoefOps[Any], + scl: _SupportsCoefOps[Any], + ) -> _Line[np.object_]: ... + +@type_check_only +class _FuncFromRoots(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__(self, /, roots: _SeriesLikeFloat_co) -> _FloatSeries: ... + @overload + def __call__(self, /, roots: _SeriesLikeComplex_co) -> _ComplexSeries: ... + @overload + def __call__(self, /, roots: _SeriesLikeCoef_co) -> _ObjectSeries: ... + +@type_check_only +class _FuncBinOp(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c1: _SeriesLikeBool_co, + c2: _SeriesLikeBool_co, + ) -> NoReturn: ... + @overload + def __call__( + self, + /, + c1: _SeriesLikeFloat_co, + c2: _SeriesLikeFloat_co, + ) -> _FloatSeries: ... + @overload + def __call__( + self, + /, + c1: _SeriesLikeComplex_co, + c2: _SeriesLikeComplex_co, + ) -> _ComplexSeries: ... + @overload + def __call__( + self, + /, + c1: _SeriesLikeCoef_co, + c2: _SeriesLikeCoef_co, + ) -> _ObjectSeries: ... + +@type_check_only +class _FuncUnOp(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__(self, /, c: _SeriesLikeFloat_co) -> _FloatSeries: ... + @overload + def __call__(self, /, c: _SeriesLikeComplex_co) -> _ComplexSeries: ... + @overload + def __call__(self, /, c: _SeriesLikeCoef_co) -> _ObjectSeries: ... + +@type_check_only +class _FuncPoly2Ortho(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__(self, /, pol: _SeriesLikeFloat_co) -> _FloatSeries: ... + @overload + def __call__(self, /, pol: _SeriesLikeComplex_co) -> _ComplexSeries: ... + @overload + def __call__(self, /, pol: _SeriesLikeCoef_co) -> _ObjectSeries: ... + +@type_check_only +class _FuncPow(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _SeriesLikeFloat_co, + pow: _IntLike_co, + maxpower: None | _IntLike_co = ..., + ) -> _FloatSeries: ... + @overload + def __call__( + self, + /, + c: _SeriesLikeComplex_co, + pow: _IntLike_co, + maxpower: None | _IntLike_co = ..., + ) -> _ComplexSeries: ... + @overload + def __call__( + self, + /, + c: _SeriesLikeCoef_co, + pow: _IntLike_co, + maxpower: None | _IntLike_co = ..., + ) -> _ObjectSeries: ... + +@type_check_only +class _FuncDer(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _ArrayLikeFloat_co, + m: SupportsIndex = ..., + scl: _FloatLike_co = ..., + axis: SupportsIndex = ..., + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + c: _ArrayLikeComplex_co, + m: SupportsIndex = ..., + scl: _ComplexLike_co = ..., + axis: SupportsIndex = ..., + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + c: _ArrayLikeCoef_co, + m: SupportsIndex = ..., + scl: _CoefLike_co = ..., + axis: SupportsIndex = ..., + ) -> _ObjectArray: ... + +@type_check_only +class _FuncInteg(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _ArrayLikeFloat_co, + m: SupportsIndex = ..., + k: _FloatLike_co | _SeriesLikeFloat_co = ..., + lbnd: _FloatLike_co = ..., + scl: _FloatLike_co = ..., + axis: SupportsIndex = ..., + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + c: _ArrayLikeComplex_co, + m: SupportsIndex = ..., + k: _ComplexLike_co | _SeriesLikeComplex_co = ..., + lbnd: _ComplexLike_co = ..., + scl: _ComplexLike_co = ..., + axis: SupportsIndex = ..., + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + c: _ArrayLikeCoef_co, + m: SupportsIndex = ..., + k: _CoefLike_co | _SeriesLikeCoef_co = ..., + lbnd: _CoefLike_co = ..., + scl: _CoefLike_co = ..., + axis: SupportsIndex = ..., + ) -> _ObjectArray: ... + +@type_check_only +class _FuncValFromRoots(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _FloatLike_co, + r: _FloatLike_co, + tensor: bool = ..., + ) -> np.floating[Any]: ... + @overload + def __call__( + self, + /, + x: _NumberLike_co, + r: _NumberLike_co, + tensor: bool = ..., + ) -> np.complexfloating[Any, Any]: ... + @overload + def __call__( + self, + /, + x: _FloatLike_co | _ArrayLikeFloat_co, + r: _ArrayLikeFloat_co, + tensor: bool = ..., + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _NumberLike_co | _ArrayLikeComplex_co, + r: _ArrayLikeComplex_co, + tensor: bool = ..., + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _CoefLike_co | _ArrayLikeCoef_co, + r: _ArrayLikeCoef_co, + tensor: bool = ..., + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: _CoefLike_co, + r: _CoefLike_co, + tensor: bool = ..., + ) -> _SupportsCoefOps[Any]: ... + +@type_check_only +class _FuncVal(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _FloatLike_co, + c: _SeriesLikeFloat_co, + tensor: bool = ..., + ) -> np.floating[Any]: ... + @overload + def __call__( + self, + /, + x: _NumberLike_co, + c: _SeriesLikeComplex_co, + tensor: bool = ..., + ) -> np.complexfloating[Any, Any]: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + c: _ArrayLikeFloat_co, + tensor: bool = ..., + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + c: _ArrayLikeComplex_co, + tensor: bool = ..., + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + c: _ArrayLikeCoef_co, + tensor: bool = ..., + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: _CoefLike_co, + c: _SeriesLikeObject_co, + tensor: bool = ..., + ) -> _SupportsCoefOps[Any]: ... + +@type_check_only +class _FuncVal2D(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _FloatLike_co, + y: _FloatLike_co, + c: _SeriesLikeFloat_co, + ) -> np.floating[Any]: ... + @overload + def __call__( + self, + /, + x: _NumberLike_co, + y: _NumberLike_co, + c: _SeriesLikeComplex_co, + ) -> np.complexfloating[Any, Any]: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + y: _ArrayLikeFloat_co, + c: _ArrayLikeFloat_co, + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + y: _ArrayLikeComplex_co, + c: _ArrayLikeComplex_co, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + y: _ArrayLikeCoef_co, + c: _ArrayLikeCoef_co, + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: _CoefLike_co, + y: _CoefLike_co, + c: _SeriesLikeCoef_co, + ) -> _SupportsCoefOps[Any]: ... + +@type_check_only +class _FuncVal3D(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _FloatLike_co, + y: _FloatLike_co, + z: _FloatLike_co, + c: _SeriesLikeFloat_co + ) -> np.floating[Any]: ... + @overload + def __call__( + self, + /, + x: _NumberLike_co, + y: _NumberLike_co, + z: _NumberLike_co, + c: _SeriesLikeComplex_co, + ) -> np.complexfloating[Any, Any]: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + y: _ArrayLikeFloat_co, + z: _ArrayLikeFloat_co, + c: _ArrayLikeFloat_co, + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + y: _ArrayLikeComplex_co, + z: _ArrayLikeComplex_co, + c: _ArrayLikeComplex_co, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + y: _ArrayLikeCoef_co, + z: _ArrayLikeCoef_co, + c: _ArrayLikeCoef_co, + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: _CoefLike_co, + y: _CoefLike_co, + z: _CoefLike_co, + c: _SeriesLikeCoef_co, + ) -> _SupportsCoefOps[Any]: ... + +_AnyValF: TypeAlias = Callable[ + [npt.ArrayLike, npt.ArrayLike, bool], + _CoefArray, +] + +@type_check_only +class _FuncValND(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + val_f: _AnyValF, + c: _SeriesLikeFloat_co, + /, + *args: _FloatLike_co, + ) -> np.floating[Any]: ... + @overload + def __call__( + self, + val_f: _AnyValF, + c: _SeriesLikeComplex_co, + /, + *args: _NumberLike_co, + ) -> np.complexfloating[Any, Any]: ... + @overload + def __call__( + self, + val_f: _AnyValF, + c: _ArrayLikeFloat_co, + /, + *args: _ArrayLikeFloat_co, + ) -> _FloatArray: ... + @overload + def __call__( + self, + val_f: _AnyValF, + c: _ArrayLikeComplex_co, + /, + *args: _ArrayLikeComplex_co, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + val_f: _AnyValF, + c: _SeriesLikeObject_co, + /, + *args: _CoefObjectLike_co, + ) -> _SupportsCoefOps[Any]: ... + @overload + def __call__( + self, + val_f: _AnyValF, + c: _ArrayLikeCoef_co, + /, + *args: _ArrayLikeCoef_co, + ) -> _ObjectArray: ... + +@type_check_only +class _FuncVander(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + deg: SupportsIndex, + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + deg: SupportsIndex, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + deg: SupportsIndex, + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: npt.ArrayLike, + deg: SupportsIndex, + ) -> _CoefArray: ... + +_AnyDegrees: TypeAlias = Sequence[SupportsIndex] + +@type_check_only +class _FuncVander2D(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + y: _ArrayLikeFloat_co, + deg: _AnyDegrees, + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + y: _ArrayLikeComplex_co, + deg: _AnyDegrees, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + y: _ArrayLikeCoef_co, + deg: _AnyDegrees, + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: npt.ArrayLike, + y: npt.ArrayLike, + deg: _AnyDegrees, + ) -> _CoefArray: ... + +@type_check_only +class _FuncVander3D(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _ArrayLikeFloat_co, + y: _ArrayLikeFloat_co, + z: _ArrayLikeFloat_co, + deg: _AnyDegrees, + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeComplex_co, + y: _ArrayLikeComplex_co, + z: _ArrayLikeComplex_co, + deg: _AnyDegrees, + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + x: _ArrayLikeCoef_co, + y: _ArrayLikeCoef_co, + z: _ArrayLikeCoef_co, + deg: _AnyDegrees, + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + x: npt.ArrayLike, + y: npt.ArrayLike, + z: npt.ArrayLike, + deg: _AnyDegrees, + ) -> _CoefArray: ... + +# keep in sync with the broadest overload of `._FuncVander` +_AnyFuncVander: TypeAlias = Callable[ + [npt.ArrayLike, SupportsIndex], + _CoefArray, +] + +@type_check_only +class _FuncVanderND(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + vander_fs: Sequence[_AnyFuncVander], + points: Sequence[_ArrayLikeFloat_co], + degrees: Sequence[SupportsIndex], + ) -> _FloatArray: ... + @overload + def __call__( + self, + /, + vander_fs: Sequence[_AnyFuncVander], + points: Sequence[_ArrayLikeComplex_co], + degrees: Sequence[SupportsIndex], + ) -> _ComplexArray: ... + @overload + def __call__( + self, + /, + vander_fs: Sequence[_AnyFuncVander], + points: Sequence[ + _ArrayLikeObject_co | _ArrayLikeComplex_co, + ], + degrees: Sequence[SupportsIndex], + ) -> _ObjectArray: ... + @overload + def __call__( + self, + /, + vander_fs: Sequence[_AnyFuncVander], + points: Sequence[npt.ArrayLike], + degrees: Sequence[SupportsIndex], + ) -> _CoefArray: ... + +_FullFitResult: TypeAlias = Sequence[np.inexact[Any] | np.int32] + +@type_check_only +class _FuncFit(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + x: _SeriesLikeFloat_co, + y: _ArrayLikeFloat_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeFloat_co = ..., + ) -> _FloatArray: ... + @overload + def __call__( + self, + x: _SeriesLikeFloat_co, + y: _ArrayLikeFloat_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float, + full: Literal[True], + /, + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_FloatArray, _FullFitResult]: ... + @overload + def __call__( + self, + /, + x: _SeriesLikeFloat_co, + y: _ArrayLikeFloat_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + *, + full: Literal[True], + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_FloatArray, _FullFitResult]: ... + + @overload + def __call__( + self, + /, + x: _SeriesLikeComplex_co, + y: _ArrayLikeComplex_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeFloat_co = ..., + ) -> _ComplexArray: ... + @overload + def __call__( + self, + x: _SeriesLikeComplex_co, + y: _ArrayLikeComplex_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float, + full: Literal[True], + /, + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_ComplexArray, _FullFitResult]: ... + @overload + def __call__( + self, + /, + x: _SeriesLikeComplex_co, + y: _ArrayLikeComplex_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + *, + full: Literal[True], + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_ComplexArray, _FullFitResult]: ... + + @overload + def __call__( + self, + /, + x: _SeriesLikeComplex_co, + y: _ArrayLikeCoef_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeFloat_co = ..., + ) -> _ObjectArray: ... + @overload + def __call__( + self, + x: _SeriesLikeComplex_co, + y: _ArrayLikeCoef_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float, + full: Literal[True], + /, + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_ObjectArray, _FullFitResult]: ... + @overload + def __call__( + self, + /, + x: _SeriesLikeComplex_co, + y: _ArrayLikeCoef_co, + deg: int | _SeriesLikeInt_co, + rcond: None | float = ..., + *, + full: Literal[True], + w: None | _SeriesLikeFloat_co = ..., + ) -> tuple[_ObjectArray, _FullFitResult]: ... + +@type_check_only +class _FuncRoots(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _SeriesLikeFloat_co, + ) -> _Series[np.float64]: ... + @overload + def __call__( + self, + /, + c: _SeriesLikeComplex_co, + ) -> _Series[np.complex128]: ... + @overload + def __call__(self, /, c: _SeriesLikeCoef_co) -> _ObjectSeries: ... + + +_Companion: TypeAlias = np.ndarray[tuple[int, int], np.dtype[_SCT]] + +@type_check_only +class _FuncCompanion(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _SeriesLikeFloat_co, + ) -> _Companion[np.float64]: ... + @overload + def __call__( + self, + /, + c: _SeriesLikeComplex_co, + ) -> _Companion[np.complex128]: ... + @overload + def __call__(self, /, c: _SeriesLikeCoef_co) -> _Companion[np.object_]: ... + +@type_check_only +class _FuncGauss(_Named[_Name_co], Protocol[_Name_co]): + def __call__( + self, + /, + deg: SupportsIndex, + ) -> _Tuple2[_Series[np.float64]]: ... + +@type_check_only +class _FuncWeight(_Named[_Name_co], Protocol[_Name_co]): + @overload + def __call__( + self, + /, + c: _ArrayLikeFloat_co, + ) -> npt.NDArray[np.float64]: ... + @overload + def __call__( + self, + /, + c: _ArrayLikeComplex_co, + ) -> npt.NDArray[np.complex128]: ... + @overload + def __call__(self, /, c: _ArrayLikeCoef_co) -> _ObjectArray: ... + +@type_check_only +class _FuncPts(_Named[_Name_co], Protocol[_Name_co]): + def __call__(self, /, npts: _AnyInt) -> _Series[np.float64]: ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.py b/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.py new file mode 100644 index 0000000000000000000000000000000000000000..837847e45110a9cf5cf202c496c68c5e437c4e67 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.py @@ -0,0 +1,2003 @@ +""" +==================================================== +Chebyshev Series (:mod:`numpy.polynomial.chebyshev`) +==================================================== + +This module provides a number of objects (mostly functions) useful for +dealing with Chebyshev series, including a `Chebyshev` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with such polynomials is in the +docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- + +.. autosummary:: + :toctree: generated/ + + Chebyshev + + +Constants +--------- + +.. autosummary:: + :toctree: generated/ + + chebdomain + chebzero + chebone + chebx + +Arithmetic +---------- + +.. autosummary:: + :toctree: generated/ + + chebadd + chebsub + chebmulx + chebmul + chebdiv + chebpow + chebval + chebval2d + chebval3d + chebgrid2d + chebgrid3d + +Calculus +-------- + +.. autosummary:: + :toctree: generated/ + + chebder + chebint + +Misc Functions +-------------- + +.. autosummary:: + :toctree: generated/ + + chebfromroots + chebroots + chebvander + chebvander2d + chebvander3d + chebgauss + chebweight + chebcompanion + chebfit + chebpts1 + chebpts2 + chebtrim + chebline + cheb2poly + poly2cheb + chebinterpolate + +See also +-------- +`numpy.polynomial` + +Notes +----- +The implementations of multiplication, division, integration, and +differentiation use the algebraic identities [1]_: + +.. math:: + T_n(x) = \\frac{z^n + z^{-n}}{2} \\\\ + z\\frac{dx}{dz} = \\frac{z - z^{-1}}{2}. + +where + +.. math:: x = \\frac{z + z^{-1}}{2}. + +These identities allow a Chebyshev series to be expressed as a finite, +symmetric Laurent series. In this module, this sort of Laurent series +is referred to as a "z-series." + +References +---------- +.. [1] A. T. Benjamin, et al., "Combinatorial Trigonometry with Chebyshev + Polynomials," *Journal of Statistical Planning and Inference 14*, 2008 + (https://web.archive.org/web/20080221202153/https://www.math.hmc.edu/~benjamin/papers/CombTrig.pdf, pg. 4) + +""" +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +__all__ = [ + 'chebzero', 'chebone', 'chebx', 'chebdomain', 'chebline', 'chebadd', + 'chebsub', 'chebmulx', 'chebmul', 'chebdiv', 'chebpow', 'chebval', + 'chebder', 'chebint', 'cheb2poly', 'poly2cheb', 'chebfromroots', + 'chebvander', 'chebfit', 'chebtrim', 'chebroots', 'chebpts1', + 'chebpts2', 'Chebyshev', 'chebval2d', 'chebval3d', 'chebgrid2d', + 'chebgrid3d', 'chebvander2d', 'chebvander3d', 'chebcompanion', + 'chebgauss', 'chebweight', 'chebinterpolate'] + +chebtrim = pu.trimcoef + +# +# A collection of functions for manipulating z-series. These are private +# functions and do minimal error checking. +# + +def _cseries_to_zseries(c): + """Convert Chebyshev series to z-series. + + Convert a Chebyshev series to the equivalent z-series. The result is + never an empty array. The dtype of the return is the same as that of + the input. No checks are run on the arguments as this routine is for + internal use. + + Parameters + ---------- + c : 1-D ndarray + Chebyshev coefficients, ordered from low to high + + Returns + ------- + zs : 1-D ndarray + Odd length symmetric z-series, ordered from low to high. + + """ + n = c.size + zs = np.zeros(2*n-1, dtype=c.dtype) + zs[n-1:] = c/2 + return zs + zs[::-1] + + +def _zseries_to_cseries(zs): + """Convert z-series to a Chebyshev series. + + Convert a z series to the equivalent Chebyshev series. The result is + never an empty array. The dtype of the return is the same as that of + the input. No checks are run on the arguments as this routine is for + internal use. + + Parameters + ---------- + zs : 1-D ndarray + Odd length symmetric z-series, ordered from low to high. + + Returns + ------- + c : 1-D ndarray + Chebyshev coefficients, ordered from low to high. + + """ + n = (zs.size + 1)//2 + c = zs[n-1:].copy() + c[1:n] *= 2 + return c + + +def _zseries_mul(z1, z2): + """Multiply two z-series. + + Multiply two z-series to produce a z-series. + + Parameters + ---------- + z1, z2 : 1-D ndarray + The arrays must be 1-D but this is not checked. + + Returns + ------- + product : 1-D ndarray + The product z-series. + + Notes + ----- + This is simply convolution. If symmetric/anti-symmetric z-series are + denoted by S/A then the following rules apply: + + S*S, A*A -> S + S*A, A*S -> A + + """ + return np.convolve(z1, z2) + + +def _zseries_div(z1, z2): + """Divide the first z-series by the second. + + Divide `z1` by `z2` and return the quotient and remainder as z-series. + Warning: this implementation only applies when both z1 and z2 have the + same symmetry, which is sufficient for present purposes. + + Parameters + ---------- + z1, z2 : 1-D ndarray + The arrays must be 1-D and have the same symmetry, but this is not + checked. + + Returns + ------- + + (quotient, remainder) : 1-D ndarrays + Quotient and remainder as z-series. + + Notes + ----- + This is not the same as polynomial division on account of the desired form + of the remainder. If symmetric/anti-symmetric z-series are denoted by S/A + then the following rules apply: + + S/S -> S,S + A/A -> S,A + + The restriction to types of the same symmetry could be fixed but seems like + unneeded generality. There is no natural form for the remainder in the case + where there is no symmetry. + + """ + z1 = z1.copy() + z2 = z2.copy() + lc1 = len(z1) + lc2 = len(z2) + if lc2 == 1: + z1 /= z2 + return z1, z1[:1]*0 + elif lc1 < lc2: + return z1[:1]*0, z1 + else: + dlen = lc1 - lc2 + scl = z2[0] + z2 /= scl + quo = np.empty(dlen + 1, dtype=z1.dtype) + i = 0 + j = dlen + while i < j: + r = z1[i] + quo[i] = z1[i] + quo[dlen - i] = r + tmp = r*z2 + z1[i:i+lc2] -= tmp + z1[j:j+lc2] -= tmp + i += 1 + j -= 1 + r = z1[i] + quo[i] = r + tmp = r*z2 + z1[i:i+lc2] -= tmp + quo /= scl + rem = z1[i+1:i-1+lc2].copy() + return quo, rem + + +def _zseries_der(zs): + """Differentiate a z-series. + + The derivative is with respect to x, not z. This is achieved using the + chain rule and the value of dx/dz given in the module notes. + + Parameters + ---------- + zs : z-series + The z-series to differentiate. + + Returns + ------- + derivative : z-series + The derivative + + Notes + ----- + The zseries for x (ns) has been multiplied by two in order to avoid + using floats that are incompatible with Decimal and likely other + specialized scalar types. This scaling has been compensated by + multiplying the value of zs by two also so that the two cancels in the + division. + + """ + n = len(zs)//2 + ns = np.array([-1, 0, 1], dtype=zs.dtype) + zs *= np.arange(-n, n+1)*2 + d, r = _zseries_div(zs, ns) + return d + + +def _zseries_int(zs): + """Integrate a z-series. + + The integral is with respect to x, not z. This is achieved by a change + of variable using dx/dz given in the module notes. + + Parameters + ---------- + zs : z-series + The z-series to integrate + + Returns + ------- + integral : z-series + The indefinite integral + + Notes + ----- + The zseries for x (ns) has been multiplied by two in order to avoid + using floats that are incompatible with Decimal and likely other + specialized scalar types. This scaling has been compensated by + dividing the resulting zs by two. + + """ + n = 1 + len(zs)//2 + ns = np.array([-1, 0, 1], dtype=zs.dtype) + zs = _zseries_mul(zs, ns) + div = np.arange(-n, n+1)*2 + zs[:n] /= div[:n] + zs[n+1:] /= div[n+1:] + zs[n] = 0 + return zs + +# +# Chebyshev series functions +# + + +def poly2cheb(pol): + """ + Convert a polynomial to a Chebyshev series. + + Convert an array representing the coefficients of a polynomial (relative + to the "standard" basis) ordered from lowest degree to highest, to an + array of the coefficients of the equivalent Chebyshev series, ordered + from lowest to highest degree. + + Parameters + ---------- + pol : array_like + 1-D array containing the polynomial coefficients + + Returns + ------- + c : ndarray + 1-D array containing the coefficients of the equivalent Chebyshev + series. + + See Also + -------- + cheb2poly + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy import polynomial as P + >>> p = P.Polynomial(range(4)) + >>> p + Polynomial([0., 1., 2., 3.], domain=[-1., 1.], window=[-1., 1.], symbol='x') + >>> c = p.convert(kind=P.Chebyshev) + >>> c + Chebyshev([1. , 3.25, 1. , 0.75], domain=[-1., 1.], window=[-1., ... + >>> P.chebyshev.poly2cheb(range(4)) + array([1. , 3.25, 1. , 0.75]) + + """ + [pol] = pu.as_series([pol]) + deg = len(pol) - 1 + res = 0 + for i in range(deg, -1, -1): + res = chebadd(chebmulx(res), pol[i]) + return res + + +def cheb2poly(c): + """ + Convert a Chebyshev series to a polynomial. + + Convert an array representing the coefficients of a Chebyshev series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Chebyshev series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2cheb + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy import polynomial as P + >>> c = P.Chebyshev(range(4)) + >>> c + Chebyshev([0., 1., 2., 3.], domain=[-1., 1.], window=[-1., 1.], symbol='x') + >>> p = c.convert(kind=P.Polynomial) + >>> p + Polynomial([-2., -8., 4., 12.], domain=[-1., 1.], window=[-1., 1.], ... + >>> P.chebyshev.cheb2poly(range(4)) + array([-2., -8., 4., 12.]) + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n < 3: + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], c1) + c1 = polyadd(tmp, polymulx(c1)*2) + return polyadd(c0, polymulx(c1)) + + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Chebyshev default domain. +chebdomain = np.array([-1., 1.]) + +# Chebyshev coefficients representing zero. +chebzero = np.array([0]) + +# Chebyshev coefficients representing one. +chebone = np.array([1]) + +# Chebyshev coefficients representing the identity x. +chebx = np.array([0, 1]) + + +def chebline(off, scl): + """ + Chebyshev series whose graph is a straight line. + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Chebyshev series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.legendre.legline + numpy.polynomial.laguerre.lagline + numpy.polynomial.hermite.hermline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> import numpy.polynomial.chebyshev as C + >>> C.chebline(3,2) + array([3, 2]) + >>> C.chebval(-3, C.chebline(3,2)) # should be -3 + -3.0 + + """ + if scl != 0: + return np.array([off, scl]) + else: + return np.array([off]) + + +def chebfromroots(roots): + """ + Generate a Chebyshev series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in Chebyshev form, where the :math:`r_n` are the roots specified in + `roots`. If a zero has multiplicity n, then it must appear in `roots` + n times. For instance, if 2 is a root of multiplicity three and 3 is a + root of multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. + The roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in Chebyshev form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.laguerre.lagfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.hermite_e.hermefromroots + + Examples + -------- + >>> import numpy.polynomial.chebyshev as C + >>> C.chebfromroots((-1,0,1)) # x^3 - x relative to the standard basis + array([ 0. , -0.25, 0. , 0.25]) + >>> j = complex(0,1) + >>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis + array([1.5+0.j, 0. +0.j, 0.5+0.j]) + + """ + return pu._fromroots(chebline, chebmul, roots) + + +def chebadd(c1, c2): + """ + Add one Chebyshev series to another. + + Returns the sum of two Chebyshev series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``T_0 + 2*T_1 + 3*T_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Chebyshev series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Chebyshev series of their sum. + + See Also + -------- + chebsub, chebmulx, chebmul, chebdiv, chebpow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Chebyshev series + is a Chebyshev series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> C.chebadd(c1,c2) + array([4., 4., 4.]) + + """ + return pu._add(c1, c2) + + +def chebsub(c1, c2): + """ + Subtract one Chebyshev series from another. + + Returns the difference of two Chebyshev series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``T_0 + 2*T_1 + 3*T_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Chebyshev series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Chebyshev series coefficients representing their difference. + + See Also + -------- + chebadd, chebmulx, chebmul, chebdiv, chebpow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Chebyshev + series is a Chebyshev series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> C.chebsub(c1,c2) + array([-2., 0., 2.]) + >>> C.chebsub(c2,c1) # -C.chebsub(c1,c2) + array([ 2., 0., -2.]) + + """ + return pu._sub(c1, c2) + + +def chebmulx(c): + """Multiply a Chebyshev series by x. + + Multiply the polynomial `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Chebyshev series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + chebadd, chebsub, chebmul, chebdiv, chebpow + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> C.chebmulx([1,2,3]) + array([1. , 2.5, 1. , 1.5]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0]*0 + prd[1] = c[0] + if len(c) > 1: + tmp = c[1:]/2 + prd[2:] = tmp + prd[0:-2] += tmp + return prd + + +def chebmul(c1, c2): + """ + Multiply one Chebyshev series by another. + + Returns the product of two Chebyshev series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``T_0 + 2*T_1 + 3*T_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Chebyshev series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Chebyshev series coefficients representing their product. + + See Also + -------- + chebadd, chebsub, chebmulx, chebdiv, chebpow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Chebyshev polynomial basis set. Thus, to express + the product as a C-series, it is typically necessary to "reproject" + the product onto said basis set, which typically produces + "unintuitive live" (but correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> C.chebmul(c1,c2) # multiplication requires "reprojection" + array([ 6.5, 12. , 12. , 4. , 1.5]) + + """ + # c1, c2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + z1 = _cseries_to_zseries(c1) + z2 = _cseries_to_zseries(c2) + prd = _zseries_mul(z1, z2) + ret = _zseries_to_cseries(prd) + return pu.trimseq(ret) + + +def chebdiv(c1, c2): + """ + Divide one Chebyshev series by another. + + Returns the quotient-with-remainder of two Chebyshev series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``T_0 + 2*T_1 + 3*T_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Chebyshev series coefficients ordered from low to + high. + + Returns + ------- + [quo, rem] : ndarrays + Of Chebyshev series coefficients representing the quotient and + remainder. + + See Also + -------- + chebadd, chebsub, chebmulx, chebmul, chebpow + + Notes + ----- + In general, the (polynomial) division of one C-series by another + results in quotient and remainder terms that are not in the Chebyshev + polynomial basis set. Thus, to express these results as C-series, it + is typically necessary to "reproject" the results onto said basis + set, which typically produces "unintuitive" (but correct) results; + see Examples section below. + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> C.chebdiv(c1,c2) # quotient "intuitive," remainder not + (array([3.]), array([-8., -4.])) + >>> c2 = (0,1,2,3) + >>> C.chebdiv(c2,c1) # neither "intuitive" + (array([0., 2.]), array([-2., -4.])) + + """ + # c1, c2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + if c2[-1] == 0: + raise ZeroDivisionError # FIXME: add message with details to exception + + # note: this is more efficient than `pu._div(chebmul, c1, c2)` + lc1 = len(c1) + lc2 = len(c2) + if lc1 < lc2: + return c1[:1]*0, c1 + elif lc2 == 1: + return c1/c2[-1], c1[:1]*0 + else: + z1 = _cseries_to_zseries(c1) + z2 = _cseries_to_zseries(c2) + quo, rem = _zseries_div(z1, z2) + quo = pu.trimseq(_zseries_to_cseries(quo)) + rem = pu.trimseq(_zseries_to_cseries(rem)) + return quo, rem + + +def chebpow(c, pow, maxpower=16): + """Raise a Chebyshev series to a power. + + Returns the Chebyshev series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``T_0 + 2*T_1 + 3*T_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Chebyshev series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Chebyshev series of power. + + See Also + -------- + chebadd, chebsub, chebmulx, chebmul, chebdiv + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> C.chebpow([1, 2, 3, 4], 2) + array([15.5, 22. , 16. , ..., 12.5, 12. , 8. ]) + + """ + # note: this is more efficient than `pu._pow(chebmul, c1, c2)`, as it + # avoids converting between z and c series repeatedly + + # c is a trimmed copy + [c] = pu.as_series([c]) + power = int(pow) + if power != pow or power < 0: + raise ValueError("Power must be a non-negative integer.") + elif maxpower is not None and power > maxpower: + raise ValueError("Power is too large") + elif power == 0: + return np.array([1], dtype=c.dtype) + elif power == 1: + return c + else: + # This can be made more efficient by using powers of two + # in the usual way. + zs = _cseries_to_zseries(c) + prd = zs + for i in range(2, power + 1): + prd = np.convolve(prd, zs) + return _zseries_to_cseries(prd) + + +def chebder(c, m=1, scl=1, axis=0): + """ + Differentiate a Chebyshev series. + + Returns the Chebyshev series coefficients `c` differentiated `m` times + along `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*T_0 + 2*T_1 + 3*T_2`` + while [[1,2],[1,2]] represents ``1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + + 2*T_0(x)*T_1(y) + 2*T_1(x)*T_1(y)`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + Array of Chebyshev series coefficients. If c is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Chebyshev series of the derivative. + + See Also + -------- + chebint + + Notes + ----- + In general, the result of differentiating a C-series needs to be + "reprojected" onto the C-series basis set. Thus, typically, the + result of this function is "unintuitive," albeit correct; see Examples + section below. + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c = (1,2,3,4) + >>> C.chebder(c) + array([14., 12., 24.]) + >>> C.chebder(c,3) + array([96.]) + >>> C.chebder(c,scl=-1) + array([-14., -12., -24.]) + >>> C.chebder(c,2,-1) + array([12., 96.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 2, -1): + der[j - 1] = (2*j)*c[j] + c[j - 2] += (j*c[j])/(j - 2) + if n > 1: + der[1] = 4*c[2] + der[0] = c[1] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Chebyshev series. + + Returns the Chebyshev series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``T_0 + 2*T_1 + 3*T_2`` while [[1,2],[1,2]] + represents ``1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + + 2*T_1(x)*T_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + Parameters + ---------- + c : array_like + Array of Chebyshev series coefficients. If c is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at zero + is the first value in the list, the value of the second integral + at zero is the second value, etc. If ``k == []`` (the default), + all constants are set to zero. If ``m == 1``, a single scalar can + be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + C-series coefficients of the integral. + + Raises + ------ + ValueError + If ``m < 1``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + chebder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a`- perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial import chebyshev as C + >>> c = (1,2,3) + >>> C.chebint(c) + array([ 0.5, -0.5, 0.5, 0.5]) + >>> C.chebint(c,3) + array([ 0.03125 , -0.1875 , 0.04166667, -0.05208333, 0.01041667, # may vary + 0.00625 ]) + >>> C.chebint(c, k=3) + array([ 3.5, -0.5, 0.5, 0.5]) + >>> C.chebint(c,lbnd=-2) + array([ 8.5, -0.5, 0.5, 0.5]) + >>> C.chebint(c,scl=-2) + array([-1., 1., -1., -1.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0]*0 + tmp[1] = c[0] + if n > 1: + tmp[2] = c[1]/4 + for j in range(2, n): + tmp[j + 1] = c[j]/(2*(j + 1)) + tmp[j - 1] -= c[j]/(2*(j - 1)) + tmp[0] += k[i] - chebval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def chebval(x, c, tensor=True): + """ + Evaluate a Chebyshev series at points x. + + If `c` is of length `n + 1`, this function returns the value: + + .. math:: p(x) = c_0 * T_0(x) + c_1 * T_1(x) + ... + c_n * T_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + chebval2d, chebgrid2d, chebval3d, chebgrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + x2 = 2*x + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + c0 = c[-i] - c1 + c1 = tmp + c1*x2 + return c0 + c1*x + + +def chebval2d(x, y, c): + """ + Evaluate a 2-D Chebyshev series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * T_i(x) * T_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than 2 the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Chebyshev series at points formed + from pairs of corresponding values from `x` and `y`. + + See Also + -------- + chebval, chebgrid2d, chebval3d, chebgrid3d + """ + return pu._valnd(chebval, c, x, y) + + +def chebgrid2d(x, y, c): + """ + Evaluate a 2-D Chebyshev series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * T_i(a) * T_j(b), + + where the points `(a, b)` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape + y.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j is contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Chebyshev series at points in the + Cartesian product of `x` and `y`. + + See Also + -------- + chebval, chebval2d, chebval3d, chebgrid3d + """ + return pu._gridnd(chebval, c, x, y) + + +def chebval3d(x, y, z, c): + """ + Evaluate a 3-D Chebyshev series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * T_i(x) * T_j(y) * T_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + ``(x, y, z)``, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + chebval, chebval2d, chebgrid2d, chebgrid3d + """ + return pu._valnd(chebval, c, x, y, z) + + +def chebgrid3d(x, y, z, c): + """ + Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * T_i(a) * T_j(b) * T_k(c) + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + chebval, chebval2d, chebgrid2d, chebval3d + """ + return pu._gridnd(chebval, c, x, y, z) + + +def chebvander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = T_i(x), + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the degree of the Chebyshev polynomial. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + matrix ``V = chebvander(x, n)``, then ``np.dot(V, c)`` and + ``chebval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of Chebyshev series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding Chebyshev polynomial. The dtype will be the same as + the converted `x`. + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + # Use forward recursion to generate the entries. + v[0] = x*0 + 1 + if ideg > 0: + x2 = 2*x + v[1] = x + for i in range(2, ideg + 1): + v[i] = v[i-1]*x2 - v[i-2] + return np.moveaxis(v, 0, -1) + + +def chebvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = T_i(x) * T_j(y), + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the degrees of + the Chebyshev polynomials. + + If ``V = chebvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``chebval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Chebyshev + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + chebvander, chebvander3d, chebval2d, chebval3d + """ + return pu._vander_nd_flat((chebvander, chebvander), (x, y), deg) + + +def chebvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = T_i(x)*T_j(y)*T_k(z), + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the degrees of the Chebyshev polynomials. + + If ``V = chebvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``chebval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Chebyshev + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + chebvander, chebvander3d, chebval2d, chebval3d + """ + return pu._vander_nd_flat((chebvander, chebvander, chebvander), (x, y, z), deg) + + +def chebfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Chebyshev series to data. + + Return the coefficients of a Chebyshev series of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x), + + where `n` is `deg`. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer, + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is ``len(x)*eps``, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Chebyshev coefficients ordered from low to high. If `y` was 2-D, + the coefficients for the data in column k of `y` are in column + `k`. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Warns + ----- + RankWarning + The rank of the coefficient matrix in the least-squares fit is + deficient. The warning is only raised if ``full == False``. The + warnings can be turned off by + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.polynomial.polyfit + numpy.polynomial.legendre.legfit + numpy.polynomial.laguerre.lagfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.hermite_e.hermefit + chebval : Evaluates a Chebyshev series. + chebvander : Vandermonde matrix of Chebyshev series. + chebweight : Chebyshev weight function. + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the Chebyshev series `p` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where :math:`w_j` are the weights. This problem is solved by setting up + as the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the + coefficients to be solved for, `w` are the weights, and `y` are the + observed values. This equation is then solved using the singular value + decomposition of `V`. + + If some of the singular values of `V` are so small that they are + neglected, then a `~exceptions.RankWarning` will be issued. This means that + the coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using Chebyshev series are usually better conditioned than fits + using power series, but much can depend on the distribution of the + sample points and the smoothness of the data. If the quality of the fit + is inadequate splines may be a good alternative. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + + """ + return pu._fit(chebvander, x, y, deg, rcond, full, w) + + +def chebcompanion(c): + """Return the scaled companion matrix of c. + + The basis polynomials are scaled so that the companion matrix is + symmetric when `c` is a Chebyshev basis polynomial. This provides + better eigenvalue estimates than the unscaled case and for basis + polynomials the eigenvalues are guaranteed to be real if + `numpy.linalg.eigvalsh` is used to obtain them. + + Parameters + ---------- + c : array_like + 1-D array of Chebyshev series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Scaled companion matrix of dimensions (deg, deg). + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[-c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + scl = np.array([1.] + [np.sqrt(.5)]*(n-1)) + top = mat.reshape(-1)[1::n+1] + bot = mat.reshape(-1)[n::n+1] + top[0] = np.sqrt(.5) + top[1:] = 1/2 + bot[...] = top + mat[:, -1] -= (c[:-1]/c[-1])*(scl/scl[-1])*.5 + return mat + + +def chebroots(c): + """ + Compute the roots of a Chebyshev series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * T_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.legendre.legroots + numpy.polynomial.laguerre.lagroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + The Chebyshev series basis polynomials aren't powers of `x` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> import numpy.polynomial.chebyshev as cheb + >>> cheb.chebroots((-1, 1,-1, 1)) # T3 - T2 + T1 - T0 has real roots + array([ -5.00000000e-01, 2.60860684e-17, 1.00000000e+00]) # may vary + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([-c[0]/c[1]]) + + # rotated companion matrix reduces error + m = chebcompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def chebinterpolate(func, deg, args=()): + """Interpolate a function at the Chebyshev points of the first kind. + + Returns the Chebyshev series that interpolates `func` at the Chebyshev + points of the first kind in the interval [-1, 1]. The interpolating + series tends to a minmax approximation to `func` with increasing `deg` + if the function is continuous in the interval. + + Parameters + ---------- + func : function + The function to be approximated. It must be a function of a single + variable of the form ``f(x, a, b, c...)``, where ``a, b, c...