def invh(a):
"""Compute the inverse of a Hermitian matrix.
This function computes a inverse of a real symmetric or complex hermitian
positive-definite matrix using Cholesky factorization. If matrix ``a`` is
not positive definite, Cholesky factorization fails and it raises an error.
Args:
a (cupy.ndarray): Real symmetric or complex hermitian maxtix.
Returns:
cupy.ndarray: The inverse of matrix ``a``.
"""
_util._assert_cupy_array(a)
_util._assert_nd_squareness(a)
# TODO: Remove this assert once cusolver supports nrhs > 1 for potrsBatched
_util._assert_rank2(a)
n = a.shape[-1]
identity_matrix = cupy.eye(n, dtype=a.dtype)
b = cupy.empty(a.shape, a.dtype)
b[...] = identity_matrix
return lapack.posv(a, b)
def _lu_factor(a, overwrite_a=False, check_finite=True):
a = cupy.asarray(a)
_util._assert_rank2(a)
dtype = a.dtype
if dtype.char == 'f':
getrf = cusolver.sgetrf
getrf_bufferSize = cusolver.sgetrf_bufferSize
elif dtype.char == 'd':
getrf = cusolver.dgetrf
getrf_bufferSize = cusolver.dgetrf_bufferSize
elif dtype.char == 'F':
getrf = cusolver.cgetrf
getrf_bufferSize = cusolver.cgetrf_bufferSize
elif dtype.char == 'D':
getrf = cusolver.zgetrf
getrf_bufferSize = cusolver.zgetrf_bufferSize
else:
msg = 'Only float32, float64, complex64 and complex128 are supported.'
raise NotImplementedError(msg)
a = a.astype(dtype, order='F', copy=(not overwrite_a))
if check_finite:
if a.dtype.kind == 'f' and not cupy.isfinite(a).all():
raise ValueError('array must not contain infs or NaNs')
cusolver_handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
m, n = a.shape
ipiv = cupy.empty((min(m, n), ), dtype=numpy.intc)
buffersize = getrf_bufferSize(cusolver_handle, m, n, a.data.ptr, m)
workspace = cupy.empty(buffersize, dtype=dtype)
# LU factorization
getrf(cusolver_handle, m, n, a.data.ptr, m, workspace.data.ptr,
ipiv.data.ptr, dev_info.data.ptr)
if dev_info[0] < 0:
raise ValueError('illegal value in %d-th argument of '
'internal getrf (lu_factor)' % -dev_info[0])
elif dev_info[0] > 0:
warn('Diagonal number %d is exactly zero. Singular matrix.' %
dev_info[0],
RuntimeWarning,
stacklevel=2)
# cuSolver uses 1-origin while SciPy uses 0-origin
ipiv -= 1
return (a, ipiv)
def inv(a):
"""Computes the inverse of a matrix.
This function computes matrix ``a_inv`` from n-dimensional regular matrix
``a`` such that ``dot(a, a_inv) == eye(n)``.
Args:
a (cupy.ndarray): The regular matrix
Returns:
cupy.ndarray: The inverse of a 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.inv`
"""
if a.ndim >= 3:
return _batched_inv(a)
_util._assert_cupy_array(a)
_util._assert_rank2(a)
_util._assert_nd_squareness(a)
dtype, out_dtype = _util.linalg_common_type(a)
order = 'F' if a._f_contiguous else 'C'
# prevent 'a' to be overwritten
a = a.astype(dtype, copy=True, order=order)
b = cupy.eye(a.shape[0], dtype=dtype, order=order)
if order == 'F':
cupyx.lapack.gesv(a, b)
else:
cupyx.lapack.gesv(a.T, b.T)
return b.astype(out_dtype, copy=False)
def qr(a, mode='reduced'):
"""QR decomposition.
Decompose a given two-dimensional matrix into ``Q * R``, where ``Q``
is an orthonormal and ``R`` is an upper-triangular matrix.
Args:
a (cupy.ndarray): The input matrix.
mode (str): The mode of decomposition. Currently 'reduced',
'complete', 'r', and 'raw' modes are supported. The default mode
is 'reduced', in which matrix ``A = (M, N)`` is decomposed into
``Q``, ``R`` with dimensions ``(M, K)``, ``(K, N)``, where
``K = min(M, N)``.
