diff --git a/.gitattributes b/.gitattributes index bdcd845b6ffd575a8a03a567c99b87b7be590a02..d7472fa2f9c08bd1644c0fcef65f536f5b945141 100644 --- a/.gitattributes +++ b/.gitattributes @@ -1130,3 +1130,7 @@ infer_4_37_2/lib/python3.10/site-packages/nvidia/cusolver/lib/libcusolver.so.11 infer_4_37_2/lib/python3.10/site-packages/nvidia/cublas/lib/libcublas.so.12 filter=lfs diff=lfs merge=lfs -text infer_4_37_2/lib/python3.10/site-packages/httptools/parser/parser.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text infer_4_37_2/lib/python3.10/site-packages/httptools/parser/url_parser.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text +infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text +infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/parsers.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text +infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/lib/libcurand.so.10 filter=lfs diff=lfs merge=lfs -text +infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/algos.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text diff --git a/infer_4_37_2/lib/python3.10/site-packages/httptools/__init__.py b/infer_4_37_2/lib/python3.10/site-packages/httptools/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..972053ef44931bbb6ad35da1996b43d2a8a17348 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/httptools/__init__.py @@ -0,0 +1,6 @@ +from . import parser +from .parser import * # NOQA + +from ._version import __version__ # NOQA + +__all__ = parser.__all__ + ('__version__',) # NOQA diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/__pycache__/__init__.cpython-310.pyc b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..ab93cf4e76272c68116af1ddd3342711cb9c135a Binary files /dev/null and b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/__pycache__/__init__.cpython-310.pyc differ diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_discrete2.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_discrete2.h new file mode 100644 index 0000000000000000000000000000000000000000..ac827749840488f66d71f492c14dbec80b57a3d1 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_discrete2.h @@ -0,0 +1,253 @@ + + /* Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + +#if !defined(CURAND_DISCRETE_H_) +#define CURAND_DISCRETE_H_ + +/** + * \defgroup DEVICE Device API + * + * @{ + */ + +#ifndef __CUDACC_RTC__ +#include +#endif // __CUDACC_RTC__ + +#include "curand_mrg32k3a.h" +#include "curand_mtgp32_kernel.h" +#include "curand_philox4x32_x.h" + + +template +QUALIFIERS unsigned int _curand_discrete(T x, curandDiscreteDistribution_t discrete_distribution){ + if (discrete_distribution->method == CURAND_M2){ + return _curand_M2_double(x, discrete_distribution->M2); + } + return (unsigned int)((discrete_distribution->stddev * _curand_normal_icdf_double(x)) + discrete_distribution->mean + 0.5); +} + + +template +QUALIFIERS unsigned int curand__discrete(STATE state, curandDiscreteDistribution_t discrete_distribution){ + if (discrete_distribution->method == CURAND_M2){ + return curand_M2_double(state, discrete_distribution->M2); + } + return (unsigned int)((discrete_distribution->stddev * curand_normal_double(state)) + discrete_distribution->mean + 0.5); //Round to nearest +} + +template +QUALIFIERS uint4 curand__discrete4(STATE state, curandDiscreteDistribution_t discrete_distribution){ + if (discrete_distribution->method == CURAND_M2){ + return curand_M2_double4(state, discrete_distribution->M2); + } + double4 _res; + uint4 result; + _res = curand_normal4_double(state); + result.x = (unsigned int)((discrete_distribution->stddev * _res.x) + discrete_distribution->mean + 0.5); //Round to nearest + result.y = (unsigned int)((discrete_distribution->stddev * _res.y) + discrete_distribution->mean + 0.5); //Round to nearest + result.z = (unsigned int)((discrete_distribution->stddev * _res.z) + discrete_distribution->mean + 0.5); //Round to nearest + result.w = (unsigned int)((discrete_distribution->stddev * _res.w) + discrete_distribution->mean + 0.5); //Round to nearest + return result; +} + +/* + * \brief Return a discrete distributed unsigned int from a XORWOW generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the XORWOW generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateXORWOW_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a Philox4_32_10 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the Philox4_32_10 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStatePhilox4_32_10_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return four discrete distributed unsigned ints from a Philox4_32_10 generator. + * + * Return four single discrete distributed unsigned ints derived from a + * distribution defined by \p discrete_distribution from the Philox4_32_10 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS uint4 curand_discrete4(curandStatePhilox4_32_10_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete4(state, discrete_distribution); +} +/* + * \brief Return a discrete distributed unsigned int from a MRG32k3a generator. + * + * Re turn a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the MRG32k3a generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateMRG32k3a_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a MTGP32 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the MTGP32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateMtgp32_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a Sobol32 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the Sobol32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateSobol32_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a scrambled Sobol32 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the scrambled Sobol32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateScrambledSobol32_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a Sobol64 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the Sobol64 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateSobol64_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +/* + * \brief Return a discrete distributed unsigned int from a scrambled Sobol64 generator. + * + * Return a single discrete distributed unsigned int derived from a + * distribution defined by \p discrete_distribution from the scrambled Sobol64 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param discrete_distribution - ancillary structure for discrete distribution + * + * \return unsigned int distributed by distribution defined by \p discrete_distribution. + */ +QUALIFIERS unsigned int curand_discrete(curandStateScrambledSobol64_t *state, curandDiscreteDistribution_t discrete_distribution) +{ + return curand__discrete(state, discrete_distribution); +} + +#endif // !defined(CURAND_DISCRETE_H_) diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_kernel.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_kernel.h new file mode 100644 index 0000000000000000000000000000000000000000..c9d27c5f271cae931091c85ecfe37b5e7d427bf3 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_kernel.h @@ -0,0 +1,1677 @@ + + /* Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + +#if !defined(CURAND_KERNEL_H_) +#define CURAND_KERNEL_H_ + +/** + * \defgroup DEVICE Device API + * + * @{ + */ + +#if !defined(QUALIFIERS) +#define QUALIFIERS static __forceinline__ __device__ +#endif + +/* To prevent unused parameter warnings */ +#if !defined(GCC_UNUSED_PARAMETER) +#if defined(__GNUC__) +#define GCC_UNUSED_PARAMETER __attribute__((unused)) +#else +#define GCC_UNUSED_PARAMETER +#endif /* defined(__GNUC__) */ +#endif /* !defined(GCC_UNUSED_PARAMETER) */ + +#include + +#ifdef __CUDACC_RTC__ +#define CURAND_DETAIL_USE_CUDA_STL +#endif + +#if __cplusplus >= 201103L +# ifdef CURAND_DETAIL_USE_CUDA_STL +# define CURAND_STD cuda::std +# include +# else +# define CURAND_STD std +# include +# endif // CURAND_DETAIL_USE_CUDA_STL +#else +// To support C++03 compilation +# define CURAND_STD curand_detail +namespace curand_detail { + template + struct enable_if {}; + + template + struct enable_if { typedef T type; }; + + template + struct is_same { static const bool value = false; }; + + template + struct is_same { static const bool value = true; }; +} // namespace curand_detail +#endif // __cplusplus >= 201103L + +#ifndef __CUDACC_RTC__ +#include +#endif // __CUDACC_RTC__ + +#include "curand.h" +#include "curand_discrete.h" +#include "curand_precalc.h" +#include "curand_mrg32k3a.h" +#include "curand_mtgp32_kernel.h" +#include "curand_philox4x32_x.h" +#include "curand_globals.h" + +/* Test RNG */ +/* This generator uses the formula: + x_n = x_(n-1) + 1 mod 2^32 + x_0 = (unsigned int)seed * 3 + Subsequences are spaced 31337 steps apart. +*/ +struct curandStateTest { + unsigned int v; +}; + +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateTest curandStateTest_t; +/** \endcond */ + +/* XORSHIFT FAMILY RNGs */ +/* These generators are a family proposed by Marsaglia. They keep state + in 32 bit chunks, then use repeated shift and xor operations to scramble + the bits. The following generators are a combination of a simple Weyl + generator with an N variable XORSHIFT generator. +*/ + +/* XORSHIFT RNG */ +/* This generator uses the xorwow formula of +www.jstatsoft.org/v08/i14/paper page 5 +Has period 2^192 - 2^32. +*/ +/** + * CURAND XORWOW state + */ +struct curandStateXORWOW; + +/* + * Implementation details not in reference documentation */ +struct curandStateXORWOW { + unsigned int d, v[5]; + int boxmuller_flag; + int boxmuller_flag_double; + float boxmuller_extra; + double boxmuller_extra_double; +}; + +/* + * CURAND XORWOW state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateXORWOW curandStateXORWOW_t; + +#define EXTRA_FLAG_NORMAL 0x00000001 +#define EXTRA_FLAG_LOG_NORMAL 0x00000002 +/** \endcond */ + +/* Combined Multiple Recursive Generators */ +/* These generators are a family proposed by L'Ecuyer. They keep state + in sets of doubles, then use repeated modular arithmetic multiply operations + to scramble the bits in each set, and combine the result. +*/ + +/* MRG32k3a RNG */ +/* This generator uses the MRG32k3A formula of +http://www.iro.umontreal.ca/~lecuyer/myftp/streams00/c++/streams4.pdf +Has period 2^191. +*/ + +/* moduli for the recursions */ +/** \cond UNHIDE_DEFINES */ +#define MRG32K3A_MOD1 4294967087. +#define MRG32K3A_MOD2 4294944443. + +/* Constants used in generation */ + +#define MRG32K3A_A12 1403580. +#define MRG32K3A_A13N 810728. +#define MRG32K3A_A21 527612. +#define MRG32K3A_A23N 1370589. +#define MRG32K3A_NORM (2.3283065498378288e-10) +// +// #define MRG32K3A_BITS_NORM ((double)((POW32_DOUBLE-1.0)/MOD1)) +// above constant, used verbatim, rounds differently on some host systems. +#define MRG32K3A_BITS_NORM 1.000000048662 + +/** \endcond */ + + + + +/** + * CURAND MRG32K3A state + */ +struct curandStateMRG32k3a; + +/* Implementation details not in reference documentation */ +struct curandStateMRG32k3a { + unsigned int s1[3]; + unsigned int s2[3]; + int boxmuller_flag; + int boxmuller_flag_double; + float boxmuller_extra; + double boxmuller_extra_double; +}; + +/* + * CURAND MRG32K3A state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateMRG32k3a curandStateMRG32k3a_t; +/** \endcond */ + +/* SOBOL QRNG */ +/** + * CURAND Sobol32 state + */ +struct curandStateSobol32; + +/* Implementation details not in reference documentation */ +struct curandStateSobol32 { + unsigned int i, x, c; + unsigned int direction_vectors[32]; +}; + +/* + * CURAND Sobol32 state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateSobol32 curandStateSobol32_t; +/** \endcond */ + +/** + * CURAND Scrambled Sobol32 state + */ +struct curandStateScrambledSobol32; + +/* Implementation details not in reference documentation */ +struct curandStateScrambledSobol32 { + unsigned int i, x, c; + unsigned int direction_vectors[32]; +}; + +/* + * CURAND Scrambled Sobol32 state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateScrambledSobol32 curandStateScrambledSobol32_t; +/** \endcond */ + +/** + * CURAND Sobol64 state + */ +struct curandStateSobol64; + +/* Implementation details not in reference documentation */ +struct curandStateSobol64 { + unsigned long long i, x, c; + unsigned long long direction_vectors[64]; +}; + +/* + * CURAND Sobol64 state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateSobol64 curandStateSobol64_t; +/** \endcond */ + +/** + * CURAND Scrambled Sobol64 state + */ +struct curandStateScrambledSobol64; + +/* Implementation details not in reference documentation */ +struct curandStateScrambledSobol64 { + unsigned long long i, x, c; + unsigned long long direction_vectors[64]; +}; + +/* + * CURAND Scrambled Sobol64 state + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateScrambledSobol64 curandStateScrambledSobol64_t; +/** \endcond */ + +/* + * Default RNG + */ +/** \cond UNHIDE_TYPEDEFS */ +typedef struct curandStateXORWOW curandState_t; +typedef struct curandStateXORWOW curandState; +/** \endcond */ + +/****************************************************************************/ +/* Utility functions needed by RNGs */ +/****************************************************************************/ +/** \cond UNHIDE_UTILITIES */ +/* + multiply vector by matrix, store in result + matrix is n x n, measured in 32 bit units + matrix is stored in row major order + vector and result cannot be same pointer +*/ +template +QUALIFIERS void __curand_matvec_inplace(unsigned int *vector, unsigned int *matrix) +{ + unsigned int result[N] = { 0 }; + for(int i = 0; i < N; i++) { + #ifdef __CUDA_ARCH__ + #pragma unroll 16 + #endif + for(int j = 0; j < 32; j++) { + if(vector[i] & (1 << j)) { + for(int k = 0; k < N; k++) { + result[k] ^= matrix[N * (i * 32 + j) + k]; + } + } + } + } + for(int i = 0; i < N; i++) { + vector[i] = result[i]; + } +} + +QUALIFIERS void __curand_matvec(unsigned int *vector, unsigned int *matrix, + unsigned int *result, int n) +{ + for(int i = 0; i < n; i++) { + result[i] = 0; + } + for(int i = 0; i < n; i++) { + for(int j = 0; j < 32; j++) { + if(vector[i] & (1 << j)) { + for(int k = 0; k < n; k++) { + result[k] ^= matrix[n * (i * 32 + j) + k]; + } + } + } + } +} + +/* generate identity matrix */ +QUALIFIERS void __curand_matidentity(unsigned int *matrix, int n) +{ + int r; + for(int i = 0; i < n * 32; i++) { + for(int j = 0; j < n; j++) { + r = i & 31; + if(i / 32 == j) { + matrix[i * n + j] = (1 << r); + } else { + matrix[i * n + j] = 0; + } + } + } +} + +/* multiply matrixA by matrixB, store back in matrixA + matrixA and matrixB must not be same matrix */ +QUALIFIERS void __curand_matmat(unsigned int *matrixA, unsigned int *matrixB, int n) +{ + unsigned int result[MAX_XOR_N]; + for(int i = 0; i < n * 32; i++) { + __curand_matvec(matrixA + i * n, matrixB, result, n); + for(int j = 0; j < n; j++) { + matrixA[i * n + j] = result[j]; + } + } +} + +/* copy vectorA to vector */ +QUALIFIERS void __curand_veccopy(unsigned int *vector, unsigned int *vectorA, int n) +{ + for(int i = 0; i < n; i++) { + vector[i] = vectorA[i]; + } +} + +/* copy matrixA to matrix */ +QUALIFIERS void __curand_matcopy(unsigned int *matrix, unsigned int *matrixA, int n) +{ + for(int i = 0; i < n * n * 32; i++) { + matrix[i] = matrixA[i]; + } +} + +/* compute matrixA to power p, store result in matrix */ +QUALIFIERS void __curand_matpow(unsigned int *matrix, unsigned int *matrixA, + unsigned long long p, int n) +{ + unsigned int matrixR[MAX_XOR_N * MAX_XOR_N * 32]; + unsigned int matrixS[MAX_XOR_N * MAX_XOR_N * 32]; + __curand_matidentity(matrix, n); + __curand_matcopy(matrixR, matrixA, n); + while(p) { + if(p & 1) { + __curand_matmat(matrix, matrixR, n); + } + __curand_matcopy(matrixS, matrixR, n); + __curand_matmat(matrixR, matrixS, n); + p >>= 1; + } +} + +/****************************************************************************/ +/* Utility functions needed by MRG32k3a RNG */ +/* Matrix operations modulo some integer less than 2**32, done in */ +/* double precision floating point, with care not to overflow 53 bits */ +/****************************************************************************/ + +/* return i mod m. */ +/* assumes i and m are integers represented accurately in doubles */ + +QUALIFIERS double curand_MRGmod(double i, double m) +{ + double quo; + double rem; + quo = floor(i/m); + rem = i - (quo*m); + if (rem < 0.0) rem += m; + return rem; +} + +/* Multiplication modulo m. Inputs i and j less than 2**32 */ +/* Ensure intermediate results do not exceed 2**53 */ + +QUALIFIERS double curand_MRGmodMul(double i, double j, double m) +{ + double tempHi; + double tempLo; + + tempHi = floor(i/131072.0); + tempLo = i - (tempHi*131072.0); + tempLo = curand_MRGmod( curand_MRGmod( (tempHi * j), m) * 131072.0 + curand_MRGmod(tempLo * j, m),m); + + if (tempLo < 0.0) tempLo += m; + return tempLo; +} + +/* multiply 3 by 3 matrices of doubles, modulo m */ + +QUALIFIERS void curand_MRGmatMul3x3(unsigned int i1[][3],unsigned int i2[][3],unsigned int o[][3],double m) +{ + int i,j; + double temp[3][3]; + for (i=0; i<3; i++){ + for (j=0; j<3; j++){ + temp[i][j] = ( curand_MRGmodMul(i1[i][0], i2[0][j], m) + + curand_MRGmodMul(i1[i][1], i2[1][j], m) + + curand_MRGmodMul(i1[i][2], i2[2][j], m)); + temp[i][j] = curand_MRGmod( temp[i][j], m ); + } + } + for (i=0; i<3; i++){ + for (j=0; j<3; j++){ + o[i][j] = (unsigned int)temp[i][j]; + } + } +} + +/* multiply 3 by 3 matrix times 3 by 1 vector of doubles, modulo m */ + +QUALIFIERS void curand_MRGmatVecMul3x3( unsigned int i[][3], unsigned int v[], double m) +{ + int k; + double t[3]; + for (k = 0; k < 3; k++) { + t[k] = ( curand_MRGmodMul(i[k][0], v[0], m) + + curand_MRGmodMul(i[k][1], v[1], m) + + curand_MRGmodMul(i[k][2], v[2], m) ); + t[k] = curand_MRGmod( t[k], m ); + } + for (k = 0; k < 3; k++) { + v[k] = (unsigned int)t[k]; + } + +} + +/* raise a 3 by 3 matrix of doubles to a 64 bit integer power pow, modulo m */ +/* input is index zero of an array of 3 by 3 matrices m, */ +/* each m = m[0]**(2**index) */ + +QUALIFIERS void curand_MRGmatPow3x3( unsigned int in[][3][3], unsigned int o[][3], double m, unsigned long long pow ) +{ + int i,j; + for ( i = 0; i < 3; i++ ) { + for ( j = 0; j < 3; j++ ) { + o[i][j] = 0; + if ( i == j ) o[i][j] = 1; + } + } + i = 0; + curand_MRGmatVecMul3x3(o,o[0],m); + while (pow) { + if ( pow & 1ll ) { + curand_MRGmatMul3x3(in[i], o, o, m); + } + i++; + pow >>= 1; + } +} + +/* raise a 3 by 3 matrix of doubles to the power */ +/* 2 to the power (pow modulo 191), modulo m */ + +QUALIFIERS void curnand_MRGmatPow2Pow3x3( double in[][3], double o[][3], double m, unsigned long pow ) +{ + unsigned int temp[3][3]; + int i,j; + pow = pow % 191; + for ( i = 0; i < 3; i++ ) { + for ( j = 0; j < 3; j++ ) { + temp[i][j] = (unsigned int)in[i][j]; + } + } + while (pow) { + curand_MRGmatMul3x3(temp, temp, temp, m); + pow--; + } + for ( i = 0; i < 3; i++ ) { + for ( j = 0; j < 3; j++ ) { + o[i][j] = temp[i][j]; + } + } +} + +/** \endcond */ + +/****************************************************************************/ +/* Kernel implementations of RNGs */ +/****************************************************************************/ + +/* Test RNG */ + +QUALIFIERS void curand_init(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStateTest_t *state) +{ + state->v = (unsigned int)(seed * 3) + (unsigned int)(subsequence * 31337) + \ + (unsigned int)offset; +} + + +QUALIFIERS unsigned int curand(curandStateTest_t *state) +{ + unsigned int r = state->v++; + return r; +} + +QUALIFIERS void skipahead(unsigned long long n, curandStateTest_t *state) +{ + state->v += (unsigned int)n; +} + +/* XORWOW RNG */ + +template +QUALIFIERS void __curand_generate_skipahead_matrix_xor(unsigned int matrix[]) +{ + T state; + // Generate matrix that advances one step + // matrix has n * n * 32 32-bit elements + // solve for matrix by stepping single bit states + for(int i = 0; i < 32 * n; i++) { + state.d = 0; + for(int j = 0; j < n; j++) { + state.v[j] = 0; + } + state.v[i / 32] = (1 << (i & 31)); + curand(&state); + for(int j = 0; j < n; j++) { + matrix[i * n + j] = state.v[j]; + } + } +} + +template +QUALIFIERS void _skipahead_scratch(unsigned long long x, T *state, unsigned int *scratch) +{ + // unsigned int matrix[n * n * 32]; + unsigned int *matrix = scratch; + // unsigned int matrixA[n * n * 32]; + unsigned int *matrixA = scratch + (n * n * 32); + // unsigned int vector[n]; + unsigned int *vector = scratch + (n * n * 32) + (n * n * 32); + // unsigned int result[n]; + unsigned int *result = scratch + (n * n * 32) + (n * n * 32) + n; + unsigned long long p = x; + for(int i = 0; i < n; i++) { + vector[i] = state->v[i]; + } + int matrix_num = 0; + while(p && (matrix_num < PRECALC_NUM_MATRICES - 1)) { + for(unsigned int t = 0; t < (p & PRECALC_BLOCK_MASK); t++) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matvec(vector, precalc_xorwow_offset_matrix[matrix_num], result, n); +, + __curand_matvec(vector, precalc_xorwow_offset_matrix_host[matrix_num], result, n); +) + __curand_veccopy(vector, result, n); + } + p >>= PRECALC_BLOCK_SIZE; + matrix_num++; + } + if(p) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matcopy(matrix, precalc_xorwow_offset_matrix[PRECALC_NUM_MATRICES - 1], n); + __curand_matcopy(matrixA, precalc_xorwow_offset_matrix[PRECALC_NUM_MATRICES - 1], n); +, + __curand_matcopy(matrix, precalc_xorwow_offset_matrix_host[PRECALC_NUM_MATRICES - 1], n); + __curand_matcopy(matrixA, precalc_xorwow_offset_matrix_host[PRECALC_NUM_MATRICES - 1], n); +) + } + while(p) { + for(unsigned int t = 0; t < (p & SKIPAHEAD_MASK); t++) { + __curand_matvec(vector, matrixA, result, n); + __curand_veccopy(vector, result, n); + } + p >>= SKIPAHEAD_BLOCKSIZE; + if(p) { + for(int i = 0; i < SKIPAHEAD_BLOCKSIZE; i++) { + __curand_matmat(matrix, matrixA, n); + __curand_matcopy(matrixA, matrix, n); + } + } + } + for(int i = 0; i < n; i++) { + state->v[i] = vector[i]; + } + state->d += 362437 * (unsigned int)x; +} + +template +QUALIFIERS void _skipahead_sequence_scratch(unsigned long long x, T *state, unsigned int *scratch) +{ + // unsigned int matrix[n * n * 32]; + unsigned int *matrix = scratch; + // unsigned int matrixA[n * n * 32]; + unsigned int *matrixA = scratch + (n * n * 32); + // unsigned int vector[n]; + unsigned int *vector = scratch + (n * n * 32) + (n * n * 32); + // unsigned int result[n]; + unsigned int *result = scratch + (n * n * 32) + (n * n * 32) + n; + unsigned long long p = x; + for(int i = 0; i < n; i++) { + vector[i] = state->v[i]; + } + int matrix_num = 0; + while(p && matrix_num < PRECALC_NUM_MATRICES - 1) { + for(unsigned int t = 0; t < (p & PRECALC_BLOCK_MASK); t++) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matvec(vector, precalc_xorwow_matrix[matrix_num], result, n); +, + __curand_matvec(vector, precalc_xorwow_matrix_host[matrix_num], result, n); +) + __curand_veccopy(vector, result, n); + } + p >>= PRECALC_BLOCK_SIZE; + matrix_num++; + } + if(p) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matcopy(matrix, precalc_xorwow_matrix[PRECALC_NUM_MATRICES - 1], n); + __curand_matcopy(matrixA, precalc_xorwow_matrix[PRECALC_NUM_MATRICES - 1], n); +, + __curand_matcopy(matrix, precalc_xorwow_matrix_host[PRECALC_NUM_MATRICES - 1], n); + __curand_matcopy(matrixA, precalc_xorwow_matrix_host[PRECALC_NUM_MATRICES - 1], n); +) + } + while(p) { + for(unsigned int t = 0; t < (p & SKIPAHEAD_MASK); t++) { + __curand_matvec(vector, matrixA, result, n); + __curand_veccopy(vector, result, n); + } + p >>= SKIPAHEAD_BLOCKSIZE; + if(p) { + for(int i = 0; i < SKIPAHEAD_BLOCKSIZE; i++) { + __curand_matmat(matrix, matrixA, n); + __curand_matcopy(matrixA, matrix, n); + } + } + } + for(int i = 0; i < n; i++) { + state->v[i] = vector[i]; + } + /* No update of state->d needed, guaranteed to be a multiple of 2^32 */ +} + +template +QUALIFIERS void _skipahead_inplace(const unsigned long long x, T *state) +{ + unsigned long long p = x; + int matrix_num = 0; + while(p) { + for(unsigned int t = 0; t < (p & PRECALC_BLOCK_MASK); t++) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matvec_inplace(state->v, precalc_xorwow_offset_matrix[matrix_num]); +, + __curand_matvec_inplace(state->v, precalc_xorwow_offset_matrix_host[matrix_num]); +) + } + p >>= PRECALC_BLOCK_SIZE; + matrix_num++; + } + state->d += 362437 * (unsigned int)x; +} + +template +QUALIFIERS void _skipahead_sequence_inplace(unsigned long long x, T *state) +{ + int matrix_num = 0; + while(x) { + for(unsigned int t = 0; t < (x & PRECALC_BLOCK_MASK); t++) { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + __curand_matvec_inplace(state->v, precalc_xorwow_matrix[matrix_num]); +, + __curand_matvec_inplace(state->v, precalc_xorwow_matrix_host[matrix_num]); +) + } + x >>= PRECALC_BLOCK_SIZE; + matrix_num++; + } + /* No update of state->d needed, guaranteed to be a multiple of 2^32 */ +} + +/** + * \brief Update XORWOW state to skip \p n elements. + * + * Update the XORWOW state in \p state to skip ahead \p n elements. + * + * All values of \p n are valid. Large values require more computation and so + * will take more time to complete. + * + * \param n - Number of elements to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead(unsigned long long n, curandStateXORWOW_t *state) +{ + _skipahead_inplace(n, state); +} + +/** + * \brief Update XORWOW state to skip ahead \p n subsequences. + * + * Update the XORWOW state in \p state to skip ahead \p n subsequences. Each + * subsequence is \xmlonly267\endxmlonly elements long, so this means the function will skip ahead + * \xmlonly267\endxmlonly * n elements. + * + * All values of \p n are valid. Large values require more computation and so + * will take more time to complete. + * + * \param n - Number of subsequences to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead_sequence(unsigned long long n, curandStateXORWOW_t *state) +{ + _skipahead_sequence_inplace(n, state); +} + +QUALIFIERS void _curand_init_scratch(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStateXORWOW_t *state, + unsigned int *scratch) +{ + // Break up seed, apply salt + // Constants are arbitrary nonzero values + unsigned int s0 = ((unsigned int)seed) ^ 0xaad26b49UL; + unsigned int s1 = (unsigned int)(seed >> 32) ^ 0xf7dcefddUL; + // Simple multiplication to mix up bits + // Constants are arbitrary odd values + unsigned int t0 = 1099087573UL * s0; + unsigned int t1 = 2591861531UL * s1; + state->d = 6615241 + t1 + t0; + state->v[0] = 123456789UL + t0; + state->v[1] = 362436069UL ^ t0; + state->v[2] = 521288629UL + t1; + state->v[3] = 88675123UL ^ t1; + state->v[4] = 5783321UL + t0; + _skipahead_sequence_scratch(subsequence, state, scratch); + _skipahead_scratch(offset, state, scratch); + state->boxmuller_flag = 0; + state->boxmuller_flag_double = 0; + state->boxmuller_extra = 0.f; + state->boxmuller_extra_double = 0.; +} + +QUALIFIERS void _curand_init_inplace(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStateXORWOW_t *state) +{ + // Break up seed, apply salt + // Constants are arbitrary nonzero values + unsigned int s0 = ((unsigned int)seed) ^ 0xaad26b49UL; + unsigned int s1 = (unsigned int)(seed >> 32) ^ 0xf7dcefddUL; + // Simple multiplication to mix up bits + // Constants are arbitrary odd values + unsigned int t0 = 1099087573UL * s0; + unsigned int t1 = 2591861531UL * s1; + state->d = 6615241 + t1 + t0; + state->v[0] = 123456789UL + t0; + state->v[1] = 362436069UL ^ t0; + state->v[2] = 521288629UL + t1; + state->v[3] = 88675123UL ^ t1; + state->v[4] = 5783321UL + t0; + _skipahead_sequence_inplace(subsequence, state); + _skipahead_inplace(offset, state); + state->boxmuller_flag = 0; + state->boxmuller_flag_double = 0; + state->boxmuller_extra = 0.f; + state->boxmuller_extra_double = 0.; +} + +/** + * \brief Initialize XORWOW state. + * + * Initialize XORWOW state in \p state with the given \p seed, \p subsequence, + * and \p offset. + * + * All input values of \p seed, \p subsequence, and \p offset are legal. Large + * values for \p subsequence and \p offset require more computation and so will + * take more time to complete. + * + * A value of 0 for \p seed sets the state to the values of the original + * published version of the \p xorwow algorithm. + * + * \param seed - Arbitrary bits to use as a seed + * \param subsequence - Subsequence to start at + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStateXORWOW_t *state) +{ + _curand_init_inplace(seed, subsequence, offset, state); +} + +/** + * \brief Return 32-bits of pseudorandomness from an XORWOW generator. + * + * Return 32-bits of pseudorandomness from the XORWOW generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 32-bits of pseudorandomness as an unsigned int, all bits valid to use. + */ +QUALIFIERS unsigned int curand(curandStateXORWOW_t *state) +{ + unsigned int t; + t = (state->v[0] ^ (state->v[0] >> 2)); + state->v[0] = state->v[1]; + state->v[1] = state->v[2]; + state->v[2] = state->v[3]; + state->v[3] = state->v[4]; + state->v[4] = (state->v[4] ^ (state->v[4] <<4)) ^ (t ^ (t << 1)); + state->d += 362437; + return state->v[4] + state->d; +} + + +/** + * \brief Return 32-bits of pseudorandomness from an Philox4_32_10 generator. + * + * Return 32-bits of pseudorandomness from the Philox4_32_10 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 32-bits of pseudorandomness as an unsigned int, all bits valid to use. + */ + +QUALIFIERS unsigned int curand(curandStatePhilox4_32_10_t *state) +{ + // Maintain the invariant: output[STATE] is always "good" and + // is the next value to be returned by curand. + unsigned int ret; + switch(state->STATE++){ + default: + ret = state->output.x; + break; + case 1: + ret = state->output.y; + break; + case 2: + ret = state->output.z; + break; + case 3: + ret = state->output.w; + break; + } + if(state->STATE == 4){ + Philox_State_Incr(state); + state->output = curand_Philox4x32_10(state->ctr,state->key); + state->STATE = 0; + } + return ret; +} + +/** + * \brief Return tuple of 4 32-bit pseudorandoms from a Philox4_32_10 generator. + * + * Return 128 bits of pseudorandomness from the Philox4_32_10 generator in \p state, + * increment position of generator by four. + * + * \param state - Pointer to state to update + * + * \return 128-bits of pseudorandomness as a uint4, all bits valid to use. + */ + +QUALIFIERS uint4 curand4(curandStatePhilox4_32_10_t *state) +{ + uint4 r; + + uint4 tmp = state->output; + Philox_State_Incr(state); + state->output= curand_Philox4x32_10(state->ctr,state->key); + switch(state->STATE){ + case 0: + return tmp; + case 1: + r.x = tmp.y; + r.y = tmp.z; + r.z = tmp.w; + r.w = state->output.x; + break; + case 2: + r.x = tmp.z; + r.y = tmp.w; + r.z = state->output.x; + r.w = state->output.y; + break; + case 3: + r.x = tmp.w; + r.y = state->output.x; + r.z = state->output.y; + r.w = state->output.z; + break; + default: + // NOT possible but needed to avoid compiler warnings + return tmp; + } + return r; +} + +/** + * \brief Update Philox4_32_10 state to skip \p n elements. + * + * Update the Philox4_32_10 state in \p state to skip ahead \p n elements. + * + * All values of \p n are valid. + * + * \param n - Number of elements to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead(unsigned long long n, curandStatePhilox4_32_10_t *state) +{ + state->STATE += (n & 3); + n /= 4; + if( state->STATE > 3 ){ + n += 1; + state->STATE -= 4; + } + Philox_State_Incr(state, n); + state->output = curand_Philox4x32_10(state->ctr,state->key); +} + +/** + * \brief Update Philox4_32_10 state to skip ahead \p n subsequences. + * + * Update the Philox4_32_10 state in \p state to skip ahead \p n subsequences. Each + * subsequence is \xmlonly266\endxmlonly elements long, so this means the function will skip ahead + * \xmlonly266\endxmlonly * n elements. + * + * All values of \p n are valid. + * + * \param n - Number of subsequences to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead_sequence(unsigned long long n, curandStatePhilox4_32_10_t *state) +{ + Philox_State_Incr_hi(state, n); + state->output = curand_Philox4x32_10(state->ctr,state->key); +} + +/** + * \brief Initialize Philox4_32_10 state. + * + * Initialize Philox4_32_10 state in \p state with the given \p seed, p\ subsequence, + * and \p offset. + * + * All input values for \p seed, \p subseqence and \p offset are legal. Each of the + * \xmlonly264\endxmlonly possible + * values of seed selects an independent sequence of length + * \xmlonly2130\endxmlonly. + * The first + * \xmlonly266 * subsequence + offset\endxmlonly. + * values of the sequence are skipped. + * I.e., subsequences are of length + * \xmlonly266\endxmlonly. + * + * \param seed - Arbitrary bits to use as a seed + * \param subsequence - Subsequence to start at + * \param offset - Absolute offset into subsequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStatePhilox4_32_10_t *state) +{ + state->ctr = make_uint4(0, 0, 0, 0); + state->key.x = (unsigned int)seed; + state->key.y = (unsigned int)(seed>>32); + state->STATE = 0; + state->boxmuller_flag = 0; + state->boxmuller_flag_double = 0; + state->boxmuller_extra = 0.f; + state->boxmuller_extra_double = 0.; + skipahead_sequence(subsequence, state); + skipahead(offset, state); +} + + +/* MRG32k3a RNG */ + +/* Base generator for MRG32k3a */ +QUALIFIERS unsigned long long __curand_umad(GCC_UNUSED_PARAMETER unsigned int a, GCC_UNUSED_PARAMETER unsigned int b, GCC_UNUSED_PARAMETER unsigned long long c) +{ + unsigned long long r = 0; +NV_IF_TARGET(NV_PROVIDES_SM_61, + asm("mad.wide.u32 %0, %1, %2, %3;" + : "=l"(r) : "r"(a), "r"(b), "l"(c)); +) + return r; +} +QUALIFIERS unsigned long long __curand_umul(GCC_UNUSED_PARAMETER unsigned int a, GCC_UNUSED_PARAMETER unsigned int b) +{ + unsigned long long r = 0; +NV_IF_TARGET(NV_PROVIDES_SM_61, + asm("mul.wide.u32 %0, %1, %2;" + : "=l"(r) : "r"(a), "r"(b)); +) + return r; +} +QUALIFIERS double curand_MRG32k3a (curandStateMRG32k3a_t *state) +{ +NV_IF_TARGET(NV_PROVIDES_SM_61, + const unsigned int m1 = 4294967087u; + const unsigned int m2 = 4294944443u; + const unsigned int m1c = 209u; + const unsigned int m2c = 22853u; + const unsigned int a12 = 1403580u; + const unsigned int a13n = 810728u; + const unsigned int a21 = 527612u; + const unsigned int a23n = 1370589u; + + unsigned long long p1; + unsigned long long p2; + const unsigned long long p3 = __curand_umul(a13n, m1 - state->s1[0]); + p1 = __curand_umad(a12, state->s1[1], p3); + + // Putting addition inside and changing umul to umad + // slowed this function down on GV100 + p1 = __curand_umul(p1 >> 32, m1c) + (p1 & 0xffffffff); + if (p1 >= m1) p1 -= m1; + + state->s1[0] = state->s1[1]; state->s1[1] = state->s1[2]; state->s1[2] = p1; + const unsigned long long p4 = __curand_umul(a23n, m2 - state->s2[0]); + p2 = __curand_umad(a21, state->s2[2], p4); + + // Putting addition inside and changing umul to umad + // slowed this function down on GV100 + p2 = __curand_umul(p2 >> 32, m2c) + (p2 & 0xffffffff); + p2 = __curand_umul(p2 >> 32, m2c) + (p2 & 0xffffffff); + if (p2 >= m2) p2 -= m2; + + state->s2[0] = state->s2[1]; state->s2[1] = state->s2[2]; state->s2[2] = p2; + + const unsigned int p5 = (unsigned int)p1 - (unsigned int)p2; + if(p1 <= p2) return p5 + m1; + return p5; +) +NV_IF_TARGET(NV_IS_DEVICE, +/* nj's implementation */ + const double m1 = 4294967087.; + const double m2 = 4294944443.; + const double a12 = 1403580.; + const double a13n = 810728.; + const double a21 = 527612.; + const double a23n = 1370589.; + + const double rh1 = 2.3283065498378290e-010; /* (1.0 / m1)__hi */ + const double rl1 = -1.7354913086174288e-026; /* (1.0 / m1)__lo */ + const double rh2 = 2.3283188252407387e-010; /* (1.0 / m2)__hi */ + const double rl2 = 2.4081018096503646e-026; /* (1.0 / m2)__lo */ + + double q; + double p1; + double p2; + p1 = a12 * state->s1[1] - a13n * state->s1[0]; + q = trunc (fma (p1, rh1, p1 * rl1)); + p1 -= q * m1; + if (p1 < 0.0) p1 += m1; + state->s1[0] = state->s1[1]; state->s1[1] = state->s1[2]; state->s1[2] = (unsigned int)p1; + p2 = a21 * state->s2[2] - a23n * state->s2[0]; + q = trunc (fma (p2, rh2, p2 * rl2)); + p2 -= q * m2; + if (p2 < 0.0) p2 += m2; + state->s2[0] = state->s2[1]; state->s2[1] = state->s2[2]; state->s2[2] = (unsigned int)p2; + if (p1 <= p2) return (p1 - p2 + m1); + else return (p1 - p2); +) +/* end nj's implementation */ + double p1; + double p2; + double r; + p1 = (MRG32K3A_A12 * state->s1[1]) - (MRG32K3A_A13N * state->s1[0]); + p1 = curand_MRGmod(p1, MRG32K3A_MOD1); + if (p1 < 0.0) p1 += MRG32K3A_MOD1; + state->s1[0] = state->s1[1]; + state->s1[1] = state->s1[2]; + state->s1[2] = (unsigned int)p1; + p2 = (MRG32K3A_A21 * state->s2[2]) - (MRG32K3A_A23N * state->s2[0]); + p2 = curand_MRGmod(p2, MRG32K3A_MOD2); + if (p2 < 0) p2 += MRG32K3A_MOD2; + state->s2[0] = state->s2[1]; + state->s2[1] = state->s2[2]; + state->s2[2] = (unsigned int)p2; + r = p1 - p2; + if (r <= 0) r += MRG32K3A_MOD1; + return r; +} + + +/** + * \brief Return 32-bits of pseudorandomness from an MRG32k3a generator. + * + * Return 32-bits of pseudorandomness from the MRG32k3a generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 32-bits of pseudorandomness as an unsigned int, all bits valid to use. + */ +QUALIFIERS unsigned int curand(curandStateMRG32k3a_t *state) +{ + double dRet; + dRet = (double)curand_MRG32k3a(state)*(double)MRG32K3A_BITS_NORM; + return (unsigned int)dRet; +} + + + +/** + * \brief Update MRG32k3a state to skip \p n elements. + * + * Update the MRG32k3a state in \p state to skip ahead \p n elements. + * + * All values of \p n are valid. Large values require more computation and so + * will take more time to complete. + * + * \param n - Number of elements to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead(unsigned long long n, curandStateMRG32k3a_t *state) +{ + unsigned int t[3][3]; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + curand_MRGmatPow3x3( mrg32k3aM1, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3(mrg32k3aM2, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +, + curand_MRGmatPow3x3( mrg32k3aM1Host, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3(mrg32k3aM2Host, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +) +} + +/** + * \brief Update MRG32k3a state to skip ahead \p n subsequences. + * + * Update the MRG32k3a state in \p state to skip ahead \p n subsequences. Each + * subsequence is \xmlonly2127\endxmlonly + * + * \xmlonly276\endxmlonly elements long, so this means the function will skip ahead + * \xmlonly267\endxmlonly * n elements. + * + * Valid values of \p n are 0 to \xmlonly251\endxmlonly. Note \p n will be masked to 51 bits + * + * \param n - Number of subsequences to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead_subsequence(unsigned long long n, curandStateMRG32k3a_t *state) +{ + unsigned int t[3][3]; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + curand_MRGmatPow3x3( mrg32k3aM1SubSeq, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3( mrg32k3aM2SubSeq, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +, + curand_MRGmatPow3x3( mrg32k3aM1SubSeqHost, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3( mrg32k3aM2SubSeqHost, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +) +} + +/** + * \brief Update MRG32k3a state to skip ahead \p n sequences. + * + * Update the MRG32k3a state in \p state to skip ahead \p n sequences. Each + * sequence is \xmlonly2127\endxmlonly elements long, so this means the function will skip ahead + * \xmlonly2127\endxmlonly * n elements. + * + * All values of \p n are valid. Large values require more computation and so + * will take more time to complete. + * + * \param n - Number of sequences to skip + * \param state - Pointer to state to update + */ +QUALIFIERS void skipahead_sequence(unsigned long long n, curandStateMRG32k3a_t *state) +{ + unsigned int t[3][3]; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + curand_MRGmatPow3x3( mrg32k3aM1Seq, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3( mrg32k3aM2Seq, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +, + curand_MRGmatPow3x3( mrg32k3aM1SeqHost, t, MRG32K3A_MOD1, n); + curand_MRGmatVecMul3x3( t, state->s1, MRG32K3A_MOD1); + curand_MRGmatPow3x3( mrg32k3aM2SeqHost, t, MRG32K3A_MOD2, n); + curand_MRGmatVecMul3x3( t, state->s2, MRG32K3A_MOD2); +) +} + + +/** + * \brief Initialize MRG32k3a state. + * + * Initialize MRG32k3a state in \p state with the given \p seed, \p subsequence, + * and \p offset. + * + * All input values of \p seed, \p subsequence, and \p offset are legal. + * \p subsequence will be truncated to 51 bits to avoid running into the next sequence + * + * A value of 0 for \p seed sets the state to the values of the original + * published version of the \p MRG32k3a algorithm. + * + * \param seed - Arbitrary bits to use as a seed + * \param subsequence - Subsequence to start at + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(unsigned long long seed, + unsigned long long subsequence, + unsigned long long offset, + curandStateMRG32k3a_t *state) +{ + int i; + for ( i=0; i<3; i++ ) { + state->s1[i] = 12345u; + state->s2[i] = 12345u; + } + if (seed != 0ull) { + unsigned int x1 = ((unsigned int)seed) ^ 0x55555555UL; + unsigned int x2 = (unsigned int)((seed >> 32) ^ 0xAAAAAAAAUL); + state->s1[0] = (unsigned int)curand_MRGmodMul(x1, state->s1[0], MRG32K3A_MOD1); + state->s1[1] = (unsigned int)curand_MRGmodMul(x2, state->s1[1], MRG32K3A_MOD1); + state->s1[2] = (unsigned int)curand_MRGmodMul(x1, state->s1[2], MRG32K3A_MOD1); + state->s2[0] = (unsigned int)curand_MRGmodMul(x2, state->s2[0], MRG32K3A_MOD2); + state->s2[1] = (unsigned int)curand_MRGmodMul(x1, state->s2[1], MRG32K3A_MOD2); + state->s2[2] = (unsigned int)curand_MRGmodMul(x2, state->s2[2], MRG32K3A_MOD2); + } + skipahead_subsequence( subsequence, state ); + skipahead( offset, state ); + state->boxmuller_flag = 0; + state->boxmuller_flag_double = 0; + state->boxmuller_extra = 0.f; + state->boxmuller_extra_double = 0.; +} + +/** + * \brief Update Sobol32 state to skip \p n elements. + * + * Update the Sobol32 state in \p state to skip ahead \p n elements. + * + * All values of \p n are valid. + * + * \param n - Number of elements to skip + * \param state - Pointer to state to update + */ +template +QUALIFIERS +typename CURAND_STD::enable_if::value || CURAND_STD::is_same::value>::type +skipahead(unsigned int n, T state) +{ + unsigned int i_gray; + state->x = state->c; + state->i += n; + /* Convert state->i to gray code */ + i_gray = state->i ^ (state->i >> 1); + for(unsigned int k = 0; k < 32; k++) { + if(i_gray & (1 << k)) { + state->x ^= state->direction_vectors[k]; + } + } + return; +} + +/** + * \brief Update Sobol64 state to skip \p n elements. + * + * Update the Sobol64 state in \p state to skip ahead \p n elements. + * + * All values of \p n are valid. + * + * \param n - Number of elements to skip + * \param state - Pointer to state to update + */ +template +QUALIFIERS +typename CURAND_STD::enable_if::value || CURAND_STD::is_same::value>::type +skipahead(unsigned long long n, T state) +{ + unsigned long long i_gray; + state->x = state->c; + state->i += n; + /* Convert state->i to gray code */ + i_gray = state->i ^ (state->i >> 1); + for(unsigned k = 0; k < 64; k++) { + if(i_gray & (1ULL << k)) { + state->x ^= state->direction_vectors[k]; + } + } + return; +} + +/** + * \brief Initialize Sobol32 state. + * + * Initialize Sobol32 state in \p state with the given \p direction \p vectors and + * \p offset. + * + * The direction vector is a device pointer to an array of 32 unsigned ints. + * All input values of \p offset are legal. + * + * \param direction_vectors - Pointer to array of 32 unsigned ints representing the + * direction vectors for the desired dimension + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(curandDirectionVectors32_t direction_vectors, + unsigned int offset, + curandStateSobol32_t *state) +{ + state->i = 0; + state->c = 0; + for(int i = 0; i < 32; i++) { + state->direction_vectors[i] = direction_vectors[i]; + } + state->x = 0; + skipahead(offset, state); +} +/** + * \brief Initialize Scrambled Sobol32 state. + * + * Initialize Sobol32 state in \p state with the given \p direction \p vectors and + * \p offset. + * + * The direction vector is a device pointer to an array of 32 unsigned ints. + * All input values of \p offset are legal. + * + * \param direction_vectors - Pointer to array of 32 unsigned ints representing the + direction vectors for the desired dimension + * \param scramble_c Scramble constant + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(curandDirectionVectors32_t direction_vectors, + unsigned int scramble_c, + unsigned int offset, + curandStateScrambledSobol32_t *state) +{ + state->i = 0; + state->c = scramble_c; + for(int i = 0; i < 32; i++) { + state->direction_vectors[i] = direction_vectors[i]; + } + state->x = state->c; + skipahead(offset, state); +} + +QUALIFIERS int __curand_find_trailing_zero(unsigned int x) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + int y = __ffs(~x); + if(y) + return y - 1; + return 31; +, + int i = 1; + while(x & 1) { + i++; + x >>= 1; + } + i = i - 1; + return i == 32 ? 31 : i; +) +} + +QUALIFIERS int __curand_find_trailing_zero(unsigned long long x) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + int y = __ffsll(~x); + if(y) + return y - 1; + return 63; +, + int i = 1; + while(x & 1) { + i++; + x >>= 1; + } + i = i - 1; + return i == 64 ? 63 : i; +) +} + +/** + * \brief Initialize Sobol64 state. + * + * Initialize Sobol64 state in \p state with the given \p direction \p vectors and + * \p offset. + * + * The direction vector is a device pointer to an array of 64 unsigned long longs. + * All input values of \p offset are legal. + * + * \param direction_vectors - Pointer to array of 64 unsigned long longs representing the + direction vectors for the desired dimension + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(curandDirectionVectors64_t direction_vectors, + unsigned long long offset, + curandStateSobol64_t *state) +{ + state->i = 0; + state->c = 0; + for(int i = 0; i < 64; i++) { + state->direction_vectors[i] = direction_vectors[i]; + } + state->x = 0; + skipahead(offset, state); +} + +/** + * \brief Initialize Scrambled Sobol64 state. + * + * Initialize Sobol64 state in \p state with the given \p direction \p vectors and + * \p offset. + * + * The direction vector is a device pointer to an array of 64 unsigned long longs. + * All input values of \p offset are legal. + * + * \param direction_vectors - Pointer to array of 64 unsigned long longs representing the + direction vectors for the desired dimension + * \param scramble_c Scramble constant + * \param offset - Absolute offset into sequence + * \param state - Pointer to state to initialize + */ +QUALIFIERS void curand_init(curandDirectionVectors64_t direction_vectors, + unsigned long long scramble_c, + unsigned long long offset, + curandStateScrambledSobol64_t *state) +{ + state->i = 0; + state->c = scramble_c; + for(int i = 0; i < 64; i++) { + state->direction_vectors[i] = direction_vectors[i]; + } + state->x = state->c; + skipahead(offset, state); +} + +/** + * \brief Return 32-bits of quasirandomness from a Sobol32 generator. + * + * Return 32-bits of quasirandomness from the Sobol32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 32-bits of quasirandomness as an unsigned int, all bits valid to use. + */ + +QUALIFIERS unsigned int curand(curandStateSobol32_t * state) +{ + /* Moving from i to i+1 element in gray code is flipping one bit, + the trailing zero bit of i + */ + unsigned int res = state->x; + state->x ^= state->direction_vectors[__curand_find_trailing_zero(state->i)]; + state->i ++; + return res; +} + +/** + * \brief Return 32-bits of quasirandomness from a scrambled Sobol32 generator. + * + * Return 32-bits of quasirandomness from the scrambled Sobol32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 32-bits of quasirandomness as an unsigned int, all bits valid to use. + */ + +QUALIFIERS unsigned int curand(curandStateScrambledSobol32_t * state) +{ + /* Moving from i to i+1 element in gray code is flipping one bit, + the trailing zero bit of i + */ + unsigned int res = state->x; + state->x ^= state->direction_vectors[__curand_find_trailing_zero(state->i)]; + state->i ++; + return res; +} + +/** + * \brief Return 64-bits of quasirandomness from a Sobol64 generator. + * + * Return 64-bits of quasirandomness from the Sobol64 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 64-bits of quasirandomness as an unsigned long long, all bits valid to use. + */ + +QUALIFIERS unsigned long long curand(curandStateSobol64_t * state) +{ + /* Moving from i to i+1 element in gray code is flipping one bit, + the trailing zero bit of i + */ + unsigned long long res = state->x; + state->x ^= state->direction_vectors[__curand_find_trailing_zero(state->i)]; + state->i ++; + return res; +} + +/** + * \brief Return 64-bits of quasirandomness from a scrambled Sobol64 generator. + * + * Return 64-bits of quasirandomness from the scrambled Sobol32 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * + * \return 64-bits of quasirandomness as an unsigned long long, all bits valid to use. + */ + +QUALIFIERS unsigned long long curand(curandStateScrambledSobol64_t * state) +{ + /* Moving from i to i+1 element in gray code is flipping one bit, + the trailing zero bit of i + */ + unsigned long long res = state->x; + state->x ^= state->direction_vectors[__curand_find_trailing_zero(state->i)]; + state->i ++; + return res; +} + +#include "curand_uniform.h" +#include "curand_normal.h" +#include "curand_lognormal.h" +#include "curand_poisson.h" +#include "curand_discrete2.h" + +__device__ static inline unsigned int *__get_precalculated_matrix(int n) +{ + if(n == 0) { + return precalc_xorwow_matrix[n]; + } + if(n == 2) { + return precalc_xorwow_offset_matrix[n]; + } + return precalc_xorwow_matrix[n]; +} + +#ifndef __CUDACC_RTC__ +__host__ static inline unsigned int *__get_precalculated_matrix_host(int n) +{ + if(n == 1) { + return precalc_xorwow_matrix_host[n]; + } + if(n == 3) { + return precalc_xorwow_offset_matrix_host[n]; + } + return precalc_xorwow_matrix_host[n]; +} +#endif // #ifndef __CUDACC_RTC__ + +__device__ static inline unsigned int *__get_mrg32k3a_matrix(int n) +{ + if(n == 0) { + return mrg32k3aM1[n][0]; + } + if(n == 2) { + return mrg32k3aM2[n][0]; + } + if(n == 4) { + return mrg32k3aM1SubSeq[n][0]; + } + if(n == 6) { + return mrg32k3aM2SubSeq[n][0]; + } + if(n == 8) { + return mrg32k3aM1Seq[n][0]; + } + if(n == 10) { + return mrg32k3aM2Seq[n][0]; + } + return mrg32k3aM1[n][0]; +} + +#ifndef __CUDACC_RTC__ +__host__ static inline unsigned int *__get_mrg32k3a_matrix_host(int n) +{ + if(n == 1) { + return mrg32k3aM1Host[n][0]; + } + if(n == 3) { + return mrg32k3aM2Host[n][0]; + } + if(n == 5) { + return mrg32k3aM1SubSeqHost[n][0]; + } + if(n == 7) { + return mrg32k3aM2SubSeqHost[n][0]; + } + if(n == 9) { + return mrg32k3aM1SeqHost[n][0]; + } + if(n == 11) { + return mrg32k3aM2SeqHost[n][0]; + } + return mrg32k3aM1Host[n][0]; +} + +__host__ static inline double *__get__cr_lgamma_table_host(void) { + return __cr_lgamma_table; +} +#endif // #ifndef __CUDACC_RTC__ + +/** @} */ + +#endif // !defined(CURAND_KERNEL_H_) diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_host.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_host.h new file mode 100644 index 0000000000000000000000000000000000000000..7b9a2d31b314194e6999aeb7046db67b6c9e19ac --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_host.h @@ -0,0 +1,516 @@ +/* + * Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +/* + * curand_mtgp32_host.h + * + * + * MTGP32-11213 + * + * Mersenne Twister RNG for the GPU + * + * The period of generated integers is 211213-1. + * + * This code generates 32-bit unsigned integers, and + * single precision floating point numbers uniformly distributed + * in the range [1, 2). (float r; 1.0 <= r < 2.0) + */ + +/* + * Copyright (c) 2009, 2010 Mutsuo Saito, Makoto Matsumoto and Hiroshima + * University. All rights reserved. + * Copyright (c) 2011 Mutsuo Saito, Makoto Matsumoto, Hiroshima + * University and University of Tokyo. