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import os
import numpy
from numpy import linalg
import cupy
import cupy._util
from cupy import _core
import cupyx
_default_precision = os.getenv('CUPY_DEFAULT_PRECISION')
# The helper functions raise LinAlgError if the conditions are not met.
def _assert_cupy_array(*arrays):
for a in arrays:
if not isinstance(a, cupy._core.ndarray):
raise linalg.LinAlgError(
'cupy.linalg only supports cupy.ndarray')
def _assert_2d(*arrays):
for a in arrays:
if a.ndim != 2:
raise linalg.LinAlgError(
'{}-dimensional array given. Array must be '
'two-dimensional'.format(a.ndim))
def _assert_stacked_2d(*arrays):
for a in arrays:
if a.ndim < 2:
raise linalg.LinAlgError(
'{}-dimensional array given. Array must be '
'at least two-dimensional'.format(a.ndim))
def _assert_stacked_square(*arrays):
"""Assert that stacked matrices are square matrices
Precondition: `arrays` are at least 2d. The caller should assert it
beforehand. For example,
>>> def det(a):
... _assert_stacked_2d(a)
... _assert_stacked_square(a)
... ...
"""
for a in arrays:
m, n = a.shape[-2:]
if m != n:
raise linalg.LinAlgError(
'Last 2 dimensions of the array must be square')
def linalg_common_type(*arrays, reject_float16=True):
"""Common type for linalg
The logic is intended to be equivalent with
`numpy.linalg.linalg._commonType`.
The differences from `numpy.common_type` are
- to accept ``bool_`` arrays, and
- to reject ``float16`` arrays.
Args:
*arrays (ndarray): Input arrays.
reject_float16 (bool): Flag to follow NumPy to raise TypeError for
``float16`` inputs.
Returns:
compute_dtype (dtype): The precision to be used in linalg calls.
result_dtype (dtype): The dtype of (possibly complex) output(s).
"""
dtypes = [arr.dtype for arr in arrays]
if reject_float16 and 'float16' in dtypes:
raise TypeError('float16 is unsupported in linalg')
if _default_precision is not None:
cupy._util.experimental('CUPY_DEFAULT_PRECISION')
if _default_precision not in ('32', '64'):
raise ValueError(
'invalid CUPY_DEFAULT_PRECISION: {}'.format(
_default_precision))
default = 'float' + _default_precision
else:
default = 'float64'
compute_dtype = _common_type_internal(default, *dtypes)
# No fp16 cuSOLVER routines
if compute_dtype == 'float16':
compute_dtype = numpy.dtype('float32')
# numpy casts integer types to float64
result_dtype = _common_type_internal('float64', *dtypes)
return compute_dtype, result_dtype
def _common_type_internal(default_dtype, *dtypes):
inexact_dtypes = [
dtype if dtype.kind in 'fc' else default_dtype
for dtype in dtypes]
return numpy.result_type(*inexact_dtypes)
def _check_cusolver_dev_info_if_synchronization_allowed(routine, dev_info):
# `dev_info` contains integers, the status code of a cuSOLVER
# routine call. It is referred to as "infoArray" or "devInfo" in the
# official cuSOLVER documentation.
assert isinstance(dev_info, _core.ndarray)
config_linalg = cupyx._ufunc_config.get_config_linalg()
# Only 'ignore' and 'raise' are currently supported.
if config_linalg == 'ignore':
return
try:
name = routine.__name__
except AttributeError:
name = routine # routine is a str
assert config_linalg == 'raise'
if (dev_info != 0).any():
raise linalg.LinAlgError(
'Error reported by {} in cuSOLVER. devInfo = {}. Please refer'
' to the cuSOLVER documentation.'.format(
name, dev_info))
def _check_cublas_info_array_if_synchronization_allowed(routine, info_array):
# `info_array` contains integers, the status codes of a cuBLAS routine
# call. It is referrd to as "infoArray" or "devInfoArray" in the official
# cuBLAS documentation.
assert isinstance(info_array, _core.ndarray)
assert info_array.ndim == 1
config_linalg = cupyx._ufunc_config.get_config_linalg()
# Only 'ignore' and 'raise' are currently supported.
if config_linalg == 'ignore':
return
assert config_linalg == 'raise'
if (info_array != 0).any():
raise linalg.LinAlgError(
'Error reported by {} in cuBLAS. infoArray/devInfoArray = {}.'
' Please refer to the cuBLAS documentation.'.format(
routine.__name__, info_array))
_tril_kernel = _core.ElementwiseKernel(
'int64 k', 'S x',
'x = (_ind.get()[1] - _ind.get()[0] <= k) ? x : 0',
'cupy_tril_kernel',
reduce_dims=False
)
def _tril(x, k=0):
_tril_kernel(k, x)
return x
# support a batch of matrices
_triu_kernel = _core.ElementwiseKernel(
'int64 k', 'S x',
'x = (_ind.get()[_ind.ndim - 1] - _ind.get()[_ind.ndim - 2] >= k) ? x : 0',
'cupy_triu_kernel',
reduce_dims=False
)
def _triu(x, k=0):
_triu_kernel(k, x)
return x
def stacked_identity(batch_shape, n, dtype):
shape = batch_shape + (n, n)
idx = cupy.arange(n)
x = cupy.zeros(shape, dtype)
x[..., idx, idx] = 1
return x
def stacked_identity_like(x):
"""
Precondition: ``x`` is `cupy.ndarray` of shape ``(..., N, N)``
"""
n = x.shape[-1]
idx = cupy.arange(n)
x = cupy.zeros_like(x)
x[..., idx, idx] = 1
return x