Returns:
cupy.ndarray, or tuple of ndarray:
Although the type of returned object depends on the mode,
it returns a tuple of ``(Q, R)`` by default.
For details, please see the document of :func:`numpy.linalg.qr`.
.. 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.qr`
"""
# TODO(Saito): Current implementation only accepts two-dimensional arrays
_util._assert_cupy_array(a)
_util._assert_rank2(a)
if mode not in ('reduced', 'complete', 'r', 'raw'):
if mode in ('f', 'full', 'e', 'economic'):
msg = 'The deprecated mode \'{}\' is not supported'.format(mode)
raise ValueError(msg)
else:
raise ValueError('Unrecognized mode \'{}\''.format(mode))
# support float32, float64, complex64, and complex128
if a.dtype.char in 'fdFD':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
m, n = a.shape
mn = min(m, n)
if mn == 0:
if mode == 'reduced':
return cupy.empty((m, 0), dtype), cupy.empty((0, n), dtype)
elif mode == 'complete':
return cupy.identity(m, dtype), cupy.empty((m, n), dtype)
elif mode == 'r':
return cupy.empty((0, n), dtype)
else: # mode == 'raw'
# compatibility with numpy.linalg.qr
dtype = numpy.promote_types(dtype, 'd')
return cupy.empty((n, m), dtype), cupy.empty((0, ), dtype)
x = a.transpose().astype(dtype, order='C', copy=True)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
geqrf_bufferSize = cusolver.sgeqrf_bufferSize
geqrf = cusolver.sgeqrf
elif dtype == 'd':
geqrf_bufferSize = cusolver.dgeqrf_bufferSize
geqrf = cusolver.dgeqrf
elif dtype == 'F':
geqrf_bufferSize = cusolver.cgeqrf_bufferSize
geqrf = cusolver.cgeqrf
elif dtype == 'D':
geqrf_bufferSize = cusolver.zgeqrf_bufferSize
geqrf = cusolver.zgeqrf
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
# compute working space of geqrf and solve R
buffersize = geqrf_bufferSize(handle, m, n, x.data.ptr, n)
workspace = cupy.empty(buffersize, dtype=dtype)
tau = cupy.empty(mn, dtype=dtype)
geqrf(handle, m, n, x.data.ptr, m, tau.data.ptr, workspace.data.ptr,
buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
geqrf, dev_info)
if mode == 'r':
r = x[:, :mn].transpose()
return _util._triu(r)
if mode == 'raw':
if a.dtype.char == 'f':
# The original numpy.linalg.qr returns float64 in raw mode,
# whereas the cusolver returns float32. We agree that the
# following code would be inappropriate, however, in this time
# we explicitly convert them to float64 for compatibility.
return x.astype(numpy.float64), tau.astype(numpy.float64)
elif a.dtype.char == 'F':
# The same applies to complex64
return x.astype(numpy.complex128), tau.astype(numpy.complex128)
return x, tau
if mode == 'complete' and m > n:
mc = m
q = cupy.empty((m, m), dtype)
else:
mc = mn
q = cupy.empty((n, m), dtype)
q[:n] = x
# compute working space of orgqr and solve Q
if dtype == 'f':
orgqr_bufferSize = cusolver.sorgqr_bufferSize
orgqr = cusolver.sorgqr
elif dtype == 'd':
orgqr_bufferSize = cusolver.dorgqr_bufferSize
orgqr = cusolver.dorgqr
elif dtype == 'F':
orgqr_bufferSize = cusolver.cungqr_bufferSize
orgqr = cusolver.cungqr
elif dtype == 'D':
orgqr_bufferSize = cusolver.zungqr_bufferSize
orgqr = cusolver.zungqr
buffersize = orgqr_bufferSize(handle, m, mc, mn, q.data.ptr, m,
tau.data.ptr)
workspace = cupy.empty(buffersize, dtype=dtype)
orgqr(handle, m, mc, mn, q.data.ptr, m, tau.data.ptr, workspace.data.ptr,
buffersize, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
orgqr, dev_info)
q = q[:mc].transpose()
r = x[:, :mc].transpose()
return q, _util._triu(r)
def lstsq(a, b, rcond='warn'):
"""Return the least-squares solution to a linear matrix equation.