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are + * met: + * + * * Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above + * copyright notice, this list of conditions and the following + * disclaimer in the documentation and/or other materials provided + * with the distribution. + * * Neither the name of the Hiroshima University nor the names of + * its contributors may be used to endorse or promote products + * derived from this software without specific prior written + * permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT + * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT + * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +#if !defined CURAND_MTGP32_HOST_H +#define CURAND_MTGP32_HOST_H + +#if !defined(QUALIFIERS) +#define QUALIFIERS static inline __device__ +#endif + +#include +#include +#include +#include +#include "curand.h" +#include "curand_mtgp32.h" +#include "curand_mtgp32dc_p_11213.h" + + +/** + * \addtogroup DEVICE Device API + * + * @{ + */ + +static const unsigned int non_zero = 0x4d544750; + +/* + * This function represents a function used in the initialization + * by mtgp32_init_by_array() and mtgp32_init_by_str(). + * @param[in] x 32-bit integer + * @return 32-bit integer + */ +static __forceinline__ unsigned int ini_func1(unsigned int x) { + return (x ^ (x >> 27)) * (1664525); +} + +/* + * This function represents a function used in the initialization + * by mtgp32_init_by_array() and mtgp32_init_by_str(). + * @param[in] x 32-bit integer + * @return 32-bit integer + */ +static __forceinline__ unsigned int ini_func2(unsigned int x) { + return (x ^ (x >> 27)) * (1566083941); +} + +/* + * This function initializes the internal state array with a 32-bit + * integer seed. The allocated memory should be freed by calling + * mtgp32_free(). \b para should be one of the elements in the + * parameter table (mtgp32-param-ref.c). + * + * This function is call by cuda program, because cuda program uses + * another structure and another allocation method. + * + * @param[out] array MTGP internal status vector. + * @param[in] para parameter structure + * @param[in] seed a 32-bit integer used as the seed. + */ +static __forceinline__ __host__ +void mtgp32_init_state(unsigned int state[], + const mtgp32_params_fast_t *para, unsigned int seed) { + int i; + int size = para->mexp / 32 + 1; + unsigned int hidden_seed; + unsigned int tmp; + hidden_seed = para->tbl[4] ^ (para->tbl[8] << 16); + tmp = hidden_seed; + tmp += tmp >> 16; + tmp += tmp >> 8; + memset(state, tmp & 0xff, sizeof(unsigned int) * size); + state[0] = seed; + state[1] = hidden_seed; + for (i = 1; i < size; i++) { + state[i] ^= (1812433253) * (state[i - 1] ^ (state[i - 1] >> 30)) + i; + } +} + +/* + * This function initializes the internal state array + * with a 32-bit integer array. \b para should be one of the elements in + * the parameter table (mtgp32-param-ref.c). + * + * @param[out] mtgp32 MTGP structure. + * @param[in] para parameter structure + * @param[in] array a 32-bit integer array used as a seed. + * @param[in] length length of the array. + * @return CURAND_STATUS_SUCCESS + */ +static __forceinline__ __host__ +int mtgp32_init_by_array(unsigned int state[], + const mtgp32_params_fast_t *para, + unsigned int *array, int length) { + int i, j, count; + unsigned int r; + int lag; + int mid; + int size = para->mexp / 32 + 1; + unsigned int hidden_seed; + unsigned int tmp; + + if (size >= 623) { + lag = 11; + } else if (size >= 68) { + lag = 7; + } else if (size >= 39) { + lag = 5; + } else { + lag = 3; + } + mid = (size - lag) / 2; + + hidden_seed = para->tbl[4] ^ (para->tbl[8] << 16); + tmp = hidden_seed; + tmp += tmp >> 16; + tmp += tmp >> 8; + memset(state, tmp & 0xff, sizeof(unsigned int) * size); + state[0] = hidden_seed; + + if (length + 1 > size) { + count = length + 1; + } else { + count = size; + } + r = ini_func1(state[0] ^ state[mid] ^ state[size - 1]); + state[mid] += r; + r += length; + state[(mid + lag) % size] += r; + state[0] = r; + i = 1; + count--; + for (i = 1, j = 0; (j < count) && (j < length); j++) { + r = ini_func1(state[i] ^ state[(i + mid) % size] + ^ state[(i + size - 1) % size]); + state[(i + mid) % size] += r; + r += array[j] + i; + state[(i + mid + lag) % size] += r; + state[i] = r; + i = (i + 1) % size; + } + for (; j < count; j++) { + r = ini_func1(state[i] ^ state[(i + mid) % size] + ^ state[(i + size - 1) % size]); + state[(i + mid) % size] += r; + r += i; + state[(i + mid + lag) % size] += r; + state[i] = r; + i = (i + 1) % size; + } + for (j = 0; j < size; j++) { + r = ini_func2(state[i] + state[(i + mid) % size] + + state[(i + size - 1) % size]); + state[(i + mid) % size] ^= r; + r -= i; + state[(i + mid + lag) % size] ^= r; + state[i] = r; + i = (i + 1) % size; + } + if (state[size - 1] == 0) { + state[size - 1] = non_zero; + } + return 0; +} + +/* + * This function initializes the internal state array + * with a character array. \b para should be one of the elements in + * the parameter table (mtgp32-param-ref.c). + * This is the same algorithm with mtgp32_init_by_array(), but hope to + * be more useful. + * + * @param[out] mtgp32 MTGP structure. + * @param[in] para parameter structure + * @param[in] array a character array used as a seed. (terminated by zero.) + * @return memory allocation result. if 0 then O.K. + */ +static __forceinline__ __host__ +int mtgp32_init_by_str(unsigned int state[], + const mtgp32_params_fast_t *para, unsigned char *array) { + int i, j, count; + unsigned int r; + int lag; + int mid; + int size = para->mexp / 32 + 1; + int length = (unsigned int)strlen((char *)array); + unsigned int hidden_seed; + unsigned int tmp; + + if (size >= 623) { + lag = 11; + } else if (size >= 68) { + lag = 7; + } else if (size >= 39) { + lag = 5; + } else { + lag = 3; + } + mid = (size - lag) / 2; + + hidden_seed = para->tbl[4] ^ (para->tbl[8] << 16); + tmp = hidden_seed; + tmp += tmp >> 16; + tmp += tmp >> 8; + memset(state, tmp & 0xff, sizeof(unsigned int) * size); + state[0] = hidden_seed; + + if (length + 1 > size) { + count = length + 1; + } else { + count = size; + } + r = ini_func1(state[0] ^ state[mid] ^ state[size - 1]); + state[mid] += r; + r += length; + state[(mid + lag) % size] += r; + state[0] = r; + i = 1; + count--; + for (i = 1, j = 0; (j < count) && (j < length); j++) { + r = ini_func1(state[i] ^ state[(i + mid) % size] + ^ state[(i + size - 1) % size]); + state[(i + mid) % size] += r; + r += array[j] + i; + state[(i + mid + lag) % size] += r; + state[i] = r; + i = (i + 1) % size; + } + for (; j < count; j++) { + r = ini_func1(state[i] ^ state[(i + mid) % size] + ^ state[(i + size - 1) % size]); + state[(i + mid) % size] += r; + r += i; + state[(i + mid + lag) % size] += r; + state[i] = r; + i = (i + 1) % size; + } + for (j = 0; j < size; j++) { + r = ini_func2(state[i] + state[(i + mid) % size] + + state[(i + size - 1) % size]); + state[(i + mid) % size] ^= r; + r -= i; + state[(i + mid + lag) % size] ^= r; + state[i] = r; + i = (i + 1) % size; + } + if (state[size - 1] == 0) { + state[size - 1] = non_zero; + } + return 0; +} + +template +static __forceinline__ __host__ +curandStatus_t curandMakeMTGP32ConstantsImpl(const mtgp32_params_fast_t params[], ParamsType * p, const int block_num) +{ + const int size1 = sizeof(unsigned int) * block_num; + const int size2 = sizeof(unsigned int) * block_num * TBL_SIZE; + unsigned int *h_pos_tbl; + unsigned int *h_sh1_tbl; + unsigned int *h_sh2_tbl; + unsigned int *h_param_tbl; + unsigned int *h_temper_tbl; + unsigned int *h_single_temper_tbl; + unsigned int *h_mask; + curandStatus_t status = CURAND_STATUS_SUCCESS; + + h_pos_tbl = (unsigned int *)malloc(size1); + h_sh1_tbl = (unsigned int *)malloc(size1); + h_sh2_tbl = (unsigned int *)malloc(size1); + h_param_tbl = (unsigned int *)malloc(size2); + h_temper_tbl = (unsigned int *)malloc(size2); + h_single_temper_tbl = (unsigned int *)malloc(size2); + h_mask = (unsigned int *)malloc(sizeof(unsigned int)); + if (h_pos_tbl == NULL + || h_sh1_tbl == NULL + || h_sh2_tbl == NULL + || h_param_tbl == NULL + || h_temper_tbl == NULL + || h_single_temper_tbl == NULL + || h_mask == NULL) { + if (h_pos_tbl != NULL) free(h_pos_tbl); + if (h_sh1_tbl != NULL) free(h_sh1_tbl); + if (h_sh2_tbl != NULL) free(h_sh2_tbl); + if (h_param_tbl != NULL) free(h_param_tbl); + if (h_temper_tbl != NULL) free(h_temper_tbl); + if (h_single_temper_tbl != NULL) free(h_single_temper_tbl); + if (h_mask != NULL) free(h_mask); + status = CURAND_STATUS_ALLOCATION_FAILED; + } else { + + h_mask[0] = params[0].mask; + for (int i = 0; i < block_num; i++) { + h_pos_tbl[i] = params[i].pos; + h_sh1_tbl[i] = params[i].sh1; + h_sh2_tbl[i] = params[i].sh2; + for (int j = 0; j < TBL_SIZE; j++) { + h_param_tbl[i * TBL_SIZE + j] = params[i].tbl[j]; + h_temper_tbl[i * TBL_SIZE + j] = params[i].tmp_tbl[j]; + h_single_temper_tbl[i * TBL_SIZE + j] = params[i].flt_tmp_tbl[j]; + } + } + if (cudaMemcpy( p->pos_tbl, + h_pos_tbl, size1, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->sh1_tbl, + h_sh1_tbl, size1, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->sh2_tbl, + h_sh2_tbl, size1, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->param_tbl, + h_param_tbl, size2, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->temper_tbl, + h_temper_tbl, size2, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->single_temper_tbl, + h_single_temper_tbl, size2, cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } else + if (cudaMemcpy( p->mask, + h_mask, sizeof(unsigned int), cudaMemcpyHostToDevice) != cudaSuccess) + { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } + } + if (h_pos_tbl != NULL) free(h_pos_tbl); + if (h_sh1_tbl != NULL) free(h_sh1_tbl); + if (h_sh2_tbl != NULL) free(h_sh2_tbl); + if (h_param_tbl != NULL) free(h_param_tbl); + if (h_temper_tbl != NULL) free(h_temper_tbl); + if (h_single_temper_tbl != NULL)free(h_single_temper_tbl); + if (h_mask != NULL) free(h_mask); + return status; +} + +/** + * \brief Set up constant parameters for the mtgp32 generator + * + * This host-side helper function re-organizes CURAND_NUM_MTGP32_PARAMS sets of + * generator parameters for use by kernel functions and copies the + * result to the specified location in device memory. + * + * \param params - Pointer to an array of type mtgp32_params_fast_t in host memory + * \param p - pointer to a structure of type mtgp32_kernel_params_t in device memory. + * + * \return + * - CURAND_STATUS_ALLOCATION_FAILED if host memory could not be allocated + * - CURAND_STATUS_INITIALIZATION_FAILED if the copy to device memory failed + * - CURAND_STATUS_SUCCESS otherwise + */ +static __forceinline__ __host__ +curandStatus_t curandMakeMTGP32Constants(const mtgp32_params_fast_t params[], mtgp32_kernel_params_t * p) +{ + return curandMakeMTGP32ConstantsImpl(params, p, CURAND_NUM_MTGP32_PARAMS); +} + +/** + * \brief Set up initial states for the mtgp32 generator + * + * This host-side helper function initializes a number of states (one parameter set per state) for + * an mtgp32 generator. To accomplish this it allocates a state array in host memory, + * initializes that array, and copies the result to device memory. + * + * \param s - pointer to an array of states in device memory + * \param params - Pointer to an array of type mtgp32_params_fast_t in host memory + * \param k - pointer to a structure of type mtgp32_kernel_params_t in device memory + * \param n - number of parameter sets/states to initialize + * \param seed - seed value + * + * \return + * - CURAND_STATUS_ALLOCATION_FAILED if host memory state could not be allocated + * - CURAND_STATUS_INITIALIZATION_FAILED if the copy to device memory failed + * - CURAND_STATUS_SUCCESS otherwise + */ +static __forceinline__ __host__ +curandStatus_t CURANDAPI curandMakeMTGP32KernelState(curandStateMtgp32_t *s, + mtgp32_params_fast_t params[], + mtgp32_kernel_params_t *k, + int n, + unsigned long long seed) +{ + int i; + curandStatus_t status = CURAND_STATUS_SUCCESS; + curandStateMtgp32_t *h_status =(curandStateMtgp32_t *) malloc(sizeof(curandStateMtgp32_t) * n); + if (h_status == NULL) { + status = CURAND_STATUS_ALLOCATION_FAILED; + } else { + seed = seed ^ (seed >> 32); + for (i = 0; i < n; i++) { + mtgp32_init_state(&(h_status[i].s[0]), ¶ms[i],(unsigned int)seed + i + 1); + h_status[i].offset = 0; + h_status[i].pIdx = i; + h_status[i].k = k; + } + if (cudaMemcpy(s, h_status, + sizeof(curandStateMtgp32_t) * n, + cudaMemcpyHostToDevice) != cudaSuccess) { + status = CURAND_STATUS_INITIALIZATION_FAILED; + } + } + free(h_status); + return status; +} + +/** @} */ + +#endif + + diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_kernel.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_kernel.h new file mode 100644 index 0000000000000000000000000000000000000000..087cdd0796d1e6d6731acd74a07718dfd1312275 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_mtgp32_kernel.h @@ -0,0 +1,386 @@ +/* + * Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * This source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * These Licensed Deliverables contained herein is PROPRIETARY and + * CONFIDENTIAL to NVIDIA and is being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. IT IS + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and is provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + +/* + * curand_mtgp32_kernel.h + * + * + * MTGP32-11213 + * + * Mersenne Twister RNG for the GPU + * + * The period of generated integers is 211213-1. + * + * This code generates 32-bit unsigned integers, and + * single precision floating point numbers uniformly distributed + * in the range [1, 2). (float r; 1.0 <= r < 2.0) + */ + +/* + * Copyright (c) 2009, 2010 Mutsuo Saito, Makoto Matsumoto and Hiroshima + * University. All rights reserved. + * Copyright (c) 2011 Mutsuo Saito, Makoto Matsumoto, Hiroshima + * University and University of Tokyo. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions are + * met: + * + * * Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above + * copyright notice, this list of conditions and the following + * disclaimer in the documentation and/or other materials provided + * with the distribution. + * * Neither the name of the Hiroshima University nor the names of + * its contributors may be used to endorse or promote products + * derived from this software without specific prior written + * permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT + * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT + * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +#if !defined CURAND_MTGP32_KERNEL_H +#define CURAND_MTGP32_KERNEL_H + +#if !defined(QUALIFIERS) +#define QUALIFIERS static __forceinline__ __device__ +#endif + +#ifndef __CUDACC_RTC__ +#include +#include +#include +#include +#endif // ifndef __CUDACC_RTC__ +#include +#include "curand.h" +#include "curand_mtgp32.h" + +/** + * \addtogroup DEVICE Device API + * + * @{ + */ + +#ifndef __CUDA_ARCH__ +// define blockDim and threadIdx for host compatibility call +extern const dim3 blockDim; +extern const uint3 threadIdx; +#endif + + +/* + * The function of the recursion formula calculation. + * + * @param[in] X1 the farthest part of state array. + * @param[in] X2 the second farthest part of state array. + * @param[in] Y a part of state array. + * @param[in] bid block id. + * @return output + */ +QUALIFIERS unsigned int para_rec(mtgp32_kernel_params_t * k,unsigned int X1, unsigned int X2, unsigned int Y, int bid) { + unsigned int X = (X1 & k->mask[0]) ^ X2; + unsigned int MAT; + + X ^= X << k->sh1_tbl[bid]; + Y = X ^ (Y >> k->sh2_tbl[bid]); + MAT = k->param_tbl[bid][Y & 0x0f]; + return Y ^ MAT; +} + +/* + * The tempering function. + * + * @param[in] V the output value should be tempered. + * @param[in] T the tempering helper value. + * @param[in] bid block id. + * @return the tempered value. + */ +QUALIFIERS unsigned int temper(mtgp32_kernel_params_t * k,unsigned int V, unsigned int T, int bid) { + unsigned int MAT; + + T ^= T >> 16; + T ^= T >> 8; + MAT = k->temper_tbl[bid][T & 0x0f]; + return V ^ MAT; +} + +/* + * The tempering and converting function. + * By using the preset table, converting to IEEE format + * and tempering are done simultaneously. + * + * @param[in] V the output value should be tempered. + * @param[in] T the tempering helper value. + * @param[in] bid block id. + * @return the tempered and converted value. + */ +QUALIFIERS unsigned int temper_single(mtgp32_kernel_params_t * k,unsigned int V, unsigned int T, int bid) { + unsigned int MAT; + unsigned int r; + + T ^= T >> 16; + T ^= T >> 8; + MAT = k->single_temper_tbl[bid][T & 0x0f]; + r = (V >> 9) ^ MAT; + return r; +} + +/** + * \brief Return 32-bits of pseudorandomness from a mtgp32 generator. + * + * Return 32-bits of pseudorandomness from the mtgp32 generator in \p state, + * increment position of generator by the number of threads in the block. + * Note the number of threads in the block can not exceed 256. + * + * \param state - Pointer to state to update + * + * \return 32-bits of pseudorandomness as an unsigned int, all bits valid to use. + */ +QUALIFIERS unsigned int curand(curandStateMtgp32_t *state) +{ + unsigned int t; + unsigned int d; + int pos = state->k->pos_tbl[state->pIdx]; + unsigned int r; + unsigned int o; + + d = blockDim.z * blockDim.y * blockDim.x; + //assert( d <= 256 ); + t = (blockDim.z * blockDim.y * threadIdx.z) + (blockDim.x * threadIdx.y) + threadIdx.x; + r = para_rec(state->k, state->s[(t + state->offset) & MTGP32_STATE_MASK], + state->s[(t + state->offset + 1) & MTGP32_STATE_MASK], + state->s[(t + state->offset + pos) & MTGP32_STATE_MASK], + state->pIdx); + + state->s[(t + state->offset + MTGPDC_N) & MTGP32_STATE_MASK] = r; + o = temper(state->k, r, + state->s[(t + state->offset + pos -1) & MTGP32_STATE_MASK], + state->pIdx); +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + if (t == 0) + { + state->offset = (state->offset + d) & MTGP32_STATE_MASK; + } +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + return o; + +} +/** + * \brief Return 32-bits of pseudorandomness from a specific position in a mtgp32 generator. + * + * Return 32-bits of pseudorandomness from position \p index of the mtgp32 generator in \p state, + * increment position of generator by \p n positions, which must be the total number of positions + * upddated in the state by the thread block, for this invocation. + * + * Note : + * Thread indices must range from 0...\ n - 1. + * The number of positions updated may not exceed 256. + * A thread block may update more than one state, but a given state may not be updated by more than one thread block. + * + * \param state - Pointer to state to update + * \param index - Index (0..255) of the position within the state to draw from and update + * \param n - The total number of postions in this state that are being updated by this invocation + * + * \return 32-bits of pseudorandomness as an unsigned int, all bits valid to use. + */ +QUALIFIERS unsigned int curand_mtgp32_specific(curandStateMtgp32_t *state, unsigned char index, unsigned char n) +{ + unsigned int t; + int pos = state->k->pos_tbl[state->pIdx]; + unsigned int r; + unsigned int o; + + t = index; + r = para_rec(state->k, state->s[(t + state->offset) & MTGP32_STATE_MASK], + state->s[(t + state->offset + 1) & MTGP32_STATE_MASK], + state->s[(t + state->offset + pos) & MTGP32_STATE_MASK], + state->pIdx); + + state->s[(t + state->offset + MTGPDC_N) & MTGP32_STATE_MASK] = r; + o = temper(state->k, r, + state->s[(t + state->offset + pos -1) & MTGP32_STATE_MASK], + state->pIdx); +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + if (index == 0) + { + state->offset = (state->offset + n) & MTGP32_STATE_MASK; + } +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + return o; +} +/** + * \brief Return a uniformly distributed float from a mtgp32 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the mtgp32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * Note: This alternate derivation of a uniform float is provided for completeness + * with the original source + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_mtgp32_single(curandStateMtgp32_t *state) +{ + unsigned int t; + unsigned int d; + int pos = state->k->pos_tbl[state->pIdx]; + unsigned int r; + unsigned int o_u; + float o_f; + + + t = blockDim.z * blockDim.y; + d = t * blockDim.x; + //assert( d <= 256 ); + t += threadIdx.x; + r = para_rec(state->k, state->s[(t + state->offset) & MTGP32_STATE_MASK], + state->s[(t + state->offset + 1) & MTGP32_STATE_MASK], + state->s[(t + state->offset + pos) & MTGP32_STATE_MASK], + state->pIdx); + + state->s[t] = r; + o_u = temper_single(state->k, r, + state->s[(t + state->offset + pos -1) & MTGP32_STATE_MASK], + state->pIdx); +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + if (threadIdx.x == 0) + { + state->offset = (state->offset + d) & MTGP32_STATE_MASK; + } +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + memcpy(&o_f, &o_u, sizeof(o_u)); + return o_f; +} + +/** + * \brief Return a uniformly distributed float from a specific position in a mtgp32 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from position \p index of the mtgp32 generator in \p state, and + * increment position of generator by \p n positions, which must be the total number of positions + * upddated in the state by the thread block, for this invocation. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * Note 1: + * Thread indices must range from 0...\p n - 1. + * The number of positions updated may not exceed 256. + * A thread block may update more than one state, but a given state may not be updated by more than one thread block. + * + * Note 2: This alternate derivation of a uniform float is provided for completeness + * with the original source + * + * \param state - Pointer to state to update + * \param index - Index (0..255) of the position within the state to draw from and update + * \param n - The total number of postions in this state that are being updated by this invocation + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_mtgp32_single_specific(curandStateMtgp32_t *state, unsigned char index, unsigned char n) +{ + unsigned int t; + int pos = state->k->pos_tbl[state->pIdx]; + unsigned int r; + unsigned int o_u; + float o_f; + + t = index; + r = para_rec(state->k, state->s[(t + state->offset) & MTGP32_STATE_MASK], + state->s[(t + state->offset + 1) & MTGP32_STATE_MASK], + state->s[(t + state->offset + pos) & MTGP32_STATE_MASK], + state->pIdx); + + state->s[t] = r; + o_u = temper_single(state->k, r, + state->s[(t + state->offset + pos -1) & MTGP32_STATE_MASK], + state->pIdx); +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + if (threadIdx.x == 0) + { + state->offset = (state->offset + n) & MTGP32_STATE_MASK; + } +NV_IF_TARGET(NV_IS_DEVICE, + __syncthreads(); +) + memcpy(&o_f, &o_u, sizeof(o_u)); + return o_f; +} + +/** @} */ + +#endif diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_normal.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_normal.h new file mode 100644 index 0000000000000000000000000000000000000000..e3c91001032acf253959df8b8a5464d038ee252b --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_normal.h @@ -0,0 +1,840 @@ + + /* Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + +#if !defined(CURAND_NORMAL_H_) +#define CURAND_NORMAL_H_ + +/** + * \defgroup DEVICE Device API + * + * @{ + */ + +#ifndef __CUDACC_RTC__ +#include +#endif // __CUDACC_RTC__ +#include + +#include "curand_mrg32k3a.h" +#include "curand_mtgp32_kernel.h" +#include "curand_philox4x32_x.h" +#include "curand_normal_static.h" + +QUALIFIERS float2 _curand_box_muller(unsigned int x, unsigned int y) +{ + float2 result; + float u = x * CURAND_2POW32_INV + (CURAND_2POW32_INV/2); + float v = y * CURAND_2POW32_INV_2PI + (CURAND_2POW32_INV_2PI/2); + float s; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + s = sqrtf(-2.0f * logf(u)); + __sincosf(v, &result.x, &result.y); +, + s = sqrtf(-2.0f * logf(u)); + result.x = sinf(v); + result.y = cosf(v); +) + result.x *= s; + result.y *= s; + return result; +} + +QUALIFIERS float2 curand_box_muller_mrg(curandStateMRG32k3a_t * state) +{ + float x, y; + x = curand_uniform(state); + y = curand_uniform(state) * CURAND_2PI; + float2 result; + float s; +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + s = sqrtf(-2.0f * logf(x)); + __sincosf(y, &result.x, &result.y); +, + s = sqrtf(-2.0f * logf(x)); + result.x = sinf(y); + result.y = cosf(y); +) + result.x *= s; + result.y *= s; + return result; +} + +QUALIFIERS double2 +_curand_box_muller_double(unsigned int x0, unsigned int x1, + unsigned int y0, unsigned int y1) +{ + double2 result; + unsigned long long zx = (unsigned long long)x0 ^ + ((unsigned long long)x1 << (53 - 32)); + double u = zx * CURAND_2POW53_INV_DOUBLE + (CURAND_2POW53_INV_DOUBLE/2.0); + unsigned long long zy = (unsigned long long)y0 ^ + ((unsigned long long)y1 << (53 - 32)); + double v = zy * (CURAND_2POW53_INV_DOUBLE*2.0) + CURAND_2POW53_INV_DOUBLE; + double s = sqrt(-2.0 * log(u)); + +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + sincospi(v, &result.x, &result.y); +, + result.x = sin(v*CURAND_PI_DOUBLE); + result.y = cos(v*CURAND_PI_DOUBLE); +) + result.x *= s; + result.y *= s; + + return result; +} + +QUALIFIERS double2 +curand_box_muller_mrg_double(curandStateMRG32k3a_t * state) +{ + double x, y; + double2 result; + x = curand_uniform_double(state); + y = curand_uniform_double(state) * 2.0; + + double s = sqrt(-2.0 * log(x)); +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + sincospi(y, &result.x, &result.y); +, + result.x = sin(y*CURAND_PI_DOUBLE); + result.y = cos(y*CURAND_PI_DOUBLE); +) + result.x *= s; + result.y *= s; + return result; +} + +template +QUALIFIERS float2 curand_box_muller(R *state) +{ + float2 result; + unsigned int x = curand(state); + unsigned int y = curand(state); + result = _curand_box_muller(x, y); + return result; +} + +template +QUALIFIERS float4 curand_box_muller4(R *state) +{ + float4 result; + float2 _result; + uint4 x = curand4(state); + //unsigned int y = curand(state); + _result = _curand_box_muller(x.x, x.y); + result.x = _result.x; + result.y = _result.y; + _result = _curand_box_muller(x.z, x.w); + result.z = _result.x; + result.w = _result.y; + return result; +} + +template +QUALIFIERS double2 curand_box_muller_double(R *state) +{ + double2 result; + unsigned int x0 = curand(state); + unsigned int x1 = curand(state); + unsigned int y0 = curand(state); + unsigned int y1 = curand(state); + result = _curand_box_muller_double(x0, x1, y0, y1); + return result; +} + +template +QUALIFIERS double2 curand_box_muller2_double(R *state) +{ + double2 result; + uint4 _x; + _x = curand4(state); + result = _curand_box_muller_double(_x.x, _x.y, _x.z, _x.w); + return result; +} + + +template +QUALIFIERS double4 curand_box_muller4_double(R *state) +{ + double4 result; + double2 _res1; + double2 _res2; + uint4 _x; + uint4 _y; + _x = curand4(state); + _y = curand4(state); + _res1 = _curand_box_muller_double(_x.x, _x.y, _x.z, _x.w); + _res2 = _curand_box_muller_double(_y.x, _y.y, _y.z, _y.w); + result.x = _res1.x; + result.y = _res1.y; + result.z = _res2.x; + result.w = _res2.y; + return result; +} + +//QUALIFIERS float _curand_normal_icdf(unsigned int x) +//{ +//#if __CUDA_ARCH__ > 0 || defined(HOST_HAVE_ERFCINVF) +// float s = CURAND_SQRT2; +// // Mirror to avoid loss of precision +// if(x > 0x80000000UL) { +// x = 0xffffffffUL - x; +// s = -s; +// } +// float p = x * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); +// // p is in (0, 0.5], 2p is in (0, 1] +// return s * erfcinvf(2.0f * p); +//#else +// x++; //suppress warnings +// return 0.0f; +//#endif +//} +// +//QUALIFIERS float _curand_normal_icdf(unsigned long long x) +//{ +//#if __CUDA_ARCH__ > 0 || defined(HOST_HAVE_ERFCINVF) +// unsigned int t = (unsigned int)(x >> 32); +// float s = CURAND_SQRT2; +// // Mirror to avoid loss of precision +// if(t > 0x80000000UL) { +// t = 0xffffffffUL - t; +// s = -s; +// } +// float p = t * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); +// // p is in (0, 0.5], 2p is in (0, 1] +// return s * erfcinvf(2.0f * p); +//#else +// x++; +// return 0.0f; +//#endif +//} +// +//QUALIFIERS double _curand_normal_icdf_double(unsigned int x) +//{ +//#if __CUDA_ARCH__ > 0 || defined(HOST_HAVE_ERFCINVF) +// double s = CURAND_SQRT2_DOUBLE; +// // Mirror to avoid loss of precision +// if(x > 0x80000000UL) { +// x = 0xffffffffUL - x; +// s = -s; +// } +// double p = x * CURAND_2POW32_INV_DOUBLE + (CURAND_2POW32_INV_DOUBLE/2.0); +// // p is in (0, 0.5], 2p is in (0, 1] +// return s * erfcinv(2.0 * p); +//#else +// x++; +// return 0.0; +//#endif +//} +// +//QUALIFIERS double _curand_normal_icdf_double(unsigned long long x) +//{ +//#if __CUDA_ARCH__ > 0 || defined(HOST_HAVE_ERFCINVF) +// double s = CURAND_SQRT2_DOUBLE; +// x >>= 11; +// // Mirror to avoid loss of precision +// if(x > 0x10000000000000UL) { +// x = 0x1fffffffffffffUL - x; +// s = -s; +// } +// double p = x * CURAND_2POW53_INV_DOUBLE + (CURAND_2POW53_INV_DOUBLE/2.0); +// // p is in (0, 0.5], 2p is in (0, 1] +// return s * erfcinv(2.0 * p); +//#else +// x++; +// return 0.0; +//#endif +//} +// + +/** + * \brief Return a normally distributed float from an XORWOW generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the XORWOW generator in \p state, + * increment position of generator by one. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateXORWOW_t *state) +{ + if(state->boxmuller_flag != EXTRA_FLAG_NORMAL) { + unsigned int x, y; + x = curand(state); + y = curand(state); + float2 v = _curand_box_muller(x, y); + state->boxmuller_extra = v.y; + state->boxmuller_flag = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag = 0; + return state->boxmuller_extra; +} + +/** + * \brief Return a normally distributed float from an Philox4_32_10 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the Philox4_32_10 generator in \p state, + * increment position of generator by one. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ + +QUALIFIERS float curand_normal(curandStatePhilox4_32_10_t *state) +{ + if(state->boxmuller_flag != EXTRA_FLAG_NORMAL) { + unsigned int x, y; + x = curand(state); + y = curand(state); + float2 v = _curand_box_muller(x, y); + state->boxmuller_extra = v.y; + state->boxmuller_flag = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag = 0; + return state->boxmuller_extra; +} + + + +/** + * \brief Return a normally distributed float from an MRG32k3a generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the MRG32k3a generator in \p state, + * increment position of generator by one. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateMRG32k3a_t *state) +{ + if(state->boxmuller_flag != EXTRA_FLAG_NORMAL) { + float2 v = curand_box_muller_mrg(state); + state->boxmuller_extra = v.y; + state->boxmuller_flag = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag = 0; + return state->boxmuller_extra; +} + +/** + * \brief Return two normally distributed floats from an XORWOW generator. + * + * Return two normally distributed floats with mean \p 0.0f and + * standard deviation \p 1.0f from the XORWOW generator in \p state, + * increment position of generator by two. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float2 where each element is from a + * distribution with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float2 curand_normal2(curandStateXORWOW_t *state) +{ + return curand_box_muller(state); +} +/** + * \brief Return two normally distributed floats from an Philox4_32_10 generator. + * + * Return two normally distributed floats with mean \p 0.0f and + * standard deviation \p 1.0f from the Philox4_32_10 generator in \p state, + * increment position of generator by two. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float2 where each element is from a + * distribution with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float2 curand_normal2(curandStatePhilox4_32_10_t *state) +{ + return curand_box_muller(state); +} + +/** + * \brief Return four normally distributed floats from an Philox4_32_10 generator. + * + * Return four normally distributed floats with mean \p 0.0f and + * standard deviation \p 1.0f from the Philox4_32_10 generator in \p state, + * increment position of generator by four. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float2 where each element is from a + * distribution with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float4 curand_normal4(curandStatePhilox4_32_10_t *state) +{ + return curand_box_muller4(state); +} + + + +/** + * \brief Return two normally distributed floats from an MRG32k3a generator. + * + * Return two normally distributed floats with mean \p 0.0f and + * standard deviation \p 1.0f from the MRG32k3a generator in \p state, + * increment position of generator by two. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float2 where each element is from a + * distribution with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float2 curand_normal2(curandStateMRG32k3a_t *state) +{ + return curand_box_muller_mrg(state); +} + +/** + * \brief Return a normally distributed float from a MTGP32 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the MTGP32 generator in \p state, + * increment position of generator. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateMtgp32_t *state) +{ + return _curand_normal_icdf(curand(state)); +} +/** + * \brief Return a normally distributed float from a Sobol32 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the Sobol32 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateSobol32_t *state) +{ + return _curand_normal_icdf(curand(state)); +} + +/** + * \brief Return a normally distributed float from a scrambled Sobol32 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the scrambled Sobol32 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateScrambledSobol32_t *state) +{ + return _curand_normal_icdf(curand(state)); +} + +/** + * \brief Return a normally distributed float from a Sobol64 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the Sobol64 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateSobol64_t *state) +{ + return _curand_normal_icdf(curand(state)); +} + +/** + * \brief Return a normally distributed float from a scrambled Sobol64 generator. + * + * Return a single normally distributed float with mean \p 0.0f and + * standard deviation \p 1.0f from the scrambled Sobol64 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed float with mean \p 0.0f and standard deviation \p 1.0f + */ +QUALIFIERS float curand_normal(curandStateScrambledSobol64_t *state) +{ + return _curand_normal_icdf(curand(state)); +} + +/** + * \brief Return a normally distributed double from an XORWOW generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the XORWOW generator in \p state, + * increment position of generator. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2_double() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateXORWOW_t *state) +{ + if(state->boxmuller_flag_double != EXTRA_FLAG_NORMAL) { + unsigned int x0, x1, y0, y1; + x0 = curand(state); + x1 = curand(state); + y0 = curand(state); + y1 = curand(state); + double2 v = _curand_box_muller_double(x0, x1, y0, y1); + state->boxmuller_extra_double = v.y; + state->boxmuller_flag_double = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag_double = 0; + return state->boxmuller_extra_double; +} + +/** + * \brief Return a normally distributed double from an Philox4_32_10 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the Philox4_32_10 generator in \p state, + * increment position of generator. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2_double() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ + +QUALIFIERS double curand_normal_double(curandStatePhilox4_32_10_t *state) +{ + if(state->boxmuller_flag_double != EXTRA_FLAG_NORMAL) { + uint4 _x; + _x = curand4(state); + double2 v = _curand_box_muller_double(_x.x, _x.y, _x.z, _x.w); + state->boxmuller_extra_double = v.y; + state->boxmuller_flag_double = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag_double = 0; + return state->boxmuller_extra_double; +} + + +/** + * \brief Return a normally distributed double from an MRG32k3a generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the XORWOW generator in \p state, + * increment position of generator. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results, then returns them one at a time. + * See ::curand_normal2_double() for a more efficient version that returns + * both results at once. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateMRG32k3a_t *state) +{ + if(state->boxmuller_flag_double != EXTRA_FLAG_NORMAL) { + double2 v = curand_box_muller_mrg_double(state); + state->boxmuller_extra_double = v.y; + state->boxmuller_flag_double = EXTRA_FLAG_NORMAL; + return v.x; + } + state->boxmuller_flag_double = 0; + return state->boxmuller_extra_double; +} + +/** + * \brief Return two normally distributed doubles from an XORWOW generator. + * + * Return two normally distributed doubles with mean \p 0.0 and + * standard deviation \p 1.0 from the XORWOW generator in \p state, + * increment position of generator by 2. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double2 where each element is from a + * distribution with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double2 curand_normal2_double(curandStateXORWOW_t *state) +{ + return curand_box_muller_double(state); +} + +/** + * \brief Return two normally distributed doubles from an Philox4_32_10 generator. + * + * Return two normally distributed doubles with mean \p 0.0 and + * standard deviation \p 1.0 from the Philox4_32_10 generator in \p state, + * increment position of generator by 2. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double2 where each element is from a + * distribution with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double2 curand_normal2_double(curandStatePhilox4_32_10_t *state) +{ + uint4 _x; + double2 result; + + _x = curand4(state); + double2 v1 = _curand_box_muller_double(_x.x, _x.y, _x.z, _x.w); + result.x = v1.x; + result.y = v1.y; + + return result; +} + + // not a part of API +QUALIFIERS double4 curand_normal4_double(curandStatePhilox4_32_10_t *state) +{ + uint4 _x; + uint4 _y; + double4 result; + + _x = curand4(state); + _y = curand4(state); + double2 v1 = _curand_box_muller_double(_x.x, _x.y, _x.z, _x.w); + double2 v2 = _curand_box_muller_double(_y.x, _y.y, _y.z, _y.w); + result.x = v1.x; + result.y = v1.y; + result.z = v2.x; + result.w = v2.y; + + return result; +} + + +/** + * \brief Return two normally distributed doubles from an MRG32k3a generator. + * + * Return two normally distributed doubles with mean \p 0.0 and + * standard deviation \p 1.0 from the MRG32k3a generator in \p state, + * increment position of generator. + * + * The implementation uses a Box-Muller transform to generate two + * normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double2 where each element is from a + * distribution with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double2 curand_normal2_double(curandStateMRG32k3a_t *state) +{ + return curand_box_muller_mrg_double(state); +} + +/** + * \brief Return a normally distributed double from an MTGP32 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the MTGP32 generator in \p state, + * increment position of generator. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateMtgp32_t *state) +{ + return _curand_normal_icdf_double(curand(state)); +} + +/** + * \brief Return a normally distributed double from an Sobol32 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the Sobol32 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateSobol32_t *state) +{ + return _curand_normal_icdf_double(curand(state)); +} + +/** + * \brief Return a normally distributed double from a scrambled Sobol32 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the scrambled Sobol32 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateScrambledSobol32_t *state) +{ + return _curand_normal_icdf_double(curand(state)); +} + +/** + * \brief Return a normally distributed double from a Sobol64 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the Sobol64 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateSobol64_t *state) +{ + return _curand_normal_icdf_double(curand(state)); +} + +/** + * \brief Return a normally distributed double from a scrambled Sobol64 generator. + * + * Return a single normally distributed double with mean \p 0.0 and + * standard deviation \p 1.0 from the scrambled Sobol64 generator in \p state, + * increment position of generator by one. + * + * The implementation uses the inverse cumulative distribution function + * to generate normally distributed results. + * + * \param state - Pointer to state to update + * + * \return Normally distributed double with mean \p 0.0 and standard deviation \p 1.0 + */ +QUALIFIERS double curand_normal_double(curandStateScrambledSobol64_t *state) +{ + return _curand_normal_icdf_double(curand(state)); +} +#endif // !defined(CURAND_NORMAL_H_) diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_poisson.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_poisson.h new file mode 100644 index 0000000000000000000000000000000000000000..7881194cb868be14a197b581d7c82bf9dd16d617 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_poisson.h @@ -0,0 +1,763 @@ + + /* Copyright 2010-2014 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + +#if !defined(CURAND_POISSON_H_) +#define CURAND_POISSON_H_ + +/** + * \defgroup DEVICE Device API + * + * @{ + */ + +#ifndef __CUDACC_RTC__ +#include +#endif // __CUDACC_RTC__ + +#include + +#include "curand_mrg32k3a.h" +#include "curand_mtgp32_kernel.h" +#include "curand_philox4x32_x.h" + +#define CR_CUDART_PI 3.1415926535897931e+0 +#define CR_CUDART_TWO_TO_52 4503599627370496.0 + + +QUALIFIERS float __cr_rsqrt(float a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm ("rsqrt.approx.f32.ftz %0, %1;" : "=f"(a) : "f"(a)); +, + a = 1.0f / sqrtf (a); +) + return a; +} + +QUALIFIERS float __cr_exp (float a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + a = a * 1.4426950408889634074; + asm ("ex2.approx.f32.ftz %0, %1;" : "=f"(a) : "f"(a)); +, + a = expf (a); +) + return a; +} + +QUALIFIERS float __cr_log (float a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm ("lg2.approx.f32.ftz %0, %1;" : "=f"(a) : "f"(a)); + a = a * 0.69314718055994530942; +, + a = logf (a); +) + return a; +} + +QUALIFIERS float __cr_rcp (float a) +{ +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + asm ("rcp.approx.f32.ftz %0, %1;" : "=f"(a) : "f"(a)); +, + a = 1.0f / a; +) + return a; +} + +/* Computes regularized gamma function: gammainc(a,x)/gamma(a) */ +QUALIFIERS float __cr_pgammainc (float a, float x) +{ + float t, alpha, beta; + + /* First level parametrization constants */ + float ma1 = 1.43248035075540910f, + ma2 = 0.12400979329415655f, + ma3 = 0.00025361074907033f, + mb1 = 0.21096734870196546f, + mb2 = 1.97381164089999420f, + mb3 = 0.94201734077887530f; + + /* Second level parametrization constants (depends only on a) */ + + alpha = __cr_rsqrt (a - ma2); + alpha = ma1 * alpha + ma3; + beta = __cr_rsqrt (a - mb2); + beta = mb1 * beta + mb3; + + /* Final approximation (depends on a and x) */ + + t = a - x; + t = alpha * t - beta; + t = 1.0f + __cr_exp (t); + t = t * t; + t = __cr_rcp (t); + + /* Negative a,x or a,x=NAN requires special handling */ + //t = !(x > 0 && a >= 0) ? 0.0 : t; + + return t; +} + +/* Computes inverse of pgammainc */ +QUALIFIERS float __cr_pgammaincinv (float a, float y) +{ + float t, alpha, beta; + + /* First level parametrization constants */ + + float ma1 = 1.43248035075540910f, + ma2 = 0.12400979329415655f, + ma3 = 0.00025361074907033f, + mb1 = 0.21096734870196546f, + mb2 = 1.97381164089999420f, + mb3 = 0.94201734077887530f; + + /* Second level parametrization constants (depends only on a) */ + + alpha = __cr_rsqrt (a - ma2); + alpha = ma1 * alpha + ma3; + beta = __cr_rsqrt (a - mb2); + beta = mb1 * beta + mb3; + + /* Final approximation (depends on a and y) */ + + t = __cr_rsqrt (y) - 1.0f; + t = __cr_log (t); + t = beta + t; + t = - t * __cr_rcp (alpha) + a; + /* Negative a,x or a,x=NAN requires special handling */ + //t = !(y > 0 && a >= 0) ? 0.0 : t; + return t; +} + +#if defined(__CUDACC_RDC__) && (__cplusplus >= 201703L) && defined(__cpp_inline_variables) +inline __constant__ double __cr_lgamma_table [] = { +#else +static __constant__ double __cr_lgamma_table [] = { +#endif + 0.000000000000000000e-1, + 0.000000000000000000e-1, + 6.931471805599453094e-1, + 1.791759469228055001e0, + 3.178053830347945620e0, + 4.787491742782045994e0, + 6.579251212010100995e0, + 8.525161361065414300e0, + 1.060460290274525023e1 +}; + + +QUALIFIERS double __cr_lgamma_integer(int a) +{ + double s; + double t; + double fa = fabs((float)a); + double sum; + + if (a > 8) { + /* Stirling approximation; coefficients from Hart et al, "Computer + * Approximations", Wiley 1968. Approximation 5404. + */ + s = 1.0 / fa; + t = s * s; + sum = -0.1633436431e-2; + sum = sum * t + 0.83645878922e-3; + sum = sum * t - 0.5951896861197e-3; + sum = sum * t + 0.793650576493454e-3; + sum = sum * t - 0.277777777735865004e-2; + sum = sum * t + 0.833333333333331018375e-1; + sum = sum * s + 0.918938533204672; + s = 0.5 * log (fa); + t = fa - 0.5; + s = s * t; + t = s - fa; + s = s + sum; + t = t + s; + return t; + } else { +NV_IF_ELSE_TARGET(NV_IS_DEVICE, + return __cr_lgamma_table [(int) fa-1]; +, + switch(a) { + case 1: return 0.000000000000000000e-1; + case 2: return 0.000000000000000000e-1; + case 3: return 6.931471805599453094e-1; + case 4: return 1.791759469228055001e0; + case 5: return 3.178053830347945620e0; + case 6: return 4.787491742782045994e0; + case 7: return 6.579251212010100995e0; + case 8: return 8.525161361065414300e0; + default: return 1.060460290274525023e1; + } +) + } +} + +#define KNUTH_FLOAT_CONST 60.0 +template +// Donald E. Knuth Seminumerical Algorithms. The Art of Computer Programming, Volume 2 +QUALIFIERS unsigned int curand_poisson_knuth(T *state, float lambda) +{ + unsigned int k = 0; + float p = expf(lambda); + do{ + k++; + p *= curand_uniform(state); + }while (p > 1.0); + return k-1; +} + +template +// Donald E. Knuth Seminumerical Algorithms. The Art of Computer Programming, Volume 2 +QUALIFIERS uint4 curand_poisson_knuth4(T *state, float lambda) +{ + uint4 k = {0,0,0,0}; + float exp_lambda = expf(lambda); + float4 p={ exp_lambda,exp_lambda,exp_lambda,exp_lambda }; + do{ + k.x++; + p.x *= curand_uniform(state); + }while (p.x > 1.0); + do{ + k.y++; + p.y *= curand_uniform(state); + }while (p.y > 1.0); + do{ + k.z++; + p.z *= curand_uniform(state); + }while (p.z > 1.0); + do{ + k.w++; + p.w *= curand_uniform(state); + }while (p.w > 1.0); + + k.x--; + k.y--; + k.z--; + k.w--; + return k; +} + +template +// Marsaglia, Tsang, Wang Journal of Statistical Software, square histogram. +QUALIFIERS unsigned int _curand_M2_double(T x, curandDistributionM2Shift_t distributionM2) +{ + double u = _curand_uniform_double(x); + int j = (int) floor(distributionM2->length*u); + + double histogramVj; + unsigned int histogramKj; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_35, + histogramVj = __ldg( &(distributionM2->histogram->V[j])); + histogramKj = __ldg( &(distributionM2->histogram->K[j])); +, + histogramVj = distributionM2->histogram->V[j]; + histogramKj = distributionM2->histogram->K[j]; +) + //if (u < distributionM2->histogram->V[j]) return distributionM2->shift + j; + //return distributionM2->shift + distributionM2->histogram->K[j]; + if (u < histogramVj) return distributionM2->shift + j; + return distributionM2->shift + histogramKj; +} + +template +// Marsaglia, Tsang, Wang Journal of Statistical Software, square histogram. +QUALIFIERS uint4 _curand_M2_double4(T x, curandDistributionM2Shift_t distributionM2) +{ + double4 u; + uint4 result = {0,0,0,0}; + int4 flag = {1,1,1,1}; + + u.x = _curand_uniform_double(x.x); + u.y = _curand_uniform_double(x.y); + u.z = _curand_uniform_double(x.z); + u.w = _curand_uniform_double(x.w); + + int4 j; + j.x = (int) floor(distributionM2->length*u.x); + j.y = (int) floor(distributionM2->length*u.y); + j.z = (int) floor(distributionM2->length*u.z); + j.w = (int) floor(distributionM2->length*u.w); +// int result; + + double histogramVjx; + double histogramVjy; + double histogramVjz; + double histogramVjw; + unsigned int histogramKjx; + unsigned int histogramKjy; + unsigned int histogramKjz; + unsigned int histogramKjw; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_35, + histogramVjx = __ldg( &(distributionM2->histogram->V[j.x])); + histogramVjy = __ldg( &(distributionM2->histogram->V[j.y])); + histogramVjz = __ldg( &(distributionM2->histogram->V[j.z])); + histogramVjw = __ldg( &(distributionM2->histogram->V[j.w])); + + histogramKjx = __ldg( &(distributionM2->histogram->K[j.x])); + histogramKjy = __ldg( &(distributionM2->histogram->K[j.y])); + histogramKjz = __ldg( &(distributionM2->histogram->K[j.z])); + histogramKjw = __ldg( &(distributionM2->histogram->K[j.w])); +, + histogramVjx = distributionM2->histogram->V[j.x]; + histogramVjy = distributionM2->histogram->V[j.y]; + histogramVjz = distributionM2->histogram->V[j.z]; + histogramVjw = distributionM2->histogram->V[j.w]; + + histogramKjx = distributionM2->histogram->K[j.x]; + histogramKjy = distributionM2->histogram->K[j.y]; + histogramKjz = distributionM2->histogram->K[j.z]; + histogramKjw = distributionM2->histogram->K[j.w]; +) + + if (u.x < histogramVjx){ result.x = distributionM2->shift + j.x; flag.x = 0; } + if (u.y < histogramVjy){ result.y = distributionM2->shift + j.y; flag.y = 0; } + if (u.z < histogramVjz){ result.z = distributionM2->shift + j.z; flag.z = 0; } + if (u.w < histogramVjw){ result.w = distributionM2->shift + j.w; flag.w = 0; } + //return distributionM2->shift + distributionM2->histogram->K[j]; + + if(flag.x) result.x = distributionM2->shift + histogramKjx; + if(flag.y) result.y = distributionM2->shift + histogramKjy; + if(flag.z) result.z = distributionM2->shift + histogramKjz; + if(flag.w) result.w = distributionM2->shift + histogramKjw; + + return result; +} + +template +QUALIFIERS unsigned int curand_M2_double(STATE *state, curandDistributionM2Shift_t distributionM2) +{ + return _curand_M2_double(curand(state), distributionM2); +} + +template +QUALIFIERS uint4 curand_M2_double4(STATE *state, curandDistributionM2Shift_t distributionM2) +{ + return _curand_M2_double4(curand4(state), distributionM2); +} + + +template +QUALIFIERS unsigned int _curand_binary_search_double(T x, curandDistributionShift_t distribution) +{ + double u = _curand_uniform_double(x); + int min = 0; + int max = distribution->length-1; + do{ + int mid = (max + min)/2; + double probability_mid; +NV_IF_ELSE_TARGET(NV_PROVIDES_SM_35, + probability_mid = __ldg( &(distribution->probability[mid])); +, + probability_mid = distribution->probability[mid]; +) + if (u <= probability_mid){ + max = mid; + }else{ + min = mid+1; + } + }while (min < max); + return distribution->shift + min; +} + +template +QUALIFIERS unsigned int curand_binary_search_double(STATE *state, curandDistributionShift_t distribution) +{ + return _curand_binary_search_double(curand(state), distribution); +} + +// Generates uniformly distributed double values in range (0.0; 1.0) from uniformly distributed +// unsigned int. We can't use standard _curand_uniform_double since it can generate 1.0. +// This is required only for _curand_poisson_ITR_double. +QUALIFIERS double _curand_uniform_double_excluding_one(unsigned int x) +{ + return x * CURAND_2POW32_INV_DOUBLE + (CURAND_2POW32_INV_DOUBLE/2.0); +} + +// Overload for unsigned long long. +// This is required only for _curand_poisson_ITR_double. +QUALIFIERS double _curand_uniform_double_excluding_one(unsigned long long x) +{ + return (x >> 11) * CURAND_2POW53_INV_DOUBLE + (CURAND_2POW53_INV_DOUBLE/4.0); +} + +#define MAGIC_DOUBLE_CONST 500.0 +template +//George S. Fishman Discrete-event simulation: modeling, programming, and analysis +QUALIFIERS unsigned int _curand_poisson_ITR_double(T x, double lambda) +{ + double L,p = 1.0; + double q = 1.0; + unsigned int k = 0; + int pow=0; + // This algorithm requires u to be in (0;1) range, however, _curand_uniform_double + // returns a number in range (0;1]. If u is 1.0 the inner loop never ends. The + // following operation transforms the range from (0;1] to (0;1). + double u = _curand_uniform_double_excluding_one(x); + do{ + if (lambda > (double)(pow+MAGIC_DOUBLE_CONST)){ + L = exp(-MAGIC_DOUBLE_CONST); + }else{ + L = exp((double)(pow - lambda)); + } + p *= L; + q *= L; + pow += (int) MAGIC_DOUBLE_CONST; + while (u > q){ + k++; + p *= ((double)lambda / (double) k); + q += p; + } + }while((double)pow < lambda); + return k; +} + +template +/* Rejection Method for Poisson distribution based on gammainc approximation */ +QUALIFIERS unsigned int curand_poisson_gammainc(T state, float lambda){ + float y, x, t, z,v; + float logl = __cr_log (lambda); + while (true) { + y = curand_uniform (state); + x = __cr_pgammaincinv (lambda, y); + x = floorf (x); + z = curand_uniform (state); + v = (__cr_pgammainc (lambda, x + 1.0f) - __cr_pgammainc (lambda, x)) * 1.3f; + z = z*v; + t = (float)__cr_exp (-lambda + x * logl - (float)__cr_lgamma_integer ((int)(1.0f + x))); + if ((z < t) && (v>=1e-20)) + break; + } + return (unsigned int)x; +} + +template +/* Rejection Method for Poisson distribution based on gammainc approximation */ +QUALIFIERS uint4 curand_poisson_gammainc4(T state, float lambda){ + uint4 result; + float y, x, t, z,v; + float logl = __cr_log (lambda); + while (true) { + y = curand_uniform(state); + x = __cr_pgammaincinv (lambda, y); + x = floorf (x); + z = curand_uniform (state); + v = (__cr_pgammainc (lambda, x + 1.0f) - __cr_pgammainc (lambda, x)) * 1.3f; + z = z*v; + t = (float)__cr_exp (-lambda + x * logl - (float)__cr_lgamma_integer ((int)(1.0f + x))); + if ((z < t) && (v>=1e-20)) + break; + } + result.x = (unsigned int)x; + + while (true) { + y = curand_uniform(state); + x = __cr_pgammaincinv (lambda, y); + x = floorf (x); + z = curand_uniform (state); + v = (__cr_pgammainc (lambda, x + 1.0f) - __cr_pgammainc (lambda, x)) * 1.3f; + z = z*v; + t = (float)__cr_exp (-lambda + x * logl - (float)__cr_lgamma_integer ((int)(1.0f + x))); + if ((z < t) && (v>=1e-20)) + break; + } + result.y = (unsigned int)x; + + while (true) { + y = curand_uniform(state); + x = __cr_pgammaincinv (lambda, y); + x = floorf (x); + z = curand_uniform (state); + v = (__cr_pgammainc (lambda, x + 1.0f) - __cr_pgammainc (lambda, x)) * 1.3f; + z = z*v; + t = (float)__cr_exp (-lambda + x * logl - (float)__cr_lgamma_integer ((int)(1.0f + x))); + if ((z < t) && (v>=1e-20)) + break; + } + result.z = (unsigned int)x; + + while (true) { + y = curand_uniform(state); + x = __cr_pgammaincinv (lambda, y); + x = floorf (x); + z = curand_uniform (state); + v = (__cr_pgammainc (lambda, x + 1.0f) - __cr_pgammainc (lambda, x)) * 1.3f; + z = z*v; + t = (float)__cr_exp (-lambda + x * logl - (float)__cr_lgamma_integer ((int)(1.0f + x))); + if ((z < t) && (v>=1e-20)) + break; + } + result.w = (unsigned int)x; + + return result; +} +// Note below that the round to nearest integer, where needed,is done in line with code that +// assumes the range of values is < 2**32 + +template +QUALIFIERS unsigned int _curand_poisson(T x, double lambda) +{ + if (lambda < 1000) + return _curand_poisson_ITR_double(x, lambda); + return (unsigned int)((sqrt(lambda) * _curand_normal_icdf_double(x)) + lambda + 0.5); //Round to nearest +} + +template +QUALIFIERS unsigned int _curand_poisson_from_normal(T x, double lambda) +{ + return (unsigned int)((sqrt(lambda) * _curand_normal_icdf(x)) + lambda + 0.5); //Round to nearest +} + +template +QUALIFIERS unsigned int curand_poisson_from_normal(STATE state, double lambda) +{ + return (unsigned int)((sqrt(lambda) * curand_normal(state)) + lambda + 0.5); //Round to nearest +} + +template +QUALIFIERS uint4 curand_poisson_from_normal4(STATE state, double lambda) +{ + uint4 result; + float4 _res; + + _res = curand_normal4(state); + + result.x = (unsigned int)((sqrt(lambda) * _res.x) + lambda + 0.5); //Round to nearest + result.y = (unsigned int)((sqrt(lambda) * _res.y) + lambda + 0.5); //Round to nearest + result.z = (unsigned int)((sqrt(lambda) * _res.z) + lambda + 0.5); //Round to nearest + result.w = (unsigned int)((sqrt(lambda) * _res.w) + lambda + 0.5); //Round to nearest + return result; //Round to nearest +} + +/** + * \brief Return a Poisson-distributed unsigned int from a XORWOW generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the XORWOW generator in \p state, + * increment the position of the generator by a variable amount, depending + * on the algorithm used. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateXORWOW_t *state, double lambda) +{ + if (lambda < 64) + return curand_poisson_knuth(state, (float)lambda); + if (lambda > 4000) + return (unsigned int)((sqrt(lambda) * curand_normal_double(state)) + lambda + 0.5); //Round to nearest + return curand_poisson_gammainc(state, (float)lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a Philox4_32_10 generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the Philox4_32_10 generator in \p state, + * increment the position of the generator by a variable amount, depending + * on the algorithm used. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStatePhilox4_32_10_t *state, double lambda) +{ + if (lambda < 64) + return curand_poisson_knuth(state, (float)lambda); + if (lambda > 4000) + return (unsigned int)((sqrt(lambda) * curand_normal_double(state)) + lambda + 0.5); //Round to nearest + return curand_poisson_gammainc(state, (float)lambda); +} +/** + * \brief Return four Poisson-distributed unsigned ints from a Philox4_32_10 generator. + * + * Return a four unsigned ints from a Poisson + * distribution with lambda \p lambda from the Philox4_32_10 generator in \p state, + * increment the position of the generator by a variable amount, depending + * on the algorithm used. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS uint4 curand_poisson4(curandStatePhilox4_32_10_t *state, double lambda) +{ + uint4 result; + double4 _res; + if (lambda < 64) + return curand_poisson_knuth4(state, (float)lambda); + if (lambda > 4000) { + _res = curand_normal4_double(state); + result.x = (unsigned int)((sqrt(lambda) * _res.x) + lambda + 0.5); //Round to nearest + result.y = (unsigned int)((sqrt(lambda) * _res.y) + lambda + 0.5); //Round to nearest + result.z = (unsigned int)((sqrt(lambda) * _res.z) + lambda + 0.5); //Round to nearest + result.w = (unsigned int)((sqrt(lambda) * _res.w) + lambda + 0.5); //Round to nearest + return result; + } + return curand_poisson_gammainc4(state, (float)lambda); +} + + + +/** + * \brief Return a Poisson-distributed unsigned int from a MRG32k3A generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the MRG32k3a generator in \p state, + * increment the position of the generator by a variable amount, depending + * on the algorithm used. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateMRG32k3a_t *state, double lambda) +{ + if (lambda < 64) + return curand_poisson_knuth(state, (float)lambda); + if (lambda > 4000) + return (unsigned int)((sqrt(lambda) * curand_normal_double(state)) + lambda + 0.5); //Round to nearest + return curand_poisson_gammainc(state, (float)lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a MTGP32 generator. + * + * Return a single int from a Poisson + * distribution with lambda \p lambda from the MTGP32 generator in \p state, + * increment the position of the generator by one. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateMtgp32_t *state, double lambda) +{ + return _curand_poisson(curand(state), lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a Sobol32 generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the Sobol32 generator in \p state, + * increment the position of the generator by one. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ + +QUALIFIERS unsigned int curand_poisson(curandStateSobol32_t *state, double lambda) +{ + return _curand_poisson(curand(state), lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a scrambled Sobol32 generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the scrambled Sobol32 generator in \p state, + * increment the position of the generator by one. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateScrambledSobol32_t *state, double lambda) +{ + return _curand_poisson(curand(state), lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a Sobol64 generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the Sobol64 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateSobol64_t *state, double lambda) +{ + return _curand_poisson(curand(state), lambda); +} + +/** + * \brief Return a Poisson-distributed unsigned int from a scrambled Sobol64 generator. + * + * Return a single unsigned int from a Poisson + * distribution with lambda \p lambda from the scrambled Sobol64 generator in \p state, + * increment position of generator by one. + * + * \param state - Pointer to state to update + * \param lambda - Lambda of the Poisson distribution + * + * \return Poisson-distributed unsigned int with lambda \p lambda + */ +QUALIFIERS unsigned int curand_poisson(curandStateScrambledSobol64_t *state, double lambda) +{ + return _curand_poisson(curand(state), lambda); +} +#endif // !defined(CURAND_POISSON_H_) diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_precalc.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_precalc.h new file mode 100644 index 0000000000000000000000000000000000000000..01818fb642856eb09f7e3fa0b8202d34c37c8566 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_precalc.h @@ -0,0 +1,3548 @@ +/* Copyright 2010-2012 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ +#if !defined(CURAND_XORWOW_PRECALCULATED_H_) +#define CURAND_XORWOW_PRECALCULATED_H_ + +#define PRECALC_NUM_MATRICES (32) +#define PRECALC_BLOCK_SIZE (2) +#define PRECALC_BLOCK_MASK ((1<= 201703L) && defined(__cpp_inline_variables) +#define CURAND_XORWOW_PRECALCULATED_DEVICE_QUALIFIERS inline __device__ +#else +#define CURAND_XORWOW_PRECALCULATED_DEVICE_QUALIFIERS static __device__ +#endif + +#if (__cplusplus >= 201703L) && defined(__cpp_inline_variables) +#define CURAND_XORWOW_PRECALCULATED_HOST_QUALIFIERS inline +#else +#define CURAND_XORWOW_PRECALCULATED_HOST_QUALIFIERS static +#endif +CURAND_XORWOW_PRECALCULATED_DEVICE_QUALIFIERS unsigned int precalc_xorwow_matrix[32][800] = { +{ +850664906UL, 2293210629UL, 1517805917UL, 1215500405UL, 1612415445UL, 645388200UL, 824349799UL, 3517232886UL, 4075591755UL, 3089899292UL, 4249786064UL, 3811424903UL, 1100783479UL, 53649761UL, 2817264826UL, 3159462529UL, 1654848550UL, 950025444UL, 3095510002UL, 4080567211UL, 4111078399UL, 3241719305UL, 2788212779UL, 4256963770UL, 2426893717UL, 4190211142UL, 1420776905UL, 3780537969UL, 1102912875UL, 1657948873UL, 3354905256UL, 2519610308UL, +515777663UL, 3396785394UL, 1832603711UL, 1154211550UL, 1915690212UL, 1933919046UL, 789578337UL, 337961173UL, 1359089498UL, 2249086205UL, 3417955173UL, 862571348UL, 528120760UL, 1265685672UL, 1970052076UL, 3585976752UL, 3645339918UL, 312171257UL, 1360991400UL, 1994321680UL, 2327168468UL, 2540437053UL, 1180483641UL, 2217962701UL, 182726833UL, 590204372UL, 1904496495UL, 2545607041UL, 3697978033UL, 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2375539210UL, 557544627UL, +273611522UL, 2717517554UL, 1935966767UL, 1738732887UL, 29153600UL, 20993454UL, 3758163226UL, 1692844400UL, 2176938194UL, 378940221UL, 2888599759UL, 1173120554UL, 2732575460UL, 3912766812UL, 522606644UL, 1925230852UL, 3887440328UL, 2111843275UL, 3549473366UL, 922916775UL, 2889744544UL, 2970467682UL, 3039277863UL, 990580154UL, 55435595UL, 1665634070UL, 3043418336UL, 2792050230UL, 2762503138UL, 1402344059UL, 2099263558UL, 3945248675UL, +3925566467UL, 2413979948UL, 463637252UL, 3768636616UL, 3374572388UL, 2217956879UL, 791988933UL, 382210765UL, 1715859444UL, 3462446413UL, 971427992UL, 3255404695UL, 2001750035UL, 2214129237UL, 320812374UL, 3688098101UL, 920365480UL, 2819401059UL, 2932570681UL, 3749857130UL, 523943786UL, 1271514748UL, 4078439472UL, 3501181265UL, 2475869985UL, 1797996951UL, 2300820710UL, 3994893924UL, 1739992082UL, 2475950326UL, 3780826558UL, 1018851411UL, +}, + +}; +#ifndef __CUDACC_RTC__ +CURAND_XORWOW_PRECALCULATED_HOST_QUALIFIERS unsigned int precalc_xorwow_matrix_host[32][800] = { +{ +850664906UL, 2293210629UL, 1517805917UL, 1215500405UL, 1612415445UL, 645388200UL, 824349799UL, 3517232886UL, 4075591755UL, 3089899292UL, 4249786064UL, 3811424903UL, 1100783479UL, 53649761UL, 2817264826UL, 3159462529UL, 1654848550UL, 950025444UL, 3095510002UL, 4080567211UL, 4111078399UL, 3241719305UL, 2788212779UL, 4256963770UL, 2426893717UL, 4190211142UL, 1420776905UL, 3780537969UL, 1102912875UL, 1657948873UL, 3354905256UL, 2519610308UL, +515777663UL, 3396785394UL, 1832603711UL, 1154211550UL, 1915690212UL, 1933919046UL, 789578337UL, 337961173UL, 1359089498UL, 2249086205UL, 3417955173UL, 862571348UL, 528120760UL, 1265685672UL, 1970052076UL, 3585976752UL, 3645339918UL, 312171257UL, 1360991400UL, 1994321680UL, 2327168468UL, 2540437053UL, 1180483641UL, 2217962701UL, 182726833UL, 590204372UL, 1904496495UL, 2545607041UL, 3697978033UL, 1084030545UL, 3397906968UL, 2192325323UL, +2704204176UL, 1069092002UL, 2364406907UL, 1578647245UL, 3561974633UL, 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20993454UL, 3758163226UL, 1692844400UL, 2176938194UL, 378940221UL, 2888599759UL, 1173120554UL, 2732575460UL, 3912766812UL, 522606644UL, 1925230852UL, 3887440328UL, 2111843275UL, 3549473366UL, 922916775UL, 2889744544UL, 2970467682UL, 3039277863UL, 990580154UL, 55435595UL, 1665634070UL, 3043418336UL, 2792050230UL, 2762503138UL, 1402344059UL, 2099263558UL, 3945248675UL, +3925566467UL, 2413979948UL, 463637252UL, 3768636616UL, 3374572388UL, 2217956879UL, 791988933UL, 382210765UL, 1715859444UL, 3462446413UL, 971427992UL, 3255404695UL, 2001750035UL, 2214129237UL, 320812374UL, 3688098101UL, 920365480UL, 2819401059UL, 2932570681UL, 3749857130UL, 523943786UL, 1271514748UL, 4078439472UL, 3501181265UL, 2475869985UL, 1797996951UL, 2300820710UL, 3994893924UL, 1739992082UL, 2475950326UL, 3780826558UL, 1018851411UL, +}, + +}; +#endif +CURAND_XORWOW_PRECALCULATED_DEVICE_QUALIFIERS unsigned int precalc_xorwow_offset_matrix[32][800] = { +{ +0UL, 0UL, 0UL, 0UL, 3UL, 0UL, 0UL, 0UL, 0UL, 6UL, 0UL, 0UL, 0UL, 0UL, 15UL, 0UL, 0UL, 0UL, 0UL, 30UL, 0UL, 0UL, 0UL, 0UL, 60UL, 0UL, 0UL, 0UL, 0UL, 120UL, 0UL, 0UL, +0UL, 0UL, 240UL, 0UL, 0UL, 0UL, 0UL, 480UL, 0UL, 0UL, 0UL, 0UL, 960UL, 0UL, 0UL, 0UL, 0UL, 1920UL, 0UL, 0UL, 0UL, 0UL, 3840UL, 0UL, 0UL, 0UL, 0UL, 7680UL, 0UL, 0UL, 0UL, 0UL, +15360UL, 0UL, 0UL, 0UL, 0UL, 30720UL, 0UL, 0UL, 0UL, 0UL, 61440UL, 0UL, 0UL, 0UL, 0UL, 122880UL, 0UL, 0UL, 0UL, 0UL, 245760UL, 0UL, 0UL, 0UL, 0UL, 491520UL, 0UL, 0UL, 0UL, 0UL, 983040UL, 0UL, +0UL, 0UL, 0UL, 1966080UL, 0UL, 0UL, 0UL, 0UL, 3932160UL, 0UL, 0UL, 0UL, 0UL, 7864320UL, 0UL, 0UL, 0UL, 0UL, 15728640UL, 0UL, 0UL, 0UL, 0UL, 31457280UL, 0UL, 0UL, 0UL, 0UL, 62914560UL, 0UL, 0UL, 0UL, +0UL, 125829120UL, 0UL, 0UL, 0UL, 0UL, 251658240UL, 0UL, 0UL, 0UL, 0UL, 503316480UL, 0UL, 0UL, 0UL, 0UL, 1006632960UL, 0UL, 0UL, 0UL, 0UL, 2013265920UL, 0UL, 0UL, 0UL, 0UL, 4026531840UL, 0UL, 0UL, 0UL, 0UL, 3758096384UL, +1UL, 0UL, 0UL, 0UL, 0UL, 2UL, 0UL, 0UL, 0UL, 0UL, 4UL, 0UL, 0UL, 0UL, 0UL, 8UL, 0UL, 0UL, 0UL, 0UL, 16UL, 0UL, 0UL, 0UL, 0UL, 32UL, 0UL, 0UL, 0UL, 0UL, 64UL, 0UL, +0UL, 0UL, 0UL, 128UL, 0UL, 0UL, 0UL, 0UL, 256UL, 0UL, 0UL, 0UL, 0UL, 512UL, 0UL, 0UL, 0UL, 0UL, 1024UL, 0UL, 0UL, 0UL, 0UL, 2048UL, 0UL, 0UL, 0UL, 0UL, 4096UL, 0UL, 0UL, 0UL, +0UL, 8192UL, 0UL, 0UL, 0UL, 0UL, 16384UL, 0UL, 0UL, 0UL, 0UL, 32768UL, 0UL, 0UL, 0UL, 0UL, 65536UL, 0UL, 0UL, 0UL, 0UL, 131072UL, 0UL, 0UL, 0UL, 0UL, 262144UL, 0UL, 0UL, 0UL, 0UL, 524288UL, +0UL, 0UL, 0UL, 0UL, 1048576UL, 0UL, 0UL, 0UL, 0UL, 2097152UL, 0UL, 0UL, 0UL, 0UL, 4194304UL, 0UL, 0UL, 0UL, 0UL, 8388608UL, 0UL, 0UL, 0UL, 0UL, 16777216UL, 0UL, 0UL, 0UL, 0UL, 33554432UL, 0UL, 0UL, +0UL, 0UL, 67108864UL, 0UL, 0UL, 0UL, 0UL, 134217728UL, 0UL, 0UL, 0UL, 0UL, 268435456UL, 0UL, 0UL, 0UL, 0UL, 536870912UL, 0UL, 0UL, 0UL, 0UL, 1073741824UL, 0UL, 0UL, 0UL, 0UL, 2147483648UL, 0UL, 0UL, 0UL, 0UL, +0UL, 1UL, 0UL, 0UL, 0UL, 0UL, 2UL, 0UL, 0UL, 0UL, 0UL, 4UL, 0UL, 0UL, 0UL, 0UL, 8UL, 0UL, 0UL, 0UL, 0UL, 16UL, 0UL, 0UL, 0UL, 0UL, 32UL, 0UL, 0UL, 0UL, 0UL, 64UL, 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0UL, 0UL, 0UL, 0UL, 512UL, 0UL, 0UL, 0UL, 0UL, 1024UL, 0UL, 0UL, 0UL, 0UL, 2048UL, 0UL, 0UL, 0UL, 0UL, 4096UL, 0UL, +0UL, 0UL, 0UL, 8192UL, 0UL, 0UL, 0UL, 0UL, 16384UL, 0UL, 0UL, 0UL, 0UL, 32768UL, 0UL, 0UL, 0UL, 0UL, 65536UL, 0UL, 0UL, 0UL, 0UL, 131072UL, 0UL, 0UL, 0UL, 0UL, 262144UL, 0UL, 0UL, 0UL, +0UL, 524288UL, 0UL, 0UL, 0UL, 0UL, 1048576UL, 0UL, 0UL, 0UL, 0UL, 2097152UL, 0UL, 0UL, 0UL, 0UL, 4194304UL, 0UL, 0UL, 0UL, 0UL, 8388608UL, 0UL, 0UL, 0UL, 0UL, 16777216UL, 0UL, 0UL, 0UL, 0UL, 33554432UL, +0UL, 0UL, 0UL, 0UL, 67108864UL, 0UL, 0UL, 0UL, 0UL, 134217728UL, 0UL, 0UL, 0UL, 0UL, 268435456UL, 0UL, 0UL, 0UL, 0UL, 536870912UL, 0UL, 0UL, 0UL, 0UL, 1073741824UL, 0UL, 0UL, 0UL, 0UL, 2147483648UL, 0UL, 0UL, +0UL, 0UL, 0UL, 1UL, 17UL, 0UL, 0UL, 0UL, 2UL, 34UL, 0UL, 0UL, 0UL, 4UL, 68UL, 0UL, 0UL, 0UL, 8UL, 136UL, 0UL, 0UL, 0UL, 16UL, 272UL, 0UL, 0UL, 0UL, 32UL, 544UL, 0UL, 0UL, +0UL, 64UL, 1088UL, 0UL, 0UL, 0UL, 128UL, 2176UL, 0UL, 0UL, 0UL, 256UL, 4352UL, 0UL, 0UL, 0UL, 512UL, 8704UL, 0UL, 0UL, 0UL, 1024UL, 17408UL, 0UL, 0UL, 0UL, 2048UL, 34816UL, 0UL, 0UL, 0UL, 4096UL, +69632UL, 0UL, 0UL, 0UL, 8192UL, 139264UL, 0UL, 0UL, 0UL, 16384UL, 278528UL, 0UL, 0UL, 0UL, 32768UL, 557056UL, 0UL, 0UL, 0UL, 65536UL, 1114112UL, 0UL, 0UL, 0UL, 131072UL, 2228224UL, 0UL, 0UL, 0UL, 262144UL, 4456448UL, 0UL, +0UL, 0UL, 524288UL, 8912896UL, 0UL, 0UL, 0UL, 1048576UL, 17825792UL, 0UL, 0UL, 0UL, 2097152UL, 35651584UL, 0UL, 0UL, 0UL, 4194304UL, 71303168UL, 0UL, 0UL, 0UL, 8388608UL, 142606336UL, 0UL, 0UL, 0UL, 16777216UL, 285212672UL, 0UL, 0UL, 0UL, +33554432UL, 570425344UL, 0UL, 0UL, 0UL, 67108864UL, 1140850688UL, 0UL, 0UL, 0UL, 134217728UL, 2281701376UL, 0UL, 0UL, 0UL, 268435456UL, 268435456UL, 0UL, 0UL, 0UL, 536870912UL, 536870912UL, 0UL, 0UL, 0UL, 1073741824UL, 1073741824UL, 0UL, 0UL, 0UL, 2147483648UL, 2147483648UL, +}, +{ +0UL, 3UL, 51UL, 771UL, 13107UL, 0UL, 6UL, 102UL, 1542UL, 26214UL, 0UL, 15UL, 255UL, 3855UL, 65535UL, 0UL, 30UL, 510UL, 7710UL, 131070UL, 0UL, 60UL, 1020UL, 15420UL, 262140UL, 0UL, 120UL, 2040UL, 30840UL, 524280UL, 0UL, 240UL, +4080UL, 61680UL, 1048560UL, 0UL, 480UL, 8160UL, 123360UL, 2097120UL, 0UL, 960UL, 16320UL, 246720UL, 4194240UL, 0UL, 1920UL, 32640UL, 493440UL, 8388480UL, 0UL, 3840UL, 65280UL, 986880UL, 16776960UL, 0UL, 7680UL, 130560UL, 1973760UL, 33553920UL, 0UL, 15360UL, 261120UL, 3947520UL, +67107840UL, 0UL, 30720UL, 522240UL, 7895040UL, 134215680UL, 0UL, 61440UL, 1044480UL, 15790080UL, 268431360UL, 0UL, 122880UL, 2088960UL, 31580160UL, 536862720UL, 0UL, 245760UL, 4177920UL, 63160320UL, 1073725440UL, 0UL, 491520UL, 8355840UL, 126320640UL, 2147450880UL, 0UL, 983040UL, 16711680UL, 252641280UL, 4294901760UL, 0UL, +1966080UL, 33423360UL, 505282560UL, 4294836224UL, 0UL, 3932160UL, 66846720UL, 1010565120UL, 4294705152UL, 0UL, 7864320UL, 133693440UL, 2021130240UL, 4294443008UL, 0UL, 15728640UL, 267386880UL, 4042260480UL, 4293918720UL, 0UL, 31457280UL, 534773760UL, 3789553664UL, 4292870144UL, 0UL, 62914560UL, 1069547520UL, 3284140032UL, 4290772992UL, 0UL, 125829120UL, 2139095040UL, +2273312768UL, 4286578688UL, 0UL, 251658240UL, 4278190080UL, 251658240UL, 4278190080UL, 0UL, 503316480UL, 4261412864UL, 503316480UL, 4261412864UL, 0UL, 1006632960UL, 4227858432UL, 1006632960UL, 4227858432UL, 0UL, 2013265920UL, 4160749568UL, 2013265920UL, 4160749568UL, 0UL, 4026531840UL, 4026531840UL, 4026531840UL, 4026531840UL, 0UL, 3758096384UL, 3758096384UL, 3758096384UL, 3758096384UL, +0UL, 0UL, 3UL, 51UL, 771UL, 0UL, 0UL, 6UL, 102UL, 1542UL, 0UL, 0UL, 15UL, 255UL, 3855UL, 0UL, 0UL, 30UL, 510UL, 7710UL, 0UL, 0UL, 60UL, 1020UL, 15420UL, 0UL, 0UL, 120UL, 2040UL, 30840UL, 0UL, 0UL, +240UL, 4080UL, 61680UL, 0UL, 0UL, 480UL, 8160UL, 123360UL, 0UL, 0UL, 960UL, 16320UL, 246720UL, 0UL, 0UL, 1920UL, 32640UL, 493440UL, 0UL, 0UL, 3840UL, 65280UL, 986880UL, 0UL, 0UL, 7680UL, 130560UL, 1973760UL, 0UL, 0UL, 15360UL, 261120UL, +3947520UL, 0UL, 0UL, 30720UL, 522240UL, 7895040UL, 0UL, 0UL, 61440UL, 1044480UL, 15790080UL, 0UL, 0UL, 122880UL, 2088960UL, 31580160UL, 0UL, 0UL, 245760UL, 4177920UL, 63160320UL, 0UL, 0UL, 491520UL, 8355840UL, 126320640UL, 0UL, 0UL, 983040UL, 16711680UL, 252641280UL, 0UL, +0UL, 1966080UL, 33423360UL, 505282560UL, 0UL, 0UL, 3932160UL, 66846720UL, 1010565120UL, 0UL, 0UL, 7864320UL, 133693440UL, 2021130240UL, 0UL, 0UL, 15728640UL, 267386880UL, 4042260480UL, 0UL, 0UL, 31457280UL, 534773760UL, 3789553664UL, 0UL, 0UL, 62914560UL, 1069547520UL, 3284140032UL, 0UL, 0UL, 125829120UL, +2139095040UL, 2273312768UL, 0UL, 0UL, 251658240UL, 4278190080UL, 251658240UL, 0UL, 0UL, 503316480UL, 4261412864UL, 503316480UL, 0UL, 0UL, 1006632960UL, 4227858432UL, 1006632960UL, 0UL, 0UL, 2013265920UL, 4160749568UL, 2013265920UL, 0UL, 0UL, 4026531840UL, 4026531840UL, 4026531840UL, 0UL, 0UL, 3758096384UL, 3758096384UL, 3758096384UL, +0UL, 0UL, 0UL, 3UL, 51UL, 0UL, 0UL, 0UL, 6UL, 102UL, 0UL, 0UL, 0UL, 15UL, 255UL, 0UL, 0UL, 0UL, 30UL, 510UL, 0UL, 0UL, 0UL, 60UL, 1020UL, 0UL, 0UL, 0UL, 120UL, 2040UL, 0UL, 0UL, +0UL, 240UL, 4080UL, 0UL, 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262148UL, 8UL, 136UL, 2056UL, 34952UL, 524296UL, 16UL, 272UL, 4112UL, 69904UL, 1048592UL, 32UL, 544UL, 8224UL, 139808UL, 2097184UL, 64UL, 1088UL, +16448UL, 279616UL, 4194368UL, 128UL, 2176UL, 32896UL, 559232UL, 8388736UL, 256UL, 4352UL, 65792UL, 1118464UL, 16777472UL, 512UL, 8704UL, 131584UL, 2236928UL, 33554944UL, 1024UL, 17408UL, 263168UL, 4473856UL, 67109888UL, 2048UL, 34816UL, 526336UL, 8947712UL, 134219776UL, 4096UL, 69632UL, 1052672UL, 17895424UL, +268439552UL, 8192UL, 139264UL, 2105344UL, 35790848UL, 536879104UL, 16384UL, 278528UL, 4210688UL, 71581696UL, 1073758208UL, 32768UL, 557056UL, 8421376UL, 143163392UL, 2147516416UL, 65536UL, 1114112UL, 16842752UL, 286326784UL, 65536UL, 131072UL, 2228224UL, 33685504UL, 572653568UL, 131072UL, 262144UL, 4456448UL, 67371008UL, 1145307136UL, 262144UL, 524288UL, +8912896UL, 134742016UL, 2290614272UL, 524288UL, 1048576UL, 17825792UL, 269484032UL, 286261248UL, 1048576UL, 2097152UL, 35651584UL, 538968064UL, 572522496UL, 2097152UL, 4194304UL, 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3320520455UL, 3070067913UL, 3808621884UL, 252917069UL, 3394860294UL, 1092442235UL, 2876536384UL, 1684120191UL, 431096075UL, 1701716708UL, 639881684UL, 3066183997UL, 3660504927UL, 2047274UL, 3424756424UL, 760932520UL, 2457976057UL, 1705265011UL, 2691137533UL, 3684307557UL, 3532744498UL, 2319162513UL, 1015534908UL, 1907173398UL, 2820698743UL, 1264455116UL, 2323788906UL, 3062240844UL, +1878550513UL, 1717353426UL, 1805673248UL, 62425157UL, 3662381032UL, 1964107209UL, 2559831960UL, 2117844804UL, 1228721677UL, 4240498866UL, 3212920337UL, 2338600301UL, 931588693UL, 2379606585UL, 3643222352UL, 4154645082UL, 1115847065UL, 2079427925UL, 2256943798UL, 2795103368UL, 2688136486UL, 1458062143UL, 1767222217UL, 635424385UL, 284062050UL, 1547163554UL, 3380046528UL, 1145758046UL, 3935976713UL, 4017430175UL, 3863367362UL, 3041367424UL, +303263160UL, 1465965696UL, 3757919837UL, 3083072836UL, 4024514094UL, 1381331179UL, 2393446325UL, 3256476469UL, 4066482738UL, 3437941107UL, 1051266504UL, 921764078UL, 2933305619UL, 1358097211UL, 4100978724UL, 2709958834UL, 574590507UL, 961767386UL, 21100886UL, 753746372UL, 4072632446UL, 733729367UL, 3060214669UL, 289165105UL, 426065754UL, 2036100240UL, 2172365757UL, 502856627UL, 84490194UL, 2630806596UL, 1206161269UL, 1009438449UL, +569581317UL, 1836947000UL, 3125379675UL, 1756936428UL, 3772694822UL, 3670337911UL, 3020603818UL, 2376224883UL, 2539951453UL, 2053395002UL, 3525193914UL, 1991480838UL, 3786481083UL, 873873707UL, 1693894743UL, 2450223985UL, 754878026UL, 1943356492UL, 401524329UL, 759931885UL, 611231307UL, 147950334UL, 599693701UL, 3358729722UL, 3649058074UL, 906423787UL, 1333804225UL, 875187278UL, 1115838692UL, 2476325972UL, 3307226674UL, 3539078918UL, +}, + +}; +#ifndef __CUDACC_RTC__ +CURAND_XORWOW_PRECALCULATED_HOST_QUALIFIERS unsigned int precalc_xorwow_offset_matrix_host[32][800] = { +{ +0UL, 0UL, 0UL, 0UL, 3UL, 0UL, 0UL, 0UL, 0UL, 6UL, 0UL, 0UL, 0UL, 0UL, 15UL, 0UL, 0UL, 0UL, 0UL, 30UL, 0UL, 0UL, 0UL, 0UL, 60UL, 0UL, 0UL, 0UL, 0UL, 120UL, 0UL, 0UL, +0UL, 0UL, 240UL, 0UL, 0UL, 0UL, 0UL, 480UL, 0UL, 0UL, 0UL, 0UL, 960UL, 0UL, 0UL, 0UL, 0UL, 1920UL, 0UL, 0UL, 0UL, 0UL, 3840UL, 0UL, 0UL, 0UL, 0UL, 7680UL, 0UL, 0UL, 0UL, 0UL, +15360UL, 0UL, 0UL, 0UL, 0UL, 30720UL, 0UL, 0UL, 0UL, 0UL, 61440UL, 0UL, 0UL, 0UL, 0UL, 122880UL, 0UL, 0UL, 0UL, 0UL, 245760UL, 0UL, 0UL, 0UL, 0UL, 491520UL, 0UL, 0UL, 0UL, 0UL, 983040UL, 0UL, +0UL, 0UL, 0UL, 1966080UL, 0UL, 0UL, 0UL, 0UL, 3932160UL, 0UL, 0UL, 0UL, 0UL, 7864320UL, 0UL, 0UL, 0UL, 0UL, 15728640UL, 0UL, 0UL, 0UL, 0UL, 31457280UL, 0UL, 0UL, 0UL, 0UL, 62914560UL, 0UL, 0UL, 0UL, +0UL, 125829120UL, 0UL, 0UL, 0UL, 0UL, 251658240UL, 0UL, 0UL, 0UL, 0UL, 503316480UL, 0UL, 0UL, 0UL, 0UL, 1006632960UL, 0UL, 0UL, 0UL, 0UL, 2013265920UL, 0UL, 0UL, 0UL, 0UL, 4026531840UL, 0UL, 0UL, 0UL, 0UL, 3758096384UL, +1UL, 0UL, 0UL, 0UL, 0UL, 2UL, 0UL, 0UL, 0UL, 0UL, 4UL, 0UL, 0UL, 0UL, 0UL, 8UL, 0UL, 0UL, 0UL, 0UL, 16UL, 0UL, 0UL, 0UL, 0UL, 32UL, 0UL, 0UL, 0UL, 0UL, 64UL, 0UL, +0UL, 0UL, 0UL, 128UL, 0UL, 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a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_uniform.h b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_uniform.h new file mode 100644 index 0000000000000000000000000000000000000000..7a4af8afa328c186d9ea33a8c8226e19aba4793e --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/include/curand_uniform.h @@ -0,0 +1,498 @@ + + /* Copyright 2010-2018 NVIDIA Corporation. All rights reserved. + * + * NOTICE TO LICENSEE: + * + * The source code and/or documentation ("Licensed Deliverables") are + * subject to NVIDIA intellectual property rights under U.S. and + * international Copyright laws. + * + * The Licensed Deliverables contained herein are PROPRIETARY and + * CONFIDENTIAL to NVIDIA and are being provided under the terms and + * conditions of a form of NVIDIA software license agreement by and + * between NVIDIA and Licensee ("License Agreement") or electronically + * accepted by Licensee. Notwithstanding any terms or conditions to + * the contrary in the License Agreement, reproduction or disclosure + * of the Licensed Deliverables to any third party without the express + * written consent of NVIDIA is prohibited. + * + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, NVIDIA MAKES NO REPRESENTATION ABOUT THE + * SUITABILITY OF THESE LICENSED DELIVERABLES FOR ANY PURPOSE. THEY ARE + * PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF ANY KIND. + * NVIDIA DISCLAIMS ALL WARRANTIES WITH REGARD TO THESE LICENSED + * DELIVERABLES, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY, + * NONINFRINGEMENT, AND FITNESS FOR A PARTICULAR PURPOSE. + * NOTWITHSTANDING ANY TERMS OR CONDITIONS TO THE CONTRARY IN THE + * LICENSE AGREEMENT, IN NO EVENT SHALL NVIDIA BE LIABLE FOR ANY + * SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, OR ANY + * DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, + * WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS + * ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE + * OF THESE LICENSED DELIVERABLES. + * + * U.S. Government End Users. These Licensed Deliverables are a + * "commercial item" as that term is defined at 48 C.F.R. 2.101 (OCT + * 1995), consisting of "commercial computer software" and "commercial + * computer software documentation" as such terms are used in 48 + * C.F.R. 12.212 (SEPT 1995) and are provided to the U.S. Government + * only as a commercial end item. Consistent with 48 C.F.R.12.212 and + * 48 C.F.R. 227.7202-1 through 227.7202-4 (JUNE 1995), all + * U.S. Government End Users acquire the Licensed Deliverables with + * only those rights set forth herein. + * + * Any use of the Licensed Deliverables in individual and commercial + * software must include, in the user documentation and internal + * comments to the code, the above Disclaimer and U.S. Government End + * Users Notice. + */ + + +#if !defined(CURAND_UNIFORM_H_) +#define CURAND_UNIFORM_H_ + +/** + * \defgroup DEVICE Device API + * + * @{ + */ + +#ifndef __CUDACC_RTC__ +#include +#endif // __CUDACC_RTC__ + +#include "curand_mrg32k3a.h" +#include "curand_mtgp32_kernel.h" +#include "curand_philox4x32_x.h" + + +QUALIFIERS float _curand_uniform(unsigned int x) +{ + return x * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); +} + +QUALIFIERS float4 _curand_uniform4(uint4 x) +{ + float4 y; + y.x = x.x * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); + y.y = x.y * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); + y.z = x.z * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); + y.w = x.w * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); + return y; +} + +QUALIFIERS float _curand_uniform(unsigned long long x) +{ + unsigned int t; + t = (unsigned int)(x >> 32); + return t * CURAND_2POW32_INV + (CURAND_2POW32_INV/2.0f); +} + +QUALIFIERS double _curand_uniform_double(unsigned int x) +{ + return x * CURAND_2POW32_INV_DOUBLE + CURAND_2POW32_INV_DOUBLE; +} + +QUALIFIERS double _curand_uniform_double(unsigned long long x) +{ + return (x >> 11) * CURAND_2POW53_INV_DOUBLE + (CURAND_2POW53_INV_DOUBLE/2.0); +} + +QUALIFIERS double _curand_uniform_double_hq(unsigned int x, unsigned int y) +{ + unsigned long long z = (unsigned long long)x ^ + ((unsigned long long)y << (53 - 32)); + return z * CURAND_2POW53_INV_DOUBLE + (CURAND_2POW53_INV_DOUBLE/2.0); +} + +QUALIFIERS float curand_uniform(curandStateTest_t *state) +{ + return _curand_uniform(curand(state)); +} + +QUALIFIERS double curand_uniform_double(curandStateTest_t *state) +{ + return _curand_uniform_double(curand(state)); +} + +/** + * \brief Return a uniformly distributed float from an XORWOW generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the XORWOW generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation may use any number of calls to \p curand() to + * get enough random bits to create the return value. The current + * implementation uses one call. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateXORWOW_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from an XORWOW generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the XORWOW generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * The implementation may use any number of calls to \p curand() to + * get enough random bits to create the return value. The current + * implementation uses exactly two calls. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateXORWOW_t *state) +{ + unsigned int x, y; + x = curand(state); + y = curand(state); + return _curand_uniform_double_hq(x, y); +} +/** + * \brief Return a uniformly distributed float from an MRG32k3a generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the MRG32k3a generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation returns up to 23 bits of mantissa, with the minimum + * return value \f$ 2^{-32} \f$ + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateMRG32k3a_t *state) +{ + return ((float)(curand_MRG32k3a(state)*MRG32K3A_NORM)); +} + +/** + * \brief Return a uniformly distributed double from an MRG32k3a generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the MRG32k3a generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * Note the implementation returns at most 32 random bits of mantissa as + * outlined in the seminal paper by L'Ecuyer. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateMRG32k3a_t *state) +{ + return curand_MRG32k3a(state)*MRG32K3A_NORM; +} + + + +/** + * \brief Return a uniformly distributed tuple of 2 doubles from an Philox4_32_10 generator. + * + * Return a uniformly distributed 2 doubles (double4) between \p 0.0 and \p 1.0 + * from the Philox4_32_10 generator in \p state, increment position of generator by 4. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * \param state - Pointer to state to update + * + * \return 2 uniformly distributed doubles between \p 0.0 and \p 1.0 + */ + +QUALIFIERS double2 curand_uniform2_double(curandStatePhilox4_32_10_t *state) +{ + uint4 _x; + double2 result; + _x = curand4(state); + result.x = _curand_uniform_double_hq(_x.x,_x.y); + result.y = _curand_uniform_double_hq(_x.z,_x.w); + return result; +} + + +// not a part of API +QUALIFIERS double4 curand_uniform4_double(curandStatePhilox4_32_10_t *state) +{ + uint4 _x, _y; + double4 result; + _x = curand4(state); + _y = curand4(state); + result.x = _curand_uniform_double_hq(_x.x,_x.y); + result.y = _curand_uniform_double_hq(_x.z,_x.w); + result.z = _curand_uniform_double_hq(_y.x,_y.y); + result.w = _curand_uniform_double_hq(_y.z,_y.w); + return result; +} + +/** + * \brief Return a uniformly distributed float from a Philox4_32_10 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the Philox4_32_10 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0 and \p 1.0 + * + */ +QUALIFIERS float curand_uniform(curandStatePhilox4_32_10_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed tuple of 4 floats from a Philox4_32_10 generator. + * + * Return a uniformly distributed 4 floats between \p 0.0f and \p 1.0f + * from the Philox4_32_10 generator in \p state, increment position of generator by 4. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0 and \p 1.0 + * + */ +QUALIFIERS float4 curand_uniform4(curandStatePhilox4_32_10_t *state) +{ + return _curand_uniform4(curand4(state)); +} + +/** + * \brief Return a uniformly distributed float from a MTGP32 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the MTGP32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateMtgp32_t *state) +{ + return _curand_uniform(curand(state)); +} +/** + * \brief Return a uniformly distributed double from a MTGP32 generator. + * + * Return a uniformly distributed double between \p 0.0f and \p 1.0f + * from the MTGP32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * Note that the implementation uses only 32 random bits to generate a single double + * precision value. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0f and \p 1.0f + */ +QUALIFIERS double curand_uniform_double(curandStateMtgp32_t *state) +{ + return _curand_uniform_double(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from a Philox4_32_10 generator. + * + * Return a uniformly distributed double between \p 0.0f and \p 1.0f + * from the Philox4_32_10 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * Note that the implementation uses only 32 random bits to generate a single double + * precision value. + * + * \p curand_uniform2_double() is recommended for higher quality uniformly distributed + * double precision values. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0f and \p 1.0f + */ + +QUALIFIERS double curand_uniform_double(curandStatePhilox4_32_10_t *state) +{ + return _curand_uniform_double(curand(state)); +} + + +/** + * \brief Return a uniformly distributed float from a Sobol32 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the Sobol32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand(). + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateSobol32_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from a Sobol32 generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the Sobol32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand() + * to preserve the quasirandom properties of the sequence. + * + * Note that the implementation uses only 32 random bits to generate a single double + * precision value. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateSobol32_t *state) +{ + return _curand_uniform_double(curand(state)); +} +/** + * \brief Return a uniformly distributed float from a scrambled Sobol32 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the scrambled Sobol32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand(). + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateScrambledSobol32_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from a scrambled Sobol32 generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the scrambled Sobol32 generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand() + * to preserve the quasirandom properties of the sequence. + * + * Note that the implementation uses only 32 random bits to generate a single double + * precision value. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateScrambledSobol32_t *state) +{ + return _curand_uniform_double(curand(state)); +} +/** + * \brief Return a uniformly distributed float from a Sobol64 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the Sobol64 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand(). + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateSobol64_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from a Sobol64 generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the Sobol64 generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand() + * to preserve the quasirandom properties of the sequence. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateSobol64_t *state) +{ + return _curand_uniform_double(curand(state)); +} +/** + * \brief Return a uniformly distributed float from a scrambled Sobol64 generator. + * + * Return a uniformly distributed float between \p 0.0f and \p 1.0f + * from the scrambled Sobol64 generator in \p state, increment position of generator. + * Output range excludes \p 0.0f but includes \p 1.0f. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand(). + * + * \param state - Pointer to state to update + * + * \return uniformly distributed float between \p 0.0f and \p 1.0f + */ +QUALIFIERS float curand_uniform(curandStateScrambledSobol64_t *state) +{ + return _curand_uniform(curand(state)); +} + +/** + * \brief Return a uniformly distributed double from a scrambled Sobol64 generator. + * + * Return a uniformly distributed double between \p 0.0 and \p 1.0 + * from the scrambled Sobol64 generator in \p state, increment position of generator. + * Output range excludes \p 0.0 but includes \p 1.0. Denormalized floating + * point outputs are never returned. + * + * The implementation is guaranteed to use a single call to \p curand() + * to preserve the quasirandom properties of the sequence. + * + * \param state - Pointer to state to update + * + * \return uniformly distributed double between \p 0.0 and \p 1.0 + */ +QUALIFIERS double curand_uniform_double(curandStateScrambledSobol64_t *state) +{ + return _curand_uniform_double(curand(state)); +} + +#endif // !defined(CURAND_UNIFORM_H_) diff --git a/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/lib/libcurand.so.10 b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/lib/libcurand.so.10 new file mode 100644 index 0000000000000000000000000000000000000000..0e1e97c3fdb4016af69bfd41bd5b11803c27685a --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/nvidia/curand/lib/libcurand.so.10 @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dab8074b610b82a863a42eceda788e9b08364b545bab948509306b48c46018cf +size 96525744 diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/algos.cpython-310-x86_64-linux-gnu.so b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/algos.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..1c696792f775aac331735a0a710b870ee0b16cb1 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/algos.cpython-310-x86_64-linux-gnu.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e428449e985790af8faa2227d6c2c989c54cc093110f476200d68f36b4a524df +size 2194056 diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.cpython-310-x86_64-linux-gnu.so b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..8021e91459d4e521bb1f751f670f7dfdc39769e7 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.cpython-310-x86_64-linux-gnu.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d7d4536852551fda02d7d1b2d2f4aaf559877db06a6a40e8d5fa73bc0e1d048c +size 133184 diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.pyi b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.pyi new file mode 100644 index 0000000000000000000000000000000000000000..86f69c3cdfc75f3101a8e0afe59f9b102d90ad79 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/arrays.pyi @@ -0,0 +1,40 @@ +from typing import Sequence + +import numpy as np + +from pandas._typing import ( + AxisInt, + DtypeObj, + Self, + Shape, +) + +class NDArrayBacked: + _dtype: DtypeObj + _ndarray: np.ndarray + def __init__(self, values: np.ndarray, dtype: DtypeObj) -> None: ... + @classmethod + def _simple_new(cls, values: np.ndarray, dtype: DtypeObj): ... + def _from_backing_data(self, values: np.ndarray): ... + def __setstate__(self, state): ... + def __len__(self) -> int: ... + @property + def shape(self) -> Shape: ... + @property + def ndim(self) -> int: ... + @property + def size(self) -> int: ... + @property + def nbytes(self) -> int: ... + def copy(self, order=...): ... + def delete(self, loc, axis=...): ... + def swapaxes(self, axis1, axis2): ... + def repeat(self, repeats: int | Sequence[int], axis: int | None = ...): ... + def reshape(self, *args, **kwargs): ... + def ravel(self, order=...): ... + @property + def T(self): ... + @classmethod + def _concat_same_type( + cls, to_concat: Sequence[Self], axis: AxisInt = ... + ) -> Self: ... diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/byteswap.cpython-310-x86_64-linux-gnu.so b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/byteswap.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..526edcc3ad89c1886fef21f19ba990df8df3d3db Binary files /dev/null and b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/byteswap.cpython-310-x86_64-linux-gnu.so differ diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/hashing.pyi b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/hashing.pyi new file mode 100644 index 0000000000000000000000000000000000000000..8361026e4a87d462e04c53f7f1f8aee8a7f6ffe0 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/hashing.pyi @@ -0,0 +1,9 @@ +import numpy as np + +from pandas._typing import npt + +def hash_object_array( + arr: npt.NDArray[np.object_], + key: str, + encoding: str = ..., +) -> npt.NDArray[np.uint64]: ... diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/lib.pyi b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/lib.pyi new file mode 100644 index 0000000000000000000000000000000000000000..b9fd970e68f5bd1d635737f65228f4ac7bc43080 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/lib.pyi @@ -0,0 +1,213 @@ +# TODO(npdtypes): Many types specified here can be made more specific/accurate; +# the more specific versions are specified in comments +from decimal import Decimal +from typing import ( + Any, + Callable, + Final, + Generator, + Hashable, + Literal, + TypeAlias, + overload, +) + +import numpy as np + +from pandas._libs.interval import Interval +from pandas._libs.tslibs import Period +from pandas._typing import ( + ArrayLike, + DtypeObj, + TypeGuard, + npt, +) + +# placeholder until we can specify np.ndarray[object, ndim=2] +ndarray_obj_2d = np.ndarray + +from enum import Enum + +class _NoDefault(Enum): + no_default = ... + +no_default: Final = _NoDefault.no_default +NoDefault: TypeAlias = Literal[_NoDefault.no_default] + +i8max: int +u8max: int + +def is_np_dtype(dtype: object, kinds: str | None = ...) -> TypeGuard[np.dtype]: ... +def item_from_zerodim(val: object) -> object: ... +def infer_dtype(value: object, skipna: bool = ...) -> str: ... +def is_iterator(obj: object) -> bool: ... +def is_scalar(val: object) -> bool: ... +def is_list_like(obj: object, allow_sets: bool = ...) -> bool: ... +def is_pyarrow_array(obj: object) -> bool: ... +def is_period(val: object) -> TypeGuard[Period]: ... +def is_interval(obj: object) -> TypeGuard[Interval]: ... +def is_decimal(obj: object) -> TypeGuard[Decimal]: ... +def is_complex(obj: object) -> TypeGuard[complex]: ... +def is_bool(obj: object) -> TypeGuard[bool | np.bool_]: ... +def is_integer(obj: object) -> TypeGuard[int | np.integer]: ... +def is_int_or_none(obj) -> bool: ... +def is_float(obj: object) -> TypeGuard[float]: ... +def is_interval_array(values: np.ndarray) -> bool: ... +def is_datetime64_array(values: np.ndarray, skipna: bool = True) -> bool: ... +def is_timedelta_or_timedelta64_array( + values: np.ndarray, skipna: bool = True +) -> bool: ... +def is_datetime_with_singletz_array(values: np.ndarray) -> bool: ... +def is_time_array(values: np.ndarray, skipna: bool = ...): ... +def is_date_array(values: np.ndarray, skipna: bool = ...): ... +def is_datetime_array(values: np.ndarray, skipna: bool = ...): ... +def is_string_array(values: np.ndarray, skipna: bool = ...): ... +def is_float_array(values: np.ndarray): ... +def is_integer_array(values: np.ndarray, skipna: bool = ...): ... +def is_bool_array(values: np.ndarray, skipna: bool = ...): ... +def fast_multiget( + mapping: dict, + keys: np.ndarray, # object[:] + default=..., +) -> np.ndarray: ... +def fast_unique_multiple_list_gen(gen: Generator, sort: bool = ...) -> list: ... +def fast_unique_multiple_list(lists: list, sort: bool | None = ...) -> list: ... +def map_infer( + arr: np.ndarray, + f: Callable[[Any], Any], + convert: bool = ..., + ignore_na: bool = ..., +) -> np.ndarray: ... +@overload +def maybe_convert_objects( + objects: npt.NDArray[np.object_], + *, + try_float: bool = ..., + safe: bool = ..., + convert_numeric: bool = ..., + convert_non_numeric: Literal[False] = ..., + convert_to_nullable_dtype: Literal[False] = ..., + dtype_if_all_nat: DtypeObj | None = ..., +) -> npt.NDArray[np.object_ | np.number]: ... +@overload +def maybe_convert_objects( + objects: npt.NDArray[np.object_], + *, + try_float: bool = ..., + safe: bool = ..., + convert_numeric: bool = ..., + convert_non_numeric: bool = ..., + convert_to_nullable_dtype: Literal[True] = ..., + dtype_if_all_nat: DtypeObj | None = ..., +) -> ArrayLike: ... +@overload +def maybe_convert_objects( + objects: npt.NDArray[np.object_], + *, + try_float: bool = ..., + safe: bool = ..., + convert_numeric: bool = ..., + convert_non_numeric: bool = ..., + convert_to_nullable_dtype: bool = ..., + dtype_if_all_nat: DtypeObj | None = ..., +) -> ArrayLike: ... +@overload +def maybe_convert_numeric( + values: npt.NDArray[np.object_], + na_values: set, + convert_empty: bool = ..., + coerce_numeric: bool = ..., + convert_to_masked_nullable: Literal[False] = ..., +) -> tuple[np.ndarray, None]: ... +@overload +def maybe_convert_numeric( + values: npt.NDArray[np.object_], + na_values: set, + convert_empty: bool = ..., + coerce_numeric: bool = ..., + *, + convert_to_masked_nullable: Literal[True], +) -> tuple[np.ndarray, np.ndarray]: ... + +# TODO: restrict `arr`? +def ensure_string_array( + arr, + na_value: object = ..., + convert_na_value: bool = ..., + copy: bool = ..., + skipna: bool = ..., +) -> npt.NDArray[np.object_]: ... +def convert_nans_to_NA( + arr: npt.NDArray[np.object_], +) -> npt.NDArray[np.object_]: ... +def fast_zip(ndarrays: list) -> npt.NDArray[np.object_]: ... + +# TODO: can we be more specific about rows? +def to_object_array_tuples(rows: object) -> ndarray_obj_2d: ... +def tuples_to_object_array( + tuples: npt.NDArray[np.object_], +) -> ndarray_obj_2d: ... + +# TODO: can we be more specific about rows? +def to_object_array(rows: object, min_width: int = ...) -> ndarray_obj_2d: ... +def dicts_to_array(dicts: list, columns: list) -> ndarray_obj_2d: ... +def maybe_booleans_to_slice( + mask: npt.NDArray[np.uint8], +) -> slice | npt.NDArray[np.uint8]: ... +def maybe_indices_to_slice( + indices: npt.NDArray[np.intp], + max_len: int, +) -> slice | npt.NDArray[np.intp]: ... +def is_all_arraylike(obj: list) -> bool: ... + +# ----------------------------------------------------------------- +# Functions which in reality take memoryviews + +def memory_usage_of_objects(arr: np.ndarray) -> int: ... # object[:] # np.int64 +def map_infer_mask( + arr: np.ndarray, + f: Callable[[Any], Any], + mask: np.ndarray, # const uint8_t[:] + convert: bool = ..., + na_value: Any = ..., + dtype: np.dtype = ..., +) -> np.ndarray: ... +def indices_fast( + index: npt.NDArray[np.intp], + labels: np.ndarray, # const int64_t[:] + keys: list, + sorted_labels: list[npt.NDArray[np.int64]], +) -> dict[Hashable, npt.NDArray[np.intp]]: ... +def generate_slices( + labels: np.ndarray, ngroups: int # const intp_t[:] +) -> tuple[npt.NDArray[np.int64], npt.NDArray[np.int64]]: ... +def count_level_2d( + mask: np.ndarray, # ndarray[uint8_t, ndim=2, cast=True], + labels: np.ndarray, # const intp_t[:] + max_bin: int, +) -> np.ndarray: ... # np.ndarray[np.int64, ndim=2] +def get_level_sorter( + codes: np.ndarray, # const int64_t[:] + starts: np.ndarray, # const intp_t[:] +) -> np.ndarray: ... # np.ndarray[np.intp, ndim=1] +def generate_bins_dt64( + values: npt.NDArray[np.int64], + binner: np.ndarray, # const int64_t[:] + closed: object = ..., + hasnans: bool = ..., +) -> np.ndarray: ... # np.ndarray[np.int64, ndim=1] +def array_equivalent_object( + left: npt.NDArray[np.object_], + right: npt.NDArray[np.object_], +) -> bool: ... +def has_infs(arr: np.ndarray) -> bool: ... # const floating[:] +def has_only_ints_or_nan(arr: np.ndarray) -> bool: ... # const floating[:] +def get_reverse_indexer( + indexer: np.ndarray, # const intp_t[:] + length: int, +) -> npt.NDArray[np.intp]: ... +def is_bool_list(obj: list) -> bool: ... +def dtypes_all_equal(types: list[DtypeObj]) -> bool: ... +def is_range_indexer( + left: np.ndarray, n: int # np.ndarray[np.int64, ndim=1] +) -> bool: ... diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/parsers.cpython-310-x86_64-linux-gnu.so b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/parsers.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..129e50b6bbad0ed02b38197fc3c2b22cf48bbf02 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/parsers.cpython-310-x86_64-linux-gnu.so @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c9e1a4899b63e3a9a6431882897273d1797a9c2d2baff27406c8b8211eceaf34 +size 594760 diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/properties.pyi b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/properties.pyi new file mode 100644 index 0000000000000000000000000000000000000000..aaa44a0cf47bf8635727ea9f354227de72bbff29 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/properties.pyi @@ -0,0 +1,27 @@ +from typing import ( + Sequence, + overload, +) + +from pandas._typing import ( + AnyArrayLike, + DataFrame, + Index, + Series, +) + +# note: this is a lie to make type checkers happy (they special +# case property). cache_readonly uses attribute names similar to +# property (fget) but it does not provide fset and fdel. +cache_readonly = property + +class AxisProperty: + axis: int + def __init__(self, axis: int = ..., doc: str = ...) -> None: ... + @overload + def __get__(self, obj: DataFrame | Series, type) -> Index: ... + @overload + def __get__(self, obj: None, type) -> AxisProperty: ... + def __set__( + self, obj: DataFrame | Series, value: AnyArrayLike | Sequence + ) -> None: ... diff --git a/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/tslib.pyi b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/tslib.pyi new file mode 100644 index 0000000000000000000000000000000000000000..5a340c1d88bc439663c2e482c9eb7270f8ebc5c6 --- /dev/null +++ b/infer_4_37_2/lib/python3.10/site-packages/pandas/_libs/tslib.pyi @@ -0,0 +1,37 @@ +from datetime import tzinfo + +import numpy as np + +from pandas._typing import npt + +def format_array_from_datetime( + values: npt.NDArray[np.int64], + tz: tzinfo | None = ..., + format: str | None = ..., + na_rep: str | float = ..., + reso: int = ..., # NPY_DATETIMEUNIT +) -> npt.NDArray[np.object_]: ... +def array_with_unit_to_datetime( + values: npt.NDArray[np.object_], + unit: str, + errors: str = ..., +) -> tuple[np.ndarray, tzinfo | None]: ... +def first_non_null(values: np.ndarray) -> int: ... +def array_to_datetime( + values: npt.NDArray[np.object_], + errors: str = ..., + dayfirst: bool = ..., + yearfirst: bool = ..., + utc: bool = ..., + creso: int = ..., +) -> tuple[np.ndarray, tzinfo | None]: ... + +# returned ndarray may be object dtype or datetime64[ns] + +def array_to_datetime_with_tz( + values: npt.NDArray[np.object_], + tz: tzinfo, + dayfirst: bool, + yearfirst: bool, + creso: int, +) -> npt.NDArray[np.int64]: ... diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/__init__.py b/janus/lib/python3.10/site-packages/sympy/codegen/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..62b195633bae28371bdf9e79317050d7fa7125ae --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/__init__.py @@ -0,0 +1,24 @@ +""" The ``sympy.codegen`` module contains classes and functions for building +abstract syntax trees of algorithms. These trees may then be printed by the +code-printers in ``sympy.printing``. + +There are several submodules available: +- ``sympy.codegen.ast``: AST nodes useful across multiple languages. +- ``sympy.codegen.cnodes``: AST nodes useful for the C family of languages. +- ``sympy.codegen.fnodes``: AST nodes useful for Fortran. +- ``sympy.codegen.cfunctions``: functions specific to C (C99 math functions) +- ``sympy.codegen.ffunctions``: functions specific to Fortran (e.g. ``kind``). + + + +""" +from .ast import ( + Assignment, aug_assign, CodeBlock, For, Attribute, Variable, Declaration, + While, Scope, Print, FunctionPrototype, FunctionDefinition, FunctionCall +) + +__all__ = [ + 'Assignment', 'aug_assign', 'CodeBlock', 'For', 'Attribute', 'Variable', + 'Declaration', 'While', 'Scope', 'Print', 'FunctionPrototype', + 'FunctionDefinition', 'FunctionCall', +] diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/__pycache__/__init__.cpython-310.pyc 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new file mode 100644 index 0000000000000000000000000000000000000000..4be4310671835d70c9f6f28327033b79fa6099a3 Binary files /dev/null and b/janus/lib/python3.10/site-packages/sympy/codegen/__pycache__/pynodes.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py b/janus/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py new file mode 100644 index 0000000000000000000000000000000000000000..ae0a8b3e996a7112edf2568c00138e11c3f3327d --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/abstract_nodes.py @@ -0,0 +1,18 @@ +"""This module provides containers for python objects that are valid +printing targets but are not a subclass of SymPy's Printable. +""" + + +from sympy.core.containers import Tuple + + +class List(Tuple): + """Represents a (frozen) (Python) list (for code printing purposes).""" + def __eq__(self, other): + if isinstance(other, list): + return self == List(*other) + else: + return self.args == other + + def __hash__(self): + return super().__hash__() diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/approximations.py b/janus/lib/python3.10/site-packages/sympy/codegen/approximations.py new file mode 100644 index 0000000000000000000000000000000000000000..4f15266ab18f93b18b50269356c94484dd2f8ac4 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/approximations.py @@ -0,0 +1,187 @@ +import math +from sympy.sets.sets import Interval +from sympy.calculus.singularities import is_increasing, is_decreasing +from sympy.codegen.rewriting import Optimization +from sympy.core.function import UndefinedFunction + +""" +This module collects classes useful for approimate rewriting of expressions. +This can be beneficial when generating numeric code for which performance is +of greater importance than precision (e.g. for preconditioners used in iterative +methods). +""" + +class SumApprox(Optimization): + """ + Approximates sum by neglecting small terms. + + Explanation + =========== + + If terms are expressions which can be determined to be monotonic, then + bounds for those expressions are added. + + Parameters + ========== + + bounds : dict + Mapping expressions to length 2 tuple of bounds (low, high). + reltol : number + Threshold for when to ignore a term. Taken relative to the largest + lower bound among bounds. + + Examples + ======== + + >>> from sympy import exp + >>> from sympy.abc import x, y, z + >>> from sympy.codegen.rewriting import optimize + >>> from sympy.codegen.approximations import SumApprox + >>> bounds = {x: (-1, 1), y: (1000, 2000), z: (-10, 3)} + >>> sum_approx3 = SumApprox(bounds, reltol=1e-3) + >>> sum_approx2 = SumApprox(bounds, reltol=1e-2) + >>> sum_approx1 = SumApprox(bounds, reltol=1e-1) + >>> expr = 3*(x + y + exp(z)) + >>> optimize(expr, [sum_approx3]) + 3*(x + y + exp(z)) + >>> optimize(expr, [sum_approx2]) + 3*y + 3*exp(z) + >>> optimize(expr, [sum_approx1]) + 3*y + + """ + + def __init__(self, bounds, reltol, **kwargs): + super().__init__(**kwargs) + self.bounds = bounds + self.reltol = reltol + + def __call__(self, expr): + return expr.factor().replace(self.query, lambda arg: self.value(arg)) + + def query(self, expr): + return expr.is_Add + + def value(self, add): + for term in add.args: + if term.is_number or term in self.bounds or len(term.free_symbols) != 1: + continue + fs, = term.free_symbols + if fs not in self.bounds: + continue + intrvl = Interval(*self.bounds[fs]) + if is_increasing(term, intrvl, fs): + self.bounds[term] = ( + term.subs({fs: self.bounds[fs][0]}), + term.subs({fs: self.bounds[fs][1]}) + ) + elif is_decreasing(term, intrvl, fs): + self.bounds[term] = ( + term.subs({fs: self.bounds[fs][1]}), + term.subs({fs: self.bounds[fs][0]}) + ) + else: + return add + + if all(term.is_number or term in self.bounds for term in add.args): + bounds = [(term, term) if term.is_number else self.bounds[term] for term in add.args] + largest_abs_guarantee = 0 + for lo, hi in bounds: + if lo <= 0 <= hi: + continue + largest_abs_guarantee = max(largest_abs_guarantee, + min(abs(lo), abs(hi))) + new_terms = [] + for term, (lo, hi) in zip(add.args, bounds): + if max(abs(lo), abs(hi)) >= largest_abs_guarantee*self.reltol: + new_terms.append(term) + return add.func(*new_terms) + else: + return add + + +class SeriesApprox(Optimization): + """ Approximates functions by expanding them as a series. + + Parameters + ========== + + bounds : dict + Mapping expressions to length 2 tuple of bounds (low, high). + reltol : number + Threshold for when to ignore a term. Taken relative to the largest + lower bound among bounds. + max_order : int + Largest order to include in series expansion + n_point_checks : int (even) + The validity of an expansion (with respect to reltol) is checked at + discrete points (linearly spaced over the bounds of the variable). The + number of points used in this numerical check is given by this number. + + Examples + ======== + + >>> from sympy import sin, pi + >>> from sympy.abc import x, y + >>> from sympy.codegen.rewriting import optimize + >>> from sympy.codegen.approximations import SeriesApprox + >>> bounds = {x: (-.1, .1), y: (pi-1, pi+1)} + >>> series_approx2 = SeriesApprox(bounds, reltol=1e-2) + >>> series_approx3 = SeriesApprox(bounds, reltol=1e-3) + >>> series_approx8 = SeriesApprox(bounds, reltol=1e-8) + >>> expr = sin(x)*sin(y) + >>> optimize(expr, [series_approx2]) + x*(-y + (y - pi)**3/6 + pi) + >>> optimize(expr, [series_approx3]) + (-x**3/6 + x)*sin(y) + >>> optimize(expr, [series_approx8]) + sin(x)*sin(y) + + """ + def __init__(self, bounds, reltol, max_order=4, n_point_checks=4, **kwargs): + super().__init__(**kwargs) + self.bounds = bounds + self.reltol = reltol + self.max_order = max_order + if n_point_checks % 2 == 1: + raise ValueError("Checking the solution at expansion point is not helpful") + self.n_point_checks = n_point_checks + self._prec = math.ceil(-math.log10(self.reltol)) + + def __call__(self, expr): + return expr.factor().replace(self.query, lambda arg: self.value(arg)) + + def query(self, expr): + return (expr.is_Function and not isinstance(expr, UndefinedFunction) + and len(expr.args) == 1) + + def value(self, fexpr): + free_symbols = fexpr.free_symbols + if len(free_symbols) != 1: + return fexpr + symb, = free_symbols + if symb not in self.bounds: + return fexpr + lo, hi = self.bounds[symb] + x0 = (lo + hi)/2 + cheapest = None + for n in range(self.max_order+1, 0, -1): + fseri = fexpr.series(symb, x0=x0, n=n).removeO() + n_ok = True + for idx in range(self.n_point_checks): + x = lo + idx*(hi - lo)/(self.n_point_checks - 1) + val = fseri.xreplace({symb: x}) + ref = fexpr.xreplace({symb: x}) + if abs((1 - val/ref).evalf(self._prec)) > self.reltol: + n_ok = False + break + + if n_ok: + cheapest = fseri + else: + break + + if cheapest is None: + return fexpr + else: + return cheapest diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/cfunctions.py b/janus/lib/python3.10/site-packages/sympy/codegen/cfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..2eb3176ea8cd0967de9aa6d93b54f0c1c1354755 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/cfunctions.py @@ -0,0 +1,536 @@ +""" +This module contains SymPy functions mathcin corresponding to special math functions in the +C standard library (since C99, also available in C++11). + +The functions defined in this module allows the user to express functions such as ``expm1`` +as a SymPy function for symbolic manipulation. + +""" +from sympy.core.function import ArgumentIndexError, Function +from sympy.core.numbers import Rational +from sympy.core.power import Pow +from sympy.core.singleton import S +from sympy.functions.elementary.exponential import exp, log +from sympy.functions.elementary.miscellaneous import sqrt + + +def _expm1(x): + return exp(x) - S.One + + +class expm1(Function): + """ + Represents the exponential function minus one. + + Explanation + =========== + + The benefit of using ``expm1(x)`` over ``exp(x) - 1`` + is that the latter is prone to cancellation under finite precision + arithmetic when x is close to zero. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import expm1 + >>> '%.0e' % expm1(1e-99).evalf() + '1e-99' + >>> from math import exp + >>> exp(1e-99) - 1 + 0.0 + >>> expm1(x).diff(x) + exp(x) + + See Also + ======== + + log1p + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return exp(*self.args) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_expand_func(self, **hints): + return _expm1(*self.args) + + def _eval_rewrite_as_exp(self, arg, **kwargs): + return exp(arg) - S.One + + _eval_rewrite_as_tractable = _eval_rewrite_as_exp + + @classmethod + def eval(cls, arg): + exp_arg = exp.eval(arg) + if exp_arg is not None: + return exp_arg - S.One + + def _eval_is_real(self): + return self.args[0].is_real + + def _eval_is_finite(self): + return self.args[0].is_finite + + +def _log1p(x): + return log(x + S.One) + + +class log1p(Function): + """ + Represents the natural logarithm of a number plus one. + + Explanation + =========== + + The benefit of using ``log1p(x)`` over ``log(x + 1)`` + is that the latter is prone to cancellation under finite precision + arithmetic when x is close to zero. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log1p + >>> from sympy import expand_log + >>> '%.0e' % expand_log(log1p(1e-99)).evalf() + '1e-99' + >>> from math import log + >>> log(1 + 1e-99) + 0.0 + >>> log1p(x).diff(x) + 1/(x + 1) + + See Also + ======== + + expm1 + """ + nargs = 1 + + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(self.args[0] + S.One) + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _log1p(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log1p(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + @classmethod + def eval(cls, arg): + if arg.is_Rational: + return log(arg + S.One) + elif not arg.is_Float: # not safe to add 1 to Float + return log.eval(arg + S.One) + elif arg.is_number: + return log(Rational(arg) + S.One) + + def _eval_is_real(self): + return (self.args[0] + S.One).is_nonnegative + + def _eval_is_finite(self): + if (self.args[0] + S.One).is_zero: + return False + return self.args[0].is_finite + + def _eval_is_positive(self): + return self.args[0].is_positive + + def _eval_is_zero(self): + return self.args[0].is_zero + + def _eval_is_nonnegative(self): + return self.args[0].is_nonnegative + +_Two = S(2) + +def _exp2(x): + return Pow(_Two, x) + +class exp2(Function): + """ + Represents the exponential function with base two. + + Explanation + =========== + + The benefit of using ``exp2(x)`` over ``2**x`` + is that the latter is not as efficient under finite precision + arithmetic. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import exp2 + >>> exp2(2).evalf() == 4.0 + True + >>> exp2(x).diff(x) + log(2)*exp2(x) + + See Also + ======== + + log2 + """ + nargs = 1 + + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return self*log(_Two) + else: + raise ArgumentIndexError(self, argindex) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _exp2(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + def _eval_expand_func(self, **hints): + return _exp2(*self.args) + + @classmethod + def eval(cls, arg): + if arg.is_number: + return _exp2(arg) + + +def _log2(x): + return log(x)/log(_Two) + + +class log2(Function): + """ + Represents the logarithm function with base two. + + Explanation + =========== + + The benefit of using ``log2(x)`` over ``log(x)/log(2)`` + is that the latter is not as efficient under finite precision + arithmetic. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log2 + >>> log2(4).evalf() == 2.0 + True + >>> log2(x).diff(x) + 1/(x*log(2)) + + See Also + ======== + + exp2 + log10 + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(log(_Two)*self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + + @classmethod + def eval(cls, arg): + if arg.is_number: + result = log.eval(arg, base=_Two) + if result.is_Atom: + return result + elif arg.is_Pow and arg.base == _Two: + return arg.exp + + def _eval_evalf(self, *args, **kwargs): + return self.rewrite(log).evalf(*args, **kwargs) + + def _eval_expand_func(self, **hints): + return _log2(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log2(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + +def _fma(x, y, z): + return x*y + z + + +class fma(Function): + """ + Represents "fused multiply add". + + Explanation + =========== + + The benefit of using ``fma(x, y, z)`` over ``x*y + z`` + is that, under finite precision arithmetic, the former is + supported by special instructions on some CPUs. + + Examples + ======== + + >>> from sympy.abc import x, y, z + >>> from sympy.codegen.cfunctions import fma + >>> fma(x, y, z).diff(x) + y + + """ + nargs = 3 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex in (1, 2): + return self.args[2 - argindex] + elif argindex == 3: + return S.One + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _fma(*self.args) + + def _eval_rewrite_as_tractable(self, arg, limitvar=None, **kwargs): + return _fma(arg) + + +_Ten = S(10) + + +def _log10(x): + return log(x)/log(_Ten) + + +class log10(Function): + """ + Represents the logarithm function with base ten. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import log10 + >>> log10(100).evalf() == 2.0 + True + >>> log10(x).diff(x) + 1/(x*log(10)) + + See Also + ======== + + log2 + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return S.One/(log(_Ten)*self.args[0]) + else: + raise ArgumentIndexError(self, argindex) + + + @classmethod + def eval(cls, arg): + if arg.is_number: + result = log.eval(arg, base=_Ten) + if result.is_Atom: + return result + elif arg.is_Pow and arg.base == _Ten: + return arg.exp + + def _eval_expand_func(self, **hints): + return _log10(*self.args) + + def _eval_rewrite_as_log(self, arg, **kwargs): + return _log10(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_log + + +def _Sqrt(x): + return Pow(x, S.Half) + + +class Sqrt(Function): # 'sqrt' already defined in sympy.functions.elementary.miscellaneous + """ + Represents the square root function. + + Explanation + =========== + + The reason why one would use ``Sqrt(x)`` over ``sqrt(x)`` + is that the latter is internally represented as ``Pow(x, S.Half)`` which + may not be what one wants when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import Sqrt + >>> Sqrt(x) + Sqrt(x) + >>> Sqrt(x).diff(x) + 1/(2*sqrt(x)) + + See Also + ======== + + Cbrt + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return Pow(self.args[0], Rational(-1, 2))/_Two + else: + raise ArgumentIndexError(self, argindex) + + def _eval_expand_func(self, **hints): + return _Sqrt(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _Sqrt(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +def _Cbrt(x): + return Pow(x, Rational(1, 3)) + + +class Cbrt(Function): # 'cbrt' already defined in sympy.functions.elementary.miscellaneous + """ + Represents the cube root function. + + Explanation + =========== + + The reason why one would use ``Cbrt(x)`` over ``cbrt(x)`` + is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which + may not be what one wants when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cfunctions import Cbrt + >>> Cbrt(x) + Cbrt(x) + >>> Cbrt(x).diff(x) + 1/(3*x**(2/3)) + + See Also + ======== + + Sqrt + """ + nargs = 1 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex == 1: + return Pow(self.args[0], Rational(-_Two/3))/3 + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _Cbrt(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _Cbrt(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +def _hypot(x, y): + return sqrt(Pow(x, 2) + Pow(y, 2)) + + +class hypot(Function): + """ + Represents the hypotenuse function. + + Explanation + =========== + + The hypotenuse function is provided by e.g. the math library + in the C99 standard, hence one may want to represent the function + symbolically when doing code-generation. + + Examples + ======== + + >>> from sympy.abc import x, y + >>> from sympy.codegen.cfunctions import hypot + >>> hypot(3, 4).evalf() == 5.0 + True + >>> hypot(x, y) + hypot(x, y) + >>> hypot(x, y).diff(x) + x/hypot(x, y) + + """ + nargs = 2 + + def fdiff(self, argindex=1): + """ + Returns the first derivative of this function. + """ + if argindex in (1, 2): + return 2*self.args[argindex-1]/(_Two*self.func(*self.args)) + else: + raise ArgumentIndexError(self, argindex) + + + def _eval_expand_func(self, **hints): + return _hypot(*self.args) + + def _eval_rewrite_as_Pow(self, arg, **kwargs): + return _hypot(arg) + + _eval_rewrite_as_tractable = _eval_rewrite_as_Pow + + +class isnan(Function): + nargs = 1 diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/cnodes.py b/janus/lib/python3.10/site-packages/sympy/codegen/cnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..dd2a324ee49cabcd42e99ca5d8e5379cc9262c4e --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/cnodes.py @@ -0,0 +1,156 @@ +""" +AST nodes specific to the C family of languages +""" + +from sympy.codegen.ast import ( + Attribute, Declaration, Node, String, Token, Type, none, + FunctionCall, CodeBlock + ) +from sympy.core.basic import Basic +from sympy.core.containers import Tuple +from sympy.core.sympify import sympify + +void = Type('void') + +restrict = Attribute('restrict') # guarantees no pointer aliasing +volatile = Attribute('volatile') +static = Attribute('static') + + +def alignof(arg): + """ Generate of FunctionCall instance for calling 'alignof' """ + return FunctionCall('alignof', [String(arg) if isinstance(arg, str) else arg]) + + +def sizeof(arg): + """ Generate of FunctionCall instance for calling 'sizeof' + + Examples + ======== + + >>> from sympy.codegen.ast import real + >>> from sympy.codegen.cnodes import sizeof + >>> from sympy import ccode + >>> ccode(sizeof(real)) + 'sizeof(double)' + """ + return FunctionCall('sizeof', [String(arg) if isinstance(arg, str) else arg]) + + +class CommaOperator(Basic): + """ Represents the comma operator in C """ + def __new__(cls, *args): + return Basic.__new__(cls, *[sympify(arg) for arg in args]) + + +class Label(Node): + """ Label for use with e.g. goto statement. + + Examples + ======== + + >>> from sympy import ccode, Symbol + >>> from sympy.codegen.cnodes import Label, PreIncrement + >>> print(ccode(Label('foo'))) + foo: + >>> print(ccode(Label('bar', [PreIncrement(Symbol('a'))]))) + bar: + ++(a); + + """ + __slots__ = _fields = ('name', 'body') + defaults = {'body': none} + _construct_name = String + + @classmethod + def _construct_body(cls, itr): + if isinstance(itr, CodeBlock): + return itr + else: + return CodeBlock(*itr) + + +class goto(Token): + """ Represents goto in C """ + __slots__ = _fields = ('label',) + _construct_label = Label + + +class PreDecrement(Basic): + """ Represents the pre-decrement operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PreDecrement + >>> from sympy import ccode + >>> ccode(PreDecrement(x)) + '--(x)' + + """ + nargs = 1 + + +class PostDecrement(Basic): + """ Represents the post-decrement operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PostDecrement + >>> from sympy import ccode + >>> ccode(PostDecrement(x)) + '(x)--' + + """ + nargs = 1 + + +class PreIncrement(Basic): + """ Represents the pre-increment operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PreIncrement + >>> from sympy import ccode + >>> ccode(PreIncrement(x)) + '++(x)' + + """ + nargs = 1 + + +class PostIncrement(Basic): + """ Represents the post-increment operator + + Examples + ======== + + >>> from sympy.abc import x + >>> from sympy.codegen.cnodes import PostIncrement + >>> from sympy import ccode + >>> ccode(PostIncrement(x)) + '(x)++' + + """ + nargs = 1 + + +class struct(Node): + """ Represents a struct in C """ + __slots__ = _fields = ('name', 'declarations') + defaults = {'name': none} + _construct_name = String + + @classmethod + def _construct_declarations(cls, args): + return Tuple(*[Declaration(arg) for arg in args]) + + +class union(struct): + """ Represents a union in C """ + __slots__ = () diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/cxxnodes.py b/janus/lib/python3.10/site-packages/sympy/codegen/cxxnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..7f7aafd01ab2de99ad0f668275889863fc73f5aa --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/cxxnodes.py @@ -0,0 +1,14 @@ +""" +AST nodes specific to C++. +""" + +from sympy.codegen.ast import Attribute, String, Token, Type, none + +class using(Token): + """ Represents a 'using' statement in C++ """ + __slots__ = _fields = ('type', 'alias') + defaults = {'alias': none} + _construct_type = Type + _construct_alias = String + +constexpr = Attribute('constexpr') diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/futils.py b/janus/lib/python3.10/site-packages/sympy/codegen/futils.py new file mode 100644 index 0000000000000000000000000000000000000000..4a1f5751fbd4d6b44d99c69a74ad89a8496f8648 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/futils.py @@ -0,0 +1,40 @@ +from itertools import chain +from sympy.codegen.fnodes import Module +from sympy.core.symbol import Dummy +from sympy.printing.fortran import FCodePrinter + +""" This module collects utilities for rendering Fortran code. """ + + +def render_as_module(definitions, name, declarations=(), printer_settings=None): + """ Creates a ``Module`` instance and renders it as a string. + + This generates Fortran source code for a module with the correct ``use`` statements. + + Parameters + ========== + + definitions : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. + name : str + Passed to :class:`sympy.codegen.fnodes.Module`. + declarations : iterable + Passed to :class:`sympy.codegen.fnodes.Module`. It will be extended with + use statements, 'implicit none' and public list generated from ``definitions``. + printer_settings : dict + Passed to ``FCodePrinter`` (default: ``{'standard': 2003, 'source_format': 'free'}``). + + """ + printer_settings = printer_settings or {'standard': 2003, 'source_format': 'free'} + printer = FCodePrinter(printer_settings) + dummy = Dummy() + if isinstance(definitions, Module): + raise ValueError("This function expects to construct a module on its own.") + mod = Module(name, chain(declarations, [dummy]), definitions) + fstr = printer.doprint(mod) + module_use_str = ' %s\n' % ' \n'.join(['use %s, only: %s' % (k, ', '.join(v)) for + k, v in printer.module_uses.items()]) + module_use_str += ' implicit none\n' + module_use_str += ' private\n' + module_use_str += ' public %s\n' % ', '.join([str(node.name) for node in definitions if getattr(node, 'name', None)]) + return fstr.replace(printer.doprint(dummy), module_use_str) diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/pynodes.py b/janus/lib/python3.10/site-packages/sympy/codegen/pynodes.py new file mode 100644 index 0000000000000000000000000000000000000000..f0a08b4a79d32f63d345947d6be310b44504dbf5 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/pynodes.py @@ -0,0 +1,11 @@ +from .abstract_nodes import List as AbstractList +from .ast import Token + + +class List(AbstractList): + pass + + +class NumExprEvaluate(Token): + """represents a call to :class:`numexpr`s :func:`evaluate`""" + __slots__ = _fields = ('expr',) diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/tests/__init__.py b/janus/lib/python3.10/site-packages/sympy/codegen/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_abstract_nodes.cpython-310.pyc b/janus/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_abstract_nodes.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..0a12c2ee3c7720442c234999f3d3e45767a3b9cf Binary files /dev/null and b/janus/lib/python3.10/site-packages/sympy/codegen/tests/__pycache__/test_abstract_nodes.cpython-310.pyc differ diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_ast.py b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_ast.py new file mode 100644 index 0000000000000000000000000000000000000000..c447ac86ce4ff8478f193b2b2e37775b08a7208f --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_ast.py @@ -0,0 +1,661 @@ +import math +from sympy.core.containers import Tuple +from sympy.core.numbers import nan, oo, Float, Integer +from sympy.core.relational import Lt +from sympy.core.symbol import symbols, Symbol +from sympy.functions.elementary.trigonometric import sin +from sympy.matrices.dense import Matrix +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.sets.fancysets import Range +from sympy.tensor.indexed import Idx, IndexedBase +from sympy.testing.pytest import raises + + +from sympy.codegen.ast import ( + Assignment, Attribute, aug_assign, CodeBlock, For, Type, Variable, Pointer, Declaration, + AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment, + DivAugmentedAssignment, ModAugmentedAssignment, value_const, pointer_const, + integer, real, complex_, int8, uint8, float16 as f16, float32 as f32, + float64 as f64, float80 as f80, float128 as f128, complex64 as c64, complex128 as c128, + While, Scope, String, Print, QuotedString, FunctionPrototype, FunctionDefinition, Return, + FunctionCall, untyped, IntBaseType, intc, Node, none, NoneToken, Token, Comment +) + +x, y, z, t, x0, x1, x2, a, b = symbols("x, y, z, t, x0, x1, x2, a, b") +n = symbols("n", integer=True) +A = MatrixSymbol('A', 3, 1) +mat = Matrix([1, 2, 3]) +B = IndexedBase('B') +i = Idx("i", n) +A22 = MatrixSymbol('A22',2,2) +B22 = MatrixSymbol('B22',2,2) + + +def test_Assignment(): + # Here we just do things to show they don't error + Assignment(x, y) + Assignment(x, 0) + Assignment(A, mat) + Assignment(A[1,0], 0) + Assignment(A[1,0], x) + Assignment(B[i], x) + Assignment(B[i], 0) + a = Assignment(x, y) + assert a.func(*a.args) == a + assert a.op == ':=' + # Here we test things to show that they error + # Matrix to scalar + raises(ValueError, lambda: Assignment(B[i], A)) + raises(ValueError, lambda: Assignment(B[i], mat)) + raises(ValueError, lambda: Assignment(x, mat)) + raises(ValueError, lambda: Assignment(x, A)) + raises(ValueError, lambda: Assignment(A[1,0], mat)) + # Scalar to matrix + raises(ValueError, lambda: Assignment(A, x)) + raises(ValueError, lambda: Assignment(A, 0)) + # Non-atomic lhs + raises(TypeError, lambda: Assignment(mat, A)) + raises(TypeError, lambda: Assignment(0, x)) + raises(TypeError, lambda: Assignment(x*x, 1)) + raises(TypeError, lambda: Assignment(A + A, mat)) + raises(TypeError, lambda: Assignment(B, 0)) + + +def test_AugAssign(): + # Here we just do things to show they don't error + aug_assign(x, '+', y) + aug_assign(x, '+', 0) + aug_assign(A, '+', mat) + aug_assign(A[1, 0], '+', 0) + aug_assign(A[1, 0], '+', x) + aug_assign(B[i], '+', x) + aug_assign(B[i], '+', 0) + + # Check creation via aug_assign vs constructor + for binop, cls in [ + ('+', AddAugmentedAssignment), + ('-', SubAugmentedAssignment), + ('*', MulAugmentedAssignment), + ('/', DivAugmentedAssignment), + ('%', ModAugmentedAssignment), + ]: + a = aug_assign(x, binop, y) + b = cls(x, y) + assert a.func(*a.args) == a == b + assert a.binop == binop + assert a.op == binop + '=' + + # Here we test things to show that they error + # Matrix to scalar + raises(ValueError, lambda: aug_assign(B[i], '+', A)) + raises(ValueError, lambda: aug_assign(B[i], '+', mat)) + raises(ValueError, lambda: aug_assign(x, '+', mat)) + raises(ValueError, lambda: aug_assign(x, '+', A)) + raises(ValueError, lambda: aug_assign(A[1, 0], '+', mat)) + # Scalar to matrix + raises(ValueError, lambda: aug_assign(A, '+', x)) + raises(ValueError, lambda: aug_assign(A, '+', 0)) + # Non-atomic lhs + raises(TypeError, lambda: aug_assign(mat, '+', A)) + raises(TypeError, lambda: aug_assign(0, '+', x)) + raises(TypeError, lambda: aug_assign(x * x, '+', 1)) + raises(TypeError, lambda: aug_assign(A + A, '+', mat)) + raises(TypeError, lambda: aug_assign(B, '+', 0)) + + +def test_Assignment_printing(): + assignment_classes = [ + Assignment, + AddAugmentedAssignment, + SubAugmentedAssignment, + MulAugmentedAssignment, + DivAugmentedAssignment, + ModAugmentedAssignment, + ] + pairs = [ + (x, 2 * y + 2), + (B[i], x), + (A22, B22), + (A[0, 0], x), + ] + + for cls in assignment_classes: + for lhs, rhs in pairs: + a = cls(lhs, rhs) + assert repr(a) == '%s(%s, %s)' % (cls.__name__, repr(lhs), repr(rhs)) + + +def test_CodeBlock(): + c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1)) + assert c.func(*c.args) == c + + assert c.left_hand_sides == Tuple(x, y) + assert c.right_hand_sides == Tuple(1, x + 1) + +def test_CodeBlock_topological_sort(): + assignments = [ + Assignment(x, y + z), + Assignment(z, 1), + Assignment(t, x), + Assignment(y, 2), + ] + + ordered_assignments = [ + # Note that the unrelated z=1 and y=2 are kept in that order + Assignment(z, 1), + Assignment(y, 2), + Assignment(x, y + z), + Assignment(t, x), + ] + c1 = CodeBlock.topological_sort(assignments) + assert c1 == CodeBlock(*ordered_assignments) + + # Cycle + invalid_assignments = [ + Assignment(x, y + z), + Assignment(z, 1), + Assignment(y, x), + Assignment(y, 2), + ] + + raises(ValueError, lambda: CodeBlock.topological_sort(invalid_assignments)) + + # Free symbols + free_assignments = [ + Assignment(x, y + z), + Assignment(z, a * b), + Assignment(t, x), + Assignment(y, b + 3), + ] + + free_assignments_ordered = [ + Assignment(z, a * b), + Assignment(y, b + 3), + Assignment(x, y + z), + Assignment(t, x), + ] + + c2 = CodeBlock.topological_sort(free_assignments) + assert c2 == CodeBlock(*free_assignments_ordered) + +def test_CodeBlock_free_symbols(): + c1 = CodeBlock( + Assignment(x, y + z), + Assignment(z, 1), + Assignment(t, x), + Assignment(y, 2), + ) + assert c1.free_symbols == set() + + c2 = CodeBlock( + Assignment(x, y + z), + Assignment(z, a * b), + Assignment(t, x), + Assignment(y, b + 3), + ) + assert c2.free_symbols == {a, b} + +def test_CodeBlock_cse(): + c1 = CodeBlock( + Assignment(y, 1), + Assignment(x, sin(y)), + Assignment(z, sin(y)), + Assignment(t, x*z), + ) + assert c1.cse() == CodeBlock( + Assignment(y, 1), + Assignment(x0, sin(y)), + Assignment(x, x0), + Assignment(z, x0), + Assignment(t, x*z), + ) + + # Multiple assignments to same symbol not supported + raises(NotImplementedError, lambda: CodeBlock( + Assignment(x, 1), + Assignment(y, 1), Assignment(y, 2) + ).cse()) + + # Check auto-generated symbols do not collide with existing ones + c2 = CodeBlock( + Assignment(x0, sin(y) + 1), + Assignment(x1, 2 * sin(y)), + Assignment(z, x * y), + ) + assert c2.cse() == CodeBlock( + Assignment(x2, sin(y)), + Assignment(x0, x2 + 1), + Assignment(x1, 2 * x2), + Assignment(z, x * y), + ) + + +def test_CodeBlock_cse__issue_14118(): + # see https://github.com/sympy/sympy/issues/14118 + c = CodeBlock( + Assignment(A22, Matrix([[x, sin(y)],[3, 4]])), + Assignment(B22, Matrix([[sin(y), 2*sin(y)], [sin(y)**2, 7]])) + ) + assert c.cse() == CodeBlock( + Assignment(x0, sin(y)), + Assignment(A22, Matrix([[x, x0],[3, 4]])), + Assignment(B22, Matrix([[x0, 2*x0], [x0**2, 7]])) + ) + +def test_For(): + f = For(n, Range(0, 3), (Assignment(A[n, 0], x + n), aug_assign(x, '+', y))) + f = For(n, (1, 2, 3, 4, 5), (Assignment(A[n, 0], x + n),)) + assert f.func(*f.args) == f + raises(TypeError, lambda: For(n, x, (x + y,))) + + +def test_none(): + assert none.is_Atom + assert none == none + class Foo(Token): + pass + foo = Foo() + assert foo != none + assert none == None + assert none == NoneToken() + assert none.func(*none.args) == none + + +def test_String(): + st = String('foobar') + assert st.is_Atom + assert st == String('foobar') + assert st.text == 'foobar' + assert st.func(**st.kwargs()) == st + assert st.func(*st.args) == st + + + class Signifier(String): + pass + + si = Signifier('foobar') + assert si != st + assert si.text == st.text + s = String('foo') + assert str(s) == 'foo' + assert repr(s) == "String('foo')" + +def test_Comment(): + c = Comment('foobar') + assert c.text == 'foobar' + assert str(c) == 'foobar' + +def test_Node(): + n = Node() + assert n == Node() + assert n.func(*n.args) == n + + +def test_Type(): + t = Type('MyType') + assert len(t.args) == 1 + assert t.name == String('MyType') + assert str(t) == 'MyType' + assert repr(t) == "Type(String('MyType'))" + assert Type(t) == t + assert t.func(*t.args) == t + t1 = Type('t1') + t2 = Type('t2') + assert t1 != t2 + assert t1 == t1 and t2 == t2 + t1b = Type('t1') + assert t1 == t1b + assert t2 != t1b + + +def test_Type__from_expr(): + assert Type.from_expr(i) == integer + u = symbols('u', real=True) + assert Type.from_expr(u) == real + assert Type.from_expr(n) == integer + assert Type.from_expr(3) == integer + assert Type.from_expr(3.0) == real + assert Type.from_expr(3+1j) == complex_ + raises(ValueError, lambda: Type.from_expr(sum)) + + +def test_Type__cast_check__integers(): + # Rounding + raises(ValueError, lambda: integer.cast_check(3.5)) + assert integer.cast_check('3') == 3 + assert integer.cast_check(Float('3.0000000000000000000')) == 3 + assert integer.cast_check(Float('3.0000000000000000001')) == 3 # unintuitive maybe? + + # Range + assert int8.cast_check(127.0) == 127 + raises(ValueError, lambda: int8.cast_check(128)) + assert int8.cast_check(-128) == -128 + raises(ValueError, lambda: int8.cast_check(-129)) + + assert uint8.cast_check(0) == 0 + assert uint8.cast_check(128) == 128 + raises(ValueError, lambda: uint8.cast_check(256.0)) + raises(ValueError, lambda: uint8.cast_check(-1)) + +def test_Attribute(): + noexcept = Attribute('noexcept') + assert noexcept == Attribute('noexcept') + alignas16 = Attribute('alignas', [16]) + alignas32 = Attribute('alignas', [32]) + assert alignas16 != alignas32 + assert alignas16.func(*alignas16.args) == alignas16 + + +def test_Variable(): + v = Variable(x, type=real) + assert v == Variable(v) + assert v == Variable('x', type=real) + assert v.symbol == x + assert v.type == real + assert value_const not in v.attrs + assert v.func(*v.args) == v + assert str(v) == 'Variable(x, type=real)' + + w = Variable(y, f32, attrs={value_const}) + assert w.symbol == y + assert w.type == f32 + assert value_const in w.attrs + assert w.func(*w.args) == w + + v_n = Variable(n, type=Type.from_expr(n)) + assert v_n.type == integer + assert v_n.func(*v_n.args) == v_n + v_i = Variable(i, type=Type.from_expr(n)) + assert v_i.type == integer + assert v_i != v_n + + a_i = Variable.deduced(i) + assert a_i.type == integer + assert Variable.deduced(Symbol('x', real=True)).type == real + assert a_i.func(*a_i.args) == a_i + + v_n2 = Variable.deduced(n, value=3.5, cast_check=False) + assert v_n2.func(*v_n2.args) == v_n2 + assert abs(v_n2.value - 3.5) < 1e-15 + raises(ValueError, lambda: Variable.deduced(n, value=3.5, cast_check=True)) + + v_n3 = Variable.deduced(n) + assert v_n3.type == integer + assert str(v_n3) == 'Variable(n, type=integer)' + assert Variable.deduced(z, value=3).type == integer + assert Variable.deduced(z, value=3.0).type == real + assert Variable.deduced(z, value=3.0+1j).type == complex_ + + +def test_Pointer(): + p = Pointer(x) + assert p.symbol == x + assert p.type == untyped + assert value_const not in p.attrs + assert pointer_const not in p.attrs + assert p.func(*p.args) == p + + u = symbols('u', real=True) + pu = Pointer(u, type=Type.from_expr(u), attrs={value_const, pointer_const}) + assert pu.symbol is u + assert pu.type == real + assert value_const in pu.attrs + assert pointer_const in pu.attrs + assert pu.func(*pu.args) == pu + + i = symbols('i', integer=True) + deref = pu[i] + assert deref.indices == (i,) + + +def test_Declaration(): + u = symbols('u', real=True) + vu = Variable(u, type=Type.from_expr(u)) + assert Declaration(vu).variable.type == real + vn = Variable(n, type=Type.from_expr(n)) + assert Declaration(vn).variable.type == integer + + # PR 19107, does not allow comparison between expressions and Basic + # lt = StrictLessThan(vu, vn) + # assert isinstance(lt, StrictLessThan) + + vuc = Variable(u, Type.from_expr(u), value=3.0, attrs={value_const}) + assert value_const in vuc.attrs + assert pointer_const not in vuc.attrs + decl = Declaration(vuc) + assert decl.variable == vuc + assert isinstance(decl.variable.value, Float) + assert decl.variable.value == 3.0 + assert decl.func(*decl.args) == decl + assert vuc.as_Declaration() == decl + assert vuc.as_Declaration(value=None, attrs=None) == Declaration(vu) + + vy = Variable(y, type=integer, value=3) + decl2 = Declaration(vy) + assert decl2.variable == vy + assert decl2.variable.value == Integer(3) + + vi = Variable(i, type=Type.from_expr(i), value=3.0) + decl3 = Declaration(vi) + assert decl3.variable.type == integer + assert decl3.variable.value == 3.0 + + raises(ValueError, lambda: Declaration(vi, 42)) + + +def test_IntBaseType(): + assert intc.name == String('intc') + assert intc.args == (intc.name,) + assert str(IntBaseType('a').name) == 'a' + + +def test_FloatType(): + assert f16.dig == 3 + assert f32.dig == 6 + assert f64.dig == 15 + assert f80.dig == 18 + assert f128.dig == 33 + + assert f16.decimal_dig == 5 + assert f32.decimal_dig == 9 + assert f64.decimal_dig == 17 + assert f80.decimal_dig == 21 + assert f128.decimal_dig == 36 + + assert f16.max_exponent == 16 + assert f32.max_exponent == 128 + assert f64.max_exponent == 1024 + assert f80.max_exponent == 16384 + assert f128.max_exponent == 16384 + + assert f16.min_exponent == -13 + assert f32.min_exponent == -125 + assert f64.min_exponent == -1021 + assert f80.min_exponent == -16381 + assert f128.min_exponent == -16381 + + assert abs(f16.eps / Float('0.00097656', precision=16) - 1) < 0.1*10**-f16.dig + assert abs(f32.eps / Float('1.1920929e-07', precision=32) - 1) < 0.1*10**-f32.dig + assert abs(f64.eps / Float('2.2204460492503131e-16', precision=64) - 1) < 0.1*10**-f64.dig + assert abs(f80.eps / Float('1.08420217248550443401e-19', precision=80) - 1) < 0.1*10**-f80.dig + assert abs(f128.eps / Float(' 1.92592994438723585305597794258492732e-34', precision=128) - 1) < 0.1*10**-f128.dig + + assert abs(f16.max / Float('65504', precision=16) - 1) < .1*10**-f16.dig + assert abs(f32.max / Float('3.40282347e+38', precision=32) - 1) < 0.1*10**-f32.dig + assert abs(f64.max / Float('1.79769313486231571e+308', precision=64) - 1) < 0.1*10**-f64.dig # cf. np.finfo(np.float64).max + assert abs(f80.max / Float('1.18973149535723176502e+4932', precision=80) - 1) < 0.1*10**-f80.dig + assert abs(f128.max / Float('1.18973149535723176508575932662800702e+4932', precision=128) - 1) < 0.1*10**-f128.dig + + # cf. np.finfo(np.float32).tiny + assert abs(f16.tiny / Float('6.1035e-05', precision=16) - 1) < 0.1*10**-f16.dig + assert abs(f32.tiny / Float('1.17549435e-38', precision=32) - 1) < 0.1*10**-f32.dig + assert abs(f64.tiny / Float('2.22507385850720138e-308', precision=64) - 1) < 0.1*10**-f64.dig + assert abs(f80.tiny / Float('3.36210314311209350626e-4932', precision=80) - 1) < 0.1*10**-f80.dig + assert abs(f128.tiny / Float('3.3621031431120935062626778173217526e-4932', precision=128) - 1) < 0.1*10**-f128.dig + + assert f64.cast_check(0.5) == Float(0.5, 17) + assert abs(f64.cast_check(3.7) - 3.7) < 3e-17 + assert isinstance(f64.cast_check(3), (Float, float)) + + assert f64.cast_nocheck(oo) == float('inf') + assert f64.cast_nocheck(-oo) == float('-inf') + assert f64.cast_nocheck(float(oo)) == float('inf') + assert f64.cast_nocheck(float(-oo)) == float('-inf') + assert math.isnan(f64.cast_nocheck(nan)) + + assert f32 != f64 + assert f64 == f64.func(*f64.args) + + +def test_Type__cast_check__floating_point(): + raises(ValueError, lambda: f32.cast_check(123.45678949)) + raises(ValueError, lambda: f32.cast_check(12.345678949)) + raises(ValueError, lambda: f32.cast_check(1.2345678949)) + raises(ValueError, lambda: f32.cast_check(.12345678949)) + assert abs(123.456789049 - f32.cast_check(123.456789049) - 4.9e-8) < 1e-8 + assert abs(0.12345678904 - f32.cast_check(0.12345678904) - 4e-11) < 1e-11 + + dcm21 = Float('0.123456789012345670499') # 21 decimals + assert abs(dcm21 - f64.cast_check(dcm21) - 4.99e-19) < 1e-19 + + f80.cast_check(Float('0.12345678901234567890103', precision=88)) + raises(ValueError, lambda: f80.cast_check(Float('0.12345678901234567890149', precision=88))) + + v10 = 12345.67894 + raises(ValueError, lambda: f32.cast_check(v10)) + assert abs(Float(str(v10), precision=64+8) - f64.cast_check(v10)) < v10*1e-16 + + assert abs(f32.cast_check(2147483647) - 2147483650) < 1 + + +def test_Type__cast_check__complex_floating_point(): + val9_11 = 123.456789049 + 0.123456789049j + raises(ValueError, lambda: c64.cast_check(.12345678949 + .12345678949j)) + assert abs(val9_11 - c64.cast_check(val9_11) - 4.9e-8) < 1e-8 + + dcm21 = Float('0.123456789012345670499') + 1e-20j # 21 decimals + assert abs(dcm21 - c128.cast_check(dcm21) - 4.99e-19) < 1e-19 + v19 = Float('0.1234567890123456749') + 1j*Float('0.1234567890123456749') + raises(ValueError, lambda: c128.cast_check(v19)) + + +def test_While(): + xpp = AddAugmentedAssignment(x, 1) + whl1 = While(x < 2, [xpp]) + assert whl1.condition.args[0] == x + assert whl1.condition.args[1] == 2 + assert whl1.condition == Lt(x, 2, evaluate=False) + assert whl1.body.args == (xpp,) + assert whl1.func(*whl1.args) == whl1 + + cblk = CodeBlock(AddAugmentedAssignment(x, 1)) + whl2 = While(x < 2, cblk) + assert whl1 == whl2 + assert whl1 != While(x < 3, [xpp]) + + +def test_Scope(): + assign = Assignment(x, y) + incr = AddAugmentedAssignment(x, 1) + scp = Scope([assign, incr]) + cblk = CodeBlock(assign, incr) + assert scp.body == cblk + assert scp == Scope(cblk) + assert scp != Scope([incr, assign]) + assert scp.func(*scp.args) == scp + + +def test_Print(): + fmt = "%d %.3f" + ps = Print([n, x], fmt) + assert str(ps.format_string) == fmt + assert ps.print_args == Tuple(n, x) + assert ps.args == (Tuple(n, x), QuotedString(fmt), none) + assert ps == Print((n, x), fmt) + assert ps != Print([x, n], fmt) + assert ps.func(*ps.args) == ps + + ps2 = Print([n, x]) + assert ps2 == Print([n, x]) + assert ps2 != ps + assert ps2.format_string == None + + +def test_FunctionPrototype_and_FunctionDefinition(): + vx = Variable(x, type=real) + vn = Variable(n, type=integer) + fp1 = FunctionPrototype(real, 'power', [vx, vn]) + assert fp1.return_type == real + assert fp1.name == String('power') + assert fp1.parameters == Tuple(vx, vn) + assert fp1 == FunctionPrototype(real, 'power', [vx, vn]) + assert fp1 != FunctionPrototype(real, 'power', [vn, vx]) + assert fp1.func(*fp1.args) == fp1 + + + body = [Assignment(x, x**n), Return(x)] + fd1 = FunctionDefinition(real, 'power', [vx, vn], body) + assert fd1.return_type == real + assert str(fd1.name) == 'power' + assert fd1.parameters == Tuple(vx, vn) + assert fd1.body == CodeBlock(*body) + assert fd1 == FunctionDefinition(real, 'power', [vx, vn], body) + assert fd1 != FunctionDefinition(real, 'power', [vx, vn], body[::-1]) + assert fd1.func(*fd1.args) == fd1 + + fp2 = FunctionPrototype.from_FunctionDefinition(fd1) + assert fp2 == fp1 + + fd2 = FunctionDefinition.from_FunctionPrototype(fp1, body) + assert fd2 == fd1 + + +def test_Return(): + rs = Return(x) + assert rs.args == (x,) + assert rs == Return(x) + assert rs != Return(y) + assert rs.func(*rs.args) == rs + + +def test_FunctionCall(): + fc = FunctionCall('power', (x, 3)) + assert fc.function_args[0] == x + assert fc.function_args[1] == 3 + assert len(fc.function_args) == 2 + assert isinstance(fc.function_args[1], Integer) + assert fc == FunctionCall('power', (x, 3)) + assert fc != FunctionCall('power', (3, x)) + assert fc != FunctionCall('Power', (x, 3)) + assert fc.func(*fc.args) == fc + + fc2 = FunctionCall('fma', [2, 3, 4]) + assert len(fc2.function_args) == 3 + assert fc2.function_args[0] == 2 + assert fc2.function_args[1] == 3 + assert fc2.function_args[2] == 4 + assert str(fc2) in ( # not sure if QuotedString is a better default... + 'FunctionCall(fma, function_args=(2, 3, 4))', + 'FunctionCall("fma", function_args=(2, 3, 4))', + ) + +def test_ast_replace(): + x = Variable('x', real) + y = Variable('y', real) + n = Variable('n', integer) + + pwer = FunctionDefinition(real, 'pwer', [x, n], [pow(x.symbol, n.symbol)]) + pname = pwer.name + pcall = FunctionCall('pwer', [y, 3]) + + tree1 = CodeBlock(pwer, pcall) + assert str(tree1.args[0].name) == 'pwer' + assert str(tree1.args[1].name) == 'pwer' + for a, b in zip(tree1, [pwer, pcall]): + assert a == b + + tree2 = tree1.replace(pname, String('power')) + assert str(tree1.args[0].name) == 'pwer' + assert str(tree1.args[1].name) == 'pwer' + assert str(tree2.args[0].name) == 'power' + assert str(tree2.args[1].name) == 'power' diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cfunctions.py b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..ca85758d3461f61f33e3d27386e20d47b39de804 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cfunctions.py @@ -0,0 +1,165 @@ +from sympy.core.numbers import (Rational, pi) +from sympy.core.singleton import S +from sympy.core.symbol import (Symbol, symbols) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.codegen.cfunctions import ( + expm1, log1p, exp2, log2, fma, log10, Sqrt, Cbrt, hypot +) +from sympy.core.function import expand_log + + +def test_expm1(): + # Eval + assert expm1(0) == 0 + + x = Symbol('x', real=True) + + # Expand and rewrite + assert expm1(x).expand(func=True) - exp(x) == -1 + assert expm1(x).rewrite('tractable') - exp(x) == -1 + assert expm1(x).rewrite('exp') - exp(x) == -1 + + # Precision + assert not ((exp(1e-10).evalf() - 1) - 1e-10 - 5e-21) < 1e-22 # for comparison + assert abs(expm1(1e-10).evalf() - 1e-10 - 5e-21) < 1e-22 + + # Properties + assert expm1(x).is_real + assert expm1(x).is_finite + + # Diff + assert expm1(42*x).diff(x) - 42*exp(42*x) == 0 + assert expm1(42*x).diff(x) - expm1(42*x).expand(func=True).diff(x) == 0 + + +def test_log1p(): + # Eval + assert log1p(0) == 0 + d = S(10) + assert expand_log(log1p(d**-1000) - log(d**1000 + 1) + log(d**1000)) == 0 + + x = Symbol('x', real=True) + + # Expand and rewrite + assert log1p(x).expand(func=True) - log(x + 1) == 0 + assert log1p(x).rewrite('tractable') - log(x + 1) == 0 + assert log1p(x).rewrite('log') - log(x + 1) == 0 + + # Precision + assert not abs(log(1e-99 + 1).evalf() - 1e-99) < 1e-100 # for comparison + assert abs(expand_log(log1p(1e-99)).evalf() - 1e-99) < 1e-100 + + # Properties + assert log1p(-2**Rational(-1, 2)).is_real + + assert not log1p(-1).is_finite + assert log1p(pi).is_finite + + assert not log1p(x).is_positive + assert log1p(Symbol('y', positive=True)).is_positive + + assert not log1p(x).is_zero + assert log1p(Symbol('z', zero=True)).is_zero + + assert not log1p(x).is_nonnegative + assert log1p(Symbol('o', nonnegative=True)).is_nonnegative + + # Diff + assert log1p(42*x).diff(x) - 42/(42*x + 1) == 0 + assert log1p(42*x).diff(x) - log1p(42*x).expand(func=True).diff(x) == 0 + + +def test_exp2(): + # Eval + assert exp2(2) == 4 + + x = Symbol('x', real=True) + + # Expand + assert exp2(x).expand(func=True) - 2**x == 0 + + # Diff + assert exp2(42*x).diff(x) - 42*exp2(42*x)*log(2) == 0 + assert exp2(42*x).diff(x) - exp2(42*x).diff(x) == 0 + + +def test_log2(): + # Eval + assert log2(8) == 3 + assert log2(pi) != log(pi)/log(2) # log2 should *save* (CPU) instructions + + x = Symbol('x', real=True) + assert log2(x) != log(x)/log(2) + assert log2(2**x) == x + + # Expand + assert log2(x).expand(func=True) - log(x)/log(2) == 0 + + # Diff + assert log2(42*x).diff() - 1/(log(2)*x) == 0 + assert log2(42*x).diff() - log2(42*x).expand(func=True).diff(x) == 0 + + +def test_fma(): + x, y, z = symbols('x y z') + + # Expand + assert fma(x, y, z).expand(func=True) - x*y - z == 0 + + expr = fma(17*x, 42*y, 101*z) + + # Diff + assert expr.diff(x) - expr.expand(func=True).diff(x) == 0 + assert expr.diff(y) - expr.expand(func=True).diff(y) == 0 + assert expr.diff(z) - expr.expand(func=True).diff(z) == 0 + + assert expr.diff(x) - 17*42*y == 0 + assert expr.diff(y) - 17*42*x == 0 + assert expr.diff(z) - 101 == 0 + + +def test_log10(): + x = Symbol('x') + + # Expand + assert log10(x).expand(func=True) - log(x)/log(10) == 0 + + # Diff + assert log10(42*x).diff(x) - 1/(log(10)*x) == 0 + assert log10(42*x).diff(x) - log10(42*x).expand(func=True).diff(x) == 0 + + +def test_Cbrt(): + x = Symbol('x') + + # Expand + assert Cbrt(x).expand(func=True) - x**Rational(1, 3) == 0 + + # Diff + assert Cbrt(42*x).diff(x) - 42*(42*x)**(Rational(1, 3) - 1)/3 == 0 + assert Cbrt(42*x).diff(x) - Cbrt(42*x).expand(func=True).diff(x) == 0 + + +def test_Sqrt(): + x = Symbol('x') + + # Expand + assert Sqrt(x).expand(func=True) - x**S.Half == 0 + + # Diff + assert Sqrt(42*x).diff(x) - 42*(42*x)**(S.Half - 1)/2 == 0 + assert Sqrt(42*x).diff(x) - Sqrt(42*x).expand(func=True).diff(x) == 0 + + +def test_hypot(): + x, y = symbols('x y') + + # Expand + assert hypot(x, y).expand(func=True) - (x**2 + y**2)**S.Half == 0 + + # Diff + assert hypot(17*x, 42*y).diff(x).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(x) == 0 + assert hypot(17*x, 42*y).diff(y).expand(func=True) - hypot(17*x, 42*y).expand(func=True).diff(y) == 0 + + assert hypot(17*x, 42*y).diff(x).expand(func=True) - 2*17*17*x*((17*x)**2 + (42*y)**2)**Rational(-1, 2)/2 == 0 + assert hypot(17*x, 42*y).diff(y).expand(func=True) - 2*42*42*y*((17*x)**2 + (42*y)**2)**Rational(-1, 2)/2 == 0 diff --git a/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cnodes.py b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cnodes.py new file mode 100644 index 0000000000000000000000000000000000000000..f0578d66e8cd5f5bce4089580c96fbe23fd7c624 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/codegen/tests/test_cnodes.py @@ -0,0 +1,112 @@ +from sympy.core.symbol import symbols +from sympy.printing.codeprinter import ccode +from sympy.codegen.ast import Declaration, Variable, float64, int64, String, CodeBlock +from sympy.codegen.cnodes import ( + alignof, CommaOperator, goto, Label, PreDecrement, PostDecrement, PreIncrement, PostIncrement, + sizeof, union, struct +) + +x, y = symbols('x y') + + +def test_alignof(): + ax = alignof(x) + assert ccode(ax) == 'alignof(x)' + assert ax.func(*ax.args) == ax + + +def test_CommaOperator(): + expr = CommaOperator(PreIncrement(x), 2*x) + assert ccode(expr) == '(++(x), 2*x)' + assert expr.func(*expr.args) == expr + + +def test_goto_Label(): + s = 'early_exit' + g = goto(s) + assert g.func(*g.args) == g + assert g != goto('foobar') + assert ccode(g) == 'goto early_exit' + + l1 = Label(s) + assert ccode(l1) == 'early_exit:' + assert l1 == Label('early_exit') + assert l1 != Label('foobar') + + body = [PreIncrement(x)] + l2 = Label(s, body) + assert l2.name == String("early_exit") + assert l2.body == CodeBlock(PreIncrement(x)) + assert ccode(l2) == ("early_exit:\n" + "++(x);") + + body = [PreIncrement(x), PreDecrement(y)] + l2 = Label(s, body) + assert l2.name == String("early_exit") + assert l2.body == CodeBlock(PreIncrement(x), PreDecrement(y)) + assert ccode(l2) == ("early_exit:\n" + "{\n ++(x);\n --(y);\n}") + + +def test_PreDecrement(): + p = PreDecrement(x) + assert p.func(*p.args) == p + assert ccode(p) == '--(x)' + + +def test_PostDecrement(): + p = PostDecrement(x) + assert p.func(*p.args) == p + assert ccode(p) == '(x)--' + + +def test_PreIncrement(): + p = PreIncrement(x) + assert p.func(*p.args) == p + assert ccode(p) == '++(x)' + + +def test_PostIncrement(): + p = PostIncrement(x) + assert p.func(*p.args) == p + assert ccode(p) == '(x)++' + + +def test_sizeof(): + typename = 'unsigned int' + sz = sizeof(typename) + assert ccode(sz) == 'sizeof(%s)' % typename + assert sz.func(*sz.args) == sz + assert not sz.is_Atom + assert sz.atoms() == {String('unsigned int'), String('sizeof')} + + +def test_struct(): + vx, vy = Variable(x, type=float64), Variable(y, type=float64) + s = struct('vec2', [vx, vy]) + assert s.func(*s.args) == s + assert s == struct('vec2', (vx, vy)) + assert s != struct('vec2', (vy, vx)) + assert str(s.name) == 'vec2' + assert len(s.declarations) == 2 + assert all(isinstance(arg, Declaration) for arg in s.declarations) + assert ccode(s) == ( + "struct vec2 {\n" + " double x;\n" 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a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py new file mode 100644 index 0000000000000000000000000000000000000000..ab3f62880445c5deb526797ee0623fe3510bcbc3 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_coset_table.py @@ -0,0 +1,825 @@ +from sympy.combinatorics.fp_groups import FpGroup +from sympy.combinatorics.coset_table import (CosetTable, + coset_enumeration_r, coset_enumeration_c) +from sympy.combinatorics.coset_table import modified_coset_enumeration_r +from sympy.combinatorics.free_groups import free_group + +from sympy.testing.pytest import slow + +""" +References +========== + +[1] Holt, D., Eick, B., O'Brien, E. +"Handbook of Computational Group Theory" + +[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson +Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490. +"Implementation and Analysis of the Todd-Coxeter Algorithm" + +""" + +def test_scan_1(): + # Example 5.1 from [1] + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + c = CosetTable(f, [x]) + + c.scan_and_fill(0, x) + assert c.table == [[0, 0, None, None]] + assert c.p == [0] + assert c.n == 1 + assert c.omega == [0] + + c.scan_and_fill(0, x**3) + assert c.table == [[0, 0, None, None]] + assert c.p == [0] + assert c.n == 1 + assert c.omega == [0] + + c.scan_and_fill(0, y**3) + assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [None, None, 0, 1]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(0, x**-1*y**-1*x*y) + assert c.table == [[0, 0, 1, 2], [None, None, 2, 0], [2, 2, 0, 1]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, x**3) + assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \ + [4, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(1, y**3) + assert c.table == [[0, 0, 1, 2], [3, 4, 2, 0], [2, 2, 0, 1], \ + [4, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(1, x**-1*y**-1*x*y) + assert c.table == [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1], \ + [None, 1, None, None], [1, 3, None, None]] + assert c.p == [0, 1, 2, 1, 1] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + # Example 5.2 from [1] + f = FpGroup(F, [x**2, y**3, (x*y)**3]) + c = CosetTable(f, [x*y]) + + c.scan_and_fill(0, x*y) + assert c.table == [[1, None, None, 1], [None, 0, 0, None]] + assert c.p == [0, 1] + assert c.n == 2 + assert c.omega == [0, 1] + + c.scan_and_fill(0, x**2) + assert c.table == [[1, 1, None, 1], [0, 0, 0, None]] + assert c.p == [0, 1] + assert c.n == 2 + assert c.omega == [0, 1] + + c.scan_and_fill(0, y**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(0, (x*y)**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, x**2) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, y**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [None, None, 1, 0]] + assert c.p == [0, 1, 2] + assert c.n == 3 + assert c.omega == [0, 1, 2] + + c.scan_and_fill(1, (x*y)**3) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 4, 1, 0], [None, 2, 4, None], [2, None, None, 3]] + assert c.p == [0, 1, 2, 3, 4] + assert c.n == 5 + assert c.omega == [0, 1, 2, 3, 4] + + c.scan_and_fill(2, x**2) + assert c.table == [[1, 1, 2, 1], [0, 0, 0, 2], [3, 3, 1, 0], [2, 2, 3, 3], [2, None, None, 3]] + assert c.p == [0, 1, 2, 3, 3] + assert c.n == 4 + assert c.omega == [0, 1, 2, 3] + + +@slow +def test_coset_enumeration(): + # this test function contains the combined tests for the two strategies + # i.e. HLT and Felsch strategies. + + # Example 5.1 from [1] + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + C_r = coset_enumeration_r(f, [x]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(f, [x]) + C_c.compress(); C_c.standardize() + table1 = [[0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]] + assert C_r.table == table1 + assert C_c.table == table1 + + # E1 from [2] Pg. 474 + F, r, s, t = free_group("r, s, t") + E1 = FpGroup(F, [t**-1*r*t*r**-2, r**-1*s*r*s**-2, s**-1*t*s*t**-2]) + C_r = coset_enumeration_r(E1, []) + C_r.compress() + C_c = coset_enumeration_c(E1, []) + C_c.compress() + table2 = [[0, 0, 0, 0, 0, 0]] + assert C_r.table == table2 + # test for issue #11449 + assert C_c.table == table2 + + # Cox group from [2] Pg. 474 + F, a, b = free_group("a, b") + Cox = FpGroup(F, [a**6, b**6, (a*b)**2, (a**2*b**2)**2, (a**3*b**3)**5]) + C_r = coset_enumeration_r(Cox, [a]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(Cox, [a]) + C_c.compress(); C_c.standardize() + table3 = [[0, 0, 1, 2], + [2, 3, 4, 0], + [5, 1, 0, 6], + [1, 7, 8, 9], + [9, 10, 11, 1], + [12, 2, 9, 13], + [14, 9, 2, 11], + [3, 12, 15, 16], + [16, 17, 18, 3], + [6, 4, 3, 5], + [4, 19, 20, 21], + [21, 22, 6, 4], + [7, 5, 23, 24], + [25, 23, 5, 18], + [19, 6, 22, 26], + [24, 27, 28, 7], + [29, 8, 7, 30], + [8, 31, 32, 33], + [33, 34, 13, 8], + [10, 14, 35, 35], + [35, 36, 37, 10], + [30, 11, 10, 29], + [11, 38, 39, 14], + [13, 39, 38, 12], + [40, 15, 12, 41], + [42, 13, 34, 43], + [44, 35, 14, 45], + [15, 46, 47, 34], + [34, 48, 49, 15], + [50, 16, 21, 51], + [52, 21, 16, 49], + [17, 50, 53, 54], + [54, 55, 56, 17], + [41, 18, 17, 40], + [18, 28, 27, 25], + [26, 20, 19, 19], + [20, 57, 58, 59], + [59, 60, 51, 20], + [22, 52, 61, 23], + [23, 62, 63, 22], + [64, 24, 33, 65], + [48, 33, 24, 61], + [62, 25, 54, 66], + [67, 54, 25, 68], + [57, 26, 59, 69], + [70, 59, 26, 63], + [27, 64, 71, 72], + [72, 73, 68, 27], + [28, 41, 74, 75], + [75, 76, 30, 28], + [31, 29, 77, 78], + [79, 77, 29, 37], + [38, 30, 76, 80], + [78, 81, 82, 31], + [43, 32, 31, 42], + [32, 83, 84, 85], + [85, 86, 65, 32], + [36, 44, 87, 88], + [88, 89, 90, 36], + [45, 37, 36, 44], + [37, 82, 81, 79], + [80, 74, 41, 38], + [39, 42, 91, 92], + [92, 93, 45, 39], + [46, 40, 94, 95], + [96, 94, 40, 56], + [97, 91, 42, 82], + [83, 43, 98, 99], + [100, 98, 43, 47], + [101, 87, 44, 90], + [82, 45, 93, 97], + [95, 102, 103, 46], + [104, 47, 46, 105], + [47, 106, 107, 100], + [61, 108, 109, 48], + [105, 49, 48, 104], + [49, 110, 111, 52], + [51, 111, 110, 50], + [112, 53, 50, 113], + [114, 51, 60, 115], + [116, 61, 52, 117], + [53, 118, 119, 60], + [60, 70, 66, 53], + [55, 67, 120, 121], + [121, 122, 123, 55], + [113, 56, 55, 112], + [56, 103, 102, 96], + [69, 124, 125, 57], + [115, 58, 57, 114], + [58, 126, 127, 128], + [128, 128, 69, 58], + [66, 129, 130, 62], + [117, 63, 62, 116], + [63, 125, 124, 70], + [65, 109, 108, 64], + [131, 71, 64, 132], + [133, 65, 86, 134], + [135, 66, 70, 136], + [68, 130, 129, 67], + [137, 120, 67, 138], + [132, 68, 73, 131], + [139, 69, 128, 140], + [71, 141, 142, 86], + [86, 143, 144, 71], + [145, 72, 75, 146], + [147, 75, 72, 144], + [73, 145, 148, 120], + [120, 149, 150, 73], + [74, 151, 152, 94], + [94, 153, 146, 74], + [76, 147, 154, 77], + [77, 155, 156, 76], + [157, 78, 85, 158], + [143, 85, 78, 154], + [155, 79, 88, 159], + [160, 88, 79, 161], + [151, 80, 92, 162], + [163, 92, 80, 156], + [81, 157, 164, 165], + [165, 166, 161, 81], + [99, 107, 106, 83], + [134, 84, 83, 133], + [84, 167, 168, 169], + [169, 170, 158, 84], + [87, 171, 172, 93], + [93, 163, 159, 87], + [89, 160, 173, 174], + [174, 175, 176, 89], + [90, 90, 89, 101], + [91, 177, 178, 98], + [98, 179, 162, 91], + [180, 95, 100, 181], + [179, 100, 95, 152], + [153, 96, 121, 148], + [182, 121, 96, 183], + [177, 97, 165, 184], + [185, 165, 97, 172], + [186, 99, 169, 187], + [188, 169, 99, 178], + [171, 101, 174, 189], + [190, 174, 101, 176], + [102, 180, 191, 192], + [192, 193, 183, 102], + [103, 113, 194, 195], + [195, 196, 105, 103], + [106, 104, 197, 198], + [199, 197, 104, 109], + [110, 105, 196, 200], + [198, 201, 133, 106], + [107, 186, 202, 203], + [203, 204, 181, 107], + [108, 116, 205, 206], + [206, 207, 132, 108], + [109, 133, 201, 199], + [200, 194, 113, 110], + [111, 114, 208, 209], + [209, 210, 117, 111], + [118, 112, 211, 212], + [213, 211, 112, 123], + [214, 208, 114, 125], + [126, 115, 215, 216], + [217, 215, 115, 119], + [218, 205, 116, 130], + [125, 117, 210, 214], + [212, 219, 220, 118], + [136, 119, 118, 135], + [119, 221, 222, 217], + [122, 182, 223, 224], + [224, 225, 226, 122], + [138, 123, 122, 137], + [123, 220, 219, 213], + [124, 139, 227, 228], + [228, 229, 136, 124], + [216, 222, 221, 126], + [140, 127, 126, 139], + [127, 230, 231, 232], + [232, 233, 140, 127], + [129, 135, 234, 235], + [235, 236, 138, 129], + [130, 132, 207, 218], + [141, 131, 237, 238], + [239, 237, 131, 150], + [167, 134, 240, 241], + [242, 240, 134, 142], + [243, 234, 135, 220], + [221, 136, 229, 244], + [149, 137, 245, 246], + [247, 245, 137, 226], + [220, 138, 236, 243], + [244, 227, 139, 221], + [230, 140, 233, 248], + [238, 249, 250, 141], + [251, 142, 141, 252], + [142, 253, 254, 242], + [154, 255, 256, 143], + [252, 144, 143, 251], + [144, 257, 258, 147], + [146, 258, 257, 145], + [259, 148, 145, 260], + [261, 146, 153, 262], + [263, 154, 147, 264], + [148, 265, 266, 153], + [246, 267, 268, 149], + [260, 150, 149, 259], + [150, 250, 249, 239], + [162, 269, 270, 151], + [262, 152, 151, 261], + [152, 271, 272, 179], + [159, 273, 274, 155], + [264, 156, 155, 263], + [156, 270, 269, 163], + [158, 256, 255, 157], + [275, 164, 157, 276], + [277, 158, 170, 278], + [279, 159, 163, 280], + [161, 274, 273, 160], + [281, 173, 160, 282], + [276, 161, 166, 275], + [283, 162, 179, 284], + [164, 285, 286, 170], + [170, 188, 184, 164], + [166, 185, 189, 173], + [173, 287, 288, 166], + [241, 254, 253, 167], + [278, 168, 167, 277], + [168, 289, 290, 291], + [291, 292, 187, 168], + [189, 293, 294, 171], + [280, 172, 171, 279], + [172, 295, 296, 185], + [175, 190, 297, 297], + [297, 298, 299, 175], + [282, 176, 175, 281], + [176, 294, 293, 190], + [184, 296, 295, 177], + [284, 178, 177, 283], + [178, 300, 301, 188], + [181, 272, 271, 180], + [302, 191, 180, 303], + [304, 181, 204, 305], + [183, 266, 265, 182], + [306, 223, 182, 307], + [303, 183, 193, 302], + [308, 184, 188, 309], + [310, 189, 185, 311], + [187, 301, 300, 186], + [305, 202, 186, 304], + [312, 187, 292, 313], + [314, 297, 190, 315], + [191, 316, 317, 204], + [204, 318, 319, 191], + [320, 192, 195, 321], + [322, 195, 192, 319], + [193, 320, 323, 223], + [223, 324, 325, 193], + [194, 326, 327, 211], + [211, 328, 321, 194], + [196, 322, 329, 197], + [197, 330, 331, 196], + [332, 198, 203, 333], + [318, 203, 198, 329], + [330, 199, 206, 334], + [335, 206, 199, 336], + [326, 200, 209, 337], + [338, 209, 200, 331], + [201, 332, 339, 240], + [240, 340, 336, 201], + [202, 341, 342, 292], + [292, 343, 333, 202], + [205, 344, 345, 210], + [210, 338, 334, 205], + [207, 335, 346, 237], + [237, 347, 348, 207], + [208, 349, 350, 215], + [215, 351, 337, 208], + [352, 212, 217, 353], + [351, 217, 212, 327], + [328, 213, 224, 323], + [354, 224, 213, 355], + [349, 214, 228, 356], + [357, 228, 214, 345], + [358, 216, 232, 359], + [360, 232, 216, 350], + [344, 218, 235, 361], + [362, 235, 218, 348], + [219, 352, 363, 364], + [364, 365, 355, 219], + [222, 358, 366, 367], + [367, 368, 353, 222], + [225, 354, 369, 370], + [370, 371, 372, 225], + [307, 226, 225, 306], + [226, 268, 267, 247], + [227, 373, 374, 233], + [233, 360, 356, 227], + [229, 357, 361, 234], + [234, 375, 376, 229], + [248, 231, 230, 230], + [231, 377, 378, 379], + [379, 380, 359, 231], + [236, 362, 381, 245], + [245, 382, 383, 236], + [384, 238, 242, 385], + [340, 242, 238, 346], + [347, 239, 246, 381], + [386, 246, 239, 387], + [388, 241, 291, 389], + [343, 291, 241, 339], + [375, 243, 364, 390], + [391, 364, 243, 383], + [373, 244, 367, 392], + [393, 367, 244, 376], + [382, 247, 370, 394], + [395, 370, 247, 396], + [377, 248, 379, 397], + [398, 379, 248, 374], + [249, 384, 399, 400], + [400, 401, 387, 249], + [250, 260, 402, 403], + [403, 404, 252, 250], + [253, 251, 405, 406], + [407, 405, 251, 256], + [257, 252, 404, 408], + [406, 409, 277, 253], + [254, 388, 410, 411], + [411, 412, 385, 254], + [255, 263, 413, 414], + [414, 415, 276, 255], + [256, 277, 409, 407], + [408, 402, 260, 257], + [258, 261, 416, 417], + [417, 418, 264, 258], + [265, 259, 419, 420], + [421, 419, 259, 268], + [422, 416, 261, 270], + [271, 262, 423, 424], + [425, 423, 262, 266], + [426, 413, 263, 274], + [270, 264, 418, 422], + [420, 427, 307, 265], + [266, 303, 428, 425], + [267, 386, 429, 430], + [430, 431, 396, 267], + [268, 307, 427, 421], + [269, 283, 432, 433], + [433, 434, 280, 269], + [424, 428, 303, 271], + [272, 304, 435, 436], + [436, 437, 284, 272], + [273, 279, 438, 439], + [439, 440, 282, 273], + [274, 276, 415, 426], + [285, 275, 441, 442], + [443, 441, 275, 288], + [289, 278, 444, 445], + [446, 444, 278, 286], + [447, 438, 