`` are + extra arguments passed in the `args` parameter. + deg : int + Degree of the interpolating polynomial + args : tuple, optional + Extra arguments to be used in the function call. Default is no extra + arguments. + + Returns + ------- + coef : ndarray, shape (deg + 1,) + Chebyshev coefficients of the interpolating series ordered from low to + high. + + Examples + -------- + >>> import numpy.polynomial.chebyshev as C + >>> C.chebinterpolate(lambda x: np.tanh(x) + 0.5, 8) + array([ 5.00000000e-01, 8.11675684e-01, -9.86864911e-17, + -5.42457905e-02, -2.71387850e-16, 4.51658839e-03, + 2.46716228e-17, -3.79694221e-04, -3.26899002e-16]) + + Notes + ----- + The Chebyshev polynomials used in the interpolation are orthogonal when + sampled at the Chebyshev points of the first kind. If it is desired to + constrain some of the coefficients they can simply be set to the desired + value after the interpolation, no new interpolation or fit is needed. This + is especially useful if it is known apriori that some of coefficients are + zero. For instance, if the function is even then the coefficients of the + terms of odd degree in the result can be set to zero. + + """ + deg = np.asarray(deg) + + # check arguments. + if deg.ndim > 0 or deg.dtype.kind not in 'iu' or deg.size == 0: + raise TypeError("deg must be an int") + if deg < 0: + raise ValueError("expected deg >= 0") + + order = deg + 1 + xcheb = chebpts1(order) + yfunc = func(xcheb, *args) + m = chebvander(xcheb, deg) + c = np.dot(m.T, yfunc) + c[0] /= order + c[1:] /= 0.5*order + + return c + + +def chebgauss(deg): + """ + Gauss-Chebyshev quadrature. + + Computes the sample points and weights for Gauss-Chebyshev quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[-1, 1]` with + the weight function :math:`f(x) = 1/\\sqrt{1 - x^2}`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + The results have only been tested up to degree 100, higher degrees may + be problematic. For Gauss-Chebyshev there are closed form solutions for + the sample points and weights. If n = `deg`, then + + .. math:: x_i = \\cos(\\pi (2 i - 1) / (2 n)) + + .. math:: w_i = \\pi / n + + """ + ideg = pu._as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + x = np.cos(np.pi * np.arange(1, 2*ideg, 2) / (2.0*ideg)) + w = np.ones(ideg)*(np.pi/ideg) + + return x, w + + +def chebweight(x): + """ + The weight function of the Chebyshev polynomials. + + The weight function is :math:`1/\\sqrt{1 - x^2}` and the interval of + integration is :math:`[-1, 1]`. The Chebyshev polynomials are + orthogonal, but not normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + """ + w = 1./(np.sqrt(1. + x) * np.sqrt(1. - x)) + return w + + +def chebpts1(npts): + """ + Chebyshev points of the first kind. + + The Chebyshev points of the first kind are the points ``cos(x)``, + where ``x = [pi*(k + .5)/npts for k in range(npts)]``. + + Parameters + ---------- + npts : int + Number of sample points desired. + + Returns + ------- + pts : ndarray + The Chebyshev points of the first kind. + + See Also + -------- + chebpts2 + """ + _npts = int(npts) + if _npts != npts: + raise ValueError("npts must be integer") + if _npts < 1: + raise ValueError("npts must be >= 1") + + x = 0.5 * np.pi / _npts * np.arange(-_npts+1, _npts+1, 2) + return np.sin(x) + + +def chebpts2(npts): + """ + Chebyshev points of the second kind. + + The Chebyshev points of the second kind are the points ``cos(x)``, + where ``x = [pi*k/(npts - 1) for k in range(npts)]`` sorted in ascending + order. + + Parameters + ---------- + npts : int + Number of sample points desired. + + Returns + ------- + pts : ndarray + The Chebyshev points of the second kind. + """ + _npts = int(npts) + if _npts != npts: + raise ValueError("npts must be integer") + if _npts < 2: + raise ValueError("npts must be >= 2") + + x = np.linspace(-np.pi, 0, _npts) + return np.cos(x) + + +# +# Chebyshev series class +# + +class Chebyshev(ABCPolyBase): + """A Chebyshev series class. + + The Chebyshev class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + Chebyshev coefficients in order of increasing degree, i.e., + ``(1, 2, 3)`` gives ``1*T_0(x) + 2*T_1(x) + 3*T_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [-1., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [-1., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(chebadd) + _sub = staticmethod(chebsub) + _mul = staticmethod(chebmul) + _div = staticmethod(chebdiv) + _pow = staticmethod(chebpow) + _val = staticmethod(chebval) + _int = staticmethod(chebint) + _der = staticmethod(chebder) + _fit = staticmethod(chebfit) + _line = staticmethod(chebline) + _roots = staticmethod(chebroots) + _fromroots = staticmethod(chebfromroots) + + @classmethod + def interpolate(cls, func, deg, domain=None, args=()): + """Interpolate a function at the Chebyshev points of the first kind. + + Returns the series that interpolates `func` at the Chebyshev points of + the first kind scaled and shifted to the `domain`. The resulting series + tends to a minmax approximation of `func` when the function is + continuous in the domain. + + Parameters + ---------- + func : function + The function to be interpolated. It must be a function of a single + variable of the form ``f(x, a, b, c...)``, where ``a, b, c...`` are + extra arguments passed in the `args` parameter. + deg : int + Degree of the interpolating polynomial. + domain : {None, [beg, end]}, optional + Domain over which `func` is interpolated. The default is None, in + which case the domain is [-1, 1]. + args : tuple, optional + Extra arguments to be used in the function call. Default is no + extra arguments. + + Returns + ------- + polynomial : Chebyshev instance + Interpolating Chebyshev instance. + + Notes + ----- + See `numpy.polynomial.chebinterpolate` for more details. + + """ + if domain is None: + domain = cls.domain + xfunc = lambda x: func(pu.mapdomain(x, cls.window, domain), *args) + coef = chebinterpolate(xfunc, deg) + return cls(coef, domain=domain) + + # Virtual properties + domain = np.array(chebdomain) + window = np.array(chebdomain) + basis_name = 'T' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.pyi new file mode 100644 index 0000000000000000000000000000000000000000..067af81d635d75511469f6cd130d774f00391be6 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/chebyshev.pyi @@ -0,0 +1,192 @@ +from collections.abc import Callable, Iterable +from typing import ( + Any, + Concatenate, + Final, + Literal as L, + TypeVar, + overload, +) + +import numpy as np +import numpy.typing as npt +from numpy._typing import _IntLike_co + +from ._polybase import ABCPolyBase +from ._polytypes import ( + _SeriesLikeCoef_co, + _Array1, + _Series, + _Array2, + _CoefSeries, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncGauss, + _FuncInteg, + _FuncLine, + _FuncPoly2Ortho, + _FuncPow, + _FuncPts, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVal2D, + _FuncVal3D, + _FuncValFromRoots, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncWeight, +) +from .polyutils import trimcoef as chebtrim + +__all__ = [ + "chebzero", + "chebone", + "chebx", + "chebdomain", + "chebline", + "chebadd", + "chebsub", + "chebmulx", + "chebmul", + "chebdiv", + "chebpow", + "chebval", + "chebder", + "chebint", + "cheb2poly", + "poly2cheb", + "chebfromroots", + "chebvander", + "chebfit", + "chebtrim", + "chebroots", + "chebpts1", + "chebpts2", + "Chebyshev", + "chebval2d", + "chebval3d", + "chebgrid2d", + "chebgrid3d", + "chebvander2d", + "chebvander3d", + "chebcompanion", + "chebgauss", + "chebweight", + "chebinterpolate", +] + +_SCT = TypeVar("_SCT", bound=np.number[Any] | np.object_) +def _cseries_to_zseries(c: npt.NDArray[_SCT]) -> _Series[_SCT]: ... +def _zseries_to_cseries(zs: npt.NDArray[_SCT]) -> _Series[_SCT]: ... +def _zseries_mul( + z1: npt.NDArray[_SCT], + z2: npt.NDArray[_SCT], +) -> _Series[_SCT]: ... +def _zseries_div( + z1: npt.NDArray[_SCT], + z2: npt.NDArray[_SCT], +) -> _Series[_SCT]: ... +def _zseries_der(zs: npt.NDArray[_SCT]) -> _Series[_SCT]: ... +def _zseries_int(zs: npt.NDArray[_SCT]) -> _Series[_SCT]: ... + +poly2cheb: _FuncPoly2Ortho[L["poly2cheb"]] +cheb2poly: _FuncUnOp[L["cheb2poly"]] + +chebdomain: Final[_Array2[np.float64]] +chebzero: Final[_Array1[np.int_]] +chebone: Final[_Array1[np.int_]] +chebx: Final[_Array2[np.int_]] + +chebline: _FuncLine[L["chebline"]] +chebfromroots: _FuncFromRoots[L["chebfromroots"]] +chebadd: _FuncBinOp[L["chebadd"]] +chebsub: _FuncBinOp[L["chebsub"]] +chebmulx: _FuncUnOp[L["chebmulx"]] +chebmul: _FuncBinOp[L["chebmul"]] +chebdiv: _FuncBinOp[L["chebdiv"]] +chebpow: _FuncPow[L["chebpow"]] +chebder: _FuncDer[L["chebder"]] +chebint: _FuncInteg[L["chebint"]] +chebval: _FuncVal[L["chebval"]] +chebval2d: _FuncVal2D[L["chebval2d"]] +chebval3d: _FuncVal3D[L["chebval3d"]] +chebvalfromroots: _FuncValFromRoots[L["chebvalfromroots"]] +chebgrid2d: _FuncVal2D[L["chebgrid2d"]] +chebgrid3d: _FuncVal3D[L["chebgrid3d"]] +chebvander: _FuncVander[L["chebvander"]] +chebvander2d: _FuncVander2D[L["chebvander2d"]] +chebvander3d: _FuncVander3D[L["chebvander3d"]] +chebfit: _FuncFit[L["chebfit"]] +chebcompanion: _FuncCompanion[L["chebcompanion"]] +chebroots: _FuncRoots[L["chebroots"]] +chebgauss: _FuncGauss[L["chebgauss"]] +chebweight: _FuncWeight[L["chebweight"]] +chebpts1: _FuncPts[L["chebpts1"]] +chebpts2: _FuncPts[L["chebpts2"]] + +# keep in sync with `Chebyshev.interpolate` +_RT = TypeVar("_RT", bound=np.number[Any] | np.bool | np.object_) +@overload +def chebinterpolate( + func: np.ufunc, + deg: _IntLike_co, + args: tuple[()] = ..., +) -> npt.NDArray[np.float64 | np.complex128 | np.object_]: ... +@overload +def chebinterpolate( + func: Callable[[npt.NDArray[np.float64]], _RT], + deg: _IntLike_co, + args: tuple[()] = ..., +) -> npt.NDArray[_RT]: ... +@overload +def chebinterpolate( + func: Callable[Concatenate[npt.NDArray[np.float64], ...], _RT], + deg: _IntLike_co, + args: Iterable[Any], +) -> npt.NDArray[_RT]: ... + +_Self = TypeVar("_Self", bound=object) + +class Chebyshev(ABCPolyBase[L["T"]]): + @overload + @classmethod + def interpolate( + cls: type[_Self], + /, + func: Callable[[npt.NDArray[np.float64]], _CoefSeries], + deg: _IntLike_co, + domain: None | _SeriesLikeCoef_co = ..., + args: tuple[()] = ..., + ) -> _Self: ... + @overload + @classmethod + def interpolate( + cls: type[_Self], + /, + func: Callable[ + Concatenate[npt.NDArray[np.float64], ...], + _CoefSeries, + ], + deg: _IntLike_co, + domain: None | _SeriesLikeCoef_co = ..., + *, + args: Iterable[Any], + ) -> _Self: ... + @overload + @classmethod + def interpolate( + cls: type[_Self], + func: Callable[ + Concatenate[npt.NDArray[np.float64], ...], + _CoefSeries, + ], + deg: _IntLike_co, + domain: None | _SeriesLikeCoef_co, + args: Iterable[Any], + /, + ) -> _Self: ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.py b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.py new file mode 100644 index 0000000000000000000000000000000000000000..24e51dca7fa55c83dfa467013440e160b260d9d9 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.py @@ -0,0 +1,1740 @@ +""" +============================================================== +Hermite Series, "Physicists" (:mod:`numpy.polynomial.hermite`) +============================================================== + +This module provides a number of objects (mostly functions) useful for +dealing with Hermite series, including a `Hermite` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with such polynomials is in the +docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- +.. autosummary:: + :toctree: generated/ + + Hermite + +Constants +--------- +.. autosummary:: + :toctree: generated/ + + hermdomain + hermzero + hermone + hermx + +Arithmetic +---------- +.. autosummary:: + :toctree: generated/ + + hermadd + hermsub + hermmulx + hermmul + hermdiv + hermpow + hermval + hermval2d + hermval3d + hermgrid2d + hermgrid3d + +Calculus +-------- +.. autosummary:: + :toctree: generated/ + + hermder + hermint + +Misc Functions +-------------- +.. autosummary:: + :toctree: generated/ + + hermfromroots + hermroots + hermvander + hermvander2d + hermvander3d + hermgauss + hermweight + hermcompanion + hermfit + hermtrim + hermline + herm2poly + poly2herm + +See also +-------- +`numpy.polynomial` + +""" +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +__all__ = [ + 'hermzero', 'hermone', 'hermx', 'hermdomain', 'hermline', 'hermadd', + 'hermsub', 'hermmulx', 'hermmul', 'hermdiv', 'hermpow', 'hermval', + 'hermder', 'hermint', 'herm2poly', 'poly2herm', 'hermfromroots', + 'hermvander', 'hermfit', 'hermtrim', 'hermroots', 'Hermite', + 'hermval2d', 'hermval3d', 'hermgrid2d', 'hermgrid3d', 'hermvander2d', + 'hermvander3d', 'hermcompanion', 'hermgauss', 'hermweight'] + +hermtrim = pu.trimcoef + + +def poly2herm(pol): + """ + poly2herm(pol) + + Convert a polynomial to a Hermite series. + + Convert an array representing the coefficients of a polynomial (relative + to the "standard" basis) ordered from lowest degree to highest, to an + array of the coefficients of the equivalent Hermite series, ordered + from lowest to highest degree. + + Parameters + ---------- + pol : array_like + 1-D array containing the polynomial coefficients + + Returns + ------- + c : ndarray + 1-D array containing the coefficients of the equivalent Hermite + series. + + See Also + -------- + herm2poly + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy.polynomial.hermite import poly2herm + >>> poly2herm(np.arange(4)) + array([1. , 2.75 , 0.5 , 0.375]) + + """ + [pol] = pu.as_series([pol]) + deg = len(pol) - 1 + res = 0 + for i in range(deg, -1, -1): + res = hermadd(hermmulx(res), pol[i]) + return res + + +def herm2poly(c): + """ + Convert a Hermite series to a polynomial. + + Convert an array representing the coefficients of a Hermite series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Hermite series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2herm + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy.polynomial.hermite import herm2poly + >>> herm2poly([ 1. , 2.75 , 0.5 , 0.375]) + array([0., 1., 2., 3.]) + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n == 1: + return c + if n == 2: + c[1] *= 2 + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], c1*(2*(i - 1))) + c1 = polyadd(tmp, polymulx(c1)*2) + return polyadd(c0, polymulx(c1)*2) + + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Hermite +hermdomain = np.array([-1., 1.]) + +# Hermite coefficients representing zero. +hermzero = np.array([0]) + +# Hermite coefficients representing one. +hermone = np.array([1]) + +# Hermite coefficients representing the identity x. +hermx = np.array([0, 1/2]) + + +def hermline(off, scl): + """ + Hermite series whose graph is a straight line. + + + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Hermite series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.chebyshev.chebline + numpy.polynomial.legendre.legline + numpy.polynomial.laguerre.lagline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> from numpy.polynomial.hermite import hermline, hermval + >>> hermval(0,hermline(3, 2)) + 3.0 + >>> hermval(1,hermline(3, 2)) + 5.0 + + """ + if scl != 0: + return np.array([off, scl/2]) + else: + return np.array([off]) + + +def hermfromroots(roots): + """ + Generate a Hermite series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in Hermite form, where the :math:`r_n` are the roots specified in `roots`. + If a zero has multiplicity n, then it must appear in `roots` n times. + For instance, if 2 is a root of multiplicity three and 3 is a root of + multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The + roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in Hermite form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.laguerre.lagfromroots + numpy.polynomial.chebyshev.chebfromroots + numpy.polynomial.hermite_e.hermefromroots + + Examples + -------- + >>> from numpy.polynomial.hermite import hermfromroots, hermval + >>> coef = hermfromroots((-1, 0, 1)) + >>> hermval((-1, 0, 1), coef) + array([0., 0., 0.]) + >>> coef = hermfromroots((-1j, 1j)) + >>> hermval((-1j, 1j), coef) + array([0.+0.j, 0.+0.j]) + + """ + return pu._fromroots(hermline, hermmul, roots) + + +def hermadd(c1, c2): + """ + Add one Hermite series to another. + + Returns the sum of two Hermite series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Hermite series of their sum. + + See Also + -------- + hermsub, hermmulx, hermmul, hermdiv, hermpow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Hermite series + is a Hermite series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.hermite import hermadd + >>> hermadd([1, 2, 3], [1, 2, 3, 4]) + array([2., 4., 6., 4.]) + + """ + return pu._add(c1, c2) + + +def hermsub(c1, c2): + """ + Subtract one Hermite series from another. + + Returns the difference of two Hermite series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Hermite series coefficients representing their difference. + + See Also + -------- + hermadd, hermmulx, hermmul, hermdiv, hermpow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Hermite + series is a Hermite series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.hermite import hermsub + >>> hermsub([1, 2, 3, 4], [1, 2, 3]) + array([0., 0., 0., 4.]) + + """ + return pu._sub(c1, c2) + + +def hermmulx(c): + """Multiply a Hermite series by x. + + Multiply the Hermite series `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + hermadd, hermsub, hermmul, hermdiv, hermpow + + Notes + ----- + The multiplication uses the recursion relationship for Hermite + polynomials in the form + + .. math:: + + xP_i(x) = (P_{i + 1}(x)/2 + i*P_{i - 1}(x)) + + Examples + -------- + >>> from numpy.polynomial.hermite import hermmulx + >>> hermmulx([1, 2, 3]) + array([2. , 6.5, 1. , 1.5]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0]*0 + prd[1] = c[0]/2 + for i in range(1, len(c)): + prd[i + 1] = c[i]/2 + prd[i - 1] += c[i]*i + return prd + + +def hermmul(c1, c2): + """ + Multiply one Hermite series by another. + + Returns the product of two Hermite series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Hermite series coefficients representing their product. + + See Also + -------- + hermadd, hermsub, hermmulx, hermdiv, hermpow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Hermite polynomial basis set. Thus, to express + the product as a Hermite series, it is necessary to "reproject" the + product onto said basis set, which may produce "unintuitive" (but + correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermmul + >>> hermmul([1, 2, 3], [0, 1, 2]) + array([52., 29., 52., 7., 6.]) + + """ + # s1, s2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + + if len(c1) > len(c2): + c = c2 + xs = c1 + else: + c = c1 + xs = c2 + + if len(c) == 1: + c0 = c[0]*xs + c1 = 0 + elif len(c) == 2: + c0 = c[0]*xs + c1 = c[1]*xs + else: + nd = len(c) + c0 = c[-2]*xs + c1 = c[-1]*xs + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = hermsub(c[-i]*xs, c1*(2*(nd - 1))) + c1 = hermadd(tmp, hermmulx(c1)*2) + return hermadd(c0, hermmulx(c1)*2) + + +def hermdiv(c1, c2): + """ + Divide one Hermite series by another. + + Returns the quotient-with-remainder of two Hermite series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + [quo, rem] : ndarrays + Of Hermite series coefficients representing the quotient and + remainder. + + See Also + -------- + hermadd, hermsub, hermmulx, hermmul, hermpow + + Notes + ----- + In general, the (polynomial) division of one Hermite series by another + results in quotient and remainder terms that are not in the Hermite + polynomial basis set. Thus, to express these results as a Hermite + series, it is necessary to "reproject" the results onto the Hermite + basis set, which may produce "unintuitive" (but correct) results; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermdiv + >>> hermdiv([ 52., 29., 52., 7., 6.], [0, 1, 2]) + (array([1., 2., 3.]), array([0.])) + >>> hermdiv([ 54., 31., 52., 7., 6.], [0, 1, 2]) + (array([1., 2., 3.]), array([2., 2.])) + >>> hermdiv([ 53., 30., 52., 7., 6.], [0, 1, 2]) + (array([1., 2., 3.]), array([1., 1.])) + + """ + return pu._div(hermmul, c1, c2) + + +def hermpow(c, pow, maxpower=16): + """Raise a Hermite series to a power. + + Returns the Hermite series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Hermite series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Hermite series of power. + + See Also + -------- + hermadd, hermsub, hermmulx, hermmul, hermdiv + + Examples + -------- + >>> from numpy.polynomial.hermite import hermpow + >>> hermpow([1, 2, 3], 2) + array([81., 52., 82., 12., 9.]) + + """ + return pu._pow(hermmul, c, pow, maxpower) + + +def hermder(c, m=1, scl=1, axis=0): + """ + Differentiate a Hermite series. + + Returns the Hermite series coefficients `c` differentiated `m` times + along `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*H_0 + 2*H_1 + 3*H_2`` + while [[1,2],[1,2]] represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + + 2*H_0(x)*H_1(y) + 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + Array of Hermite series coefficients. If `c` is multidimensional the + different axis correspond to different variables with the degree in + each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Hermite series of the derivative. + + See Also + -------- + hermint + + Notes + ----- + In general, the result of differentiating a Hermite series does not + resemble the same operation on a power series. Thus the result of this + function may be "unintuitive," albeit correct; see Examples section + below. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermder + >>> hermder([ 1. , 0.5, 0.5, 0.5]) + array([1., 2., 3.]) + >>> hermder([-0.5, 1./2., 1./8., 1./12., 1./16.], m=2) + array([1., 2., 3.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 0, -1): + der[j - 1] = (2*j)*c[j] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Hermite series. + + Returns the Hermite series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]] + represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + + 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + Parameters + ---------- + c : array_like + Array of Hermite series coefficients. If c is multidimensional the + different axis correspond to different variables with the degree in + each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at + ``lbnd`` is the first value in the list, the value of the second + integral at ``lbnd`` is the second value, etc. If ``k == []`` (the + default), all constants are set to zero. If ``m == 1``, a single + scalar can be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + Hermite series coefficients of the integral. + + Raises + ------ + ValueError + If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + hermder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermint + >>> hermint([1,2,3]) # integrate once, value 0 at 0. + array([1. , 0.5, 0.5, 0.5]) + >>> hermint([1,2,3], m=2) # integrate twice, value & deriv 0 at 0 + array([-0.5 , 0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary + >>> hermint([1,2,3], k=1) # integrate once, value 1 at 0. + array([2. , 0.5, 0.5, 0.5]) + >>> hermint([1,2,3], lbnd=-1) # integrate once, value 0 at -1 + array([-2. , 0.5, 0.5, 0.5]) + >>> hermint([1,2,3], m=2, k=[1,2], lbnd=-1) + array([ 1.66666667, -0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0]*0 + tmp[1] = c[0]/2 + for j in range(1, n): + tmp[j + 1] = c[j]/(2*(j + 1)) + tmp[0] += k[i] - hermval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def hermval(x, c, tensor=True): + """ + Evaluate an Hermite series at points x. + + If `c` is of length ``n + 1``, this function returns the value: + + .. math:: p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + hermval2d, hermgrid2d, hermval3d, hermgrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermval + >>> coef = [1,2,3] + >>> hermval(1, coef) + 11.0 + >>> hermval([[1,2],[3,4]], coef) + array([[ 11., 51.], + [115., 203.]]) + + """ + c = np.array(c, ndmin=1, copy=None) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + x2 = x*2 + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + nd = len(c) + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = c[-i] - c1*(2*(nd - 1)) + c1 = tmp + c1*x2 + return c0 + c1*x2 + + +def hermval2d(x, y, c): + """ + Evaluate a 2-D Hermite series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * H_i(x) * H_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points formed with + pairs of corresponding values from `x` and `y`. + + See Also + -------- + hermval, hermgrid2d, hermval3d, hermgrid3d + + Examples + -------- + >>> from numpy.polynomial.hermite import hermval2d + >>> x = [1, 2] + >>> y = [4, 5] + >>> c = [[1, 2, 3], [4, 5, 6]] + >>> hermval2d(x, y, c) + array([1035., 2883.]) + + """ + return pu._valnd(hermval, c, x, y) + + +def hermgrid2d(x, y, c): + """ + Evaluate a 2-D Hermite series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b) + + where the points ``(a, b)`` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + hermval, hermval2d, hermval3d, hermgrid3d + + Examples + -------- + >>> from numpy.polynomial.hermite import hermgrid2d + >>> x = [1, 2, 3] + >>> y = [4, 5] + >>> c = [[1, 2, 3], [4, 5, 6]] + >>> hermgrid2d(x, y, c) + array([[1035., 1599.], + [1867., 2883.], + [2699., 4167.]]) + + """ + return pu._gridnd(hermval, c, x, y) + + +def hermval3d(x, y, z, c): + """ + Evaluate a 3-D Hermite series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * H_i(x) * H_j(y) * H_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + ``(x, y, z)``, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + hermval, hermval2d, hermgrid2d, hermgrid3d + + Examples + -------- + >>> from numpy.polynomial.hermite import hermval3d + >>> x = [1, 2] + >>> y = [4, 5] + >>> z = [6, 7] + >>> c = [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]] + >>> hermval3d(x, y, z, c) + array([ 40077., 120131.]) + + """ + return pu._valnd(hermval, c, x, y, z) + + +def hermgrid3d(x, y, z, c): + """ + Evaluate a 3-D Hermite series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * H_i(a) * H_j(b) * H_k(c) + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + hermval, hermval2d, hermgrid2d, hermval3d + + Examples + -------- + >>> from numpy.polynomial.hermite import hermgrid3d + >>> x = [1, 2] + >>> y = [4, 5] + >>> z = [6, 7] + >>> c = [[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]] + >>> hermgrid3d(x, y, z, c) + array([[[ 40077., 54117.], + [ 49293., 66561.]], + [[ 72375., 97719.], + [ 88975., 120131.]]]) + + """ + return pu._gridnd(hermval, c, x, y, z) + + +def hermvander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = H_i(x), + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the degree of the Hermite polynomial. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + array ``V = hermvander(x, n)``, then ``np.dot(V, c)`` and + ``hermval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of Hermite series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo-Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding Hermite polynomial. The dtype will be the same as + the converted `x`. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite import hermvander + >>> x = np.array([-1, 0, 1]) + >>> hermvander(x, 3) + array([[ 1., -2., 2., 4.], + [ 1., 0., -2., -0.], + [ 1., 2., 2., -4.]]) + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + v[0] = x*0 + 1 + if ideg > 0: + x2 = x*2 + v[1] = x2 + for i in range(2, ideg + 1): + v[i] = (v[i-1]*x2 - v[i-2]*(2*(i - 1))) + return np.moveaxis(v, 0, -1) + + +def hermvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = H_i(x) * H_j(y), + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the degrees of + the Hermite polynomials. + + If ``V = hermvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``hermval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Hermite + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + hermvander, hermvander3d, hermval2d, hermval3d + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite import hermvander2d + >>> x = np.array([-1, 0, 1]) + >>> y = np.array([-1, 0, 1]) + >>> hermvander2d(x, y, [2, 2]) + array([[ 1., -2., 2., -2., 4., -4., 2., -4., 4.], + [ 1., 0., -2., 0., 0., -0., -2., -0., 4.], + [ 1., 2., 2., 2., 4., 4., 2., 4., 4.]]) + + """ + return pu._vander_nd_flat((hermvander, hermvander), (x, y), deg) + + +def hermvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = H_i(x)*H_j(y)*H_k(z), + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the degrees of the Hermite polynomials. + + If ``V = hermvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``hermval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Hermite + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + hermvander, hermvander3d, hermval2d, hermval3d + + Examples + -------- + >>> from numpy.polynomial.hermite import hermvander3d + >>> x = np.array([-1, 0, 1]) + >>> y = np.array([-1, 0, 1]) + >>> z = np.array([-1, 0, 1]) + >>> hermvander3d(x, y, z, [0, 1, 2]) + array([[ 1., -2., 2., -2., 4., -4.], + [ 1., 0., -2., 0., 0., -0.], + [ 1., 2., 2., 2., 4., 4.]]) + + """ + return pu._vander_nd_flat((hermvander, hermvander, hermvander), (x, y, z), deg) + + +def hermfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Hermite series to data. + + Return the coefficients of a Hermite series of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * H_1(x) + ... + c_n * H_n(x), + + where `n` is `deg`. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is len(x)*eps, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Hermite coefficients ordered from low to high. If `y` was 2-D, + the coefficients for the data in column k of `y` are in column + `k`. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Warns + ----- + RankWarning + The rank of the coefficient matrix in the least-squares fit is + deficient. The warning is only raised if ``full == False``. The + warnings can be turned off by + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.legendre.legfit + numpy.polynomial.laguerre.lagfit + numpy.polynomial.polynomial.polyfit + numpy.polynomial.hermite_e.hermefit + hermval : Evaluates a Hermite series. + hermvander : Vandermonde matrix of Hermite series. + hermweight : Hermite weight function + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the Hermite series `p` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where the :math:`w_j` are the weights. This problem is solved by + setting up the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the + coefficients to be solved for, `w` are the weights, `y` are the + observed values. This equation is then solved using the singular value + decomposition of `V`. + + If some of the singular values of `V` are so small that they are + neglected, then a `~exceptions.RankWarning` will be issued. This means that + the coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using Hermite series are probably most useful when the data can be + approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the Hermite + weight. In that case the weight ``sqrt(w(x[i]))`` should be used + together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is + available as `hermweight`. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite import hermfit, hermval + >>> x = np.linspace(-10, 10) + >>> rng = np.random.default_rng() + >>> err = rng.normal(scale=1./10, size=len(x)) + >>> y = hermval(x, [1, 2, 3]) + err + >>> hermfit(x, y, 2) + array([1.02294967, 2.00016403, 2.99994614]) # may vary + + """ + return pu._fit(hermvander, x, y, deg, rcond, full, w) + + +def hermcompanion(c): + """Return the scaled companion matrix of c. + + The basis polynomials are scaled so that the companion matrix is + symmetric when `c` is an Hermite basis polynomial. This provides + better eigenvalue estimates than the unscaled case and for basis + polynomials the eigenvalues are guaranteed to be real if + `numpy.linalg.eigvalsh` is used to obtain them. + + Parameters + ---------- + c : array_like + 1-D array of Hermite series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Scaled companion matrix of dimensions (deg, deg). + + Examples + -------- + >>> from numpy.polynomial.hermite import hermcompanion + >>> hermcompanion([1, 0, 1]) + array([[0. , 0.35355339], + [0.70710678, 0. ]]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[-.5*c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + scl = np.hstack((1., 1./np.sqrt(2.*np.arange(n - 1, 0, -1)))) + scl = np.multiply.accumulate(scl)[::-1] + top = mat.reshape(-1)[1::n+1] + bot = mat.reshape(-1)[n::n+1] + top[...] = np.sqrt(.5*np.arange(1, n)) + bot[...] = top + mat[:, -1] -= scl*c[:-1]/(2.0*c[-1]) + return mat + + +def hermroots(c): + """ + Compute the roots of a Hermite series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * H_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.legendre.legroots + numpy.polynomial.laguerre.lagroots + numpy.polynomial.chebyshev.chebroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + The Hermite series basis polynomials aren't powers of `x` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermroots, hermfromroots + >>> coef = hermfromroots([-1, 0, 1]) + >>> coef + array([0. , 0.25 , 0. , 0.125]) + >>> hermroots(coef) + array([-1.00000000e+00, -1.38777878e-17, 1.00000000e+00]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) <= 1: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([-.5*c[0]/c[1]]) + + # rotated companion matrix reduces error + m = hermcompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def _normed_hermite_n(x, n): + """ + Evaluate a normalized Hermite polynomial. + + Compute the value of the normalized Hermite polynomial of degree ``n`` + at the points ``x``. + + + Parameters + ---------- + x : ndarray of double. + Points at which to evaluate the function + n : int + Degree of the normalized Hermite function to be evaluated. + + Returns + ------- + values : ndarray + The shape of the return value is described above. + + Notes + ----- + This function is needed for finding the Gauss points and integration + weights for high degrees. The values of the standard Hermite functions + overflow when n >= 207. + + """ + if n == 0: + return np.full(x.shape, 1/np.sqrt(np.sqrt(np.pi))) + + c0 = 0. + c1 = 1./np.sqrt(np.sqrt(np.pi)) + nd = float(n) + for i in range(n - 1): + tmp = c0 + c0 = -c1*np.sqrt((nd - 1.)/nd) + c1 = tmp + c1*x*np.sqrt(2./nd) + nd = nd - 1.0 + return c0 + c1*x*np.sqrt(2) + + +def hermgauss(deg): + """ + Gauss-Hermite quadrature. + + Computes the sample points and weights for Gauss-Hermite quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[-\\inf, \\inf]` + with the weight function :math:`f(x) = \\exp(-x^2)`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + The results have only been tested up to degree 100, higher degrees may + be problematic. The weights are determined by using the fact that + + .. math:: w_k = c / (H'_n(x_k) * H_{n-1}(x_k)) + + where :math:`c` is a constant independent of :math:`k` and :math:`x_k` + is the k'th root of :math:`H_n`, and then scaling the results to get + the right value when integrating 1. + + Examples + -------- + >>> from numpy.polynomial.hermite import hermgauss + >>> hermgauss(2) + (array([-0.70710678, 0.70710678]), array([0.88622693, 0.88622693])) + + """ + ideg = pu._as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + # first approximation of roots. We use the fact that the companion + # matrix is symmetric in this case in order to obtain better zeros. + c = np.array([0]*deg + [1], dtype=np.float64) + m = hermcompanion(c) + x = la.eigvalsh(m) + + # improve roots by one application of Newton + dy = _normed_hermite_n(x, ideg) + df = _normed_hermite_n(x, ideg - 1) * np.sqrt(2*ideg) + x -= dy/df + + # compute the weights. We scale the factor to avoid possible numerical + # overflow. + fm = _normed_hermite_n(x, ideg - 1) + fm /= np.abs(fm).max() + w = 1/(fm * fm) + + # for Hermite we can also symmetrize + w = (w + w[::-1])/2 + x = (x - x[::-1])/2 + + # scale w to get the right value + w *= np.sqrt(np.pi) / w.sum() + + return x, w + + +def hermweight(x): + """ + Weight function of the Hermite polynomials. + + The weight function is :math:`\\exp(-x^2)` and the interval of + integration is :math:`[-\\inf, \\inf]`. the Hermite polynomials are + orthogonal, but not normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite import hermweight + >>> x = np.arange(-2, 2) + >>> hermweight(x) + array([0.01831564, 0.36787944, 1. , 0.36787944]) + + """ + w = np.exp(-x**2) + return w + + +# +# Hermite series class +# + +class Hermite(ABCPolyBase): + """An Hermite series class. + + The Hermite class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + Hermite coefficients in order of increasing degree, i.e, + ``(1, 2, 3)`` gives ``1*H_0(x) + 2*H_1(x) + 3*H_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [-1., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [-1., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(hermadd) + _sub = staticmethod(hermsub) + _mul = staticmethod(hermmul) + _div = staticmethod(hermdiv) + _pow = staticmethod(hermpow) + _val = staticmethod(hermval) + _int = staticmethod(hermint) + _der = staticmethod(hermder) + _fit = staticmethod(hermfit) + _line = staticmethod(hermline) + _roots = staticmethod(hermroots) + _fromroots = staticmethod(hermfromroots) + + # Virtual properties + domain = np.array(hermdomain) + window = np.array(hermdomain) + basis_name = 'H' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.pyi new file mode 100644 index 0000000000000000000000000000000000000000..07db43d0c0006601781cd24ee3269ae2f32a0445 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite.pyi @@ -0,0 +1,106 @@ +from typing import Any, Final, Literal as L, TypeVar + +import numpy as np + +from ._polybase import ABCPolyBase +from ._polytypes import ( + _Array1, + _Array2, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncGauss, + _FuncInteg, + _FuncLine, + _FuncPoly2Ortho, + _FuncPow, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVal2D, + _FuncVal3D, + _FuncValFromRoots, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncWeight, +) +from .polyutils import trimcoef as hermtrim + +__all__ = [ + "hermzero", + "hermone", + "hermx", + "hermdomain", + "hermline", + "hermadd", + "hermsub", + "hermmulx", + "hermmul", + "hermdiv", + "hermpow", + "hermval", + "hermder", + "hermint", + "herm2poly", + "poly2herm", + "hermfromroots", + "hermvander", + "hermfit", + "hermtrim", + "hermroots", + "Hermite", + "hermval2d", + "hermval3d", + "hermgrid2d", + "hermgrid3d", + "hermvander2d", + "hermvander3d", + "hermcompanion", + "hermgauss", + "hermweight", +] + +poly2herm: _FuncPoly2Ortho[L["poly2herm"]] +herm2poly: _FuncUnOp[L["herm2poly"]] + +hermdomain: Final[_Array2[np.float64]] +hermzero: Final[_Array1[np.int_]] +hermone: Final[_Array1[np.int_]] +hermx: Final[_Array2[np.int_]] + +hermline: _FuncLine[L["hermline"]] +hermfromroots: _FuncFromRoots[L["hermfromroots"]] +hermadd: _FuncBinOp[L["hermadd"]] +hermsub: _FuncBinOp[L["hermsub"]] +hermmulx: _FuncUnOp[L["hermmulx"]] +hermmul: _FuncBinOp[L["hermmul"]] +hermdiv: _FuncBinOp[L["hermdiv"]] +hermpow: _FuncPow[L["hermpow"]] +hermder: _FuncDer[L["hermder"]] +hermint: _FuncInteg[L["hermint"]] +hermval: _FuncVal[L["hermval"]] +hermval2d: _FuncVal2D[L["hermval2d"]] +hermval3d: _FuncVal3D[L["hermval3d"]] +hermvalfromroots: _FuncValFromRoots[L["hermvalfromroots"]] +hermgrid2d: _FuncVal2D[L["hermgrid2d"]] +hermgrid3d: _FuncVal3D[L["hermgrid3d"]] +hermvander: _FuncVander[L["hermvander"]] +hermvander2d: _FuncVander2D[L["hermvander2d"]] +hermvander3d: _FuncVander3D[L["hermvander3d"]] +hermfit: _FuncFit[L["hermfit"]] +hermcompanion: _FuncCompanion[L["hermcompanion"]] +hermroots: _FuncRoots[L["hermroots"]] + +_ND = TypeVar("_ND", bound=Any) +def _normed_hermite_n( + x: np.ndarray[_ND, np.dtype[np.float64]], + n: int | np.intp, +) -> np.ndarray[_ND, np.dtype[np.float64]]: ... + +hermgauss: _FuncGauss[L["hermgauss"]] +hermweight: _FuncWeight[L["hermweight"]] + +class Hermite(ABCPolyBase[L["H"]]): ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.py b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.py new file mode 100644 index 0000000000000000000000000000000000000000..c820760ef75c1db162b0a6e0897c88ba18582464 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.py @@ -0,0 +1,1642 @@ +""" +=================================================================== +HermiteE Series, "Probabilists" (:mod:`numpy.polynomial.hermite_e`) +=================================================================== + +This module provides a number of objects (mostly functions) useful for +dealing with Hermite_e series, including a `HermiteE` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with such polynomials is in the +docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- +.. autosummary:: + :toctree: generated/ + + HermiteE + +Constants +--------- +.. autosummary:: + :toctree: generated/ + + hermedomain + hermezero + hermeone + hermex + +Arithmetic +---------- +.. autosummary:: + :toctree: generated/ + + hermeadd + hermesub + hermemulx + hermemul + hermediv + hermepow + hermeval + hermeval2d + hermeval3d + hermegrid2d + hermegrid3d + +Calculus +-------- +.. autosummary:: + :toctree: generated/ + + hermeder + hermeint + +Misc Functions +-------------- +.. autosummary:: + :toctree: generated/ + + hermefromroots + hermeroots + hermevander + hermevander2d + hermevander3d + hermegauss + hermeweight + hermecompanion + hermefit + hermetrim + hermeline + herme2poly + poly2herme + +See also +-------- +`numpy.polynomial` + +""" +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +__all__ = [ + 'hermezero', 'hermeone', 'hermex', 'hermedomain', 'hermeline', + 'hermeadd', 'hermesub', 'hermemulx', 'hermemul', 'hermediv', + 'hermepow', 'hermeval', 'hermeder', 'hermeint', 'herme2poly', + 'poly2herme', 'hermefromroots', 'hermevander', 'hermefit', 'hermetrim', + 'hermeroots', 'HermiteE', 'hermeval2d', 'hermeval3d', 'hermegrid2d', + 'hermegrid3d', 'hermevander2d', 'hermevander3d', 'hermecompanion', + 'hermegauss', 'hermeweight'] + +hermetrim = pu.trimcoef + + +def poly2herme(pol): + """ + poly2herme(pol) + + Convert a polynomial to a Hermite series. + + Convert an array representing the coefficients of a polynomial (relative + to the "standard" basis) ordered from lowest degree to highest, to an + array of the coefficients of the equivalent Hermite series, ordered + from lowest to highest degree. + + Parameters + ---------- + pol : array_like + 1-D array containing the polynomial coefficients + + Returns + ------- + c : ndarray + 1-D array containing the coefficients of the equivalent Hermite + series. + + See Also + -------- + herme2poly + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite_e import poly2herme + >>> poly2herme(np.arange(4)) + array([ 2., 10., 2., 3.]) + + """ + [pol] = pu.as_series([pol]) + deg = len(pol) - 1 + res = 0 + for i in range(deg, -1, -1): + res = hermeadd(hermemulx(res), pol[i]) + return res + + +def herme2poly(c): + """ + Convert a Hermite series to a polynomial. + + Convert an array representing the coefficients of a Hermite series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Hermite series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2herme + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import herme2poly + >>> herme2poly([ 2., 10., 2., 3.]) + array([0., 1., 2., 3.]) + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n == 1: + return c + if n == 2: + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], c1*(i - 1)) + c1 = polyadd(tmp, polymulx(c1)) + return polyadd(c0, polymulx(c1)) + + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Hermite +hermedomain = np.array([-1., 1.]) + +# Hermite coefficients representing zero. +hermezero = np.array([0]) + +# Hermite coefficients representing one. +hermeone = np.array([1]) + +# Hermite coefficients representing the identity x. +hermex = np.array([0, 1]) + + +def hermeline(off, scl): + """ + Hermite series whose graph is a straight line. + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Hermite series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.chebyshev.chebline + numpy.polynomial.legendre.legline + numpy.polynomial.laguerre.lagline + numpy.polynomial.hermite.hermline + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeline + >>> from numpy.polynomial.hermite_e import hermeline, hermeval + >>> hermeval(0,hermeline(3, 2)) + 3.0 + >>> hermeval(1,hermeline(3, 2)) + 5.0 + + """ + if scl != 0: + return np.array([off, scl]) + else: + return np.array([off]) + + +def hermefromroots(roots): + """ + Generate a HermiteE series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in HermiteE form, where the :math:`r_n` are the roots specified in `roots`. + If a zero has multiplicity n, then it must appear in `roots` n times. + For instance, if 2 is a root of multiplicity three and 3 is a root of + multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The + roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in HermiteE form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.laguerre.lagfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.chebyshev.chebfromroots + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermefromroots, hermeval + >>> coef = hermefromroots((-1, 0, 1)) + >>> hermeval((-1, 0, 1), coef) + array([0., 0., 0.]) + >>> coef = hermefromroots((-1j, 1j)) + >>> hermeval((-1j, 1j), coef) + array([0.+0.j, 0.