Solves the equation `a x = b` by computing a vector `x` that
minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may
be under-, well-, or over- determined (i.e., the number of
linearly independent rows of `a` can be less than, equal to, or
greater than its number of linearly independent columns). If `a`
is square and of full rank, then `x` (but for round-off error) is
the "exact" solution of the equation.
Args:
a (cupy.ndarray): "Coefficient" matrix with dimension ``(M, N)``
b (cupy.ndarray): "Dependent variable" values with dimension ``(M,)``
or ``(M, K)``
rcond (float): Cutoff parameter for small singular values.
For stability it computes the largest singular value denoted by
``s``, and sets all singular values smaller than ``s`` to zero.
Returns:
tuple:
A tuple of ``(x, residuals, rank, s)``. Note ``x`` is the
least-squares solution with shape ``(N,)`` or ``(N, K)`` depending
if ``b`` was two-dimensional. The sums of ``residuals`` is the
squared Euclidean 2-norm for each column in b - a*x. The
``residuals`` is an empty array if the rank of a is < N or M <= N,
but iff b is 1-dimensional, this is a (1,) shape array, Otherwise
the shape is (K,). The ``rank`` of matrix ``a`` is an integer. The
singular values of ``a`` are ``s``.
.. 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.lstsq`
"""
if rcond == 'warn':
warnings.warn(
'`rcond` parameter will change to the default of '
'machine precision times ``max(M, N)`` where M and N '
'are the input matrix dimensions.\n'
'To use the future default and silence this warning '
'we advise to pass `rcond=None`, to keep using the old, '
'explicitly pass `rcond=-1`.',
FutureWarning)
rcond = -1
_util._assert_cupy_array(a, b)
_util._assert_rank2(a)
if b.ndim > 2:
raise linalg.LinAlgError('{}-dimensional array given. Array must be at'
' most two-dimensional'.format(b.ndim))
m, n = a.shape[-2:]
m2 = b.shape[0]
if m != m2:
raise linalg.LinAlgError('Incompatible dimensions')
u, s, vh = cupy.linalg.svd(a, full_matrices=False)
if rcond is None:
rcond = numpy.finfo(s.dtype).eps * max(m, n)
elif rcond <= 0 or rcond >= 1:
# some doc of gelss/gelsd says "rcond < 0", but it's not true!
rcond = numpy.finfo(s.dtype).eps
# number of singular values and matrix rank
cutoff = rcond * s.max()
s1 = 1 / s
sing_vals = s <= cutoff
s1[sing_vals] = 0
rank = s.size - sing_vals.sum(dtype=numpy.int32)
# Solve the least-squares solution
# x = vh.T.conj() @ diag(s1) @ u.T.conj() @ b
z = (cupy.dot(b.T, u.conj()) * s1).T
x = cupy.dot(vh.T.conj(), z)
# Calculate squared Euclidean 2-norm for each column in b - a*x
if m <= n or rank != n:
resids = cupy.empty((0,), dtype=s.dtype)
else:
e = b - a.dot(x)
resids = cupy.atleast_1d(_nrm2_last_axis(e.T))
return x, resids, rank, s
def inv(a):
"""Computes the inverse of a matrix.
This function computes matrix ``a_inv`` from n-dimensional regular matrix
``a`` such that ``dot(a, a_inv) == eye(n)``.
