def solve(a, b):
"""Solves a linear matrix equation.
It computes the exact solution of ``x`` in ``ax = b``,
where ``a`` is a square and full rank matrix.
Args:
a (cupy.ndarray): The matrix with dimension ``(..., M, M)``.
b (cupy.ndarray): The matrix with dimension ``(...,M)`` or
``(..., M, K)``.
Returns:
cupy.ndarray:
The matrix with dimension ``(..., M)`` or ``(..., M, K)``.
.. 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.solve`
"""
if a.ndim > 2 and a.shape[-1] <= get_batched_gesv_limit():
# Note: There is a low performance issue in batched_gesv when matrix is
# large, so it is not used in such cases.
return batched_gesv(a, b)
# TODO(kataoka): Move the checks to the beginning
_util._assert_cupy_array(a, b)
_util._assert_stacked_2d(a)
_util._assert_stacked_square(a)
if not ((a.ndim == b.ndim or a.ndim == b.ndim + 1)
and a.shape[:-1] == b.shape[:a.ndim - 1]):
raise ValueError(
'a must have (..., M, M) shape and b must have (..., M) '
'or (..., M, K)')
dtype, out_dtype = _util.linalg_common_type(a, b)
if a.ndim == 2:
# prevent 'a' and 'b' to be overwritten
a = a.astype(dtype, copy=True, order='F')
b = b.astype(dtype, copy=True, order='F')
cupyx.lapack.gesv(a, b)
return b.astype(out_dtype, copy=False)
# prevent 'a' to be overwritten
a = a.astype(dtype, copy=True, order='C')
x = cupy.empty_like(b, dtype=out_dtype)
shape = a.shape[:-2]
for i in range(numpy.prod(shape)):
index = numpy.unravel_index(i, shape)
# prevent 'b' to be overwritten
bi = b[index].astype(dtype, copy=True, order='F')
cupyx.lapack.gesv(a[index], bi)
x[index] = bi
return x
def solve(a, b):
"""Solves a linear matrix equation.
It computes the exact solution of ``x`` in ``ax = b``,
where ``a`` is a square and full rank matrix.
Args:
a (cupy.ndarray): The matrix with dimension ``(..., M, M)``.
b (cupy.ndarray): The matrix with dimension ``(...,M)`` or
``(..., M, K)``.
Returns:
cupy.ndarray:
The matrix with dimension ``(..., M)`` or ``(..., M, K)``.
.. 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.solve`
"""
if a.ndim > 2 and a.shape[-1] <= get_batched_gesv_limit():
# Note: There is a low performance issue in batched_gesv when matrix is
# large, so it is not used in such cases.
return batched_gesv(a, b)
_util._assert_cupy_array(a, b)
_util._assert_nd_squareness(a)
if not ((a.ndim == b.ndim or a.ndim == b.ndim + 1)
and a.shape[:-1] == b.shape[:a.ndim - 1]):
raise ValueError(
'a must have (..., M, M) shape and b must have (..., M) '
'or (..., M, K)')
# Cast to float32 or float64
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype
else:
dtype = numpy.promote_types(a.dtype.char, 'f')
a = a.astype(dtype)
b = b.astype(dtype)
if a.ndim == 2:
return cupyx.lapack.gesv(a, b)
x = cupy.empty_like(b)
shape = a.shape[:-2]
for i in range(numpy.prod(shape)):
index = numpy.unravel_index(i, shape)
x[index] = cupyx.lapack.gesv(a[index], b[index])
return x
def test_batched_gesv(self):
x = cublas.batched_gesv(self.a, self.b)
cupy.testing.assert_allclose(x, self.x_ref,
rtol=self.tol, atol=self.tol)