+0.j]) + + """ + return pu._fromroots(hermeline, hermemul, roots) + + +def hermeadd(c1, c2): + """ + Add one Hermite series to another. + + Returns the sum of two Hermite series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Hermite series of their sum. + + See Also + -------- + hermesub, hermemulx, hermemul, hermediv, hermepow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Hermite series + is a Hermite series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeadd + >>> hermeadd([1, 2, 3], [1, 2, 3, 4]) + array([2., 4., 6., 4.]) + + """ + return pu._add(c1, c2) + + +def hermesub(c1, c2): + """ + Subtract one Hermite series from another. + + Returns the difference of two Hermite series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Hermite series coefficients representing their difference. + + See Also + -------- + hermeadd, hermemulx, hermemul, hermediv, hermepow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Hermite + series is a Hermite series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermesub + >>> hermesub([1, 2, 3, 4], [1, 2, 3]) + array([0., 0., 0., 4.]) + + """ + return pu._sub(c1, c2) + + +def hermemulx(c): + """Multiply a Hermite series by x. + + Multiply the Hermite series `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + hermeadd, hermesub, hermemul, hermediv, hermepow + + Notes + ----- + The multiplication uses the recursion relationship for Hermite + polynomials in the form + + .. math:: + + xP_i(x) = (P_{i + 1}(x) + iP_{i - 1}(x))) + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermemulx + >>> hermemulx([1, 2, 3]) + array([2., 7., 2., 3.]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0]*0 + prd[1] = c[0] + for i in range(1, len(c)): + prd[i + 1] = c[i] + prd[i - 1] += c[i]*i + return prd + + +def hermemul(c1, c2): + """ + Multiply one Hermite series by another. + + Returns the product of two Hermite series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Hermite series coefficients representing their product. + + See Also + -------- + hermeadd, hermesub, hermemulx, hermediv, hermepow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Hermite polynomial basis set. Thus, to express + the product as a Hermite series, it is necessary to "reproject" the + product onto said basis set, which may produce "unintuitive" (but + correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermemul + >>> hermemul([1, 2, 3], [0, 1, 2]) + array([14., 15., 28., 7., 6.]) + + """ + # s1, s2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + + if len(c1) > len(c2): + c = c2 + xs = c1 + else: + c = c1 + xs = c2 + + if len(c) == 1: + c0 = c[0]*xs + c1 = 0 + elif len(c) == 2: + c0 = c[0]*xs + c1 = c[1]*xs + else: + nd = len(c) + c0 = c[-2]*xs + c1 = c[-1]*xs + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = hermesub(c[-i]*xs, c1*(nd - 1)) + c1 = hermeadd(tmp, hermemulx(c1)) + return hermeadd(c0, hermemulx(c1)) + + +def hermediv(c1, c2): + """ + Divide one Hermite series by another. + + Returns the quotient-with-remainder of two Hermite series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Hermite series coefficients ordered from low to + high. + + Returns + ------- + [quo, rem] : ndarrays + Of Hermite series coefficients representing the quotient and + remainder. + + See Also + -------- + hermeadd, hermesub, hermemulx, hermemul, hermepow + + Notes + ----- + In general, the (polynomial) division of one Hermite series by another + results in quotient and remainder terms that are not in the Hermite + polynomial basis set. Thus, to express these results as a Hermite + series, it is necessary to "reproject" the results onto the Hermite + basis set, which may produce "unintuitive" (but correct) results; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermediv + >>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2]) + (array([1., 2., 3.]), array([0.])) + >>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2]) + (array([1., 2., 3.]), array([1., 2.])) + + """ + return pu._div(hermemul, c1, c2) + + +def hermepow(c, pow, maxpower=16): + """Raise a Hermite series to a power. + + Returns the Hermite series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Hermite series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Hermite series of power. + + See Also + -------- + hermeadd, hermesub, hermemulx, hermemul, hermediv + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermepow + >>> hermepow([1, 2, 3], 2) + array([23., 28., 46., 12., 9.]) + + """ + return pu._pow(hermemul, c, pow, maxpower) + + +def hermeder(c, m=1, scl=1, axis=0): + """ + Differentiate a Hermite_e series. + + Returns the series coefficients `c` differentiated `m` times along + `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*He_0 + 2*He_1 + 3*He_2`` + while [[1,2],[1,2]] represents ``1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y) + + 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y)`` if axis=0 is ``x`` and axis=1 + is ``y``. + + Parameters + ---------- + c : array_like + Array of Hermite_e series coefficients. If `c` is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Hermite series of the derivative. + + See Also + -------- + hermeint + + Notes + ----- + In general, the result of differentiating a Hermite series does not + resemble the same operation on a power series. Thus the result of this + function may be "unintuitive," albeit correct; see Examples section + below. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeder + >>> hermeder([ 1., 1., 1., 1.]) + array([1., 2., 3.]) + >>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2) + array([1., 2., 3.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + return c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 0, -1): + der[j - 1] = j*c[j] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Hermite_e series. + + Returns the Hermite_e series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]] + represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + + 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + Parameters + ---------- + c : array_like + Array of Hermite_e series coefficients. If c is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at + ``lbnd`` is the first value in the list, the value of the second + integral at ``lbnd`` is the second value, etc. If ``k == []`` (the + default), all constants are set to zero. If ``m == 1``, a single + scalar can be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + Hermite_e series coefficients of the integral. + + Raises + ------ + ValueError + If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + hermeder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeint + >>> hermeint([1, 2, 3]) # integrate once, value 0 at 0. + array([1., 1., 1., 1.]) + >>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0 + array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary + >>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0. + array([2., 1., 1., 1.]) + >>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1 + array([-1., 1., 1., 1.]) + >>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1) + array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0]*0 + tmp[1] = c[0] + for j in range(1, n): + tmp[j + 1] = c[j]/(j + 1) + tmp[0] += k[i] - hermeval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def hermeval(x, c, tensor=True): + """ + Evaluate an HermiteE series at points x. + + If `c` is of length ``n + 1``, this function returns the value: + + .. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + with themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + hermeval2d, hermegrid2d, hermeval3d, hermegrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeval + >>> coef = [1,2,3] + >>> hermeval(1, coef) + 3.0 + >>> hermeval([[1,2],[3,4]], coef) + array([[ 3., 14.], + [31., 54.]]) + + """ + c = np.array(c, ndmin=1, copy=None) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + nd = len(c) + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = c[-i] - c1*(nd - 1) + c1 = tmp + c1*x + return c0 + c1*x + + +def hermeval2d(x, y, c): + """ + Evaluate a 2-D HermiteE series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * He_i(x) * He_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points formed with + pairs of corresponding values from `x` and `y`. + + See Also + -------- + hermeval, hermegrid2d, hermeval3d, hermegrid3d + """ + return pu._valnd(hermeval, c, x, y) + + +def hermegrid2d(x, y, c): + """ + Evaluate a 2-D HermiteE series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b) + + where the points ``(a, b)`` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + hermeval, hermeval2d, hermeval3d, hermegrid3d + """ + return pu._gridnd(hermeval, c, x, y) + + +def hermeval3d(x, y, z, c): + """ + Evaluate a 3-D Hermite_e series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * He_i(x) * He_j(y) * He_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + hermeval, hermeval2d, hermegrid2d, hermegrid3d + """ + return pu._valnd(hermeval, c, x, y, z) + + +def hermegrid3d(x, y, z, c): + """ + Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c) + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + hermeval, hermeval2d, hermegrid2d, hermeval3d + """ + return pu._gridnd(hermeval, c, x, y, z) + + +def hermevander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = He_i(x), + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the degree of the HermiteE polynomial. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + array ``V = hermevander(x, n)``, then ``np.dot(V, c)`` and + ``hermeval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of HermiteE series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo-Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding HermiteE polynomial. The dtype will be the same as + the converted `x`. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite_e import hermevander + >>> x = np.array([-1, 0, 1]) + >>> hermevander(x, 3) + array([[ 1., -1., 0., 2.], + [ 1., 0., -1., -0.], + [ 1., 1., 0., -2.]]) + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + v[0] = x*0 + 1 + if ideg > 0: + v[1] = x + for i in range(2, ideg + 1): + v[i] = (v[i-1]*x - v[i-2]*(i - 1)) + return np.moveaxis(v, 0, -1) + + +def hermevander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = He_i(x) * He_j(y), + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the degrees of + the HermiteE polynomials. + + If ``V = hermevander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``hermeval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D HermiteE + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + hermevander, hermevander3d, hermeval2d, hermeval3d + """ + return pu._vander_nd_flat((hermevander, hermevander), (x, y), deg) + + +def hermevander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then Hehe pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z), + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the degrees of the HermiteE polynomials. + + If ``V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``hermeval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D HermiteE + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + hermevander, hermevander3d, hermeval2d, hermeval3d + """ + return pu._vander_nd_flat((hermevander, hermevander, hermevander), (x, y, z), deg) + + +def hermefit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Hermite series to data. + + Return the coefficients of a HermiteE series of degree `deg` that is + the least squares fit to the data values `y` given at points `x`. If + `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D + multiple fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x), + + where `n` is `deg`. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is len(x)*eps, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Hermite coefficients ordered from low to high. If `y` was 2-D, + the coefficients for the data in column k of `y` are in column + `k`. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Warns + ----- + RankWarning + The rank of the coefficient matrix in the least-squares fit is + deficient. The warning is only raised if ``full = False``. The + warnings can be turned off by + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.legendre.legfit + numpy.polynomial.polynomial.polyfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.laguerre.lagfit + hermeval : Evaluates a Hermite series. + hermevander : pseudo Vandermonde matrix of Hermite series. + hermeweight : HermiteE weight function. + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the HermiteE series `p` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where the :math:`w_j` are the weights. This problem is solved by + setting up the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c` + are the coefficients to be solved for, and the elements of `y` are the + observed values. This equation is then solved using the singular value + decomposition of `V`. + + If some of the singular values of `V` are so small that they are + neglected, then a `~exceptions.RankWarning` will be issued. This means that + the coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using HermiteE series are probably most useful when the data can + be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the HermiteE + weight. In that case the weight ``sqrt(w(x[i]))`` should be used + together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is + available as `hermeweight`. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.hermite_e import hermefit, hermeval + >>> x = np.linspace(-10, 10) + >>> rng = np.random.default_rng() + >>> err = rng.normal(scale=1./10, size=len(x)) + >>> y = hermeval(x, [1, 2, 3]) + err + >>> hermefit(x, y, 2) + array([1.02284196, 2.00032805, 2.99978457]) # may vary + + """ + return pu._fit(hermevander, x, y, deg, rcond, full, w) + + +def hermecompanion(c): + """ + Return the scaled companion matrix of c. + + The basis polynomials are scaled so that the companion matrix is + symmetric when `c` is an HermiteE basis polynomial. This provides + better eigenvalue estimates than the unscaled case and for basis + polynomials the eigenvalues are guaranteed to be real if + `numpy.linalg.eigvalsh` is used to obtain them. + + Parameters + ---------- + c : array_like + 1-D array of HermiteE series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Scaled companion matrix of dimensions (deg, deg). + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[-c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + scl = np.hstack((1., 1./np.sqrt(np.arange(n - 1, 0, -1)))) + scl = np.multiply.accumulate(scl)[::-1] + top = mat.reshape(-1)[1::n+1] + bot = mat.reshape(-1)[n::n+1] + top[...] = np.sqrt(np.arange(1, n)) + bot[...] = top + mat[:, -1] -= scl*c[:-1]/c[-1] + return mat + + +def hermeroots(c): + """ + Compute the roots of a HermiteE series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * He_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.legendre.legroots + numpy.polynomial.laguerre.lagroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.chebyshev.chebroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + The HermiteE series basis polynomials aren't powers of `x` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots + >>> coef = hermefromroots([-1, 0, 1]) + >>> coef + array([0., 2., 0., 1.]) + >>> hermeroots(coef) + array([-1., 0., 1.]) # may vary + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) <= 1: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([-c[0]/c[1]]) + + # rotated companion matrix reduces error + m = hermecompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def _normed_hermite_e_n(x, n): + """ + Evaluate a normalized HermiteE polynomial. + + Compute the value of the normalized HermiteE polynomial of degree ``n`` + at the points ``x``. + + + Parameters + ---------- + x : ndarray of double. + Points at which to evaluate the function + n : int + Degree of the normalized HermiteE function to be evaluated. + + Returns + ------- + values : ndarray + The shape of the return value is described above. + + Notes + ----- + This function is needed for finding the Gauss points and integration + weights for high degrees. The values of the standard HermiteE functions + overflow when n >= 207. + + """ + if n == 0: + return np.full(x.shape, 1/np.sqrt(np.sqrt(2*np.pi))) + + c0 = 0. + c1 = 1./np.sqrt(np.sqrt(2*np.pi)) + nd = float(n) + for i in range(n - 1): + tmp = c0 + c0 = -c1*np.sqrt((nd - 1.)/nd) + c1 = tmp + c1*x*np.sqrt(1./nd) + nd = nd - 1.0 + return c0 + c1*x + + +def hermegauss(deg): + """ + Gauss-HermiteE quadrature. + + Computes the sample points and weights for Gauss-HermiteE quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[-\\inf, \\inf]` + with the weight function :math:`f(x) = \\exp(-x^2/2)`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + The results have only been tested up to degree 100, higher degrees may + be problematic. The weights are determined by using the fact that + + .. math:: w_k = c / (He'_n(x_k) * He_{n-1}(x_k)) + + where :math:`c` is a constant independent of :math:`k` and :math:`x_k` + is the k'th root of :math:`He_n`, and then scaling the results to get + the right value when integrating 1. + + """ + ideg = pu._as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + # first approximation of roots. We use the fact that the companion + # matrix is symmetric in this case in order to obtain better zeros. + c = np.array([0]*deg + [1]) + m = hermecompanion(c) + x = la.eigvalsh(m) + + # improve roots by one application of Newton + dy = _normed_hermite_e_n(x, ideg) + df = _normed_hermite_e_n(x, ideg - 1) * np.sqrt(ideg) + x -= dy/df + + # compute the weights. We scale the factor to avoid possible numerical + # overflow. + fm = _normed_hermite_e_n(x, ideg - 1) + fm /= np.abs(fm).max() + w = 1/(fm * fm) + + # for Hermite_e we can also symmetrize + w = (w + w[::-1])/2 + x = (x - x[::-1])/2 + + # scale w to get the right value + w *= np.sqrt(2*np.pi) / w.sum() + + return x, w + + +def hermeweight(x): + """Weight function of the Hermite_e polynomials. + + The weight function is :math:`\\exp(-x^2/2)` and the interval of + integration is :math:`[-\\inf, \\inf]`. the HermiteE polynomials are + orthogonal, but not normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + """ + w = np.exp(-.5*x**2) + return w + + +# +# HermiteE series class +# + +class HermiteE(ABCPolyBase): + """An HermiteE series class. + + The HermiteE class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + HermiteE coefficients in order of increasing degree, i.e, + ``(1, 2, 3)`` gives ``1*He_0(x) + 2*He_1(X) + 3*He_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [-1., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [-1., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(hermeadd) + _sub = staticmethod(hermesub) + _mul = staticmethod(hermemul) + _div = staticmethod(hermediv) + _pow = staticmethod(hermepow) + _val = staticmethod(hermeval) + _int = staticmethod(hermeint) + _der = staticmethod(hermeder) + _fit = staticmethod(hermefit) + _line = staticmethod(hermeline) + _roots = staticmethod(hermeroots) + _fromroots = staticmethod(hermefromroots) + + # Virtual properties + domain = np.array(hermedomain) + window = np.array(hermedomain) + basis_name = 'He' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.pyi new file mode 100644 index 0000000000000000000000000000000000000000..94ad7248f268b9d4e4de1685063187c94db25fd7 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/hermite_e.pyi @@ -0,0 +1,106 @@ +from typing import Any, Final, Literal as L, TypeVar + +import numpy as np + +from ._polybase import ABCPolyBase +from ._polytypes import ( + _Array1, + _Array2, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncGauss, + _FuncInteg, + _FuncLine, + _FuncPoly2Ortho, + _FuncPow, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVal2D, + _FuncVal3D, + _FuncValFromRoots, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncWeight, +) +from .polyutils import trimcoef as hermetrim + +__all__ = [ + "hermezero", + "hermeone", + "hermex", + "hermedomain", + "hermeline", + "hermeadd", + "hermesub", + "hermemulx", + "hermemul", + "hermediv", + "hermepow", + "hermeval", + "hermeder", + "hermeint", + "herme2poly", + "poly2herme", + "hermefromroots", + "hermevander", + "hermefit", + "hermetrim", + "hermeroots", + "HermiteE", + "hermeval2d", + "hermeval3d", + "hermegrid2d", + "hermegrid3d", + "hermevander2d", + "hermevander3d", + "hermecompanion", + "hermegauss", + "hermeweight", +] + +poly2herme: _FuncPoly2Ortho[L["poly2herme"]] +herme2poly: _FuncUnOp[L["herme2poly"]] + +hermedomain: Final[_Array2[np.float64]] +hermezero: Final[_Array1[np.int_]] +hermeone: Final[_Array1[np.int_]] +hermex: Final[_Array2[np.int_]] + +hermeline: _FuncLine[L["hermeline"]] +hermefromroots: _FuncFromRoots[L["hermefromroots"]] +hermeadd: _FuncBinOp[L["hermeadd"]] +hermesub: _FuncBinOp[L["hermesub"]] +hermemulx: _FuncUnOp[L["hermemulx"]] +hermemul: _FuncBinOp[L["hermemul"]] +hermediv: _FuncBinOp[L["hermediv"]] +hermepow: _FuncPow[L["hermepow"]] +hermeder: _FuncDer[L["hermeder"]] +hermeint: _FuncInteg[L["hermeint"]] +hermeval: _FuncVal[L["hermeval"]] +hermeval2d: _FuncVal2D[L["hermeval2d"]] +hermeval3d: _FuncVal3D[L["hermeval3d"]] +hermevalfromroots: _FuncValFromRoots[L["hermevalfromroots"]] +hermegrid2d: _FuncVal2D[L["hermegrid2d"]] +hermegrid3d: _FuncVal3D[L["hermegrid3d"]] +hermevander: _FuncVander[L["hermevander"]] +hermevander2d: _FuncVander2D[L["hermevander2d"]] +hermevander3d: _FuncVander3D[L["hermevander3d"]] +hermefit: _FuncFit[L["hermefit"]] +hermecompanion: _FuncCompanion[L["hermecompanion"]] +hermeroots: _FuncRoots[L["hermeroots"]] + +_ND = TypeVar("_ND", bound=Any) +def _normed_hermite_e_n( + x: np.ndarray[_ND, np.dtype[np.float64]], + n: int | np.intp, +) -> np.ndarray[_ND, np.dtype[np.float64]]: ... + +hermegauss: _FuncGauss[L["hermegauss"]] +hermeweight: _FuncWeight[L["hermeweight"]] + +class HermiteE(ABCPolyBase[L["He"]]): ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.py b/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.py new file mode 100644 index 0000000000000000000000000000000000000000..b2cc5817c30cb892f58f1c366746b5967670d2ad --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.py @@ -0,0 +1,1675 @@ +""" +================================================== +Laguerre Series (:mod:`numpy.polynomial.laguerre`) +================================================== + +This module provides a number of objects (mostly functions) useful for +dealing with Laguerre series, including a `Laguerre` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with such polynomials is in the +docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- +.. autosummary:: + :toctree: generated/ + + Laguerre + +Constants +--------- +.. autosummary:: + :toctree: generated/ + + lagdomain + lagzero + lagone + lagx + +Arithmetic +---------- +.. autosummary:: + :toctree: generated/ + + lagadd + lagsub + lagmulx + lagmul + lagdiv + lagpow + lagval + lagval2d + lagval3d + laggrid2d + laggrid3d + +Calculus +-------- +.. autosummary:: + :toctree: generated/ + + lagder + lagint + +Misc Functions +-------------- +.. autosummary:: + :toctree: generated/ + + lagfromroots + lagroots + lagvander + lagvander2d + lagvander3d + laggauss + lagweight + lagcompanion + lagfit + lagtrim + lagline + lag2poly + poly2lag + +See also +-------- +`numpy.polynomial` + +""" +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +__all__ = [ + 'lagzero', 'lagone', 'lagx', 'lagdomain', 'lagline', 'lagadd', + 'lagsub', 'lagmulx', 'lagmul', 'lagdiv', 'lagpow', 'lagval', 'lagder', + 'lagint', 'lag2poly', 'poly2lag', 'lagfromroots', 'lagvander', + 'lagfit', 'lagtrim', 'lagroots', 'Laguerre', 'lagval2d', 'lagval3d', + 'laggrid2d', 'laggrid3d', 'lagvander2d', 'lagvander3d', 'lagcompanion', + 'laggauss', 'lagweight'] + +lagtrim = pu.trimcoef + + +def poly2lag(pol): + """ + poly2lag(pol) + + Convert a polynomial to a Laguerre series. + + Convert an array representing the coefficients of a polynomial (relative + to the "standard" basis) ordered from lowest degree to highest, to an + array of the coefficients of the equivalent Laguerre series, ordered + from lowest to highest degree. + + Parameters + ---------- + pol : array_like + 1-D array containing the polynomial coefficients + + Returns + ------- + c : ndarray + 1-D array containing the coefficients of the equivalent Laguerre + series. + + See Also + -------- + lag2poly + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.laguerre import poly2lag + >>> poly2lag(np.arange(4)) + array([ 23., -63., 58., -18.]) + + """ + [pol] = pu.as_series([pol]) + res = 0 + for p in pol[::-1]: + res = lagadd(lagmulx(res), p) + return res + + +def lag2poly(c): + """ + Convert a Laguerre series to a polynomial. + + Convert an array representing the coefficients of a Laguerre series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Laguerre series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2lag + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lag2poly + >>> lag2poly([ 23., -63., 58., -18.]) + array([0., 1., 2., 3.]) + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n == 1: + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], (c1*(i - 1))/i) + c1 = polyadd(tmp, polysub((2*i - 1)*c1, polymulx(c1))/i) + return polyadd(c0, polysub(c1, polymulx(c1))) + + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Laguerre +lagdomain = np.array([0., 1.]) + +# Laguerre coefficients representing zero. +lagzero = np.array([0]) + +# Laguerre coefficients representing one. +lagone = np.array([1]) + +# Laguerre coefficients representing the identity x. +lagx = np.array([1, -1]) + + +def lagline(off, scl): + """ + Laguerre series whose graph is a straight line. + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Laguerre series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.chebyshev.chebline + numpy.polynomial.legendre.legline + numpy.polynomial.hermite.hermline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagline, lagval + >>> lagval(0,lagline(3, 2)) + 3.0 + >>> lagval(1,lagline(3, 2)) + 5.0 + + """ + if scl != 0: + return np.array([off + scl, -scl]) + else: + return np.array([off]) + + +def lagfromroots(roots): + """ + Generate a Laguerre series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in Laguerre form, where the :math:`r_n` are the roots specified in `roots`. + If a zero has multiplicity n, then it must appear in `roots` n times. + For instance, if 2 is a root of multiplicity three and 3 is a root of + multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The + roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in Laguerre form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.chebyshev.chebfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.hermite_e.hermefromroots + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagfromroots, lagval + >>> coef = lagfromroots((-1, 0, 1)) + >>> lagval((-1, 0, 1), coef) + array([0., 0., 0.]) + >>> coef = lagfromroots((-1j, 1j)) + >>> lagval((-1j, 1j), coef) + array([0.+0.j, 0.+0.j]) + + """ + return pu._fromroots(lagline, lagmul, roots) + + +def lagadd(c1, c2): + """ + Add one Laguerre series to another. + + Returns the sum of two Laguerre series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Laguerre series of their sum. + + See Also + -------- + lagsub, lagmulx, lagmul, lagdiv, lagpow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Laguerre series + is a Laguerre series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagadd + >>> lagadd([1, 2, 3], [1, 2, 3, 4]) + array([2., 4., 6., 4.]) + + """ + return pu._add(c1, c2) + + +def lagsub(c1, c2): + """ + Subtract one Laguerre series from another. + + Returns the difference of two Laguerre series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Laguerre series coefficients representing their difference. + + See Also + -------- + lagadd, lagmulx, lagmul, lagdiv, lagpow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Laguerre + series is a Laguerre series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagsub + >>> lagsub([1, 2, 3, 4], [1, 2, 3]) + array([0., 0., 0., 4.]) + + """ + return pu._sub(c1, c2) + + +def lagmulx(c): + """Multiply a Laguerre series by x. + + Multiply the Laguerre series `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + lagadd, lagsub, lagmul, lagdiv, lagpow + + Notes + ----- + The multiplication uses the recursion relationship for Laguerre + polynomials in the form + + .. math:: + + xP_i(x) = (-(i + 1)*P_{i + 1}(x) + (2i + 1)P_{i}(x) - iP_{i - 1}(x)) + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagmulx + >>> lagmulx([1, 2, 3]) + array([-1., -1., 11., -9.]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0] + prd[1] = -c[0] + for i in range(1, len(c)): + prd[i + 1] = -c[i]*(i + 1) + prd[i] += c[i]*(2*i + 1) + prd[i - 1] -= c[i]*i + return prd + + +def lagmul(c1, c2): + """ + Multiply one Laguerre series by another. + + Returns the product of two Laguerre series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Laguerre series coefficients representing their product. + + See Also + -------- + lagadd, lagsub, lagmulx, lagdiv, lagpow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Laguerre polynomial basis set. Thus, to express + the product as a Laguerre series, it is necessary to "reproject" the + product onto said basis set, which may produce "unintuitive" (but + correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagmul + >>> lagmul([1, 2, 3], [0, 1, 2]) + array([ 8., -13., 38., -51., 36.]) + + """ + # s1, s2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + + if len(c1) > len(c2): + c = c2 + xs = c1 + else: + c = c1 + xs = c2 + + if len(c) == 1: + c0 = c[0]*xs + c1 = 0 + elif len(c) == 2: + c0 = c[0]*xs + c1 = c[1]*xs + else: + nd = len(c) + c0 = c[-2]*xs + c1 = c[-1]*xs + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = lagsub(c[-i]*xs, (c1*(nd - 1))/nd) + c1 = lagadd(tmp, lagsub((2*nd - 1)*c1, lagmulx(c1))/nd) + return lagadd(c0, lagsub(c1, lagmulx(c1))) + + +def lagdiv(c1, c2): + """ + Divide one Laguerre series by another. + + Returns the quotient-with-remainder of two Laguerre series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + [quo, rem] : ndarrays + Of Laguerre series coefficients representing the quotient and + remainder. + + See Also + -------- + lagadd, lagsub, lagmulx, lagmul, lagpow + + Notes + ----- + In general, the (polynomial) division of one Laguerre series by another + results in quotient and remainder terms that are not in the Laguerre + polynomial basis set. Thus, to express these results as a Laguerre + series, it is necessary to "reproject" the results onto the Laguerre + basis set, which may produce "unintuitive" (but correct) results; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagdiv + >>> lagdiv([ 8., -13., 38., -51., 36.], [0, 1, 2]) + (array([1., 2., 3.]), array([0.])) + >>> lagdiv([ 9., -12., 38., -51., 36.], [0, 1, 2]) + (array([1., 2., 3.]), array([1., 1.])) + + """ + return pu._div(lagmul, c1, c2) + + +def lagpow(c, pow, maxpower=16): + """Raise a Laguerre series to a power. + + Returns the Laguerre series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Laguerre series of power. + + See Also + -------- + lagadd, lagsub, lagmulx, lagmul, lagdiv + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagpow + >>> lagpow([1, 2, 3], 2) + array([ 14., -16., 56., -72., 54.]) + + """ + return pu._pow(lagmul, c, pow, maxpower) + + +def lagder(c, m=1, scl=1, axis=0): + """ + Differentiate a Laguerre series. + + Returns the Laguerre series coefficients `c` differentiated `m` times + along `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*L_0 + 2*L_1 + 3*L_2`` + while [[1,2],[1,2]] represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + Array of Laguerre series coefficients. If `c` is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Laguerre series of the derivative. + + See Also + -------- + lagint + + Notes + ----- + In general, the result of differentiating a Laguerre series does not + resemble the same operation on a power series. Thus the result of this + function may be "unintuitive," albeit correct; see Examples section + below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagder + >>> lagder([ 1., 1., 1., -3.]) + array([1., 2., 3.]) + >>> lagder([ 1., 0., 0., -4., 3.], m=2) + array([1., 2., 3.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 1, -1): + der[j - 1] = -c[j] + c[j - 1] += c[j] + der[0] = -c[1] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Laguerre series. + + Returns the Laguerre series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``L_0 + 2*L_1 + 3*L_2`` while [[1,2],[1,2]] + represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + + Parameters + ---------- + c : array_like + Array of Laguerre series coefficients. If `c` is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at + ``lbnd`` is the first value in the list, the value of the second + integral at ``lbnd`` is the second value, etc. If ``k == []`` (the + default), all constants are set to zero. If ``m == 1``, a single + scalar can be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + Laguerre series coefficients of the integral. + + Raises + ------ + ValueError + If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + lagder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagint + >>> lagint([1,2,3]) + array([ 1., 1., 1., -3.]) + >>> lagint([1,2,3], m=2) + array([ 1., 0., 0., -4., 3.]) + >>> lagint([1,2,3], k=1) + array([ 2., 1., 1., -3.]) + >>> lagint([1,2,3], lbnd=-1) + array([11.5, 1. , 1. , -3. ]) + >>> lagint([1,2], m=2, k=[1,2], lbnd=-1) + array([ 11.16666667, -5. , -3. , 2. ]) # may vary + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0] + tmp[1] = -c[0] + for j in range(1, n): + tmp[j] += c[j] + tmp[j + 1] = -c[j] + tmp[0] += k[i] - lagval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def lagval(x, c, tensor=True): + """ + Evaluate a Laguerre series at points x. + + If `c` is of length ``n + 1``, this function returns the value: + + .. math:: p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + lagval2d, laggrid2d, lagval3d, laggrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagval + >>> coef = [1, 2, 3] + >>> lagval(1, coef) + -0.5 + >>> lagval([[1, 2],[3, 4]], coef) + array([[-0.5, -4. ], + [-4.5, -2. ]]) + + """ + c = np.array(c, ndmin=1, copy=None) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + nd = len(c) + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = c[-i] - (c1*(nd - 1))/nd + c1 = tmp + (c1*((2*nd - 1) - x))/nd + return c0 + c1*(1 - x) + + +def lagval2d(x, y, c): + """ + Evaluate a 2-D Laguerre series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points formed with + pairs of corresponding values from `x` and `y`. + + See Also + -------- + lagval, laggrid2d, lagval3d, laggrid3d + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagval2d + >>> c = [[1, 2],[3, 4]] + >>> lagval2d(1, 1, c) + 1.0 + """ + return pu._valnd(lagval, c, x, y) + + +def laggrid2d(x, y, c): + """ + Evaluate a 2-D Laguerre series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * L_i(a) * L_j(b) + + where the points ``(a, b)`` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape + y.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j is contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Chebyshev series at points in the + Cartesian product of `x` and `y`. + + See Also + -------- + lagval, lagval2d, lagval3d, laggrid3d + + Examples + -------- + >>> from numpy.polynomial.laguerre import laggrid2d + >>> c = [[1, 2], [3, 4]] + >>> laggrid2d([0, 1], [0, 1], c) + array([[10., 4.], + [ 3., 1.]]) + + """ + return pu._gridnd(lagval, c, x, y) + + +def lagval3d(x, y, z, c): + """ + Evaluate a 3-D Laguerre series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + ``(x, y, z)``, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + lagval, lagval2d, laggrid2d, laggrid3d + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagval3d + >>> c = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] + >>> lagval3d(1, 1, 2, c) + -1.0 + + """ + return pu._valnd(lagval, c, x, y, z) + + +def laggrid3d(x, y, z, c): + """ + Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c) + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + lagval, lagval2d, laggrid2d, lagval3d + + Examples + -------- + >>> from numpy.polynomial.laguerre import laggrid3d + >>> c = [[[1, 2], [3, 4]], [[5, 6], [7, 8]]] + >>> laggrid3d([0, 1], [0, 1], [2, 4], c) + array([[[ -4., -44.], + [ -2., -18.]], + [[ -2., -14.], + [ -1., -5.]]]) + + """ + return pu._gridnd(lagval, c, x, y, z) + + +def lagvander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = L_i(x) + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the degree of the Laguerre polynomial. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + array ``V = lagvander(x, n)``, then ``np.dot(V, c)`` and + ``lagval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of Laguerre series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo-Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding Laguerre polynomial. The dtype will be the same as + the converted `x`. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.laguerre import lagvander + >>> x = np.array([0, 1, 2]) + >>> lagvander(x, 3) + array([[ 1. , 1. , 1. , 1. ], + [ 1. , 0. , -0.5 , -0.66666667], + [ 1. , -1. , -1. , -0.33333333]]) + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + v[0] = x*0 + 1 + if ideg > 0: + v[1] = 1 - x + for i in range(2, ideg + 1): + v[i] = (v[i-1]*(2*i - 1 - x) - v[i-2]*(i - 1))/i + return np.moveaxis(v, 0, -1) + + +def lagvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y), + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the degrees of + the Laguerre polynomials. + + If ``V = lagvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``lagval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Laguerre + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + lagvander, lagvander3d, lagval2d, lagval3d + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.laguerre import lagvander2d + >>> x = np.array([0]) + >>> y = np.array([2]) + >>> lagvander2d(x, y, [2, 1]) + array([[ 1., -1., 1., -1., 1., -1.]]) + + """ + return pu._vander_nd_flat((lagvander, lagvander), (x, y), deg) + + +def lagvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = L_i(x)*L_j(y)*L_k(z), + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the degrees of the Laguerre polynomials. + + If ``V = lagvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``lagval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Laguerre + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + lagvander, lagvander3d, lagval2d, lagval3d + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.laguerre import lagvander3d + >>> x = np.array([0]) + >>> y = np.array([2]) + >>> z = np.array([0]) + >>> lagvander3d(x, y, z, [2, 1, 3]) + array([[ 1., 1., 1., 1., -1., -1., -1., -1., 1., 1., 1., 1., -1., + -1., -1., -1., 1., 1., 1., 1., -1., -1., -1., -1.]]) + + """ + return pu._vander_nd_flat((lagvander, lagvander, lagvander), (x, y, z), deg) + + +def lagfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Laguerre series to data. + + Return the coefficients of a Laguerre series of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x), + + where ``n`` is `deg`. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is len(x)*eps, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Laguerre coefficients ordered from low to high. If `y` was 2-D, + the coefficients for the data in column *k* of `y` are in column + *k*. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Warns + ----- + RankWarning + The rank of the coefficient matrix in the least-squares fit is + deficient. The warning is only raised if ``full == False``. The + warnings can be turned off by + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.polynomial.polyfit + numpy.polynomial.legendre.legfit + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.hermite_e.hermefit + lagval : Evaluates a Laguerre series. + lagvander : pseudo Vandermonde matrix of Laguerre series. + lagweight : Laguerre weight function. + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the Laguerre series ``p`` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where the :math:`w_j` are the weights. This problem is solved by + setting up as the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where ``V`` is the weighted pseudo Vandermonde matrix of `x`, ``c`` are the + coefficients to be solved for, `w` are the weights, and `y` are the + observed values. This equation is then solved using the singular value + decomposition of ``V``. + + If some of the singular values of `V` are so small that they are + neglected, then a `~exceptions.RankWarning` will be issued. This means that + the coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using Laguerre series are probably most useful when the data can + be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the Laguerre + weight. In that case the weight ``sqrt(w(x[i]))`` should be used + together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is + available as `lagweight`. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.laguerre import lagfit, lagval + >>> x = np.linspace(0, 10) + >>> rng = np.random.default_rng() + >>> err = rng.normal(scale=1./10, size=len(x)) + >>> y = lagval(x, [1, 2, 3]) + err + >>> lagfit(x, y, 2) + array([1.00578369, 1.99417356, 2.99827656]) # may vary + + """ + return pu._fit(lagvander, x, y, deg, rcond, full, w) + + +def lagcompanion(c): + """ + Return the companion matrix of c. + + The usual companion matrix of the Laguerre polynomials is already + symmetric when `c` is a basis Laguerre polynomial, so no scaling is + applied. + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Companion matrix of dimensions (deg, deg). + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagcompanion + >>> lagcompanion([1, 2, 3]) + array([[ 1. , -0.33333333], + [-1. , 4.33333333]]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[1 + c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + top = mat.reshape(-1)[1::n+1] + mid = mat.reshape(-1)[0::n+1] + bot = mat.reshape(-1)[n::n+1] + top[...] = -np.arange(1, n) + mid[...] = 2.