279, 294], + [295, 280, 434, 448], + [287, 281, 449, 450], + [451, 449, 281, 299], + [294, 282, 440, 447], + [448, 432, 283, 295], + [300, 284, 437, 452], + [442, 453, 454, 285], + [309, 286, 285, 308], + [286, 455, 456, 446], + [450, 457, 458, 287], + [311, 288, 287, 310], + [288, 454, 453, 443], + [445, 456, 455, 289], + [313, 290, 289, 312], + [290, 459, 460, 461], + [461, 462, 389, 290], + [293, 310, 463, 464], + [464, 465, 315, 293], + [296, 308, 466, 467], + [467, 468, 311, 296], + [298, 314, 469, 470], + [470, 471, 472, 298], + [315, 299, 298, 314], + [299, 458, 457, 451], + [452, 435, 304, 300], + [301, 312, 473, 474], + [474, 475, 309, 301], + [316, 302, 476, 477], + [478, 476, 302, 325], + [341, 305, 479, 480], + [481, 479, 305, 317], + [324, 306, 482, 483], + [484, 482, 306, 372], + [485, 466, 308, 454], + [455, 309, 475, 486], + [487, 463, 310, 458], + [454, 311, 468, 485], + [486, 473, 312, 455], + [459, 313, 488, 489], + [490, 488, 313, 342], + [491, 469, 314, 472], + [458, 315, 465, 487], + [477, 492, 485, 316], + [463, 317, 316, 468], + [317, 487, 493, 481], + [329, 447, 464, 318], + [468, 319, 318, 463], + [319, 467, 448, 322], + [321, 448, 467, 320], + [475, 323, 320, 466], + [432, 321, 328, 437], + [438, 329, 322, 434], + [323, 474, 452, 328], + [483, 494, 486, 324], + [466, 325, 324, 475], + [325, 485, 492, 478], + [337, 422, 433, 326], + [437, 327, 326, 432], + [327, 436, 424, 351], + [334, 426, 439, 330], + [434, 331, 330, 438], + [331, 433, 422, 338], + [333, 464, 447, 332], + [449, 339, 332, 440], + [465, 333, 343, 469], + [413, 334, 338, 418], + [336, 439, 426, 335], + [441, 346, 335, 415], + [440, 336, 340, 449], + [416, 337, 351, 423], + [339, 451, 470, 343], + [346, 443, 450, 340], + [480, 493, 487, 341], + [469, 342, 341, 465], + [342, 491, 495, 490], + [361, 407, 414, 344], + [418, 345, 344, 413], + [345, 417, 408, 357], + [381, 446, 442, 347], + [415, 348, 347, 441], + [348, 414, 407, 362], + [356, 408, 417, 349], + [423, 350, 349, 416], + [350, 425, 420, 360], + [353, 424, 436, 352], + [479, 363, 352, 435], + [428, 353, 368, 476], + [355, 452, 474, 354], + [488, 369, 354, 473], + [435, 355, 365, 479], + [402, 356, 360, 419], + [405, 361, 357, 404], + [359, 420, 425, 358], + [476, 366, 358, 428], + [427, 359, 380, 482], + [444, 381, 362, 409], + [363, 481, 477, 368], + [368, 393, 390, 363], + [365, 391, 394, 369], + [369, 490, 480, 365], + [366, 478, 483, 380], + [380, 398, 392, 366], + [371, 395, 496, 497], + [497, 498, 489, 371], + [473, 372, 371, 488], + [372, 486, 494, 484], + [392, 400, 403, 373], + [419, 374, 373, 402], + [374, 421, 430, 398], + [390, 411, 406, 375], + [404, 376, 375, 405], + [376, 403, 400, 393], + [397, 430, 421, 377], + [482, 378, 377, 427], + [378, 484, 497, 499], + [499, 499, 397, 378], + [394, 461, 445, 382], + [409, 383, 382, 444], + [383, 406, 411, 391], + [385, 450, 443, 384], + [492, 399, 384, 453], + [457, 385, 412, 493], + [387, 442, 446, 386], + [494, 429, 386, 456], + [453, 387, 401, 492], + [389, 470, 451, 388], + [493, 410, 388, 457], + [471, 389, 462, 495], + [412, 390, 393, 399], + [462, 394, 391, 410], + [401, 392, 398, 429], + [396, 445, 461, 395], + [498, 496, 395, 460], + [456, 396, 431, 494], + [431, 397, 499, 496], + [399, 477, 481, 412], + [429, 483, 478, 401], + [410, 480, 490, 462], + [496, 497, 484, 431], + [489, 495, 491, 459], + [495, 460, 459, 471], + [460, 489, 498, 498], + [472, 472, 471, 491]] + + assert C_r.table == table3 + assert C_c.table == table3 + + # Group denoted by B2,4 from [2] Pg. 474 + F, a, b = free_group("a, b") + B_2_4 = FpGroup(F, [a**4, b**4, (a*b)**4, (a**-1*b)**4, (a**2*b)**4, \ + (a*b**2)**4, (a**2*b**2)**4, (a**-1*b*a*b)**4, (a*b**-1*a*b)**4]) + C_r = coset_enumeration_r(B_2_4, [a]) + C_c = coset_enumeration_c(B_2_4, [a]) + index_r = 0 + for i in range(len(C_r.p)): + if C_r.p[i] == i: + index_r += 1 + assert index_r == 1024 + + index_c = 0 + for i in range(len(C_c.p)): + if C_c.p[i] == i: + index_c += 1 + assert index_c == 1024 + + # trivial Macdonald group G(2,2) from [2] Pg. 480 + M = FpGroup(F, [b**-1*a**-1*b*a*b**-1*a*b*a**-2, a**-1*b**-1*a*b*a**-1*b*a*b**-2]) + C_r = coset_enumeration_r(M, [a]) + C_r.compress(); C_r.standardize() + C_c = coset_enumeration_c(M, [a]) + C_c.compress(); C_c.standardize() + table4 = [[0, 0, 0, 0]] + assert C_r.table == table4 + assert C_c.table == table4 + + +def test_look_ahead(): + # Section 3.2 [Test Example] Example (d) from [2] + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**11, b**5, c**4, (a*c)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b]) + H = [c, b, c**2] + table0 = [[1, 2, 0, 0, 0, 0], + [3, 0, 4, 5, 6, 7], + [0, 8, 9, 10, 11, 12], + [5, 1, 10, 13, 14, 15], + [16, 5, 16, 1, 17, 18], + [4, 3, 1, 8, 19, 20], + [12, 21, 22, 23, 24, 1], + [25, 26, 27, 28, 1, 24], + [2, 10, 5, 16, 22, 28], + [10, 13, 13, 2, 29, 30]] + CosetTable.max_stack_size = 10 + C_c = coset_enumeration_c(f, H) + C_c.compress(); C_c.standardize() + assert C_c.table[: 10] == table0 + +def test_modified_methods(): + ''' + Tests for modified coset table methods. + Example 5.7 from [1] Holt, D., Eick, B., O'Brien + "Handbook of Computational Group Theory". + + ''' + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + C = CosetTable(f, H) + C.modified_define(0, x) + identity = C._grp.identity + a_0 = C._grp.generators[0] + a_1 = C._grp.generators[1] + + assert C.P == [[identity, None, None, None], + [None, identity, None, None]] + assert C.table == [[1, None, None, None], + [None, 0, None, None]] + + C.modified_define(1, x) + assert C.table == [[1, None, None, None], + [2, 0, None, None], + [None, 1, None, None]] + assert C.P == [[identity, None, None, None], + [identity, identity, None, None], + [None, identity, None, None]] + + C.modified_scan(0, x**3, C._grp.identity, fill=False) + assert C.P == [[identity, identity, None, None], + [identity, identity, None, None], + [identity, identity, None, None]] + assert C.table == [[1, 2, None, None], + [2, 0, None, None], + [0, 1, None, None]] + + C.modified_scan(0, x*y, C._grp.generators[0], fill=False) + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, None]] + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, None]] + + C.modified_define(2, y**-1) + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [None, None, 2, None]] + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [None, None, identity, None]] + + C.modified_scan(0, x**-1*y**-1*x*y*x, C._grp.generators[1]) + assert C.table == [[1, 2, None, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [3, 3, 2, None]] + assert C.P == [[identity, identity, None, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [a_1, a_1**-1, identity, None]] + + C.modified_scan(2, (x*y)**2, C._grp.identity) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, None], + [0, 1, None, 3], + [3, 3, 2, 0]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, None, identity], + [a_1, a_1**-1, identity, a_1]] + + C.modified_define(2, y) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, None], + [0, 1, 4, 3], + [3, 3, 2, 0], + [None, None, None, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, None], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [None, None, None, identity]] + + C.modified_scan(0, y**5, C._grp.identity) + assert C.table == [[1, 2, 3, 1], [2, 0, 0, 4], [0, 1, 4, 3], [3, 3, 2, 0], [None, None, 1, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, a_0*a_1**-1], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [None, None, a_1*a_0**-1, identity]] + + C.modified_scan(1, (x*y)**2, C._grp.identity) + assert C.table == [[1, 2, 3, 1], + [2, 0, 0, 4], + [0, 1, 4, 3], + [3, 3, 2, 0], + [4, 4, 1, 2]] + assert C.P == [[identity, identity, a_1**-1, a_0**-1], + [identity, identity, a_0, a_0*a_1**-1], + [identity, identity, identity, identity], + [a_1, a_1**-1, identity, a_1], + [a_0*a_1**-1, a_1*a_0**-1, a_1*a_0**-1, identity]] + + # Modified coset enumeration test + f = FpGroup(F, [x**3, y**3, x**-1*y**-1*x*y]) + C = coset_enumeration_r(f, [x]) + C_m = modified_coset_enumeration_r(f, [x]) + assert C_m.table == C.table diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..3f57bdf8eff92a3022d8e01cd74ce98575987929 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_fp_groups.py @@ -0,0 +1,257 @@ +from sympy.core.singleton import S +from sympy.combinatorics.fp_groups import (FpGroup, low_index_subgroups, + reidemeister_presentation, FpSubgroup, + simplify_presentation) +from sympy.combinatorics.free_groups import (free_group, FreeGroup) + +from sympy.testing.pytest import slow + +""" +References +========== + +[1] Holt, D., Eick, B., O'Brien, E. +"Handbook of Computational Group Theory" + +[2] John J. Cannon; Lucien A. Dimino; George Havas; Jane M. Watson +Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 463-490. +"Implementation and Analysis of the Todd-Coxeter Algorithm" + +[3] PROC. SECOND INTERNAT. CONF. THEORY OF GROUPS, CANBERRA 1973, +pp. 347-356. "A Reidemeister-Schreier program" by George Havas. +http://staff.itee.uq.edu.au/havas/1973cdhw.pdf + +""" + +def test_low_index_subgroups(): + F, x, y = free_group("x, y") + + # Example 5.10 from [1] Pg. 194 + f = FpGroup(F, [x**2, y**3, (x*y)**4]) + L = low_index_subgroups(f, 4) + t1 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 3, 3]], + [[0, 0, 1, 2], [2, 2, 2, 0], [1, 1, 0, 1]], + [[1, 1, 0, 0], [0, 0, 1, 1]]] + for i in range(len(t1)): + assert L[i].table == t1[i] + + f = FpGroup(F, [x**2, y**3, (x*y)**7]) + L = low_index_subgroups(f, 15) + t2 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [4, 4, 5, 3], [6, 6, 3, 4], [5, 5, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [5, 5, 3, 4], [4, 4, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [9, 9, 6, 8], [12, 12, 11, 7], [8, 8, 7, 10], + [10, 10, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [12, 12, 6, 8], [10, 10, 11, 7], [8, 8, 7, 10], + [9, 9, 13, 14], [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], + [6, 6, 5, 3], [7, 7, 3, 4], [4, 4, 8, 9], [5, 5, 10, 11], + [11, 11, 9, 6], [12, 12, 6, 8], [13, 13, 11, 7], [8, 8, 7, 10], + [9, 9, 12, 12], [10, 10, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6] + , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [11, 11, 12, 10], [13, 13, 10, 11], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 3, 3], [2, 2, 5, 6] + , [7, 7, 6, 4], [8, 8, 4, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11], + [11, 11, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 4, 4] + , [7, 7, 6, 3], [8, 8, 3, 5], [5, 5, 8, 9], [6, 6, 9, 7], + [10, 10, 7, 8], [9, 9, 11, 12], [13, 13, 12, 10], [12, 12, 10, 11], + [11, 11, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [5, 5, 6, 3], [9, 9, 3, 5], [10, 10, 8, 4], [8, 8, 4, 7], + [6, 6, 10, 11], [7, 7, 11, 9], [12, 12, 9, 10], [11, 11, 13, 14], + [14, 14, 14, 12], [13, 13, 12, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7], + [5, 5, 10, 12], [7, 7, 12, 9], [8, 8, 11, 11], [13, 13, 9, 10], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [6, 6, 3, 5], [10, 10, 8, 4], [11, 11, 4, 7], + [5, 5, 12, 11], [7, 7, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7], + [5, 5, 9, 9], [6, 6, 11, 12], [8, 8, 12, 10], [13, 13, 10, 11], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [7, 7, 8, 4], [11, 11, 4, 7], + [5, 5, 12, 11], [6, 6, 10, 10], [8, 8, 9, 12], [13, 13, 11, 9], + [12, 12, 13, 13]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8] + , [9, 9, 6, 3], [10, 10, 3, 5], [11, 11, 8, 4], [12, 12, 4, 7], + [5, 5, 9, 9], [6, 6, 12, 13], [7, 7, 11, 11], [8, 8, 13, 10], + [13, 13, 10, 12]], + [[1, 1, 0, 0], [0, 0, 2, 3], [4, 4, 3, 1], [5, 5, 1, 2], [2, 2, 4, 4] + , [3, 3, 6, 7], [7, 7, 7, 5], [6, 6, 5, 6]]] + for i in range(len(t2)): + assert L[i].table == t2[i] + + f = FpGroup(F, [x**2, y**3, (x*y)**7]) + L = low_index_subgroups(f, 10, [x]) + t3 = [[[0, 0, 0, 0]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [4, 4, 5, 3], + [6, 6, 3, 4], [5, 5, 6, 6]], + [[0, 0, 1, 2], [1, 1, 2, 0], [3, 3, 0, 1], [2, 2, 4, 5], [6, 6, 5, 3], + [5, 5, 3, 4], [4, 4, 6, 6]], + [[0, 0, 1, 2], [3, 3, 2, 0], [4, 4, 0, 1], [1, 1, 5, 6], [2, 2, 7, 8], + [6, 6, 6, 3], [5, 5, 3, 5], [8, 8, 8, 4], [7, 7, 4, 7]]] + for i in range(len(t3)): + assert L[i].table == t3[i] + + +def test_subgroup_presentations(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + p1 = reidemeister_presentation(f, H) + assert str(p1) == "((y_1, y_2), (y_1**2, y_2**3, y_2*y_1*y_2*y_1*y_2*y_1))" + + H = f.subgroup(H) + assert (H.generators, H.relators) == p1 + + f = FpGroup(F, [x**3, y**3, (x*y)**3]) + H = [x*y, x*y**-1] + p2 = reidemeister_presentation(f, H) + assert str(p2) == "((x_0, y_0), (x_0**3, y_0**3, x_0*y_0*x_0*y_0*x_0*y_0))" + + f = FpGroup(F, [x**2*y**2, y**-1*x*y*x**-3]) + H = [x] + p3 = reidemeister_presentation(f, H) + assert str(p3) == "((x_0,), (x_0**4,))" + + f = FpGroup(F, [x**3*y**-3, (x*y)**3, (x*y**-1)**2]) + H = [x] + p4 = reidemeister_presentation(f, H) + assert str(p4) == "((x_0,), (x_0**6,))" + + # this presentation can be improved, the most simplified form + # of presentation is + # See [2] Pg 474 group PSL_2(11) + # This is the group PSL_2(11) + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**11, b**5, c**4, (b*c**2)**2, (a*b*c)**3, (a**4*c**2)**3, b**2*c**-1*b**-1*c, a**4*b**-1*a**-1*b]) + H = [a, b, c**2] + gens, rels = reidemeister_presentation(f, H) + assert str(gens) == "(b_1, c_3)" + assert len(rels) == 18 + + +@slow +def test_order(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert f.order() == 8 + + f = FpGroup(F, [x*y*x**-1*y**-1, y**2]) + assert f.order() is S.Infinity + + F, a, b, c = free_group("a, b, c") + f = FpGroup(F, [a**250, b**2, c*b*c**-1*b, c**4, c**-1*a**-1*c*a, a**-1*b**-1*a*b]) + assert f.order() == 2000 + + F, x = free_group("x") + f = FpGroup(F, []) + assert f.order() is S.Infinity + + f = FpGroup(free_group('')[0], []) + assert f.order() == 1 + +def test_fp_subgroup(): + def _test_subgroup(K, T, S): + _gens = T(K.generators) + assert all(elem in S for elem in _gens) + assert T.is_injective() + assert T.image().order() == S.order() + F, x, y = free_group("x, y") + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + S = FpSubgroup(f, [x*y]) + assert (x*y)**-3 in S + K, T = f.subgroup([x*y], homomorphism=True) + assert T(K.generators) == [y*x**-1] + _test_subgroup(K, T, S) + + S = FpSubgroup(f, [x**-1*y*x]) + assert x**-1*y**4*x in S + assert x**-1*y**4*x**2 not in S + K, T = f.subgroup([x**-1*y*x], homomorphism=True) + assert T(K.generators[0]**3) == y**3 + _test_subgroup(K, T, S) + + f = FpGroup(F, [x**3, y**5, (x*y)**2]) + H = [x*y, x**-1*y**-1*x*y*x] + K, T = f.subgroup(H, homomorphism=True) + S = FpSubgroup(f, H) + _test_subgroup(K, T, S) + +def test_permutation_methods(): + F, x, y = free_group("x, y") + # DihedralGroup(8) + G = FpGroup(F, [x**2, y**8, x*y*x**-1*y]) + T = G._to_perm_group()[1] + assert T.is_isomorphism() + assert G.center() == [y**4] + + # DiheadralGroup(4) + G = FpGroup(F, [x**2, y**4, x*y*x**-1*y]) + S = FpSubgroup(G, G.normal_closure([x])) + assert x in S + assert y**-1*x*y in S + + # Z_5xZ_4 + G = FpGroup(F, [x*y*x**-1*y**-1, y**5, x**4]) + assert G.is_abelian + assert G.is_solvable + + # AlternatingGroup(5) + G = FpGroup(F, [x**3, y**2, (x*y)**5]) + assert not G.is_solvable + + # AlternatingGroup(4) + G = FpGroup(F, [x**3, y**2, (x*y)**3]) + assert len(G.derived_series()) == 3 + S = FpSubgroup(G, G.derived_subgroup()) + assert S.order() == 4 + + +def test_simplify_presentation(): + # ref #16083 + G = simplify_presentation(FpGroup(FreeGroup([]), [])) + assert not G.generators + assert not G.relators + + # CyclicGroup(3) + # The second generator in is trivial due to relators {x^2, x^5} + F, x, y = free_group("x, y") + G = simplify_presentation(FpGroup(F, [x**2, x**5, y**3])) + assert x in G.relators + +def test_cyclic(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x]) + assert f.is_cyclic + f = FpGroup(F, [x*y, x*y**-1]) + assert f.is_cyclic + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert not f.is_cyclic + + +def test_abelian_invariants(): + F, x, y = free_group("x, y") + f = FpGroup(F, [x*y, x**-1*y**-1*x*y*x]) + assert f.abelian_invariants() == [] + f = FpGroup(F, [x*y, x*y**-1]) + assert f.abelian_invariants() == [2] + f = FpGroup(F, [x**4, y**2, x*y*x**-1*y]) + assert f.abelian_invariants() == [2, 4] diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py new file mode 100644 index 0000000000000000000000000000000000000000..0d2ac29a846db88444d275b72a85ce3debaeaf05 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_galois.py @@ -0,0 +1,82 @@ +"""Test groups defined by the galois module. """ + +from sympy.combinatorics.galois import ( + S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups, + find_transitive_subgroups_of_S6, +) +from sympy.combinatorics.homomorphisms import is_isomorphic +from sympy.combinatorics.named_groups import ( + SymmetricGroup, AlternatingGroup, CyclicGroup, +) + + +def test_four_group(): + G = S4TransitiveSubgroups.V.get_perm_group() + A4 = AlternatingGroup(4) + assert G.is_subgroup(A4) + assert G.degree == 4 + assert G.is_transitive() + assert G.order() == 4 + assert not G.is_cyclic + + +def test_M20(): + G = S5TransitiveSubgroups.M20.get_perm_group() + S5 = SymmetricGroup(5) + A5 = AlternatingGroup(5) + assert G.is_subgroup(S5) + assert not G.is_subgroup(A5) + assert G.degree == 5 + assert G.is_transitive() + assert G.order() == 20 + + +# Setting this True means that for each of the transitive subgroups of S6, +# we run a test not only on the fixed representation, but also on one freshly +# generated by the search procedure. +INCLUDE_SEARCH_REPS = False +S6_randomized = {} +if INCLUDE_SEARCH_REPS: + S6_randomized = find_transitive_subgroups_of_S6(*list(S6TransitiveSubgroups)) + + +def get_versions_of_S6_subgroup(name): + vers = [name.get_perm_group()] + if INCLUDE_SEARCH_REPS: + vers.append(S6_randomized[name]) + return vers + + +def test_S6_transitive_subgroups(): + """ + Test enough characteristics to distinguish all 16 transitive subgroups. + """ + ts = S6TransitiveSubgroups + A6 = AlternatingGroup(6) + for name, alt, order, is_isom, not_isom in [ + (ts.C6, False, 6, CyclicGroup(6), None), + (ts.S3, False, 6, SymmetricGroup(3), None), + (ts.D6, False, 12, None, None), + (ts.A4, True, 12, None, None), + (ts.G18, False, 18, None, None), + (ts.A4xC2, False, 24, None, SymmetricGroup(4)), + (ts.S4m, False, 24, SymmetricGroup(4), None), + (ts.S4p, True, 24, None, None), + (ts.G36m, False, 36, None, None), + (ts.G36p, True, 36, None, None), + (ts.S4xC2, False, 48, None, None), + (ts.PSL2F5, True, 60, None, None), + (ts.G72, False, 72, None, None), + (ts.PGL2F5, False, 120, None, None), + (ts.A6, True, 360, None, None), + (ts.S6, False, 720, None, None), + ]: + for G in get_versions_of_S6_subgroup(name): + assert G.is_transitive() + assert G.degree == 6 + assert G.is_subgroup(A6) is alt + assert G.order() == order + if is_isom: + assert is_isomorphic(G, is_isom) + if not_isom: + assert not is_isomorphic(G, not_isom) diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py new file mode 100644 index 0000000000000000000000000000000000000000..d0f7d6394bbc2e285650ea95d36be8e2ed5ea69e --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_group_constructs.py @@ -0,0 +1,15 @@ +from sympy.combinatorics.group_constructs import DirectProduct +from sympy.combinatorics.named_groups import CyclicGroup, DihedralGroup + + +def test_direct_product_n(): + C = CyclicGroup(4) + D = DihedralGroup(4) + G = DirectProduct(C, C, C) + assert G.order() == 64 + assert G.degree == 12 + assert len(G.orbits()) == 3 + assert G.is_abelian is True + H = DirectProduct(D, C) + assert H.order() == 32 + assert H.is_abelian is False diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..59bcb6ef3f020335de76d7a72152a0b58cbc6976 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_named_groups.py @@ -0,0 +1,70 @@ +from sympy.combinatorics.named_groups import (SymmetricGroup, CyclicGroup, + DihedralGroup, AlternatingGroup, + AbelianGroup, RubikGroup) +from sympy.testing.pytest import raises + + +def test_SymmetricGroup(): + G = SymmetricGroup(5) + elements = list(G.generate()) + assert (G.generators[0]).size == 5 + assert len(elements) == 120 + assert G.is_solvable is False + assert G.is_abelian is False + assert G.is_nilpotent is False + assert G.is_transitive() is True + H = SymmetricGroup(1) + assert H.order() == 1 + L = SymmetricGroup(2) + assert L.order() == 2 + + +def test_CyclicGroup(): + G = CyclicGroup(10) + elements = list(G.generate()) + assert len(elements) == 10 + assert (G.derived_subgroup()).order() == 1 + assert G.is_abelian is True + assert G.is_solvable is True + assert G.is_nilpotent is True + H = CyclicGroup(1) + assert H.order() == 1 + L = CyclicGroup(2) + assert L.order() == 2 + + +def test_DihedralGroup(): + G = DihedralGroup(6) + elements = list(G.generate()) + assert len(elements) == 12 + assert G.is_transitive() is True + assert G.is_abelian is False + assert G.is_solvable is True + assert G.is_nilpotent is False + H = DihedralGroup(1) + assert H.order() == 2 + L = DihedralGroup(2) + assert L.order() == 4 + assert L.is_abelian is True + assert L.is_nilpotent is True + + +def test_AlternatingGroup(): + G = AlternatingGroup(5) + elements = list(G.generate()) + assert len(elements) == 60 + assert [perm.is_even for perm in elements] == [True]*60 + H = AlternatingGroup(1) + assert H.order() == 1 + L = AlternatingGroup(2) + assert L.order() == 1 + + +def test_AbelianGroup(): + A = AbelianGroup(3, 3, 3) + assert A.order() == 27 + assert A.is_abelian is True + + +def test_RubikGroup(): + raises(ValueError, lambda: RubikGroup(1)) diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py new file mode 100644 index 0000000000000000000000000000000000000000..32e70e53a53aadbb17c8292bbef8f52d1144d6e0 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_partitions.py @@ -0,0 +1,118 @@ +from sympy.core.sorting import ordered, default_sort_key +from sympy.combinatorics.partitions import (Partition, IntegerPartition, + RGS_enum, RGS_unrank, RGS_rank, + random_integer_partition) +from sympy.testing.pytest import raises +from sympy.utilities.iterables import partitions +from sympy.sets.sets import Set, FiniteSet + + +def test_partition_constructor(): + raises(ValueError, lambda: Partition([1, 1, 2])) + raises(ValueError, lambda: Partition([1, 2, 3], [2, 3, 4])) + raises(ValueError, lambda: Partition(1, 2, 3)) + raises(ValueError, lambda: Partition(*list(range(3)))) + + assert Partition([1, 2, 3], [4, 5]) == Partition([4, 5], [1, 2, 3]) + assert Partition({1, 2, 3}, {4, 5}) == Partition([1, 2, 3], [4, 5]) + + a = FiniteSet(1, 2, 3) + b = FiniteSet(4, 5) + assert Partition(a, b) == Partition([1, 2, 3], [4, 5]) + assert Partition({a, b}) == Partition(FiniteSet(a, b)) + assert Partition({a, b}) != Partition(a, b) + +def test_partition(): + from sympy.abc import x + + a = Partition([1, 2, 3], [4]) + b = Partition([1, 2], [3, 4]) + c = Partition([x]) + l = [a, b, c] + l.sort(key=default_sort_key) + assert l == [c, a, b] + l.sort(key=lambda w: default_sort_key(w, order='rev-lex')) + assert l == [c, a, b] + + assert (a == b) is False + assert a <= b + assert (a > b) is False + assert a != b + assert a < b + + assert (a + 2).partition == [[1, 2], [3, 4]] + assert (b - 1).partition == [[1, 2, 4], [3]] + + assert (a - 1).partition == [[1, 2, 3, 4]] + assert (a + 1).partition == [[1, 2, 4], [3]] + assert (b + 1).partition == [[1, 2], [3], [4]] + + assert a.rank == 1 + assert b.rank == 3 + + assert a.RGS == (0, 0, 0, 1) + assert b.RGS == (0, 0, 1, 1) + + +def test_integer_partition(): + # no zeros in partition + raises(ValueError, lambda: IntegerPartition(list(range(3)))) + # check fails since 1 + 2 != 100 + raises(ValueError, lambda: IntegerPartition(100, list(range(1, 3)))) + a = IntegerPartition(8, [1, 3, 4]) + b = a.next_lex() + c = IntegerPartition([1, 3, 4]) + d = IntegerPartition(8, {1: 3, 3: 1, 2: 1}) + assert a == c + assert a.integer == d.integer + assert a.conjugate == [3, 2, 2, 1] + assert (a == b) is False + assert a <= b + assert (a > b) is False + assert a != b + + for i in range(1, 11): + next = set() + prev = set() + a = IntegerPartition([i]) + ans = {IntegerPartition(p) for p in partitions(i)} + n = len(ans) + for j in range(n): + next.add(a) + a = a.next_lex() + IntegerPartition(i, a.partition) # check it by giving i + for j in range(n): + prev.add(a) + a = a.prev_lex() + IntegerPartition(i, a.partition) # check it by giving i + assert next == ans + assert prev == ans + + assert IntegerPartition([1, 2, 3]).as_ferrers() == '###\n##\n#' + assert IntegerPartition([1, 1, 3]).as_ferrers('o') == 'ooo\no\no' + assert str(IntegerPartition([1, 1, 3])) == '[3, 1, 1]' + assert IntegerPartition([1, 1, 3]).partition == [3, 1, 1] + + raises(ValueError, lambda: random_integer_partition(-1)) + assert random_integer_partition(1) == [1] + assert random_integer_partition(10, seed=[1, 3, 2, 1, 5, 1] + ) == [5, 2, 1, 1, 1] + + +def test_rgs(): + raises(ValueError, lambda: RGS_unrank(-1, 3)) + raises(ValueError, lambda: RGS_unrank(3, 0)) + raises(ValueError, lambda: RGS_unrank(10, 1)) + + raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2)))) + raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2)))) + assert RGS_enum(-1) == 0 + assert RGS_enum(1) == 1 + assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2] + assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2] + assert RGS_rank(RGS_unrank(40, 100)) == 40 + +def test_ordered_partition_9608(): + a = Partition([1, 2, 3], [4]) + b = Partition([1, 2], [3, 4]) + assert list(ordered([a,b], Set._infimum_key)) diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..b0c146279921e1e6499534fe9e33b993348d1503 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_pc_groups.py @@ -0,0 +1,87 @@ +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, DihedralGroup +from sympy.matrices import Matrix + +def test_pc_presentation(): + Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), + SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2), DihedralGroup(10)] + + S = SymmetricGroup(125).sylow_subgroup(5) + G = S.derived_series()[2] + Groups.append(G) + + G = SymmetricGroup(25).sylow_subgroup(5) + Groups.append(G) + + S = SymmetricGroup(11**2).sylow_subgroup(11) + G = S.derived_series()[2] + Groups.append(G) + + for G in Groups: + PcGroup = G.polycyclic_group() + collector = PcGroup.collector + pc_presentation = collector.pc_presentation + + pcgs = PcGroup.pcgs + free_group = collector.free_group + free_to_perm = {} + for s, g in zip(free_group.symbols, pcgs): + free_to_perm[s] = g + + for k, v in pc_presentation.items(): + k_array = k.array_form + if v != (): + v_array = v.array_form + + lhs = Permutation() + for gen in k_array: + s = gen[0] + e = gen[1] + lhs = lhs*free_to_perm[s]**e + + if v == (): + assert lhs.is_identity + continue + + rhs = Permutation() + for gen in v_array: + s = gen[0] + e = gen[1] + rhs = rhs*free_to_perm[s]**e + + assert lhs == rhs + + +def test_exponent_vector(): + + Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), + SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2)] + + for G in Groups: + PcGroup = G.polycyclic_group() + collector = PcGroup.collector + + pcgs = PcGroup.pcgs + # free_group = collector.free_group + + for gen in G.generators: + exp = collector.exponent_vector(gen) + g = Permutation() + for i in range(len(exp)): + g = g*pcgs[i]**exp[i] if exp[i] else g + assert g == gen + + +def test_induced_pcgs(): + G = [SymmetricGroup(9).sylow_subgroup(3), SymmetricGroup(20).sylow_subgroup(2), AlternatingGroup(4), + DihedralGroup(4), DihedralGroup(10), DihedralGroup(9), SymmetricGroup(3), SymmetricGroup(4)] + + for g in G: + PcGroup = g.polycyclic_group() + collector = PcGroup.collector + gens = list(g.generators) + ipcgs = collector.induced_pcgs(gens) + m = [] + for i in ipcgs: + m.append(collector.exponent_vector(i)) + assert Matrix(m).is_upper diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py new file mode 100644 index 0000000000000000000000000000000000000000..b52fcfec0e2fb3be872efaa814077760e121c748 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_permutations.py @@ -0,0 +1,564 @@ +from itertools import permutations +from copy import copy + +from sympy.core.expr import unchanged +from sympy.core.numbers import Integer +from sympy.core.relational import Eq +from sympy.core.symbol import Symbol +from sympy.core.singleton import S +from sympy.combinatorics.permutations import \ + Permutation, _af_parity, _af_rmul, _af_rmuln, AppliedPermutation, Cycle +from sympy.printing import sstr, srepr, pretty, latex +from sympy.testing.pytest import raises, warns_deprecated_sympy + + +rmul = Permutation.rmul +a = Symbol('a', integer=True) + + +def test_Permutation(): + # don't auto fill 0 + raises(ValueError, lambda: Permutation([1])) + p = Permutation([0, 1, 2, 3]) + # call as bijective + assert [p(i) for i in range(p.size)] == list(p) + # call as operator + assert p(list(range(p.size))) == list(p) + # call as function + assert list(p(1, 2)) == [0, 2, 1, 3] + raises(TypeError, lambda: p(-1)) + raises(TypeError, lambda: p(5)) + # conversion to list + assert list(p) == list(range(4)) + assert p.copy() == p + assert copy(p) == p + assert Permutation(size=4) == Permutation(3) + assert Permutation(Permutation(3), size=5) == Permutation(4) + # cycle form with size + assert Permutation([[1, 2]], size=4) == Permutation([[1, 2], [0], [3]]) + # random generation + assert Permutation.random(2) in (Permutation([1, 0]), Permutation([0, 1])) + + p = Permutation([2, 5, 1, 6, 3, 0, 4]) + q = Permutation([[1], [0, 3, 5, 6, 2, 4]]) + assert len({p, p}) == 1 + r = Permutation([1, 3, 2, 0, 4, 6, 5]) + ans = Permutation(_af_rmuln(*[w.array_form for w in (p, q, r)])).array_form + assert rmul(p, q, r).array_form == ans + # make sure no other permutation of p, q, r could have given + # that answer + for a, b, c in permutations((p, q, r)): + if (a, b, c) == (p, q, r): + continue + assert rmul(a, b, c).array_form != ans + + assert p.support() == list(range(7)) + assert q.support() == [0, 2, 3, 4, 5, 6] + assert Permutation(p.cyclic_form).array_form == p.array_form + assert p.cardinality == 5040 + assert q.cardinality == 5040 + assert q.cycles == 2 + assert rmul(q, p) == Permutation([4, 6, 1, 2, 5, 3, 0]) + assert rmul(p, q) == Permutation([6, 5, 3, 0, 2, 4, 1]) + assert _af_rmul(p.array_form, q.array_form) == \ + [6, 5, 3, 0, 2, 4, 1] + + assert rmul(Permutation([[1, 2, 3], [0, 4]]), + Permutation([[1, 2, 4], [0], [3]])).cyclic_form == \ + [[0, 4, 2], [1, 3]] + assert q.array_form == [3, 1, 4, 5, 0, 6, 2] + assert q.cyclic_form == [[0, 3, 5, 6, 2, 4]] + assert q.full_cyclic_form == [[0, 3, 5, 6, 2, 4], [1]] + assert p.cyclic_form == [[0, 2, 1, 5], [3, 6, 4]] + t = p.transpositions() + assert t == [(0, 5), (0, 1), (0, 2), (3, 4), (3, 6)] + assert Permutation.rmul(*[Permutation(Cycle(*ti)) for ti in (t)]) + assert Permutation([1, 0]).transpositions() == [(0, 1)] + + assert p**13 == p + assert q**0 == Permutation(list(range(q.size))) + assert q**-2 == ~q**2 + assert q**2 == Permutation([5, 1, 0, 6, 3, 2, 4]) + assert q**3 == q**2*q + assert q**4 == q**2*q**2 + + a = Permutation(1, 3) + b = Permutation(2, 0, 3) + I = Permutation(3) + assert ~a == a**-1 + assert a*~a == I + assert a*b**-1 == a*~b + + ans = Permutation(0, 5, 3, 1, 6)(2, 4) + assert (p + q.rank()).rank() == ans.rank() + assert (p + q.rank())._rank == ans.rank() + assert (q + p.rank()).rank() == ans.rank() + raises(TypeError, lambda: p + Permutation(list(range(10)))) + + assert (p - q.rank()).rank() == Permutation(0, 6, 3, 1, 2, 5, 4).rank() + assert p.rank() - q.rank() < 0 # for coverage: make sure mod is used + assert (q - p.rank()).rank() == Permutation(1, 4, 6, 2)(3, 5).rank() + + assert p*q == Permutation(_af_rmuln(*[list(w) for w in (q, p)])) + assert p*Permutation([]) == p + assert Permutation([])*p == p + assert p*Permutation([[0, 1]]) == Permutation([2, 5, 0, 6, 3, 1, 4]) + assert Permutation([[0, 1]])*p == Permutation([5, 2, 1, 6, 3, 0, 4]) + + pq = p ^ q + assert pq == Permutation([5, 6, 0, 4, 1, 2, 3]) + assert pq == rmul(q, p, ~q) + qp = q ^ p + assert qp == Permutation([4, 3, 6, 2, 1, 5, 0]) + assert qp == rmul(p, q, ~p) + raises(ValueError, lambda: p ^ Permutation([])) + + assert p.commutator(q) == Permutation(0, 1, 3, 4, 6, 5, 2) + assert q.commutator(p) == Permutation(0, 2, 5, 6, 4, 3, 1) + assert p.commutator(q) == ~q.commutator(p) + raises(ValueError, lambda: p.commutator(Permutation([]))) + + assert len(p.atoms()) == 7 + assert q.atoms() == {0, 1, 2, 3, 4, 5, 6} + + assert p.inversion_vector() == [2, 4, 1, 3, 1, 0] + assert q.inversion_vector() == [3, 1, 2, 2, 0, 1] + + assert Permutation.from_inversion_vector(p.inversion_vector()) == p + assert Permutation.from_inversion_vector(q.inversion_vector()).array_form\ + == q.array_form + raises(ValueError, lambda: Permutation.from_inversion_vector([0, 2])) + assert Permutation(list(range(500, -1, -1))).inversions() == 125250 + + s = Permutation([0, 4, 1, 3, 2]) + assert s.parity() == 0 + _ = s.cyclic_form # needed to create a value for _cyclic_form + assert len(s._cyclic_form) != s.size and s.parity() == 0 + assert not s.is_odd + assert s.is_even + assert Permutation([0, 1, 4, 3, 2]).parity() == 1 + assert _af_parity([0, 4, 1, 3, 2]) == 0 + assert _af_parity([0, 1, 4, 3, 2]) == 1 + + s = Permutation([0]) + + assert s.is_Singleton + assert Permutation([]).is_Empty + + r = Permutation([3, 2, 1, 0]) + assert (r**2).is_Identity + + assert rmul(~p, p).is_Identity + assert (~p)**13 == Permutation([5, 2, 0, 4, 6, 1, 3]) + assert p.max() == 6 + assert p.min() == 0 + + q = Permutation([[6], [5], [0, 1, 2, 3, 4]]) + + assert q.max() == 4 + assert q.min() == 0 + + p = Permutation([1, 5, 2, 0, 3, 6, 4]) + q = Permutation([[1, 2, 3, 5, 6], [0, 4]]) + + assert p.ascents() == [0, 3, 4] + assert q.ascents() == [1, 2, 4] + assert r.ascents() == [] + + assert p.descents() == [1, 2, 5] + assert q.descents() == [0, 3, 5] + assert Permutation(r.descents()).is_Identity + + assert p.inversions() == 7 + # test the merge-sort with a longer permutation + big = list(p) + list(range(p.max() + 1, p.max() + 130)) + assert Permutation(big).inversions() == 7 + assert p.signature() == -1 + assert q.inversions() == 11 + assert q.signature() == -1 + assert rmul(p, ~p).inversions() == 0 + assert rmul(p, ~p).signature() == 1 + + assert p.order() == 6 + assert q.order() == 10 + assert (p**(p.order())).is_Identity + + assert p.length() == 6 + assert q.length() == 7 + assert r.length() == 4 + + assert p.runs() == [[1, 5], [2], [0, 3, 6], [4]] + assert q.runs() == [[4], [2, 3, 5], [0, 6], [1]] + assert r.runs() == [[3], [2], [1], [0]] + + assert p.index() == 8 + assert q.index() == 8 + assert r.index() == 3 + + assert p.get_precedence_distance(q) == q.get_precedence_distance(p) + assert p.get_adjacency_distance(q) == p.get_adjacency_distance(q) + assert p.get_positional_distance(q) == p.get_positional_distance(q) + p = Permutation([0, 1, 2, 3]) + q = Permutation([3, 2, 1, 0]) + assert p.get_precedence_distance(q) == 6 + assert p.get_adjacency_distance(q) == 3 + assert p.get_positional_distance(q) == 8 + p = Permutation([0, 3, 1, 2, 4]) + q = Permutation.josephus(4, 5, 2) + assert p.get_adjacency_distance(q) == 3 + raises(ValueError, lambda: p.get_adjacency_distance(Permutation([]))) + raises(ValueError, lambda: p.get_positional_distance(Permutation([]))) + raises(ValueError, lambda: p.get_precedence_distance(Permutation([]))) + + a = [Permutation.unrank_nonlex(4, i) for i in range(5)] + iden = Permutation([0, 1, 2, 3]) + for i in range(5): + for j in range(i + 1, 5): + assert a[i].commutes_with(a[j]) == \ + (rmul(a[i], a[j]) == rmul(a[j], a[i])) + if a[i].commutes_with(a[j]): + assert a[i].commutator(a[j]) == iden + assert a[j].commutator(a[i]) == iden + + a = Permutation(3) + b = Permutation(0, 6, 3)(1, 2) + assert a.cycle_structure == {1: 4} + assert b.cycle_structure == {2: 1, 3: 1, 1: 2} + # issue 11130 + raises(ValueError, lambda: Permutation(3, size=3)) + raises(ValueError, lambda: Permutation([1, 2, 0, 3], size=3)) + + +def test_Permutation_subclassing(): + # Subclass that adds permutation application on iterables + class CustomPermutation(Permutation): + def __call__(self, *i): + try: + return super().__call__(*i) + except TypeError: + pass + + try: + perm_obj = i[0] + return [self._array_form[j] for j in perm_obj] + except TypeError: + raise TypeError('unrecognized argument') + + def __eq__(self, other): + if isinstance(other, Permutation): + return self._hashable_content() == other._hashable_content() + else: + return super().__eq__(other) + + def __hash__(self): + return super().__hash__() + + p = CustomPermutation([1, 2, 3, 0]) + q = Permutation([1, 2, 3, 0]) + + assert p == q + raises(TypeError, lambda: q([1, 2])) + assert [2, 3] == p([1, 2]) + + assert type(p * q) == CustomPermutation + assert type(q * p) == Permutation # True because q.__mul__(p) is called! + + # Run all tests for the Permutation class also on the subclass + def wrapped_test_Permutation(): + # Monkeypatch the class definition in the globals + globals()['__Perm'] = globals()['Permutation'] + globals()['Permutation'] = CustomPermutation + test_Permutation() + globals()['Permutation'] = globals()['__Perm'] # Restore + del globals()['__Perm'] + + wrapped_test_Permutation() + + +def test_josephus(): + assert Permutation.josephus(4, 6, 1) == Permutation([3, 1, 0, 2, 5, 4]) + assert Permutation.josephus(1, 5, 1).is_Identity + + +def test_ranking(): + assert Permutation.unrank_lex(5, 10).rank() == 10 + p = Permutation.unrank_lex(15, 225) + assert p.rank() == 225 + p1 = p.next_lex() + assert p1.rank() == 226 + assert Permutation.unrank_lex(15, 225).rank() == 225 + assert Permutation.unrank_lex(10, 0).is_Identity + p = Permutation.unrank_lex(4, 23) + assert p.rank() == 23 + assert p.array_form == [3, 2, 1, 0] + assert p.next_lex() is None + + p = Permutation([1, 5, 2, 0, 3, 6, 4]) + q = Permutation([[1, 2, 3, 5, 6], [0, 4]]) + a = [Permutation.unrank_trotterjohnson(4, i).array_form for i in range(5)] + assert a == [[0, 1, 2, 3], [0, 1, 3, 2], [0, 3, 1, 2], [3, 0, 1, + 2], [3, 0, 2, 1] ] + assert [Permutation(pa).rank_trotterjohnson() for pa in a] == list(range(5)) + assert Permutation([0, 1, 2, 3]).next_trotterjohnson() == \ + Permutation([0, 1, 3, 2]) + + assert q.rank_trotterjohnson() == 2283 + assert p.rank_trotterjohnson() == 3389 + assert Permutation([1, 0]).rank_trotterjohnson() == 1 + a = Permutation(list(range(3))) + b = a + l = [] + tj = [] + for i in range(6): + l.append(a) + tj.append(b) + a = a.next_lex() + b = b.next_trotterjohnson() + assert a == b is None + assert {tuple(a) for a in l} == {tuple(a) for a in tj} + + p = Permutation([2, 5, 1, 6, 3, 0, 4]) + q = Permutation([[6], [5], [0, 1, 2, 3, 4]]) + assert p.rank() == 1964 + assert q.rank() == 870 + assert Permutation([]).rank_nonlex() == 0 + prank = p.rank_nonlex() + assert prank == 1600 + assert Permutation.unrank_nonlex(7, 1600) == p + qrank = q.rank_nonlex() + assert qrank == 41 + assert Permutation.unrank_nonlex(7, 41) == Permutation(q.array_form) + + a = [Permutation.unrank_nonlex(4, i).array_form for i in range(24)] + assert a == [ + [1, 2, 3, 0], [3, 2, 0, 1], [1, 3, 0, 2], [1, 2, 0, 3], [2, 3, 1, 0], + [2, 0, 3, 1], [3, 0, 1, 2], [2, 0, 1, 3], [1, 3, 2, 0], [3, 0, 2, 1], + [1, 0, 3, 2], [1, 0, 2, 3], [2, 1, 3, 0], [2, 3, 0, 1], [3, 1, 0, 2], + [2, 1, 0, 3], [3, 2, 1, 0], [0, 2, 3, 1], [0, 3, 1, 2], [0, 2, 1, 3], + [3, 1, 2, 0], [0, 3, 2, 1], [0, 1, 3, 2], [0, 1, 2, 3]] + + N = 10 + p1 = Permutation(a[0]) + for i in range(1, N+1): + p1 = p1*Permutation(a[i]) + p2 = Permutation.rmul_with_af(*[Permutation(h) for h in a[N::-1]]) + assert p1 == p2 + + ok = [] + p = Permutation([1, 0]) + for i in range(3): + ok.append(p.array_form) + p = p.next_nonlex() + if p is None: + ok.append(None) + break + assert ok == [[1, 0], [0, 1], None] + assert Permutation([3, 2, 0, 1]).next_nonlex() == Permutation([1, 3, 0, 2]) + assert [Permutation(pa).rank_nonlex() for pa in a] == list(range(24)) + + +def test_mul(): + a, b = [0, 2, 1, 3], [0, 1, 3, 2] + assert _af_rmul(a, b) == [0, 2, 3, 1] + assert _af_rmuln(a, b, list(range(4))) == [0, 2, 3, 1] + assert rmul(Permutation(a), Permutation(b)).array_form == [0, 2, 3, 1] + + a = Permutation([0, 2, 1, 3]) + b = (0, 1, 3, 2) + c = (3, 1, 2, 0) + assert Permutation.rmul(a, b, c) == Permutation([1, 2, 3, 0]) + assert Permutation.rmul(a, c) == Permutation([3, 2, 1, 0]) + raises(TypeError, lambda: Permutation.rmul(b, c)) + + n = 6 + m = 8 + a = [Permutation.unrank_nonlex(n, i).array_form for i in range(m)] + h = list(range(n)) + for i in range(m): + h = _af_rmul(h, a[i]) + h2 = _af_rmuln(*a[:i + 1]) + assert h == h2 + + +def test_args(): + p = Permutation([(0, 3, 1, 2), (4, 5)]) + assert p._cyclic_form is None + assert Permutation(p) == p + assert p.cyclic_form == [[0, 3, 1, 2], [4, 5]] + assert p._array_form == [3, 2, 0, 1, 5, 4] + p = Permutation((0, 3, 1, 2)) + assert p._cyclic_form is None + assert p._array_form == [0, 3, 1, 2] + assert Permutation([0]) == Permutation((0, )) + assert Permutation([[0], [1]]) == Permutation(((0, ), (1, ))) == \ + Permutation(((0, ), [1])) + assert Permutation([[1, 2]]) == Permutation([0, 2, 1]) + assert Permutation([[1], [4, 2]]) == Permutation([0, 1, 4, 3, 2]) + assert Permutation([[1], [4, 2]], size=1) == Permutation([0, 1, 4, 3, 2]) + assert Permutation( + [[1], [4, 2]], size=6) == Permutation([0, 1, 4, 3, 2, 5]) + assert Permutation([[0, 1], [0, 2]]) == Permutation(0, 1, 2) + assert Permutation([], size=3) == Permutation([0, 1, 2]) + assert Permutation(3).list(5) == [0, 1, 2, 3, 4] + assert Permutation(3).list(-1) == [] + assert Permutation(5)(1, 2).list(-1) == [0, 2, 1] + assert Permutation(5)(1, 2).list() == [0, 2, 1, 3, 4, 5] + raises(ValueError, lambda: Permutation([1, 2], [0])) + # enclosing brackets needed + raises(ValueError, lambda: Permutation([[1, 2], 0])) + # enclosing brackets needed on 0 + raises(ValueError, lambda: Permutation([1, 1, 0])) + raises(ValueError, lambda: Permutation([4, 5], size=10)) # where are 0-3? + # but this is ok because cycles imply that only those listed moved + assert Permutation(4, 5) == Permutation([0, 1, 2, 3, 5, 4]) + + +def test_Cycle(): + assert str(Cycle()) == '()' + assert Cycle(Cycle(1,2)) == Cycle(1, 2) + assert Cycle(1,2).copy() == Cycle(1,2) + assert list(Cycle(1, 3, 2)) == [0, 3, 1, 2] + assert Cycle(1, 2)(2, 3) == Cycle(1, 3, 2) + assert Cycle(1, 2)(2, 3)(4, 5) == Cycle(1, 3, 2)(4, 5) + assert Permutation(Cycle(1, 2)(2, 1, 0, 3)).cyclic_form, Cycle(0, 2, 1) + raises(ValueError, lambda: Cycle().list()) + assert Cycle(1, 2).list() == [0, 2, 1] + assert Cycle(1, 2).list(4) == [0, 2, 1, 3] + assert Cycle(3).list(2) == [0, 1] + assert Cycle(3).list(6) == [0, 1, 2, 3, 4, 5] + assert Permutation(Cycle(1, 2), size=4) == \ + Permutation([0, 2, 1, 3]) + assert str(Cycle(1, 2)(4, 5)) == '(1 2)(4 5)' + assert str(Cycle(1, 2)) == '(1 2)' + assert Cycle(Permutation(list(range(3)))) == Cycle() + assert Cycle(1, 2).list() == [0, 2, 1] + assert Cycle(1, 2).list(4) == [0, 2, 1, 3] + assert Cycle().size == 0 + raises(ValueError, lambda: Cycle((1, 2))) + raises(ValueError, lambda: Cycle(1, 2, 1)) + raises(TypeError, lambda: Cycle(1, 2)*{}) + raises(ValueError, lambda: Cycle(4)[a]) + raises(ValueError, lambda: Cycle(2, -4, 3)) + + # check round-trip + p = Permutation([[1, 2], [4, 3]], size=5) + assert Permutation(Cycle(p)) == p + + +def test_from_sequence(): + assert Permutation.from_sequence('SymPy') == Permutation(4)(0, 1, 3) + assert Permutation.from_sequence('SymPy', key=lambda x: x.lower()) == \ + Permutation(4)(0, 2)(1, 3) + + +def test_resize(): + p = Permutation(0, 1, 2) + assert p.resize(5) == Permutation(0, 1, 2, size=5) + assert p.resize(4) == Permutation(0, 1, 2, size=4) + assert p.resize(3) == p + raises(ValueError, lambda: p.resize(2)) + + p = Permutation(0, 1, 2)(3, 4)(5, 6) + assert p.resize(3) == Permutation(0, 1, 2) + raises(ValueError, lambda: p.resize(4)) + + +def test_printing_cyclic(): + p1 = Permutation([0, 2, 1]) + assert repr(p1) == 'Permutation(1, 2)' + assert str(p1) == '(1 2)' + p2 = Permutation() + assert repr(p2) == 'Permutation()' + assert str(p2) == '()' + p3 = Permutation([1, 2, 0, 3]) + assert repr(p3) == 'Permutation(3)(0, 1, 2)' + + +def test_printing_non_cyclic(): + p1 = Permutation([0, 1, 2, 3, 4, 5]) + assert srepr(p1, perm_cyclic=False) == 'Permutation([], size=6)' + assert sstr(p1, perm_cyclic=False) == 'Permutation([], size=6)' + p2 = Permutation([0, 1, 2]) + assert srepr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])' + assert sstr(p2, perm_cyclic=False) == 'Permutation([0, 1, 2])' + + p3 = Permutation([0, 2, 1]) + assert srepr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])' + assert sstr(p3, perm_cyclic=False) == 'Permutation([0, 2, 1])' + p4 = Permutation([0, 1, 3, 2, 4, 5, 6, 7]) + assert srepr(p4, perm_cyclic=False) == 'Permutation([0, 1, 3, 2], size=8)' + + +def test_deprecated_print_cyclic(): + p = Permutation(0, 1, 2) + try: + Permutation.print_cyclic = True + with warns_deprecated_sympy(): + assert sstr(p) == '(0 1 2)' + with warns_deprecated_sympy(): + assert srepr(p) == 'Permutation(0, 1, 2)' + with warns_deprecated_sympy(): + assert pretty(p) == '(0 1 2)' + with warns_deprecated_sympy(): + assert latex(p) == r'\left( 0\; 1\; 2\right)' + + Permutation.print_cyclic = False + with warns_deprecated_sympy(): + assert sstr(p) == 'Permutation([1, 2, 0])' + with warns_deprecated_sympy(): + assert srepr(p) == 'Permutation([1, 2, 0])' + with warns_deprecated_sympy(): + assert pretty(p, use_unicode=False) == '/0 1 2\\\n\\1 2 0/' + with warns_deprecated_sympy(): + assert latex(p) == \ + r'\begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 0 \end{pmatrix}' + finally: + Permutation.print_cyclic = None + + +def test_permutation_equality(): + a = Permutation(0, 1, 2) + b = Permutation(0, 1, 2) + assert Eq(a, b) is S.true + c = Permutation(0, 2, 1) + assert Eq(a, c) is S.false + + d = Permutation(0, 1, 2, size=4) + assert unchanged(Eq, a, d) + e = Permutation(0, 2, 1, size=4) + assert unchanged(Eq, a, e) + + i = Permutation() + assert unchanged(Eq, i, 0) + assert unchanged(Eq, 0, i) + + +def test_issue_17661(): + c1 = Cycle(1,2) + c2 = Cycle(1,2) + assert c1 == c2 + assert repr(c1) == 'Cycle(1, 2)' + assert c1 == c2 + + +def test_permutation_apply(): + x = Symbol('x') + p = Permutation(0, 1, 2) + assert p.apply(0) == 1 + assert isinstance(p.apply(0), Integer) + assert p.apply(x) == AppliedPermutation(p, x) + assert AppliedPermutation(p, x).subs(x, 0) == 1 + + x = Symbol('x', integer=False) + raises(NotImplementedError, lambda: p.apply(x)) + x = Symbol('x', negative=True) + raises(NotImplementedError, lambda: p.apply(x)) + + +def test_AppliedPermutation(): + x = Symbol('x') + p = Permutation(0, 1, 2) + raises(ValueError, lambda: AppliedPermutation((0, 1, 2), x)) + assert AppliedPermutation(p, 1, evaluate=True) == 2 + assert AppliedPermutation(p, 1, evaluate=False).__class__ == \ + AppliedPermutation diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py new file mode 100644 index 0000000000000000000000000000000000000000..b077c7cf3f023a4c36d7039505e6165ab29f275a --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_prufer.py @@ -0,0 +1,74 @@ +from sympy.combinatorics.prufer import Prufer +from sympy.testing.pytest import raises + + +def test_prufer(): + # number of nodes is optional + assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]], 5).nodes == 5 + assert Prufer([[0, 1], [0, 2], [0, 3], [0, 4]]).nodes == 5 + + a = Prufer([[0, 1], [0, 2], [0, 3], [0, 4]]) + assert a.rank == 0 + assert a.nodes == 5 + assert a.prufer_repr == [0, 0, 0] + + a = Prufer([[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]]) + assert a.rank == 924 + assert a.nodes == 6 + assert a.tree_repr == [[2, 4], [1, 4], [1, 3], [0, 5], [0, 4]] + assert a.prufer_repr == [4, 1, 4, 0] + + assert Prufer.edges([0, 1, 2, 3], [1, 4, 5], [1, 4, 6]) == \ + ([[0, 1], [1, 2], [1, 4], [2, 3], [4, 5], [4, 6]], 7) + assert Prufer([0]*4).size == Prufer([6]*4).size == 1296 + + # accept iterables but convert to list of lists + tree = [(0, 1), (1, 5), (0, 3), (0, 2), (2, 6), (4, 7), (2, 4)] + tree_lists = [list(t) for t in tree] + assert Prufer(tree).tree_repr == tree_lists + assert sorted(Prufer(set(tree)).tree_repr) == sorted(tree_lists) + + raises(ValueError, lambda: Prufer([[1, 2], [3, 4]])) # 0 is missing + raises(ValueError, lambda: Prufer([[2, 3], [3, 4]])) # 0, 1 are missing + assert Prufer(*Prufer.edges([1, 2], [3, 4])).prufer_repr == [1, 3] + raises(ValueError, lambda: Prufer.edges( + [1, 3], [3, 4])) # a broken tree but edges doesn't care + raises(ValueError, lambda: Prufer.edges([1, 2], [5, 6])) + raises(ValueError, lambda: Prufer([[]])) + + a = Prufer([[0, 1], [0, 2], [0, 3]]) + b = a.next() + assert b.tree_repr == [[0, 2], [0, 1], [1, 3]] + assert b.rank == 1 + + +def test_round_trip(): + def doit(t, b): + e, n = Prufer.edges(*t) + t = Prufer(e, n) + a = sorted(t.tree_repr) + b = [i - 1 for i in b] + assert t.prufer_repr == b + assert sorted(Prufer(b).tree_repr) == a + assert Prufer.unrank(t.rank, n).prufer_repr == b + + doit([[1, 2]], []) + doit([[2, 1, 3]], [1]) + doit([[1, 3, 2]], [3]) + doit([[1, 2, 3]], [2]) + doit([[2, 1, 4], [1, 3]], [1, 1]) + doit([[3, 2, 1, 4]], [2, 1]) + doit([[3, 2, 1], [2, 4]], [2, 2]) + doit([[1, 3, 2, 4]], [3, 2]) + doit([[1, 4, 2, 3]], [4, 2]) + doit([[3, 1, 4, 2]], [4, 1]) + doit([[4, 2, 1, 3]], [1, 2]) + doit([[1, 2, 4, 3]], [2, 4]) + doit([[1, 3, 4, 2]], [3, 4]) + doit([[2, 4, 1], [4, 3]], [4, 4]) + doit([[1, 2, 3, 4]], [2, 3]) + doit([[2, 3, 1], [3, 4]], [3, 3]) + doit([[1, 4, 3, 2]], [4, 3]) + doit([[2, 1, 4, 3]], [1, 4]) + doit([[2, 1, 3, 4]], [1, 3]) + doit([[6, 2, 1, 4], [1, 3, 5, 8], [3, 7]], [1, 2, 1, 3, 3, 5]) diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py new file mode 100644 index 0000000000000000000000000000000000000000..e6beb9b11fa993a99b71d89b8485050fc3575b8e --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_schur_number.py @@ -0,0 +1,55 @@ +from sympy.core import S, Rational +from sympy.combinatorics.schur_number import schur_partition, SchurNumber +from sympy.core.random import _randint +from sympy.testing.pytest import raises +from sympy.core.symbol import symbols + + +def _sum_free_test(subset): + """ + Checks if subset is sum-free(There are no x,y,z in the subset such that + x + y = z) + """ + for i in subset: + for j in subset: + assert (i + j in subset) is False + + +def test_schur_partition(): + raises(ValueError, lambda: schur_partition(S.Infinity)) + raises(ValueError, lambda: schur_partition(-1)) + raises(ValueError, lambda: schur_partition(0)) + assert schur_partition(2) == [[1, 2]] + + random_number_generator = _randint(1000) + for _ in range(5): + n = random_number_generator(1, 1000) + result = schur_partition(n) + t = 0 + numbers = [] + for item in result: + _sum_free_test(item) + """ + Checks if the occurrence of all numbers is exactly one + """ + t += len(item) + for l in item: + assert (l in numbers) is False + numbers.append(l) + assert n == t + + x = symbols("x") + raises(ValueError, lambda: schur_partition(x)) + +def test_schur_number(): + first_known_schur_numbers = {1: 1, 2: 4, 3: 13, 4: 44, 5: 160} + for k in first_known_schur_numbers: + assert SchurNumber(k) == first_known_schur_numbers[k] + + assert SchurNumber(S.Infinity) == S.Infinity + assert SchurNumber(0) == 0 + raises(ValueError, lambda: SchurNumber(0.5)) + + n = symbols("n") + assert SchurNumber(n).lower_bound() == 3**n/2 - Rational(1, 2) + assert SchurNumber(8).lower_bound() == 5039 diff --git a/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py new file mode 100644 index 0000000000000000000000000000000000000000..e13f4d5b9913213bac7798c4df77f6665785c9ca --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/combinatorics/tests/test_testutil.py @@ -0,0 +1,55 @@ +from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup,\ + CyclicGroup +from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists,\ + _naive_list_centralizer, _verify_centralizer,\ + _verify_normal_closure +from sympy.combinatorics.permutations import Permutation +from sympy.combinatorics.perm_groups import PermutationGroup +from sympy.core.random import shuffle + + +def test_cmp_perm_lists(): + S = SymmetricGroup(4) + els = list(S.generate_dimino()) + other = els[:] + shuffle(other) + assert _cmp_perm_lists(els, other) is True + + +def test_naive_list_centralizer(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + assert _naive_list_centralizer(S, S) == [Permutation([0, 1, 2])] + assert PermutationGroup(_naive_list_centralizer(S, A)).is_subgroup(A) + + +def test_verify_bsgs(): + S = SymmetricGroup(5) + S.schreier_sims() + base = S.base + strong_gens = S.strong_gens + assert _verify_bsgs(S, base, strong_gens) is True + assert _verify_bsgs(S, base[:-1], strong_gens) is False + assert _verify_bsgs(S, base, S.generators) is False + + +def test_verify_centralizer(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + triv = PermutationGroup([Permutation([0, 1, 2])]) + assert _verify_centralizer(S, S, centr=triv) + assert _verify_centralizer(S, A, centr=A) + + +def test_verify_normal_closure(): + # verified by GAP + S = SymmetricGroup(3) + A = AlternatingGroup(3) + assert _verify_normal_closure(S, A, closure=A) + S = SymmetricGroup(5) + A = AlternatingGroup(5) + C = CyclicGroup(5) + assert _verify_normal_closure(S, A, closure=A) + assert _verify_normal_closure(S, C, closure=A) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/__init__.py b/janus/lib/python3.10/site-packages/sympy/simplify/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..0619d1c3ebbd6c6a7d663093c7ed2202114148af --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/__init__.py @@ -0,0 +1,60 @@ +"""The module helps converting SymPy expressions into shorter forms of them. + +for example: +the expression E**(pi*I) will be converted into -1 +the expression (x+x)**2 will be converted into 4*x**2 +""" +from .simplify import (simplify, hypersimp, hypersimilar, + logcombine, separatevars, posify, besselsimp, kroneckersimp, + signsimp, nsimplify) + +from .fu import FU, fu + +from .sqrtdenest import sqrtdenest + +from .cse_main import cse + +from .epathtools import epath, EPath + +from .hyperexpand import hyperexpand + +from .radsimp import collect, rcollect, radsimp, collect_const, fraction, numer, denom + +from .trigsimp import trigsimp, exptrigsimp + +from .powsimp import powsimp, powdenest + +from .combsimp import combsimp + +from .gammasimp import gammasimp + +from .ratsimp import ratsimp, ratsimpmodprime + +__all__ = [ + 'simplify', 'hypersimp', 'hypersimilar', 'logcombine', 'separatevars', + 'posify', 'besselsimp', 'kroneckersimp', 'signsimp', + 'nsimplify', + + 'FU', 'fu', + + 'sqrtdenest', + + 'cse', + + 'epath', 'EPath', + + 'hyperexpand', + + 'collect', 'rcollect', 'radsimp', 'collect_const', 'fraction', 'numer', + 'denom', + + 'trigsimp', 'exptrigsimp', + + 'powsimp', 'powdenest', + + 'combsimp', + + 'gammasimp', + + 'ratsimp', 'ratsimpmodprime', +] diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/combsimp.py b/janus/lib/python3.10/site-packages/sympy/simplify/combsimp.py new file mode 100644 index 0000000000000000000000000000000000000000..218c998216249459bf410a75581e0f2e5bdc792d --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/combsimp.py @@ -0,0 +1,114 @@ +from sympy.core import Mul +from sympy.core.function import count_ops +from sympy.core.traversal import preorder_traversal, bottom_up +from sympy.functions.combinatorial.factorials import binomial, factorial +from sympy.functions import gamma +from sympy.simplify.gammasimp import gammasimp, _gammasimp + +from sympy.utilities.timeutils import timethis + + +@timethis('combsimp') +def combsimp(expr): + r""" + Simplify combinatorial expressions. + + Explanation + =========== + + This function takes as input an expression containing factorials, + binomials, Pochhammer symbol and other "combinatorial" functions, + and tries to minimize the number of those functions and reduce + the size of their arguments. + + The algorithm works by rewriting all combinatorial functions as + gamma functions and applying gammasimp() except simplification + steps that may make an integer argument non-integer. See docstring + of gammasimp for more information. + + Then it rewrites expression in terms of factorials and binomials by + rewriting gammas as factorials and converting (a+b)!