Args:
a (cupy.ndarray): The regular matrix
Returns:
cupy.ndarray: The inverse of a 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.inv`
"""
if a.ndim >= 3:
return _batched_inv(a)
# to prevent `a` to be overwritten
a = a.copy()
_util._assert_cupy_array(a)
_util._assert_rank2(a)
_util._assert_nd_squareness(a)
# support float32, float64, complex64, and complex128
if a.dtype.char in 'fdFD':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f')
cusolver_handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
ipiv = cupy.empty((a.shape[0], 1), dtype=numpy.intc)
if dtype == 'f':
getrf = cusolver.sgetrf
getrf_bufferSize = cusolver.sgetrf_bufferSize
getrs = cusolver.sgetrs
elif dtype == 'd':
getrf = cusolver.dgetrf
getrf_bufferSize = cusolver.dgetrf_bufferSize
getrs = cusolver.dgetrs
elif dtype == 'F':
getrf = cusolver.cgetrf
getrf_bufferSize = cusolver.cgetrf_bufferSize
getrs = cusolver.cgetrs
elif dtype == 'D':
getrf = cusolver.zgetrf
getrf_bufferSize = cusolver.zgetrf_bufferSize
getrs = cusolver.zgetrs
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
m = a.shape[0]
buffersize = getrf_bufferSize(cusolver_handle, m, m, a.data.ptr, m)
workspace = cupy.empty(buffersize, dtype=dtype)
# LU factorization
getrf(cusolver_handle, m, m, a.data.ptr, m, workspace.data.ptr,
ipiv.data.ptr, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
getrf, dev_info)
b = cupy.eye(m, dtype=dtype)
# solve for the inverse
getrs(cusolver_handle, 0, m, m, a.data.ptr, m, ipiv.data.ptr, b.data.ptr,
m, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
getrs, dev_info)
return b
def lstsq(a, b, rcond=1e-15):
"""Return the least-squares solution to a linear matrix equation.
Solves the equation `a x = b` by computing a vector `x` that
minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may
be under-, well-, or over- determined (i.e., the number of
linearly independent rows of `a` can be less than, equal to, or
greater than its number of linearly independent columns). If `a`
is square and of full rank, then `x` (but for round-off error) is
the "exact" solution of the equation.
Args:
a (cupy.ndarray): "Coefficient" matrix with dimension ``(M, N)``
b (cupy.ndarray): "Dependent variable" values with dimension ``(M,)``
or ``(M, K)``
rcond (float): Cutoff parameter for small singular values.
For stability it computes the largest singular value denoted by
``s``, and sets all singular values smaller than ``s`` to zero.
Returns:
tuple:
A tuple of ``(x, residuals, rank, s)``. Note ``x`` is the
least-squares solution with shape ``(N,)`` or ``(N, K)`` depending
if ``b`` was two-dimensional. The sums of ``residuals`` is the
squared Euclidean 2-norm for each column in b - a*x. The
``residuals`` is an empty array if the rank of a is < N or M <= N,
but iff b is 1-dimensional, this is a (1,) shape array, Otherwise
the shape is (K,). The ``rank`` of matrix ``a`` is an integer. The
singular values of ``a`` are ``s``.
.. 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.lstsq`
"""
_util._assert_cupy_array(a, b)
_util._assert_rank2(a)
if b.ndim > 2:
raise linalg.LinAlgError('{}-dimensional array given. Array must be at'
' most two-dimensional'.format(b.ndim))
m, n = a.shape[-2:]
m2 = b.shape[0]
if m != m2:
raise linalg.LinAlgError('Incompatible dimensions')
u, s, vt = cupy.linalg.svd(a, full_matrices=False)
# number of singular values and matrix rank
cutoff = rcond * s.max()
s1 = 1 / s
sing_vals = s <= cutoff
s1[sing_vals] = 0
rank = s.size - sing_vals.sum()
if b.ndim == 2:
s1 = cupy.repeat(s1.reshape(-1, 1), b.shape[1], axis=1)
# Solve the least-squares solution
z = core.dot(u.transpose(), b) * s1
x = core.dot(vt.transpose(), z)
# Calculate squared Euclidean 2-norm for each column in b - a*x
if rank != n or m <= n:
resids = cupy.array([], dtype=a.dtype)
elif b.ndim == 2:
e = b - core.dot(a, x)
resids = cupy.sum(cupy.square(e), axis=0)
else:
e = b - cupy.dot(a, x)
resids = cupy.dot(e.T, e).reshape(-1)
return x, resids, rank, s
def invh(a):
"""Compute the inverse of a Hermitian matrix.
This function computes a inverse of a real symmetric or complex hermitian
positive-definite matrix using Cholesky factorization. If matrix ``a`` is
not positive definite, Cholesky factorization fails and it raises an error.
Args:
a (cupy.ndarray): Real symmetric or complex hermitian maxtix.