*np.arange(n) + 1. + bot[...] = top + mat[:, -1] += (c[:-1]/c[-1])*n + return mat + + +def lagroots(c): + """ + Compute the roots of a Laguerre series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * L_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.legendre.legroots + numpy.polynomial.chebyshev.chebroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + The Laguerre series basis polynomials aren't powers of `x` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagroots, lagfromroots + >>> coef = lagfromroots([0, 1, 2]) + >>> coef + array([ 2., -8., 12., -6.]) + >>> lagroots(coef) + array([-4.4408921e-16, 1.0000000e+00, 2.0000000e+00]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) <= 1: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([1 + c[0]/c[1]]) + + # rotated companion matrix reduces error + m = lagcompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def laggauss(deg): + """ + Gauss-Laguerre quadrature. + + Computes the sample points and weights for Gauss-Laguerre quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[0, \\inf]` + with the weight function :math:`f(x) = \\exp(-x)`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + The results have only been tested up to degree 100 higher degrees may + be problematic. The weights are determined by using the fact that + + .. math:: w_k = c / (L'_n(x_k) * L_{n-1}(x_k)) + + where :math:`c` is a constant independent of :math:`k` and :math:`x_k` + is the k'th root of :math:`L_n`, and then scaling the results to get + the right value when integrating 1. + + Examples + -------- + >>> from numpy.polynomial.laguerre import laggauss + >>> laggauss(2) + (array([0.58578644, 3.41421356]), array([0.85355339, 0.14644661])) + + """ + ideg = pu._as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + # first approximation of roots. We use the fact that the companion + # matrix is symmetric in this case in order to obtain better zeros. + c = np.array([0]*deg + [1]) + m = lagcompanion(c) + x = la.eigvalsh(m) + + # improve roots by one application of Newton + dy = lagval(x, c) + df = lagval(x, lagder(c)) + x -= dy/df + + # compute the weights. We scale the factor to avoid possible numerical + # overflow. + fm = lagval(x, c[1:]) + fm /= np.abs(fm).max() + df /= np.abs(df).max() + w = 1/(fm * df) + + # scale w to get the right value, 1 in this case + w /= w.sum() + + return x, w + + +def lagweight(x): + """Weight function of the Laguerre polynomials. + + The weight function is :math:`exp(-x)` and the interval of integration + is :math:`[0, \\inf]`. The Laguerre polynomials are orthogonal, but not + normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagweight + >>> x = np.array([0, 1, 2]) + >>> lagweight(x) + array([1. , 0.36787944, 0.13533528]) + + """ + w = np.exp(-x) + return w + +# +# Laguerre series class +# + +class Laguerre(ABCPolyBase): + """A Laguerre series class. + + The Laguerre class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + Laguerre coefficients in order of increasing degree, i.e, + ``(1, 2, 3)`` gives ``1*L_0(x) + 2*L_1(X) + 3*L_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [0., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [0., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(lagadd) + _sub = staticmethod(lagsub) + _mul = staticmethod(lagmul) + _div = staticmethod(lagdiv) + _pow = staticmethod(lagpow) + _val = staticmethod(lagval) + _int = staticmethod(lagint) + _der = staticmethod(lagder) + _fit = staticmethod(lagfit) + _line = staticmethod(lagline) + _roots = staticmethod(lagroots) + _fromroots = staticmethod(lagfromroots) + + # Virtual properties + domain = np.array(lagdomain) + window = np.array(lagdomain) + basis_name = 'L' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.pyi new file mode 100644 index 0000000000000000000000000000000000000000..ee81157957482006cde90445fa73cf4223723d5f --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/laguerre.pyi @@ -0,0 +1,100 @@ +from typing import Final, Literal as L + +import numpy as np + +from ._polybase import ABCPolyBase +from ._polytypes import ( + _Array1, + _Array2, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncGauss, + _FuncInteg, + _FuncLine, + _FuncPoly2Ortho, + _FuncPow, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVal2D, + _FuncVal3D, + _FuncValFromRoots, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncWeight, +) +from .polyutils import trimcoef as lagtrim + +__all__ = [ + "lagzero", + "lagone", + "lagx", + "lagdomain", + "lagline", + "lagadd", + "lagsub", + "lagmulx", + "lagmul", + "lagdiv", + "lagpow", + "lagval", + "lagder", + "lagint", + "lag2poly", + "poly2lag", + "lagfromroots", + "lagvander", + "lagfit", + "lagtrim", + "lagroots", + "Laguerre", + "lagval2d", + "lagval3d", + "laggrid2d", + "laggrid3d", + "lagvander2d", + "lagvander3d", + "lagcompanion", + "laggauss", + "lagweight", +] + +poly2lag: _FuncPoly2Ortho[L["poly2lag"]] +lag2poly: _FuncUnOp[L["lag2poly"]] + +lagdomain: Final[_Array2[np.float64]] +lagzero: Final[_Array1[np.int_]] +lagone: Final[_Array1[np.int_]] +lagx: Final[_Array2[np.int_]] + +lagline: _FuncLine[L["lagline"]] +lagfromroots: _FuncFromRoots[L["lagfromroots"]] +lagadd: _FuncBinOp[L["lagadd"]] +lagsub: _FuncBinOp[L["lagsub"]] +lagmulx: _FuncUnOp[L["lagmulx"]] +lagmul: _FuncBinOp[L["lagmul"]] +lagdiv: _FuncBinOp[L["lagdiv"]] +lagpow: _FuncPow[L["lagpow"]] +lagder: _FuncDer[L["lagder"]] +lagint: _FuncInteg[L["lagint"]] +lagval: _FuncVal[L["lagval"]] +lagval2d: _FuncVal2D[L["lagval2d"]] +lagval3d: _FuncVal3D[L["lagval3d"]] +lagvalfromroots: _FuncValFromRoots[L["lagvalfromroots"]] +laggrid2d: _FuncVal2D[L["laggrid2d"]] +laggrid3d: _FuncVal3D[L["laggrid3d"]] +lagvander: _FuncVander[L["lagvander"]] +lagvander2d: _FuncVander2D[L["lagvander2d"]] +lagvander3d: _FuncVander3D[L["lagvander3d"]] +lagfit: _FuncFit[L["lagfit"]] +lagcompanion: _FuncCompanion[L["lagcompanion"]] +lagroots: _FuncRoots[L["lagroots"]] +laggauss: _FuncGauss[L["laggauss"]] +lagweight: _FuncWeight[L["lagweight"]] + + +class Laguerre(ABCPolyBase[L["L"]]): ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.py b/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.py new file mode 100644 index 0000000000000000000000000000000000000000..c2cd3fbfe76021c908b0e5a004f68617c1da6d7f --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.py @@ -0,0 +1,1605 @@ +""" +================================================== +Legendre Series (:mod:`numpy.polynomial.legendre`) +================================================== + +This module provides a number of objects (mostly functions) useful for +dealing with Legendre series, including a `Legendre` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with such polynomials is in the +docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- +.. autosummary:: + :toctree: generated/ + + Legendre + +Constants +--------- + +.. autosummary:: + :toctree: generated/ + + legdomain + legzero + legone + legx + +Arithmetic +---------- + +.. autosummary:: + :toctree: generated/ + + legadd + legsub + legmulx + legmul + legdiv + legpow + legval + legval2d + legval3d + leggrid2d + leggrid3d + +Calculus +-------- + +.. autosummary:: + :toctree: generated/ + + legder + legint + +Misc Functions +-------------- + +.. autosummary:: + :toctree: generated/ + + legfromroots + legroots + legvander + legvander2d + legvander3d + leggauss + legweight + legcompanion + legfit + legtrim + legline + leg2poly + poly2leg + +See also +-------- +numpy.polynomial + +""" +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +__all__ = [ + 'legzero', 'legone', 'legx', 'legdomain', 'legline', 'legadd', + 'legsub', 'legmulx', 'legmul', 'legdiv', 'legpow', 'legval', 'legder', + 'legint', 'leg2poly', 'poly2leg', 'legfromroots', 'legvander', + 'legfit', 'legtrim', 'legroots', 'Legendre', 'legval2d', 'legval3d', + 'leggrid2d', 'leggrid3d', 'legvander2d', 'legvander3d', 'legcompanion', + 'leggauss', 'legweight'] + +legtrim = pu.trimcoef + + +def poly2leg(pol): + """ + Convert a polynomial to a Legendre series. + + Convert an array representing the coefficients of a polynomial (relative + to the "standard" basis) ordered from lowest degree to highest, to an + array of the coefficients of the equivalent Legendre series, ordered + from lowest to highest degree. + + Parameters + ---------- + pol : array_like + 1-D array containing the polynomial coefficients + + Returns + ------- + c : ndarray + 1-D array containing the coefficients of the equivalent Legendre + series. + + See Also + -------- + leg2poly + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> import numpy as np + >>> from numpy import polynomial as P + >>> p = P.Polynomial(np.arange(4)) + >>> p + Polynomial([0., 1., 2., 3.], domain=[-1., 1.], window=[-1., 1.], ... + >>> c = P.Legendre(P.legendre.poly2leg(p.coef)) + >>> c + Legendre([ 1. , 3.25, 1. , 0.75], domain=[-1, 1], window=[-1, 1]) # may vary + + """ + [pol] = pu.as_series([pol]) + deg = len(pol) - 1 + res = 0 + for i in range(deg, -1, -1): + res = legadd(legmulx(res), pol[i]) + return res + + +def leg2poly(c): + """ + Convert a Legendre series to a polynomial. + + Convert an array representing the coefficients of a Legendre series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Legendre series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2leg + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy import polynomial as P + >>> c = P.Legendre(range(4)) + >>> c + Legendre([0., 1., 2., 3.], domain=[-1., 1.], window=[-1., 1.], symbol='x') + >>> p = c.convert(kind=P.Polynomial) + >>> p + Polynomial([-1. , -3.5, 3. , 7.5], domain=[-1., 1.], window=[-1., ... + >>> P.legendre.leg2poly(range(4)) + array([-1. , -3.5, 3. , 7.5]) + + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n < 3: + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], (c1*(i - 1))/i) + c1 = polyadd(tmp, (polymulx(c1)*(2*i - 1))/i) + return polyadd(c0, polymulx(c1)) + + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Legendre +legdomain = np.array([-1., 1.]) + +# Legendre coefficients representing zero. +legzero = np.array([0]) + +# Legendre coefficients representing one. +legone = np.array([1]) + +# Legendre coefficients representing the identity x. +legx = np.array([0, 1]) + + +def legline(off, scl): + """ + Legendre series whose graph is a straight line. + + + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Legendre series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.chebyshev.chebline + numpy.polynomial.laguerre.lagline + numpy.polynomial.hermite.hermline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> import numpy.polynomial.legendre as L + >>> L.legline(3,2) + array([3, 2]) + >>> L.legval(-3, L.legline(3,2)) # should be -3 + -3.0 + + """ + if scl != 0: + return np.array([off, scl]) + else: + return np.array([off]) + + +def legfromroots(roots): + """ + Generate a Legendre series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in Legendre form, where the :math:`r_n` are the roots specified in `roots`. + If a zero has multiplicity n, then it must appear in `roots` n times. + For instance, if 2 is a root of multiplicity three and 3 is a root of + multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The + roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in Legendre form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.chebyshev.chebfromroots + numpy.polynomial.laguerre.lagfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.hermite_e.hermefromroots + + Examples + -------- + >>> import numpy.polynomial.legendre as L + >>> L.legfromroots((-1,0,1)) # x^3 - x relative to the standard basis + array([ 0. , -0.4, 0. , 0.4]) + >>> j = complex(0,1) + >>> L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis + array([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j]) # may vary + + """ + return pu._fromroots(legline, legmul, roots) + + +def legadd(c1, c2): + """ + Add one Legendre series to another. + + Returns the sum of two Legendre series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Legendre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Legendre series of their sum. + + See Also + -------- + legsub, legmulx, legmul, legdiv, legpow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Legendre series + is a Legendre series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> L.legadd(c1,c2) + array([4., 4., 4.]) + + """ + return pu._add(c1, c2) + + +def legsub(c1, c2): + """ + Subtract one Legendre series from another. + + Returns the difference of two Legendre series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Legendre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Legendre series coefficients representing their difference. + + See Also + -------- + legadd, legmulx, legmul, legdiv, legpow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Legendre + series is a Legendre series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> L.legsub(c1,c2) + array([-2., 0., 2.]) + >>> L.legsub(c2,c1) # -C.legsub(c1,c2) + array([ 2., 0., -2.]) + + """ + return pu._sub(c1, c2) + + +def legmulx(c): + """Multiply a Legendre series by x. + + Multiply the Legendre series `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Legendre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + legadd, legsub, legmul, legdiv, legpow + + Notes + ----- + The multiplication uses the recursion relationship for Legendre + polynomials in the form + + .. math:: + + xP_i(x) = ((i + 1)*P_{i + 1}(x) + i*P_{i - 1}(x))/(2i + 1) + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> L.legmulx([1,2,3]) + array([ 0.66666667, 2.2, 1.33333333, 1.8]) # may vary + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0]*0 + prd[1] = c[0] + for i in range(1, len(c)): + j = i + 1 + k = i - 1 + s = i + j + prd[j] = (c[i]*j)/s + prd[k] += (c[i]*i)/s + return prd + + +def legmul(c1, c2): + """ + Multiply one Legendre series by another. + + Returns the product of two Legendre series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Legendre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Legendre series coefficients representing their product. + + See Also + -------- + legadd, legsub, legmulx, legdiv, legpow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Legendre polynomial basis set. Thus, to express + the product as a Legendre series, it is necessary to "reproject" the + product onto said basis set, which may produce "unintuitive" (but + correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c1 = (1,2,3) + >>> c2 = (3,2) + >>> L.legmul(c1,c2) # multiplication requires "reprojection" + array([ 4.33333333, 10.4 , 11.66666667, 3.6 ]) # may vary + + """ + # s1, s2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + + if len(c1) > len(c2): + c = c2 + xs = c1 + else: + c = c1 + xs = c2 + + if len(c) == 1: + c0 = c[0]*xs + c1 = 0 + elif len(c) == 2: + c0 = c[0]*xs + c1 = c[1]*xs + else: + nd = len(c) + c0 = c[-2]*xs + c1 = c[-1]*xs + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = legsub(c[-i]*xs, (c1*(nd - 1))/nd) + c1 = legadd(tmp, (legmulx(c1)*(2*nd - 1))/nd) + return legadd(c0, legmulx(c1)) + + +def legdiv(c1, c2): + """ + Divide one Legendre series by another. + + Returns the quotient-with-remainder of two Legendre series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Legendre series coefficients ordered from low to + high. + + Returns + ------- + quo, rem : ndarrays + Of Legendre series coefficients representing the quotient and + remainder. + + See Also + -------- + legadd, legsub, legmulx, legmul, legpow + + Notes + ----- + In general, the (polynomial) division of one Legendre series by another + results in quotient and remainder terms that are not in the Legendre + polynomial basis set. Thus, to express these results as a Legendre + series, it is necessary to "reproject" the results onto the Legendre + basis set, which may produce "unintuitive" (but correct) results; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c1 = (1,2,3) + >>> c2 = (3,2,1) + >>> L.legdiv(c1,c2) # quotient "intuitive," remainder not + (array([3.]), array([-8., -4.])) + >>> c2 = (0,1,2,3) + >>> L.legdiv(c2,c1) # neither "intuitive" + (array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852])) # may vary + + """ + return pu._div(legmul, c1, c2) + + +def legpow(c, pow, maxpower=16): + """Raise a Legendre series to a power. + + Returns the Legendre series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Legendre series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Legendre series of power. + + See Also + -------- + legadd, legsub, legmulx, legmul, legdiv + + """ + return pu._pow(legmul, c, pow, maxpower) + + +def legder(c, m=1, scl=1, axis=0): + """ + Differentiate a Legendre series. + + Returns the Legendre series coefficients `c` differentiated `m` times + along `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*L_0 + 2*L_1 + 3*L_2`` + while [[1,2],[1,2]] represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + Array of Legendre series coefficients. If c is multidimensional the + different axis correspond to different variables with the degree in + each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Legendre series of the derivative. + + See Also + -------- + legint + + Notes + ----- + In general, the result of differentiating a Legendre series does not + resemble the same operation on a power series. Thus the result of this + function may be "unintuitive," albeit correct; see Examples section + below. + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c = (1,2,3,4) + >>> L.legder(c) + array([ 6., 9., 20.]) + >>> L.legder(c, 3) + array([60.]) + >>> L.legder(c, scl=-1) + array([ -6., -9., -20.]) + >>> L.legder(c, 2,-1) + array([ 9., 60.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 2, -1): + der[j - 1] = (2*j - 1)*c[j] + c[j - 2] += c[j] + if n > 1: + der[1] = 3*c[2] + der[0] = c[1] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def legint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Legendre series. + + Returns the Legendre series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``L_0 + 2*L_1 + 3*L_2`` while [[1,2],[1,2]] + represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + Parameters + ---------- + c : array_like + Array of Legendre series coefficients. If c is multidimensional the + different axis correspond to different variables with the degree in + each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at + ``lbnd`` is the first value in the list, the value of the second + integral at ``lbnd`` is the second value, etc. If ``k == []`` (the + default), all constants are set to zero. If ``m == 1``, a single + scalar can be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + Legendre series coefficient array of the integral. + + Raises + ------ + ValueError + If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + legder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial import legendre as L + >>> c = (1,2,3) + >>> L.legint(c) + array([ 0.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary + >>> L.legint(c, 3) + array([ 1.66666667e-02, -1.78571429e-02, 4.76190476e-02, # may vary + -1.73472348e-18, 1.90476190e-02, 9.52380952e-03]) + >>> L.legint(c, k=3) + array([ 3.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary + >>> L.legint(c, lbnd=-2) + array([ 7.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary + >>> L.legint(c, scl=2) + array([ 0.66666667, 0.8 , 1.33333333, 1.2 ]) # may vary + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0]*0 + tmp[1] = c[0] + if n > 1: + tmp[2] = c[1]/3 + for j in range(2, n): + t = c[j]/(2*j + 1) + tmp[j + 1] = t + tmp[j - 1] -= t + tmp[0] += k[i] - legval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def legval(x, c, tensor=True): + """ + Evaluate a Legendre series at points x. + + If `c` is of length ``n + 1``, this function returns the value: + + .. math:: p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + legval2d, leggrid2d, legval3d, leggrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + """ + c = np.array(c, ndmin=1, copy=None) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + nd = len(c) + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = c[-i] - (c1*(nd - 1))/nd + c1 = tmp + (c1*x*(2*nd - 1))/nd + return c0 + c1*x + + +def legval2d(x, y, c): + """ + Evaluate a 2-D Legendre series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Legendre series at points formed + from pairs of corresponding values from `x` and `y`. + + See Also + -------- + legval, leggrid2d, legval3d, leggrid3d + """ + return pu._valnd(legval, c, x, y) + + +def leggrid2d(x, y, c): + """ + Evaluate a 2-D Legendre series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * L_i(a) * L_j(b) + + where the points ``(a, b)`` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape + y.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j is contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Chebyshev series at points in the + Cartesian product of `x` and `y`. + + See Also + -------- + legval, legval2d, legval3d, leggrid3d + """ + return pu._gridnd(legval, c, x, y) + + +def legval3d(x, y, z, c): + """ + Evaluate a 3-D Legendre series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + ``(x, y, z)``, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + legval, legval2d, leggrid2d, leggrid3d + """ + return pu._valnd(legval, c, x, y, z) + + +def leggrid3d(x, y, z, c): + """ + Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c) + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + legval, legval2d, leggrid2d, legval3d + """ + return pu._gridnd(legval, c, x, y, z) + + +def legvander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = L_i(x) + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the degree of the Legendre polynomial. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + array ``V = legvander(x, n)``, then ``np.dot(V, c)`` and + ``legval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of Legendre series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo-Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding Legendre polynomial. The dtype will be the same as + the converted `x`. + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + # Use forward recursion to generate the entries. This is not as accurate + # as reverse recursion in this application but it is more efficient. + v[0] = x*0 + 1 + if ideg > 0: + v[1] = x + for i in range(2, ideg + 1): + v[i] = (v[i-1]*x*(2*i - 1) - v[i-2]*(i - 1))/i + return np.moveaxis(v, 0, -1) + + +def legvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y), + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the degrees of + the Legendre polynomials. + + If ``V = legvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``legval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Legendre + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + legvander, legvander3d, legval2d, legval3d + """ + return pu._vander_nd_flat((legvander, legvander), (x, y), deg) + + +def legvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = L_i(x)*L_j(y)*L_k(z), + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the degrees of the Legendre polynomials. + + If ``V = legvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``legval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Legendre + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + legvander, legvander3d, legval2d, legval3d + """ + return pu._vander_nd_flat((legvander, legvander, legvander), (x, y, z), deg) + + +def legfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Legendre series to data. + + Return the coefficients of a Legendre series of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x), + + where `n` is `deg`. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is len(x)*eps, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Legendre coefficients ordered from low to high. If `y` was + 2-D, the coefficients for the data in column k of `y` are in + column `k`. If `deg` is specified as a list, coefficients for + terms not included in the fit are set equal to zero in the + returned `coef`. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Warns + ----- + RankWarning + The rank of the coefficient matrix in the least-squares fit is + deficient. The warning is only raised if ``full == False``. The + warnings can be turned off by + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.polynomial.polyfit + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.laguerre.lagfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.hermite_e.hermefit + legval : Evaluates a Legendre series. + legvander : Vandermonde matrix of Legendre series. + legweight : Legendre weight function (= 1). + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the Legendre series `p` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where :math:`w_j` are the weights. This problem is solved by setting up + as the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the + coefficients to be solved for, `w` are the weights, and `y` are the + observed values. This equation is then solved using the singular value + decomposition of `V`. + + If some of the singular values of `V` are so small that they are + neglected, then a `~exceptions.RankWarning` will be issued. This means that + the coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using Legendre series are usually better conditioned than fits + using power series, but much can depend on the distribution of the + sample points and the smoothness of the data. If the quality of the fit + is inadequate splines may be a good alternative. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + + """ + return pu._fit(legvander, x, y, deg, rcond, full, w) + + +def legcompanion(c): + """Return the scaled companion matrix of c. + + The basis polynomials are scaled so that the companion matrix is + symmetric when `c` is an Legendre basis polynomial. This provides + better eigenvalue estimates than the unscaled case and for basis + polynomials the eigenvalues are guaranteed to be real if + `numpy.linalg.eigvalsh` is used to obtain them. + + Parameters + ---------- + c : array_like + 1-D array of Legendre series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Scaled companion matrix of dimensions (deg, deg). + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[-c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + scl = 1./np.sqrt(2*np.arange(n) + 1) + top = mat.reshape(-1)[1::n+1] + bot = mat.reshape(-1)[n::n+1] + top[...] = np.arange(1, n)*scl[:n-1]*scl[1:n] + bot[...] = top + mat[:, -1] -= (c[:-1]/c[-1])*(scl/scl[-1])*(n/(2*n - 1)) + return mat + + +def legroots(c): + """ + Compute the roots of a Legendre series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * L_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.chebyshev.chebroots + numpy.polynomial.laguerre.lagroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such values. + Roots with multiplicity greater than 1 will also show larger errors as + the value of the series near such points is relatively insensitive to + errors in the roots. Isolated roots near the origin can be improved by + a few iterations of Newton's method. + + The Legendre series basis polynomials aren't powers of ``x`` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> import numpy.polynomial.legendre as leg + >>> leg.legroots((1, 2, 3, 4)) # 4L_3 + 3L_2 + 2L_1 + 1L_0, all real roots + array([-0.85099543, -0.11407192, 0.51506735]) # may vary + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([-c[0]/c[1]]) + + # rotated companion matrix reduces error + m = legcompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def leggauss(deg): + """ + Gauss-Legendre quadrature. + + Computes the sample points and weights for Gauss-Legendre quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[-1, 1]` with + the weight function :math:`f(x) = 1`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + The results have only been tested up to degree 100, higher degrees may + be problematic. The weights are determined by using the fact that + + .. math:: w_k = c / (L'_n(x_k) * L_{n-1}(x_k)) + + where :math:`c` is a constant independent of :math:`k` and :math:`x_k` + is the k'th root of :math:`L_n`, and then scaling the results to get + the right value when integrating 1. + + """ + ideg = pu._as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + # first approximation of roots. We use the fact that the companion + # matrix is symmetric in this case in order to obtain better zeros. + c = np.array([0]*deg + [1]) + m = legcompanion(c) + x = la.eigvalsh(m) + + # improve roots by one application of Newton + dy = legval(x, c) + df = legval(x, legder(c)) + x -= dy/df + + # compute the weights. We scale the factor to avoid possible numerical + # overflow. + fm = legval(x, c[1:]) + fm /= np.abs(fm).max() + df /= np.abs(df).max() + w = 1/(fm * df) + + # for Legendre we can also symmetrize + w = (w + w[::-1])/2 + x = (x - x[::-1])/2 + + # scale w to get the right value + w *= 2. / w.sum() + + return x, w + + +def legweight(x): + """ + Weight function of the Legendre polynomials. + + The weight function is :math:`1` and the interval of integration is + :math:`[-1, 1]`. The Legendre polynomials are orthogonal, but not + normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + """ + w = x*0.0 + 1.0 + return w + +# +# Legendre series class +# + +class Legendre(ABCPolyBase): + """A Legendre series class. + + The Legendre class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + Legendre coefficients in order of increasing degree, i.e., + ``(1, 2, 3)`` gives ``1*P_0(x) + 2*P_1(x) + 3*P_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [-1., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [-1., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(legadd) + _sub = staticmethod(legsub) + _mul = staticmethod(legmul) + _div = staticmethod(legdiv) + _pow = staticmethod(legpow) + _val = staticmethod(legval) + _int = staticmethod(legint) + _der = staticmethod(legder) + _fit = staticmethod(legfit) + _line = staticmethod(legline) + _roots = staticmethod(legroots) + _fromroots = staticmethod(legfromroots) + + # Virtual properties + domain = np.array(legdomain) + window = np.array(legdomain) + basis_name = 'P' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi new file mode 100644 index 0000000000000000000000000000000000000000..d81f3e6f54a4f72fd2cbc341f0efaa973aa3195a --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi @@ -0,0 +1,99 @@ +from typing import Final, Literal as L + +import numpy as np + +from ._polybase import ABCPolyBase +from ._polytypes import ( + _Array1, + _Array2, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncGauss, + _FuncInteg, + _FuncLine, + _FuncPoly2Ortho, + _FuncPow, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVal2D, + _FuncVal3D, + _FuncValFromRoots, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncWeight, +) +from .polyutils import trimcoef as legtrim + +__all__ = [ + "legzero", + "legone", + "legx", + "legdomain", + "legline", + "legadd", + "legsub", + "legmulx", + "legmul", + "legdiv", + "legpow", + "legval", + "legder", + "legint", + "leg2poly", + "poly2leg", + "legfromroots", + "legvander", + "legfit", + "legtrim", + "legroots", + "Legendre", + "legval2d", + "legval3d", + "leggrid2d", + "leggrid3d", + "legvander2d", + "legvander3d", + "legcompanion", + "leggauss", + "legweight", +] + +poly2leg: _FuncPoly2Ortho[L["poly2leg"]] +leg2poly: _FuncUnOp[L["leg2poly"]] + +legdomain: Final[_Array2[np.float64]] +legzero: Final[_Array1[np.int_]] +legone: Final[_Array1[np.int_]] +legx: Final[_Array2[np.int_]] + +legline: _FuncLine[L["legline"]] +legfromroots: _FuncFromRoots[L["legfromroots"]] +legadd: _FuncBinOp[L["legadd"]] +legsub: _FuncBinOp[L["legsub"]] +legmulx: _FuncUnOp[L["legmulx"]] +legmul: _FuncBinOp[L["legmul"]] +legdiv: _FuncBinOp[L["legdiv"]] +legpow: _FuncPow[L["legpow"]] +legder: _FuncDer[L["legder"]] +legint: _FuncInteg[L["legint"]] +legval: _FuncVal[L["legval"]] +legval2d: _FuncVal2D[L["legval2d"]] +legval3d: _FuncVal3D[L["legval3d"]] +legvalfromroots: _FuncValFromRoots[L["legvalfromroots"]] +leggrid2d: _FuncVal2D[L["leggrid2d"]] +leggrid3d: _FuncVal3D[L["leggrid3d"]] +legvander: _FuncVander[L["legvander"]] +legvander2d: _FuncVander2D[L["legvander2d"]] +legvander3d: _FuncVander3D[L["legvander3d"]] +legfit: _FuncFit[L["legfit"]] +legcompanion: _FuncCompanion[L["legcompanion"]] +legroots: _FuncRoots[L["legroots"]] +leggauss: _FuncGauss[L["leggauss"]] +legweight: _FuncWeight[L["legweight"]] + +class Legendre(ABCPolyBase[L["P"]]): ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.py b/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.py new file mode 100644 index 0000000000000000000000000000000000000000..86ea3a5d1d6e030929bc9de2f4744983a2a0417e --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.py @@ -0,0 +1,1617 @@ +""" +================================================= +Power Series (:mod:`numpy.polynomial.polynomial`) +================================================= + +This module provides a number of objects (mostly functions) useful for +dealing with polynomials, including a `Polynomial` class that +encapsulates the usual arithmetic operations. (General information +on how this module represents and works with polynomial objects is in +the docstring for its "parent" sub-package, `numpy.polynomial`). + +Classes +------- +.. autosummary:: + :toctree: generated/ + + Polynomial + +Constants +--------- +.. autosummary:: + :toctree: generated/ + + polydomain + polyzero + polyone + polyx + +Arithmetic +---------- +.. autosummary:: + :toctree: generated/ + + polyadd + polysub + polymulx + polymul + polydiv + polypow + polyval + polyval2d + polyval3d + polygrid2d + polygrid3d + +Calculus +-------- +.. autosummary:: + :toctree: generated/ + + polyder + polyint + +Misc Functions +-------------- +.. autosummary:: + :toctree: generated/ + + polyfromroots + polyroots + polyvalfromroots + polyvander + polyvander2d + polyvander3d + polycompanion + polyfit + polytrim + polyline + +See Also +-------- +`numpy.polynomial` + +""" +__all__ = [ + 'polyzero', 'polyone', 'polyx', 'polydomain', 'polyline', 'polyadd', + 'polysub', 'polymulx', 'polymul', 'polydiv', 'polypow', 'polyval', + 'polyvalfromroots', 'polyder', 'polyint', 'polyfromroots', 'polyvander', + 'polyfit', 'polytrim', 'polyroots', 'Polynomial', 'polyval2d', 'polyval3d', + 'polygrid2d', 'polygrid3d', 'polyvander2d', 'polyvander3d', + 'polycompanion'] + +import numpy as np +import numpy.linalg as la +from numpy.lib.array_utils import normalize_axis_index + +from . import polyutils as pu +from ._polybase import ABCPolyBase + +polytrim = pu.trimcoef + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Polynomial default domain. +polydomain = np.array([-1., 1.]) + +# Polynomial coefficients representing zero. +polyzero = np.array([0]) + +# Polynomial coefficients representing one. +polyone = np.array([1]) + +# Polynomial coefficients representing the identity x. +polyx = np.array([0, 1]) + +# +# Polynomial series functions +# + + +def polyline(off, scl): + """ + Returns an array representing a linear polynomial. + + Parameters + ---------- + off, scl : scalars + The "y-intercept" and "slope" of the line, respectively. + + Returns + ------- + y : ndarray + This module's representation of the linear polynomial ``off + + scl*x``. + + See Also + -------- + numpy.polynomial.chebyshev.chebline + numpy.polynomial.legendre.legline + numpy.polynomial.laguerre.lagline + numpy.polynomial.hermite.hermline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> P.polyline(1, -1) + array([ 1, -1]) + >>> P.polyval(1, P.polyline(1, -1)) # should be 0 + 0.0 + + """ + if scl != 0: + return np.array([off, scl]) + else: + return np.array([off]) + + +def polyfromroots(roots): + """ + Generate a monic polynomial with given roots. + + Return the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + where the :math:`r_n` are the roots specified in `roots`. If a zero has + multiplicity n, then it must appear in `roots` n times. For instance, + if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, + then `roots` looks something like [2, 2, 2, 3, 3]. The roots can appear + in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * x + ... + x^n + + The coefficient of the last term is 1 for monic polynomials in this + form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of the polynomial's coefficients If all the roots are + real, then `out` is also real, otherwise it is complex. (see + Examples below). + + See Also + -------- + numpy.polynomial.chebyshev.chebfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.laguerre.lagfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.hermite_e.hermefromroots + + Notes + ----- + The coefficients are determined by multiplying together linear factors + of the form ``(x - r_i)``, i.e. + + .. math:: p(x) = (x - r_0) (x - r_1) ... (x - r_n) + + where ``n == len(roots) - 1``; note that this implies that ``1`` is always + returned for :math:`a_n`. + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> P.polyfromroots((-1,0,1)) # x(x - 1)(x + 1) = x^3 - x + array([ 0., -1., 0., 1.]) + >>> j = complex(0,1) + >>> P.polyfromroots((-j,j)) # complex returned, though values are real + array([1.+0.j, 0.+0.j, 1.+0.j]) + + """ + return pu._fromroots(polyline, polymul, roots) + + +def polyadd(c1, c2): + """ + Add one polynomial to another. + + Returns the sum of two polynomials `c1` + `c2`. The arguments are + sequences of coefficients from lowest order term to highest, i.e., + [1,2,3] represents the polynomial ``1 + 2*x + 3*x**2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of polynomial coefficients ordered from low to high. + + Returns + ------- + out : ndarray + The coefficient array representing their sum. + + See Also + -------- + polysub, polymulx, polymul, polydiv, polypow + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c1 = (1, 2, 3) + >>> c2 = (3, 2, 1) + >>> sum = P.polyadd(c1,c2); sum + array([4., 4., 4.]) + >>> P.polyval(2, sum) # 4 + 4(2) + 4(2**2) + 28.0 + + """ + return pu._add(c1, c2) + + +def polysub(c1, c2): + """ + Subtract one polynomial from another. + + Returns the difference of two polynomials `c1` - `c2`. The arguments + are sequences of coefficients from lowest order term to highest, i.e., + [1,2,3] represents the polynomial ``1 + 2*x + 3*x**2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of polynomial coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of coefficients representing their difference. + + See Also + -------- + polyadd, polymulx, polymul, polydiv, polypow + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c1 = (1, 2, 3) + >>> c2 = (3, 2, 1) + >>> P.polysub(c1,c2) + array([-2., 0., 2.]) + >>> P.polysub(c2, c1) # -P.polysub(c1,c2) + array([ 2., 0., -2.]) + + """ + return pu._sub(c1, c2) + + +def polymulx(c): + """Multiply a polynomial by x. + + Multiply the polynomial `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of polynomial coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + polyadd, polysub, polymul, polydiv, polypow + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = (1, 2, 3) + >>> P.polymulx(c) + array([0., 1., 2., 3.]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0]*0 + prd[1:] = c + return prd + + +def polymul(c1, c2): + """ + Multiply one polynomial by another. + + Returns the product of two polynomials `c1` * `c2`. The arguments are + sequences of coefficients, from lowest order term to highest, e.g., + [1,2,3] represents the polynomial ``1 + 2*x + 3*x**2.`` + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of coefficients representing a polynomial, relative to the + "standard" basis, and ordered from lowest order term to highest. + + Returns + ------- + out : ndarray + Of the coefficients of their product. + + See Also + -------- + polyadd, polysub, polymulx, polydiv, polypow + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c1 = (1, 2, 3) + >>> c2 = (3, 2, 1) + >>> P.polymul(c1, c2) + array([ 3., 8., 14., 8., 3.]) + + """ + # c1, c2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + ret = np.convolve(c1, c2) + return pu.trimseq(ret) + + +def polydiv(c1, c2): + """ + Divide one polynomial by another. + + Returns the quotient-with-remainder of two polynomials `c1` / `c2`. + The arguments are sequences of coefficients, from lowest order term + to highest, e.g., [1,2,3] represents ``1 + 2*x + 3*x**2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of polynomial coefficients ordered from low to high. + + Returns + ------- + [quo, rem] : ndarrays + Of coefficient series representing the quotient and remainder. + + See Also + -------- + polyadd, polysub, polymulx, polymul, polypow + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c1 = (1, 2, 3) + >>> c2 = (3, 2, 1) + >>> P.polydiv(c1, c2) + (array([3.]), array([-8., -4.])) + >>> P.polydiv(c2, c1) + (array([ 0.33333333]), array([ 2.66666667, 1.33333333])) # may vary + + """ + # c1, c2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + if c2[-1] == 0: + raise ZeroDivisionError # FIXME: add message with details to exception + + # note: this is more efficient than `pu._div(polymul, c1, c2)` + lc1 = len(c1) + lc2 = len(c2) + if lc1 < lc2: + return c1[:1]*0, c1 + elif lc2 == 1: + return c1/c2[-1], c1[:1]*0 + else: + dlen = lc1 - lc2 + scl = c2[-1] + c2 = c2[:-1]/scl + i = dlen + j = lc1 - 1 + while i >= 0: + c1[i:j] -= c2*c1[j] + i -= 1 + j -= 1 + return c1[j+1:]/scl, pu.trimseq(c1[:j+1]) + + +def polypow(c, pow, maxpower=None): + """Raise a polynomial to a power. + + Returns the polynomial `c` raised to the power `pow`. The argument + `c` is a sequence of coefficients ordered from low to high. i.e., + [1,2,3] is the series ``1 + 2*x + 3*x**2.`` + + Parameters + ---------- + c : array_like + 1-D array of array of series coefficients ordered from low to + high degree. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Power series of power. + + See Also + -------- + polyadd, polysub, polymulx, polymul, polydiv + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> P.polypow([1, 2, 3], 2) + array([ 1., 4., 10., 12., 9.]) + + """ + # note: this is more efficient than `pu._pow(polymul, c1, c2)`, as it + # avoids calling `as_series` repeatedly + return pu._pow(np.convolve, c, pow, maxpower) + + +def polyder(c, m=1, scl=1, axis=0): + """ + Differentiate a polynomial. + + Returns the polynomial coefficients `c` differentiated `m` times along + `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The + argument `c` is an array of coefficients from low to high degree along + each axis, e.g., [1,2,3] represents the polynomial ``1 + 2*x + 3*x**2`` + while [[1,2],[1,2]] represents ``1 + 1*x + 2*y + 2*x*y`` if axis=0 is + ``x`` and axis=1 is ``y``. + + Parameters + ---------- + c : array_like + Array of polynomial coefficients. If c is multidimensional the + different axis correspond to different variables with the degree + in each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change + of variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + Returns + ------- + der : ndarray + Polynomial coefficients of the derivative. + + See Also + -------- + polyint + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = (1, 2, 3, 4) + >>> P.polyder(c) # (d/dx)(c) + array([ 2., 6., 12.]) + >>> P.polyder(c, 3) # (d**3/dx**3)(c) + array([24.]) + >>> P.polyder(c, scl=-1) # (d/d(-x))(c) + array([ -2., -6., -12.]) + >>> P.polyder(c, 2, -1) # (d**2/d(-x)**2)(c) + array([ 6., 24.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + # astype fails with NA + c = c + 0.0 + cdt = c.dtype + cnt = pu._as_int(m, "the order of derivation") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=cdt) + for j in range(n, 0, -1): + der[j - 1] = j*c[j] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def polyint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a polynomial. + + Returns the polynomial coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients, from low to high degree along each axis, e.g., [1,2,3] + represents the polynomial ``1 + 2*x + 3*x**2`` while [[1,2],[1,2]] + represents ``1 + 1*x + 2*y + 2*x*y`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + 1-D array of polynomial coefficients, ordered from low to high. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at zero + is the first value in the list, the value of the second integral + at zero is the second value, etc. If ``k == []`` (the default), + all constants are set to zero. If ``m == 1``, a single scalar can + be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + Returns + ------- + S : ndarray + Coefficient array of the integral. + + Raises + ------ + ValueError + If ``m < 1``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + polyder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. Why + is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = (1, 2, 3) + >>> P.polyint(c) # should return array([0, 1, 1, 1]) + array([0., 1., 1., 1.]) + >>> P.polyint(c, 3) # should return array([0, 0, 0, 1/6, 1/12, 1/20]) + array([ 0. , 0. , 0. , 0.16666667, 0.08333333, # may vary + 0.05 ]) + >>> P.polyint(c, k=3) # should return array([3, 1, 1, 1]) + array([3., 1., 1., 1.]) + >>> P.polyint(c,lbnd=-2) # should return array([6, 1, 1, 1]) + array([6., 1., 1., 1.]) + >>> P.polyint(c,scl=-2) # should return array([0, -2, -2, -2]) + array([ 0., -2., -2., -2.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + # astype doesn't preserve mask attribute. + c = c + 0.0 + cdt = c.dtype + if not np.iterable(k): + k = [k] + cnt = pu._as_int(m, "the order of integration") + iaxis = pu._as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + k = list(k) + [0]*(cnt - len(k)) + c = np.moveaxis(c, iaxis, 0) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=cdt) + tmp[0] = c[0]*0 + tmp[1] = c[0] + for j in range(1, n): + tmp[j + 1] = c[j]/(j + 1) + tmp[0] += k[i] - polyval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def polyval(x, c, tensor=True): + """ + Evaluate a polynomial at points x. + + If `c` is of length ``n + 1``, this function returns the value + + .. math:: p(x) = c_0 + c_1 * x + ... + c_n * x^n + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + with themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + Returns + ------- + values : ndarray, compatible object + The shape of the returned array is described above. + + See Also + -------- + polyval2d, polygrid2d, polyval3d, polygrid3d + + Notes + ----- + The evaluation uses Horner's method. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial.polynomial import polyval + >>> polyval(1, [1,2,3]) + 6.0 + >>> a = np.arange(4).reshape(2,2) + >>> a + array([[0, 1], + [2, 3]]) + >>> polyval(a, [1, 2, 3]) + array([[ 1., 6.], + [17., 34.]]) + >>> coef = np.arange(4).reshape(2, 2) # multidimensional coefficients + >>> coef + array([[0, 1], + [2, 3]]) + >>> polyval([1, 2], coef, tensor=True) + array([[2., 4.], + [4., 7.]]) + >>> polyval([1, 2], coef, tensor=False) + array([2., 7.]) + + """ + c = np.array(c, ndmin=1, copy=None) + if c.dtype.char in '?bBhHiIlLqQpP': + # astype fails with NA + c = c + 0.0 + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + c0 = c[-1] + x*0 + for i in range(2, len(c) + 1): + c0 = c[-i] + c0*x + return c0 + + +def polyvalfromroots(x, r, tensor=True): + """ + Evaluate a polynomial specified by its roots at points x. + + If `r` is of length ``N``, this function returns the value + + .. math:: p(x) = \\prod_{n=1}^{N} (x - r_n) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `r`. + + If `r` is a 1-D array, then ``p(x)`` will have the same shape as `x`. If `r` + is multidimensional, then the shape of the result depends on the value of + `tensor`. If `tensor` is ``True`` the shape will be r.shape[1:] + x.shape; + that is, each polynomial is evaluated at every value of `x`. If `tensor` is + ``False``, the shape will be r.shape[1:]; that is, each polynomial is + evaluated only for the corresponding broadcast value of `x`. Note that + scalars have shape (,). + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + with themselves and with the elements of `r`. + r : array_like + Array of roots. If `r` is multidimensional the first index is the + root index, while the remaining indices enumerate multiple + polynomials. For instance, in the two dimensional case the roots + of each polynomial may be thought of as stored in the columns of `r`. + tensor : boolean, optional + If True, the shape of the roots array is extended with ones on the + right, one for each dimension of `x`. Scalars have dimension 0 for this + action. The result is that every column of coefficients in `r` is + evaluated for every element of `x`. If False, `x` is broadcast over the + columns of `r` for the evaluation. This keyword is useful when `r` is + multidimensional. The default value is True. + + Returns + ------- + values : ndarray, compatible object + The shape of the returned array is described above. + + See Also + -------- + polyroots, polyfromroots, polyval + + Examples + -------- + >>> from numpy.polynomial.polynomial import polyvalfromroots + >>> polyvalfromroots(1, [1, 2, 3]) + 0.0 + >>> a = np.arange(4).reshape(2, 2) + >>> a + array([[0, 1], + [2, 3]]) + >>> polyvalfromroots(a, [-1, 0, 1]) + array([[-0., 0.], + [ 6., 24.]]) + >>> r = np.arange(-2, 2).reshape(2,2) # multidimensional coefficients + >>> r # each column of r defines one polynomial + array([[-2, -1], + [ 0, 1]]) + >>> b = [-2, 1] + >>> polyvalfromroots(b, r, tensor=True) + array([[-0., 3.], + [ 3., 0.]]) + >>> polyvalfromroots(b, r, tensor=False) + array([-0., 0.]) + + """ + r = np.array(r, ndmin=1, copy=None) + if r.dtype.char in '?bBhHiIlLqQpP': + r = r.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray): + if tensor: + r = r.reshape(r.shape + (1,)*x.ndim) + elif x.ndim >= r.ndim: + raise ValueError("x.ndim must be < r.ndim when tensor == False") + return np.prod(x - r, axis=0) + + +def polyval2d(x, y, c): + """ + Evaluate a 2-D polynomial at points (x, y). + + This function returns the value + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * x^i * y^j + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points ``(x, y)``, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points formed with + pairs of corresponding values from `x` and `y`. + + See Also + -------- + polyval, polygrid2d, polyval3d, polygrid3d + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = ((1, 2, 3), (4, 5, 6)) + >>> P.polyval2d(1, 1, c) + 21.0 + + """ + return pu._valnd(polyval, c, x, y) + + +def polygrid2d(x, y, c): + """ + Evaluate a 2-D polynomial on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * a^i * b^j + + where the points ``(a, b)`` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape + y.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + polyval, polyval2d, polyval3d, polygrid3d + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = ((1, 2, 3), (4, 5, 6)) + >>> P.polygrid2d([0, 1], [0, 1], c) + array([[ 1., 6.], + [ 5., 21.]]) + + """ + return pu._gridnd(polyval, c, x, y) + + +def polyval3d(x, y, z, c): + """ + Evaluate a 3-D polynomial at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * x^i * y^j * z^k + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + ``(x, y, z)``, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + polyval, polyval2d, polygrid2d, polygrid3d + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = ((1, 2, 3), (4, 5, 6), (7, 8, 9)) + >>> P.polyval3d(1, 1, 1, c) + 45.0 + + """ + return pu._valnd(polyval, c, x, y, z) + + +def polygrid3d(x, y, z, c): + """ + Evaluate a 3-D polynomial on the Cartesian product of x, y and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * a^i * b^j * c^k + + where the points ``(a, b, c)`` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`, `y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + polyval, polyval2d, polygrid2d, polyval3d + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = ((1, 2, 3), (4, 5, 6), (7, 8, 9)) + >>> P.polygrid3d([0, 1], [0, 1], [0, 1], c) + array([[ 1., 13.], + [ 6., 51.]]) + + """ + return pu._gridnd(polyval, c, x, y, z) + + +def polyvander(x, deg): + """Vandermonde matrix of given degree. + + Returns the Vandermonde matrix of degree `deg` and sample points + `x`. The Vandermonde matrix is defined by + + .. math:: V[..., i] = x^i, + + where ``0 <= i <= deg``. The leading indices of `V` index the elements of + `x` and the last index is the power of `x`. + + If `c` is a 1-D array of coefficients of length ``n + 1`` and `V` is the + matrix ``V = polyvander(x, n)``, then ``np.dot(V, c)`` and + ``polyval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of polynomials of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray. + The Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where the last index is the power of `x`. + The dtype will be the same as the converted `x`. + + See Also + -------- + polyvander2d, polyvander3d + + Examples + -------- + The Vandermonde matrix of degree ``deg = 5`` and sample points + ``x = [-1, 2, 3]`` contains the element-wise powers of `x` + from 0 to 5 as its columns. + + >>> from numpy.polynomial import polynomial as P + >>> x, deg = [-1, 2, 3], 5 + >>> P.polyvander(x=x, deg=deg) + array([[ 1., -1., 1., -1., 1., -1.], + [ 1., 2., 4., 8., 16., 32.], + [ 1., 3., 9., 27., 81., 243.]]) + + """ + ideg = pu._as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=None, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + v[0] = x*0 + 1 + if ideg > 0: + v[1] = x + for i in range(2, ideg + 1): + v[i] = v[i-1]*x + return np.moveaxis(v, 0, -1) + + +def polyvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y)``. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = x^i * y^j, + + where ``0 <= i <= deg[0]`` and ``0 <= j <= deg[1]``. The leading indices of + `V` index the points ``(x, y)`` and the last index encodes the powers of + `x` and `y`. + + If ``V = polyvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``polyval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D polynomials + of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg([1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + polyvander, polyvander3d, polyval2d, polyval3d + + Examples + -------- + >>> import numpy as np + + The 2-D pseudo-Vandermonde matrix of degree ``[1, 2]`` and sample + points ``x = [-1, 2]`` and ``y = [1, 3]`` is as follows: + + >>> from numpy.polynomial import polynomial as P + >>> x = np.array([-1, 2]) + >>> y = np.array([1, 3]) + >>> m, n = 1, 2 + >>> deg = np.array([m, n]) + >>> V = P.polyvander2d(x=x, y=y, deg=deg) + >>> V + array([[ 1., 1., 1., -1., -1., -1.], + [ 1., 3., 9., 2., 6., 18.]]) + + We can verify the columns for any ``0 <= i <= m`` and ``0 <= j <= n``: + + >>> i, j = 0, 1 + >>> V[:, (deg[1]+1)*i + j] == x**i * y**j + array([ True, True]) + + The (1D) Vandermonde matrix of sample points ``x`` and degree ``m`` is a + special case of the (2D) pseudo-Vandermonde matrix with ``y`` points all + zero and degree ``[m, 0]``. + + >>> P.polyvander2d(x=x, y=0*x, deg=(m, 0)) == P.polyvander(x=x, deg=m) + array([[ True, True], + [ True, True]]) + + """ + return pu._vander_nd_flat((polyvander, polyvander), (x, y), deg) + + +def polyvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points ``(x, y, z)``. If `l`, `m`, `n` are the given degrees in `x`, `y`, `z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = x^i * y^j * z^k, + + where ``0 <= i <= l``, ``0 <= j <= m``, and ``0 <= j <= n``. The leading + indices of `V` index the points ``(x, y, z)`` and the last index encodes + the powers of `x`, `y`, and `z`. + + If ``V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``polyval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D polynomials + of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg([1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + polyvander, polyvander3d, polyval2d, polyval3d + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial import polynomial as P + >>> x = np.asarray([-1, 2, 1]) + >>> y = np.asarray([1, -2, -3]) + >>> z = np.asarray([2, 2, 5]) + >>> l, m, n = [2, 2, 1] + >>> deg = [l, m, n] + >>> V = P.polyvander3d(x=x, y=y, z=z, deg=deg) + >>> V + array([[ 1., 2., 1., 2., 1., 2., -1., -2., -1., + -2., -1., -2., 1., 2., 1., 2., 1., 2.], + [ 1., 2., -2., -4., 4., 8., 2., 4., -4., + -8., 8., 16., 4., 8., -8., -16., 16., 32.], + [ 1., 5., -3., -15., 9., 45., 1., 5., -3., + -15., 9., 45., 1., 5., -3., -15., 9., 45.]]) + + We can verify the columns for any ``0 <= i <= l``, ``0 <= j <= m``, + and ``0 <= k <= n`` + + >>> i, j, k = 2, 1, 0 + >>> V[:, (m+1)*(n+1)*i + (n+1)*j + k] == x**i * y**j * z**k + array([ True, True, True]) + + """ + return pu._vander_nd_flat((polyvander, polyvander, polyvander), (x, y, z), deg) + + +def polyfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least-squares fit of a polynomial to data. + + Return the coefficients of a polynomial of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * x + ... + c_n * x^n, + + where `n` is `deg`. + + Parameters + ---------- + x : array_like, shape (`M`,) + x-coordinates of the `M` sample (data) points ``(x[i], y[i])``. + y : array_like, shape (`M`,) or (`M`, `K`) + y-coordinates of the sample points. Several sets of sample points + sharing the same x-coordinates can be (independently) fit with one + call to `polyfit` by passing in for `y` a 2-D array that contains + one data set per column. + deg : int or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + rcond : float, optional + Relative condition number of the fit. Singular values smaller + than `rcond`, relative to the largest singular value, will be + ignored. The default value is ``len(x)*eps``, where `eps` is the + relative precision of the platform's float type, about 2e-16 in + most cases. + full : bool, optional + Switch determining the nature of the return value. When ``False`` + (the default) just the coefficients are returned; when ``True``, + diagnostic information from the singular value decomposition (used + to solve the fit's matrix equation) is also returned. + w : array_like, shape (`M`,), optional + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. + + Returns + ------- + coef : ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`) + Polynomial coefficients ordered from low to high. If `y` was 2-D, + the coefficients in column `k` of `coef` represent the polynomial + fit to the data in `y`'s `k`-th column. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + Raises + ------ + RankWarning + Raised if the matrix in the least-squares fit is rank deficient. + The warning is only raised if ``full == False``. The warnings can + be turned off by: + + >>> import warnings + >>> warnings.simplefilter('ignore', np.exceptions.RankWarning) + + See Also + -------- + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.legendre.legfit + numpy.polynomial.laguerre.lagfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.hermite_e.hermefit + polyval : Evaluates a polynomial. + polyvander : Vandermonde matrix for powers. + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the polynomial `p` that minimizes + the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where the :math:`w_j` are the weights. This problem is solved by + setting up the (typically) over-determined matrix equation: + + .. math:: V(x) * c = w * y, + + where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the + coefficients to be solved for, `w` are the weights, and `y` are the + observed values. This equation is then solved using the singular value + decomposition of `V`. + + If some of the singular values of `V` are so small that they are + neglected (and `full` == ``False``), a `~exceptions.RankWarning` will be + raised. This means that the coefficient values may be poorly determined. + Fitting to a lower order polynomial will usually get rid of the warning + (but may not be what you want, of course; if you have independent + reason(s) for choosing the degree which isn't working, you may have to: + a) reconsider those reasons, and/or b) reconsider the quality of your + data). The `rcond` parameter can also be set to a value smaller than + its default, but the resulting fit may be spurious and have large + contributions from roundoff error. + + Polynomial fits using double precision tend to "fail" at about + (polynomial) degree 20. Fits using Chebyshev or Legendre series are + generally better conditioned, but much can still depend on the + distribution of the sample points and the smoothness of the data. If + the quality of the fit is inadequate, splines may be a good + alternative. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial import polynomial as P + >>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1] + >>> rng = np.random.default_rng() + >>> err = rng.normal(size=len(x)) + >>> y = x**3 - x + err # x^3 - x + Gaussian noise + >>> c, stats = P.polyfit(x,y,3,full=True) + >>> c # c[0], c[1] approx. -1, c[2] should be approx. 0, c[3] approx. 1 + array([ 0.23111996, -1.02785049, -0.2241444 , 1.08405657]) # may vary + >>> stats # note the large SSR, explaining the rather poor results + [array([48.312088]), # may vary + 4, + array([1.38446749, 1.32119158, 0.50443316, 0.28853036]), + 1.1324274851176597e-14] + + Same thing without the added noise + + >>> y = x**3 - x + >>> c, stats = P.polyfit(x,y,3,full=True) + >>> c # c[0], c[1] ~= -1, c[2] should be "very close to 0", c[3] ~= 1 + array([-6.73496154e-17, -1.00000000e+00, 0.00000000e+00, 1.00000000e+00]) + >>> stats # note the minuscule SSR + [array([8.79579319e-31]), + np.int32(4), + array([1.38446749, 1.32119158, 0.50443316, 0.28853036]), + 1.1324274851176597e-14] + + """ + return pu._fit(polyvander, x, y, deg, rcond, full, w) + + +def polycompanion(c): + """ + Return the companion matrix of c. + + The companion matrix for power series cannot be made symmetric by + scaling the basis, so this function differs from those for the + orthogonal polynomials. + + Parameters + ---------- + c : array_like + 1-D array of polynomial coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Companion matrix of dimensions (deg, deg). + + Examples + -------- + >>> from numpy.polynomial import polynomial as P + >>> c = (1, 2, 3) + >>> P.polycompanion(c) + array([[ 0. , -0.33333333], + [ 1. , -0.66666667]]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[-c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + bot = mat.reshape(-1)[n::n+1] + bot[...] = 1 + mat[:, -1] -= c[:-1]/c[-1] + return mat + + +def polyroots(c): + """ + Compute the roots of a polynomial. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * x^i. + + Parameters + ---------- + c : 1-D array_like + 1-D array of polynomial coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the polynomial. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.chebyshev.chebroots + numpy.polynomial.legendre.legroots + numpy.polynomial.laguerre.lagroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the power series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + Examples + -------- + >>> import numpy.polynomial.polynomial as poly + >>> poly.polyroots(poly.polyfromroots((-1,0,1))) + array([-1., 0., 1.]) + >>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype + dtype('float64') + >>> j = complex(0,1) + >>> poly.polyroots(poly.polyfromroots((-j,0,j))) + array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary + + """ # noqa: E501 + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([-c[0]/c[1]]) + + # rotated companion matrix reduces error + m = polycompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +# +# polynomial class +# + +class Polynomial(ABCPolyBase): + """A power series class. + + The Polynomial class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed below. + + Parameters + ---------- + coef : array_like + Polynomial coefficients in order of increasing degree, i.e., + ``(1, 2, 3)`` give ``1 + 2*x + 3*x**2``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [-1., 1.]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [-1., 1.]. + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(polyadd) + _sub = staticmethod(polysub) + _mul = staticmethod(polymul) + _div = staticmethod(polydiv) + _pow = staticmethod(polypow) + _val = staticmethod(polyval) + _int = staticmethod(polyint) + _der = staticmethod(polyder) + _fit = staticmethod(polyfit) + _line = staticmethod(polyline) + _roots = staticmethod(polyroots) + _fromroots = staticmethod(polyfromroots) + + # Virtual properties + domain = np.array(polydomain) + window = np.array(polydomain) + basis_name = None + + @classmethod + def _str_term_unicode(cls, i, arg_str): + if i == '1': + return f"·{arg_str}" + else: + return f"·{arg_str}{i.translate(cls._superscript_mapping)}" + + @staticmethod + def _str_term_ascii(i, arg_str): + if i == '1': + return f" {arg_str}" + else: + return f" {arg_str}**{i}" + + @staticmethod + def _repr_latex_term(i, arg_str, needs_parens): + if needs_parens: + arg_str = rf"\left({arg_str}\right)" + if i == 0: + return '1' + elif i == 1: + return arg_str + else: + return f"{arg_str}^{{{i}}}" diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.pyi new file mode 100644 index 0000000000000000000000000000000000000000..89a8b57185f3e326f8891e71ab2b47f48cd908e9 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/polynomial.pyi @@ -0,0 +1,87 @@ +from typing import Final, Literal as L + +import numpy as np +from ._polybase import ABCPolyBase +from ._polytypes import ( + _Array1, + _Array2, + _FuncVal2D, + _FuncVal3D, + _FuncBinOp, + _FuncCompanion, + _FuncDer, + _FuncFit, + _FuncFromRoots, + _FuncInteg, + _FuncLine, + _FuncPow, + _FuncRoots, + _FuncUnOp, + _FuncVal, + _FuncVander, + _FuncVander2D, + _FuncVander3D, + _FuncValFromRoots, +) +from .polyutils import trimcoef as polytrim + +__all__ = [ + "polyzero", + "polyone", + "polyx", + "polydomain", + "polyline", + "polyadd", + "polysub", + "polymulx", + "polymul", + "polydiv", + "polypow", + "polyval", + "polyvalfromroots", + "polyder", + "polyint", + "polyfromroots", + "polyvander", + "polyfit", + "polytrim", + "polyroots", + "Polynomial", + "polyval2d", + "polyval3d", + "polygrid2d", + "polygrid3d", + "polyvander2d", + "polyvander3d", + "polycompanion", +] + +polydomain: Final[_Array2[np.float64]] +polyzero: Final[_Array1[np.int_]] +polyone: Final[_Array1[np.int_]] +polyx: Final[_Array2[np.int_]] + +polyline: _FuncLine[L["Polyline"]] +polyfromroots: _FuncFromRoots[L["polyfromroots"]] +polyadd: _FuncBinOp[L["polyadd"]] +polysub: _FuncBinOp[L["polysub"]] +polymulx: _FuncUnOp[L["polymulx"]] +polymul: _FuncBinOp[L["polymul"]] +polydiv: _FuncBinOp[L["polydiv"]] +polypow: _FuncPow[L["polypow"]] +polyder: _FuncDer[L["polyder"]] +polyint: _FuncInteg[L["polyint"]] +polyval: _FuncVal[L["polyval"]] +polyval2d: _FuncVal2D[L["polyval2d"]] +polyval3d: _FuncVal3D[L["polyval3d"]] +polyvalfromroots: _FuncValFromRoots[L["polyvalfromroots"]] +polygrid2d: _FuncVal2D[L["polygrid2d"]] +polygrid3d: _FuncVal3D[L["polygrid3d"]] +polyvander: _FuncVander[L["polyvander"]] +polyvander2d: _FuncVander2D[L["polyvander2d"]] +polyvander3d: _FuncVander3D[L["polyvander3d"]] +polyfit: _FuncFit[L["polyfit"]] +polycompanion: _FuncCompanion[L["polycompanion"]] +polyroots: _FuncRoots[L["polyroots"]] + +class Polynomial(ABCPolyBase[None]): ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.py b/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..1a6813b786c9bdd7eaa7961b5c50a5b187f7837a --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.py @@ -0,0 +1,757 @@ +""" +Utility classes and functions for the polynomial modules. + +This module provides: error and warning objects; a polynomial base class; +and some routines used in both the `polynomial` and `chebyshev` modules. + +Functions +--------- + +.. autosummary:: + :toctree: generated/ + + as_series convert list of array_likes into 1-D arrays of common type. + trimseq remove trailing zeros. + trimcoef remove small trailing coefficients. + getdomain return the domain appropriate for a given set of abscissae. + mapdomain maps points between domains. + mapparms parameters of the linear map between domains. + +""" +import operator +import functools +import warnings + +import numpy as np + +from numpy._core.multiarray import dragon4_positional, dragon4_scientific +from numpy.exceptions import RankWarning + +__all__ = [ + 'as_series', 'trimseq', 'trimcoef', 'getdomain', 'mapdomain', 'mapparms', + 'format_float'] + +# +# Helper functions to convert inputs to 1-D arrays +# +def trimseq(seq): + """Remove small Poly series coefficients. + + Parameters + ---------- + seq : sequence + Sequence of Poly series coefficients. + + Returns + ------- + series : sequence + Subsequence with trailing zeros removed. If the resulting sequence + would be empty, return the first element. The returned sequence may + or may not be a view. + + Notes + ----- + Do not lose the type info if the sequence contains unknown objects. + + """ + if len(seq) == 0 or seq[-1] != 0: + return seq + else: + for i in range(len(seq) - 1, -1, -1): + if seq[i] != 0: + break + return seq[:i+1] + + +def as_series(alist, trim=True): + """ + Return argument as a list of 1-d arrays. + + The returned list contains array(s) of dtype double, complex double, or + object. A 1-d argument of shape ``(N,)`` is parsed into ``N`` arrays of + size one; a 2-d argument of shape ``(M,N)`` is parsed into ``M`` arrays + of size ``N`` (i.e., is "parsed by row"); and a higher dimensional array + raises a Value Error if it is not first reshaped into either a 1-d or 2-d + array. + + Parameters + ---------- + alist : array_like + A 1- or 2-d array_like + trim : boolean, optional + When True, trailing zeros are removed from the inputs. + When False, the inputs are passed through intact. + + Returns + ------- + [a1, a2,...] : list of 1-D arrays + A copy of the input data as a list of 1-d arrays. + + Raises + ------ + ValueError + Raised when `as_series` cannot convert its input to 1-d arrays, or at + least one of the resulting arrays is empty. + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial import polyutils as pu + >>> a = np.arange(4) + >>> pu.as_series(a) + [array([0.]), array([1.]), array([2.]), array([3.])] + >>> b = np.arange(6).reshape((2,3)) + >>> pu.as_series(b) + [array([0., 1., 2.]), array([3., 4., 5.])] + + >>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16))) + [array([1.]), array([0., 1., 2.]), array([0., 1.])] + + >>> pu.as_series([2, [1.1, 0.]]) + [array([2.]), array([1.1])] + + >>> pu.as_series([2, [1.1, 0.]], trim=False) + [array([2.]), array([1.1, 0. ])] + + """ + arrays = [np.array(a, ndmin=1, copy=None) for a in alist] + for a in arrays: + if a.size == 0: + raise ValueError("Coefficient array is empty") + if any(a.ndim != 1 for a in arrays): + raise ValueError("Coefficient array is not 1-d") + if trim: + arrays = [trimseq(a) for a in arrays] + + if any(a.dtype == np.dtype(object) for a in arrays): + ret = [] + for a in arrays: + if a.dtype != np.dtype(object): + tmp = np.empty(len(a), dtype=np.dtype(object)) + tmp[:] = a[:] + ret.append(tmp) + else: + ret.append(a.copy()) + else: + try: + dtype = np.common_type(*arrays) + except Exception as e: + raise ValueError("Coefficient arrays have no common type") from e + ret = [np.array(a, copy=True, dtype=dtype) for a in arrays] + return ret + + +def trimcoef(c, tol=0): + """ + Remove "small" "trailing" coefficients from a polynomial. + + "Small" means "small in absolute value" and is controlled by the + parameter `tol`; "trailing" means highest order coefficient(s), e.g., in + ``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``) + both the 3-rd and 4-th order coefficients would be "trimmed." + + Parameters + ---------- + c : array_like + 1-d array of coefficients, ordered from lowest order to highest. + tol : number, optional + Trailing (i.e., highest order) elements with absolute value less + than or equal to `tol` (default value is zero) are removed. + + Returns + ------- + trimmed : ndarray + 1-d array with trailing zeros removed. If the resulting series + would be empty, a series containing a single zero is returned. + + Raises + ------ + ValueError + If `tol` < 0 + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> pu.trimcoef((0,0,3,0,5,0,0)) + array([0., 0., 3., 0., 5.]) + >>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed + array([0.]) + >>> i = complex(0,1) # works for complex + >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) + array([0.0003+0.j , 0.001 -0.001j]) + + """ + if tol < 0: + raise ValueError("tol must be non-negative") + + [c] = as_series([c]) + [ind] = np.nonzero(np.abs(c) > tol) + if len(ind) == 0: + return c[:1]*0 + else: + return c[:ind[-1] + 1].copy() + +def getdomain(x): + """ + Return a domain suitable for given abscissae. + + Find a domain suitable for a polynomial or Chebyshev series + defined at the values supplied. + + Parameters + ---------- + x : array_like + 1-d array of abscissae whose domain will be determined. + + Returns + ------- + domain : ndarray + 1-d array containing two values. If the inputs are complex, then + the two returned points are the lower left and upper right corners + of the smallest rectangle (aligned with the axes) in the complex + plane containing the points `x`. If the inputs are real, then the + two points are the ends of the smallest interval containing the + points `x`. + + See Also + -------- + mapparms, mapdomain + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial import polyutils as pu + >>> points = np.arange(4)**2 - 5; points + array([-5, -4, -1, 4]) + >>> pu.getdomain(points) + array([-5., 4.]) + >>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle + >>> pu.getdomain(c) + array([-1.-1.j, 1.+1.j]) + + """ + [x] = as_series([x], trim=False) + if x.dtype.char in np.typecodes['Complex']: + rmin, rmax = x.real.min(), x.real.max() + imin, imax = x.imag.min(), x.imag.max() + return np.array((complex(rmin, imin), complex(rmax, imax))) + else: + return np.array((x.min(), x.max())) + +def mapparms(old, new): + """ + Linear map parameters between domains. + + Return the parameters of the linear map ``offset + scale*x`` that maps + `old` to `new` such that ``old[i] -> new[i]``, ``i = 0, 1``. + + Parameters + ---------- + old, new : array_like + Domains. Each domain must (successfully) convert to a 1-d array + containing precisely two values. + + Returns + ------- + offset, scale : scalars + The map ``L(x) = offset + scale*x`` maps the first domain to the + second. + + See Also + -------- + getdomain, mapdomain + + Notes + ----- + Also works for complex numbers, and thus can be used to calculate the + parameters required to map any line in the complex plane to any other + line therein. + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> pu.mapparms((-1,1),(-1,1)) + (0.0, 1.0) + >>> pu.mapparms((1,-1),(-1,1)) + (-0.0, -1.0) + >>> i = complex(0,1) + >>> pu.mapparms((-i,-1),(1,i)) + ((1+1j), (1-0j)) + + """ + oldlen = old[1] - old[0] + newlen = new[1] - new[0] + off = (old[1]*new[0] - old[0]*new[1])/oldlen + scl = newlen/oldlen + return off, scl + +def mapdomain(x, old, new): + """ + Apply linear map to input points. + + The linear map ``offset + scale*x`` that maps the domain `old` to + the domain `new` is applied to the points `x`. + + Parameters + ---------- + x : array_like + Points to be mapped. If `x` is a subtype of ndarray the subtype + will be preserved. + old, new : array_like + The two domains that determine the map. Each must (successfully) + convert to 1-d arrays containing precisely two values. + + Returns + ------- + x_out : ndarray + Array of points of the same shape as `x`, after application of the + linear map between the two domains. + + See Also + -------- + getdomain, mapparms + + Notes + ----- + Effectively, this implements: + + .. math:: + x\\_out = new[0] + m(x - old[0]) + + where + + .. math:: + m = \\frac{new[1]-new[0]}{old[1]-old[0]} + + Examples + -------- + >>> import numpy as np + >>> from numpy.polynomial import polyutils as pu + >>> old_domain = (-1,1) + >>> new_domain = (0,2*np.pi) + >>> x = np.linspace(-1,1,6); x + array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ]) + >>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out + array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary + 6.28318531]) + >>> x - pu.mapdomain(x_out, new_domain, old_domain) + array([0., 0., 0., 0., 0., 0.]) + + Also works for complex numbers (and thus can be used to map any line in + the complex plane to any other line therein). + + >>> i = complex(0,1) + >>> old = (-1 - i, 1 + i) + >>> new = (-1 + i, 1 - i) + >>> z = np.linspace(old[0], old[1], 6); z + array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ]) + >>> new_z = pu.mapdomain(z, old, new); new_z + array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary + + """ + if type(x) not in (int, float, complex) and not isinstance(x, np.generic): + x = np.asanyarray(x) + off, scl = mapparms(old, new) + return off + scl*x + + +def _nth_slice(i, ndim): + sl = [np.newaxis] * ndim + sl[i] = slice(None) + return tuple(sl) + + +def _vander_nd(vander_fs, points, degrees): + r""" + A generalization of the Vandermonde matrix for N dimensions + + The result is built by combining the results of 1d Vandermonde matrices, + + .. math:: + W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{V_k(x_k)[i_0, \ldots, i_M, j_k]} + + where + + .. math:: + N &= \texttt{len(points)} = \texttt{len(degrees)} = \texttt{len(vander\_fs)} \\ + M &= \texttt{points[k].ndim} \\ + V_k &= \texttt{vander\_fs[k]} \\ + x_k &= \texttt{points[k]} \\ + 0 \le j_k &\le \texttt{degrees[k]} + + Expanding the one-dimensional :math:`V_k` functions gives: + + .. math:: + W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{B_{k, j_k}(x_k[i_0, \ldots, i_M])} + + where :math:`B_{k,m}` is the m'th basis of the polynomial construction used along + dimension :math:`k`. For a regular polynomial, :math:`B_{k, m}(x) = P_m(x) = x^m`. + + Parameters + ---------- + vander_fs : Sequence[function(array_like, int) -> ndarray] + The 1d vander function to use for each axis, such as ``polyvander`` + points : Sequence[array_like] + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + This must be the same length as `vander_fs`. + degrees : Sequence[int] + The maximum degree (inclusive) to use for each axis. + This must be the same length as `vander_fs`. + + Returns + ------- + vander_nd : ndarray + An array of shape ``points[0].shape + tuple(d + 1 for d in degrees)``. + """ + n_dims = len(vander_fs) + if n_dims != len(points): + raise ValueError( + f"Expected {n_dims} dimensions of sample points, got {len(points)}") + if n_dims != len(degrees): + raise ValueError( + f"Expected {n_dims} dimensions of degrees, got {len(degrees)}") + if n_dims == 0: + raise ValueError("Unable to guess a dtype or shape when no points are given") + + # convert to the same shape and type + points = tuple(np.asarray(tuple(points)) + 0.0) + + # produce the vandermonde matrix for each dimension, placing the last + # axis of each in an independent trailing axis of the output + vander_arrays = ( + vander_fs[i](points[i], degrees[i])[(...,) + _nth_slice(i, n_dims)] + for i in range(n_dims) + ) + + # we checked this wasn't empty already, so no `initial` needed + return functools.reduce(operator.mul, vander_arrays) + + +def _vander_nd_flat(vander_fs, points, degrees): + """ + Like `_vander_nd`, but flattens the last ``len(degrees)`` axes into a single axis + + Used to implement the public ``vanderd`` functions. + """ + v = _vander_nd(vander_fs, points, degrees) + return v.reshape(v.shape[:-len(degrees)] + (-1,)) + + +def _fromroots(line_f, mul_f, roots): + """ + Helper function used to implement the ``fromroots`` functions. + + Parameters + ---------- + line_f : function(float, float) -> ndarray + The ``line`` function, such as ``polyline`` + mul_f : function(array_like, array_like) -> ndarray + The ``mul`` function, such as ``polymul`` + roots + See the ``fromroots`` functions for more detail + """ + if len(roots) == 0: + return np.ones(1) + else: + [roots] = as_series([roots], trim=False) + roots.sort() + p = [line_f(-r, 1) for r in roots] + n = len(p) + while n > 1: + m, r = divmod(n, 2) + tmp = [mul_f(p[i], p[i+m]) for i in range(m)] + if r: + tmp[0] = mul_f(tmp[0], p[-1]) + p = tmp + n = m + return p[0] + + +def _valnd(val_f, c, *args): + """ + Helper function used to implement the ``vald`` functions. + + Parameters + ---------- + val_f : function(array_like, array_like, tensor: bool) -> array_like + The ``val`` function, such as ``polyval`` + c, args + See the ``vald`` functions for more detail + """ + args = [np.asanyarray(a) for a in args] + shape0 = args[0].shape + if not all(a.shape == shape0 for a in args[1:]): + if len(args) == 3: + raise ValueError('x, y, z are incompatible') + elif len(args) == 2: + raise ValueError('x, y are incompatible') + else: + raise ValueError('ordinates are incompatible') + it = iter(args) + x0 = next(it) + + # use tensor on only the first + c = val_f(x0, c) + for xi in it: + c = val_f(xi, c, tensor=False) + return c + + +def _gridnd(val_f, c, *args): + """ + Helper function used to implement the ``gridd`` functions. + + Parameters + ---------- + val_f : function(array_like, array_like, tensor: bool) -> array_like + The ``val`` function, such as ``polyval`` + c, args + See the ``gridd`` functions for more detail + """ + for xi in args: + c = val_f(xi, c) + return c + + +def _div(mul_f, c1, c2): + """ + Helper function used to implement the ``div`` functions. + + Implementation uses repeated subtraction of c2 multiplied by the nth basis. + For some polynomial types, a more efficient approach may be possible. + + Parameters + ---------- + mul_f : function(array_like, array_like) -> array_like + The ``mul`` function, such as ``polymul`` + c1, c2 + See the ``div`` functions for more detail + """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if c2[-1] == 0: + raise ZeroDivisionError # FIXME: add message with details to exception + + lc1 = len(c1) + lc2 = len(c2) + if lc1 < lc2: + return c1[:1]*0, c1 + elif lc2 == 1: + return c1/c2[-1], c1[:1]*0 + else: + quo = np.empty(lc1 - lc2 + 1, dtype=c1.dtype) + rem = c1 + for i in range(lc1 - lc2, - 1, -1): + p = mul_f([0]*i + [1], c2) + q = rem[-1]/p[-1] + rem = rem[:-1] - q*p[:-1] + quo[i] = q + return quo, trimseq(rem) + + +def _add(c1, c2): + """ Helper function used to implement the ``add`` functions. """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if len(c1) > len(c2): + c1[:c2.size] += c2 + ret = c1 + else: + c2[:c1.size] += c1 + ret = c2 + return trimseq(ret) + + +def _sub(c1, c2): + """ Helper function used to implement the ``sub`` functions. """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if len(c1) > len(c2): + c1[:c2.size] -= c2 + ret = c1 + else: + c2 = -c2 + c2[:c1.size] += c1 + ret = c2 + return trimseq(ret) + + +def _fit(vander_f, x, y, deg, rcond=None, full=False, w=None): + """ + Helper function used to implement the ``fit`` functions. + + Parameters + ---------- + vander_f : function(array_like, int) -> ndarray + The 1d vander function, such as ``polyvander`` + c1, c2 + See the ``fit`` functions for more detail + """ + x = np.asarray(x) + 0.0 + y = np.asarray(y) + 0.0 + deg = np.asarray(deg) + + # check arguments. + if deg.ndim > 1 or deg.dtype.kind not in 'iu' or deg.size == 0: + raise TypeError("deg must be an int or non-empty 1-D array of int") + if deg.min() < 0: + raise ValueError("expected deg >= 0") + if x.ndim != 1: + raise TypeError("expected 1D vector for x") + if x.size == 0: + raise TypeError("expected non-empty vector for x") + if y.ndim < 1 or y.ndim > 2: + raise TypeError("expected 1D or 2D array for y") + if len(x) != len(y): + raise TypeError("expected x and y to have same length") + + if deg.ndim == 0: + lmax = deg + order = lmax + 1 + van = vander_f(x, lmax) + else: + deg = np.sort(deg) + lmax = deg[-1] + order = len(deg) + van = vander_f(x, lmax)[:, deg] + + # set up the least squares matrices in transposed form + lhs = van.T + rhs = y.T + if w is not None: + w = np.asarray(w) + 0.0 + if w.ndim != 1: + raise TypeError("expected 1D vector for w") + if len(x) != len(w): + raise TypeError("expected x and w to have same length") + # apply weights. Don't use inplace operations as they + # can cause problems with NA. + lhs = lhs * w + rhs = rhs * w + + # set rcond + if rcond is None: + rcond = len(x)*np.finfo(x.dtype).eps + + # Determine the norms of the design matrix columns. + if issubclass(lhs.dtype.type, np.complexfloating): + scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1)) + else: + scl = np.sqrt(np.square(lhs).sum(1)) + scl[scl == 0] = 1 + + # Solve the least squares problem. + c, resids, rank, s = np.linalg.lstsq(lhs.T/scl, rhs.T, rcond) + c = (c.T/scl).T + + # Expand c to include non-fitted coefficients which are set to zero + if deg.ndim > 0: + if c.ndim == 2: + cc = np.zeros((lmax+1, c.shape[1]), dtype=c.dtype) + else: + cc = np.zeros(lmax+1, dtype=c.dtype) + cc[deg] = c + c = cc + + # warn on rank reduction + if rank != order and not full: + msg = "The fit may be poorly conditioned" + warnings.warn(msg, RankWarning, stacklevel=2) + + if full: + return c, [resids, rank, s, rcond] + else: + return c + + +def _pow(mul_f, c, pow, maxpower): + """ + Helper function used to implement the ``pow`` functions. + + Parameters + ---------- + mul_f : function(array_like, array_like) -> ndarray + The ``mul`` function, such as ``polymul`` + c : array_like + 1-D array of array of series coefficients + pow, maxpower + See the ``pow`` functions for more detail + """ + # c is a trimmed copy + [c] = as_series([c]) + power = int(pow) + if power != pow or power < 0: + raise ValueError("Power must be a non-negative integer.") + elif maxpower is not None and power > maxpower: + raise ValueError("Power is too large") + elif power == 0: + return np.array([1], dtype=c.dtype) + elif power == 1: + return c + else: + # This can be made more efficient by using powers of two + # in the usual way. + prd = c + for i in range(2, power + 1): + prd = mul_f(prd, c) + return prd + + +def _as_int(x, desc): + """ + Like `operator.index`, but emits a custom exception when passed an + incorrect type + + Parameters + ---------- + x : int-like + Value to interpret as an integer + desc : str + description to include in any error message + + Raises + ------ + TypeError : if x is a float or non-numeric + """ + try: + return operator.index(x) + except TypeError as e: + raise TypeError(f"{desc} must be an integer, received {x}") from e + + +def format_float(x, parens=False): + if not np.issubdtype(type(x), np.floating): + return str(x) + + opts = np.get_printoptions() + + if np.isnan(x): + return opts['nanstr'] + elif np.isinf(x): + return opts['infstr'] + + exp_format = False + if x != 0: + a = np.abs(x) + if a >= 1.e8 or a < 10**min(0, -(opts['precision']-1)//2): + exp_format = True + + trim, unique = '0', True + if opts['floatmode'] == 'fixed': + trim, unique = 'k', False + + if exp_format: + s = dragon4_scientific(x, precision=opts['precision'], + unique=unique, trim=trim, + sign=opts['sign'] == '+') + if parens: + s = '(' + s + ')' + else: + s = dragon4_positional(x, precision=opts['precision'], + fractional=True, + unique=unique, trim=trim, + sign=opts['sign'] == '+') + return s diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.pyi b/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.pyi new file mode 100644 index 0000000000000000000000000000000000000000..9299b23975b1ff9c59d36c9e6e804e06d415cf4b --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/polyutils.pyi @@ -0,0 +1,431 @@ +from collections.abc import Callable, Iterable, Sequence +from typing import ( + Any, + Final, + Literal, + SupportsIndex, + TypeAlias, + TypeVar, + overload, +) + +import numpy as np +import numpy.typing as npt +from numpy._typing import ( + _FloatLike_co, + _NumberLike_co, + + _ArrayLikeFloat_co, + _ArrayLikeComplex_co, +) + +from ._polytypes import ( + _AnyInt, + _CoefLike_co, + + _Array2, + _Tuple2, + + _FloatSeries, + _CoefSeries, + _ComplexSeries, + _ObjectSeries, + + _ComplexArray, + _FloatArray, + _CoefArray, + _ObjectArray, + + _SeriesLikeInt_co, + _SeriesLikeFloat_co, + _SeriesLikeComplex_co, + _SeriesLikeCoef_co, + + _ArrayLikeCoef_co, + + _FuncBinOp, + _FuncValND, + _FuncVanderND, +) + +__all__: Final[Sequence[str]] = [ + "as_series", + "format_float", + "getdomain", + "mapdomain", + "mapparms", + "trimcoef", + "trimseq", +] + +_AnyLineF: TypeAlias = Callable[ + [_CoefLike_co, _CoefLike_co], + _CoefArray, +] +_AnyMulF: TypeAlias = Callable[ + [npt.ArrayLike, npt.ArrayLike], + _CoefArray, +] +_AnyVanderF: TypeAlias = Callable[ + [npt.ArrayLike, SupportsIndex], + _CoefArray, +] + +@overload +def as_series( + alist: npt.NDArray[np.integer[Any]] | _FloatArray, + trim: bool = ..., +) -> list[_FloatSeries]: ... +@overload +def as_series( + alist: _ComplexArray, + trim: bool = ..., +) -> list[_ComplexSeries]: ... +@overload +def as_series( + alist: _ObjectArray, + trim: bool = ..., +) -> list[_ObjectSeries]: ... +@overload +def as_series( # type: ignore[overload-overlap] + alist: Iterable[_FloatArray | npt.NDArray[np.integer[Any]]], + trim: bool = ..., +) -> list[_FloatSeries]: ... +@overload +def as_series( + alist: Iterable[_ComplexArray], + trim: bool = ..., +) -> list[_ComplexSeries]: ... +@overload +def as_series( + alist: Iterable[_ObjectArray], + trim: bool = ..., +) -> list[_ObjectSeries]: ... +@overload +def as_series( # type: ignore[overload-overlap] + alist: Iterable[_SeriesLikeFloat_co | float], + trim: bool = ..., +) -> list[_FloatSeries]: ... +@overload +def as_series( + alist: Iterable[_SeriesLikeComplex_co | complex], + trim: bool = ..., +) -> list[_ComplexSeries]: ... +@overload +def as_series( + alist: Iterable[_SeriesLikeCoef_co | object], + trim: bool = ..., +) -> list[_ObjectSeries]: ... + +_T_seq = TypeVar("_T_seq", bound=_CoefArray | Sequence[_CoefLike_co]) +def trimseq(seq: _T_seq) -> _T_seq: ... + +@overload +def trimcoef( # type: ignore[overload-overlap] + c: npt.NDArray[np.integer[Any]] | _FloatArray, + tol: _FloatLike_co = ..., +) -> _FloatSeries: ... +@overload +def trimcoef( + c: _ComplexArray, + tol: _FloatLike_co = ..., +) -> _ComplexSeries: ... +@overload +def trimcoef( + c: _ObjectArray, + tol: _FloatLike_co = ..., +) -> _ObjectSeries: ... +@overload +def trimcoef( # type: ignore[overload-overlap] + c: _SeriesLikeFloat_co | float, + tol: _FloatLike_co = ..., +) -> _FloatSeries: ... +@overload +def trimcoef( + c: _SeriesLikeComplex_co | complex, + tol: _FloatLike_co = ..., +) -> _ComplexSeries: ... +@overload +def trimcoef( + c: _SeriesLikeCoef_co | object, + tol: _FloatLike_co = ..., +) -> _ObjectSeries: ... + +@overload +def getdomain( # type: ignore[overload-overlap] + x: _FloatArray | npt.NDArray[np.integer[Any]], +) -> _Array2[np.float64]: ... +@overload +def getdomain( + x: _ComplexArray, +) -> _Array2[np.complex128]: ... +@overload +def getdomain( + x: _ObjectArray, +) -> _Array2[np.object_]: ... +@overload +def