/a!b! into + binomials. + + If expression has gamma functions or combinatorial functions + with non-integer argument, it is automatically passed to gammasimp. + + Examples + ======== + + >>> from sympy.simplify import combsimp + >>> from sympy import factorial, binomial, symbols + >>> n, k = symbols('n k', integer = True) + + >>> combsimp(factorial(n)/factorial(n - 3)) + n*(n - 2)*(n - 1) + >>> combsimp(binomial(n+1, k+1)/binomial(n, k)) + (n + 1)/(k + 1) + + """ + + expr = expr.rewrite(gamma, piecewise=False) + if any(isinstance(node, gamma) and not node.args[0].is_integer + for node in preorder_traversal(expr)): + return gammasimp(expr); + + expr = _gammasimp(expr, as_comb = True) + expr = _gamma_as_comb(expr) + return expr + + +def _gamma_as_comb(expr): + """ + Helper function for combsimp. + + Rewrites expression in terms of factorials and binomials + """ + + expr = expr.rewrite(factorial) + + def f(rv): + if not rv.is_Mul: + return rv + rvd = rv.as_powers_dict() + nd_fact_args = [[], []] # numerator, denominator + + for k in rvd: + if isinstance(k, factorial) and rvd[k].is_Integer: + if rvd[k].is_positive: + nd_fact_args[0].extend([k.args[0]]*rvd[k]) + else: + nd_fact_args[1].extend([k.args[0]]*-rvd[k]) + rvd[k] = 0 + if not nd_fact_args[0] or not nd_fact_args[1]: + return rv + + hit = False + for m in range(2): + i = 0 + while i < len(nd_fact_args[m]): + ai = nd_fact_args[m][i] + for j in range(i + 1, len(nd_fact_args[m])): + aj = nd_fact_args[m][j] + + sum = ai + aj + if sum in nd_fact_args[1 - m]: + hit = True + + nd_fact_args[1 - m].remove(sum) + del nd_fact_args[m][j] + del nd_fact_args[m][i] + + rvd[binomial(sum, ai if count_ops(ai) < + count_ops(aj) else aj)] += ( + -1 if m == 0 else 1) + break + else: + i += 1 + + if hit: + return Mul(*([k**rvd[k] for k in rvd] + [factorial(k) + for k in nd_fact_args[0]]))/Mul(*[factorial(k) + for k in nd_fact_args[1]]) + return rv + + return bottom_up(expr, f) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/cse_main.py b/janus/lib/python3.10/site-packages/sympy/simplify/cse_main.py new file mode 100644 index 0000000000000000000000000000000000000000..e03789b48f770761eb0130c8469275a47e31a702 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/cse_main.py @@ -0,0 +1,946 @@ +""" Tools for doing common subexpression elimination. +""" +from collections import defaultdict + +from sympy.core import Basic, Mul, Add, Pow, sympify +from sympy.core.containers import Tuple, OrderedSet +from sympy.core.exprtools import factor_terms +from sympy.core.singleton import S +from sympy.core.sorting import ordered +from sympy.core.symbol import symbols, Symbol +from sympy.matrices import (MatrixBase, Matrix, ImmutableMatrix, + SparseMatrix, ImmutableSparseMatrix) +from sympy.matrices.expressions import (MatrixExpr, MatrixSymbol, MatMul, + MatAdd, MatPow, Inverse) +from sympy.matrices.expressions.matexpr import MatrixElement +from sympy.polys.rootoftools import RootOf +from sympy.utilities.iterables import numbered_symbols, sift, \ + topological_sort, iterable + +from . import cse_opts + +# (preprocessor, postprocessor) pairs which are commonly useful. They should +# each take a SymPy expression and return a possibly transformed expression. +# When used in the function ``cse()``, the target expressions will be transformed +# by each of the preprocessor functions in order. After the common +# subexpressions are eliminated, each resulting expression will have the +# postprocessor functions transform them in *reverse* order in order to undo the +# transformation if necessary. This allows the algorithm to operate on +# a representation of the expressions that allows for more optimization +# opportunities. +# ``None`` can be used to specify no transformation for either the preprocessor or +# postprocessor. + + +basic_optimizations = [(cse_opts.sub_pre, cse_opts.sub_post), + (factor_terms, None)] + +# sometimes we want the output in a different format; non-trivial +# transformations can be put here for users +# =============================================================== + + +def reps_toposort(r): + """Sort replacements ``r`` so (k1, v1) appears before (k2, v2) + if k2 is in v1's free symbols. This orders items in the + way that cse returns its results (hence, in order to use the + replacements in a substitution option it would make sense + to reverse the order). + + Examples + ======== + + >>> from sympy.simplify.cse_main import reps_toposort + >>> from sympy.abc import x, y + >>> from sympy import Eq + >>> for l, r in reps_toposort([(x, y + 1), (y, 2)]): + ... print(Eq(l, r)) + ... + Eq(y, 2) + Eq(x, y + 1) + + """ + r = sympify(r) + E = [] + for c1, (k1, v1) in enumerate(r): + for c2, (k2, v2) in enumerate(r): + if k1 in v2.free_symbols: + E.append((c1, c2)) + return [r[i] for i in topological_sort((range(len(r)), E))] + + +def cse_separate(r, e): + """Move expressions that are in the form (symbol, expr) out of the + expressions and sort them into the replacements using the reps_toposort. + + Examples + ======== + + >>> from sympy.simplify.cse_main import cse_separate + >>> from sympy.abc import x, y, z + >>> from sympy import cos, exp, cse, Eq, symbols + >>> x0, x1 = symbols('x:2') + >>> eq = (x + 1 + exp((x + 1)/(y + 1)) + cos(y + 1)) + >>> cse([eq, Eq(x, z + 1), z - 2], postprocess=cse_separate) in [ + ... [[(x0, y + 1), (x, z + 1), (x1, x + 1)], + ... [x1 + exp(x1/x0) + cos(x0), z - 2]], + ... [[(x1, y + 1), (x, z + 1), (x0, x + 1)], + ... [x0 + exp(x0/x1) + cos(x1), z - 2]]] + ... + True + """ + d = sift(e, lambda w: w.is_Equality and w.lhs.is_Symbol) + r = r + [w.args for w in d[True]] + e = d[False] + return [reps_toposort(r), e] + + +def cse_release_variables(r, e): + """ + Return tuples giving ``(a, b)`` where ``a`` is a symbol and ``b`` is + either an expression or None. The value of None is used when a + symbol is no longer needed for subsequent expressions. + + Use of such output can reduce the memory footprint of lambdified + expressions that contain large, repeated subexpressions. + + Examples + ======== + + >>> from sympy import cse + >>> from sympy.simplify.cse_main import cse_release_variables + >>> from sympy.abc import x, y + >>> eqs = [(x + y - 1)**2, x, x + y, (x + y)/(2*x + 1) + (x + y - 1)**2, (2*x + 1)**(x + y)] + >>> defs, rvs = cse_release_variables(*cse(eqs)) + >>> for i in defs: + ... print(i) + ... + (x0, x + y) + (x1, (x0 - 1)**2) + (x2, 2*x + 1) + (_3, x0/x2 + x1) + (_4, x2**x0) + (x2, None) + (_0, x1) + (x1, None) + (_2, x0) + (x0, None) + (_1, x) + >>> print(rvs) + (_0, _1, _2, _3, _4) + """ + if not r: + return r, e + + s, p = zip(*r) + esyms = symbols('_:%d' % len(e)) + syms = list(esyms) + s = list(s) + in_use = set(s) + p = list(p) + # sort e so those with most sub-expressions appear first + e = [(e[i], syms[i]) for i in range(len(e))] + e, syms = zip(*sorted(e, + key=lambda x: -sum(p[s.index(i)].count_ops() + for i in x[0].free_symbols & in_use))) + syms = list(syms) + p += e + rv = [] + i = len(p) - 1 + while i >= 0: + _p = p.pop() + c = in_use & _p.free_symbols + if c: # sorting for canonical results + rv.extend([(s, None) for s in sorted(c, key=str)]) + if i >= len(r): + rv.append((syms.pop(), _p)) + else: + rv.append((s[i], _p)) + in_use -= c + i -= 1 + rv.reverse() + return rv, esyms + + +# ====end of cse postprocess idioms=========================== + + +def preprocess_for_cse(expr, optimizations): + """ Preprocess an expression to optimize for common subexpression + elimination. + + Parameters + ========== + + expr : SymPy expression + The target expression to optimize. + optimizations : list of (callable, callable) pairs + The (preprocessor, postprocessor) pairs. + + Returns + ======= + + expr : SymPy expression + The transformed expression. + """ + for pre, post in optimizations: + if pre is not None: + expr = pre(expr) + return expr + + +def postprocess_for_cse(expr, optimizations): + """Postprocess an expression after common subexpression elimination to + return the expression to canonical SymPy form. + + Parameters + ========== + + expr : SymPy expression + The target expression to transform. + optimizations : list of (callable, callable) pairs, optional + The (preprocessor, postprocessor) pairs. The postprocessors will be + applied in reversed order to undo the effects of the preprocessors + correctly. + + Returns + ======= + + expr : SymPy expression + The transformed expression. + """ + for pre, post in reversed(optimizations): + if post is not None: + expr = post(expr) + return expr + + +class FuncArgTracker: + """ + A class which manages a mapping from functions to arguments and an inverse + mapping from arguments to functions. + """ + + def __init__(self, funcs): + # To minimize the number of symbolic comparisons, all function arguments + # get assigned a value number. + self.value_numbers = {} + self.value_number_to_value = [] + + # Both of these maps use integer indices for arguments / functions. + self.arg_to_funcset = [] + self.func_to_argset = [] + + for func_i, func in enumerate(funcs): + func_argset = OrderedSet() + + for func_arg in func.args: + arg_number = self.get_or_add_value_number(func_arg) + func_argset.add(arg_number) + self.arg_to_funcset[arg_number].add(func_i) + + self.func_to_argset.append(func_argset) + + def get_args_in_value_order(self, argset): + """ + Return the list of arguments in sorted order according to their value + numbers. + """ + return [self.value_number_to_value[argn] for argn in sorted(argset)] + + def get_or_add_value_number(self, value): + """ + Return the value number for the given argument. + """ + nvalues = len(self.value_numbers) + value_number = self.value_numbers.setdefault(value, nvalues) + if value_number == nvalues: + self.value_number_to_value.append(value) + self.arg_to_funcset.append(OrderedSet()) + return value_number + + def stop_arg_tracking(self, func_i): + """ + Remove the function func_i from the argument to function mapping. + """ + for arg in self.func_to_argset[func_i]: + self.arg_to_funcset[arg].remove(func_i) + + + def get_common_arg_candidates(self, argset, min_func_i=0): + """Return a dict whose keys are function numbers. The entries of the dict are + the number of arguments said function has in common with + ``argset``. Entries have at least 2 items in common. All keys have + value at least ``min_func_i``. + """ + count_map = defaultdict(lambda: 0) + if not argset: + return count_map + + funcsets = [self.arg_to_funcset[arg] for arg in argset] + # As an optimization below, we handle the largest funcset separately from + # the others. + largest_funcset = max(funcsets, key=len) + + for funcset in funcsets: + if largest_funcset is funcset: + continue + for func_i in funcset: + if func_i >= min_func_i: + count_map[func_i] += 1 + + # We pick the smaller of the two containers (count_map, largest_funcset) + # to iterate over to reduce the number of iterations needed. + (smaller_funcs_container, + larger_funcs_container) = sorted( + [largest_funcset, count_map], + key=len) + + for func_i in smaller_funcs_container: + # Not already in count_map? It can't possibly be in the output, so + # skip it. + if count_map[func_i] < 1: + continue + + if func_i in larger_funcs_container: + count_map[func_i] += 1 + + return {k: v for k, v in count_map.items() if v >= 2} + + def get_subset_candidates(self, argset, restrict_to_funcset=None): + """ + Return a set of functions each of which whose argument list contains + ``argset``, optionally filtered only to contain functions in + ``restrict_to_funcset``. + """ + iarg = iter(argset) + + indices = OrderedSet( + fi for fi in self.arg_to_funcset[next(iarg)]) + + if restrict_to_funcset is not None: + indices &= restrict_to_funcset + + for arg in iarg: + indices &= self.arg_to_funcset[arg] + + return indices + + def update_func_argset(self, func_i, new_argset): + """ + Update a function with a new set of arguments. + """ + new_args = OrderedSet(new_argset) + old_args = self.func_to_argset[func_i] + + for deleted_arg in old_args - new_args: + self.arg_to_funcset[deleted_arg].remove(func_i) + for added_arg in new_args - old_args: + self.arg_to_funcset[added_arg].add(func_i) + + self.func_to_argset[func_i].clear() + self.func_to_argset[func_i].update(new_args) + + +class Unevaluated: + + def __init__(self, func, args): + self.func = func + self.args = args + + def __str__(self): + return "Uneval<{}>({})".format( + self.func, ", ".join(str(a) for a in self.args)) + + def as_unevaluated_basic(self): + return self.func(*self.args, evaluate=False) + + @property + def free_symbols(self): + return set().union(*[a.free_symbols for a in self.args]) + + __repr__ = __str__ + + +def match_common_args(func_class, funcs, opt_subs): + """ + Recognize and extract common subexpressions of function arguments within a + set of function calls. For instance, for the following function calls:: + + x + z + y + sin(x + y) + + this will extract a common subexpression of `x + y`:: + + w = x + y + w + z + sin(w) + + The function we work with is assumed to be associative and commutative. + + Parameters + ========== + + func_class: class + The function class (e.g. Add, Mul) + funcs: list of functions + A list of function calls. + opt_subs: dict + A dictionary of substitutions which this function may update. + """ + + # Sort to ensure that whole-function subexpressions come before the items + # that use them. + funcs = sorted(funcs, key=lambda f: len(f.args)) + arg_tracker = FuncArgTracker(funcs) + + changed = OrderedSet() + + for i in range(len(funcs)): + common_arg_candidates_counts = arg_tracker.get_common_arg_candidates( + arg_tracker.func_to_argset[i], min_func_i=i + 1) + + # Sort the candidates in order of match size. + # This makes us try combining smaller matches first. + common_arg_candidates = OrderedSet(sorted( + common_arg_candidates_counts.keys(), + key=lambda k: (common_arg_candidates_counts[k], k))) + + while common_arg_candidates: + j = common_arg_candidates.pop(last=False) + + com_args = arg_tracker.func_to_argset[i].intersection( + arg_tracker.func_to_argset[j]) + + if len(com_args) <= 1: + # This may happen if a set of common arguments was already + # combined in a previous iteration. + continue + + # For all sets, replace the common symbols by the function + # over them, to allow recursive matches. + + diff_i = arg_tracker.func_to_argset[i].difference(com_args) + if diff_i: + # com_func needs to be unevaluated to allow for recursive matches. + com_func = Unevaluated( + func_class, arg_tracker.get_args_in_value_order(com_args)) + com_func_number = arg_tracker.get_or_add_value_number(com_func) + arg_tracker.update_func_argset(i, diff_i | OrderedSet([com_func_number])) + changed.add(i) + else: + # Treat the whole expression as a CSE. + # + # The reason this needs to be done is somewhat subtle. Within + # tree_cse(), to_eliminate only contains expressions that are + # seen more than once. The problem is unevaluated expressions + # do not compare equal to the evaluated equivalent. So + # tree_cse() won't mark funcs[i] as a CSE if we use an + # unevaluated version. + com_func_number = arg_tracker.get_or_add_value_number(funcs[i]) + + diff_j = arg_tracker.func_to_argset[j].difference(com_args) + arg_tracker.update_func_argset(j, diff_j | OrderedSet([com_func_number])) + changed.add(j) + + for k in arg_tracker.get_subset_candidates( + com_args, common_arg_candidates): + diff_k = arg_tracker.func_to_argset[k].difference(com_args) + arg_tracker.update_func_argset(k, diff_k | OrderedSet([com_func_number])) + changed.add(k) + + if i in changed: + opt_subs[funcs[i]] = Unevaluated(func_class, + arg_tracker.get_args_in_value_order(arg_tracker.func_to_argset[i])) + + arg_tracker.stop_arg_tracking(i) + + +def opt_cse(exprs, order='canonical'): + """Find optimization opportunities in Adds, Muls, Pows and negative + coefficient Muls. + + Parameters + ========== + + exprs : list of SymPy expressions + The expressions to optimize. + order : string, 'none' or 'canonical' + The order by which Mul and Add arguments are processed. For large + expressions where speed is a concern, use the setting order='none'. + + Returns + ======= + + opt_subs : dictionary of expression substitutions + The expression substitutions which can be useful to optimize CSE. + + Examples + ======== + + >>> from sympy.simplify.cse_main import opt_cse + >>> from sympy.abc import x + >>> opt_subs = opt_cse([x**-2]) + >>> k, v = list(opt_subs.keys())[0], list(opt_subs.values())[0] + >>> print((k, v.as_unevaluated_basic())) + (x**(-2), 1/(x**2)) + """ + opt_subs = {} + + adds = OrderedSet() + muls = OrderedSet() + + seen_subexp = set() + collapsible_subexp = set() + + def _find_opts(expr): + + if not isinstance(expr, (Basic, Unevaluated)): + return + + if expr.is_Atom or expr.is_Order: + return + + if iterable(expr): + list(map(_find_opts, expr)) + return + + if expr in seen_subexp: + return expr + seen_subexp.add(expr) + + list(map(_find_opts, expr.args)) + + if not isinstance(expr, MatrixExpr) and expr.could_extract_minus_sign(): + # XXX -expr does not always work rigorously for some expressions + # containing UnevaluatedExpr. + # https://github.com/sympy/sympy/issues/24818 + if isinstance(expr, Add): + neg_expr = Add(*(-i for i in expr.args)) + else: + neg_expr = -expr + + if not neg_expr.is_Atom: + opt_subs[expr] = Unevaluated(Mul, (S.NegativeOne, neg_expr)) + seen_subexp.add(neg_expr) + expr = neg_expr + + if isinstance(expr, (Mul, MatMul)): + if len(expr.args) == 1: + collapsible_subexp.add(expr) + else: + muls.add(expr) + + elif isinstance(expr, (Add, MatAdd)): + if len(expr.args) == 1: + collapsible_subexp.add(expr) + else: + adds.add(expr) + + elif isinstance(expr, Inverse): + # Do not want to treat `Inverse` as a `MatPow` + pass + + elif isinstance(expr, (Pow, MatPow)): + base, exp = expr.base, expr.exp + if exp.could_extract_minus_sign(): + opt_subs[expr] = Unevaluated(Pow, (Pow(base, -exp), -1)) + + for e in exprs: + if isinstance(e, (Basic, Unevaluated)): + _find_opts(e) + + # Handle collapsing of multinary operations with single arguments + edges = [(s, s.args[0]) for s in collapsible_subexp + if s.args[0] in collapsible_subexp] + for e in reversed(topological_sort((collapsible_subexp, edges))): + opt_subs[e] = opt_subs.get(e.args[0], e.args[0]) + + # split muls into commutative + commutative_muls = OrderedSet() + for m in muls: + c, nc = m.args_cnc(cset=False) + if c: + c_mul = m.func(*c) + if nc: + if c_mul == 1: + new_obj = m.func(*nc) + else: + if isinstance(m, MatMul): + new_obj = m.func(c_mul, *nc, evaluate=False) + else: + new_obj = m.func(c_mul, m.func(*nc), evaluate=False) + opt_subs[m] = new_obj + if len(c) > 1: + commutative_muls.add(c_mul) + + match_common_args(Add, adds, opt_subs) + match_common_args(Mul, commutative_muls, opt_subs) + + return opt_subs + + +def tree_cse(exprs, symbols, opt_subs=None, order='canonical', ignore=()): + """Perform raw CSE on expression tree, taking opt_subs into account. + + Parameters + ========== + + exprs : list of SymPy expressions + The expressions to reduce. + symbols : infinite iterator yielding unique Symbols + The symbols used to label the common subexpressions which are pulled + out. + opt_subs : dictionary of expression substitutions + The expressions to be substituted before any CSE action is performed. + order : string, 'none' or 'canonical' + The order by which Mul and Add arguments are processed. For large + expressions where speed is a concern, use the setting order='none'. + ignore : iterable of Symbols + Substitutions containing any Symbol from ``ignore`` will be ignored. + """ + if opt_subs is None: + opt_subs = {} + + ## Find repeated sub-expressions + + to_eliminate = set() + + seen_subexp = set() + excluded_symbols = set() + + def _find_repeated(expr): + if not isinstance(expr, (Basic, Unevaluated)): + return + + if isinstance(expr, RootOf): + return + + if isinstance(expr, Basic) and ( + expr.is_Atom or + expr.is_Order or + isinstance(expr, (MatrixSymbol, MatrixElement))): + if expr.is_Symbol: + excluded_symbols.add(expr.name) + return + + if iterable(expr): + args = expr + + else: + if expr in seen_subexp: + for ign in ignore: + if ign in expr.free_symbols: + break + else: + to_eliminate.add(expr) + return + + seen_subexp.add(expr) + + if expr in opt_subs: + expr = opt_subs[expr] + + args = expr.args + + list(map(_find_repeated, args)) + + for e in exprs: + if isinstance(e, Basic): + _find_repeated(e) + + ## Rebuild tree + + # Remove symbols from the generator that conflict with names in the expressions. + symbols = (_ for _ in symbols if _.name not in excluded_symbols) + + replacements = [] + + subs = {} + + def _rebuild(expr): + if not isinstance(expr, (Basic, Unevaluated)): + return expr + + if not expr.args: + return expr + + if iterable(expr): + new_args = [_rebuild(arg) for arg in expr.args] + return expr.func(*new_args) + + if expr in subs: + return subs[expr] + + orig_expr = expr + if expr in opt_subs: + expr = opt_subs[expr] + + # If enabled, parse Muls and Adds arguments by order to ensure + # replacement order independent from hashes + if order != 'none': + if isinstance(expr, (Mul, MatMul)): + c, nc = expr.args_cnc() + if c == [1]: + args = nc + else: + args = list(ordered(c)) + nc + elif isinstance(expr, (Add, MatAdd)): + args = list(ordered(expr.args)) + else: + args = expr.args + else: + args = expr.args + + new_args = list(map(_rebuild, args)) + if isinstance(expr, Unevaluated) or new_args != args: + new_expr = expr.func(*new_args) + else: + new_expr = expr + + if orig_expr in to_eliminate: + try: + sym = next(symbols) + except StopIteration: + raise ValueError("Symbols iterator ran out of symbols.") + + if isinstance(orig_expr, MatrixExpr): + sym = MatrixSymbol(sym.name, orig_expr.rows, + orig_expr.cols) + + subs[orig_expr] = sym + replacements.append((sym, new_expr)) + return sym + + else: + return new_expr + + reduced_exprs = [] + for e in exprs: + if isinstance(e, Basic): + reduced_e = _rebuild(e) + else: + reduced_e = e + reduced_exprs.append(reduced_e) + return replacements, reduced_exprs + + +def cse(exprs, symbols=None, optimizations=None, postprocess=None, + order='canonical', ignore=(), list=True): + """ Perform common subexpression elimination on an expression. + + Parameters + ========== + + exprs : list of SymPy expressions, or a single SymPy expression + The expressions to reduce. + symbols : infinite iterator yielding unique Symbols + The symbols used to label the common subexpressions which are pulled + out. The ``numbered_symbols`` generator is useful. The default is a + stream of symbols of the form "x0", "x1", etc. This must be an + infinite iterator. + optimizations : list of (callable, callable) pairs + The (preprocessor, postprocessor) pairs of external optimization + functions. Optionally 'basic' can be passed for a set of predefined + basic optimizations. Such 'basic' optimizations were used by default + in old implementation, however they can be really slow on larger + expressions. Now, no pre or post optimizations are made by default. + postprocess : a function which accepts the two return values of cse and + returns the desired form of output from cse, e.g. if you want the + replacements reversed the function might be the following lambda: + lambda r, e: return reversed(r), e + order : string, 'none' or 'canonical' + The order by which Mul and Add arguments are processed. If set to + 'canonical', arguments will be canonically ordered. If set to 'none', + ordering will be faster but dependent on expressions hashes, thus + machine dependent and variable. For large expressions where speed is a + concern, use the setting order='none'. + ignore : iterable of Symbols + Substitutions containing any Symbol from ``ignore`` will be ignored. + list : bool, (default True) + Returns expression in list or else with same type as input (when False). + + Returns + ======= + + replacements : list of (Symbol, expression) pairs + All of the common subexpressions that were replaced. Subexpressions + earlier in this list might show up in subexpressions later in this + list. + reduced_exprs : list of SymPy expressions + The reduced expressions with all of the replacements above. + + Examples + ======== + + >>> from sympy import cse, SparseMatrix + >>> from sympy.abc import x, y, z, w + >>> cse(((w + x + y + z)*(w + y + z))/(w + x)**3) + ([(x0, y + z), (x1, w + x)], [(w + x0)*(x0 + x1)/x1**3]) + + + List of expressions with recursive substitutions: + + >>> m = SparseMatrix([x + y, x + y + z]) + >>> cse([(x+y)**2, x + y + z, y + z, x + z + y, m]) + ([(x0, x + y), (x1, x0 + z)], [x0**2, x1, y + z, x1, Matrix([ + [x0], + [x1]])]) + + Note: the type and mutability of input matrices is retained. + + >>> isinstance(_[1][-1], SparseMatrix) + True + + The user may disallow substitutions containing certain symbols: + + >>> cse([y**2*(x + 1), 3*y**2*(x + 1)], ignore=(y,)) + ([(x0, x + 1)], [x0*y**2, 3*x0*y**2]) + + The default return value for the reduced expression(s) is a list, even if there is only + one expression. The `list` flag preserves the type of the input in the output: + + >>> cse(x) + ([], [x]) + >>> cse(x, list=False) + ([], x) + """ + if not list: + return _cse_homogeneous(exprs, + symbols=symbols, optimizations=optimizations, + postprocess=postprocess, order=order, ignore=ignore) + + if isinstance(exprs, (int, float)): + exprs = sympify(exprs) + + # Handle the case if just one expression was passed. + if isinstance(exprs, (Basic, MatrixBase)): + exprs = [exprs] + + copy = exprs + temp = [] + for e in exprs: + if isinstance(e, (Matrix, ImmutableMatrix)): + temp.append(Tuple(*e.flat())) + elif isinstance(e, (SparseMatrix, ImmutableSparseMatrix)): + temp.append(Tuple(*e.todok().items())) + else: + temp.append(e) + exprs = temp + del temp + + if optimizations is None: + optimizations = [] + elif optimizations == 'basic': + optimizations = basic_optimizations + + # Preprocess the expressions to give us better optimization opportunities. + reduced_exprs = [preprocess_for_cse(e, optimizations) for e in exprs] + + if symbols is None: + symbols = numbered_symbols(cls=Symbol) + else: + # In case we get passed an iterable with an __iter__ method instead of + # an actual iterator. + symbols = iter(symbols) + + # Find other optimization opportunities. + opt_subs = opt_cse(reduced_exprs, order) + + # Main CSE algorithm. + replacements, reduced_exprs = tree_cse(reduced_exprs, symbols, opt_subs, + order, ignore) + + # Postprocess the expressions to return the expressions to canonical form. + exprs = copy + for i, (sym, subtree) in enumerate(replacements): + subtree = postprocess_for_cse(subtree, optimizations) + replacements[i] = (sym, subtree) + reduced_exprs = [postprocess_for_cse(e, optimizations) + for e in reduced_exprs] + + # Get the matrices back + for i, e in enumerate(exprs): + if isinstance(e, (Matrix, ImmutableMatrix)): + reduced_exprs[i] = Matrix(e.rows, e.cols, reduced_exprs[i]) + if isinstance(e, ImmutableMatrix): + reduced_exprs[i] = reduced_exprs[i].as_immutable() + elif isinstance(e, (SparseMatrix, ImmutableSparseMatrix)): + m = SparseMatrix(e.rows, e.cols, {}) + for k, v in reduced_exprs[i]: + m[k] = v + if isinstance(e, ImmutableSparseMatrix): + m = m.as_immutable() + reduced_exprs[i] = m + + if postprocess is None: + return replacements, reduced_exprs + + return postprocess(replacements, reduced_exprs) + + +def _cse_homogeneous(exprs, **kwargs): + """ + Same as ``cse`` but the ``reduced_exprs`` are returned + with the same type as ``exprs`` or a sympified version of the same. + + Parameters + ========== + + exprs : an Expr, iterable of Expr or dictionary with Expr values + the expressions in which repeated subexpressions will be identified + kwargs : additional arguments for the ``cse`` function + + Returns + ======= + + replacements : list of (Symbol, expression) pairs + All of the common subexpressions that were replaced. Subexpressions + earlier in this list might show up in subexpressions later in this + list. + reduced_exprs : list of SymPy expressions + The reduced expressions with all of the replacements above. + + Examples + ======== + + >>> from sympy.simplify.cse_main import cse + >>> from sympy import cos, Tuple, Matrix + >>> from sympy.abc import x + >>> output = lambda x: type(cse(x, list=False)[1]) + >>> output(1) + + >>> output('cos(x)') + + >>> output(cos(x)) + cos + >>> output(Tuple(1, x)) + + >>> output(Matrix([[1,0], [0,1]])) + + >>> output([1, x]) + + >>> output((1, x)) + + >>> output({1, x}) + + """ + if isinstance(exprs, str): + replacements, reduced_exprs = _cse_homogeneous( + sympify(exprs), **kwargs) + return replacements, repr(reduced_exprs) + if isinstance(exprs, (list, tuple, set)): + replacements, reduced_exprs = cse(exprs, **kwargs) + return replacements, type(exprs)(reduced_exprs) + if isinstance(exprs, dict): + keys = list(exprs.keys()) # In order to guarantee the order of the elements. + replacements, values = cse([exprs[k] for k in keys], **kwargs) + reduced_exprs = dict(zip(keys, values)) + return replacements, reduced_exprs + + try: + replacements, (reduced_exprs,) = cse(exprs, **kwargs) + except TypeError: # For example 'mpf' objects + return [], exprs + else: + return replacements, reduced_exprs diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/epathtools.py b/janus/lib/python3.10/site-packages/sympy/simplify/epathtools.py new file mode 100644 index 0000000000000000000000000000000000000000..a388ee5e7ec7a21af238f92a07e20b8f5fc6bc47 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/epathtools.py @@ -0,0 +1,356 @@ +"""Tools for manipulation of expressions using paths. """ + +from sympy.core import Basic + + +class EPath: + r""" + Manipulate expressions using paths. + + EPath grammar in EBNF notation:: + + literal ::= /[A-Za-z_][A-Za-z_0-9]*/ + number ::= /-?\d+/ + type ::= literal + attribute ::= literal "?" + all ::= "*" + slice ::= "[" number? (":" number? (":" number?)?)? "]" + range ::= all | slice + query ::= (type | attribute) ("|" (type | attribute))* + selector ::= range | query range? + path ::= "/" selector ("/" selector)* + + See the docstring of the epath() function. + + """ + + __slots__ = ("_path", "_epath") + + def __new__(cls, path): + """Construct new EPath. """ + if isinstance(path, EPath): + return path + + if not path: + raise ValueError("empty EPath") + + _path = path + + if path[0] == '/': + path = path[1:] + else: + raise NotImplementedError("non-root EPath") + + epath = [] + + for selector in path.split('/'): + selector = selector.strip() + + if not selector: + raise ValueError("empty selector") + + index = 0 + + for c in selector: + if c.isalnum() or c in ('_', '|', '?'): + index += 1 + else: + break + + attrs = [] + types = [] + + if index: + elements = selector[:index] + selector = selector[index:] + + for element in elements.split('|'): + element = element.strip() + + if not element: + raise ValueError("empty element") + + if element.endswith('?'): + attrs.append(element[:-1]) + else: + types.append(element) + + span = None + + if selector == '*': + pass + else: + if selector.startswith('['): + try: + i = selector.index(']') + except ValueError: + raise ValueError("expected ']', got EOL") + + _span, span = selector[1:i], [] + + if ':' not in _span: + span = int(_span) + else: + for elt in _span.split(':', 3): + if not elt: + span.append(None) + else: + span.append(int(elt)) + + span = slice(*span) + + selector = selector[i + 1:] + + if selector: + raise ValueError("trailing characters in selector") + + epath.append((attrs, types, span)) + + obj = object.__new__(cls) + + obj._path = _path + obj._epath = epath + + return obj + + def __repr__(self): + return "%s(%r)" % (self.__class__.__name__, self._path) + + def _get_ordered_args(self, expr): + """Sort ``expr.args`` using printing order. """ + if expr.is_Add: + return expr.as_ordered_terms() + elif expr.is_Mul: + return expr.as_ordered_factors() + else: + return expr.args + + def _hasattrs(self, expr, attrs): + """Check if ``expr`` has any of ``attrs``. """ + for attr in attrs: + if not hasattr(expr, attr): + return False + + return True + + def _hastypes(self, expr, types): + """Check if ``expr`` is any of ``types``. """ + _types = [ cls.__name__ for cls in expr.__class__.mro() ] + return bool(set(_types).intersection(types)) + + def _has(self, expr, attrs, types): + """Apply ``_hasattrs`` and ``_hastypes`` to ``expr``. """ + if not (attrs or types): + return True + + if attrs and self._hasattrs(expr, attrs): + return True + + if types and self._hastypes(expr, types): + return True + + return False + + def apply(self, expr, func, args=None, kwargs=None): + """ + Modify parts of an expression selected by a path. + + Examples + ======== + + >>> from sympy.simplify.epathtools import EPath + >>> from sympy import sin, cos, E + >>> from sympy.abc import x, y, z, t + + >>> path = EPath("/*/[0]/Symbol") + >>> expr = [((x, 1), 2), ((3, y), z)] + + >>> path.apply(expr, lambda expr: expr**2) + [((x**2, 1), 2), ((3, y**2), z)] + + >>> path = EPath("/*/*/Symbol") + >>> expr = t + sin(x + 1) + cos(x + y + E) + + >>> path.apply(expr, lambda expr: 2*expr) + t + sin(2*x + 1) + cos(2*x + 2*y + E) + + """ + def _apply(path, expr, func): + if not path: + return func(expr) + else: + selector, path = path[0], path[1:] + attrs, types, span = selector + + if isinstance(expr, Basic): + if not expr.is_Atom: + args, basic = self._get_ordered_args(expr), True + else: + return expr + elif hasattr(expr, '__iter__'): + args, basic = expr, False + else: + return expr + + args = list(args) + + if span is not None: + if isinstance(span, slice): + indices = range(*span.indices(len(args))) + else: + indices = [span] + else: + indices = range(len(args)) + + for i in indices: + try: + arg = args[i] + except IndexError: + continue + + if self._has(arg, attrs, types): + args[i] = _apply(path, arg, func) + + if basic: + return expr.func(*args) + else: + return expr.__class__(args) + + _args, _kwargs = args or (), kwargs or {} + _func = lambda expr: func(expr, *_args, **_kwargs) + + return _apply(self._epath, expr, _func) + + def select(self, expr): + """ + Retrieve parts of an expression selected by a path. + + Examples + ======== + + >>> from sympy.simplify.epathtools import EPath + >>> from sympy import sin, cos, E + >>> from sympy.abc import x, y, z, t + + >>> path = EPath("/*/[0]/Symbol") + >>> expr = [((x, 1), 2), ((3, y), z)] + + >>> path.select(expr) + [x, y] + + >>> path = EPath("/*/*/Symbol") + >>> expr = t + sin(x + 1) + cos(x + y + E) + + >>> path.select(expr) + [x, x, y] + + """ + result = [] + + def _select(path, expr): + if not path: + result.append(expr) + else: + selector, path = path[0], path[1:] + attrs, types, span = selector + + if isinstance(expr, Basic): + args = self._get_ordered_args(expr) + elif hasattr(expr, '__iter__'): + args = expr + else: + return + + if span is not None: + if isinstance(span, slice): + args = args[span] + else: + try: + args = [args[span]] + except IndexError: + return + + for arg in args: + if self._has(arg, attrs, types): + _select(path, arg) + + _select(self._epath, expr) + return result + + +def epath(path, expr=None, func=None, args=None, kwargs=None): + r""" + Manipulate parts of an expression selected by a path. + + Explanation + =========== + + This function allows to manipulate large nested expressions in single + line of code, utilizing techniques to those applied in XML processing + standards (e.g. XPath). + + If ``func`` is ``None``, :func:`epath` retrieves elements selected by + the ``path``. Otherwise it applies ``func`` to each matching element. + + Note that it is more efficient to create an EPath object and use the select + and apply methods of that object, since this will compile the path string + only once. This function should only be used as a convenient shortcut for + interactive use. + + This is the supported syntax: + + * select all: ``/*`` + Equivalent of ``for arg in args:``. + * select slice: ``/[0]`` or ``/[1:5]`` or ``/[1:5:2]`` + Supports standard Python's slice syntax. + * select by type: ``/list`` or ``/list|tuple`` + Emulates ``isinstance()``. + * select by attribute: ``/__iter__?`` + Emulates ``hasattr()``. + + Parameters + ========== + + path : str | EPath + A path as a string or a compiled EPath. + expr : Basic | iterable + An expression or a container of expressions. + func : callable (optional) + A callable that will be applied to matching parts. + args : tuple (optional) + Additional positional arguments to ``func``. + kwargs : dict (optional) + Additional keyword arguments to ``func``. + + Examples + ======== + + >>> from sympy.simplify.epathtools import epath + >>> from sympy import sin, cos, E + >>> from sympy.abc import x, y, z, t + + >>> path = "/*/[0]/Symbol" + >>> expr = [((x, 1), 2), ((3, y), z)] + + >>> epath(path, expr) + [x, y] + >>> epath(path, expr, lambda expr: expr**2) + [((x**2, 1), 2), ((3, y**2), z)] + + >>> path = "/*/*/Symbol" + >>> expr = t + sin(x + 1) + cos(x + y + E) + + >>> epath(path, expr) + [x, x, y] + >>> epath(path, expr, lambda expr: 2*expr) + t + sin(2*x + 1) + cos(2*x + 2*y + E) + + """ + _epath = EPath(path) + + if expr is None: + return _epath + if func is None: + return _epath.select(expr) + else: + return _epath.apply(expr, func, args, kwargs) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/gammasimp.py b/janus/lib/python3.10/site-packages/sympy/simplify/gammasimp.py new file mode 100644 index 0000000000000000000000000000000000000000..161cfb5d31e217fcc15191467f843c4c84086721 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/gammasimp.py @@ -0,0 +1,497 @@ +from sympy.core import Function, S, Mul, Pow, Add +from sympy.core.sorting import ordered, default_sort_key +from sympy.core.function import expand_func +from sympy.core.symbol import Dummy +from sympy.functions import gamma, sqrt, sin +from sympy.polys import factor, cancel +from sympy.utilities.iterables import sift, uniq + + +def gammasimp(expr): + r""" + Simplify expressions with gamma functions. + + Explanation + =========== + + This function takes as input an expression containing gamma + functions or functions that can be rewritten in terms of gamma + functions and tries to minimize the number of those functions and + reduce the size of their arguments. + + The algorithm works by rewriting all gamma functions as expressions + involving rising factorials (Pochhammer symbols) and applies + recurrence relations and other transformations applicable to rising + factorials, to reduce their arguments, possibly letting the resulting + rising factorial to cancel. Rising factorials with the second argument + being an integer are expanded into polynomial forms and finally all + other rising factorial are rewritten in terms of gamma functions. + + Then the following two steps are performed. + + 1. Reduce the number of gammas by applying the reflection theorem + gamma(x)*gamma(1-x) == pi/sin(pi*x). + 2. Reduce the number of gammas by applying the multiplication theorem + gamma(x)*gamma(x+1/n)*...*gamma(x+(n-1)/n) == C*gamma(n*x). + + It then reduces the number of prefactors by absorbing them into gammas + where possible and expands gammas with rational argument. + + All transformation rules can be found (or were derived from) here: + + .. [1] https://functions.wolfram.com/GammaBetaErf/Pochhammer/17/01/02/ + .. [2] https://functions.wolfram.com/GammaBetaErf/Pochhammer/27/01/0005/ + + Examples + ======== + + >>> from sympy.simplify import gammasimp + >>> from sympy import gamma, Symbol + >>> from sympy.abc import x + >>> n = Symbol('n', integer = True) + + >>> gammasimp(gamma(x)/gamma(x - 3)) + (x - 3)*(x - 2)*(x - 1) + >>> gammasimp(gamma(n + 3)) + gamma(n + 3) + + """ + + expr = expr.rewrite(gamma) + + # compute_ST will be looking for Functions and we don't want + # it looking for non-gamma functions: issue 22606 + # so we mask free, non-gamma functions + f = expr.atoms(Function) + # take out gammas + gammas = {i for i in f if isinstance(i, gamma)} + if not gammas: + return expr # avoid side effects like factoring + f -= gammas + # keep only those without bound symbols + f = f & expr.as_dummy().atoms(Function) + if f: + dum, fun, simp = zip(*[ + (Dummy(), fi, fi.func(*[ + _gammasimp(a, as_comb=False) for a in fi.args])) + for fi in ordered(f)]) + d = expr.xreplace(dict(zip(fun, dum))) + return _gammasimp(d, as_comb=False).xreplace(dict(zip(dum, simp))) + + return _gammasimp(expr, as_comb=False) + + +def _gammasimp(expr, as_comb): + """ + Helper function for gammasimp and combsimp. + + Explanation + =========== + + Simplifies expressions written in terms of gamma function. If + as_comb is True, it tries to preserve integer arguments. See + docstring of gammasimp for more information. This was part of + combsimp() in combsimp.py. + """ + expr = expr.replace(gamma, + lambda n: _rf(1, (n - 1).expand())) + + if as_comb: + expr = expr.replace(_rf, + lambda a, b: gamma(b + 1)) + else: + expr = expr.replace(_rf, + lambda a, b: gamma(a + b)/gamma(a)) + + def rule_gamma(expr, level=0): + """ Simplify products of gamma functions further. """ + + if expr.is_Atom: + return expr + + def gamma_rat(x): + # helper to simplify ratios of gammas + was = x.count(gamma) + xx = x.replace(gamma, lambda n: _rf(1, (n - 1).expand() + ).replace(_rf, lambda a, b: gamma(a + b)/gamma(a))) + if xx.count(gamma) < was: + x = xx + return x + + def gamma_factor(x): + # return True if there is a gamma factor in shallow args + if isinstance(x, gamma): + return True + if x.is_Add or x.is_Mul: + return any(gamma_factor(xi) for xi in x.args) + if x.is_Pow and (x.exp.is_integer or x.base.is_positive): + return gamma_factor(x.base) + return False + + # recursion step + if level == 0: + expr = expr.func(*[rule_gamma(x, level + 1) for x in expr.args]) + level += 1 + + if not expr.is_Mul: + return expr + + # non-commutative step + if level == 1: + args, nc = expr.args_cnc() + if not args: + return expr + if nc: + return rule_gamma(Mul._from_args(args), level + 1)*Mul._from_args(nc) + level += 1 + + # pure gamma handling, not factor absorption + if level == 2: + T, F = sift(expr.args, gamma_factor, binary=True) + gamma_ind = Mul(*F) + d = Mul(*T) + + nd, dd = d.as_numer_denom() + for ipass in range(2): + args = list(ordered(Mul.make_args(nd))) + for i, ni in enumerate(args): + if ni.is_Add: + ni, dd = Add(*[ + rule_gamma(gamma_rat(a/dd), level + 1) for a in ni.args] + ).as_numer_denom() + args[i] = ni + if not dd.has(gamma): + break + nd = Mul(*args) + if ipass == 0 and not gamma_factor(nd): + break + nd, dd = dd, nd # now process in reversed order + expr = gamma_ind*nd/dd + if not (expr.is_Mul and (gamma_factor(dd) or gamma_factor(nd))): + return expr + level += 1 + + # iteration until constant + if level == 3: + while True: + was = expr + expr = rule_gamma(expr, 4) + if expr == was: + return expr + + numer_gammas = [] + denom_gammas = [] + numer_others = [] + denom_others = [] + def explicate(p): + if p is S.One: + return None, [] + b, e = p.as_base_exp() + if e.is_Integer: + if isinstance(b, gamma): + return True, [b.args[0]]*e + else: + return False, [b]*e + else: + return False, [p] + + newargs = list(ordered(expr.args)) + while newargs: + n, d = newargs.pop().as_numer_denom() + isg, l = explicate(n) + if isg: + numer_gammas.extend(l) + elif isg is False: + numer_others.extend(l) + isg, l = explicate(d) + if isg: + denom_gammas.extend(l) + elif isg is False: + denom_others.extend(l) + + # =========== level 2 work: pure gamma manipulation ========= + + if not as_comb: + # Try to reduce the number of gamma factors by applying the + # reflection formula gamma(x)*gamma(1-x) = pi/sin(pi*x) + for gammas, numer, denom in [( + numer_gammas, numer_others, denom_others), + (denom_gammas, denom_others, numer_others)]: + new = [] + while gammas: + g1 = gammas.pop() + if g1.is_integer: + new.append(g1) + continue + for i, g2 in enumerate(gammas): + n = g1 + g2 - 1 + if not n.is_Integer: + continue + numer.append(S.Pi) + denom.append(sin(S.Pi*g1)) + gammas.pop(i) + if n > 0: + for k in range(n): + numer.append(1 - g1 + k) + elif n < 0: + for k in range(-n): + denom.append(-g1 - k) + break + else: + new.append(g1) + # /!\ updating IN PLACE + gammas[:] = new + + # Try to reduce the number of gammas by using the duplication + # theorem to cancel an upper and lower: gamma(2*s)/gamma(s) = + # 2**(2*s + 1)/(4*sqrt(pi))*gamma(s + 1/2). Although this could + # be done with higher argument ratios like gamma(3*x)/gamma(x), + # this would not reduce the number of gammas as in this case. + for ng, dg, no, do in [(numer_gammas, denom_gammas, numer_others, + denom_others), + (denom_gammas, numer_gammas, denom_others, + numer_others)]: + + while True: + for x in ng: + for y in dg: + n = x - 2*y + if n.is_Integer: + break + else: + continue + break + else: + break + ng.remove(x) + dg.remove(y) + if n > 0: + for k in range(n): + no.append(2*y + k) + elif n < 0: + for k in range(-n): + do.append(2*y - 1 - k) + ng.append(y + S.Half) + no.append(2**(2*y - 1)) + do.append(sqrt(S.Pi)) + + # Try to reduce the number of gamma factors by applying the + # multiplication theorem (used when n gammas with args differing + # by 1/n mod 1 are encountered). + # + # run of 2 with args differing by 1/2 + # + # >>> gammasimp(gamma(x)*gamma(x+S.Half)) + # 2*sqrt(2)*2**(-2*x - 1/2)*sqrt(pi)*gamma(2*x) + # + # run of 3 args differing by 1/3 (mod 1) + # + # >>> gammasimp(gamma(x)*gamma(x+S(1)/3)*gamma(x+S(2)/3)) + # 6*3**(-3*x - 1/2)*pi*gamma(3*x) + # >>> gammasimp(gamma(x)*gamma(x+S(1)/3)*gamma(x+S(5)/3)) + # 2*3**(-3*x - 1/2)*pi*(3*x + 2)*gamma(3*x) + # + def _run(coeffs): + # find runs in coeffs such that the difference in terms (mod 1) + # of t1, t2, ..., tn is 1/n + u = list(uniq(coeffs)) + for i in range(len(u)): + dj = ([((u[j] - u[i]) % 1, j) for j in range(i + 1, len(u))]) + for one, j in dj: + if one.p == 1 and one.q != 1: + n = one.q + got = [i] + get = list(range(1, n)) + for d, j in dj: + m = n*d + if m.is_Integer and m in get: + get.remove(m) + got.append(j) + if not get: + break + else: + continue + for i, j in enumerate(got): + c = u[j] + coeffs.remove(c) + got[i] = c + return one.q, got[0], got[1:] + + def _mult_thm(gammas, numer, denom): + # pull off and analyze the leading coefficient from each gamma arg + # looking for runs in those Rationals + + # expr -> coeff + resid -> rats[resid] = coeff + rats = {} + for g in gammas: + c, resid = g.as_coeff_Add() + rats.setdefault(resid, []).append(c) + + # look for runs in Rationals for each resid + keys = sorted(rats, key=default_sort_key) + for resid in keys: + coeffs = sorted(rats[resid]) + new = [] + while True: + run = _run(coeffs) + if run is None: + break + + # process the sequence that was found: + # 1) convert all the gamma functions to have the right + # argument (could be off by an integer) + # 2) append the factors corresponding to the theorem + # 3) append the new gamma function + + n, ui, other = run + + # (1) + for u in other: + con = resid + u - 1 + for k in range(int(u - ui)): + numer.append(con - k) + + con = n*(resid + ui) # for (2) and (3) + + # (2) + numer.append((2*S.Pi)**(S(n - 1)/2)* + n**(S.Half - con)) + # (3) + new.append(con) + + # restore resid to coeffs + rats[resid] = [resid + c for c in coeffs] + new + + # rebuild the gamma arguments + g = [] + for resid in keys: + g += rats[resid] + # /!\ updating IN PLACE + gammas[:] = g + + for l, numer, denom in [(numer_gammas, numer_others, denom_others), + (denom_gammas, denom_others, numer_others)]: + _mult_thm(l, numer, denom) + + # =========== level >= 2 work: factor absorption ========= + + if level >= 2: + # Try to absorb factors into the gammas: x*gamma(x) -> gamma(x + 1) + # and gamma(x)/(x - 1) -> gamma(x - 1) + # This code (in particular repeated calls to find_fuzzy) can be very + # slow. + def find_fuzzy(l, x): + if not l: + return + S1, T1 = compute_ST(x) + for y in l: + S2, T2 = inv[y] + if T1 != T2 or (not S1.intersection(S2) and + (S1 != set() or S2 != set())): + continue + # XXX we want some simplification (e.g. cancel or + # simplify) but no matter what it's slow. + a = len(cancel(x/y).free_symbols) + b = len(x.free_symbols) + c = len(y.free_symbols) + # TODO is there a better heuristic? + if a == 0 and (b > 0 or c > 0): + return y + + # We thus try to avoid expensive calls by building the following + # "invariants": For every factor or gamma function argument + # - the set of free symbols S + # - the set of functional components T + # We will only try to absorb if T1==T2 and (S1 intersect S2 != emptyset + # or S1 == S2 == emptyset) + inv = {} + + def compute_ST(expr): + if expr in inv: + return inv[expr] + return (expr.free_symbols, expr.atoms(Function).union( + {e.exp for e in expr.atoms(Pow)})) + + def update_ST(expr): + inv[expr] = compute_ST(expr) + for expr in numer_gammas + denom_gammas + numer_others + denom_others: + update_ST(expr) + + for gammas, numer, denom in [( + numer_gammas, numer_others, denom_others), + (denom_gammas, denom_others, numer_others)]: + new = [] + while gammas: + g = gammas.pop() + cont = True + while cont: + cont = False + y = find_fuzzy(numer, g) + if y is not None: + numer.remove(y) + if y != g: + numer.append(y/g) + update_ST(y/g) + g += 1 + cont = True + y = find_fuzzy(denom, g - 1) + if y is not None: + denom.remove(y) + if y != g - 1: + numer.append((g - 1)/y) + update_ST((g - 1)/y) + g -= 1 + cont = True + new.append(g) + # /!