Returns:
cupy.ndarray: The inverse of matrix ``a``.
"""
_util._assert_cupy_array(a)
_util._assert_nd_squareness(a)
# TODO: Remove this assert once cusolver supports nrhs > 1 for potrsBatched
_util._assert_rank2(a)
if a.ndim > 2:
return _batched_invh(a)
# to prevent `a` from being overwritten
a = a.copy()
# support float32, float64, complex64, and complex128
if a.dtype.char in 'fdFD':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
cusolver_handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if dtype == 'f':
potrf = cusolver.spotrf
potrf_bufferSize = cusolver.spotrf_bufferSize
potrs = cusolver.spotrs
elif dtype == 'd':
potrf = cusolver.dpotrf
potrf_bufferSize = cusolver.dpotrf_bufferSize
potrs = cusolver.dpotrs
elif dtype == 'F':
potrf = cusolver.cpotrf
potrf_bufferSize = cusolver.cpotrf_bufferSize
potrs = cusolver.cpotrs
elif dtype == 'D':
potrf = cusolver.zpotrf
potrf_bufferSize = cusolver.zpotrf_bufferSize
potrs = cusolver.zpotrs
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
m = a.shape[0]
uplo = cublas.CUBLAS_FILL_MODE_LOWER
worksize = potrf_bufferSize(cusolver_handle, uplo, m, a.data.ptr, m)
workspace = cupy.empty(worksize, dtype=dtype)
# Cholesky factorization
potrf(cusolver_handle, uplo, m, a.data.ptr, m, workspace.data.ptr,
worksize, dev_info.data.ptr)
info = dev_info[0]
if info != 0:
if info < 0:
msg = '\tThe {}-th parameter is wrong'.format(-info)
else:
msg = ('\tThe leading minor of order {} is not positive definite'
.format(info))
raise RuntimeError('matrix inversion failed at potrf.\n' + msg)
b = cupy.eye(m, dtype=dtype)
# Solve: A * X = B
potrs(cusolver_handle, uplo, m, m, a.data.ptr, m, b.data.ptr, m,
dev_info.data.ptr)
info = dev_info[0]
if info > 0:
assert False, ('Unexpected output returned by potrs (actual: {})'
.format(info))
elif info < 0:
raise RuntimeError('matrix inversion failed at potrs.\n'
'\tThe {}-th parameter is wrong'.format(-info))
return b
def svd(a, full_matrices=True, compute_uv=True):
"""Singular Value Decomposition.
Factorizes the matrix ``a`` as ``u * np.diag(s) * v``, where ``u`` and
``v`` are unitary and ``s`` is an one-dimensional array of ``a``'s
singular values.
Args:
a (cupy.ndarray): The input matrix with dimension ``(M, N)``.
full_matrices (bool): If True, it returns u and v with dimensions
``(M, M)`` and ``(N, N)``. Otherwise, the dimensions of u and v
are respectively ``(M, K)`` and ``(K, N)``, where
``K = min(M, N)``.
compute_uv (bool): If ``False``, it only returns singular values.
Returns:
tuple of :class:`cupy.ndarray`:
A tuple of ``(u, s, v)`` such that ``a = u * np.diag(s) * v``.
.. 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.svd`
"""
# TODO(Saito): Current implementation only accepts two-dimensional arrays
_util._assert_cupy_array(a)
_util._assert_rank2(a)
# Cast to float32 or float64
a_dtype = numpy.promote_types(a.dtype.char, 'f').char
if a_dtype == 'f':
s_dtype = 'f'
elif a_dtype == 'd':
s_dtype = 'd'
elif a_dtype == 'F':
s_dtype = 'f'
else: # a_dtype == 'D':
a_dtype = 'D'
s_dtype = 'd'