getdomain( # type: ignore[overload-overlap] + x: _SeriesLikeFloat_co | float, +) -> _Array2[np.float64]: ... +@overload +def getdomain( + x: _SeriesLikeComplex_co | complex, +) -> _Array2[np.complex128]: ... +@overload +def getdomain( + x: _SeriesLikeCoef_co | object, +) -> _Array2[np.object_]: ... + +@overload +def mapparms( # type: ignore[overload-overlap] + old: npt.NDArray[np.floating[Any] | np.integer[Any]], + new: npt.NDArray[np.floating[Any] | np.integer[Any]], +) -> _Tuple2[np.floating[Any]]: ... +@overload +def mapparms( + old: npt.NDArray[np.number[Any]], + new: npt.NDArray[np.number[Any]], +) -> _Tuple2[np.complexfloating[Any, Any]]: ... +@overload +def mapparms( + old: npt.NDArray[np.object_ | np.number[Any]], + new: npt.NDArray[np.object_ | np.number[Any]], +) -> _Tuple2[object]: ... +@overload +def mapparms( # type: ignore[overload-overlap] + old: Sequence[float], + new: Sequence[float], +) -> _Tuple2[float]: ... +@overload +def mapparms( + old: Sequence[complex], + new: Sequence[complex], +) -> _Tuple2[complex]: ... +@overload +def mapparms( + old: _SeriesLikeFloat_co, + new: _SeriesLikeFloat_co, +) -> _Tuple2[np.floating[Any]]: ... +@overload +def mapparms( + old: _SeriesLikeComplex_co, + new: _SeriesLikeComplex_co, +) -> _Tuple2[np.complexfloating[Any, Any]]: ... +@overload +def mapparms( + old: _SeriesLikeCoef_co, + new: _SeriesLikeCoef_co, +) -> _Tuple2[object]: ... + +@overload +def mapdomain( # type: ignore[overload-overlap] + x: _FloatLike_co, + old: _SeriesLikeFloat_co, + new: _SeriesLikeFloat_co, +) -> np.floating[Any]: ... +@overload +def mapdomain( + x: _NumberLike_co, + old: _SeriesLikeComplex_co, + new: _SeriesLikeComplex_co, +) -> np.complexfloating[Any, Any]: ... +@overload +def mapdomain( # type: ignore[overload-overlap] + x: npt.NDArray[np.floating[Any] | np.integer[Any]], + old: npt.NDArray[np.floating[Any] | np.integer[Any]], + new: npt.NDArray[np.floating[Any] | np.integer[Any]], +) -> _FloatSeries: ... +@overload +def mapdomain( + x: npt.NDArray[np.number[Any]], + old: npt.NDArray[np.number[Any]], + new: npt.NDArray[np.number[Any]], +) -> _ComplexSeries: ... +@overload +def mapdomain( + x: npt.NDArray[np.object_ | np.number[Any]], + old: npt.NDArray[np.object_ | np.number[Any]], + new: npt.NDArray[np.object_ | np.number[Any]], +) -> _ObjectSeries: ... +@overload +def mapdomain( # type: ignore[overload-overlap] + x: _SeriesLikeFloat_co, + old: _SeriesLikeFloat_co, + new: _SeriesLikeFloat_co, +) -> _FloatSeries: ... +@overload +def mapdomain( + x: _SeriesLikeComplex_co, + old: _SeriesLikeComplex_co, + new: _SeriesLikeComplex_co, +) -> _ComplexSeries: ... +@overload +def mapdomain( + x: _SeriesLikeCoef_co, + old:_SeriesLikeCoef_co, + new: _SeriesLikeCoef_co, +) -> _ObjectSeries: ... +@overload +def mapdomain( + x: _CoefLike_co, + old: _SeriesLikeCoef_co, + new: _SeriesLikeCoef_co, +) -> object: ... + +def _nth_slice( + i: SupportsIndex, + ndim: SupportsIndex, +) -> tuple[None | slice, ...]: ... + +_vander_nd: _FuncVanderND[Literal["_vander_nd"]] +_vander_nd_flat: _FuncVanderND[Literal["_vander_nd_flat"]] + +# keep in sync with `._polytypes._FuncFromRoots` +@overload +def _fromroots( # type: ignore[overload-overlap] + line_f: _AnyLineF, + mul_f: _AnyMulF, + roots: _SeriesLikeFloat_co, +) -> _FloatSeries: ... +@overload +def _fromroots( + line_f: _AnyLineF, + mul_f: _AnyMulF, + roots: _SeriesLikeComplex_co, +) -> _ComplexSeries: ... +@overload +def _fromroots( + line_f: _AnyLineF, + mul_f: _AnyMulF, + roots: _SeriesLikeCoef_co, +) -> _ObjectSeries: ... +@overload +def _fromroots( + line_f: _AnyLineF, + mul_f: _AnyMulF, + roots: _SeriesLikeCoef_co, +) -> _CoefSeries: ... + +_valnd: _FuncValND[Literal["_valnd"]] +_gridnd: _FuncValND[Literal["_gridnd"]] + +# keep in sync with `_polytypes._FuncBinOp` +@overload +def _div( # type: ignore[overload-overlap] + mul_f: _AnyMulF, + c1: _SeriesLikeFloat_co, + c2: _SeriesLikeFloat_co, +) -> _Tuple2[_FloatSeries]: ... +@overload +def _div( + mul_f: _AnyMulF, + c1: _SeriesLikeComplex_co, + c2: _SeriesLikeComplex_co, +) -> _Tuple2[_ComplexSeries]: ... +@overload +def _div( + mul_f: _AnyMulF, + c1: _SeriesLikeCoef_co, + c2: _SeriesLikeCoef_co, +) -> _Tuple2[_ObjectSeries]: ... +@overload +def _div( + mul_f: _AnyMulF, + c1: _SeriesLikeCoef_co, + c2: _SeriesLikeCoef_co, +) -> _Tuple2[_CoefSeries]: ... + +_add: Final[_FuncBinOp] +_sub: Final[_FuncBinOp] + +# keep in sync with `_polytypes._FuncPow` +@overload +def _pow( # type: ignore[overload-overlap] + mul_f: _AnyMulF, + c: _SeriesLikeFloat_co, + pow: _AnyInt, + maxpower: None | _AnyInt = ..., +) -> _FloatSeries: ... +@overload +def _pow( + mul_f: _AnyMulF, + c: _SeriesLikeComplex_co, + pow: _AnyInt, + maxpower: None | _AnyInt = ..., +) -> _ComplexSeries: ... +@overload +def _pow( + mul_f: _AnyMulF, + c: _SeriesLikeCoef_co, + pow: _AnyInt, + maxpower: None | _AnyInt = ..., +) -> _ObjectSeries: ... +@overload +def _pow( + mul_f: _AnyMulF, + c: _SeriesLikeCoef_co, + pow: _AnyInt, + maxpower: None | _AnyInt = ..., +) -> _CoefSeries: ... + +# keep in sync with `_polytypes._FuncFit` +@overload +def _fit( # type: ignore[overload-overlap] + vander_f: _AnyVanderF, + x: _SeriesLikeFloat_co, + y: _ArrayLikeFloat_co, + deg: _SeriesLikeInt_co, + domain: None | _SeriesLikeFloat_co = ..., + rcond: None | _FloatLike_co = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeFloat_co = ..., +) -> _FloatArray: ... +@overload +def _fit( + vander_f: _AnyVanderF, + x: _SeriesLikeComplex_co, + y: _ArrayLikeComplex_co, + deg: _SeriesLikeInt_co, + domain: None | _SeriesLikeComplex_co = ..., + rcond: None | _FloatLike_co = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeComplex_co = ..., +) -> _ComplexArray: ... +@overload +def _fit( + vander_f: _AnyVanderF, + x: _SeriesLikeCoef_co, + y: _ArrayLikeCoef_co, + deg: _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co = ..., + rcond: None | _FloatLike_co = ..., + full: Literal[False] = ..., + w: None | _SeriesLikeCoef_co = ..., +) -> _CoefArray: ... +@overload +def _fit( + vander_f: _AnyVanderF, + x: _SeriesLikeCoef_co, + y: _SeriesLikeCoef_co, + deg: _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co, + rcond: None | _FloatLike_co , + full: Literal[True], + /, + w: None | _SeriesLikeCoef_co = ..., +) -> tuple[_CoefSeries, Sequence[np.inexact[Any] | np.int32]]: ... +@overload +def _fit( + vander_f: _AnyVanderF, + x: _SeriesLikeCoef_co, + y: _SeriesLikeCoef_co, + deg: _SeriesLikeInt_co, + domain: None | _SeriesLikeCoef_co = ..., + rcond: None | _FloatLike_co = ..., + *, + full: Literal[True], + w: None | _SeriesLikeCoef_co = ..., +) -> tuple[_CoefSeries, Sequence[np.inexact[Any] | np.int32]]: ... + +def _as_int(x: SupportsIndex, desc: str) -> int: ... +def format_float(x: _FloatLike_co, parens: bool = ...) -> str: ... diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__init__.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_chebyshev.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_chebyshev.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9feca72403d1408de905e9ff0b03932ae8c37244 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_chebyshev.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_classes.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_classes.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..8fa731cb5856ac744c236edbb856e62a7870f4b3 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_classes.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..684279c371ab6dad80766407345ba7e0280b6ae4 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite_e.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite_e.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..d1d65afffa43f6190cbfabe15f4d81fa6606d6d4 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_hermite_e.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_laguerre.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_laguerre.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ca5383ab38cd4ce980a7d9ae44d20294d7d3800a Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_laguerre.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_legendre.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_legendre.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..e34a60c5346a574d2e741dae70e22a25ec285a9b Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_legendre.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polynomial.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polynomial.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1b10bef28602dd57b84ff3a37a2597bd7a58288c Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polynomial.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polyutils.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polyutils.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f35ac1f6069707339a5ae3accb54e50e98ba6c67 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_polyutils.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_printing.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_printing.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..a3b614857ab51fd9da5d8abd11178bb9a11bdeb1 Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_printing.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_symbol.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_symbol.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..cf4363aa46ee2f418c4a0290dce8d0d7a071488c Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/__pycache__/test_symbol.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_chebyshev.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_chebyshev.py new file mode 100644 index 0000000000000000000000000000000000000000..2f54bebfdb27d54f436378e4ab6d6c8f2426dd90 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_chebyshev.py @@ -0,0 +1,619 @@ +"""Tests for chebyshev module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.chebyshev as cheb +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + + +def trim(x): + return cheb.chebtrim(x, tol=1e-6) + +T0 = [1] +T1 = [0, 1] +T2 = [-1, 0, 2] +T3 = [0, -3, 0, 4] +T4 = [1, 0, -8, 0, 8] +T5 = [0, 5, 0, -20, 0, 16] +T6 = [-1, 0, 18, 0, -48, 0, 32] +T7 = [0, -7, 0, 56, 0, -112, 0, 64] +T8 = [1, 0, -32, 0, 160, 0, -256, 0, 128] +T9 = [0, 9, 0, -120, 0, 432, 0, -576, 0, 256] + +Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9] + + +class TestPrivate: + + def test__cseries_to_zseries(self): + for i in range(5): + inp = np.array([2] + [1]*i, np.double) + tgt = np.array([.5]*i + [2] + [.5]*i, np.double) + res = cheb._cseries_to_zseries(inp) + assert_equal(res, tgt) + + def test__zseries_to_cseries(self): + for i in range(5): + inp = np.array([.5]*i + [2] + [.5]*i, np.double) + tgt = np.array([2] + [1]*i, np.double) + res = cheb._zseries_to_cseries(inp) + assert_equal(res, tgt) + + +class TestConstants: + + def test_chebdomain(self): + assert_equal(cheb.chebdomain, [-1, 1]) + + def test_chebzero(self): + assert_equal(cheb.chebzero, [0]) + + def test_chebone(self): + assert_equal(cheb.chebone, [1]) + + def test_chebx(self): + assert_equal(cheb.chebx, [0, 1]) + + +class TestArithmetic: + + def test_chebadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = cheb.chebadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_chebsub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = cheb.chebsub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_chebmulx(self): + assert_equal(cheb.chebmulx([0]), [0]) + assert_equal(cheb.chebmulx([1]), [0, 1]) + for i in range(1, 5): + ser = [0]*i + [1] + tgt = [0]*(i - 1) + [.5, 0, .5] + assert_equal(cheb.chebmulx(ser), tgt) + + def test_chebmul(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(i + j + 1) + tgt[i + j] += .5 + tgt[abs(i - j)] += .5 + res = cheb.chebmul([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_chebdiv(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1] + cj = [0]*j + [1] + tgt = cheb.chebadd(ci, cj) + quo, rem = cheb.chebdiv(tgt, ci) + res = cheb.chebadd(cheb.chebmul(quo, ci), rem) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_chebpow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(cheb.chebmul, [c]*j, np.array([1])) + res = cheb.chebpow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([2.5, 2., 1.5]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = polyval(x, [1., 2., 3.]) + + def test_chebval(self): + #check empty input + assert_equal(cheb.chebval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [polyval(x, c) for c in Tlist] + for i in range(10): + msg = f"At i={i}" + tgt = y[i] + res = cheb.chebval(x, [0]*i + [1]) + assert_almost_equal(res, tgt, err_msg=msg) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(cheb.chebval(x, [1]).shape, dims) + assert_equal(cheb.chebval(x, [1, 0]).shape, dims) + assert_equal(cheb.chebval(x, [1, 0, 0]).shape, dims) + + def test_chebval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, cheb.chebval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = cheb.chebval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = cheb.chebval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_chebval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, cheb.chebval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = cheb.chebval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = cheb.chebval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_chebgrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = cheb.chebgrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = cheb.chebgrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_chebgrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = cheb.chebgrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = cheb.chebgrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_chebint(self): + # check exceptions + assert_raises(TypeError, cheb.chebint, [0], .5) + assert_raises(ValueError, cheb.chebint, [0], -1) + assert_raises(ValueError, cheb.chebint, [0], 1, [0, 0]) + assert_raises(ValueError, cheb.chebint, [0], lbnd=[0]) + assert_raises(ValueError, cheb.chebint, [0], scl=[0]) + assert_raises(TypeError, cheb.chebint, [0], axis=.5) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = cheb.chebint([0], m=i, k=k) + assert_almost_equal(res, [0, 1]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + chebpol = cheb.poly2cheb(pol) + chebint = cheb.chebint(chebpol, m=1, k=[i]) + res = cheb.cheb2poly(chebint) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + chebpol = cheb.poly2cheb(pol) + chebint = cheb.chebint(chebpol, m=1, k=[i], lbnd=-1) + assert_almost_equal(cheb.chebval(-1, chebint), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + chebpol = cheb.poly2cheb(pol) + chebint = cheb.chebint(chebpol, m=1, k=[i], scl=2) + res = cheb.cheb2poly(chebint) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = cheb.chebint(tgt, m=1) + res = cheb.chebint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = cheb.chebint(tgt, m=1, k=[k]) + res = cheb.chebint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = cheb.chebint(tgt, m=1, k=[k], lbnd=-1) + res = cheb.chebint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = cheb.chebint(tgt, m=1, k=[k], scl=2) + res = cheb.chebint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_chebint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([cheb.chebint(c) for c in c2d.T]).T + res = cheb.chebint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([cheb.chebint(c) for c in c2d]) + res = cheb.chebint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([cheb.chebint(c, k=3) for c in c2d]) + res = cheb.chebint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + +class TestDerivative: + + def test_chebder(self): + # check exceptions + assert_raises(TypeError, cheb.chebder, [0], .5) + assert_raises(ValueError, cheb.chebder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = cheb.chebder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = cheb.chebder(cheb.chebint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = cheb.chebder(cheb.chebint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_chebder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([cheb.chebder(c) for c in c2d.T]).T + res = cheb.chebder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([cheb.chebder(c) for c in c2d]) + res = cheb.chebder(c2d, axis=1) + assert_almost_equal(res, tgt) + + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_chebvander(self): + # check for 1d x + x = np.arange(3) + v = cheb.chebvander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], cheb.chebval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = cheb.chebvander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], cheb.chebval(x, coef)) + + def test_chebvander2d(self): + # also tests chebval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = cheb.chebvander2d(x1, x2, [1, 2]) + tgt = cheb.chebval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = cheb.chebvander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_chebvander3d(self): + # also tests chebval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = cheb.chebvander3d(x1, x2, x3, [1, 2, 3]) + tgt = cheb.chebval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = cheb.chebvander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + +class TestFitting: + + def test_chebfit(self): + def f(x): + return x*(x - 1)*(x - 2) + + def f2(x): + return x**4 + x**2 + 1 + + # Test exceptions + assert_raises(ValueError, cheb.chebfit, [1], [1], -1) + assert_raises(TypeError, cheb.chebfit, [[1]], [1], 0) + assert_raises(TypeError, cheb.chebfit, [], [1], 0) + assert_raises(TypeError, cheb.chebfit, [1], [[[1]]], 0) + assert_raises(TypeError, cheb.chebfit, [1, 2], [1], 0) + assert_raises(TypeError, cheb.chebfit, [1], [1, 2], 0) + assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, cheb.chebfit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, cheb.chebfit, [1], [1], [-1,]) + assert_raises(ValueError, cheb.chebfit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, cheb.chebfit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = cheb.chebfit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(cheb.chebval(x, coef3), y) + coef3 = cheb.chebfit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(cheb.chebval(x, coef3), y) + # + coef4 = cheb.chebfit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(cheb.chebval(x, coef4), y) + coef4 = cheb.chebfit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(cheb.chebval(x, coef4), y) + # check things still work if deg is not in strict increasing + coef4 = cheb.chebfit(x, y, [2, 3, 4, 1, 0]) + assert_equal(len(coef4), 5) + assert_almost_equal(cheb.chebval(x, coef4), y) + # + coef2d = cheb.chebfit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = cheb.chebfit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + y[0::2] = 0 + wcoef3 = cheb.chebfit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = cheb.chebfit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = cheb.chebfit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = cheb.chebfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(cheb.chebfit(x, x, 1), [0, 1]) + assert_almost_equal(cheb.chebfit(x, x, [0, 1]), [0, 1]) + # test fitting only even polynomials + x = np.linspace(-1, 1) + y = f2(x) + coef1 = cheb.chebfit(x, y, 4) + assert_almost_equal(cheb.chebval(x, coef1), y) + coef2 = cheb.chebfit(x, y, [0, 2, 4]) + assert_almost_equal(cheb.chebval(x, coef2), y) + assert_almost_equal(coef1, coef2) + + +class TestInterpolate: + + def f(self, x): + return x * (x - 1) * (x - 2) + + def test_raises(self): + assert_raises(ValueError, cheb.chebinterpolate, self.f, -1) + assert_raises(TypeError, cheb.chebinterpolate, self.f, 10.) + + def test_dimensions(self): + for deg in range(1, 5): + assert_(cheb.chebinterpolate(self.f, deg).shape == (deg + 1,)) + + def test_approximation(self): + + def powx(x, p): + return x**p + + x = np.linspace(-1, 1, 10) + for deg in range(0, 10): + for p in range(0, deg + 1): + c = cheb.chebinterpolate(powx, deg, (p,)) + assert_almost_equal(cheb.chebval(x, c), powx(x, p), decimal=12) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, cheb.chebcompanion, []) + assert_raises(ValueError, cheb.chebcompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(cheb.chebcompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(cheb.chebcompanion([1, 2])[0, 0] == -.5) + + +class TestGauss: + + def test_100(self): + x, w = cheb.chebgauss(100) + + # test orthogonality. Note that the results need to be normalized, + # otherwise the huge values that can arise from fast growing + # functions like Laguerre can be very confusing. + v = cheb.chebvander(x, 99) + vv = np.dot(v.T * w, v) + vd = 1/np.sqrt(vv.diagonal()) + vv = vd[:, None] * vv * vd + assert_almost_equal(vv, np.eye(100)) + + # check that the integral of 1 is correct + tgt = np.pi + assert_almost_equal(w.sum(), tgt) + + +class TestMisc: + + def test_chebfromroots(self): + res = cheb.chebfromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + tgt = [0]*i + [1] + res = cheb.chebfromroots(roots)*2**(i-1) + assert_almost_equal(trim(res), trim(tgt)) + + def test_chebroots(self): + assert_almost_equal(cheb.chebroots([1]), []) + assert_almost_equal(cheb.chebroots([1, 2]), [-.5]) + for i in range(2, 5): + tgt = np.linspace(-1, 1, i) + res = cheb.chebroots(cheb.chebfromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_chebtrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, cheb.chebtrim, coef, -1) + + # Test results + assert_equal(cheb.chebtrim(coef), coef[:-1]) + assert_equal(cheb.chebtrim(coef, 1), coef[:-3]) + assert_equal(cheb.chebtrim(coef, 2), [0]) + + def test_chebline(self): + assert_equal(cheb.chebline(3, 4), [3, 4]) + + def test_cheb2poly(self): + for i in range(10): + assert_almost_equal(cheb.cheb2poly([0]*i + [1]), Tlist[i]) + + def test_poly2cheb(self): + for i in range(10): + assert_almost_equal(cheb.poly2cheb(Tlist[i]), [0]*i + [1]) + + def test_weight(self): + x = np.linspace(-1, 1, 11)[1:-1] + tgt = 1./(np.sqrt(1 + x) * np.sqrt(1 - x)) + res = cheb.chebweight(x) + assert_almost_equal(res, tgt) + + def test_chebpts1(self): + #test exceptions + assert_raises(ValueError, cheb.chebpts1, 1.5) + assert_raises(ValueError, cheb.chebpts1, 0) + + #test points + tgt = [0] + assert_almost_equal(cheb.chebpts1(1), tgt) + tgt = [-0.70710678118654746, 0.70710678118654746] + assert_almost_equal(cheb.chebpts1(2), tgt) + tgt = [-0.86602540378443871, 0, 0.86602540378443871] + assert_almost_equal(cheb.chebpts1(3), tgt) + tgt = [-0.9238795325, -0.3826834323, 0.3826834323, 0.9238795325] + assert_almost_equal(cheb.chebpts1(4), tgt) + + def test_chebpts2(self): + #test exceptions + assert_raises(ValueError, cheb.chebpts2, 1.5) + assert_raises(ValueError, cheb.chebpts2, 1) + + #test points + tgt = [-1, 1] + assert_almost_equal(cheb.chebpts2(2), tgt) + tgt = [-1, 0, 1] + assert_almost_equal(cheb.chebpts2(3), tgt) + tgt = [-1, -0.5, .5, 1] + assert_almost_equal(cheb.chebpts2(4), tgt) + tgt = [-1.0, -0.707106781187, 0, 0.707106781187, 1.0] + assert_almost_equal(cheb.chebpts2(5), tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_classes.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_classes.py new file mode 100644 index 0000000000000000000000000000000000000000..75672a148524d8887663b986ec5d9e6c13d1193a --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_classes.py @@ -0,0 +1,607 @@ +"""Test inter-conversion of different polynomial classes. + +This tests the convert and cast methods of all the polynomial classes. + +""" +import operator as op +from numbers import Number + +import pytest +import numpy as np +from numpy.polynomial import ( + Polynomial, Legendre, Chebyshev, Laguerre, Hermite, HermiteE) +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) +from numpy.exceptions import RankWarning + +# +# fixtures +# + +classes = ( + Polynomial, Legendre, Chebyshev, Laguerre, + Hermite, HermiteE + ) +classids = tuple(cls.__name__ for cls in classes) + +@pytest.fixture(params=classes, ids=classids) +def Poly(request): + return request.param + +# +# helper functions +# +random = np.random.random + + +def assert_poly_almost_equal(p1, p2, msg=""): + try: + assert_(np.all(p1.domain == p2.domain)) + assert_(np.all(p1.window == p2.window)) + assert_almost_equal(p1.coef, p2.coef) + except AssertionError: + msg = f"Result: {p1}\nTarget: {p2}" + raise AssertionError(msg) + + +# +# Test conversion methods that depend on combinations of two classes. +# + +Poly1 = Poly +Poly2 = Poly + + +def test_conversion(Poly1, Poly2): + x = np.linspace(0, 1, 10) + coef = random((3,)) + + d1 = Poly1.domain + random((2,))*.25 + w1 = Poly1.window + random((2,))*.25 + p1 = Poly1(coef, domain=d1, window=w1) + + d2 = Poly2.domain + random((2,))*.25 + w2 = Poly2.window + random((2,))*.25 + p2 = p1.convert(kind=Poly2, domain=d2, window=w2) + + assert_almost_equal(p2.domain, d2) + assert_almost_equal(p2.window, w2) + assert_almost_equal(p2(x), p1(x)) + + +def test_cast(Poly1, Poly2): + x = np.linspace(0, 1, 10) + coef = random((3,)) + + d1 = Poly1.domain + random((2,))*.25 + w1 = Poly1.window + random((2,))*.25 + p1 = Poly1(coef, domain=d1, window=w1) + + d2 = Poly2.domain + random((2,))*.25 + w2 = Poly2.window + random((2,))*.25 + p2 = Poly2.cast(p1, domain=d2, window=w2) + + assert_almost_equal(p2.domain, d2) + assert_almost_equal(p2.window, w2) + assert_almost_equal(p2(x), p1(x)) + + +# +# test methods that depend on one class +# + + +def test_identity(Poly): + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + x = np.linspace(d[0], d[1], 11) + p = Poly.identity(domain=d, window=w) + assert_equal(p.domain, d) + assert_equal(p.window, w) + assert_almost_equal(p(x), x) + + +def test_basis(Poly): + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + p = Poly.basis(5, domain=d, window=w) + assert_equal(p.domain, d) + assert_equal(p.window, w) + assert_equal(p.coef, [0]*5 + [1]) + + +def test_fromroots(Poly): + # check that requested roots are zeros of a polynomial + # of correct degree, domain, and window. + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + r = random((5,)) + p1 = Poly.fromroots(r, domain=d, window=w) + assert_equal(p1.degree(), len(r)) + assert_equal(p1.domain, d) + assert_equal(p1.window, w) + assert_almost_equal(p1(r), 0) + + # check that polynomial is monic + pdom = Polynomial.domain + pwin = Polynomial.window + p2 = Polynomial.cast(p1, domain=pdom, window=pwin) + assert_almost_equal(p2.coef[-1], 1) + + +def test_bad_conditioned_fit(Poly): + + x = [0., 0., 1.] + y = [1., 2., 3.] + + # check RankWarning is raised + with pytest.warns(RankWarning) as record: + Poly.fit(x, y, 2) + assert record[0].message.args[0] == "The fit may be poorly conditioned" + + +def test_fit(Poly): + + def f(x): + return x*(x - 1)*(x - 2) + x = np.linspace(0, 3) + y = f(x) + + # check default value of domain and window + p = Poly.fit(x, y, 3) + assert_almost_equal(p.domain, [0, 3]) + assert_almost_equal(p(x), y) + assert_equal(p.degree(), 3) + + # check with given domains and window + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + p = Poly.fit(x, y, 3, domain=d, window=w) + assert_almost_equal(p(x), y) + assert_almost_equal(p.domain, d) + assert_almost_equal(p.window, w) + p = Poly.fit(x, y, [0, 1, 2, 3], domain=d, window=w) + assert_almost_equal(p(x), y) + assert_almost_equal(p.domain, d) + assert_almost_equal(p.window, w) + + # check with class domain default + p = Poly.fit(x, y, 3, []) + assert_equal(p.domain, Poly.domain) + assert_equal(p.window, Poly.window) + p = Poly.fit(x, y, [0, 1, 2, 3], []) + assert_equal(p.domain, Poly.domain) + assert_equal(p.window, Poly.window) + + # check that fit accepts weights. + w = np.zeros_like(x) + z = y + random(y.shape)*.25 + w[::2] = 1 + p1 = Poly.fit(x[::2], z[::2], 3) + p2 = Poly.fit(x, z, 3, w=w) + p3 = Poly.fit(x, z, [0, 1, 2, 3], w=w) + assert_almost_equal(p1(x), p2(x)) + assert_almost_equal(p2(x), p3(x)) + + +def test_equal(Poly): + p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3]) + p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3]) + p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3]) + p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2]) + assert_(p1 == p1) + assert_(not p1 == p2) + assert_(not p1 == p3) + assert_(not p1 == p4) + + +def test_not_equal(Poly): + p1 = Poly([1, 2, 3], domain=[0, 1], window=[2, 3]) + p2 = Poly([1, 1, 1], domain=[0, 1], window=[2, 3]) + p3 = Poly([1, 2, 3], domain=[1, 2], window=[2, 3]) + p4 = Poly([1, 2, 3], domain=[0, 1], window=[1, 2]) + assert_(not p1 != p1) + assert_(p1 != p2) + assert_(p1 != p3) + assert_(p1 != p4) + + +def test_add(Poly): + # This checks commutation, not numerical correctness + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = p1 + p2 + assert_poly_almost_equal(p2 + p1, p3) + assert_poly_almost_equal(p1 + c2, p3) + assert_poly_almost_equal(c2 + p1, p3) + assert_poly_almost_equal(p1 + tuple(c2), p3) + assert_poly_almost_equal(tuple(c2) + p1, p3) + assert_poly_almost_equal(p1 + np.array(c2), p3) + assert_poly_almost_equal(np.array(c2) + p1, p3) + assert_raises(TypeError, op.add, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.add, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.add, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.add, p1, Polynomial([0])) + + +def test_sub(Poly): + # This checks commutation, not numerical correctness + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = p1 - p2 + assert_poly_almost_equal(p2 - p1, -p3) + assert_poly_almost_equal(p1 - c2, p3) + assert_poly_almost_equal(c2 - p1, -p3) + assert_poly_almost_equal(p1 - tuple(c2), p3) + assert_poly_almost_equal(tuple(c2) - p1, -p3) + assert_poly_almost_equal(p1 - np.array(c2), p3) + assert_poly_almost_equal(np.array(c2) - p1, -p3) + assert_raises(TypeError, op.sub, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.sub, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.sub, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.sub, p1, Polynomial([0])) + + +def test_mul(Poly): + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = p1 * p2 + assert_poly_almost_equal(p2 * p1, p3) + assert_poly_almost_equal(p1 * c2, p3) + assert_poly_almost_equal(c2 * p1, p3) + assert_poly_almost_equal(p1 * tuple(c2), p3) + assert_poly_almost_equal(tuple(c2) * p1, p3) + assert_poly_almost_equal(p1 * np.array(c2), p3) + assert_poly_almost_equal(np.array(c2) * p1, p3) + assert_poly_almost_equal(p1 * 2, p1 * Poly([2])) + assert_poly_almost_equal(2 * p1, p1 * Poly([2])) + assert_raises(TypeError, op.mul, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.mul, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.mul, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.mul, p1, Polynomial([0])) + + +def test_floordiv(Poly): + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + c3 = list(random((2,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = Poly(c3) + p4 = p1 * p2 + p3 + c4 = list(p4.coef) + assert_poly_almost_equal(p4 // p2, p1) + assert_poly_almost_equal(p4 // c2, p1) + assert_poly_almost_equal(c4 // p2, p1) + assert_poly_almost_equal(p4 // tuple(c2), p1) + assert_poly_almost_equal(tuple(c4) // p2, p1) + assert_poly_almost_equal(p4 // np.array(c2), p1) + assert_poly_almost_equal(np.array(c4) // p2, p1) + assert_poly_almost_equal(2 // p2, Poly([0])) + assert_poly_almost_equal(p2 // 2, 0.5*p2) + assert_raises( + TypeError, op.floordiv, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises( + TypeError, op.floordiv, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.floordiv, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.floordiv, p1, Polynomial([0])) + + +def test_truediv(Poly): + # true division is valid only if the denominator is a Number and + # not a python bool. + p1 = Poly([1,2,3]) + p2 = p1 * 5 + + for stype in np.ScalarType: + if not issubclass(stype, Number) or issubclass(stype, bool): + continue + s = stype(5) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for stype in (int, float): + s = stype(5) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for stype in [complex]: + s = stype(5, 0) + assert_poly_almost_equal(op.truediv(p2, s), p1) + assert_raises(TypeError, op.truediv, s, p2) + for s in [tuple(), list(), dict(), bool(), np.array([1])]: + assert_raises(TypeError, op.truediv, p2, s) + assert_raises(TypeError, op.truediv, s, p2) + for ptype in classes: + assert_raises(TypeError, op.truediv, p2, ptype(1)) + + +def test_mod(Poly): + # This checks commutation, not numerical correctness + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + c3 = list(random((2,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = Poly(c3) + p4 = p1 * p2 + p3 + c4 = list(p4.coef) + assert_poly_almost_equal(p4 % p2, p3) + assert_poly_almost_equal(p4 % c2, p3) + assert_poly_almost_equal(c4 % p2, p3) + assert_poly_almost_equal(p4 % tuple(c2), p3) + assert_poly_almost_equal(tuple(c4) % p2, p3) + assert_poly_almost_equal(p4 % np.array(c2), p3) + assert_poly_almost_equal(np.array(c4) % p2, p3) + assert_poly_almost_equal(2 % p2, Poly([2])) + assert_poly_almost_equal(p2 % 2, Poly([0])) + assert_raises(TypeError, op.mod, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, op.mod, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, op.mod, p1, Chebyshev([0])) + else: + assert_raises(TypeError, op.mod, p1, Polynomial([0])) + + +def test_divmod(Poly): + # This checks commutation, not numerical correctness + c1 = list(random((4,)) + .5) + c2 = list(random((3,)) + .5) + c3 = list(random((2,)) + .5) + p1 = Poly(c1) + p2 = Poly(c2) + p3 = Poly(c3) + p4 = p1 * p2 + p3 + c4 = list(p4.coef) + quo, rem = divmod(p4, p2) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(p4, c2) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(c4, p2) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(p4, tuple(c2)) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(tuple(c4), p2) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(p4, np.array(c2)) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(np.array(c4), p2) + assert_poly_almost_equal(quo, p1) + assert_poly_almost_equal(rem, p3) + quo, rem = divmod(p2, 2) + assert_poly_almost_equal(quo, 0.5*p2) + assert_poly_almost_equal(rem, Poly([0])) + quo, rem = divmod(2, p2) + assert_poly_almost_equal(quo, Poly([0])) + assert_poly_almost_equal(rem, Poly([2])) + assert_raises(TypeError, divmod, p1, Poly([0], domain=Poly.domain + 1)) + assert_raises(TypeError, divmod, p1, Poly([0], window=Poly.window + 1)) + if Poly is Polynomial: + assert_raises(TypeError, divmod, p1, Chebyshev([0])) + else: + assert_raises(TypeError, divmod, p1, Polynomial([0])) + + +def test_roots(Poly): + d = Poly.domain * 1.25 + .25 + w = Poly.window + tgt = np.linspace(d[0], d[1], 5) + res = np.sort(Poly.fromroots(tgt, domain=d, window=w).roots()) + assert_almost_equal(res, tgt) + # default domain and window + res = np.sort(Poly.fromroots(tgt).roots()) + assert_almost_equal(res, tgt) + + +def test_degree(Poly): + p = Poly.basis(5) + assert_equal(p.degree(), 5) + + +def test_copy(Poly): + p1 = Poly.basis(5) + p2 = p1.copy() + assert_(p1 == p2) + assert_(p1 is not p2) + assert_(p1.coef is not p2.coef) + assert_(p1.domain is not p2.domain) + assert_(p1.window is not p2.window) + + +def test_integ(Poly): + P = Polynomial + # Check defaults + p0 = Poly.cast(P([1*2, 2*3, 3*4])) + p1 = P.cast(p0.integ()) + p2 = P.cast(p0.integ(2)) + assert_poly_almost_equal(p1, P([0, 2, 3, 4])) + assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1])) + # Check with k + p0 = Poly.cast(P([1*2, 2*3, 3*4])) + p1 = P.cast(p0.integ(k=1)) + p2 = P.cast(p0.integ(2, k=[1, 1])) + assert_poly_almost_equal(p1, P([1, 2, 3, 4])) + assert_poly_almost_equal(p2, P([1, 1, 1, 1, 1])) + # Check with lbnd + p0 = Poly.cast(P([1*2, 2*3, 3*4])) + p1 = P.cast(p0.integ(lbnd=1)) + p2 = P.cast(p0.integ(2, lbnd=1)) + assert_poly_almost_equal(p1, P([-9, 2, 3, 4])) + assert_poly_almost_equal(p2, P([6, -9, 1, 1, 1])) + # Check scaling + d = 2*Poly.domain + p0 = Poly.cast(P([1*2, 2*3, 3*4]), domain=d) + p1 = P.cast(p0.integ()) + p2 = P.cast(p0.integ(2)) + assert_poly_almost_equal(p1, P([0, 2, 3, 4])) + assert_poly_almost_equal(p2, P([0, 0, 1, 1, 1])) + + +def test_deriv(Poly): + # Check that the derivative is the inverse of integration. It is + # assumes that the integration has been checked elsewhere. + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + p1 = Poly([1, 2, 3], domain=d, window=w) + p2 = p1.integ(2, k=[1, 2]) + p3 = p1.integ(1, k=[1]) + assert_almost_equal(p2.deriv(1).coef, p3.coef) + assert_almost_equal(p2.deriv(2).coef, p1.coef) + # default domain and window + p1 = Poly([1, 2, 3]) + p2 = p1.integ(2, k=[1, 2]) + p3 = p1.integ(1, k=[1]) + assert_almost_equal(p2.deriv(1).coef, p3.coef) + assert_almost_equal(p2.deriv(2).coef, p1.coef) + + +def test_linspace(Poly): + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + p = Poly([1, 2, 3], domain=d, window=w) + # check default domain + xtgt = np.linspace(d[0], d[1], 20) + ytgt = p(xtgt) + xres, yres = p.linspace(20) + assert_almost_equal(xres, xtgt) + assert_almost_equal(yres, ytgt) + # check specified domain + xtgt = np.linspace(0, 2, 20) + ytgt = p(xtgt) + xres, yres = p.linspace(20, domain=[0, 2]) + assert_almost_equal(xres, xtgt) + assert_almost_equal(yres, ytgt) + + +def test_pow(Poly): + d = Poly.domain + random((2,))*.25 + w = Poly.window + random((2,))*.25 + tgt = Poly([1], domain=d, window=w) + tst = Poly([1, 2, 3], domain=d, window=w) + for i in range(5): + assert_poly_almost_equal(tst**i, tgt) + tgt = tgt * tst + # default domain and window + tgt = Poly([1]) + tst = Poly([1, 2, 3]) + for i in range(5): + assert_poly_almost_equal(tst**i, tgt) + tgt = tgt * tst + # check error for invalid powers + assert_raises(ValueError, op.pow, tgt, 1.5) + assert_raises(ValueError, op.pow, tgt, -1) + + +def test_call(Poly): + P = Polynomial + d = Poly.domain + x = np.linspace(d[0], d[1], 11) + + # Check defaults + p = Poly.cast(P([1, 2, 3])) + tgt = 1 + x*(2 + 3*x) + res = p(x) + assert_almost_equal(res, tgt) + + +def test_call_with_list(Poly): + p = Poly([1, 2, 3]) + x = [-1, 0, 2] + res = p(x) + assert_equal(res, p(np.array(x))) + + +def test_cutdeg(Poly): + p = Poly([1, 2, 3]) + assert_raises(ValueError, p.cutdeg, .5) + assert_raises(ValueError, p.cutdeg, -1) + assert_equal(len(p.cutdeg(3)), 3) + assert_equal(len(p.cutdeg(2)), 3) + assert_equal(len(p.cutdeg(1)), 2) + assert_equal(len(p.cutdeg(0)), 1) + + +def test_truncate(Poly): + p = Poly([1, 2, 3]) + assert_raises(ValueError, p.truncate, .5) + assert_raises(ValueError, p.truncate, 0) + assert_equal(len(p.truncate(4)), 3) + assert_equal(len(p.truncate(3)), 3) + assert_equal(len(p.truncate(2)), 2) + assert_equal(len(p.truncate(1)), 1) + + +def test_trim(Poly): + c = [1, 1e-6, 1e-12, 0] + p = Poly(c) + assert_equal(p.trim().coef, c[:3]) + assert_equal(p.trim(1e-10).coef, c[:2]) + assert_equal(p.trim(1e-5).coef, c[:1]) + + +def test_mapparms(Poly): + # check with defaults. Should be identity. + d = Poly.domain + w = Poly.window + p = Poly([1], domain=d, window=w) + assert_almost_equal([0, 1], p.mapparms()) + # + w = 2*d + 1 + p = Poly([1], domain=d, window=w) + assert_almost_equal([1, 2], p.mapparms()) + + +def test_ufunc_override(Poly): + p = Poly([1, 2, 3]) + x = np.ones(3) + assert_raises(TypeError, np.add, p, x) + assert_raises(TypeError, np.add, x, p) + + +# +# Test class method that only exists for some classes +# + + +class TestInterpolate: + + def f(self, x): + return x * (x - 1) * (x - 2) + + def test_raises(self): + assert_raises(ValueError, Chebyshev.interpolate, self.f, -1) + assert_raises(TypeError, Chebyshev.interpolate, self.f, 10.) + + def test_dimensions(self): + for deg in range(1, 5): + assert_(Chebyshev.interpolate(self.f, deg).degree() == deg) + + def test_approximation(self): + + def powx(x, p): + return x**p + + x = np.linspace(0, 2, 10) + for deg in range(0, 10): + for t in range(0, deg + 1): + p = Chebyshev.interpolate(powx, deg, domain=[0, 2], args=(t,)) + assert_almost_equal(p(x), powx(x, t), decimal=11) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite.py new file mode 100644 index 0000000000000000000000000000000000000000..2188800853f2f5e9a98d2d7087893a7cf11440ef --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite.py @@ -0,0 +1,555 @@ +"""Tests for hermite module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.hermite as herm +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + +H0 = np.array([1]) +H1 = np.array([0, 2]) +H2 = np.array([-2, 0, 4]) +H3 = np.array([0, -12, 0, 8]) +H4 = np.array([12, 0, -48, 0, 16]) +H5 = np.array([0, 120, 0, -160, 0, 32]) +H6 = np.array([-120, 0, 720, 0, -480, 0, 64]) +H7 = np.array([0, -1680, 0, 3360, 0, -1344, 0, 128]) +H8 = np.array([1680, 0, -13440, 0, 13440, 0, -3584, 0, 256]) +H9 = np.array([0, 30240, 0, -80640, 0, 48384, 0, -9216, 0, 512]) + +Hlist = [H0, H1, H2, H3, H4, H5, H6, H7, H8, H9] + + +def trim(x): + return herm.hermtrim(x, tol=1e-6) + + +class TestConstants: + + def test_hermdomain(self): + assert_equal(herm.hermdomain, [-1, 1]) + + def test_hermzero(self): + assert_equal(herm.hermzero, [0]) + + def test_hermone(self): + assert_equal(herm.hermone, [1]) + + def test_hermx(self): + assert_equal(herm.hermx, [0, .5]) + + +class TestArithmetic: + x = np.linspace(-3, 3, 100) + + def test_hermadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = herm.hermadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermsub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = herm.hermsub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermmulx(self): + assert_equal(herm.hermmulx([0]), [0]) + assert_equal(herm.hermmulx([1]), [0, .5]) + for i in range(1, 5): + ser = [0]*i + [1] + tgt = [0]*(i - 1) + [i, 0, .5] + assert_equal(herm.hermmulx(ser), tgt) + + def test_hermmul(self): + # check values of result + for i in range(5): + pol1 = [0]*i + [1] + val1 = herm.hermval(self.x, pol1) + for j in range(5): + msg = f"At i={i}, j={j}" + pol2 = [0]*j + [1] + val2 = herm.hermval(self.x, pol2) + pol3 = herm.hermmul(pol1, pol2) + val3 = herm.hermval(self.x, pol3) + assert_(len(pol3) == i + j + 1, msg) + assert_almost_equal(val3, val1*val2, err_msg=msg) + + def test_hermdiv(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1] + cj = [0]*j + [1] + tgt = herm.hermadd(ci, cj) + quo, rem = herm.hermdiv(tgt, ci) + res = herm.hermadd(herm.hermmul(quo, ci), rem) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermpow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(herm.hermmul, [c]*j, np.array([1])) + res = herm.hermpow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([2.5, 1., .75]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = polyval(x, [1., 2., 3.]) + + def test_hermval(self): + #check empty input + assert_equal(herm.hermval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [polyval(x, c) for c in Hlist] + for i in range(10): + msg = f"At i={i}" + tgt = y[i] + res = herm.hermval(x, [0]*i + [1]) + assert_almost_equal(res, tgt, err_msg=msg) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(herm.hermval(x, [1]).shape, dims) + assert_equal(herm.hermval(x, [1, 0]).shape, dims) + assert_equal(herm.hermval(x, [1, 0, 0]).shape, dims) + + def test_hermval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, herm.hermval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = herm.hermval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herm.hermval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_hermval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, herm.hermval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = herm.hermval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herm.hermval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_hermgrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = herm.hermgrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herm.hermgrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_hermgrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = herm.hermgrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herm.hermgrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_hermint(self): + # check exceptions + assert_raises(TypeError, herm.hermint, [0], .5) + assert_raises(ValueError, herm.hermint, [0], -1) + assert_raises(ValueError, herm.hermint, [0], 1, [0, 