\ updating IN PLACE + gammas[:] = new + + # =========== rebuild expr ================================== + + return Mul(*[gamma(g) for g in numer_gammas]) \ + / Mul(*[gamma(g) for g in denom_gammas]) \ + * Mul(*numer_others) / Mul(*denom_others) + + was = factor(expr) + # (for some reason we cannot use Basic.replace in this case) + expr = rule_gamma(was) + if expr != was: + expr = factor(expr) + + expr = expr.replace(gamma, + lambda n: expand_func(gamma(n)) if n.is_Rational else gamma(n)) + + return expr + + +class _rf(Function): + @classmethod + def eval(cls, a, b): + if b.is_Integer: + if not b: + return S.One + + n = int(b) + + if n > 0: + return Mul(*[a + i for i in range(n)]) + elif n < 0: + return 1/Mul(*[a - i for i in range(1, -n + 1)]) + else: + if b.is_Add: + c, _b = b.as_coeff_Add() + + if c.is_Integer: + if c > 0: + return _rf(a, _b)*_rf(a + _b, c) + elif c < 0: + return _rf(a, _b)/_rf(a + _b + c, -c) + + if a.is_Add: + c, _a = a.as_coeff_Add() + + if c.is_Integer: + if c > 0: + return _rf(_a, b)*_rf(_a + b, c)/_rf(_a, c) + elif c < 0: + return _rf(_a, b)*_rf(_a + c, -c)/_rf(_a + b + c, -c) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/powsimp.py b/janus/lib/python3.10/site-packages/sympy/simplify/powsimp.py new file mode 100644 index 0000000000000000000000000000000000000000..51baa56c9779e9b886bb0ff922e50192cd746dac --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/powsimp.py @@ -0,0 +1,714 @@ +from collections import defaultdict +from functools import reduce +from math import prod + +from sympy.core.function import expand_log, count_ops, _coeff_isneg +from sympy.core import sympify, Basic, Dummy, S, Add, Mul, Pow, expand_mul, factor_terms +from sympy.core.sorting import ordered, default_sort_key +from sympy.core.numbers import Integer, Rational +from sympy.core.mul import _keep_coeff +from sympy.core.rules import Transform +from sympy.functions import exp_polar, exp, log, root, polarify, unpolarify +from sympy.matrices.expressions.matexpr import MatrixSymbol +from sympy.polys import lcm, gcd +from sympy.ntheory.factor_ import multiplicity + + + +def powsimp(expr, deep=False, combine='all', force=False, measure=count_ops): + """ + Reduce expression by combining powers with similar bases and exponents. + + Explanation + =========== + + If ``deep`` is ``True`` then powsimp() will also simplify arguments of + functions. By default ``deep`` is set to ``False``. + + If ``force`` is ``True`` then bases will be combined without checking for + assumptions, e.g. sqrt(x)*sqrt(y) -> sqrt(x*y) which is not true + if x and y are both negative. + + You can make powsimp() only combine bases or only combine exponents by + changing combine='base' or combine='exp'. By default, combine='all', + which does both. combine='base' will only combine:: + + a a a 2x x + x * y => (x*y) as well as things like 2 => 4 + + and combine='exp' will only combine + :: + + a b (a + b) + x * x => x + + combine='exp' will strictly only combine exponents in the way that used + to be automatic. Also use deep=True if you need the old behavior. + + When combine='all', 'exp' is evaluated first. Consider the first + example below for when there could be an ambiguity relating to this. + This is done so things like the second example can be completely + combined. If you want 'base' combined first, do something like + powsimp(powsimp(expr, combine='base'), combine='exp'). + + Examples + ======== + + >>> from sympy import powsimp, exp, log, symbols + >>> from sympy.abc import x, y, z, n + >>> powsimp(x**y*x**z*y**z, combine='all') + x**(y + z)*y**z + >>> powsimp(x**y*x**z*y**z, combine='exp') + x**(y + z)*y**z + >>> powsimp(x**y*x**z*y**z, combine='base', force=True) + x**y*(x*y)**z + + >>> powsimp(x**z*x**y*n**z*n**y, combine='all', force=True) + (n*x)**(y + z) + >>> powsimp(x**z*x**y*n**z*n**y, combine='exp') + n**(y + z)*x**(y + z) + >>> powsimp(x**z*x**y*n**z*n**y, combine='base', force=True) + (n*x)**y*(n*x)**z + + >>> x, y = symbols('x y', positive=True) + >>> powsimp(log(exp(x)*exp(y))) + log(exp(x)*exp(y)) + >>> powsimp(log(exp(x)*exp(y)), deep=True) + x + y + + Radicals with Mul bases will be combined if combine='exp' + + >>> from sympy import sqrt + >>> x, y = symbols('x y') + + Two radicals are automatically joined through Mul: + + >>> a=sqrt(x*sqrt(y)) + >>> a*a**3 == a**4 + True + + But if an integer power of that radical has been + autoexpanded then Mul does not join the resulting factors: + + >>> a**4 # auto expands to a Mul, no longer a Pow + x**2*y + >>> _*a # so Mul doesn't combine them + x**2*y*sqrt(x*sqrt(y)) + >>> powsimp(_) # but powsimp will + (x*sqrt(y))**(5/2) + >>> powsimp(x*y*a) # but won't when doing so would violate assumptions + x*y*sqrt(x*sqrt(y)) + + """ + def recurse(arg, **kwargs): + _deep = kwargs.get('deep', deep) + _combine = kwargs.get('combine', combine) + _force = kwargs.get('force', force) + _measure = kwargs.get('measure', measure) + return powsimp(arg, _deep, _combine, _force, _measure) + + expr = sympify(expr) + + if (not isinstance(expr, Basic) or isinstance(expr, MatrixSymbol) or ( + expr.is_Atom or expr in (exp_polar(0), exp_polar(1)))): + return expr + + if deep or expr.is_Add or expr.is_Mul and _y not in expr.args: + expr = expr.func(*[recurse(w) for w in expr.args]) + + if expr.is_Pow: + return recurse(expr*_y, deep=False)/_y + + if not expr.is_Mul: + return expr + + # handle the Mul + if combine in ('exp', 'all'): + # Collect base/exp data, while maintaining order in the + # non-commutative parts of the product + c_powers = defaultdict(list) + nc_part = [] + newexpr = [] + coeff = S.One + for term in expr.args: + if term.is_Rational: + coeff *= term + continue + if term.is_Pow: + term = _denest_pow(term) + if term.is_commutative: + b, e = term.as_base_exp() + if deep: + b, e = [recurse(i) for i in [b, e]] + if b.is_Pow or isinstance(b, exp): + # don't let smthg like sqrt(x**a) split into x**a, 1/2 + # or else it will be joined as x**(a/2) later + b, e = b**e, S.One + c_powers[b].append(e) + else: + # This is the logic that combines exponents for equal, + # but non-commutative bases: A**x*A**y == A**(x+y). + if nc_part: + b1, e1 = nc_part[-1].as_base_exp() + b2, e2 = term.as_base_exp() + if (b1 == b2 and + e1.is_commutative and e2.is_commutative): + nc_part[-1] = Pow(b1, Add(e1, e2)) + continue + nc_part.append(term) + + # add up exponents of common bases + for b, e in ordered(iter(c_powers.items())): + # allow 2**x/4 -> 2**(x - 2); don't do this when b and e are + # Numbers since autoevaluation will undo it, e.g. + # 2**(1/3)/4 -> 2**(1/3 - 2) -> 2**(1/3)/4 + if (b and b.is_Rational and not all(ei.is_Number for ei in e) and \ + coeff is not S.One and + b not in (S.One, S.NegativeOne)): + m = multiplicity(abs(b), abs(coeff)) + if m: + e.append(m) + coeff /= b**m + c_powers[b] = Add(*e) + if coeff is not S.One: + if coeff in c_powers: + c_powers[coeff] += S.One + else: + c_powers[coeff] = S.One + + # convert to plain dictionary + c_powers = dict(c_powers) + + # check for base and inverted base pairs + be = list(c_powers.items()) + skip = set() # skip if we already saw them + for b, e in be: + if b in skip: + continue + bpos = b.is_positive or b.is_polar + if bpos: + binv = 1/b + if b != binv and binv in c_powers: + if b.as_numer_denom()[0] is S.One: + c_powers.pop(b) + c_powers[binv] -= e + else: + skip.add(binv) + e = c_powers.pop(binv) + c_powers[b] -= e + + # check for base and negated base pairs + be = list(c_powers.items()) + _n = S.NegativeOne + for b, e in be: + if (b.is_Symbol or b.is_Add) and -b in c_powers and b in c_powers: + if (b.is_positive is not None or e.is_integer): + if e.is_integer or b.is_negative: + c_powers[-b] += c_powers.pop(b) + else: # (-b).is_positive so use its e + e = c_powers.pop(-b) + c_powers[b] += e + if _n in c_powers: + c_powers[_n] += e + else: + c_powers[_n] = e + + # filter c_powers and convert to a list + c_powers = [(b, e) for b, e in c_powers.items() if e] + + # ============================================================== + # check for Mul bases of Rational powers that can be combined with + # separated bases, e.g. x*sqrt(x*y)*sqrt(x*sqrt(x*y)) -> + # (x*sqrt(x*y))**(3/2) + # ---------------- helper functions + + def ratq(x): + '''Return Rational part of x's exponent as it appears in the bkey. + ''' + return bkey(x)[0][1] + + def bkey(b, e=None): + '''Return (b**s, c.q), c.p where e -> c*s. If e is not given then + it will be taken by using as_base_exp() on the input b. + e.g. + x**3/2 -> (x, 2), 3 + x**y -> (x**y, 1), 1 + x**(2*y/3) -> (x**y, 3), 2 + exp(x/2) -> (exp(a), 2), 1 + + ''' + if e is not None: # coming from c_powers or from below + if e.is_Integer: + return (b, S.One), e + elif e.is_Rational: + return (b, Integer(e.q)), Integer(e.p) + else: + c, m = e.as_coeff_Mul(rational=True) + if c is not S.One: + if m.is_integer: + return (b, Integer(c.q)), m*Integer(c.p) + return (b**m, Integer(c.q)), Integer(c.p) + else: + return (b**e, S.One), S.One + else: + return bkey(*b.as_base_exp()) + + def update(b): + '''Decide what to do with base, b. If its exponent is now an + integer multiple of the Rational denominator, then remove it + and put the factors of its base in the common_b dictionary or + update the existing bases if necessary. If it has been zeroed + out, simply remove the base. + ''' + newe, r = divmod(common_b[b], b[1]) + if not r: + common_b.pop(b) + if newe: + for m in Mul.make_args(b[0]**newe): + b, e = bkey(m) + if b not in common_b: + common_b[b] = 0 + common_b[b] += e + if b[1] != 1: + bases.append(b) + # ---------------- end of helper functions + + # assemble a dictionary of the factors having a Rational power + common_b = {} + done = [] + bases = [] + for b, e in c_powers: + b, e = bkey(b, e) + if b in common_b: + common_b[b] = common_b[b] + e + else: + common_b[b] = e + if b[1] != 1 and b[0].is_Mul: + bases.append(b) + bases.sort(key=default_sort_key) # this makes tie-breaking canonical + bases.sort(key=measure, reverse=True) # handle longest first + for base in bases: + if base not in common_b: # it may have been removed already + continue + b, exponent = base + last = False # True when no factor of base is a radical + qlcm = 1 # the lcm of the radical denominators + while True: + bstart = b + qstart = qlcm + + bb = [] # list of factors + ee = [] # (factor's expo. and it's current value in common_b) + for bi in Mul.make_args(b): + bib, bie = bkey(bi) + if bib not in common_b or common_b[bib] < bie: + ee = bb = [] # failed + break + ee.append([bie, common_b[bib]]) + bb.append(bib) + if ee: + # find the number of integral extractions possible + # e.g. [(1, 2), (2, 2)] -> min(2/1, 2/2) -> 1 + min1 = ee[0][1]//ee[0][0] + for i in range(1, len(ee)): + rat = ee[i][1]//ee[i][0] + if rat < 1: + break + min1 = min(min1, rat) + else: + # update base factor counts + # e.g. if ee = [(2, 5), (3, 6)] then min1 = 2 + # and the new base counts will be 5-2*2 and 6-2*3 + for i in range(len(bb)): + common_b[bb[i]] -= min1*ee[i][0] + update(bb[i]) + # update the count of the base + # e.g. x**2*y*sqrt(x*sqrt(y)) the count of x*sqrt(y) + # will increase by 4 to give bkey (x*sqrt(y), 2, 5) + common_b[base] += min1*qstart*exponent + if (last # no more radicals in base + or len(common_b) == 1 # nothing left to join with + or all(k[1] == 1 for k in common_b) # no rad's in common_b + ): + break + # see what we can exponentiate base by to remove any radicals + # so we know what to search for + # e.g. if base were x**(1/2)*y**(1/3) then we should + # exponentiate by 6 and look for powers of x and y in the ratio + # of 2 to 3 + qlcm = lcm([ratq(bi) for bi in Mul.make_args(bstart)]) + if qlcm == 1: + break # we are done + b = bstart**qlcm + qlcm *= qstart + if all(ratq(bi) == 1 for bi in Mul.make_args(b)): + last = True # we are going to be done after this next pass + # this base no longer can find anything to join with and + # since it was longer than any other we are done with it + b, q = base + done.append((b, common_b.pop(base)*Rational(1, q))) + + # update c_powers and get ready to continue with powsimp + c_powers = done + # there may be terms still in common_b that were bases that were + # identified as needing processing, so remove those, too + for (b, q), e in common_b.items(): + if (b.is_Pow or isinstance(b, exp)) and \ + q is not S.One and not b.exp.is_Rational: + b, be = b.as_base_exp() + b = b**(be/q) + else: + b = root(b, q) + c_powers.append((b, e)) + check = len(c_powers) + c_powers = dict(c_powers) + assert len(c_powers) == check # there should have been no duplicates + # ============================================================== + + # rebuild the expression + newexpr = expr.func(*(newexpr + [Pow(b, e) for b, e in c_powers.items()])) + if combine == 'exp': + return expr.func(newexpr, expr.func(*nc_part)) + else: + return recurse(expr.func(*nc_part), combine='base') * \ + recurse(newexpr, combine='base') + + elif combine == 'base': + + # Build c_powers and nc_part. These must both be lists not + # dicts because exp's are not combined. + c_powers = [] + nc_part = [] + for term in expr.args: + if term.is_commutative: + c_powers.append(list(term.as_base_exp())) + else: + nc_part.append(term) + + # Pull out numerical coefficients from exponent if assumptions allow + # e.g., 2**(2*x) => 4**x + for i in range(len(c_powers)): + b, e = c_powers[i] + if not (all(x.is_nonnegative for x in b.as_numer_denom()) or e.is_integer or force or b.is_polar): + continue + exp_c, exp_t = e.as_coeff_Mul(rational=True) + if exp_c is not S.One and exp_t is not S.One: + c_powers[i] = [Pow(b, exp_c), exp_t] + + # Combine bases whenever they have the same exponent and + # assumptions allow + # first gather the potential bases under the common exponent + c_exp = defaultdict(list) + for b, e in c_powers: + if deep: + e = recurse(e) + if e.is_Add and (b.is_positive or e.is_integer): + e = factor_terms(e) + if _coeff_isneg(e): + e = -e + b = 1/b + c_exp[e].append(b) + del c_powers + + # Merge back in the results of the above to form a new product + c_powers = defaultdict(list) + for e in c_exp: + bases = c_exp[e] + + # calculate the new base for e + + if len(bases) == 1: + new_base = bases[0] + elif e.is_integer or force: + new_base = expr.func(*bases) + else: + # see which ones can be joined + unk = [] + nonneg = [] + neg = [] + for bi in bases: + if bi.is_negative: + neg.append(bi) + elif bi.is_nonnegative: + nonneg.append(bi) + elif bi.is_polar: + nonneg.append( + bi) # polar can be treated like non-negative + else: + unk.append(bi) + if len(unk) == 1 and not neg or len(neg) == 1 and not unk: + # a single neg or a single unk can join the rest + nonneg.extend(unk + neg) + unk = neg = [] + elif neg: + # their negative signs cancel in groups of 2*q if we know + # that e = p/q else we have to treat them as unknown + israt = False + if e.is_Rational: + israt = True + else: + p, d = e.as_numer_denom() + if p.is_integer and d.is_integer: + israt = True + if israt: + neg = [-w for w in neg] + unk.extend([S.NegativeOne]*len(neg)) + else: + unk.extend(neg) + neg = [] + del israt + + # these shouldn't be joined + for b in unk: + c_powers[b].append(e) + # here is a new joined base + new_base = expr.func(*(nonneg + neg)) + # if there are positive parts they will just get separated + # again unless some change is made + + def _terms(e): + # return the number of terms of this expression + # when multiplied out -- assuming no joining of terms + if e.is_Add: + return sum(_terms(ai) for ai in e.args) + if e.is_Mul: + return prod([_terms(mi) for mi in e.args]) + return 1 + xnew_base = expand_mul(new_base, deep=False) + if len(Add.make_args(xnew_base)) < _terms(new_base): + new_base = factor_terms(xnew_base) + + c_powers[new_base].append(e) + + # break out the powers from c_powers now + c_part = [Pow(b, ei) for b, e in c_powers.items() for ei in e] + + # we're done + return expr.func(*(c_part + nc_part)) + + else: + raise ValueError("combine must be one of ('all', 'exp', 'base').") + + +def powdenest(eq, force=False, polar=False): + r""" + Collect exponents on powers as assumptions allow. + + Explanation + =========== + + Given ``(bb**be)**e``, this can be simplified as follows: + * if ``bb`` is positive, or + * ``e`` is an integer, or + * ``|be| < 1`` then this simplifies to ``bb**(be*e)`` + + Given a product of powers raised to a power, ``(bb1**be1 * + bb2**be2...)**e``, simplification can be done as follows: + + - if e is positive, the gcd of all bei can be joined with e; + - all non-negative bb can be separated from those that are negative + and their gcd can be joined with e; autosimplification already + handles this separation. + - integer factors from powers that have integers in the denominator + of the exponent can be removed from any term and the gcd of such + integers can be joined with e + + Setting ``force`` to ``True`` will make symbols that are not explicitly + negative behave as though they are positive, resulting in more + denesting. + + Setting ``polar`` to ``True`` will do simplifications on the Riemann surface of + the logarithm, also resulting in more denestings. + + When there are sums of logs in exp() then a product of powers may be + obtained e.g. ``exp(3*(log(a) + 2*log(b)))`` - > ``a**3*b**6``. + + Examples + ======== + + >>> from sympy.abc import a, b, x, y, z + >>> from sympy import Symbol, exp, log, sqrt, symbols, powdenest + + >>> powdenest((x**(2*a/3))**(3*x)) + (x**(2*a/3))**(3*x) + >>> powdenest(exp(3*x*log(2))) + 2**(3*x) + + Assumptions may prevent expansion: + + >>> powdenest(sqrt(x**2)) + sqrt(x**2) + + >>> p = symbols('p', positive=True) + >>> powdenest(sqrt(p**2)) + p + + No other expansion is done. + + >>> i, j = symbols('i,j', integer=True) + >>> powdenest((x**x)**(i + j)) # -X-> (x**x)**i*(x**x)**j + x**(x*(i + j)) + + But exp() will be denested by moving all non-log terms outside of + the function; this may result in the collapsing of the exp to a power + with a different base: + + >>> powdenest(exp(3*y*log(x))) + x**(3*y) + >>> powdenest(exp(y*(log(a) + log(b)))) + (a*b)**y + >>> powdenest(exp(3*(log(a) + log(b)))) + a**3*b**3 + + If assumptions allow, symbols can also be moved to the outermost exponent: + + >>> i = Symbol('i', integer=True) + >>> powdenest(((x**(2*i))**(3*y))**x) + ((x**(2*i))**(3*y))**x + >>> powdenest(((x**(2*i))**(3*y))**x, force=True) + x**(6*i*x*y) + + >>> powdenest(((x**(2*a/3))**(3*y/i))**x) + ((x**(2*a/3))**(3*y/i))**x + >>> powdenest((x**(2*i)*y**(4*i))**z, force=True) + (x*y**2)**(2*i*z) + + >>> n = Symbol('n', negative=True) + + >>> powdenest((x**i)**y, force=True) + x**(i*y) + >>> powdenest((n**i)**x, force=True) + (n**i)**x + + """ + from sympy.simplify.simplify import posify + + if force: + def _denest(b, e): + if not isinstance(b, (Pow, exp)): + return b.is_positive, Pow(b, e, evaluate=False) + return _denest(b.base, b.exp*e) + reps = [] + for p in eq.atoms(Pow, exp): + if isinstance(p.base, (Pow, exp)): + ok, dp = _denest(*p.args) + if ok is not False: + reps.append((p, dp)) + if reps: + eq = eq.subs(reps) + eq, reps = posify(eq) + return powdenest(eq, force=False, polar=polar).xreplace(reps) + + if polar: + eq, rep = polarify(eq) + return unpolarify(powdenest(unpolarify(eq, exponents_only=True)), rep) + + new = powsimp(eq) + return new.xreplace(Transform( + _denest_pow, filter=lambda m: m.is_Pow or isinstance(m, exp))) + +_y = Dummy('y') + + +def _denest_pow(eq): + """ + Denest powers. + + This is a helper function for powdenest that performs the actual + transformation. + """ + from sympy.simplify.simplify import logcombine + + b, e = eq.as_base_exp() + if b.is_Pow or isinstance(b, exp) and e != 1: + new = b._eval_power(e) + if new is not None: + eq = new + b, e = new.as_base_exp() + + # denest exp with log terms in exponent + if b is S.Exp1 and e.is_Mul: + logs = [] + other = [] + for ei in e.args: + if any(isinstance(ai, log) for ai in Add.make_args(ei)): + logs.append(ei) + else: + other.append(ei) + logs = logcombine(Mul(*logs)) + return Pow(exp(logs), Mul(*other)) + + _, be = b.as_base_exp() + if be is S.One and not (b.is_Mul or + b.is_Rational and b.q != 1 or + b.is_positive): + return eq + + # denest eq which is either pos**e or Pow**e or Mul**e or + # Mul(b1**e1, b2**e2) + + # handle polar numbers specially + polars, nonpolars = [], [] + for bb in Mul.make_args(b): + if bb.is_polar: + polars.append(bb.as_base_exp()) + else: + nonpolars.append(bb) + if len(polars) == 1 and not polars[0][0].is_Mul: + return Pow(polars[0][0], polars[0][1]*e)*powdenest(Mul(*nonpolars)**e) + elif polars: + return Mul(*[powdenest(bb**(ee*e)) for (bb, ee) in polars]) \ + *powdenest(Mul(*nonpolars)**e) + + if b.is_Integer: + # use log to see if there is a power here + logb = expand_log(log(b)) + if logb.is_Mul: + c, logb = logb.args + e *= c + base = logb.args[0] + return Pow(base, e) + + # if b is not a Mul or any factor is an atom then there is nothing to do + if not b.is_Mul or any(s.is_Atom for s in Mul.make_args(b)): + return eq + + # let log handle the case of the base of the argument being a Mul, e.g. + # sqrt(x**(2*i)*y**(6*i)) -> x**i*y**(3**i) if x and y are positive; we + # will take the log, expand it, and then factor out the common powers that + # now appear as coefficient. We do this manually since terms_gcd pulls out + # fractions, terms_gcd(x+x*y/2) -> x*(y + 2)/2 and we don't want the 1/2; + # gcd won't pull out numerators from a fraction: gcd(3*x, 9*x/2) -> x but + # we want 3*x. Neither work with noncommutatives. + + def nc_gcd(aa, bb): + a, b = [i.as_coeff_Mul() for i in [aa, bb]] + c = gcd(a[0], b[0]).as_numer_denom()[0] + g = Mul(*(a[1].args_cnc(cset=True)[0] & b[1].args_cnc(cset=True)[0])) + return _keep_coeff(c, g) + + glogb = expand_log(log(b)) + if glogb.is_Add: + args = glogb.args + g = reduce(nc_gcd, args) + if g != 1: + cg, rg = g.as_coeff_Mul() + glogb = _keep_coeff(cg, rg*Add(*[a/g for a in args])) + + # now put the log back together again + if isinstance(glogb, log) or not glogb.is_Mul: + if glogb.args[0].is_Pow or isinstance(glogb.args[0], exp): + glogb = _denest_pow(glogb.args[0]) + if (abs(glogb.exp) < 1) == True: + return Pow(glogb.base, glogb.exp*e) + return eq + + # the log(b) was a Mul so join any adds with logcombine + add = [] + other = [] + for a in glogb.args: + if a.is_Add: + add.append(a) + else: + other.append(a) + return Pow(exp(logcombine(Mul(*add))), e*Mul(*other)) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/radsimp.py b/janus/lib/python3.10/site-packages/sympy/simplify/radsimp.py new file mode 100644 index 0000000000000000000000000000000000000000..8c1fe8d5c33aeb8f0210d176fd8bc350e15a55b9 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/radsimp.py @@ -0,0 +1,1227 @@ +from collections import defaultdict + +from sympy.core import sympify, S, Mul, Derivative, Pow +from sympy.core.add import _unevaluated_Add, Add +from sympy.core.assumptions import assumptions +from sympy.core.exprtools import Factors, gcd_terms +from sympy.core.function import _mexpand, expand_mul, expand_power_base +from sympy.core.mul import _keep_coeff, _unevaluated_Mul, _mulsort +from sympy.core.numbers import Rational, zoo, nan +from sympy.core.parameters import global_parameters +from sympy.core.sorting import ordered, default_sort_key +from sympy.core.symbol import Dummy, Wild, symbols +from sympy.functions import exp, sqrt, log +from sympy.functions.elementary.complexes import Abs +from sympy.polys import gcd +from sympy.simplify.sqrtdenest import sqrtdenest +from sympy.utilities.iterables import iterable, sift + + + + +def collect(expr, syms, func=None, evaluate=None, exact=False, distribute_order_term=True): + """ + Collect additive terms of an expression. + + Explanation + =========== + + This function collects additive terms of an expression with respect + to a list of expression up to powers with rational exponents. By the + term symbol here are meant arbitrary expressions, which can contain + powers, products, sums etc. In other words symbol is a pattern which + will be searched for in the expression's terms. + + The input expression is not expanded by :func:`collect`, so user is + expected to provide an expression in an appropriate form. This makes + :func:`collect` more predictable as there is no magic happening behind the + scenes. However, it is important to note, that powers of products are + converted to products of powers using the :func:`~.expand_power_base` + function. + + There are two possible types of output. First, if ``evaluate`` flag is + set, this function will return an expression with collected terms or + else it will return a dictionary with expressions up to rational powers + as keys and collected coefficients as values. + + Examples + ======== + + >>> from sympy import S, collect, expand, factor, Wild + >>> from sympy.abc import a, b, c, x, y + + This function can collect symbolic coefficients in polynomials or + rational expressions. It will manage to find all integer or rational + powers of collection variable:: + + >>> collect(a*x**2 + b*x**2 + a*x - b*x + c, x) + c + x**2*(a + b) + x*(a - b) + + The same result can be achieved in dictionary form:: + + >>> d = collect(a*x**2 + b*x**2 + a*x - b*x + c, x, evaluate=False) + >>> d[x**2] + a + b + >>> d[x] + a - b + >>> d[S.One] + c + + You can also work with multivariate polynomials. However, remember that + this function is greedy so it will care only about a single symbol at time, + in specification order:: + + >>> collect(x**2 + y*x**2 + x*y + y + a*y, [x, y]) + x**2*(y + 1) + x*y + y*(a + 1) + + Also more complicated expressions can be used as patterns:: + + >>> from sympy import sin, log + >>> collect(a*sin(2*x) + b*sin(2*x), sin(2*x)) + (a + b)*sin(2*x) + + >>> collect(a*x*log(x) + b*(x*log(x)), x*log(x)) + x*(a + b)*log(x) + + You can use wildcards in the pattern:: + + >>> w = Wild('w1') + >>> collect(a*x**y - b*x**y, w**y) + x**y*(a - b) + + It is also possible to work with symbolic powers, although it has more + complicated behavior, because in this case power's base and symbolic part + of the exponent are treated as a single symbol:: + + >>> collect(a*x**c + b*x**c, x) + a*x**c + b*x**c + >>> collect(a*x**c + b*x**c, x**c) + x**c*(a + b) + + However if you incorporate rationals to the exponents, then you will get + well known behavior:: + + >>> collect(a*x**(2*c) + b*x**(2*c), x**c) + x**(2*c)*(a + b) + + Note also that all previously stated facts about :func:`collect` function + apply to the exponential function, so you can get:: + + >>> from sympy import exp + >>> collect(a*exp(2*x) + b*exp(2*x), exp(x)) + (a + b)*exp(2*x) + + If you are interested only in collecting specific powers of some symbols + then set ``exact`` flag to True:: + + >>> collect(a*x**7 + b*x**7, x, exact=True) + a*x**7 + b*x**7 + >>> collect(a*x**7 + b*x**7, x**7, exact=True) + x**7*(a + b) + + If you want to collect on any object containing symbols, set + ``exact`` to None: + + >>> collect(x*exp(x) + sin(x)*y + sin(x)*2 + 3*x, x, exact=None) + x*exp(x) + 3*x + (y + 2)*sin(x) + >>> collect(a*x*y + x*y + b*x + x, [x, y], exact=None) + x*y*(a + 1) + x*(b + 1) + + You can also apply this function to differential equations, where + derivatives of arbitrary order can be collected. Note that if you + collect with respect to a function or a derivative of a function, all + derivatives of that function will also be collected. Use + ``exact=True`` to prevent this from happening:: + + >>> from sympy import Derivative as D, collect, Function + >>> f = Function('f') (x) + + >>> collect(a*D(f,x) + b*D(f,x), D(f,x)) + (a + b)*Derivative(f(x), x) + + >>> collect(a*D(D(f,x),x) + b*D(D(f,x),x), f) + (a + b)*Derivative(f(x), (x, 2)) + + >>> collect(a*D(D(f,x),x) + b*D(D(f,x),x), D(f,x), exact=True) + a*Derivative(f(x), (x, 2)) + b*Derivative(f(x), (x, 2)) + + >>> collect(a*D(f,x) + b*D(f,x) + a*f + b*f, f) + (a + b)*f(x) + (a + b)*Derivative(f(x), x) + + Or you can even match both derivative order and exponent at the same time:: + + >>> collect(a*D(D(f,x),x)**2 + b*D(D(f,x),x)**2, D(f,x)) + (a + b)*Derivative(f(x), (x, 2))**2 + + Finally, you can apply a function to each of the collected coefficients. + For example you can factorize symbolic coefficients of polynomial:: + + >>> f = expand((x + a + 1)**3) + + >>> collect(f, x, factor) + x**3 + 3*x**2*(a + 1) + 3*x*(a + 1)**2 + (a + 1)**3 + + .. note:: Arguments are expected to be in expanded form, so you might have + to call :func:`~.expand` prior to calling this function. + + See Also + ======== + + collect_const, collect_sqrt, rcollect + """ + expr = sympify(expr) + syms = [sympify(i) for i in (syms if iterable(syms) else [syms])] + + # replace syms[i] if it is not x, -x or has Wild symbols + cond = lambda x: x.is_Symbol or (-x).is_Symbol or bool( + x.atoms(Wild)) + _, nonsyms = sift(syms, cond, binary=True) + if nonsyms: + reps = dict(zip(nonsyms, [Dummy(**assumptions(i)) for i in nonsyms])) + syms = [reps.get(s, s) for s in syms] + rv = collect(expr.subs(reps), syms, + func=func, evaluate=evaluate, exact=exact, + distribute_order_term=distribute_order_term) + urep = {v: k for k, v in reps.items()} + if not isinstance(rv, dict): + return rv.xreplace(urep) + else: + return {urep.get(k, k).xreplace(urep): v.xreplace(urep) + for k, v in rv.items()} + + # see if other expressions should be considered + if exact is None: + _syms = set() + for i in Add.make_args(expr): + if not i.has_free(*syms) or i in syms: + continue + if not i.is_Mul and i not in syms: + _syms.add(i) + else: + # identify compound generators + g = i._new_rawargs(*i.as_coeff_mul(*syms)[1]) + if g not in syms: + _syms.add(g) + simple = all(i.is_Pow and i.base in syms for i in _syms) + syms = syms + list(ordered(_syms)) + if not simple: + return collect(expr, syms, + func=func, evaluate=evaluate, exact=False, + distribute_order_term=distribute_order_term) + + if evaluate is None: + evaluate = global_parameters.evaluate + + def make_expression(terms): + product = [] + + for term, rat, sym, deriv in terms: + if deriv is not None: + var, order = deriv + + while order > 0: + term, order = Derivative(term, var), order - 1 + + if sym is None: + if rat is S.One: + product.append(term) + else: + product.append(Pow(term, rat)) + else: + product.append(Pow(term, rat*sym)) + + return Mul(*product) + + def parse_derivative(deriv): + # scan derivatives tower in the input expression and return + # underlying function and maximal differentiation order + expr, sym, order = deriv.expr, deriv.variables[0], 1 + + for s in deriv.variables[1:]: + if s == sym: + order += 1 + else: + raise NotImplementedError( + 'Improve MV Derivative support in collect') + + while isinstance(expr, Derivative): + s0 = expr.variables[0] + + for s in expr.variables: + if s != s0: + raise NotImplementedError( + 'Improve MV Derivative support in collect') + + if s0 == sym: + expr, order = expr.expr, order + len(expr.variables) + else: + break + + return expr, (sym, Rational(order)) + + def parse_term(expr): + """Parses expression expr and outputs tuple (sexpr, rat_expo, + sym_expo, deriv) + where: + - sexpr is the base expression + - rat_expo is the rational exponent that sexpr is raised to + - sym_expo is the symbolic exponent that sexpr is raised to + - deriv contains the derivatives of the expression + + For example, the output of x would be (x, 1, None, None) + the output of 2**x would be (2, 1, x, None). + """ + rat_expo, sym_expo = S.One, None + sexpr, deriv = expr, None + + if expr.is_Pow: + if isinstance(expr.base, Derivative): + sexpr, deriv = parse_derivative(expr.base) + else: + sexpr = expr.base + + if expr.base == S.Exp1: + arg = expr.exp + if arg.is_Rational: + sexpr, rat_expo = S.Exp1, arg + elif arg.is_Mul: + coeff, tail = arg.as_coeff_Mul(rational=True) + sexpr, rat_expo = exp(tail), coeff + + elif expr.exp.is_Number: + rat_expo = expr.exp + else: + coeff, tail = expr.exp.as_coeff_Mul() + + if coeff.is_Number: + rat_expo, sym_expo = coeff, tail + else: + sym_expo = expr.exp + elif isinstance(expr, exp): + arg = expr.exp + if arg.is_Rational: + sexpr, rat_expo = S.Exp1, arg + elif arg.is_Mul: + coeff, tail = arg.as_coeff_Mul(rational=True) + sexpr, rat_expo = exp(tail), coeff + elif isinstance(expr, Derivative): + sexpr, deriv = parse_derivative(expr) + + return sexpr, rat_expo, sym_expo, deriv + + def parse_expression(terms, pattern): + """Parse terms searching for a pattern. + Terms is a list of tuples as returned by parse_terms; + Pattern is an expression treated as a product of factors. + """ + pattern = Mul.make_args(pattern) + + if len(terms) < len(pattern): + # pattern is longer than matched product + # so no chance for positive parsing result + return None + else: + pattern = [parse_term(elem) for elem in pattern] + + terms = terms[:] # need a copy + elems, common_expo, has_deriv = [], None, False + + for elem, e_rat, e_sym, e_ord in pattern: + + if elem.is_Number and e_rat == 1 and e_sym is None: + # a constant is a match for everything + continue + + for j in range(len(terms)): + if terms[j] is None: + continue + + term, t_rat, t_sym, t_ord = terms[j] + + # keeping track of whether one of the terms had + # a derivative or not as this will require rebuilding + # the expression later + if t_ord is not None: + has_deriv = True + + if (term.match(elem) is not None and + (t_sym == e_sym or t_sym is not None and + e_sym is not None and + t_sym.match(e_sym) is not None)): + if exact is False: + # we don't have to be exact so find common exponent + # for both expression's term and pattern's element + expo = t_rat / e_rat + + if common_expo is None: + # first time + common_expo = expo + else: + # common exponent was negotiated before so + # there is no chance for a pattern match unless + # common and current exponents are equal + if common_expo != expo: + common_expo = 1 + else: + # we ought to be exact so all fields of + # interest must match in every details + if e_rat != t_rat or e_ord != t_ord: + continue + + # found common term so remove it from the expression + # and try to match next element in the pattern + elems.append(terms[j]) + terms[j] = None + + break + + else: + # pattern element not found + return None + + return [_f for _f in terms if _f], elems, common_expo, has_deriv + + if evaluate: + if expr.is_Add: + o = expr.getO() or 0 + expr = expr.func(*[ + collect(a, syms, func, True, exact, distribute_order_term) + for a in expr.args if a != o]) + o + elif expr.is_Mul: + return expr.func(*[ + collect(term, syms, func, True, exact, distribute_order_term) + for term in expr.args]) + elif expr.is_Pow: + b = collect( + expr.base, syms, func, True, exact, distribute_order_term) + return Pow(b, expr.exp) + + syms = [expand_power_base(i, deep=False) for i in syms] + + order_term = None + + if distribute_order_term: + order_term = expr.getO() + + if order_term is not None: + if order_term.has(*syms): + order_term = None + else: + expr = expr.removeO() + + summa = [expand_power_base(i, deep=False) for i in Add.make_args(expr)] + + collected, disliked = defaultdict(list), S.Zero + for product in summa: + c, nc = product.args_cnc(split_1=False) + args = list(ordered(c)) + nc + terms = [parse_term(i) for i in args] + small_first = True + + for symbol in syms: + if isinstance(symbol, Derivative) and small_first: + terms = list(reversed(terms)) + small_first = not small_first + result = parse_expression(terms, symbol) + + if result is not None: + if not symbol.is_commutative: + raise AttributeError("Can not collect noncommutative symbol") + + terms, elems, common_expo, has_deriv = result + + # when there was derivative in current pattern we + # will need to rebuild its expression from scratch + if not has_deriv: + margs = [] + for elem in elems: + if elem[2] is None: + e = elem[1] + else: + e = elem[1]*elem[2] + margs.append(Pow(elem[0], e)) + index = Mul(*margs) + else: + index = make_expression(elems) + terms = expand_power_base(make_expression(terms), deep=False) + index = expand_power_base(index, deep=False) + collected[index].append(terms) + break + else: + # none of the patterns matched + disliked += product + # add terms now for each key + collected = {k: Add(*v) for k, v in collected.items()} + + if disliked is not S.Zero: + collected[S.One] = disliked + + if order_term is not None: + for key, val in collected.items(): + collected[key] = val + order_term + + if func is not None: + collected = { + key: func(val) for key, val in collected.items()} + + if evaluate: + return Add(*[key*val for key, val in collected.items()]) + else: + return collected + + +def rcollect(expr, *vars): + """ + Recursively collect sums in an expression. + + Examples + ======== + + >>> from sympy.simplify import rcollect + >>> from sympy.abc import x, y + + >>> expr = (x**2*y + x*y + x + y)/(x + y) + + >>> rcollect(expr, y) + (x + y*(x**2 + x + 1))/(x + y) + + See Also + ======== + + collect, collect_const, collect_sqrt + """ + if expr.is_Atom or not expr.has(*vars): + return expr + else: + expr = expr.__class__(*[rcollect(arg, *vars) for arg in expr.args]) + + if expr.is_Add: + return collect(expr, vars) + else: + return expr + + +def collect_sqrt(expr, evaluate=None): + """Return expr with terms having common square roots collected together. + If ``evaluate`` is False a count indicating the number of sqrt-containing + terms will be returned and, if non-zero, the terms of the Add will be + returned, else the expression itself will be returned as a single term. + If ``evaluate`` is True, the expression with any collected terms will be + returned. + + Note: since I = sqrt(-1), it is collected, too. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.radsimp import collect_sqrt + >>> from sympy.abc import a, b + + >>> r2, r3, r5 = [sqrt(i) for i in [2, 3, 5]] + >>> collect_sqrt(a*r2 + b*r2) + sqrt(2)*(a + b) + >>> collect_sqrt(a*r2 + b*r2 + a*r3 + b*r3) + sqrt(2)*(a + b) + sqrt(3)*(a + b) + >>> collect_sqrt(a*r2 + b*r2 + a*r3 + b*r5) + sqrt(3)*a + sqrt(5)*b + sqrt(2)*(a + b) + + If evaluate is False then the arguments will be sorted and + returned as a list and a count of the number of sqrt-containing + terms will be returned: + + >>> collect_sqrt(a*r2 + b*r2 + a*r3 + b*r5, evaluate=False) + ((sqrt(3)*a, sqrt(5)*b, sqrt(2)*(a + b)), 3) + >>> collect_sqrt(a*sqrt(2) + b, evaluate=False) + ((b, sqrt(2)*a), 1) + >>> collect_sqrt(a + b, evaluate=False) + ((a + b,), 0) + + See Also + ======== + + collect, collect_const, rcollect + """ + if evaluate is None: + evaluate = global_parameters.evaluate + # this step will help to standardize any complex arguments + # of sqrts + coeff, expr = expr.as_content_primitive() + vars = set() + for a in Add.make_args(expr): + for m in a.args_cnc()[0]: + if m.is_number and ( + m.is_Pow and m.exp.is_Rational and m.exp.q == 2 or + m is S.ImaginaryUnit): + vars.add(m) + + # we only want radicals, so exclude Number handling; in this case + # d will be evaluated + d = collect_const(expr, *vars, Numbers=False) + hit = expr != d + + if not evaluate: + nrad = 0 + # make the evaluated args canonical + args = list(ordered(Add.make_args(d))) + for i, m in enumerate(args): + c, nc = m.args_cnc() + for ci in c: + # XXX should this be restricted to ci.is_number as above? + if ci.is_Pow and ci.exp.is_Rational and ci.exp.q == 2 or \ + ci is S.ImaginaryUnit: + nrad += 1 + break + args[i] *= coeff + if not (hit or nrad): + args = [Add(*args)] + return tuple(args), nrad + + return coeff*d + + +def collect_abs(expr): + """Return ``expr`` with arguments of multiple Abs in a term collected + under a single instance. + + Examples + ======== + + >>> from sympy.simplify.radsimp import collect_abs + >>> from sympy.abc import x + >>> collect_abs(abs(x + 1)/abs(x**2 - 1)) + Abs((x + 1)/(x**2 - 1)) + >>> collect_abs(abs(1/x)) + Abs(1/x) + """ + def _abs(mul): + c, nc = mul.args_cnc() + a = [] + o = [] + for i in c: + if isinstance(i, Abs): + a.append(i.args[0]) + elif isinstance(i, Pow) and isinstance(i.base, Abs) and i.exp.is_real: + a.append(i.base.args[0]**i.exp) + else: + o.append(i) + if len(a) < 2 and not any(i.exp.is_negative for i in a if isinstance(i, Pow)): + return mul + absarg = Mul(*a) + A = Abs(absarg) + args = [A] + args.extend(o) + if not A.has(Abs): + args.extend(nc) + return Mul(*args) + if not isinstance(A, Abs): + # reevaluate and make it unevaluated + A = Abs(absarg, evaluate=False) + args[0] = A + _mulsort(args) + args.extend(nc) # nc always go last + return Mul._from_args(args, is_commutative=not nc) + + return expr.replace( + lambda x: isinstance(x, Mul), + lambda x: _abs(x)).replace( + lambda x: isinstance(x, Pow), + lambda x: _abs(x)) + + +def collect_const(expr, *vars, Numbers=True): + """A non-greedy collection of terms with similar number coefficients in + an Add expr. If ``vars`` is given then only those constants will be + targeted. Although any Number can also be targeted, if this is not + desired set ``Numbers=False`` and no Float or Rational will be collected. + + Parameters + ========== + + expr : SymPy expression + This parameter defines the expression the expression from which + terms with similar coefficients are to be collected. A non-Add + expression is returned as it is. + + vars : variable length collection of Numbers, optional + Specifies the constants to target for collection. Can be multiple in + number. + + Numbers : bool + Specifies to target all instance of + :class:`sympy.core.numbers.Number` class. If ``Numbers=False``, then + no Float or Rational will be collected. + + Returns + ======= + + expr : Expr + Returns an expression with similar coefficient terms collected. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.abc import s, x, y, z + >>> from sympy.simplify.radsimp import collect_const + >>> collect_const(sqrt(3) + sqrt(3)*(1 + sqrt(2))) + sqrt(3)*(sqrt(2) + 2) + >>> collect_const(sqrt(3)*s + sqrt(7)*s + sqrt(3) + sqrt(7)) + (sqrt(3) + sqrt(7))*(s + 1) + >>> s = sqrt(2) + 2 + >>> collect_const(sqrt(3)*s + sqrt(3) + sqrt(7)*s + sqrt(7)) + (sqrt(2) + 3)*(sqrt(3) + sqrt(7)) + >>> collect_const(sqrt(3)*s + sqrt(3) + sqrt(7)*s + sqrt(7), sqrt(3)) + sqrt(7) + sqrt(3)*(sqrt(2) + 3) + sqrt(7)*(sqrt(2) + 2) + + The collection is sign-sensitive, giving higher precedence to the + unsigned values: + + >>> collect_const(x - y - z) + x - (y + z) + >>> collect_const(-y - z) + -(y + z) + >>> collect_const(2*x - 2*y - 2*z, 2) + 2*(x - y - z) + >>> collect_const(2*x - 2*y - 2*z, -2) + 2*x - 2*(y + z) + + See Also + ======== + + collect, collect_sqrt, rcollect + """ + if not expr.is_Add: + return expr + + recurse = False + + if not vars: + recurse = True + vars = set() + for a in expr.args: + for m in Mul.make_args(a): + if m.is_number: + vars.add(m) + else: + vars = sympify(vars) + if not Numbers: + vars = [v for v in vars if not v.is_Number] + + vars = list(ordered(vars)) + for v in vars: + terms = defaultdict(list) + Fv = Factors(v) + for m in Add.make_args(expr): + f = Factors(m) + q, r = f.div(Fv) + if r.is_one: + # only accept this as a true factor if + # it didn't change an exponent from an Integer + # to a non-Integer, e.g. 2/sqrt(2) -> sqrt(2) + # -- we aren't looking for this sort of change + fwas = f.factors.copy() + fnow = q.factors + if not any(k in fwas and fwas[k].is_Integer and not + fnow[k].is_Integer for k in fnow): + terms[v].append(q.as_expr()) + continue + terms[S.One].append(m) + + args = [] + hit = False + uneval = False + for k in ordered(terms): + v = terms[k] + if k is S.One: + args.extend(v) + continue + + if len(v) > 1: + v = Add(*v) + hit = True + if recurse and v != expr: + vars.append(v) + else: + v = v[0] + + # be careful not to let uneval become True unless + # it must be because it's going to be more expensive + # to rebuild the expression as an unevaluated one + if Numbers and k.is_Number and v.is_Add: + args.append(_keep_coeff(k, v, sign=True)) + uneval = True + else: + args.append(k*v) + + if hit: + if uneval: + expr = _unevaluated_Add(*args) + else: + expr = Add(*args) + if not expr.is_Add: + break + + return expr + + +def radsimp(expr, symbolic=True, max_terms=4): + r""" + Rationalize the denominator by removing square roots. + + Explanation + =========== + + The expression returned from radsimp must be used with caution + since if the denominator contains symbols, it will be possible to make + substitutions that violate the assumptions of the simplification process: + that for a denominator matching a + b*sqrt(c), a != +/-b*sqrt(c). (If + there are no symbols, this assumptions is made valid by collecting terms + of sqrt(c) so the match variable ``a`` does not contain ``sqrt(c)``.) If + you do not want the simplification to occur for symbolic denominators, set + ``symbolic`` to False. + + If there are more than ``max_terms`` radical terms then the expression is + returned unchanged. + + Examples + ======== + + >>> from sympy import radsimp, sqrt, Symbol, pprint + >>> from sympy import factor_terms, fraction, signsimp + >>> from sympy.simplify.radsimp import collect_sqrt + >>> from sympy.abc import a, b, c + + >>> radsimp(1/(2 + sqrt(2))) + (2 - sqrt(2))/2 + >>> x,y = map(Symbol, 'xy') + >>> e = ((2 + 2*sqrt(2))*x + (2 + sqrt(8))*y)/(2 + sqrt(2)) + >>> radsimp(e) + sqrt(2)*(x + y) + + No simplification beyond removal of the gcd is done. One might + want to polish the result a little, however, by collecting + square root terms: + + >>> r2 = sqrt(2) + >>> r5 = sqrt(5) + >>> ans = radsimp(1/(y*r2 + x*r2 + a*r5 + b*r5)); pprint(ans) + ___ ___ ___ ___ + \/ 5 *a + \/ 5 *b - \/ 2 *x - \/ 2 *y + ------------------------------------------ + 2 2 2 2 + 5*a + 10*a*b + 5*b - 2*x - 4*x*y - 2*y + + >>> n, d = fraction(ans) + >>> pprint(factor_terms(signsimp(collect_sqrt(n))/d, radical=True)) + ___ ___ + \/ 5 *(a + b) - \/ 2 *(x + y) + ------------------------------------------ + 2 2 2 2 + 5*a + 10*a*b + 5*b - 2*x - 4*x*y - 2*y + + If radicals in the denominator cannot be removed or there is no denominator, + the original expression will be returned. + + >>> radsimp(sqrt(2)*x + sqrt(2)) + sqrt(2)*x + sqrt(2) + + Results with symbols will not always be valid for all substitutions: + + >>> eq = 1/(a + b*sqrt(c)) + >>> eq.subs(a, b*sqrt(c)) + 1/(2*b*sqrt(c)) + >>> radsimp(eq).subs(a, b*sqrt(c)) + nan + + If ``symbolic=False``, symbolic denominators will not be transformed (but + numeric denominators will still be processed): + + >>> radsimp(eq, symbolic=False) + 1/(a + b*sqrt(c)) + + """ + from sympy.simplify.simplify import signsimp + + syms = symbols("a:d A:D") + def _num(rterms): + # return the multiplier that will simplify the expression described + # by rterms [(sqrt arg, coeff), ... ] + a, b, c, d, A, B, C, D = syms + if len(rterms) == 2: + reps = dict(list(zip([A, a, B, b], [j for i in rterms for j in i]))) + return ( + sqrt(A)*a - sqrt(B)*b).xreplace(reps) + if len(rterms) == 3: + reps = dict(list(zip([A, a, B, b, C, c], [j for i in rterms for j in i]))) + return ( + (sqrt(A)*a + sqrt(B)*b - sqrt(C)*c)*(2*sqrt(A)*sqrt(B)*a*b - A*a**2 - + B*b**2 + C*c**2)).xreplace(reps) + elif len(rterms) == 4: + reps = dict(list(zip([A, a, B, b, C, c, D, d], [j for i in rterms for j in i]))) + return ((sqrt(A)*a + sqrt(B)*b - sqrt(C)*c - sqrt(D)*d)*(2*sqrt(A)*sqrt(B)*a*b + - A*a**2 - B*b**2 - 2*sqrt(C)*sqrt(D)*c*d + C*c**2 + + D*d**2)*(-8*sqrt(A)*sqrt(B)*sqrt(C)*sqrt(D)*a*b*c*d + A**2*a**4 - + 2*A*B*a**2*b**2 - 2*A*C*a**2*c**2 - 2*A*D*a**2*d**2 + B**2*b**4 - + 2*B*C*b**2*c**2 - 2*B*D*b**2*d**2 + C**2*c**4 - 2*C*D*c**2*d**2 + + D**2*d**4)).xreplace(reps) + elif len(rterms) == 1: + return sqrt(rterms[0][0]) + else: + raise NotImplementedError + + def ispow2(d, log2=False): + if not d.is_Pow: + return False + e = d.exp + if e.is_Rational and e.q == 2 or symbolic and denom(e) == 2: + return True + if log2: + q = 1 + if e.is_Rational: + q = e.q + elif symbolic: + d = denom(e) + if d.is_Integer: + q = d + if q != 1 and log(q, 2).is_Integer: + return True + return False + + def handle(expr): + # Handle first reduces to the case + # expr = 1/d, where d is an add, or d is base**p/2. + # We do this by recursively calling handle on each piece. + from sympy.simplify.simplify import nsimplify + + n, d = fraction(expr) + + if expr.is_Atom or (d.is_Atom and n.is_Atom): + return expr + elif not n.is_Atom: + n = n.func(*[handle(a) for a in n.args]) + return _unevaluated_Mul(n, handle(1/d)) + elif n is not S.One: + return _unevaluated_Mul(n, handle(1/d)) + elif d.is_Mul: + return _unevaluated_Mul(*[handle(1/d) for d in d.args]) + + # By this step, expr is 1/d, and d is not a mul. + if not symbolic and d.free_symbols: + return expr + + if ispow2(d): + d2 = sqrtdenest(sqrt(d.base))**numer(d.exp) + if d2 != d: + return handle(1/d2) + elif d.is_Pow and (d.exp.is_integer or d.base.is_positive): + # (1/d**i) = (1/d)**i + return handle(1/d.base)**d.exp + + if not (d.is_Add or ispow2(d)): + return 1/d.func(*[handle(a) for a in d.args]) + + # handle 1/d treating d as an Add (though it may not be) + + keep = True # keep changes that are made + + # flatten it and collect radicals after checking for special + # conditions + d = _mexpand(d) + + # did it change? + if d.is_Atom: + return 1/d + + # is it a number that might be handled easily? + if d.is_number: + _d = nsimplify(d) + if _d.is_Number and _d.equals(d): + return 1/_d + + while True: + # collect similar terms + collected = defaultdict(list) + for m in Add.make_args(d): # d might have become non-Add + p2 = [] + other = [] + for i in Mul.make_args(m): + if ispow2(i, log2=True): + p2.append(i.base if i.exp is S.Half else i.base**(2*i.exp)) + elif i is S.ImaginaryUnit: + p2.append(S.NegativeOne) + else: + other.append(i) + collected[tuple(ordered(p2))].append(Mul(*other)) + rterms = list(ordered(list(collected.items()))) + rterms = [(Mul(*i), Add(*j)) for i, j in rterms] + nrad = len(rterms) - (1 if rterms[0][0] is S.One else 0) + if nrad < 1: + break + elif nrad > max_terms: + # there may have been invalid operations leading to this point + # so don't keep changes, e.g. this expression is troublesome + # in collecting terms so as not to raise the issue of 2834: + # r = sqrt(sqrt(5) + 5) + # eq = 1/(sqrt(5)*r + 2*sqrt(5)*sqrt(-sqrt(5) + 5) + 5*r) + keep = False + break + if len(rterms) > 4: + # in general, only 4 terms can be removed with repeated squaring + # but other considerations can guide selection of radical terms + # so that radicals are removed + if all(x.is_Integer and (y**2).is_Rational for x, y in rterms): + nd, d = rad_rationalize(S.One, Add._from_args( + [sqrt(x)*y for x, y in rterms])) + n *= nd + else: + # is there anything else that might be attempted? + keep = False + break + from sympy.simplify.powsimp import powsimp, powdenest + + num = powsimp(_num(rterms)) + n *= num + d *= num + d = powdenest(_mexpand(d), force=symbolic) + if d.has(S.Zero, nan, zoo): + return expr + if d.is_Atom: + break + + if not keep: + return expr + return _unevaluated_Mul(n, 1/d) + + coeff, expr = expr.as_coeff_Add() + expr = expr.normal() + old = fraction(expr) + n, d = fraction(handle(expr)) + if old != (n, d): + if not d.is_Atom: + was = (n, d) + n = signsimp(n, evaluate=False) + d = signsimp(d, evaluate=False) + u = Factors(_unevaluated_Mul(n, 1/d)) + u = _unevaluated_Mul(*[k**v for k, v in u.factors.items()]) + n, d = fraction(u) + if old == (n, d): + n, d = was + n = expand_mul(n) + if d.is_Number or d.is_Add: + n2, d2 = fraction(gcd_terms(_unevaluated_Mul(n, 1/d))) + if d2.is_Number or (d2.count_ops() <= d.count_ops()): + n, d = [signsimp(i) for i in (n2, d2)] + if n.is_Mul and n.args[0].is_Number: + n = n.func(*n.args) + + return coeff + _unevaluated_Mul(n, 1/d) + + +def rad_rationalize(num, den): + """ + Rationalize ``num/den`` by removing square roots in the denominator; + num and den are sum of terms whose squares are positive rationals. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.radsimp import rad_rationalize + >>> rad_rationalize(sqrt(3), 1 + sqrt(2)/3) + (-sqrt(3) + sqrt(6)/3, -7/9) + """ + if not den.is_Add: + return num, den + g, a, b = split_surds(den) + a = a*sqrt(g) + num = _mexpand((a - b)*num) + den = _mexpand(a**2 - b**2) + return rad_rationalize(num, den) + + +def fraction(expr, exact=False): + """Returns a pair with expression's numerator and denominator. + If the given expression is not a fraction then this function + will return the tuple (expr, 1). + + This function will not make any attempt to simplify nested + fractions or to do any term rewriting at all. + + If only one of the numerator/denominator pair is needed then + use numer(expr) or denom(expr) functions respectively. + + >>> from sympy import fraction, Rational, Symbol + >>> from sympy.abc import x, y + + >>> fraction(x/y) + (x, y) + >>> fraction(x) + (x, 1) + + >>> fraction(1/y**2) + (1, y**2) + + >>> fraction(x*y/2) + (x*y, 2) + >>> fraction(Rational(1, 2)) + (1, 2) + + This function will also work fine with assumptions: + + >>> k = Symbol('k', negative=True) + >>> fraction(x * y**k) + (x, y**(-k)) + + If we know nothing about sign of some exponent and ``exact`` + flag is unset, then the exponent's structure will + be analyzed and pretty fraction will be returned: + + >>> from sympy import exp, Mul + >>> fraction(2*x**(-y)) + (2, x**y) + + >>> fraction(exp(-x)) + (1, exp(x)) + + >>> fraction(exp(-x), exact=True) + (exp(-x), 1) + + The ``exact`` flag will also keep any unevaluated Muls from + being evaluated: + + >>> u = Mul(2, x + 1, evaluate=False) + >>> fraction(u) + (2*x + 2, 1) + >>> fraction(u, exact=True) + (2*(x + 1), 1) + """ + expr = sympify(expr) + + numer, denom = [], [] + + for term in Mul.make_args(expr): + if term.is_commutative and (term.is_Pow or isinstance(term, exp)): + b, ex = term.as_base_exp() + if ex.is_negative: + if ex is S.NegativeOne: + denom.append(b) + elif exact: + if ex.is_constant(): + denom.append(Pow(b, -ex)) + else: + numer.append(term) + else: + denom.append(Pow(b, -ex)) + elif ex.is_positive: + numer.append(term) + elif not exact and ex.is_Mul: + n, d = term.as_numer_denom() # this will cause evaluation + if n != 1: + numer.append(n) + denom.append(d) + else: + numer.append(term) + elif term.is_Rational and not term.is_Integer: + if term.p != 1: + numer.append(term.p) + denom.append(term.q) + else: + numer.append(term) + return Mul(*numer, evaluate=not exact), Mul(*denom, evaluate=not exact) + + +def numer(expr, exact=False): # default matches fraction's default + return fraction(expr, exact=exact)[0] + + +def denom(expr, exact=False): # default matches fraction's default + return fraction(expr, exact=exact)[1] + + +def fraction_expand(expr, **hints): + return expr.expand(frac=True, **hints) + + +def numer_expand(expr, **hints): + # default matches fraction's default + a, b = fraction(expr, exact=hints.get('exact', False)) + return a.expand(numer=True, **hints) / b + + +def denom_expand(expr, **hints): + # default matches fraction's default + a, b = fraction(expr, exact=hints.get('exact', False)) + return a / b.expand(denom=True, **hints) + + +expand_numer = numer_expand +expand_denom = denom_expand +expand_fraction = fraction_expand + + +def split_surds(expr): + """ + Split an expression with terms whose squares are positive rationals + into a sum of terms whose surds squared have gcd equal to g + and a sum of terms with surds squared prime with g. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.radsimp import split_surds + >>> split_surds(3*sqrt(3) + sqrt(5)/7 + sqrt(6) + sqrt(10) + sqrt(15)) + (3, sqrt(2) + sqrt(5) + 3, sqrt(5)/7 + sqrt(10)) + """ + args = sorted(expr.args, key=default_sort_key) + coeff_muls = [x.as_coeff_Mul() for x in args] + surds = [x[1]**2 for x in coeff_muls if x[1].is_Pow] + surds.sort(key=default_sort_key) + g, b1, b2 = _split_gcd(*surds) + g2 = g + if not b2 and len(b1) >= 2: + b1n = [x/g for x in b1] + b1n = [x for x in b1n if x != 1] + # only a common factor has been factored; split again + g1, b1n, b2 = _split_gcd(*b1n) + g2 = g*g1 + a1v, a2v = [], [] + for c, s in coeff_muls: + if s.is_Pow and s.exp == S.Half: + s1 = s.base + if s1 in b1: + a1v.append(c*sqrt(s1/g2)) + else: + a2v.append(c*s) + else: + a2v.append(c*s) + a = Add(*a1v) + b = Add(*a2v) + return g2, a, b + + +def _split_gcd(*a): + """ + Split the list of integers ``a`` into a list of integers, ``a1`` having + ``g = gcd(a1)``, and a list ``a2`` whose elements are not divisible by + ``g``. Returns ``g, a1, a2``. + + Examples + ======== + + >>> from sympy.simplify.radsimp import _split_gcd + >>> _split_gcd(55, 35, 22, 14, 77, 10) + (5, [55, 35, 10], [22, 14, 77]) + """ + g = a[0] + b1 = [g] + b2 = [] + for x in a[1:]: + g1 = gcd(g, x) + if g1 == 1: + b2.append(x) + else: + g = g1 + b1.append(x) + return g, b1, b2 diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/sqrtdenest.py b/janus/lib/python3.10/site-packages/sympy/simplify/sqrtdenest.py new file mode 100644 index 0000000000000000000000000000000000000000..a133a3f3fa41a689c4c014e7cf24e03351a6ad17 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/sqrtdenest.py @@ -0,0 +1,678 @@ +from sympy.core import Add, Expr, Mul, S, sympify +from sympy.core.function import _mexpand, count_ops, expand_mul +from sympy.core.sorting import default_sort_key +from sympy.core.symbol import Dummy +from sympy.functions import root, sign, sqrt +from sympy.polys import Poly, PolynomialError + + +def is_sqrt(expr): + """Return True if expr is a sqrt, otherwise False.""" + + return expr.is_Pow and expr.exp.is_Rational and abs(expr.exp) is S.Half + + +def sqrt_depth(p) -> int: + """Return the maximum depth of any square root argument of p. + + >>> from sympy.functions.elementary.miscellaneous import sqrt + >>> from sympy.simplify.sqrtdenest import sqrt_depth + + Neither of these square roots contains any other square roots + so the depth is 1: + + >>> sqrt_depth(1 + sqrt(2)*(1 + sqrt(3))) + 1 + + The sqrt(3) is contained within a square root so the depth is + 2: + + >>> sqrt_depth(1 + sqrt(2)*sqrt(1 + sqrt(3))) + 2 + """ + if p is S.ImaginaryUnit: + return 1 + if p.is_Atom: + return 0 + if p.is_Add or p.is_Mul: + return max(sqrt_depth(x) for x in p.args) + if is_sqrt(p): + return sqrt_depth(p.base) + 1 + return 0 + + +def is_algebraic(p): + """Return True if p is comprised of only Rationals or square roots + of Rationals and algebraic operations. + + Examples + ======== + + >>> from sympy.functions.elementary.miscellaneous import sqrt + >>> from sympy.simplify.sqrtdenest import is_algebraic + >>> from sympy import cos + >>> is_algebraic(sqrt(2)*(3/(sqrt(7) + sqrt(5)*sqrt(2)))) + True + >>> is_algebraic(sqrt(2)*(3/(sqrt(7) + sqrt(5)*cos(2)))) + False + """ + + if p.is_Rational: + return True + elif p.is_Atom: + return False + elif is_sqrt(p) or p.is_Pow and p.exp.is_Integer: + return is_algebraic(p.base) + elif p.is_Add or p.is_Mul: + return all(is_algebraic(x) for x in p.args) + else: + return False + + +def _subsets(n): + """ + Returns all possible subsets of the set (0, 1, ..., n-1) except the + empty set, listed in reversed lexicographical order according to binary + representation, so that the case of the fourth root is treated last. + + Examples + ======== + + >>> from sympy.simplify.sqrtdenest import _subsets + >>> _subsets(2) + [[1, 0], [0, 1], [1, 1]] + + """ + if n == 1: + a = [[1]] + elif n == 2: + a = [[1, 0], [0, 1], [1, 1]] + elif n == 3: + a = [[1, 0, 0], [0, 1, 0], [1, 1, 0], + [0, 0, 1], [1, 0, 1], [0, 1, 1], [1, 1, 1]] + else: + b = _subsets(n - 1) + a0 = [x + [0] for x in b] + a1 = [x + [1] for x in b] + a = a0 + [[0]*(n - 1) + [1]] + a1 + return a + + +def sqrtdenest(expr, max_iter=3): + """Denests sqrts in an expression that contain other square roots + if possible, otherwise returns the expr unchanged. This is based on the + algorithms of [1]. + + Examples + ======== + + >>> from sympy.simplify.sqrtdenest import sqrtdenest + >>> from sympy import sqrt + >>> sqrtdenest(sqrt(5 + 2 * sqrt(6))) + sqrt(2) + sqrt(3) + + See Also + ======== + + sympy.solvers.solvers.unrad + + References + ========== + + .. [1] https://web.archive.org/web/20210806201615/https://researcher.watson.ibm.com/researcher/files/us-fagin/symb85.pdf + + .. [2] D. J. Jeffrey and A. D. Rich, 'Symplifying Square Roots of Square Roots + by Denesting' (available at https://www.cybertester.com/data/denest.pdf) + + """ + expr = expand_mul(expr) + for i in range(max_iter): + z = _sqrtdenest0(expr) + if expr == z: + return expr + expr = z + return expr + + +def _sqrt_match(p): + """Return [a, b, r] for p.match(a + b*sqrt(r)) where, in addition to + matching, sqrt(r) also has then maximal sqrt_depth among addends of p. + + Examples + ======== + + >>> from sympy.functions.elementary.miscellaneous import sqrt + >>> from sympy.simplify.sqrtdenest import _sqrt_match + >>> _sqrt_match(1 + sqrt(2) + sqrt(2)*sqrt(3) + 2*sqrt(1+sqrt(5))) + [1 + sqrt(2) + sqrt(6), 2, 1 + sqrt(5)] + """ + from sympy.simplify.radsimp import split_surds + + p = _mexpand(p) + if p.is_Number: + res = (p, S.Zero, S.Zero) + elif p.is_Add: + pargs = sorted(p.args, key=default_sort_key) + sqargs = [x**2 for x in pargs] + if all(sq.is_Rational and sq.is_positive for sq in sqargs): + r, b, a = split_surds(p) + res = a, b, r + return list(res) + # to make the process canonical, the argument is included in the tuple + # so when the max is selected, it will be the largest arg having a + # given depth + v = [(sqrt_depth(x), x, i) for i, x in enumerate(pargs)] + nmax = max(v, key=default_sort_key) + if nmax[0] == 0: + res = [] + else: + # select r + depth, _, i = nmax + r = pargs.pop(i) + v.pop(i) + b = S.One + if r.is_Mul: + bv = [] + rv = [] + for x in r.args: + if sqrt_depth(x) < depth: + bv.append(x) + else: + rv.append(x) + b = Mul._from_args(bv) + r = Mul._from_args(rv) + # collect terms comtaining r + a1 = [] + b1 = [b] + for x in v: + if x[0] < depth: + a1.append(x[1]) + else: + x1 = x[1] + if x1 == r: + b1.append(1) + else: + if x1.is_Mul: + x1args = list(x1.args) + if r in x1args: + x1args.remove(r) + b1.append(Mul(*x1args)) + else: + a1.append(x[1]) + else: + a1.append(x[1]) + a = Add(*a1) + b = Add(*b1) + res = (a, b, r**2) + else: + b, r = p.as_coeff_Mul() + if is_sqrt(r): + res = (S.Zero, b, r**2) + else: + res = [] + return list(res) + + +class SqrtdenestStopIteration(StopIteration): + pass + + +def _sqrtdenest0(expr): + """Returns expr after denesting its arguments.""" + + if is_sqrt(expr): + n, d = expr.as_numer_denom() + if d is S.One: # n is a square root + if n.base.is_Add: + args = sorted(n.base.args, key=default_sort_key) + if len(args) > 2 and all((x**2).is_Integer for x in args): + try: + return _sqrtdenest_rec(n) + except SqrtdenestStopIteration: + pass + expr = sqrt(_mexpand(Add(*[_sqrtdenest0(x) for x in args]))) + return _sqrtdenest1(expr) + else: + n, d = [_sqrtdenest0(i) for i in (n, d)] + return n/d + + if isinstance(expr, Add): + cs = [] + args = [] + for arg in expr.args: + c, a = arg.as_coeff_Mul() + cs.append(c) + args.append(a) + + if all(c.is_Rational for c in cs) and all(is_sqrt(arg) for arg in args): + return _sqrt_ratcomb(cs, args) + + if isinstance(expr, Expr): + args = expr.args + if args: + return expr.func(*[_sqrtdenest0(a) for a in args]) + return expr + + +def _sqrtdenest_rec(expr): + """Helper that denests the square root of three or more surds. + + Explanation + =========== + + It returns the denested expression; if it cannot be denested it + throws SqrtdenestStopIteration + + Algorithm: expr.base is in the extension Q_m = Q(sqrt(r_1),..,sqrt(r_k)); + split expr.base = a + b*sqrt(r_k), where `a` and `b` are on + Q_(m-1) = Q(sqrt(r_1),..,sqrt(r_(k-1))); then a**2 - b**2*r_k is + on Q_(m-1); denest sqrt(a**2 - b**2*r_k) and so on. + See [1], section 6. