def cholesky(a):
"""Cholesky decomposition.
Decompose a given two-dimensional square matrix into ``L * L.T``,
where ``L`` is a lower-triangular matrix and ``.T`` is a conjugate
transpose operator.
Args:
a (cupy.ndarray): The input matrix with dimension ``(N, N)``
Returns:
cupy.ndarray: The lower-triangular matrix.
.. warning::
This function calls one or more cuSOLVER routine(s) which may yield
invalid results if input conditions are not met.
To detect these invalid results, you can set the `linalg`
configuration to a value that is not `ignore` in
:func:`cupyx.errstate` or :func:`cupyx.seterr`.
.. seealso:: :func:`numpy.linalg.cholesky`
"""
# TODO(Saito): Current implementation only accepts two-dimensional arrays
util._assert_cupy_array(a)
util._assert_rank2(a)
util._assert_nd_squareness(a)
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
x = a.astype(dtype, order='C', copy=True)
n = len(a)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
potrf = cusolver.spotrf
potrf_bufferSize = cusolver.spotrf_bufferSize
elif dtype == 'd':
potrf = cusolver.dpotrf
potrf_bufferSize = cusolver.dpotrf_bufferSize
elif dtype == 'F':
potrf = cusolver.cpotrf
potrf_bufferSize = cusolver.cpotrf_bufferSize
else: # dtype == 'D':
potrf = cusolver.zpotrf
potrf_bufferSize = cusolver.zpotrf_bufferSize
buffersize = potrf_bufferSize(handle, cublas.CUBLAS_FILL_MODE_UPPER, n,
x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=dtype)
potrf(handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n,
workspace.data.ptr, buffersize, dev_info.data.ptr)
cupy.linalg.util._check_cusolver_dev_info_if_synchronization_allowed(
potrf, dev_info)
util._tril(x, k=0)
return x
def cholesky(a):
"""Cholesky decomposition.
Decompose a given two-dimensional square matrix into ``L * L.T``,
where ``L`` is a lower-triangular matrix and ``.T`` is a conjugate
transpose operator. Note that in the current implementation ``a`` must be
a real matrix, and only float32 and float64 are supported.
Args:
a (cupy.ndarray): The input matrix with dimension ``(N, N)``
Returns:
cupy.ndarray: The lower-triangular matrix.
.. seealso:: :func:`numpy.linalg.cholesky`
"""
if not cuda.cusolver_enabled:
raise RuntimeError('Current cupy only supports cusolver in CUDA 8.0')
# TODO(Saito): Current implementation only accepts two-dimensional arrays
util._assert_cupy_array(a)
util._assert_rank2(a)
util._assert_nd_squareness(a)
# Cast to float32 or float64
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.find_common_type((a.dtype.char, 'f'), ()).char
x = a.astype(dtype, order='C', copy=True)
n = len(a)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
buffersize = cusolver.spotrf_bufferSize(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=numpy.float32)
cusolver.spotrf(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n,
workspace.data.ptr, buffersize, dev_info.data.ptr)
else: # dtype == 'd'
buffersize = cusolver.dpotrf_bufferSize(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=numpy.float64)
cusolver.dpotrf(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, x.data.ptr, n,
workspace.data.ptr, buffersize, dev_info.data.ptr)
status = int(dev_info[0])
if status > 0:
raise linalg.LinAlgError(
'The leading minor of order {} '
'is not positive definite'.format(status))
elif status < 0:
raise linalg.LinAlgError(
'Parameter error (maybe caused by a bug in cupy.linalg?)')
util._tril(x, k=0)
return x