0]) + assert_raises(ValueError, herm.hermint, [0], lbnd=[0]) + assert_raises(ValueError, herm.hermint, [0], scl=[0]) + assert_raises(TypeError, herm.hermint, [0], axis=.5) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = herm.hermint([0], m=i, k=k) + assert_almost_equal(res, [0, .5]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + hermpol = herm.poly2herm(pol) + hermint = herm.hermint(hermpol, m=1, k=[i]) + res = herm.herm2poly(hermint) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + hermpol = herm.poly2herm(pol) + hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1) + assert_almost_equal(herm.hermval(-1, hermint), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + hermpol = herm.poly2herm(pol) + hermint = herm.hermint(hermpol, m=1, k=[i], scl=2) + res = herm.herm2poly(hermint) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herm.hermint(tgt, m=1) + res = herm.hermint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herm.hermint(tgt, m=1, k=[k]) + res = herm.hermint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herm.hermint(tgt, m=1, k=[k], lbnd=-1) + res = herm.hermint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herm.hermint(tgt, m=1, k=[k], scl=2) + res = herm.hermint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([herm.hermint(c) for c in c2d.T]).T + res = herm.hermint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herm.hermint(c) for c in c2d]) + res = herm.hermint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herm.hermint(c, k=3) for c in c2d]) + res = herm.hermint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + +class TestDerivative: + + def test_hermder(self): + # check exceptions + assert_raises(TypeError, herm.hermder, [0], .5) + assert_raises(ValueError, herm.hermder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = herm.hermder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = herm.hermder(herm.hermint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = herm.hermder(herm.hermint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([herm.hermder(c) for c in c2d.T]).T + res = herm.hermder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herm.hermder(c) for c in c2d]) + res = herm.hermder(c2d, axis=1) + assert_almost_equal(res, tgt) + + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_hermvander(self): + # check for 1d x + x = np.arange(3) + v = herm.hermvander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], herm.hermval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = herm.hermvander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], herm.hermval(x, coef)) + + def test_hermvander2d(self): + # also tests hermval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = herm.hermvander2d(x1, x2, [1, 2]) + tgt = herm.hermval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = herm.hermvander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_hermvander3d(self): + # also tests hermval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = herm.hermvander3d(x1, x2, x3, [1, 2, 3]) + tgt = herm.hermval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = herm.hermvander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + +class TestFitting: + + def test_hermfit(self): + def f(x): + return x*(x - 1)*(x - 2) + + def f2(x): + return x**4 + x**2 + 1 + + # Test exceptions + assert_raises(ValueError, herm.hermfit, [1], [1], -1) + assert_raises(TypeError, herm.hermfit, [[1]], [1], 0) + assert_raises(TypeError, herm.hermfit, [], [1], 0) + assert_raises(TypeError, herm.hermfit, [1], [[[1]]], 0) + assert_raises(TypeError, herm.hermfit, [1, 2], [1], 0) + assert_raises(TypeError, herm.hermfit, [1], [1, 2], 0) + assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, herm.hermfit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, herm.hermfit, [1], [1], [-1,]) + assert_raises(ValueError, herm.hermfit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, herm.hermfit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = herm.hermfit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(herm.hermval(x, coef3), y) + coef3 = herm.hermfit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(herm.hermval(x, coef3), y) + # + coef4 = herm.hermfit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(herm.hermval(x, coef4), y) + coef4 = herm.hermfit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(herm.hermval(x, coef4), y) + # check things still work if deg is not in strict increasing + coef4 = herm.hermfit(x, y, [2, 3, 4, 1, 0]) + assert_equal(len(coef4), 5) + assert_almost_equal(herm.hermval(x, coef4), y) + # + coef2d = herm.hermfit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = herm.hermfit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + y[0::2] = 0 + wcoef3 = herm.hermfit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = herm.hermfit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = herm.hermfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(herm.hermfit(x, x, 1), [0, .5]) + assert_almost_equal(herm.hermfit(x, x, [0, 1]), [0, .5]) + # test fitting only even Legendre polynomials + x = np.linspace(-1, 1) + y = f2(x) + coef1 = herm.hermfit(x, y, 4) + assert_almost_equal(herm.hermval(x, coef1), y) + coef2 = herm.hermfit(x, y, [0, 2, 4]) + assert_almost_equal(herm.hermval(x, coef2), y) + assert_almost_equal(coef1, coef2) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, herm.hermcompanion, []) + assert_raises(ValueError, herm.hermcompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(herm.hermcompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(herm.hermcompanion([1, 2])[0, 0] == -.25) + + +class TestGauss: + + def test_100(self): + x, w = herm.hermgauss(100) + + # test orthogonality. Note that the results need to be normalized, + # otherwise the huge values that can arise from fast growing + # functions like Laguerre can be very confusing. + v = herm.hermvander(x, 99) + vv = np.dot(v.T * w, v) + vd = 1/np.sqrt(vv.diagonal()) + vv = vd[:, None] * vv * vd + assert_almost_equal(vv, np.eye(100)) + + # check that the integral of 1 is correct + tgt = np.sqrt(np.pi) + assert_almost_equal(w.sum(), tgt) + + +class TestMisc: + + def test_hermfromroots(self): + res = herm.hermfromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + pol = herm.hermfromroots(roots) + res = herm.hermval(roots, pol) + tgt = 0 + assert_(len(pol) == i + 1) + assert_almost_equal(herm.herm2poly(pol)[-1], 1) + assert_almost_equal(res, tgt) + + def test_hermroots(self): + assert_almost_equal(herm.hermroots([1]), []) + assert_almost_equal(herm.hermroots([1, 1]), [-.5]) + for i in range(2, 5): + tgt = np.linspace(-1, 1, i) + res = herm.hermroots(herm.hermfromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermtrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, herm.hermtrim, coef, -1) + + # Test results + assert_equal(herm.hermtrim(coef), coef[:-1]) + assert_equal(herm.hermtrim(coef, 1), coef[:-3]) + assert_equal(herm.hermtrim(coef, 2), [0]) + + def test_hermline(self): + assert_equal(herm.hermline(3, 4), [3, 2]) + + def test_herm2poly(self): + for i in range(10): + assert_almost_equal(herm.herm2poly([0]*i + [1]), Hlist[i]) + + def test_poly2herm(self): + for i in range(10): + assert_almost_equal(herm.poly2herm(Hlist[i]), [0]*i + [1]) + + def test_weight(self): + x = np.linspace(-5, 5, 11) + tgt = np.exp(-x**2) + res = herm.hermweight(x) + assert_almost_equal(res, tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite_e.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite_e.py new file mode 100644 index 0000000000000000000000000000000000000000..2d262a3306222bd79f682b09763b0bd2b90ba8fe --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_hermite_e.py @@ -0,0 +1,556 @@ +"""Tests for hermite_e module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.hermite_e as herme +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + +He0 = np.array([1]) +He1 = np.array([0, 1]) +He2 = np.array([-1, 0, 1]) +He3 = np.array([0, -3, 0, 1]) +He4 = np.array([3, 0, -6, 0, 1]) +He5 = np.array([0, 15, 0, -10, 0, 1]) +He6 = np.array([-15, 0, 45, 0, -15, 0, 1]) +He7 = np.array([0, -105, 0, 105, 0, -21, 0, 1]) +He8 = np.array([105, 0, -420, 0, 210, 0, -28, 0, 1]) +He9 = np.array([0, 945, 0, -1260, 0, 378, 0, -36, 0, 1]) + +Helist = [He0, He1, He2, He3, He4, He5, He6, He7, He8, He9] + + +def trim(x): + return herme.hermetrim(x, tol=1e-6) + + +class TestConstants: + + def test_hermedomain(self): + assert_equal(herme.hermedomain, [-1, 1]) + + def test_hermezero(self): + assert_equal(herme.hermezero, [0]) + + def test_hermeone(self): + assert_equal(herme.hermeone, [1]) + + def test_hermex(self): + assert_equal(herme.hermex, [0, 1]) + + +class TestArithmetic: + x = np.linspace(-3, 3, 100) + + def test_hermeadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = herme.hermeadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermesub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = herme.hermesub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermemulx(self): + assert_equal(herme.hermemulx([0]), [0]) + assert_equal(herme.hermemulx([1]), [0, 1]) + for i in range(1, 5): + ser = [0]*i + [1] + tgt = [0]*(i - 1) + [i, 0, 1] + assert_equal(herme.hermemulx(ser), tgt) + + def test_hermemul(self): + # check values of result + for i in range(5): + pol1 = [0]*i + [1] + val1 = herme.hermeval(self.x, pol1) + for j in range(5): + msg = f"At i={i}, j={j}" + pol2 = [0]*j + [1] + val2 = herme.hermeval(self.x, pol2) + pol3 = herme.hermemul(pol1, pol2) + val3 = herme.hermeval(self.x, pol3) + assert_(len(pol3) == i + j + 1, msg) + assert_almost_equal(val3, val1*val2, err_msg=msg) + + def test_hermediv(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1] + cj = [0]*j + [1] + tgt = herme.hermeadd(ci, cj) + quo, rem = herme.hermediv(tgt, ci) + res = herme.hermeadd(herme.hermemul(quo, ci), rem) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_hermepow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(herme.hermemul, [c]*j, np.array([1])) + res = herme.hermepow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([4., 2., 3.]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = polyval(x, [1., 2., 3.]) + + def test_hermeval(self): + #check empty input + assert_equal(herme.hermeval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [polyval(x, c) for c in Helist] + for i in range(10): + msg = f"At i={i}" + tgt = y[i] + res = herme.hermeval(x, [0]*i + [1]) + assert_almost_equal(res, tgt, err_msg=msg) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(herme.hermeval(x, [1]).shape, dims) + assert_equal(herme.hermeval(x, [1, 0]).shape, dims) + assert_equal(herme.hermeval(x, [1, 0, 0]).shape, dims) + + def test_hermeval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, herme.hermeval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = herme.hermeval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herme.hermeval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_hermeval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, herme.hermeval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = herme.hermeval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herme.hermeval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_hermegrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = herme.hermegrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herme.hermegrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_hermegrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = herme.hermegrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = herme.hermegrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_hermeint(self): + # check exceptions + assert_raises(TypeError, herme.hermeint, [0], .5) + assert_raises(ValueError, herme.hermeint, [0], -1) + assert_raises(ValueError, herme.hermeint, [0], 1, [0, 0]) + assert_raises(ValueError, herme.hermeint, [0], lbnd=[0]) + assert_raises(ValueError, herme.hermeint, [0], scl=[0]) + assert_raises(TypeError, herme.hermeint, [0], axis=.5) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = herme.hermeint([0], m=i, k=k) + assert_almost_equal(res, [0, 1]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + hermepol = herme.poly2herme(pol) + hermeint = herme.hermeint(hermepol, m=1, k=[i]) + res = herme.herme2poly(hermeint) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + hermepol = herme.poly2herme(pol) + hermeint = herme.hermeint(hermepol, m=1, k=[i], lbnd=-1) + assert_almost_equal(herme.hermeval(-1, hermeint), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + hermepol = herme.poly2herme(pol) + hermeint = herme.hermeint(hermepol, m=1, k=[i], scl=2) + res = herme.herme2poly(hermeint) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herme.hermeint(tgt, m=1) + res = herme.hermeint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herme.hermeint(tgt, m=1, k=[k]) + res = herme.hermeint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herme.hermeint(tgt, m=1, k=[k], lbnd=-1) + res = herme.hermeint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = herme.hermeint(tgt, m=1, k=[k], scl=2) + res = herme.hermeint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermeint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([herme.hermeint(c) for c in c2d.T]).T + res = herme.hermeint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herme.hermeint(c) for c in c2d]) + res = herme.hermeint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herme.hermeint(c, k=3) for c in c2d]) + res = herme.hermeint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + +class TestDerivative: + + def test_hermeder(self): + # check exceptions + assert_raises(TypeError, herme.hermeder, [0], .5) + assert_raises(ValueError, herme.hermeder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = herme.hermeder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = herme.hermeder(herme.hermeint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = herme.hermeder( + herme.hermeint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermeder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([herme.hermeder(c) for c in c2d.T]).T + res = herme.hermeder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([herme.hermeder(c) for c in c2d]) + res = herme.hermeder(c2d, axis=1) + assert_almost_equal(res, tgt) + + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_hermevander(self): + # check for 1d x + x = np.arange(3) + v = herme.hermevander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], herme.hermeval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = herme.hermevander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], herme.hermeval(x, coef)) + + def test_hermevander2d(self): + # also tests hermeval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = herme.hermevander2d(x1, x2, [1, 2]) + tgt = herme.hermeval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = herme.hermevander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_hermevander3d(self): + # also tests hermeval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = herme.hermevander3d(x1, x2, x3, [1, 2, 3]) + tgt = herme.hermeval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = herme.hermevander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + +class TestFitting: + + def test_hermefit(self): + def f(x): + return x*(x - 1)*(x - 2) + + def f2(x): + return x**4 + x**2 + 1 + + # Test exceptions + assert_raises(ValueError, herme.hermefit, [1], [1], -1) + assert_raises(TypeError, herme.hermefit, [[1]], [1], 0) + assert_raises(TypeError, herme.hermefit, [], [1], 0) + assert_raises(TypeError, herme.hermefit, [1], [[[1]]], 0) + assert_raises(TypeError, herme.hermefit, [1, 2], [1], 0) + assert_raises(TypeError, herme.hermefit, [1], [1, 2], 0) + assert_raises(TypeError, herme.hermefit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, herme.hermefit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, herme.hermefit, [1], [1], [-1,]) + assert_raises(ValueError, herme.hermefit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, herme.hermefit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = herme.hermefit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(herme.hermeval(x, coef3), y) + coef3 = herme.hermefit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(herme.hermeval(x, coef3), y) + # + coef4 = herme.hermefit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(herme.hermeval(x, coef4), y) + coef4 = herme.hermefit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(herme.hermeval(x, coef4), y) + # check things still work if deg is not in strict increasing + coef4 = herme.hermefit(x, y, [2, 3, 4, 1, 0]) + assert_equal(len(coef4), 5) + assert_almost_equal(herme.hermeval(x, coef4), y) + # + coef2d = herme.hermefit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = herme.hermefit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + y[0::2] = 0 + wcoef3 = herme.hermefit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = herme.hermefit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = herme.hermefit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = herme.hermefit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(herme.hermefit(x, x, 1), [0, 1]) + assert_almost_equal(herme.hermefit(x, x, [0, 1]), [0, 1]) + # test fitting only even Legendre polynomials + x = np.linspace(-1, 1) + y = f2(x) + coef1 = herme.hermefit(x, y, 4) + assert_almost_equal(herme.hermeval(x, coef1), y) + coef2 = herme.hermefit(x, y, [0, 2, 4]) + assert_almost_equal(herme.hermeval(x, coef2), y) + assert_almost_equal(coef1, coef2) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, herme.hermecompanion, []) + assert_raises(ValueError, herme.hermecompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(herme.hermecompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(herme.hermecompanion([1, 2])[0, 0] == -.5) + + +class TestGauss: + + def test_100(self): + x, w = herme.hermegauss(100) + + # test orthogonality. Note that the results need to be normalized, + # otherwise the huge values that can arise from fast growing + # functions like Laguerre can be very confusing. + v = herme.hermevander(x, 99) + vv = np.dot(v.T * w, v) + vd = 1/np.sqrt(vv.diagonal()) + vv = vd[:, None] * vv * vd + assert_almost_equal(vv, np.eye(100)) + + # check that the integral of 1 is correct + tgt = np.sqrt(2*np.pi) + assert_almost_equal(w.sum(), tgt) + + +class TestMisc: + + def test_hermefromroots(self): + res = herme.hermefromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + pol = herme.hermefromroots(roots) + res = herme.hermeval(roots, pol) + tgt = 0 + assert_(len(pol) == i + 1) + assert_almost_equal(herme.herme2poly(pol)[-1], 1) + assert_almost_equal(res, tgt) + + def test_hermeroots(self): + assert_almost_equal(herme.hermeroots([1]), []) + assert_almost_equal(herme.hermeroots([1, 1]), [-1]) + for i in range(2, 5): + tgt = np.linspace(-1, 1, i) + res = herme.hermeroots(herme.hermefromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_hermetrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, herme.hermetrim, coef, -1) + + # Test results + assert_equal(herme.hermetrim(coef), coef[:-1]) + assert_equal(herme.hermetrim(coef, 1), coef[:-3]) + assert_equal(herme.hermetrim(coef, 2), [0]) + + def test_hermeline(self): + assert_equal(herme.hermeline(3, 4), [3, 4]) + + def test_herme2poly(self): + for i in range(10): + assert_almost_equal(herme.herme2poly([0]*i + [1]), Helist[i]) + + def test_poly2herme(self): + for i in range(10): + assert_almost_equal(herme.poly2herme(Helist[i]), [0]*i + [1]) + + def test_weight(self): + x = np.linspace(-5, 5, 11) + tgt = np.exp(-.5*x**2) + res = herme.hermeweight(x) + assert_almost_equal(res, tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_laguerre.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_laguerre.py new file mode 100644 index 0000000000000000000000000000000000000000..49f7c7e115bec499a04f58c38d803d3e8be1247e --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_laguerre.py @@ -0,0 +1,537 @@ +"""Tests for laguerre module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.laguerre as lag +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + +L0 = np.array([1])/1 +L1 = np.array([1, -1])/1 +L2 = np.array([2, -4, 1])/2 +L3 = np.array([6, -18, 9, -1])/6 +L4 = np.array([24, -96, 72, -16, 1])/24 +L5 = np.array([120, -600, 600, -200, 25, -1])/120 +L6 = np.array([720, -4320, 5400, -2400, 450, -36, 1])/720 + +Llist = [L0, L1, L2, L3, L4, L5, L6] + + +def trim(x): + return lag.lagtrim(x, tol=1e-6) + + +class TestConstants: + + def test_lagdomain(self): + assert_equal(lag.lagdomain, [0, 1]) + + def test_lagzero(self): + assert_equal(lag.lagzero, [0]) + + def test_lagone(self): + assert_equal(lag.lagone, [1]) + + def test_lagx(self): + assert_equal(lag.lagx, [1, -1]) + + +class TestArithmetic: + x = np.linspace(-3, 3, 100) + + def test_lagadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = lag.lagadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_lagsub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = lag.lagsub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_lagmulx(self): + assert_equal(lag.lagmulx([0]), [0]) + assert_equal(lag.lagmulx([1]), [1, -1]) + for i in range(1, 5): + ser = [0]*i + [1] + tgt = [0]*(i - 1) + [-i, 2*i + 1, -(i + 1)] + assert_almost_equal(lag.lagmulx(ser), tgt) + + def test_lagmul(self): + # check values of result + for i in range(5): + pol1 = [0]*i + [1] + val1 = lag.lagval(self.x, pol1) + for j in range(5): + msg = f"At i={i}, j={j}" + pol2 = [0]*j + [1] + val2 = lag.lagval(self.x, pol2) + pol3 = lag.lagmul(pol1, pol2) + val3 = lag.lagval(self.x, pol3) + assert_(len(pol3) == i + j + 1, msg) + assert_almost_equal(val3, val1*val2, err_msg=msg) + + def test_lagdiv(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1] + cj = [0]*j + [1] + tgt = lag.lagadd(ci, cj) + quo, rem = lag.lagdiv(tgt, ci) + res = lag.lagadd(lag.lagmul(quo, ci), rem) + assert_almost_equal(trim(res), trim(tgt), err_msg=msg) + + def test_lagpow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(lag.lagmul, [c]*j, np.array([1])) + res = lag.lagpow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([9., -14., 6.]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = polyval(x, [1., 2., 3.]) + + def test_lagval(self): + #check empty input + assert_equal(lag.lagval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [polyval(x, c) for c in Llist] + for i in range(7): + msg = f"At i={i}" + tgt = y[i] + res = lag.lagval(x, [0]*i + [1]) + assert_almost_equal(res, tgt, err_msg=msg) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(lag.lagval(x, [1]).shape, dims) + assert_equal(lag.lagval(x, [1, 0]).shape, dims) + assert_equal(lag.lagval(x, [1, 0, 0]).shape, dims) + + def test_lagval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, lag.lagval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = lag.lagval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = lag.lagval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_lagval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, lag.lagval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = lag.lagval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = lag.lagval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_laggrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = lag.laggrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = lag.laggrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_laggrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = lag.laggrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = lag.laggrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_lagint(self): + # check exceptions + assert_raises(TypeError, lag.lagint, [0], .5) + assert_raises(ValueError, lag.lagint, [0], -1) + assert_raises(ValueError, lag.lagint, [0], 1, [0, 0]) + assert_raises(ValueError, lag.lagint, [0], lbnd=[0]) + assert_raises(ValueError, lag.lagint, [0], scl=[0]) + assert_raises(TypeError, lag.lagint, [0], axis=.5) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = lag.lagint([0], m=i, k=k) + assert_almost_equal(res, [1, -1]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + lagpol = lag.poly2lag(pol) + lagint = lag.lagint(lagpol, m=1, k=[i]) + res = lag.lag2poly(lagint) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + lagpol = lag.poly2lag(pol) + lagint = lag.lagint(lagpol, m=1, k=[i], lbnd=-1) + assert_almost_equal(lag.lagval(-1, lagint), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + lagpol = lag.poly2lag(pol) + lagint = lag.lagint(lagpol, m=1, k=[i], scl=2) + res = lag.lag2poly(lagint) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = lag.lagint(tgt, m=1) + res = lag.lagint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = lag.lagint(tgt, m=1, k=[k]) + res = lag.lagint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = lag.lagint(tgt, m=1, k=[k], lbnd=-1) + res = lag.lagint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = lag.lagint(tgt, m=1, k=[k], scl=2) + res = lag.lagint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_lagint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([lag.lagint(c) for c in c2d.T]).T + res = lag.lagint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([lag.lagint(c) for c in c2d]) + res = lag.lagint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([lag.lagint(c, k=3) for c in c2d]) + res = lag.lagint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + +class TestDerivative: + + def test_lagder(self): + # check exceptions + assert_raises(TypeError, lag.lagder, [0], .5) + assert_raises(ValueError, lag.lagder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = lag.lagder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = lag.lagder(lag.lagint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = lag.lagder(lag.lagint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_lagder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([lag.lagder(c) for c in c2d.T]).T + res = lag.lagder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([lag.lagder(c) for c in c2d]) + res = lag.lagder(c2d, axis=1) + assert_almost_equal(res, tgt) + + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_lagvander(self): + # check for 1d x + x = np.arange(3) + v = lag.lagvander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], lag.lagval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = lag.lagvander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], lag.lagval(x, coef)) + + def test_lagvander2d(self): + # also tests lagval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = lag.lagvander2d(x1, x2, [1, 2]) + tgt = lag.lagval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = lag.lagvander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_lagvander3d(self): + # also tests lagval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = lag.lagvander3d(x1, x2, x3, [1, 2, 3]) + tgt = lag.lagval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = lag.lagvander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + +class TestFitting: + + def test_lagfit(self): + def f(x): + return x*(x - 1)*(x - 2) + + # Test exceptions + assert_raises(ValueError, lag.lagfit, [1], [1], -1) + assert_raises(TypeError, lag.lagfit, [[1]], [1], 0) + assert_raises(TypeError, lag.lagfit, [], [1], 0) + assert_raises(TypeError, lag.lagfit, [1], [[[1]]], 0) + assert_raises(TypeError, lag.lagfit, [1, 2], [1], 0) + assert_raises(TypeError, lag.lagfit, [1], [1, 2], 0) + assert_raises(TypeError, lag.lagfit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, lag.lagfit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, lag.lagfit, [1], [1], [-1,]) + assert_raises(ValueError, lag.lagfit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, lag.lagfit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = lag.lagfit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(lag.lagval(x, coef3), y) + coef3 = lag.lagfit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(lag.lagval(x, coef3), y) + # + coef4 = lag.lagfit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(lag.lagval(x, coef4), y) + coef4 = lag.lagfit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(lag.lagval(x, coef4), y) + # + coef2d = lag.lagfit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = lag.lagfit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + y[0::2] = 0 + wcoef3 = lag.lagfit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = lag.lagfit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = lag.lagfit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = lag.lagfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(lag.lagfit(x, x, 1), [1, -1]) + assert_almost_equal(lag.lagfit(x, x, [0, 1]), [1, -1]) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, lag.lagcompanion, []) + assert_raises(ValueError, lag.lagcompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(lag.lagcompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(lag.lagcompanion([1, 2])[0, 0] == 1.5) + + +class TestGauss: + + def test_100(self): + x, w = lag.laggauss(100) + + # test orthogonality. Note that the results need to be normalized, + # otherwise the huge values that can arise from fast growing + # functions like Laguerre can be very confusing. + v = lag.lagvander(x, 99) + vv = np.dot(v.T * w, v) + vd = 1/np.sqrt(vv.diagonal()) + vv = vd[:, None] * vv * vd + assert_almost_equal(vv, np.eye(100)) + + # check that the integral of 1 is correct + tgt = 1.0 + assert_almost_equal(w.sum(), tgt) + + +class TestMisc: + + def test_lagfromroots(self): + res = lag.lagfromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + pol = lag.lagfromroots(roots) + res = lag.lagval(roots, pol) + tgt = 0 + assert_(len(pol) == i + 1) + assert_almost_equal(lag.lag2poly(pol)[-1], 1) + assert_almost_equal(res, tgt) + + def test_lagroots(self): + assert_almost_equal(lag.lagroots([1]), []) + assert_almost_equal(lag.lagroots([0, 1]), [1]) + for i in range(2, 5): + tgt = np.linspace(0, 3, i) + res = lag.lagroots(lag.lagfromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_lagtrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, lag.lagtrim, coef, -1) + + # Test results + assert_equal(lag.lagtrim(coef), coef[:-1]) + assert_equal(lag.lagtrim(coef, 1), coef[:-3]) + assert_equal(lag.lagtrim(coef, 2), [0]) + + def test_lagline(self): + assert_equal(lag.lagline(3, 4), [7, -4]) + + def test_lag2poly(self): + for i in range(7): + assert_almost_equal(lag.lag2poly([0]*i + [1]), Llist[i]) + + def test_poly2lag(self): + for i in range(7): + assert_almost_equal(lag.poly2lag(Llist[i]), [0]*i + [1]) + + def test_weight(self): + x = np.linspace(0, 10, 11) + tgt = np.exp(-x) + res = lag.lagweight(x) + assert_almost_equal(res, tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_legendre.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_legendre.py new file mode 100644 index 0000000000000000000000000000000000000000..9f1c9733a91121e208d7037f8e93b27f0cdbf9bb --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_legendre.py @@ -0,0 +1,568 @@ +"""Tests for legendre module. + +""" +from functools import reduce + +import numpy as np +import numpy.polynomial.legendre as leg +from numpy.polynomial.polynomial import polyval +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + +L0 = np.array([1]) +L1 = np.array([0, 1]) +L2 = np.array([-1, 0, 3])/2 +L3 = np.array([0, -3, 0, 5])/2 +L4 = np.array([3, 0, -30, 0, 35])/8 +L5 = np.array([0, 15, 0, -70, 0, 63])/8 +L6 = np.array([-5, 0, 105, 0, -315, 0, 231])/16 +L7 = np.array([0, -35, 0, 315, 0, -693, 0, 429])/16 +L8 = np.array([35, 0, -1260, 0, 6930, 0, -12012, 0, 6435])/128 +L9 = np.array([0, 315, 0, -4620, 0, 18018, 0, -25740, 0, 12155])/128 + +Llist = [L0, L1, L2, L3, L4, L5, L6, L7, L8, L9] + + +def trim(x): + return leg.legtrim(x, tol=1e-6) + + +class TestConstants: + + def test_legdomain(self): + assert_equal(leg.legdomain, [-1, 1]) + + def test_legzero(self): + assert_equal(leg.legzero, [0]) + + def test_legone(self): + assert_equal(leg.legone, [1]) + + def test_legx(self): + assert_equal(leg.legx, [0, 1]) + + +class TestArithmetic: + x = np.linspace(-1, 1, 100) + + def test_legadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = leg.legadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_legsub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = leg.legsub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_legmulx(self): + assert_equal(leg.legmulx([0]), [0]) + assert_equal(leg.legmulx([1]), [0, 1]) + for i in range(1, 5): + tmp = 2*i + 1 + ser = [0]*i + [1] + tgt = [0]*(i - 1) + [i/tmp, 0, (i + 1)/tmp] + assert_equal(leg.legmulx(ser), tgt) + + def test_legmul(self): + # check values of result + for i in range(5): + pol1 = [0]*i + [1] + val1 = leg.legval(self.x, pol1) + for j in range(5): + msg = f"At i={i}, j={j}" + pol2 = [0]*j + [1] + val2 = leg.legval(self.x, pol2) + pol3 = leg.legmul(pol1, pol2) + val3 = leg.legval(self.x, pol3) + assert_(len(pol3) == i + j + 1, msg) + assert_almost_equal(val3, val1*val2, err_msg=msg) + + def test_legdiv(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1] + cj = [0]*j + [1] + tgt = leg.legadd(ci, cj) + quo, rem = leg.legdiv(tgt, ci) + res = leg.legadd(leg.legmul(quo, ci), rem) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_legpow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(leg.legmul, [c]*j, np.array([1])) + res = leg.legpow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([2., 2., 2.]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = polyval(x, [1., 2., 3.]) + + def test_legval(self): + #check empty input + assert_equal(leg.legval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [polyval(x, c) for c in Llist] + for i in range(10): + msg = f"At i={i}" + tgt = y[i] + res = leg.legval(x, [0]*i + [1]) + assert_almost_equal(res, tgt, err_msg=msg) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(leg.legval(x, [1]).shape, dims) + assert_equal(leg.legval(x, [1, 0]).shape, dims) + assert_equal(leg.legval(x, [1, 0, 0]).shape, dims) + + def test_legval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, leg.legval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = leg.legval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = leg.legval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_legval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises(ValueError, leg.legval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = leg.legval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = leg.legval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_leggrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = leg.leggrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = leg.leggrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_leggrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = leg.leggrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = leg.leggrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_legint(self): + # check exceptions + assert_raises(TypeError, leg.legint, [0], .5) + assert_raises(ValueError, leg.legint, [0], -1) + assert_raises(ValueError, leg.legint, [0], 1, [0, 0]) + assert_raises(ValueError, leg.legint, [0], lbnd=[0]) + assert_raises(ValueError, leg.legint, [0], scl=[0]) + assert_raises(TypeError, leg.legint, [0], axis=.5) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = leg.legint([0], m=i, k=k) + assert_almost_equal(res, [0, 1]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + legpol = leg.poly2leg(pol) + legint = leg.legint(legpol, m=1, k=[i]) + res = leg.leg2poly(legint) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + legpol = leg.poly2leg(pol) + legint = leg.legint(legpol, m=1, k=[i], lbnd=-1) + assert_almost_equal(leg.legval(-1, legint), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + legpol = leg.poly2leg(pol) + legint = leg.legint(legpol, m=1, k=[i], scl=2) + res = leg.leg2poly(legint) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = leg.legint(tgt, m=1) + res = leg.legint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = leg.legint(tgt, m=1, k=[k]) + res = leg.legint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = leg.legint(tgt, m=1, k=[k], lbnd=-1) + res = leg.legint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = leg.legint(tgt, m=1, k=[k], scl=2) + res = leg.legint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_legint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([leg.legint(c) for c in c2d.T]).T + res = leg.legint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([leg.legint(c) for c in c2d]) + res = leg.legint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([leg.legint(c, k=3) for c in c2d]) + res = leg.legint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + def test_legint_zerointord(self): + assert_equal(leg.legint((1, 2, 3), 0), (1, 2, 3)) + + +class TestDerivative: + + def test_legder(self): + # check exceptions + assert_raises(TypeError, leg.legder, [0], .5) + assert_raises(ValueError, leg.legder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = leg.legder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = leg.legder(leg.legint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = leg.legder(leg.legint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_legder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([leg.legder(c) for c in c2d.T]).T + res = leg.legder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([leg.legder(c) for c in c2d]) + res = leg.legder(c2d, axis=1) + assert_almost_equal(res, tgt) + + def test_legder_orderhigherthancoeff(self): + c = (1, 2, 3, 4) + assert_equal(leg.legder(c, 4), [0]) + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_legvander(self): + # check for 1d x + x = np.arange(3) + v = leg.legvander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], leg.legval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = leg.legvander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], leg.legval(x, coef)) + + def test_legvander2d(self): + # also tests polyval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = leg.legvander2d(x1, x2, [1, 2]) + tgt = leg.legval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = leg.legvander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_legvander3d(self): + # also tests polyval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = leg.legvander3d(x1, x2, x3, [1, 2, 3]) + tgt = leg.legval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = leg.legvander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + def test_legvander_negdeg(self): + assert_raises(ValueError, leg.legvander, (1, 2, 3), -1) + + +class TestFitting: + + def test_legfit(self): + def f(x): + return x*(x - 1)*(x - 2) + + def f2(x): + return x**4 + x**2 + 1 + + # Test exceptions + assert_raises(ValueError, leg.legfit, [1], [1], -1) + assert_raises(TypeError, leg.legfit, [[1]], [1], 0) + assert_raises(TypeError, leg.legfit, [], [1], 0) + assert_raises(TypeError, leg.legfit, [1], [[[1]]], 0) + assert_raises(TypeError, leg.legfit, [1, 2], [1], 0) + assert_raises(TypeError, leg.legfit, [1], [1, 2], 0) + assert_raises(TypeError, leg.legfit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, leg.legfit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, leg.legfit, [1], [1], [-1,]) + assert_raises(ValueError, leg.legfit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, leg.legfit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = leg.legfit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(leg.legval(x, coef3), y) + coef3 = leg.legfit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(leg.legval(x, coef3), y) + # + coef4 = leg.legfit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(leg.legval(x, coef4), y) + coef4 = leg.legfit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(leg.legval(x, coef4), y) + # check things still work if deg is not in strict increasing + coef4 = leg.legfit(x, y, [2, 3, 4, 1, 0]) + assert_equal(len(coef4), 5) + assert_almost_equal(leg.legval(x, coef4), y) + # + coef2d = leg.legfit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = leg.legfit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + y[0::2] = 0 + wcoef3 = leg.legfit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = leg.legfit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = leg.legfit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = leg.legfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(leg.legfit(x, x, 1), [0, 1]) + assert_almost_equal(leg.legfit(x, x, [0, 1]), [0, 1]) + # test fitting only even Legendre polynomials + x = np.linspace(-1, 1) + y = f2(x) + coef1 = leg.legfit(x, y, 4) + assert_almost_equal(leg.legval(x, coef1), y) + coef2 = leg.legfit(x, y, [0, 2, 4]) + assert_almost_equal(leg.legval(x, coef2), y) + assert_almost_equal(coef1, coef2) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, leg.legcompanion, []) + assert_raises(ValueError, leg.legcompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(leg.legcompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(leg.legcompanion([1, 2])[0, 0] == -.5) + + +class TestGauss: + + def test_100(self): + x, w = leg.leggauss(100) + + # test orthogonality. Note that the results need to be normalized, + # otherwise the huge values that can arise from fast growing + # functions like Laguerre can be very confusing. + v = leg.legvander(x, 99) + vv = np.dot(v.T * w, v) + vd = 1/np.sqrt(vv.diagonal()) + vv = vd[:, None] * vv * vd + assert_almost_equal(vv, np.eye(100)) + + # check that the integral of 1 is correct + tgt = 2.0 + assert_almost_equal(w.sum(), tgt) + + +class TestMisc: + + def test_legfromroots(self): + res = leg.legfromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + pol = leg.legfromroots(roots) + res = leg.legval(roots, pol) + tgt = 0 + assert_(len(pol) == i + 1) + assert_almost_equal(leg.leg2poly(pol)[-1], 1) + assert_almost_equal(res, tgt) + + def test_legroots(self): + assert_almost_equal(leg.legroots([1]), []) + assert_almost_equal(leg.legroots([1, 2]), [-.5]) + for i in range(2, 5): + tgt = np.linspace(-1, 1, i) + res = leg.legroots(leg.legfromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_legtrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, leg.legtrim, coef, -1) + + # Test results + assert_equal(leg.legtrim(coef), coef[:-1]) + assert_equal(leg.legtrim(coef, 1), coef[:-3]) + assert_equal(leg.legtrim(coef, 2), [0]) + + def test_legline(self): + assert_equal(leg.legline(3, 4), [3, 4]) + + def test_legline_zeroscl(self): + assert_equal(leg.legline(3, 0), [3]) + + def test_leg2poly(self): + for i in range(10): + assert_almost_equal(leg.leg2poly([0]*i + [1]), Llist[i]) + + def test_poly2leg(self): + for i in range(10): + assert_almost_equal(leg.poly2leg(Llist[i]), [0]*i + [1]) + + def test_weight(self): + x = np.linspace(-1, 1, 11) + tgt = 1. + res = leg.legweight(x) + assert_almost_equal(res, tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polynomial.