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.sqrtdenest import _sqrtdenest_rec + >>> _sqrtdenest_rec(sqrt(-72*sqrt(2) + 158*sqrt(5) + 498)) + -sqrt(10) + sqrt(2) + 9 + 9*sqrt(5) + >>> w=-6*sqrt(55)-6*sqrt(35)-2*sqrt(22)-2*sqrt(14)+2*sqrt(77)+6*sqrt(10)+65 + >>> _sqrtdenest_rec(sqrt(w)) + -sqrt(11) - sqrt(7) + sqrt(2) + 3*sqrt(5) + """ + from sympy.simplify.radsimp import radsimp, rad_rationalize, split_surds + if not expr.is_Pow: + return sqrtdenest(expr) + if expr.base < 0: + return sqrt(-1)*_sqrtdenest_rec(sqrt(-expr.base)) + g, a, b = split_surds(expr.base) + a = a*sqrt(g) + if a < b: + a, b = b, a + c2 = _mexpand(a**2 - b**2) + if len(c2.args) > 2: + g, a1, b1 = split_surds(c2) + a1 = a1*sqrt(g) + if a1 < b1: + a1, b1 = b1, a1 + c2_1 = _mexpand(a1**2 - b1**2) + c_1 = _sqrtdenest_rec(sqrt(c2_1)) + d_1 = _sqrtdenest_rec(sqrt(a1 + c_1)) + num, den = rad_rationalize(b1, d_1) + c = _mexpand(d_1/sqrt(2) + num/(den*sqrt(2))) + else: + c = _sqrtdenest1(sqrt(c2)) + + if sqrt_depth(c) > 1: + raise SqrtdenestStopIteration + ac = a + c + if len(ac.args) >= len(expr.args): + if count_ops(ac) >= count_ops(expr.base): + raise SqrtdenestStopIteration + d = sqrtdenest(sqrt(ac)) + if sqrt_depth(d) > 1: + raise SqrtdenestStopIteration + num, den = rad_rationalize(b, d) + r = d/sqrt(2) + num/(den*sqrt(2)) + r = radsimp(r) + return _mexpand(r) + + +def _sqrtdenest1(expr, denester=True): + """Return denested expr after denesting with simpler methods or, that + failing, using the denester.""" + + from sympy.simplify.simplify import radsimp + + if not is_sqrt(expr): + return expr + + a = expr.base + if a.is_Atom: + return expr + val = _sqrt_match(a) + if not val: + return expr + + a, b, r = val + # try a quick numeric denesting + d2 = _mexpand(a**2 - b**2*r) + if d2.is_Rational: + if d2.is_positive: + z = _sqrt_numeric_denest(a, b, r, d2) + if z is not None: + return z + else: + # fourth root case + # sqrtdenest(sqrt(3 + 2*sqrt(3))) = + # sqrt(2)*3**(1/4)/2 + sqrt(2)*3**(3/4)/2 + dr2 = _mexpand(-d2*r) + dr = sqrt(dr2) + if dr.is_Rational: + z = _sqrt_numeric_denest(_mexpand(b*r), a, r, dr2) + if z is not None: + return z/root(r, 4) + + else: + z = _sqrt_symbolic_denest(a, b, r) + if z is not None: + return z + + if not denester or not is_algebraic(expr): + return expr + + res = sqrt_biquadratic_denest(expr, a, b, r, d2) + if res: + return res + + # now call to the denester + av0 = [a, b, r, d2] + z = _denester([radsimp(expr**2)], av0, 0, sqrt_depth(expr))[0] + if av0[1] is None: + return expr + if z is not None: + if sqrt_depth(z) == sqrt_depth(expr) and count_ops(z) > count_ops(expr): + return expr + return z + return expr + + +def _sqrt_symbolic_denest(a, b, r): + """Given an expression, sqrt(a + b*sqrt(b)), return the denested + expression or None. + + Explanation + =========== + + If r = ra + rb*sqrt(rr), try replacing sqrt(rr) in ``a`` with + (y**2 - ra)/rb, and if the result is a quadratic, ca*y**2 + cb*y + cc, and + (cb + b)**2 - 4*ca*cc is 0, then sqrt(a + b*sqrt(r)) can be rewritten as + sqrt(ca*(sqrt(r) + (cb + b)/(2*ca))**2). + + Examples + ======== + + >>> from sympy.simplify.sqrtdenest import _sqrt_symbolic_denest, sqrtdenest + >>> from sympy import sqrt, Symbol + >>> from sympy.abc import x + + >>> a, b, r = 16 - 2*sqrt(29), 2, -10*sqrt(29) + 55 + >>> _sqrt_symbolic_denest(a, b, r) + sqrt(11 - 2*sqrt(29)) + sqrt(5) + + If the expression is numeric, it will be simplified: + + >>> w = sqrt(sqrt(sqrt(3) + 1) + 1) + 1 + sqrt(2) + >>> sqrtdenest(sqrt((w**2).expand())) + 1 + sqrt(2) + sqrt(1 + sqrt(1 + sqrt(3))) + + Otherwise, it will only be simplified if assumptions allow: + + >>> w = w.subs(sqrt(3), sqrt(x + 3)) + >>> sqrtdenest(sqrt((w**2).expand())) + sqrt((sqrt(sqrt(sqrt(x + 3) + 1) + 1) + 1 + sqrt(2))**2) + + Notice that the argument of the sqrt is a square. If x is made positive + then the sqrt of the square is resolved: + + >>> _.subs(x, Symbol('x', positive=True)) + sqrt(sqrt(sqrt(x + 3) + 1) + 1) + 1 + sqrt(2) + """ + + a, b, r = map(sympify, (a, b, r)) + rval = _sqrt_match(r) + if not rval: + return None + ra, rb, rr = rval + if rb: + y = Dummy('y', positive=True) + try: + newa = Poly(a.subs(sqrt(rr), (y**2 - ra)/rb), y) + except PolynomialError: + return None + if newa.degree() == 2: + ca, cb, cc = newa.all_coeffs() + cb += b + if _mexpand(cb**2 - 4*ca*cc).equals(0): + z = sqrt(ca*(sqrt(r) + cb/(2*ca))**2) + if z.is_number: + z = _mexpand(Mul._from_args(z.as_content_primitive())) + return z + + +def _sqrt_numeric_denest(a, b, r, d2): + r"""Helper that denest + $\sqrt{a + b \sqrt{r}}, d^2 = a^2 - b^2 r > 0$ + + If it cannot be denested, it returns ``None``. + """ + d = sqrt(d2) + s = a + d + # sqrt_depth(res) <= sqrt_depth(s) + 1 + # sqrt_depth(expr) = sqrt_depth(r) + 2 + # there is denesting if sqrt_depth(s) + 1 < sqrt_depth(r) + 2 + # if s**2 is Number there is a fourth root + if sqrt_depth(s) < sqrt_depth(r) + 1 or (s**2).is_Rational: + s1, s2 = sign(s), sign(b) + if s1 == s2 == -1: + s1 = s2 = 1 + res = (s1 * sqrt(a + d) + s2 * sqrt(a - d)) * sqrt(2) / 2 + return res.expand() + + +def sqrt_biquadratic_denest(expr, a, b, r, d2): + """denest expr = sqrt(a + b*sqrt(r)) + where a, b, r are linear combinations of square roots of + positive rationals on the rationals (SQRR) and r > 0, b != 0, + d2 = a**2 - b**2*r > 0 + + If it cannot denest it returns None. + + Explanation + =========== + + Search for a solution A of type SQRR of the biquadratic equation + 4*A**4 - 4*a*A**2 + b**2*r = 0 (1) + sqd = sqrt(a**2 - b**2*r) + Choosing the sqrt to be positive, the possible solutions are + A = sqrt(a/2 +/- sqd/2) + Since a, b, r are SQRR, then a**2 - b**2*r is a SQRR, + so if sqd can be denested, it is done by + _sqrtdenest_rec, and the result is a SQRR. + Similarly for A. + Examples of solutions (in both cases a and sqd are positive): + + Example of expr with solution sqrt(a/2 + sqd/2) but not + solution sqrt(a/2 - sqd/2): + expr = sqrt(-sqrt(15) - sqrt(2)*sqrt(-sqrt(5) + 5) - sqrt(3) + 8) + a = -sqrt(15) - sqrt(3) + 8; sqd = -2*sqrt(5) - 2 + 4*sqrt(3) + + Example of expr with solution sqrt(a/2 - sqd/2) but not + solution sqrt(a/2 + sqd/2): + w = 2 + r2 + r3 + (1 + r3)*sqrt(2 + r2 + 5*r3) + expr = sqrt((w**2).expand()) + a = 4*sqrt(6) + 8*sqrt(2) + 47 + 28*sqrt(3) + sqd = 29 + 20*sqrt(3) + + Define B = b/2*A; eq.(1) implies a = A**2 + B**2*r; then + expr**2 = a + b*sqrt(r) = (A + B*sqrt(r))**2 + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.sqrtdenest import _sqrt_match, sqrt_biquadratic_denest + >>> z = sqrt((2*sqrt(2) + 4)*sqrt(2 + sqrt(2)) + 5*sqrt(2) + 8) + >>> a, b, r = _sqrt_match(z**2) + >>> d2 = a**2 - b**2*r + >>> sqrt_biquadratic_denest(z, a, b, r, d2) + sqrt(2) + sqrt(sqrt(2) + 2) + 2 + """ + from sympy.simplify.radsimp import radsimp, rad_rationalize + if r <= 0 or d2 < 0 or not b or sqrt_depth(expr.base) < 2: + return None + for x in (a, b, r): + for y in x.args: + y2 = y**2 + if not y2.is_Integer or not y2.is_positive: + return None + sqd = _mexpand(sqrtdenest(sqrt(radsimp(d2)))) + if sqrt_depth(sqd) > 1: + return None + x1, x2 = [a/2 + sqd/2, a/2 - sqd/2] + # look for a solution A with depth 1 + for x in (x1, x2): + A = sqrtdenest(sqrt(x)) + if sqrt_depth(A) > 1: + continue + Bn, Bd = rad_rationalize(b, _mexpand(2*A)) + B = Bn/Bd + z = A + B*sqrt(r) + if z < 0: + z = -z + return _mexpand(z) + return None + + +def _denester(nested, av0, h, max_depth_level): + """Denests a list of expressions that contain nested square roots. + + Explanation + =========== + + Algorithm based on . + + It is assumed that all of the elements of 'nested' share the same + bottom-level radicand. (This is stated in the paper, on page 177, in + the paragraph immediately preceding the algorithm.) + + When evaluating all of the arguments in parallel, the bottom-level + radicand only needs to be denested once. This means that calling + _denester with x arguments results in a recursive invocation with x+1 + arguments; hence _denester has polynomial complexity. + + However, if the arguments were evaluated separately, each call would + result in two recursive invocations, and the algorithm would have + exponential complexity. + + This is discussed in the paper in the middle paragraph of page 179. + """ + from sympy.simplify.simplify import radsimp + if h > max_depth_level: + return None, None + if av0[1] is None: + return None, None + if (av0[0] is None and + all(n.is_Number for n in nested)): # no arguments are nested + for f in _subsets(len(nested)): # test subset 'f' of nested + p = _mexpand(Mul(*[nested[i] for i in range(len(f)) if f[i]])) + if f.count(1) > 1 and f[-1]: + p = -p + sqp = sqrt(p) + if sqp.is_Rational: + return sqp, f # got a perfect square so return its square root. + # Otherwise, return the radicand from the previous invocation. + return sqrt(nested[-1]), [0]*len(nested) + else: + R = None + if av0[0] is not None: + values = [av0[:2]] + R = av0[2] + nested2 = [av0[3], R] + av0[0] = None + else: + values = list(filter(None, [_sqrt_match(expr) for expr in nested])) + for v in values: + if v[2]: # Since if b=0, r is not defined + if R is not None: + if R != v[2]: + av0[1] = None + return None, None + else: + R = v[2] + if R is None: + # return the radicand from the previous invocation + return sqrt(nested[-1]), [0]*len(nested) + nested2 = [_mexpand(v[0]**2) - + _mexpand(R*v[1]**2) for v in values] + [R] + d, f = _denester(nested2, av0, h + 1, max_depth_level) + if not f: + return None, None + if not any(f[i] for i in range(len(nested))): + v = values[-1] + return sqrt(v[0] + _mexpand(v[1]*d)), f + else: + p = Mul(*[nested[i] for i in range(len(nested)) if f[i]]) + v = _sqrt_match(p) + if 1 in f and f.index(1) < len(nested) - 1 and f[len(nested) - 1]: + v[0] = -v[0] + v[1] = -v[1] + if not f[len(nested)]: # Solution denests with square roots + vad = _mexpand(v[0] + d) + if vad <= 0: + # return the radicand from the previous invocation. + return sqrt(nested[-1]), [0]*len(nested) + if not(sqrt_depth(vad) <= sqrt_depth(R) + 1 or + (vad**2).is_Number): + av0[1] = None + return None, None + + sqvad = _sqrtdenest1(sqrt(vad), denester=False) + if not (sqrt_depth(sqvad) <= sqrt_depth(R) + 1): + av0[1] = None + return None, None + sqvad1 = radsimp(1/sqvad) + res = _mexpand(sqvad/sqrt(2) + (v[1]*sqrt(R)*sqvad1/sqrt(2))) + return res, f + + # sign(v[1])*sqrt(_mexpand(v[1]**2*R*vad1/2))), f + else: # Solution requires a fourth root + s2 = _mexpand(v[1]*R) + d + if s2 <= 0: + return sqrt(nested[-1]), [0]*len(nested) + FR, s = root(_mexpand(R), 4), sqrt(s2) + return _mexpand(s/(sqrt(2)*FR) + v[0]*FR/(sqrt(2)*s)), f + + +def _sqrt_ratcomb(cs, args): + """Denest rational combinations of radicals. + + Based on section 5 of [1]. + + Examples + ======== + + >>> from sympy import sqrt + >>> from sympy.simplify.sqrtdenest import sqrtdenest + >>> z = sqrt(1+sqrt(3)) + sqrt(3+3*sqrt(3)) - sqrt(10+6*sqrt(3)) + >>> sqrtdenest(z) + 0 + """ + from sympy.simplify.radsimp import radsimp + + # check if there exists a pair of sqrt that can be denested + def find(a): + n = len(a) + for i in range(n - 1): + for j in range(i + 1, n): + s1 = a[i].base + s2 = a[j].base + p = _mexpand(s1 * s2) + s = sqrtdenest(sqrt(p)) + if s != sqrt(p): + return s, i, j + + indices = find(args) + if indices is None: + return Add(*[c * arg for c, arg in zip(cs, args)]) + + s, i1, i2 = indices + + c2 = cs.pop(i2) + args.pop(i2) + a1 = args[i1] + + # replace a2 by s/a1 + cs[i1] += radsimp(c2 * s / a1.base) + + return _sqrt_ratcomb(cs, args) diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/tests/__init__.py b/janus/lib/python3.10/site-packages/sympy/simplify/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/janus/lib/python3.10/site-packages/sympy/simplify/traversaltools.py b/janus/lib/python3.10/site-packages/sympy/simplify/traversaltools.py new file mode 100644 index 0000000000000000000000000000000000000000..75b0bd0d8fd198cb12640ab8a0fe63a23c81ed8f --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/simplify/traversaltools.py @@ -0,0 +1,15 @@ +from sympy.core.traversal import use as _use +from sympy.utilities.decorator import deprecated + +use = deprecated( + """ + Using use from the sympy.simplify.traversaltools submodule is + deprecated. + + Instead, use use from the top-level sympy namespace, like + + sympy.use + """, + deprecated_since_version="1.10", + active_deprecations_target="deprecated-traversal-functions-moved" +)(_use) diff --git a/janus/lib/python3.10/site-packages/sympy/stats/__init__.py b/janus/lib/python3.10/site-packages/sympy/stats/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..adb79261954924305c1837555d7d47cd53b8430b --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/stats/__init__.py @@ -0,0 +1,202 @@ +""" +SymPy statistics module + +Introduces a random variable type into the SymPy language. + +Random variables may be declared using prebuilt functions such as +Normal, Exponential, Coin, Die, etc... or built with functions like FiniteRV. + +Queries on random expressions can be made using the functions + +========================= ============================= + Expression Meaning +------------------------- ----------------------------- + ``P(condition)`` Probability + ``E(expression)`` Expected value + ``H(expression)`` Entropy + ``variance(expression)`` Variance + ``density(expression)`` Probability Density Function + ``sample(expression)`` Produce a realization + ``where(condition)`` Where the condition is true +========================= ============================= + +Examples +======== + +>>> from sympy.stats import P, E, variance, Die, Normal +>>> from sympy import simplify +>>> X, Y = Die('X', 6), Die('Y', 6) # Define two six sided dice +>>> Z = Normal('Z', 0, 1) # Declare a Normal random variable with mean 0, std 1 +>>> P(X>3) # Probability X is greater than 3 +1/2 +>>> E(X+Y) # Expectation of the sum of two dice +7 +>>> variance(X+Y) # Variance of the sum of two dice +35/6 +>>> simplify(P(Z>1)) # Probability of Z being greater than 1 +1/2 - erf(sqrt(2)/2)/2 + + +One could also create custom distribution and define custom random variables +as follows: + +1. If you want to create a Continuous Random Variable: + +>>> from sympy.stats import ContinuousRV, P, E +>>> from sympy import exp, Symbol, Interval, oo +>>> x = Symbol('x') +>>> pdf = exp(-x) # pdf of the Continuous Distribution +>>> Z = ContinuousRV(x, pdf, set=Interval(0, oo)) +>>> E(Z) +1 +>>> P(Z > 5) +exp(-5) + +1.1 To create an instance of Continuous Distribution: + +>>> from sympy.stats import ContinuousDistributionHandmade +>>> from sympy import Lambda +>>> dist = ContinuousDistributionHandmade(Lambda(x, pdf), set=Interval(0, oo)) +>>> dist.pdf(x) +exp(-x) + +2. If you want to create a Discrete Random Variable: + +>>> from sympy.stats import DiscreteRV, P, E +>>> from sympy import Symbol, S +>>> p = S(1)/2 +>>> x = Symbol('x', integer=True, positive=True) +>>> pdf = p*(1 - p)**(x - 1) +>>> D = DiscreteRV(x, pdf, set=S.Naturals) +>>> E(D) +2 +>>> P(D > 3) +1/8 + +2.1 To create an instance of Discrete Distribution: + +>>> from sympy.stats import DiscreteDistributionHandmade +>>> from sympy import Lambda +>>> dist = DiscreteDistributionHandmade(Lambda(x, pdf), set=S.Naturals) +>>> dist.pdf(x) +2**(1 - x)/2 + +3. If you want to create a Finite Random Variable: + +>>> from sympy.stats import FiniteRV, P, E +>>> from sympy import Rational, Eq +>>> pmf = {1: Rational(1, 3), 2: Rational(1, 6), 3: Rational(1, 4), 4: Rational(1, 4)} +>>> X = FiniteRV('X', pmf) +>>> E(X) +29/12 +>>> P(X > 3) +1/4 + +3.1 To create an instance of Finite Distribution: + +>>> from sympy.stats import FiniteDistributionHandmade +>>> dist = FiniteDistributionHandmade(pmf) +>>> dist.pmf(x) +Lambda(x, Piecewise((1/3, Eq(x, 1)), (1/6, Eq(x, 2)), (1/4, Eq(x, 3) | Eq(x, 4)), (0, True))) +""" + +__all__ = [ + 'P', 'E', 'H', 'density', 'where', 'given', 'sample', 'cdf','median', + 'characteristic_function', 'pspace', 'sample_iter', 'variance', 'std', + 'skewness', 'kurtosis', 'covariance', 'dependent', 'entropy', 'independent', + 'random_symbols', 'correlation', 'factorial_moment', 'moment', 'cmoment', + 'sampling_density', 'moment_generating_function', 'smoment', 'quantile', + 'coskewness', 'sample_stochastic_process', + + 'FiniteRV', 'DiscreteUniform', 'Die', 'Bernoulli', 'Coin', 'Binomial', + 'BetaBinomial', 'Hypergeometric', 'Rademacher', 'IdealSoliton', 'RobustSoliton', + 'FiniteDistributionHandmade', + + 'ContinuousRV', 'Arcsin', 'Benini', 'Beta', 'BetaNoncentral', 'BetaPrime', + 'BoundedPareto', 'Cauchy', 'Chi', 'ChiNoncentral', 'ChiSquared', 'Dagum', 'Davis', 'Erlang', + 'ExGaussian', 'Exponential', 'ExponentialPower', 'FDistribution', + 'FisherZ', 'Frechet', 'Gamma', 'GammaInverse', 'Gompertz', 'Gumbel', + 'Kumaraswamy', 'Laplace', 'Levy', 'Logistic','LogCauchy', 'LogLogistic', 'LogitNormal', 'LogNormal', 'Lomax', + 'Moyal', 'Maxwell', 'Nakagami', 'Normal', 'GaussianInverse', 'Pareto', 'PowerFunction', + 'QuadraticU', 'RaisedCosine', 'Rayleigh','Reciprocal', 'StudentT', 'ShiftedGompertz', + 'Trapezoidal', 'Triangular', 'Uniform', 'UniformSum', 'VonMises', 'Wald', + 'Weibull', 'WignerSemicircle', 'ContinuousDistributionHandmade', + + 'FlorySchulz', 'Geometric','Hermite', 'Logarithmic', 'NegativeBinomial', 'Poisson', 'Skellam', + 'YuleSimon', 'Zeta', 'DiscreteRV', 'DiscreteDistributionHandmade', + + 'JointRV', 'Dirichlet', 'GeneralizedMultivariateLogGamma', + 'GeneralizedMultivariateLogGammaOmega', 'Multinomial', 'MultivariateBeta', + 'MultivariateEwens', 'MultivariateT', 'NegativeMultinomial', + 'NormalGamma', 'MultivariateNormal', 'MultivariateLaplace', 'marginal_distribution', + + 'StochasticProcess', 'DiscreteTimeStochasticProcess', + 'DiscreteMarkovChain', 'TransitionMatrixOf', 'StochasticStateSpaceOf', + 'GeneratorMatrixOf', 'ContinuousMarkovChain', 'BernoulliProcess', + 'PoissonProcess', 'WienerProcess', 'GammaProcess', + + 'CircularEnsemble', 'CircularUnitaryEnsemble', + 'CircularOrthogonalEnsemble', 'CircularSymplecticEnsemble', + 'GaussianEnsemble', 'GaussianUnitaryEnsemble', + 'GaussianOrthogonalEnsemble', 'GaussianSymplecticEnsemble', + 'joint_eigen_distribution', 'JointEigenDistribution', + 'level_spacing_distribution', + + 'MatrixGamma', 'Wishart', 'MatrixNormal', 'MatrixStudentT', + + 'Probability', 'Expectation', 'Variance', 'Covariance', 'Moment', + 'CentralMoment', + + 'ExpectationMatrix', 'VarianceMatrix', 'CrossCovarianceMatrix' + +] +from .rv_interface import (P, E, H, density, where, given, sample, cdf, median, + characteristic_function, pspace, sample_iter, variance, std, skewness, + kurtosis, covariance, dependent, entropy, independent, random_symbols, + correlation, factorial_moment, moment, cmoment, sampling_density, + moment_generating_function, smoment, quantile, coskewness, + sample_stochastic_process) + +from .frv_types import (FiniteRV, DiscreteUniform, Die, Bernoulli, Coin, + Binomial, BetaBinomial, Hypergeometric, Rademacher, + FiniteDistributionHandmade, IdealSoliton, RobustSoliton) + +from .crv_types import (ContinuousRV, Arcsin, Benini, Beta, BetaNoncentral, + BetaPrime, BoundedPareto, Cauchy, Chi, ChiNoncentral, ChiSquared, + Dagum, Davis, Erlang, ExGaussian, Exponential, ExponentialPower, + FDistribution, FisherZ, Frechet, Gamma, GammaInverse, GaussianInverse, + Gompertz, Gumbel, Kumaraswamy, Laplace, Levy, Logistic, LogCauchy, + LogLogistic, LogitNormal, LogNormal, Lomax, Maxwell, Moyal, Nakagami, + Normal, Pareto, QuadraticU, RaisedCosine, Rayleigh, Reciprocal, + StudentT, PowerFunction, ShiftedGompertz, Trapezoidal, Triangular, + Uniform, UniformSum, VonMises, Wald, Weibull, WignerSemicircle, + ContinuousDistributionHandmade) + +from .drv_types import (FlorySchulz, Geometric, Hermite, Logarithmic, NegativeBinomial, Poisson, + Skellam, YuleSimon, Zeta, DiscreteRV, DiscreteDistributionHandmade) + +from .joint_rv_types import (JointRV, Dirichlet, + GeneralizedMultivariateLogGamma, GeneralizedMultivariateLogGammaOmega, + Multinomial, MultivariateBeta, MultivariateEwens, MultivariateT, + NegativeMultinomial, NormalGamma, MultivariateNormal, MultivariateLaplace, + marginal_distribution) + +from .stochastic_process_types import (StochasticProcess, + DiscreteTimeStochasticProcess, DiscreteMarkovChain, + TransitionMatrixOf, StochasticStateSpaceOf, GeneratorMatrixOf, + ContinuousMarkovChain, BernoulliProcess, PoissonProcess, WienerProcess, + GammaProcess) + +from .random_matrix_models import (CircularEnsemble, CircularUnitaryEnsemble, + CircularOrthogonalEnsemble, CircularSymplecticEnsemble, + GaussianEnsemble, GaussianUnitaryEnsemble, GaussianOrthogonalEnsemble, + GaussianSymplecticEnsemble, joint_eigen_distribution, + JointEigenDistribution, level_spacing_distribution) + +from .matrix_distributions import MatrixGamma, Wishart, MatrixNormal, MatrixStudentT + +from .symbolic_probability import (Probability, Expectation, Variance, + Covariance, Moment, CentralMoment) + +from .symbolic_multivariate_probability import (ExpectationMatrix, VarianceMatrix, + CrossCovarianceMatrix) diff --git a/janus/lib/python3.10/site-packages/sympy/stats/drv_types.py b/janus/lib/python3.10/site-packages/sympy/stats/drv_types.py new file mode 100644 index 0000000000000000000000000000000000000000..a2ce892168bdbbe24d8f8a5586e7295e07df25ea --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/stats/drv_types.py @@ -0,0 +1,835 @@ +""" + +Contains +======== +FlorySchulz +Geometric +Hermite +Logarithmic +NegativeBinomial +Poisson +Skellam +YuleSimon +Zeta +""" + + + +from sympy.concrete.summations import Sum +from sympy.core.basic import Basic +from sympy.core.function import Lambda +from sympy.core.numbers import I +from sympy.core.relational import Eq +from sympy.core.singleton import S +from sympy.core.symbol import Dummy +from sympy.core.sympify import sympify +from sympy.functions.combinatorial.factorials import (binomial, factorial) +from sympy.functions.elementary.exponential import (exp, log) +from sympy.functions.elementary.integers import floor +from sympy.functions.elementary.miscellaneous import sqrt +from sympy.functions.elementary.piecewise import Piecewise +from sympy.functions.special.bessel import besseli +from sympy.functions.special.beta_functions import beta +from sympy.functions.special.hyper import hyper +from sympy.functions.special.zeta_functions import (polylog, zeta) +from sympy.stats.drv import SingleDiscreteDistribution, SingleDiscretePSpace +from sympy.stats.rv import _value_check, is_random + + +__all__ = ['FlorySchulz', +'Geometric', +'Hermite', +'Logarithmic', +'NegativeBinomial', +'Poisson', +'Skellam', +'YuleSimon', +'Zeta' +] + + +def rv(symbol, cls, *args, **kwargs): + args = list(map(sympify, args)) + dist = cls(*args) + if kwargs.pop('check', True): + dist.check(*args) + pspace = SingleDiscretePSpace(symbol, dist) + if any(is_random(arg) for arg in args): + from sympy.stats.compound_rv import CompoundPSpace, CompoundDistribution + pspace = CompoundPSpace(symbol, CompoundDistribution(dist)) + return pspace.value + + +class DiscreteDistributionHandmade(SingleDiscreteDistribution): + _argnames = ('pdf',) + + def __new__(cls, pdf, set=S.Integers): + return Basic.__new__(cls, pdf, set) + + @property + def set(self): + return self.args[1] + + @staticmethod + def check(pdf, set): + x = Dummy('x') + val = Sum(pdf(x), (x, set._inf, set._sup)).doit() + _value_check(Eq(val, 1) != S.false, "The pdf is incorrect on the given set.") + + + +def DiscreteRV(symbol, density, set=S.Integers, **kwargs): + """ + Create a Discrete Random Variable given the following: + + Parameters + ========== + + symbol : Symbol + Represents name of the random variable. + density : Expression containing symbol + Represents probability density function. + set : set + Represents the region where the pdf is valid, by default is real line. + check : bool + If True, it will check whether the given density + integrates to 1 over the given set. If False, it + will not perform this check. Default is False. + + Examples + ======== + + >>> from sympy.stats import DiscreteRV, P, E + >>> from sympy import Rational, Symbol + >>> x = Symbol('x') + >>> n = 10 + >>> density = Rational(1, 10) + >>> X = DiscreteRV(x, density, set=set(range(n))) + >>> E(X) + 9/2 + >>> P(X>3) + 3/5 + + Returns + ======= + + RandomSymbol + + """ + set = sympify(set) + pdf = Piecewise((density, set.as_relational(symbol)), (0, True)) + pdf = Lambda(symbol, pdf) + # have a default of False while `rv` should have a default of True + kwargs['check'] = kwargs.pop('check', False) + return rv(symbol.name, DiscreteDistributionHandmade, pdf, set, **kwargs) + + +#------------------------------------------------------------------------------- +# Flory-Schulz distribution ------------------------------------------------------------ + +class FlorySchulzDistribution(SingleDiscreteDistribution): + _argnames = ('a',) + set = S.Naturals + + @staticmethod + def check(a): + _value_check((0 < a, a < 1), "a must be between 0 and 1") + + def pdf(self, k): + a = self.a + return (a**2 * k * (1 - a)**(k - 1)) + + def _characteristic_function(self, t): + a = self.a + return a**2*exp(I*t)/((1 + (a - 1)*exp(I*t))**2) + + def _moment_generating_function(self, t): + a = self.a + return a**2*exp(t)/((1 + (a - 1)*exp(t))**2) + + +def FlorySchulz(name, a): + r""" + Create a discrete random variable with a FlorySchulz distribution. + + The density of the FlorySchulz distribution is given by + + .. math:: + f(k) := (a^2) k (1 - a)^{k-1} + + Parameters + ========== + + a : A real number between 0 and 1 + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import density, E, variance, FlorySchulz + >>> from sympy import Symbol, S + + >>> a = S.One / 5 + >>> z = Symbol("z") + + >>> X = FlorySchulz("x", a) + + >>> density(X)(z) + (5/4)**(1 - z)*z/25 + + >>> E(X) + 9 + + >>> variance(X) + 40 + + References + ========== + + https://en.wikipedia.org/wiki/Flory%E2%80%93Schulz_distribution + """ + return rv(name, FlorySchulzDistribution, a) + + +#------------------------------------------------------------------------------- +# Geometric distribution ------------------------------------------------------------ + +class GeometricDistribution(SingleDiscreteDistribution): + _argnames = ('p',) + set = S.Naturals + + @staticmethod + def check(p): + _value_check((0 < p, p <= 1), "p must be between 0 and 1") + + def pdf(self, k): + return (1 - self.p)**(k - 1) * self.p + + def _characteristic_function(self, t): + p = self.p + return p * exp(I*t) / (1 - (1 - p)*exp(I*t)) + + def _moment_generating_function(self, t): + p = self.p + return p * exp(t) / (1 - (1 - p) * exp(t)) + + +def Geometric(name, p): + r""" + Create a discrete random variable with a Geometric distribution. + + Explanation + =========== + + The density of the Geometric distribution is given by + + .. math:: + f(k) := p (1 - p)^{k - 1} + + Parameters + ========== + + p : A probability between 0 and 1 + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Geometric, density, E, variance + >>> from sympy import Symbol, S + + >>> p = S.One / 5 + >>> z = Symbol("z") + + >>> X = Geometric("x", p) + + >>> density(X)(z) + (5/4)**(1 - z)/5 + + >>> E(X) + 5 + + >>> variance(X) + 20 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Geometric_distribution + .. [2] https://mathworld.wolfram.com/GeometricDistribution.html + + """ + return rv(name, GeometricDistribution, p) + + +#------------------------------------------------------------------------------- +# Hermite distribution --------------------------------------------------------- + + +class HermiteDistribution(SingleDiscreteDistribution): + _argnames = ('a1', 'a2') + set = S.Naturals0 + + @staticmethod + def check(a1, a2): + _value_check(a1.is_nonnegative, 'Parameter a1 must be >= 0.') + _value_check(a2.is_nonnegative, 'Parameter a2 must be >= 0.') + + def pdf(self, k): + a1, a2 = self.a1, self.a2 + term1 = exp(-(a1 + a2)) + j = Dummy("j", integer=True) + num = a1**(k - 2*j) * a2**j + den = factorial(k - 2*j) * factorial(j) + return term1 * Sum(num/den, (j, 0, k//2)).doit() + + def _moment_generating_function(self, t): + a1, a2 = self.a1, self.a2 + term1 = a1 * (exp(t) - 1) + term2 = a2 * (exp(2*t) - 1) + return exp(term1 + term2) + + def _characteristic_function(self, t): + a1, a2 = self.a1, self.a2 + term1 = a1 * (exp(I*t) - 1) + term2 = a2 * (exp(2*I*t) - 1) + return exp(term1 + term2) + +def Hermite(name, a1, a2): + r""" + Create a discrete random variable with a Hermite distribution. + + Explanation + =========== + + The density of the Hermite distribution is given by + + .. math:: + f(x):= e^{-a_1 -a_2}\sum_{j=0}^{\left \lfloor x/2 \right \rfloor} + \frac{a_{1}^{x-2j}a_{2}^{j}}{(x-2j)!j!} + + Parameters + ========== + + a1 : A Positive number greater than equal to 0. + a2 : A Positive number greater than equal to 0. + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Hermite, density, E, variance + >>> from sympy import Symbol + + >>> a1 = Symbol("a1", positive=True) + >>> a2 = Symbol("a2", positive=True) + >>> x = Symbol("x") + + >>> H = Hermite("H", a1=5, a2=4) + + >>> density(H)(2) + 33*exp(-9)/2 + + >>> E(H) + 13 + + >>> variance(H) + 21 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Hermite_distribution + + """ + + return rv(name, HermiteDistribution, a1, a2) + + +#------------------------------------------------------------------------------- +# Logarithmic distribution ------------------------------------------------------------ + +class LogarithmicDistribution(SingleDiscreteDistribution): + _argnames = ('p',) + + set = S.Naturals + + @staticmethod + def check(p): + _value_check((p > 0, p < 1), "p should be between 0 and 1") + + def pdf(self, k): + p = self.p + return (-1) * p**k / (k * log(1 - p)) + + def _characteristic_function(self, t): + p = self.p + return log(1 - p * exp(I*t)) / log(1 - p) + + def _moment_generating_function(self, t): + p = self.p + return log(1 - p * exp(t)) / log(1 - p) + + +def Logarithmic(name, p): + r""" + Create a discrete random variable with a Logarithmic distribution. + + Explanation + =========== + + The density of the Logarithmic distribution is given by + + .. math:: + f(k) := \frac{-p^k}{k \ln{(1 - p)}} + + Parameters + ========== + + p : A value between 0 and 1 + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Logarithmic, density, E, variance + >>> from sympy import Symbol, S + + >>> p = S.One / 5 + >>> z = Symbol("z") + + >>> X = Logarithmic("x", p) + + >>> density(X)(z) + -1/(5**z*z*log(4/5)) + + >>> E(X) + -1/(-4*log(5) + 8*log(2)) + + >>> variance(X) + -1/((-4*log(5) + 8*log(2))*(-2*log(5) + 4*log(2))) + 1/(-64*log(2)*log(5) + 64*log(2)**2 + 16*log(5)**2) - 10/(-32*log(5) + 64*log(2)) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Logarithmic_distribution + .. [2] https://mathworld.wolfram.com/LogarithmicDistribution.html + + """ + return rv(name, LogarithmicDistribution, p) + + +#------------------------------------------------------------------------------- +# Negative binomial distribution ------------------------------------------------------------ + +class NegativeBinomialDistribution(SingleDiscreteDistribution): + _argnames = ('r', 'p') + set = S.Naturals0 + + @staticmethod + def check(r, p): + _value_check(r > 0, 'r should be positive') + _value_check((p > 0, p < 1), 'p should be between 0 and 1') + + def pdf(self, k): + r = self.r + p = self.p + + return binomial(k + r - 1, k) * (1 - p)**r * p**k + + def _characteristic_function(self, t): + r = self.r + p = self.p + + return ((1 - p) / (1 - p * exp(I*t)))**r + + def _moment_generating_function(self, t): + r = self.r + p = self.p + + return ((1 - p) / (1 - p * exp(t)))**r + +def NegativeBinomial(name, r, p): + r""" + Create a discrete random variable with a Negative Binomial distribution. + + Explanation + =========== + + The density of the Negative Binomial distribution is given by + + .. math:: + f(k) := \binom{k + r - 1}{k} (1 - p)^r p^k + + Parameters + ========== + + r : A positive value + p : A value between 0 and 1 + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import NegativeBinomial, density, E, variance + >>> from sympy import Symbol, S + + >>> r = 5 + >>> p = S.One / 5 + >>> z = Symbol("z") + + >>> X = NegativeBinomial("x", r, p) + + >>> density(X)(z) + 1024*binomial(z + 4, z)/(3125*5**z) + + >>> E(X) + 5/4 + + >>> variance(X) + 25/16 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Negative_binomial_distribution + .. [2] https://mathworld.wolfram.com/NegativeBinomialDistribution.html + + """ + return rv(name, NegativeBinomialDistribution, r, p) + + +#------------------------------------------------------------------------------- +# Poisson distribution ------------------------------------------------------------ + +class PoissonDistribution(SingleDiscreteDistribution): + _argnames = ('lamda',) + + set = S.Naturals0 + + @staticmethod + def check(lamda): + _value_check(lamda > 0, "Lambda must be positive") + + def pdf(self, k): + return self.lamda**k / factorial(k) * exp(-self.lamda) + + def _characteristic_function(self, t): + return exp(self.lamda * (exp(I*t) - 1)) + + def _moment_generating_function(self, t): + return exp(self.lamda * (exp(t) - 1)) + + +def Poisson(name, lamda): + r""" + Create a discrete random variable with a Poisson distribution. + + Explanation + =========== + + The density of the Poisson distribution is given by + + .. math:: + f(k) := \frac{\lambda^{k} e^{- \lambda}}{k!} + + Parameters + ========== + + lamda : Positive number, a rate + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Poisson, density, E, variance + >>> from sympy import Symbol, simplify + + >>> rate = Symbol("lambda", positive=True) + >>> z = Symbol("z") + + >>> X = Poisson("x", rate) + + >>> density(X)(z) + lambda**z*exp(-lambda)/factorial(z) + + >>> E(X) + lambda + + >>> simplify(variance(X)) + lambda + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Poisson_distribution + .. [2] https://mathworld.wolfram.com/PoissonDistribution.html + + """ + return rv(name, PoissonDistribution, lamda) + + +# ----------------------------------------------------------------------------- +# Skellam distribution -------------------------------------------------------- + + +class SkellamDistribution(SingleDiscreteDistribution): + _argnames = ('mu1', 'mu2') + set = S.Integers + + @staticmethod + def check(mu1, mu2): + _value_check(mu1 >= 0, 'Parameter mu1 must be >= 0') + _value_check(mu2 >= 0, 'Parameter mu2 must be >= 0') + + def pdf(self, k): + (mu1, mu2) = (self.mu1, self.mu2) + term1 = exp(-(mu1 + mu2)) * (mu1 / mu2) ** (k / 2) + term2 = besseli(k, 2 * sqrt(mu1 * mu2)) + return term1 * term2 + + def _cdf(self, x): + raise NotImplementedError( + "Skellam doesn't have closed form for the CDF.") + + def _characteristic_function(self, t): + (mu1, mu2) = (self.mu1, self.mu2) + return exp(-(mu1 + mu2) + mu1 * exp(I * t) + mu2 * exp(-I * t)) + + def _moment_generating_function(self, t): + (mu1, mu2) = (self.mu1, self.mu2) + return exp(-(mu1 + mu2) + mu1 * exp(t) + mu2 * exp(-t)) + + +def Skellam(name, mu1, mu2): + r""" + Create a discrete random variable with a Skellam distribution. + + Explanation + =========== + + The Skellam is the distribution of the difference N1 - N2 + of two statistically independent random variables N1 and N2 + each Poisson-distributed with respective expected values mu1 and mu2. + + The density of the Skellam distribution is given by + + .. math:: + f(k) := e^{-(\mu_1+\mu_2)}(\frac{\mu_1}{\mu_2})^{k/2}I_k(2\sqrt{\mu_1\mu_2}) + + Parameters + ========== + + mu1 : A non-negative value + mu2 : A non-negative value + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Skellam, density, E, variance + >>> from sympy import Symbol, pprint + + >>> z = Symbol("z", integer=True) + >>> mu1 = Symbol("mu1", positive=True) + >>> mu2 = Symbol("mu2", positive=True) + >>> X = Skellam("x", mu1, mu2) + + >>> pprint(density(X)(z), use_unicode=False) + z + - + 2 + /mu1\ -mu1 - mu2 / _____ _____\ + |---| *e *besseli\z, 2*\/ mu1 *\/ mu2 / + \mu2/ + >>> E(X) + mu1 - mu2 + >>> variance(X).expand() + mu1 + mu2 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Skellam_distribution + + """ + return rv(name, SkellamDistribution, mu1, mu2) + + +#------------------------------------------------------------------------------- +# Yule-Simon distribution ------------------------------------------------------------ + +class YuleSimonDistribution(SingleDiscreteDistribution): + _argnames = ('rho',) + set = S.Naturals + + @staticmethod + def check(rho): + _value_check(rho > 0, 'rho should be positive') + + def pdf(self, k): + rho = self.rho + return rho * beta(k, rho + 1) + + def _cdf(self, x): + return Piecewise((1 - floor(x) * beta(floor(x), self.rho + 1), x >= 1), (0, True)) + + def _characteristic_function(self, t): + rho = self.rho + return rho * hyper((1, 1), (rho + 2,), exp(I*t)) * exp(I*t) / (rho + 1) + + def _moment_generating_function(self, t): + rho = self.rho + return rho * hyper((1, 1), (rho + 2,), exp(t)) * exp(t) / (rho + 1) + + +def YuleSimon(name, rho): + r""" + Create a discrete random variable with a Yule-Simon distribution. + + Explanation + =========== + + The density of the Yule-Simon distribution is given by + + .. math:: + f(k) := \rho B(k, \rho + 1) + + Parameters + ========== + + rho : A positive value + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import YuleSimon, density, E, variance + >>> from sympy import Symbol, simplify + + >>> p = 5 + >>> z = Symbol("z") + + >>> X = YuleSimon("x", p) + + >>> density(X)(z) + 5*beta(z, 6) + + >>> simplify(E(X)) + 5/4 + + >>> simplify(variance(X)) + 25/48 + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Yule%E2%80%93Simon_distribution + + """ + return rv(name, YuleSimonDistribution, rho) + + +#------------------------------------------------------------------------------- +# Zeta distribution ------------------------------------------------------------ + +class ZetaDistribution(SingleDiscreteDistribution): + _argnames = ('s',) + set = S.Naturals + + @staticmethod + def check(s): + _value_check(s > 1, 's should be greater than 1') + + def pdf(self, k): + s = self.s + return 1 / (k**s * zeta(s)) + + def _characteristic_function(self, t): + return polylog(self.s, exp(I*t)) / zeta(self.s) + + def _moment_generating_function(self, t): + return polylog(self.s, exp(t)) / zeta(self.s) + + +def Zeta(name, s): + r""" + Create a discrete random variable with a Zeta distribution. + + Explanation + =========== + + The density of the Zeta distribution is given by + + .. math:: + f(k) := \frac{1}{k^s \zeta{(s)}} + + Parameters + ========== + + s : A value greater than 1 + + Returns + ======= + + RandomSymbol + + Examples + ======== + + >>> from sympy.stats import Zeta, density, E, variance + >>> from sympy import Symbol + + >>> s = 5 + >>> z = Symbol("z") + + >>> X = Zeta("x", s) + + >>> density(X)(z) + 1/(z**5*zeta(5)) + + >>> E(X) + pi**4/(90*zeta(5)) + + >>> variance(X) + -pi**8/(8100*zeta(5)**2) + zeta(3)/zeta(5) + + References + ========== + + .. [1] https://en.wikipedia.org/wiki/Zeta_distribution + + """ + return rv(name, ZetaDistribution, s) diff --git a/janus/lib/python3.10/site-packages/sympy/stats/joint_rv.py b/janus/lib/python3.10/site-packages/sympy/stats/joint_rv.py new file mode 100644 index 0000000000000000000000000000000000000000..d147942f08b998e167b246628360fa27fc8ef348 --- /dev/null +++ b/janus/lib/python3.10/site-packages/sympy/stats/joint_rv.py @@ -0,0 +1,426 @@ +""" +Joint Random Variables Module + +See Also +======== +sympy.stats.rv +sympy.stats.frv +sympy.stats.crv +sympy.stats.drv +""" +from math import prod + +from sympy.core.basic import Basic +from sympy.core.function import Lambda +from sympy.core.singleton import S +from sympy.core.symbol import (Dummy, Symbol) +from sympy.core.sympify import sympify +from sympy.sets.sets import ProductSet +from sympy.tensor.indexed import Indexed +from sympy.concrete.products import Product +from sympy.concrete.summations import Sum, summation +from sympy.core.containers import Tuple +from sympy.integrals.integrals import Integral, integrate +from sympy.matrices import ImmutableMatrix, matrix2numpy, list2numpy +from sympy.stats.crv import SingleContinuousDistribution, SingleContinuousPSpace +from sympy.stats.drv import SingleDiscreteDistribution, SingleDiscretePSpace +from sympy.stats.rv import (ProductPSpace, NamedArgsMixin, Distribution, + ProductDomain, RandomSymbol, random_symbols, + SingleDomain, _symbol_converter) +from sympy.utilities.iterables import iterable +from sympy.utilities.misc import filldedent +from sympy.external import import_module + +# __all__ = ['marginal_distribution'] + +class JointPSpace(ProductPSpace): + """ + Represents a joint probability space. Represented using symbols for + each component and a distribution. + """ + def __new__(cls, sym, dist): + if isinstance(dist, SingleContinuousDistribution): + return SingleContinuousPSpace(sym, dist) + if isinstance(dist, SingleDiscreteDistribution): + return SingleDiscretePSpace(sym, dist) + sym = _symbol_converter(sym) + return Basic.__new__(cls, sym, dist) + + @property + def set(self): + return self.domain.set + + @property + def symbol(self): + return self.args[0] + + @property + def distribution(self): + return self.args[1] + + @property + def value(self): + return JointRandomSymbol(self.symbol, self) + + @property + def component_count(self): + _set = self.distribution.set + if isinstance(_set, ProductSet): + return S(len(_set.args)) + elif isinstance(_set, Product): + return _set.limits[0][-1] + return S.One + + @property + def pdf(self): + sym = [Indexed(self.symbol, i) for i in range(self.component_count)] + return self.distribution(*sym) + + @property + def domain(self): + rvs = random_symbols(self.distribution) + if not rvs: + return SingleDomain(self.symbol, self.distribution.set) + return ProductDomain(*[rv.pspace.domain for rv in rvs]) + + def component_domain(self, index): + return self.set.args[index] + + def marginal_distribution(self, *indices): + count = self.component_count + if count.atoms(Symbol): + raise ValueError("Marginal distributions cannot be computed " + "for symbolic dimensions. It is a work under progress.") + orig = [Indexed(self.symbol, i) for i in range(count)] + all_syms = [Symbol(str(i)) for i in orig] + replace_dict = dict(zip(all_syms, orig)) + sym = tuple(Symbol(str(Indexed(self.symbol, i))) for i in indices) + limits = [[i,] for i in all_syms if i not in sym] + index = 0 + for i in range(count): + if i not in indices: + limits[index].append(self.distribution.set.args[i]) + limits[index] = tuple(limits[index]) + index += 1 + if self.distribution.is_Continuous: + f = Lambda(sym, integrate(self.distribution(*all_syms), *limits)) + elif self.distribution.is_Discrete: + f = Lambda(sym, summation(self.distribution(*all_syms), *limits)) + return f.xreplace(replace_dict) + + def compute_expectation(self, expr, rvs=None, evaluate=False, **kwargs): + syms = tuple(self.value[i] for i in range(self.component_count)) + rvs = rvs or syms + if not any(i in rvs for i in syms): + return expr + expr = expr*self.pdf + for rv in rvs: + if isinstance(rv, Indexed): + expr = expr.xreplace({rv: Indexed(str(rv.base), rv.args[1])}) + elif isinstance(rv, RandomSymbol): + expr = expr.xreplace({rv: rv.symbol}) + if self.value in random_symbols(expr): + raise NotImplementedError(filldedent(''' + Expectations of expression with unindexed joint random symbols + cannot be calculated yet.''')) + limits = tuple((Indexed(str(rv.base),rv.args[1]), + self.distribution.set.args[rv.args[1]]) for rv in syms) + return Integral(expr, *limits) + + def where(self, condition): + raise NotImplementedError() + + def compute_density(self, expr): + raise NotImplementedError() + + def sample(self, size=(), library='scipy', seed=None): + """ + Internal sample method + + Returns dictionary mapping RandomSymbol to realization value. + """ + return {RandomSymbol(self.symbol, self): self.distribution.sample(size, + library=library, seed=seed)} + + def probability(self, condition): + raise NotImplementedError() + + +class SampleJointScipy: + """Returns the sample from scipy of the given distribution""" + def __new__(cls, dist, size, seed=None): + return cls._sample_scipy(dist, size, seed) + + @classmethod + def _sample_scipy(cls, dist, size, seed): + """Sample from SciPy.""" + + import numpy + if seed is None or isinstance(seed, int): + rand_state = numpy.random.default_rng(seed=seed) + else: + rand_state = seed + from scipy import stats as scipy_stats + scipy_rv_map = { + 'MultivariateNormalDistribution': lambda dist, size: scipy_stats.multivariate_normal.rvs( + mean=matrix2numpy(dist.mu).flatten(), + cov=matrix2numpy(dist.sigma), size=size, random_state=rand_state), + 'MultivariateBetaDistribution': lambda dist, size: scipy_stats.dirichlet.rvs( + alpha=list2numpy(dist.alpha, float).flatten(), size=size, random_state=rand_state), + 'MultinomialDistribution': lambda dist, size: scipy_stats.multinomial.rvs( + n=int(dist.n), p=list2numpy(dist.p, float).flatten(), size=size, random_state=rand_state) + } + + sample_shape = { + 'MultivariateNormalDistribution': lambda dist: matrix2numpy(dist.mu).flatten().shape, + 'MultivariateBetaDistribution': lambda dist: list2numpy(dist.alpha).flatten().shape, + 'MultinomialDistribution': lambda dist: list2numpy(dist.p).flatten().shape + } + + dist_list = scipy_rv_map.keys() + + if dist.__class__.__name__ not in dist_list: + return None + + samples = scipy_rv_map[dist.__class__.__name__](dist, size) + return samples.reshape(size + sample_shape[dist.__class__.__name__](dist)) + +class SampleJointNumpy: + """Returns the sample from numpy of the given distribution""" + + def __new__(cls, dist, size, seed=None): + return cls._sample_numpy(dist, size, seed) + + @classmethod + def _sample_numpy(cls, dist, size, seed): + """Sample from NumPy.""" + + import numpy + if seed is None or isinstance(seed, int): + rand_state = numpy.random.default_rng(seed=seed) + else: + rand_state = seed + numpy_rv_map = { + 'MultivariateNormalDistribution': lambda dist, size: rand_state.multivariate_normal( + mean=matrix2numpy(dist.mu, float).flatten(), + cov=matrix2numpy(dist.sigma, float), size=size), + 'MultivariateBetaDistribution': lambda dist, size: rand_state.dirichlet( + alpha=list2numpy(dist.alpha, float).flatten(), size=size), + 'MultinomialDistribution': lambda dist, size: rand_state.multinomial( + n=int(dist.n), pvals=list2numpy(dist.p, float).flatten(), size=size) + } + + sample_shape = { + 'MultivariateNormalDistribution': lambda dist: matrix2numpy(dist.mu).flatten().shape, + 'MultivariateBetaDistribution': lambda dist: list2numpy(dist.alpha).flatten().shape, + 'MultinomialDistribution': lambda dist: list2numpy(dist.p).flatten().shape + } + + dist_list = numpy_rv_map.keys() + + if dist.__class__.__name__ not in dist_list: + return None + + samples = numpy_rv_map[dist.__class__.__name__](dist, prod(size)) + return samples.reshape(size + sample_shape[dist.__class__.__name__](dist)) + +class SampleJointPymc: + """Returns the sample from pymc of the given distribution""" + + def __new__(cls, dist, size, seed=None): + return cls._sample_pymc(dist, size, seed) + + @classmethod + def _sample_pymc(cls, dist, size, seed): + """Sample from PyMC.""" + + try: + import pymc + except ImportError: + import pymc3 as pymc + pymc_rv_map = { + 'MultivariateNormalDistribution': lambda dist: + pymc.MvNormal('X', mu=matrix2numpy(dist.mu, float).flatten(), + cov=matrix2numpy(dist.sigma, float), shape=(1, dist.mu.shape[0])), + 'MultivariateBetaDistribution': lambda dist: + pymc.Dirichlet('X', a=list2numpy(dist.alpha, float).flatten()), + 'MultinomialDistribution': lambda dist: + pymc.Multinomial('X', n=int(dist.n), + p=list2numpy(dist.p, float).flatten(), shape=(1, len(dist.p))) + } + + sample_shape = { + 'MultivariateNormalDistribution': lambda dist: matrix2numpy(dist.mu).flatten().shape, + 'MultivariateBetaDistribution': lambda dist: list2numpy(dist.alpha).flatten().shape, + 'MultinomialDistribution': lambda dist: list2numpy(dist.p).flatten().shape + } + + dist_list = pymc_rv_map.keys() + + if dist.__class__.__name__ not in dist_list: + return None + + import logging + logging.getLogger("pymc3").setLevel(logging.ERROR) + with pymc.Model(): + pymc_rv_map[dist.__class__.__name__](dist) + samples = pymc.sample(draws=prod(size), chains=1, progressbar=False, random_seed=seed, return_inferencedata=False, compute_convergence_checks=False)[:]['X'] + return samples.reshape(size + sample_shape[dist.__class__.__name__](dist)) + + +_get_sample_class_jrv = { + 'scipy': SampleJointScipy, + 'pymc3': SampleJointPymc, + 'pymc': SampleJointPymc, + 'numpy': SampleJointNumpy +} + +class JointDistribution(Distribution, NamedArgsMixin): + """ + Represented by the random variables part of the joint distribution. + Contains methods for PDF, CDF, sampling, marginal densities, etc. + """ + + _argnames = ('pdf', ) + + def __new__(cls, *args): + args = list(map(sympify, args)) + for i in range(len(args)): + if isinstance(args[i], list): + args[i] = ImmutableMatrix(args[i]) + return Basic.__new__(cls, *args) + + @property + def domain(self): + return ProductDomain(self.symbols) + + @property + def pdf(self): + return self.density.args[1] + + def cdf(self, other): + if not isinstance(other, dict): + raise ValueError("%s should be of type dict, got %s"%(other, type(other))) + rvs = other.keys() + _set = self.domain.set.sets + expr = self.pdf(tuple(i.args[0] for i in self.symbols)) + for i in range(len(other)): + if rvs[i].is_Continuous: + density = Integral(expr, (rvs[i], _set[i].inf, + other[rvs[i]])) + elif rvs[i].is_Discrete: + density = Sum(expr, (rvs[i], _set[i].inf, + other[rvs[i]])) + return density + + def sample(self, size=(), library='scipy', seed=None): + """ A random realization from the distribution """ + + libraries = ('scipy', 'numpy', 'pymc3', 'pymc') + if library not in libraries: + raise NotImplementedError("Sampling from %s is not supported yet." + % str(library)) + if not import_module(library): + raise ValueError("Failed to import %s" % library) + + samps = _get_sample_class_jrv[library](self, size, seed=seed) + + if samps is not None: + return samps + raise NotImplementedError( + "Sampling for %s is not currently implemented from %s" + % (self.__class__.__name__, library) + ) + + def __call__(self, *args): + return self.pdf(*args) + +class JointRandomSymbol(RandomSymbol): + """ + Representation of random symbols with joint probability distributions + to allow indexing." + """ + def __getitem__(self, key): + if isinstance(self.pspace, JointPSpace): + if (self.pspace.component_count <= key) == True: + raise ValueError("Index keys for %s can only up to %s." % + (self.name, self.pspace.component_count - 1)) + return Indexed(self, key) + + + +class MarginalDistribution(Distribution): + """ + Represents the marginal distribution of a joint probability space. + + Initialised using a probability distribution and random variables(or + their indexed components) which should be a part of the resultant + distribution. + """ + + def __new__(cls, dist, *rvs): + if len(rvs) == 1 and iterable(rvs[0]): + rvs = tuple(rvs[0]) + if not all(isinstance(rv, (Indexed, RandomSymbol)) for rv in rvs): + raise ValueError(filldedent('''Marginal distribution can be + intitialised only in terms of random variables or indexed random + variables''')) + rvs = Tuple.fromiter(rv for rv in rvs) + if not isinstance(dist, JointDistribution) and len(random_symbols(dist)) == 0: + return dist + return Basic.__new__(cls, dist, rvs) + + def check(self): + pass + + @property + def set(self): + rvs = [i for i in self.args[1] if isinstance(i, RandomSymbol)] + return ProductSet(*[rv.pspace.set for rv in rvs]) + + @property + def symbols(self): + rvs = self.args[1] + return {rv.pspace.symbol for rv in rvs} + + def pdf(self, *x): + expr, rvs = self.args[0], self.args[1] + marginalise_out = [i for i in random_symbols(expr) if i not in rvs] + if isinstance(expr, JointDistribution): + count = len(expr.domain.args) + x = Dummy('x', real=True) + syms = tuple(Indexed(x, i) for i in count) + expr = expr.pdf(syms) + else: + syms = tuple(rv.pspace.symbol if isinstance(rv, RandomSymbol) else rv.args[0] for rv in rvs) + return Lambda(syms, self.compute_pdf(expr, marginalise_out))(*x) + + def compute_pdf(self, expr, rvs): + for rv in rvs: + lpdf = 1 + if isinstance(rv, RandomSymbol): + lpdf = rv.pspace.pdf + expr = self.marginalise_out(expr*lpdf, rv) + return expr + + def marginalise_out(self, expr, rv): + from sympy.concrete.summations import Sum + if isinstance(rv, RandomSymbol): + dom = rv.pspace.set + elif isinstance(rv, Indexed): + dom = rv.base.component_domain( + rv.pspace.component_domain(rv.args[1])) + expr = expr.xreplace({rv: rv.pspace.symbol}) + if rv.pspace.is_Continuous: + #TODO: Modify to support integration + #for all kinds of sets. + expr = Integral(expr, (rv.pspace.symbol, dom)) + elif rv.pspace.is_Discrete: + #incorporate this into `Sum`/`summation` + if dom in (S.Integers, S.Naturals, S.Naturals0): + dom = (dom.inf, dom.sup) + expr = Sum(expr, (rv.pspace.symbol, dom)) + return expr + + def __call__(self, *args): + return self.pdf(*args)