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polynomial.py new file mode 100644 index 0000000000000000000000000000000000000000..d36b07dbd9536b4c1bd1f3129ae7ccaa2a320ed3 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polynomial.py @@ -0,0 +1,647 @@ +"""Tests for polynomial module. + +""" +from functools import reduce +from fractions import Fraction +import numpy as np +import numpy.polynomial.polynomial as poly +import numpy.polynomial.polyutils as pu +import pickle +from copy import deepcopy +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + assert_array_equal, assert_raises_regex, assert_warns) + + +def trim(x): + return poly.polytrim(x, tol=1e-6) + +T0 = [1] +T1 = [0, 1] +T2 = [-1, 0, 2] +T3 = [0, -3, 0, 4] +T4 = [1, 0, -8, 0, 8] +T5 = [0, 5, 0, -20, 0, 16] +T6 = [-1, 0, 18, 0, -48, 0, 32] +T7 = [0, -7, 0, 56, 0, -112, 0, 64] +T8 = [1, 0, -32, 0, 160, 0, -256, 0, 128] +T9 = [0, 9, 0, -120, 0, 432, 0, -576, 0, 256] + +Tlist = [T0, T1, T2, T3, T4, T5, T6, T7, T8, T9] + + +class TestConstants: + + def test_polydomain(self): + assert_equal(poly.polydomain, [-1, 1]) + + def test_polyzero(self): + assert_equal(poly.polyzero, [0]) + + def test_polyone(self): + assert_equal(poly.polyone, [1]) + + def test_polyx(self): + assert_equal(poly.polyx, [0, 1]) + + def test_copy(self): + x = poly.Polynomial([1, 2, 3]) + y = deepcopy(x) + assert_equal(x, y) + + def test_pickle(self): + x = poly.Polynomial([1, 2, 3]) + y = pickle.loads(pickle.dumps(x)) + assert_equal(x, y) + +class TestArithmetic: + + def test_polyadd(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] += 1 + res = poly.polyadd([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_polysub(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(max(i, j) + 1) + tgt[i] += 1 + tgt[j] -= 1 + res = poly.polysub([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_polymulx(self): + assert_equal(poly.polymulx([0]), [0]) + assert_equal(poly.polymulx([1]), [0, 1]) + for i in range(1, 5): + ser = [0]*i + [1] + tgt = [0]*(i + 1) + [1] + assert_equal(poly.polymulx(ser), tgt) + + def test_polymul(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + tgt = np.zeros(i + j + 1) + tgt[i + j] += 1 + res = poly.polymul([0]*i + [1], [0]*j + [1]) + assert_equal(trim(res), trim(tgt), err_msg=msg) + + def test_polydiv(self): + # check zero division + assert_raises(ZeroDivisionError, poly.polydiv, [1], [0]) + + # check scalar division + quo, rem = poly.polydiv([2], [2]) + assert_equal((quo, rem), (1, 0)) + quo, rem = poly.polydiv([2, 2], [2]) + assert_equal((quo, rem), ((1, 1), 0)) + + # check rest. + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + ci = [0]*i + [1, 2] + cj = [0]*j + [1, 2] + tgt = poly.polyadd(ci, cj) + quo, rem = poly.polydiv(tgt, ci) + res = poly.polyadd(poly.polymul(quo, ci), rem) + assert_equal(res, tgt, err_msg=msg) + + def test_polypow(self): + for i in range(5): + for j in range(5): + msg = f"At i={i}, j={j}" + c = np.arange(i + 1) + tgt = reduce(poly.polymul, [c]*j, np.array([1])) + res = poly.polypow(c, j) + assert_equal(trim(res), trim(tgt), err_msg=msg) + +class TestFraction: + + def test_Fraction(self): + # assert we can use Polynomials with coefficients of object dtype + f = Fraction(2, 3) + one = Fraction(1, 1) + zero = Fraction(0, 1) + p = poly.Polynomial([f, f], domain=[zero, one], window=[zero, one]) + + x = 2 * p + p ** 2 + assert_equal(x.coef, np.array([Fraction(16, 9), Fraction(20, 9), + Fraction(4, 9)], dtype=object)) + assert_equal(p.domain, [zero, one]) + assert_equal(p.coef.dtype, np.dtypes.ObjectDType()) + assert_(isinstance(p(f), Fraction)) + assert_equal(p(f), Fraction(10, 9)) + p_deriv = poly.Polynomial([Fraction(2, 3)], domain=[zero, one], + window=[zero, one]) + assert_equal(p.deriv(), p_deriv) + +class TestEvaluation: + # coefficients of 1 + 2*x + 3*x**2 + c1d = np.array([1., 2., 3.]) + c2d = np.einsum('i,j->ij', c1d, c1d) + c3d = np.einsum('i,j,k->ijk', c1d, c1d, c1d) + + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + y = poly.polyval(x, [1., 2., 3.]) + + def test_polyval(self): + #check empty input + assert_equal(poly.polyval([], [1]).size, 0) + + #check normal input) + x = np.linspace(-1, 1) + y = [x**i for i in range(5)] + for i in range(5): + tgt = y[i] + res = poly.polyval(x, [0]*i + [1]) + assert_almost_equal(res, tgt) + tgt = x*(x**2 - 1) + res = poly.polyval(x, [0, -1, 0, 1]) + assert_almost_equal(res, tgt) + + #check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(poly.polyval(x, [1]).shape, dims) + assert_equal(poly.polyval(x, [1, 0]).shape, dims) + assert_equal(poly.polyval(x, [1, 0, 0]).shape, dims) + + #check masked arrays are processed correctly + mask = [False, True, False] + mx = np.ma.array([1, 2, 3], mask=mask) + res = np.polyval([7, 5, 3], mx) + assert_array_equal(res.mask, mask) + + #check subtypes of ndarray are preserved + class C(np.ndarray): + pass + + cx = np.array([1, 2, 3]).view(C) + assert_equal(type(np.polyval([2, 3, 4], cx)), C) + + def test_polyvalfromroots(self): + # check exception for broadcasting x values over root array with + # too few dimensions + assert_raises(ValueError, poly.polyvalfromroots, + [1], [1], tensor=False) + + # check empty input + assert_equal(poly.polyvalfromroots([], [1]).size, 0) + assert_(poly.polyvalfromroots([], [1]).shape == (0,)) + + # check empty input + multidimensional roots + assert_equal(poly.polyvalfromroots([], [[1] * 5]).size, 0) + assert_(poly.polyvalfromroots([], [[1] * 5]).shape == (5, 0)) + + # check scalar input + assert_equal(poly.polyvalfromroots(1, 1), 0) + assert_(poly.polyvalfromroots(1, np.ones((3, 3))).shape == (3,)) + + # check normal input) + x = np.linspace(-1, 1) + y = [x**i for i in range(5)] + for i in range(1, 5): + tgt = y[i] + res = poly.polyvalfromroots(x, [0]*i) + assert_almost_equal(res, tgt) + tgt = x*(x - 1)*(x + 1) + res = poly.polyvalfromroots(x, [-1, 0, 1]) + assert_almost_equal(res, tgt) + + # check that shape is preserved + for i in range(3): + dims = [2]*i + x = np.zeros(dims) + assert_equal(poly.polyvalfromroots(x, [1]).shape, dims) + assert_equal(poly.polyvalfromroots(x, [1, 0]).shape, dims) + assert_equal(poly.polyvalfromroots(x, [1, 0, 0]).shape, dims) + + # check compatibility with factorization + ptest = [15, 2, -16, -2, 1] + r = poly.polyroots(ptest) + x = np.linspace(-1, 1) + assert_almost_equal(poly.polyval(x, ptest), + poly.polyvalfromroots(x, r)) + + # check multidimensional arrays of roots and values + # check tensor=False + rshape = (3, 5) + x = np.arange(-3, 2) + r = np.random.randint(-5, 5, size=rshape) + res = poly.polyvalfromroots(x, r, tensor=False) + tgt = np.empty(r.shape[1:]) + for ii in range(tgt.size): + tgt[ii] = poly.polyvalfromroots(x[ii], r[:, ii]) + assert_equal(res, tgt) + + # check tensor=True + x = np.vstack([x, 2*x]) + res = poly.polyvalfromroots(x, r, tensor=True) + tgt = np.empty(r.shape[1:] + x.shape) + for ii in range(r.shape[1]): + for jj in range(x.shape[0]): + tgt[ii, jj, :] = poly.polyvalfromroots(x[jj], r[:, ii]) + assert_equal(res, tgt) + + def test_polyval2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises_regex(ValueError, 'incompatible', + poly.polyval2d, x1, x2[:2], self.c2d) + + #test values + tgt = y1*y2 + res = poly.polyval2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = poly.polyval2d(z, z, self.c2d) + assert_(res.shape == (2, 3)) + + def test_polyval3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test exceptions + assert_raises_regex(ValueError, 'incompatible', + poly.polyval3d, x1, x2, x3[:2], self.c3d) + + #test values + tgt = y1*y2*y3 + res = poly.polyval3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = poly.polyval3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)) + + def test_polygrid2d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j->ij', y1, y2) + res = poly.polygrid2d(x1, x2, self.c2d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = poly.polygrid2d(z, z, self.c2d) + assert_(res.shape == (2, 3)*2) + + def test_polygrid3d(self): + x1, x2, x3 = self.x + y1, y2, y3 = self.y + + #test values + tgt = np.einsum('i,j,k->ijk', y1, y2, y3) + res = poly.polygrid3d(x1, x2, x3, self.c3d) + assert_almost_equal(res, tgt) + + #test shape + z = np.ones((2, 3)) + res = poly.polygrid3d(z, z, z, self.c3d) + assert_(res.shape == (2, 3)*3) + + +class TestIntegral: + + def test_polyint(self): + # check exceptions + assert_raises(TypeError, poly.polyint, [0], .5) + assert_raises(ValueError, poly.polyint, [0], -1) + assert_raises(ValueError, poly.polyint, [0], 1, [0, 0]) + assert_raises(ValueError, poly.polyint, [0], lbnd=[0]) + assert_raises(ValueError, poly.polyint, [0], scl=[0]) + assert_raises(TypeError, poly.polyint, [0], axis=.5) + assert_raises(TypeError, poly.polyint, [1, 1], 1.) + + # test integration of zero polynomial + for i in range(2, 5): + k = [0]*(i - 2) + [1] + res = poly.polyint([0], m=i, k=k) + assert_almost_equal(res, [0, 1]) + + # check single integration with integration constant + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [1/scl] + res = poly.polyint(pol, m=1, k=[i]) + assert_almost_equal(trim(res), trim(tgt)) + + # check single integration with integration constant and lbnd + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + res = poly.polyint(pol, m=1, k=[i], lbnd=-1) + assert_almost_equal(poly.polyval(-1, res), i) + + # check single integration with integration constant and scaling + for i in range(5): + scl = i + 1 + pol = [0]*i + [1] + tgt = [i] + [0]*i + [2/scl] + res = poly.polyint(pol, m=1, k=[i], scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with default k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = poly.polyint(tgt, m=1) + res = poly.polyint(pol, m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with defined k + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = poly.polyint(tgt, m=1, k=[k]) + res = poly.polyint(pol, m=j, k=list(range(j))) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with lbnd + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = poly.polyint(tgt, m=1, k=[k], lbnd=-1) + res = poly.polyint(pol, m=j, k=list(range(j)), lbnd=-1) + assert_almost_equal(trim(res), trim(tgt)) + + # check multiple integrations with scaling + for i in range(5): + for j in range(2, 5): + pol = [0]*i + [1] + tgt = pol[:] + for k in range(j): + tgt = poly.polyint(tgt, m=1, k=[k], scl=2) + res = poly.polyint(pol, m=j, k=list(range(j)), scl=2) + assert_almost_equal(trim(res), trim(tgt)) + + def test_polyint_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([poly.polyint(c) for c in c2d.T]).T + res = poly.polyint(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([poly.polyint(c) for c in c2d]) + res = poly.polyint(c2d, axis=1) + assert_almost_equal(res, tgt) + + tgt = np.vstack([poly.polyint(c, k=3) for c in c2d]) + res = poly.polyint(c2d, k=3, axis=1) + assert_almost_equal(res, tgt) + + +class TestDerivative: + + def test_polyder(self): + # check exceptions + assert_raises(TypeError, poly.polyder, [0], .5) + assert_raises(ValueError, poly.polyder, [0], -1) + + # check that zeroth derivative does nothing + for i in range(5): + tgt = [0]*i + [1] + res = poly.polyder(tgt, m=0) + assert_equal(trim(res), trim(tgt)) + + # check that derivation is the inverse of integration + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = poly.polyder(poly.polyint(tgt, m=j), m=j) + assert_almost_equal(trim(res), trim(tgt)) + + # check derivation with scaling + for i in range(5): + for j in range(2, 5): + tgt = [0]*i + [1] + res = poly.polyder(poly.polyint(tgt, m=j, scl=2), m=j, scl=.5) + assert_almost_equal(trim(res), trim(tgt)) + + def test_polyder_axis(self): + # check that axis keyword works + c2d = np.random.random((3, 4)) + + tgt = np.vstack([poly.polyder(c) for c in c2d.T]).T + res = poly.polyder(c2d, axis=0) + assert_almost_equal(res, tgt) + + tgt = np.vstack([poly.polyder(c) for c in c2d]) + res = poly.polyder(c2d, axis=1) + assert_almost_equal(res, tgt) + + +class TestVander: + # some random values in [-1, 1) + x = np.random.random((3, 5))*2 - 1 + + def test_polyvander(self): + # check for 1d x + x = np.arange(3) + v = poly.polyvander(x, 3) + assert_(v.shape == (3, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], poly.polyval(x, coef)) + + # check for 2d x + x = np.array([[1, 2], [3, 4], [5, 6]]) + v = poly.polyvander(x, 3) + assert_(v.shape == (3, 2, 4)) + for i in range(4): + coef = [0]*i + [1] + assert_almost_equal(v[..., i], poly.polyval(x, coef)) + + def test_polyvander2d(self): + # also tests polyval2d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3)) + van = poly.polyvander2d(x1, x2, [1, 2]) + tgt = poly.polyval2d(x1, x2, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = poly.polyvander2d([x1], [x2], [1, 2]) + assert_(van.shape == (1, 5, 6)) + + def test_polyvander3d(self): + # also tests polyval3d for non-square coefficient array + x1, x2, x3 = self.x + c = np.random.random((2, 3, 4)) + van = poly.polyvander3d(x1, x2, x3, [1, 2, 3]) + tgt = poly.polyval3d(x1, x2, x3, c) + res = np.dot(van, c.flat) + assert_almost_equal(res, tgt) + + # check shape + van = poly.polyvander3d([x1], [x2], [x3], [1, 2, 3]) + assert_(van.shape == (1, 5, 24)) + + def test_polyvandernegdeg(self): + x = np.arange(3) + assert_raises(ValueError, poly.polyvander, x, -1) + + +class TestCompanion: + + def test_raises(self): + assert_raises(ValueError, poly.polycompanion, []) + assert_raises(ValueError, poly.polycompanion, [1]) + + def test_dimensions(self): + for i in range(1, 5): + coef = [0]*i + [1] + assert_(poly.polycompanion(coef).shape == (i, i)) + + def test_linear_root(self): + assert_(poly.polycompanion([1, 2])[0, 0] == -.5) + + +class TestMisc: + + def test_polyfromroots(self): + res = poly.polyfromroots([]) + assert_almost_equal(trim(res), [1]) + for i in range(1, 5): + roots = np.cos(np.linspace(-np.pi, 0, 2*i + 1)[1::2]) + tgt = Tlist[i] + res = poly.polyfromroots(roots)*2**(i-1) + assert_almost_equal(trim(res), trim(tgt)) + + def test_polyroots(self): + assert_almost_equal(poly.polyroots([1]), []) + assert_almost_equal(poly.polyroots([1, 2]), [-.5]) + for i in range(2, 5): + tgt = np.linspace(-1, 1, i) + res = poly.polyroots(poly.polyfromroots(tgt)) + assert_almost_equal(trim(res), trim(tgt)) + + def test_polyfit(self): + def f(x): + return x*(x - 1)*(x - 2) + + def f2(x): + return x**4 + x**2 + 1 + + # Test exceptions + assert_raises(ValueError, poly.polyfit, [1], [1], -1) + assert_raises(TypeError, poly.polyfit, [[1]], [1], 0) + assert_raises(TypeError, poly.polyfit, [], [1], 0) + assert_raises(TypeError, poly.polyfit, [1], [[[1]]], 0) + assert_raises(TypeError, poly.polyfit, [1, 2], [1], 0) + assert_raises(TypeError, poly.polyfit, [1], [1, 2], 0) + assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[[1]]) + assert_raises(TypeError, poly.polyfit, [1], [1], 0, w=[1, 1]) + assert_raises(ValueError, poly.polyfit, [1], [1], [-1,]) + assert_raises(ValueError, poly.polyfit, [1], [1], [2, -1, 6]) + assert_raises(TypeError, poly.polyfit, [1], [1], []) + + # Test fit + x = np.linspace(0, 2) + y = f(x) + # + coef3 = poly.polyfit(x, y, 3) + assert_equal(len(coef3), 4) + assert_almost_equal(poly.polyval(x, coef3), y) + coef3 = poly.polyfit(x, y, [0, 1, 2, 3]) + assert_equal(len(coef3), 4) + assert_almost_equal(poly.polyval(x, coef3), y) + # + coef4 = poly.polyfit(x, y, 4) + assert_equal(len(coef4), 5) + assert_almost_equal(poly.polyval(x, coef4), y) + coef4 = poly.polyfit(x, y, [0, 1, 2, 3, 4]) + assert_equal(len(coef4), 5) + assert_almost_equal(poly.polyval(x, coef4), y) + # + coef2d = poly.polyfit(x, np.array([y, y]).T, 3) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + coef2d = poly.polyfit(x, np.array([y, y]).T, [0, 1, 2, 3]) + assert_almost_equal(coef2d, np.array([coef3, coef3]).T) + # test weighting + w = np.zeros_like(x) + yw = y.copy() + w[1::2] = 1 + yw[0::2] = 0 + wcoef3 = poly.polyfit(x, yw, 3, w=w) + assert_almost_equal(wcoef3, coef3) + wcoef3 = poly.polyfit(x, yw, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef3, coef3) + # + wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, 3, w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + wcoef2d = poly.polyfit(x, np.array([yw, yw]).T, [0, 1, 2, 3], w=w) + assert_almost_equal(wcoef2d, np.array([coef3, coef3]).T) + # test scaling with complex values x points whose square + # is zero when summed. + x = [1, 1j, -1, -1j] + assert_almost_equal(poly.polyfit(x, x, 1), [0, 1]) + assert_almost_equal(poly.polyfit(x, x, [0, 1]), [0, 1]) + # test fitting only even Polyendre polynomials + x = np.linspace(-1, 1) + y = f2(x) + coef1 = poly.polyfit(x, y, 4) + assert_almost_equal(poly.polyval(x, coef1), y) + coef2 = poly.polyfit(x, y, [0, 2, 4]) + assert_almost_equal(poly.polyval(x, coef2), y) + assert_almost_equal(coef1, coef2) + + def test_polytrim(self): + coef = [2, -1, 1, 0] + + # Test exceptions + assert_raises(ValueError, poly.polytrim, coef, -1) + + # Test results + assert_equal(poly.polytrim(coef), coef[:-1]) + assert_equal(poly.polytrim(coef, 1), coef[:-3]) + assert_equal(poly.polytrim(coef, 2), [0]) + + def test_polyline(self): + assert_equal(poly.polyline(3, 4), [3, 4]) + + def test_polyline_zero(self): + assert_equal(poly.polyline(3, 0), [3]) + + def test_fit_degenerate_domain(self): + p = poly.Polynomial.fit([1], [2], deg=0) + assert_equal(p.coef, [2.]) + p = poly.Polynomial.fit([1, 1], [2, 2.1], deg=0) + assert_almost_equal(p.coef, [2.05]) + with assert_warns(pu.RankWarning): + p = poly.Polynomial.fit([1, 1], [2, 2.1], deg=1) + + def test_result_type(self): + w = np.array([-1, 1], dtype=np.float32) + p = np.polynomial.Polynomial(w, domain=w, window=w) + v = p(2) + assert_equal(v.dtype, np.float32) + + arr = np.polydiv(1, np.float32(1)) + assert_equal(arr[0].dtype, np.float64) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polyutils.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..e5143ed5c3e4a1651c67b5260cef47112c5ea071 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_polyutils.py @@ -0,0 +1,125 @@ +"""Tests for polyutils module. + +""" +import numpy as np +import numpy.polynomial.polyutils as pu +from numpy.testing import ( + assert_almost_equal, assert_raises, assert_equal, assert_, + ) + + +class TestMisc: + + def test_trimseq(self): + tgt = [1] + for num_trailing_zeros in range(5): + res = pu.trimseq([1] + [0] * num_trailing_zeros) + assert_equal(res, tgt) + + def test_trimseq_empty_input(self): + for empty_seq in [[], np.array([], dtype=np.int32)]: + assert_equal(pu.trimseq(empty_seq), empty_seq) + + def test_as_series(self): + # check exceptions + assert_raises(ValueError, pu.as_series, [[]]) + assert_raises(ValueError, pu.as_series, [[[1, 2]]]) + assert_raises(ValueError, pu.as_series, [[1], ['a']]) + # check common types + types = ['i', 'd', 'O'] + for i in range(len(types)): + for j in range(i): + ci = np.ones(1, types[i]) + cj = np.ones(1, types[j]) + [resi, resj] = pu.as_series([ci, cj]) + assert_(resi.dtype.char == resj.dtype.char) + assert_(resj.dtype.char == types[i]) + + def test_trimcoef(self): + coef = [2, -1, 1, 0] + # Test exceptions + assert_raises(ValueError, pu.trimcoef, coef, -1) + # Test results + assert_equal(pu.trimcoef(coef), coef[:-1]) + assert_equal(pu.trimcoef(coef, 1), coef[:-3]) + assert_equal(pu.trimcoef(coef, 2), [0]) + + def test_vander_nd_exception(self): + # n_dims != len(points) + assert_raises(ValueError, pu._vander_nd, (), (1, 2, 3), [90]) + # n_dims != len(degrees) + assert_raises(ValueError, pu._vander_nd, (), (), [90.65]) + # n_dims == 0 + assert_raises(ValueError, pu._vander_nd, (), (), []) + + def test_div_zerodiv(self): + # c2[-1] == 0 + assert_raises(ZeroDivisionError, pu._div, pu._div, (1, 2, 3), [0]) + + def test_pow_too_large(self): + # power > maxpower + assert_raises(ValueError, pu._pow, (), [1, 2, 3], 5, 4) + +class TestDomain: + + def test_getdomain(self): + # test for real values + x = [1, 10, 3, -1] + tgt = [-1, 10] + res = pu.getdomain(x) + assert_almost_equal(res, tgt) + + # test for complex values + x = [1 + 1j, 1 - 1j, 0, 2] + tgt = [-1j, 2 + 1j] + res = pu.getdomain(x) + assert_almost_equal(res, tgt) + + def test_mapdomain(self): + # test for real values + dom1 = [0, 4] + dom2 = [1, 3] + tgt = dom2 + res = pu.mapdomain(dom1, dom1, dom2) + assert_almost_equal(res, tgt) + + # test for complex values + dom1 = [0 - 1j, 2 + 1j] + dom2 = [-2, 2] + tgt = dom2 + x = dom1 + res = pu.mapdomain(x, dom1, dom2) + assert_almost_equal(res, tgt) + + # test for multidimensional arrays + dom1 = [0, 4] + dom2 = [1, 3] + tgt = np.array([dom2, dom2]) + x = np.array([dom1, dom1]) + res = pu.mapdomain(x, dom1, dom2) + assert_almost_equal(res, tgt) + + # test that subtypes are preserved. + class MyNDArray(np.ndarray): + pass + + dom1 = [0, 4] + dom2 = [1, 3] + x = np.array([dom1, dom1]).view(MyNDArray) + res = pu.mapdomain(x, dom1, dom2) + assert_(isinstance(res, MyNDArray)) + + def test_mapparms(self): + # test for real values + dom1 = [0, 4] + dom2 = [1, 3] + tgt = [1, .5] + res = pu. mapparms(dom1, dom2) + assert_almost_equal(res, tgt) + + # test for complex values + dom1 = [0 - 1j, 2 + 1j] + dom2 = [-2, 2] + tgt = [-1 + 1j, 1 - 1j] + res = pu.mapparms(dom1, dom2) + assert_almost_equal(res, tgt) diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_printing.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_printing.py new file mode 100644 index 0000000000000000000000000000000000000000..6651f6cd92056f94d19f62cd818eeed642df2b2e --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_printing.py @@ -0,0 +1,552 @@ +from math import nan, inf +import pytest +from numpy._core import array, arange, printoptions +import numpy.polynomial as poly +from numpy.testing import assert_equal, assert_ + +# For testing polynomial printing with object arrays +from fractions import Fraction +from decimal import Decimal + + +class TestStrUnicodeSuperSubscripts: + + @pytest.fixture(scope='class', autouse=True) + def use_unicode(self): + poly.set_default_printstyle('unicode') + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·x + 3.0·x²"), + ([-1, 0, 3, -1], "-1.0 + 0.0·x + 3.0·x² - 1.0·x³"), + (arange(12), ("0.0 + 1.0·x + 2.0·x² + 3.0·x³ + 4.0·x⁴ + 5.0·x⁵ + " + "6.0·x⁶ + 7.0·x⁷ +\n8.0·x⁸ + 9.0·x⁹ + 10.0·x¹⁰ + " + "11.0·x¹¹")), + )) + def test_polynomial_str(self, inp, tgt): + p = poly.Polynomial(inp) + res = str(p) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·T₁(x) + 3.0·T₂(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0·T₁(x) + 3.0·T₂(x) - 1.0·T₃(x)"), + (arange(12), ("0.0 + 1.0·T₁(x) + 2.0·T₂(x) + 3.0·T₃(x) + 4.0·T₄(x) + " + "5.0·T₅(x) +\n6.0·T₆(x) + 7.0·T₇(x) + 8.0·T₈(x) + " + "9.0·T₉(x) + 10.0·T₁₀(x) + 11.0·T₁₁(x)")), + )) + def test_chebyshev_str(self, inp, tgt): + res = str(poly.Chebyshev(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·P₁(x) + 3.0·P₂(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0·P₁(x) + 3.0·P₂(x) - 1.0·P₃(x)"), + (arange(12), ("0.0 + 1.0·P₁(x) + 2.0·P₂(x) + 3.0·P₃(x) + 4.0·P₄(x) + " + "5.0·P₅(x) +\n6.0·P₆(x) + 7.0·P₇(x) + 8.0·P₈(x) + " + "9.0·P₉(x) + 10.0·P₁₀(x) + 11.0·P₁₁(x)")), + )) + def test_legendre_str(self, inp, tgt): + res = str(poly.Legendre(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·H₁(x) + 3.0·H₂(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0·H₁(x) + 3.0·H₂(x) - 1.0·H₃(x)"), + (arange(12), ("0.0 + 1.0·H₁(x) + 2.0·H₂(x) + 3.0·H₃(x) + 4.0·H₄(x) + " + "5.0·H₅(x) +\n6.0·H₆(x) + 7.0·H₇(x) + 8.0·H₈(x) + " + "9.0·H₉(x) + 10.0·H₁₀(x) + 11.0·H₁₁(x)")), + )) + def test_hermite_str(self, inp, tgt): + res = str(poly.Hermite(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·He₁(x) + 3.0·He₂(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0·He₁(x) + 3.0·He₂(x) - 1.0·He₃(x)"), + (arange(12), ("0.0 + 1.0·He₁(x) + 2.0·He₂(x) + 3.0·He₃(x) + " + "4.0·He₄(x) + 5.0·He₅(x) +\n6.0·He₆(x) + 7.0·He₇(x) + " + "8.0·He₈(x) + 9.0·He₉(x) + 10.0·He₁₀(x) +\n" + "11.0·He₁₁(x)")), + )) + def test_hermiteE_str(self, inp, tgt): + res = str(poly.HermiteE(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0·L₁(x) + 3.0·L₂(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0·L₁(x) + 3.0·L₂(x) - 1.0·L₃(x)"), + (arange(12), ("0.0 + 1.0·L₁(x) + 2.0·L₂(x) + 3.0·L₃(x) + 4.0·L₄(x) + " + "5.0·L₅(x) +\n6.0·L₆(x) + 7.0·L₇(x) + 8.0·L₈(x) + " + "9.0·L₉(x) + 10.0·L₁₀(x) + 11.0·L₁₁(x)")), + )) + def test_laguerre_str(self, inp, tgt): + res = str(poly.Laguerre(inp)) + assert_equal(res, tgt) + + def test_polynomial_str_domains(self): + res = str(poly.Polynomial([0, 1])) + tgt = '0.0 + 1.0·x' + assert_equal(res, tgt) + + res = str(poly.Polynomial([0, 1], domain=[1, 2])) + tgt = '0.0 + 1.0·(-3.0 + 2.0x)' + assert_equal(res, tgt) + +class TestStrAscii: + + @pytest.fixture(scope='class', autouse=True) + def use_ascii(self): + poly.set_default_printstyle('ascii') + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 x + 3.0 x**2"), + ([-1, 0, 3, -1], "-1.0 + 0.0 x + 3.0 x**2 - 1.0 x**3"), + (arange(12), ("0.0 + 1.0 x + 2.0 x**2 + 3.0 x**3 + 4.0 x**4 + " + "5.0 x**5 + 6.0 x**6 +\n7.0 x**7 + 8.0 x**8 + " + "9.0 x**9 + 10.0 x**10 + 11.0 x**11")), + )) + def test_polynomial_str(self, inp, tgt): + res = str(poly.Polynomial(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 T_1(x) + 3.0 T_2(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0 T_1(x) + 3.0 T_2(x) - 1.0 T_3(x)"), + (arange(12), ("0.0 + 1.0 T_1(x) + 2.0 T_2(x) + 3.0 T_3(x) + " + "4.0 T_4(x) + 5.0 T_5(x) +\n6.0 T_6(x) + 7.0 T_7(x) + " + "8.0 T_8(x) + 9.0 T_9(x) + 10.0 T_10(x) +\n" + "11.0 T_11(x)")), + )) + def test_chebyshev_str(self, inp, tgt): + res = str(poly.Chebyshev(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 P_1(x) + 3.0 P_2(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0 P_1(x) + 3.0 P_2(x) - 1.0 P_3(x)"), + (arange(12), ("0.0 + 1.0 P_1(x) + 2.0 P_2(x) + 3.0 P_3(x) + " + "4.0 P_4(x) + 5.0 P_5(x) +\n6.0 P_6(x) + 7.0 P_7(x) + " + "8.0 P_8(x) + 9.0 P_9(x) + 10.0 P_10(x) +\n" + "11.0 P_11(x)")), + )) + def test_legendre_str(self, inp, tgt): + res = str(poly.Legendre(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 H_1(x) + 3.0 H_2(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0 H_1(x) + 3.0 H_2(x) - 1.0 H_3(x)"), + (arange(12), ("0.0 + 1.0 H_1(x) + 2.0 H_2(x) + 3.0 H_3(x) + " + "4.0 H_4(x) + 5.0 H_5(x) +\n6.0 H_6(x) + 7.0 H_7(x) + " + "8.0 H_8(x) + 9.0 H_9(x) + 10.0 H_10(x) +\n" + "11.0 H_11(x)")), + )) + def test_hermite_str(self, inp, tgt): + res = str(poly.Hermite(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 He_1(x) + 3.0 He_2(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0 He_1(x) + 3.0 He_2(x) - 1.0 He_3(x)"), + (arange(12), ("0.0 + 1.0 He_1(x) + 2.0 He_2(x) + 3.0 He_3(x) + " + "4.0 He_4(x) +\n5.0 He_5(x) + 6.0 He_6(x) + " + "7.0 He_7(x) + 8.0 He_8(x) + 9.0 He_9(x) +\n" + "10.0 He_10(x) + 11.0 He_11(x)")), + )) + def test_hermiteE_str(self, inp, tgt): + res = str(poly.HermiteE(inp)) + assert_equal(res, tgt) + + @pytest.mark.parametrize(('inp', 'tgt'), ( + ([1, 2, 3], "1.0 + 2.0 L_1(x) + 3.0 L_2(x)"), + ([-1, 0, 3, -1], "-1.0 + 0.0 L_1(x) + 3.0 L_2(x) - 1.0 L_3(x)"), + (arange(12), ("0.0 + 1.0 L_1(x) + 2.0 L_2(x) + 3.0 L_3(x) + " + "4.0 L_4(x) + 5.0 L_5(x) +\n6.0 L_6(x) + 7.0 L_7(x) + " + "8.0 L_8(x) + 9.0 L_9(x) + 10.0 L_10(x) +\n" + "11.0 L_11(x)")), + )) + def test_laguerre_str(self, inp, tgt): + res = str(poly.Laguerre(inp)) + assert_equal(res, tgt) + + def test_polynomial_str_domains(self): + res = str(poly.Polynomial([0, 1])) + tgt = '0.0 + 1.0 x' + assert_equal(res, tgt) + + res = str(poly.Polynomial([0, 1], domain=[1, 2])) + tgt = '0.0 + 1.0 (-3.0 + 2.0x)' + assert_equal(res, tgt) + +class TestLinebreaking: + + @pytest.fixture(scope='class', autouse=True) + def use_ascii(self): + poly.set_default_printstyle('ascii') + + def test_single_line_one_less(self): + # With 'ascii' style, len(str(p)) is default linewidth - 1 (i.e. 74) + p = poly.Polynomial([12345678, 12345678, 12345678, 12345678, 123]) + assert_equal(len(str(p)), 74) + assert_equal(str(p), ( + '12345678.0 + 12345678.0 x + 12345678.0 x**2 + ' + '12345678.0 x**3 + 123.0 x**4' + )) + + def test_num_chars_is_linewidth(self): + # len(str(p)) == default linewidth == 75 + p = poly.Polynomial([12345678, 12345678, 12345678, 12345678, 1234]) + assert_equal(len(str(p)), 75) + assert_equal(str(p), ( + '12345678.0 + 12345678.0 x + 12345678.0 x**2 + ' + '12345678.0 x**3 +\n1234.0 x**4' + )) + + def test_first_linebreak_multiline_one_less_than_linewidth(self): + # Multiline str where len(first_line) + len(next_term) == lw - 1 == 74 + p = poly.Polynomial( + [12345678, 12345678, 12345678, 12345678, 1, 12345678] + ) + assert_equal(len(str(p).split('\n')[0]), 74) + assert_equal(str(p), ( + '12345678.0 + 12345678.0 x + 12345678.0 x**2 + ' + '12345678.0 x**3 + 1.0 x**4 +\n12345678.0 x**5' + )) + + def test_first_linebreak_multiline_on_linewidth(self): + # First line is one character longer than previous test + p = poly.Polynomial( + [12345678, 12345678, 12345678, 12345678.12, 1, 12345678] + ) + assert_equal(str(p), ( + '12345678.0 + 12345678.0 x + 12345678.0 x**2 + ' + '12345678.12 x**3 +\n1.0 x**4 + 12345678.0 x**5' + )) + + @pytest.mark.parametrize(('lw', 'tgt'), ( + (75, ('0.0 + 10.0 x + 200.0 x**2 + 3000.0 x**3 + 40000.0 x**4 + ' + '500000.0 x**5 +\n600000.0 x**6 + 70000.0 x**7 + 8000.0 x**8 + ' + '900.0 x**9')), + (45, ('0.0 + 10.0 x + 200.0 x**2 + 3000.0 x**3 +\n40000.0 x**4 + ' + '500000.0 x**5 +\n600000.0 x**6 + 70000.0 x**7 + 8000.0 x**8 +\n' + '900.0 x**9')), + (132, ('0.0 + 10.0 x + 200.0 x**2 + 3000.0 x**3 + 40000.0 x**4 + ' + '500000.0 x**5 + 600000.0 x**6 + 70000.0 x**7 + 8000.0 x**8 + ' + '900.0 x**9')), + )) + def test_linewidth_printoption(self, lw, tgt): + p = poly.Polynomial( + [0, 10, 200, 3000, 40000, 500000, 600000, 70000, 8000, 900] + ) + with printoptions(linewidth=lw): + assert_equal(str(p), tgt) + for line in str(p).split('\n'): + assert_(len(line) < lw) + + +def test_set_default_printoptions(): + p = poly.Polynomial([1, 2, 3]) + c = poly.Chebyshev([1, 2, 3]) + poly.set_default_printstyle('ascii') + assert_equal(str(p), "1.0 + 2.0 x + 3.0 x**2") + assert_equal(str(c), "1.0 + 2.0 T_1(x) + 3.0 T_2(x)") + poly.set_default_printstyle('unicode') + assert_equal(str(p), "1.0 + 2.0·x + 3.0·x²") + assert_equal(str(c), "1.0 + 2.0·T₁(x) + 3.0·T₂(x)") + with pytest.raises(ValueError): + poly.set_default_printstyle('invalid_input') + + +def test_complex_coefficients(): + """Test both numpy and built-in complex.""" + coefs = [0+1j, 1+1j, -2+2j, 3+0j] + # numpy complex + p1 = poly.Polynomial(coefs) + # Python complex + p2 = poly.Polynomial(array(coefs, dtype=object)) + poly.set_default_printstyle('unicode') + assert_equal(str(p1), "1j + (1+1j)·x - (2-2j)·x² + (3+0j)·x³") + assert_equal(str(p2), "1j + (1+1j)·x + (-2+2j)·x² + (3+0j)·x³") + poly.set_default_printstyle('ascii') + assert_equal(str(p1), "1j + (1+1j) x - (2-2j) x**2 + (3+0j) x**3") + assert_equal(str(p2), "1j + (1+1j) x + (-2+2j) x**2 + (3+0j) x**3") + + +@pytest.mark.parametrize(('coefs', 'tgt'), ( + (array([Fraction(1, 2), Fraction(3, 4)], dtype=object), ( + "1/2 + 3/4·x" + )), + (array([1, 2, Fraction(5, 7)], dtype=object), ( + "1 + 2·x + 5/7·x²" + )), + (array([Decimal('1.00'), Decimal('2.2'), 3], dtype=object), ( + "1.00 + 2.2·x + 3·x²" + )), +)) +def test_numeric_object_coefficients(coefs, tgt): + p = poly.Polynomial(coefs) + poly.set_default_printstyle('unicode') + assert_equal(str(p), tgt) + + +@pytest.mark.parametrize(('coefs', 'tgt'), ( + (array([1, 2, 'f'], dtype=object), '1 + 2·x + f·x²'), + (array([1, 2, [3, 4]], dtype=object), '1 + 2·x + [3, 4]·x²'), +)) +def test_nonnumeric_object_coefficients(coefs, tgt): + """ + Test coef fallback for object arrays of non-numeric coefficients. + """ + p = poly.Polynomial(coefs) + poly.set_default_printstyle('unicode') + assert_equal(str(p), tgt) + + +class TestFormat: + def test_format_unicode(self): + poly.set_default_printstyle('ascii') + p = poly.Polynomial([1, 2, 0, -1]) + assert_equal(format(p, 'unicode'), "1.0 + 2.0·x + 0.0·x² - 1.0·x³") + + def test_format_ascii(self): + poly.set_default_printstyle('unicode') + p = poly.Polynomial([1, 2, 0, -1]) + assert_equal( + format(p, 'ascii'), "1.0 + 2.0 x + 0.0 x**2 - 1.0 x**3" + ) + + def test_empty_formatstr(self): + poly.set_default_printstyle('ascii') + p = poly.Polynomial([1, 2, 3]) + assert_equal(format(p), "1.0 + 2.0 x + 3.0 x**2") + assert_equal(f"{p}", "1.0 + 2.0 x + 3.0 x**2") + + def test_bad_formatstr(self): + p = poly.Polynomial([1, 2, 0, -1]) + with pytest.raises(ValueError): + format(p, '.2f') + + +@pytest.mark.parametrize(('poly', 'tgt'), ( + (poly.Polynomial, '1.0 + 2.0·z + 3.0·z²'), + (poly.Chebyshev, '1.0 + 2.0·T₁(z) + 3.0·T₂(z)'), + (poly.Hermite, '1.0 + 2.0·H₁(z) + 3.0·H₂(z)'), + (poly.HermiteE, '1.0 + 2.0·He₁(z) + 3.0·He₂(z)'), + (poly.Laguerre, '1.0 + 2.0·L₁(z) + 3.0·L₂(z)'), + (poly.Legendre, '1.0 + 2.0·P₁(z) + 3.0·P₂(z)'), +)) +def test_symbol(poly, tgt): + p = poly([1, 2, 3], symbol='z') + assert_equal(f"{p:unicode}", tgt) + + +class TestRepr: + def test_polynomial_repr(self): + res = repr(poly.Polynomial([0, 1])) + tgt = ( + "Polynomial([0., 1.], domain=[-1., 1.], window=[-1., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + def test_chebyshev_repr(self): + res = repr(poly.Chebyshev([0, 1])) + tgt = ( + "Chebyshev([0., 1.], domain=[-1., 1.], window=[-1., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + def test_legendre_repr(self): + res = repr(poly.Legendre([0, 1])) + tgt = ( + "Legendre([0., 1.], domain=[-1., 1.], window=[-1., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + def test_hermite_repr(self): + res = repr(poly.Hermite([0, 1])) + tgt = ( + "Hermite([0., 1.], domain=[-1., 1.], window=[-1., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + def test_hermiteE_repr(self): + res = repr(poly.HermiteE([0, 1])) + tgt = ( + "HermiteE([0., 1.], domain=[-1., 1.], window=[-1., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + def test_laguerre_repr(self): + res = repr(poly.Laguerre([0, 1])) + tgt = ( + "Laguerre([0., 1.], domain=[0., 1.], window=[0., 1.], " + "symbol='x')" + ) + assert_equal(res, tgt) + + +class TestLatexRepr: + """Test the latex repr used by Jupyter""" + + @staticmethod + def as_latex(obj): + # right now we ignore the formatting of scalars in our tests, since + # it makes them too verbose. Ideally, the formatting of scalars will + # be fixed such that tests below continue to pass + obj._repr_latex_scalar = lambda x, parens=False: str(x) + try: + return obj._repr_latex_() + finally: + del obj._repr_latex_scalar + + def test_simple_polynomial(self): + # default input + p = poly.Polynomial([1, 2, 3]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0 + 2.0\,x + 3.0\,x^{2}$') + + # translated input + p = poly.Polynomial([1, 2, 3], domain=[-2, 0]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0 + 2.0\,\left(1.0 + x\right) + 3.0\,\left(1.0 + x\right)^{2}$') + + # scaled input + p = poly.Polynomial([1, 2, 3], domain=[-0.5, 0.5]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0 + 2.0\,\left(2.0x\right) + 3.0\,\left(2.0x\right)^{2}$') + + # affine input + p = poly.Polynomial([1, 2, 3], domain=[-1, 0]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0 + 2.0\,\left(1.0 + 2.0x\right) + 3.0\,\left(1.0 + 2.0x\right)^{2}$') + + def test_basis_func(self): + p = poly.Chebyshev([1, 2, 3]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0\,{T}_{0}(x) + 2.0\,{T}_{1}(x) + 3.0\,{T}_{2}(x)$') + # affine input - check no surplus parens are added + p = poly.Chebyshev([1, 2, 3], domain=[-1, 0]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0\,{T}_{0}(1.0 + 2.0x) + 2.0\,{T}_{1}(1.0 + 2.0x) + 3.0\,{T}_{2}(1.0 + 2.0x)$') + + def test_multichar_basis_func(self): + p = poly.HermiteE([1, 2, 3]) + assert_equal(self.as_latex(p), + r'$x \mapsto 1.0\,{He}_{0}(x) + 2.0\,{He}_{1}(x) + 3.0\,{He}_{2}(x)$') + + def test_symbol_basic(self): + # default input + p = poly.Polynomial([1, 2, 3], symbol='z') + assert_equal(self.as_latex(p), + r'$z \mapsto 1.0 + 2.0\,z + 3.0\,z^{2}$') + + # translated input + p = poly.Polynomial([1, 2, 3], domain=[-2, 0], symbol='z') + assert_equal( + self.as_latex(p), + ( + r'$z \mapsto 1.0 + 2.0\,\left(1.0 + z\right) + 3.0\,' + r'\left(1.0 + z\right)^{2}$' + ), + ) + + # scaled input + p = poly.Polynomial([1, 2, 3], domain=[-0.5, 0.5], symbol='z') + assert_equal( + self.as_latex(p), + ( + r'$z \mapsto 1.0 + 2.0\,\left(2.0z\right) + 3.0\,' + r'\left(2.0z\right)^{2}$' + ), + ) + + # affine input + p = poly.Polynomial([1, 2, 3], domain=[-1, 0], symbol='z') + assert_equal( + self.as_latex(p), + ( + r'$z \mapsto 1.0 + 2.0\,\left(1.0 + 2.0z\right) + 3.0\,' + r'\left(1.0 + 2.0z\right)^{2}$' + ), + ) + + def test_numeric_object_coefficients(self): + coefs = array([Fraction(1, 2), Fraction(1)]) + p = poly.Polynomial(coefs) + assert_equal(self.as_latex(p), '$x \\mapsto 1/2 + 1\\,x$') + +SWITCH_TO_EXP = ( + '1.0 + (1.0e-01) x + (1.0e-02) x**2', + '1.2 + (1.2e-01) x + (1.2e-02) x**2', + '1.23 + 0.12 x + (1.23e-02) x**2 + (1.23e-03) x**3', + '1.235 + 0.123 x + (1.235e-02) x**2 + (1.235e-03) x**3', + '1.2346 + 0.1235 x + 0.0123 x**2 + (1.2346e-03) x**3 + (1.2346e-04) x**4', + '1.23457 + 0.12346 x + 0.01235 x**2 + (1.23457e-03) x**3 + ' + '(1.23457e-04) x**4', + '1.234568 + 0.123457 x + 0.012346 x**2 + 0.001235 x**3 + ' + '(1.234568e-04) x**4 + (1.234568e-05) x**5', + '1.2345679 + 0.1234568 x + 0.0123457 x**2 + 0.0012346 x**3 + ' + '(1.2345679e-04) x**4 + (1.2345679e-05) x**5') + +class TestPrintOptions: + """ + Test the output is properly configured via printoptions. + The exponential notation is enabled automatically when the values + are too small or too large. + """ + + @pytest.fixture(scope='class', autouse=True) + def use_ascii(self): + poly.set_default_printstyle('ascii') + + def test_str(self): + p = poly.Polynomial([1/2, 1/7, 1/7*10**8, 1/7*10**9]) + assert_equal(str(p), '0.5 + 0.14285714 x + 14285714.28571429 x**2 ' + '+ (1.42857143e+08) x**3') + + with printoptions(precision=3): + assert_equal(str(p), '0.5 + 0.143 x + 14285714.286 x**2 ' + '+ (1.429e+08) x**3') + + def test_latex(self): + p = poly.Polynomial([1/2, 1/7, 1/7*10**8, 1/7*10**9]) + assert_equal(p._repr_latex_(), + r'$x \mapsto \text{0.5} + \text{0.14285714}\,x + ' + r'\text{14285714.28571429}\,x^{2} + ' + r'\text{(1.42857143e+08)}\,x^{3}$') + + with printoptions(precision=3): + assert_equal(p._repr_latex_(), + r'$x \mapsto \text{0.5} + \text{0.143}\,x + ' + r'\text{14285714.286}\,x^{2} + \text{(1.429e+08)}\,x^{3}$') + + def test_fixed(self): + p = poly.Polynomial([1/2]) + assert_equal(str(p), '0.5') + + with printoptions(floatmode='fixed'): + assert_equal(str(p), '0.50000000') + + with printoptions(floatmode='fixed', precision=4): + assert_equal(str(p), '0.5000') + + def test_switch_to_exp(self): + for i, s in enumerate(SWITCH_TO_EXP): + with printoptions(precision=i): + p = poly.Polynomial([1.23456789*10**-i + for i in range(i//2+3)]) + assert str(p).replace('\n', ' ') == s + + def test_non_finite(self): + p = poly.Polynomial([nan, inf]) + assert str(p) == 'nan + inf x' + assert p._repr_latex_() == r'$x \mapsto \text{nan} + \text{inf}\,x$' + with printoptions(nanstr='NAN', infstr='INF'): + assert str(p) == 'NAN + INF x' + assert p._repr_latex_() == \ + r'$x \mapsto \text{NAN} + \text{INF}\,x$' diff --git a/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_symbol.py b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_symbol.py new file mode 100644 index 0000000000000000000000000000000000000000..f985533f9fe8c639f224daead98e31dc6f798cc4 --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/polynomial/tests/test_symbol.py @@ -0,0 +1,216 @@ +""" +Tests related to the ``symbol`` attribute of the ABCPolyBase class. +""" + +import pytest +import numpy.polynomial as poly +from numpy._core import array +from numpy.testing import assert_equal, assert_raises, assert_ + + +class TestInit: + """ + Test polynomial creation with symbol kwarg. + """ + c = [1, 2, 3] + + def test_default_symbol(self): + p = poly.Polynomial(self.c) + assert_equal(p.symbol, 'x') + + @pytest.mark.parametrize(('bad_input', 'exception'), ( + ('', ValueError), + ('3', ValueError), + (None, TypeError), + (1, TypeError), + )) + def test_symbol_bad_input(self, bad_input, exception): + with pytest.raises(exception): + p = poly.Polynomial(self.c, symbol=bad_input) + + @pytest.mark.parametrize('symbol', ( + 'x', + 'x_1', + 'A', + 'xyz', + 'β', + )) + def test_valid_symbols(self, symbol): + """ + Values for symbol that should pass input validation. + """ + p = poly.Polynomial(self.c, symbol=symbol) + assert_equal(p.symbol, symbol) + + def test_property(self): + """ + 'symbol' attribute is read only. + """ + p = poly.Polynomial(self.c, symbol='x') + with pytest.raises(AttributeError): + p.symbol = 'z' + + def test_change_symbol(self): + p = poly.Polynomial(self.c, symbol='y') + # Create new polynomial from p with different symbol + pt = poly.Polynomial(p.coef, symbol='t') + assert_equal(pt.symbol, 't') + + +class TestUnaryOperators: + p = poly.Polynomial([1, 2, 3], symbol='z') + + def test_neg(self): + n = -self.p + assert_equal(n.symbol, 'z') + + def test_scalarmul(self): + out = self.p * 10 + assert_equal(out.symbol, 'z') + + def test_rscalarmul(self): + out = 10 * self.p + assert_equal(out.symbol, 'z') + + def test_pow(self): + out = self.p ** 3 + assert_equal(out.symbol, 'z') + + +@pytest.mark.parametrize( + 'rhs', + ( + poly.Polynomial([4, 5, 6], symbol='z'), + array([4, 5, 6]), + ), +) +class TestBinaryOperatorsSameSymbol: + """ + Ensure symbol is preserved for numeric operations on polynomials with + the same symbol + """ + p = poly.Polynomial([1, 2, 3], symbol='z') + + def test_add(self, rhs): + out = self.p + rhs + assert_equal(out.symbol, 'z') + + def test_sub(self, rhs): + out = self.p - rhs + assert_equal(out.symbol, 'z') + + def test_polymul(self, rhs): + out = self.p * rhs + assert_equal(out.symbol, 'z') + + def test_divmod(self, rhs): + for out in divmod(self.p, rhs): + assert_equal(out.symbol, 'z') + + def test_radd(self, rhs): + out = rhs + self.p + assert_equal(out.symbol, 'z') + + def test_rsub(self, rhs): + out = rhs - self.p + assert_equal(out.symbol, 'z') + + def test_rmul(self, rhs): + out = rhs * self.p + assert_equal(out.symbol, 'z') + + def test_rdivmod(self, rhs): + for out in divmod(rhs, self.p): + assert_equal(out.symbol, 'z') + + +class TestBinaryOperatorsDifferentSymbol: + p = poly.Polynomial([1, 2, 3], symbol='x') + other = poly.Polynomial([4, 5, 6], symbol='y') + ops = (p.__add__, p.__sub__, p.__mul__, p.__floordiv__, p.__mod__) + + @pytest.mark.parametrize('f', ops) + def test_binops_fails(self, f): + assert_raises(ValueError, f, self.other) + + +class TestEquality: + p = poly.Polynomial([1, 2, 3], symbol='x') + + def test_eq(self): + other = poly.Polynomial([1, 2, 3], symbol='x') + assert_(self.p == other) + + def test_neq(self): + other = poly.Polynomial([1, 2, 3], symbol='y') + assert_(not self.p == other) + + +class TestExtraMethods: + """ + Test other methods for manipulating/creating polynomial objects. + """ + p = poly.Polynomial([1, 2, 3, 0], symbol='z') + + def test_copy(self): + other = self.p.copy() + assert_equal(other.symbol, 'z') + + def test_trim(self): + other = self.p.trim() + assert_equal(other.symbol, 'z') + + def test_truncate(self): + other = self.p.truncate(2) + assert_equal(other.symbol, 'z') + + @pytest.mark.parametrize('kwarg', ( + {'domain': [-10, 10]}, + {'window': [-10, 10]}, + {'kind': poly.Chebyshev}, + )) + def test_convert(self, kwarg): + other = self.p.convert(**kwarg) + assert_equal(other.symbol, 'z') + + def test_integ(self): + other = self.p.integ() + assert_equal(other.symbol, 'z') + + def test_deriv(self): + other = self.p.deriv() + assert_equal(other.symbol, 'z') + + +def test_composition(): + p = poly.Polynomial([3, 2, 1], symbol="t") + q = poly.Polynomial([5, 1, 0, -1], symbol="λ_1") + r = p(q) + assert r.symbol == "λ_1" + + +# +# Class methods that result in new polynomial class instances +# + + +def test_fit(): + x, y = (range(10),)*2 + p = poly.Polynomial.fit(x, y, deg=1, symbol='z') + assert_equal(p.symbol, 'z') + + +def test_froomroots(): + roots = [-2, 2] + p = poly.Polynomial.fromroots(roots, symbol='z') + assert_equal(p.symbol, 'z') + + +def test_identity(): + p = poly.Polynomial.identity(domain=[-1, 1], window=[5, 20], symbol='z') + assert_equal(p.symbol, 'z') + + +def test_basis(): + p = poly.Polynomial.basis(3, symbol='z') + assert_equal(p.symbol, 'z') diff --git a/janus/lib/python3.10/site-packages/numpy/rec/__init__.py b/janus/lib/python3.10/site-packages/numpy/rec/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..1a439ada8c35a6971b5fa8507381bde63ead8a6e --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/rec/__init__.py @@ -0,0 +1,2 @@ +from numpy._core.records import __all__, __doc__ +from numpy._core.records import * diff --git a/janus/lib/python3.10/site-packages/numpy/rec/__init__.pyi b/janus/lib/python3.10/site-packages/numpy/rec/__init__.pyi new file mode 100644 index 0000000000000000000000000000000000000000..605770f7c9c0695bcbe71a3832690d9045a6038c --- /dev/null +++ b/janus/lib/python3.10/site-packages/numpy/rec/__init__.pyi @@ -0,0 +1,22 @@ +from numpy._core.records import ( + record, + recarray, + find_duplicate, + format_parser, + fromarrays, + fromrecords, + fromstring, + fromfile, + array, +) +__all__ = [ + "record", + "recarray", + "format_parser", + "fromarrays", + "fromrecords", + "fromstring", + "fromfile", + "array", + "find_duplicate", +] diff --git a/janus/lib/python3.10/site-packages/numpy/rec/__pycache__/__init__.cpython-310.pyc b/janus/lib/python3.10/site-packages/numpy/rec/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..942c007d3dfa0d8a92a455e1ccedc0aa53d4b8af Binary files /dev/null and b/janus/lib/python3.10/site-packages/numpy/rec/__pycache__/__init__.cpython-310.pyc differ