# Remark 1: gesvd only supports m >= n (WHAT?)
# Remark 2: gesvd only supports jobu = 'A' and jobvt = 'A'
# Remark 3: gesvd returns matrix U and V^H
# Remark 4: Remark 2 is removed since cuda 8.0 (new!)
n, m = a.shape
if m == 0 or n == 0:
s = cupy.empty((0, ), s_dtype)
if compute_uv:
if full_matrices:
u = cupy.eye(n, dtype=a_dtype)
vt = cupy.eye(m, dtype=a_dtype)
else:
u = cupy.empty((n, 0), dtype=a_dtype)
vt = cupy.empty((0, m), dtype=a_dtype)
return u, s, vt
else:
return s
# `a` must be copied because xgesvd destroys the matrix
if m >= n:
x = a.astype(a_dtype, order='C', copy=True)
trans_flag = False
else:
m, n = a.shape
x = a.transpose().astype(a_dtype, order='C', copy=True)
trans_flag = True
k = n # = min(m, n) where m >= n is ensured above
if compute_uv:
if full_matrices:
u = cupy.empty((m, m), dtype=a_dtype)
vt = x[:, :n]
job_u = ord('A')
job_vt = ord('O')
else:
u = x
vt = cupy.empty((k, n), dtype=a_dtype)
job_u = ord('O')
job_vt = ord('S')
u_ptr, vt_ptr = u.data.ptr, vt.data.ptr
else:
u_ptr, vt_ptr = 0, 0 # Use nullptr
job_u = ord('N')
job_vt = ord('N')
s = cupy.empty(k, dtype=s_dtype)
handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
if a_dtype == 'f':
gesvd = cusolver.sgesvd
gesvd_bufferSize = cusolver.sgesvd_bufferSize
elif a_dtype == 'd':
gesvd = cusolver.dgesvd
gesvd_bufferSize = cusolver.dgesvd_bufferSize
elif a_dtype == 'F':
gesvd = cusolver.cgesvd
gesvd_bufferSize = cusolver.cgesvd_bufferSize
else: # a_dtype == 'D':
gesvd = cusolver.zgesvd
gesvd_bufferSize = cusolver.zgesvd_bufferSize
buffersize = gesvd_bufferSize(handle, m, n)
workspace = cupy.empty(buffersize, dtype=a_dtype)
gesvd(handle, job_u, job_vt, m, n, x.data.ptr, m, s.data.ptr, u_ptr, m,
vt_ptr, n, workspace.data.ptr, buffersize, 0, dev_info.data.ptr)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
gesvd, dev_info)
# Note that the returned array may need to be transposed
# depending on the structure of an input
if compute_uv:
if trans_flag:
return u.transpose(), s, vt.transpose()
else:
return vt, s, u
else:
return s
def lu_solve(lu_and_piv, b, trans=0, overwrite_b=False, check_finite=True):
"""Solve an equation system, ``a * x = b``, given the LU factorization of ``a``
Args:
lu_and_piv (tuple): LU factorization of matrix ``a`` (``(M, M)``)
together with pivot indices.
b (cupy.ndarray): The matrix with dimension ``(M,)`` or
``(M, N)``.
trans ({0, 1, 2}): Type of system to solve:
======== =========
trans system
======== =========
0 a x = b
1 a^T x = b
2 a^H x = b
======== =========
overwrite_b (bool): Allow overwriting data in b (may enhance
performance)
check_finite (bool): Whether to check that the input matrices contain
only finite numbers. Disabling may give a performance gain, but may
result in problems (crashes, non-termination) if the inputs do
contain infinities or NaNs.
Returns:
cupy.ndarray:
The matrix with dimension ``(M,)`` or ``(M, N)``.
.. seealso:: :func:`scipy.linalg.lu_solve`
"""
(lu, ipiv) = lu_and_piv
_util._assert_cupy_array(lu)
_util._assert_rank2(lu)
_util._assert_nd_squareness(lu)
m = lu.shape[0]
if m != b.shape[0]:
raise ValueError('incompatible dimensions.')
dtype = lu.dtype
if dtype.char == 'f':
getrs = cusolver.sgetrs
elif dtype.char == 'd':
getrs = cusolver.dgetrs
elif dtype.char == 'F':
getrs = cusolver.cgetrs
elif dtype.char == 'D':
getrs = cusolver.zgetrs
else:
msg = 'Only float32, float64, complex64 and complex128 are supported.'
raise NotImplementedError(msg)
if trans == 0:
trans = cublas.CUBLAS_OP_N
elif trans == 1:
trans = cublas.CUBLAS_OP_T
elif trans == 2:
trans = cublas.CUBLAS_OP_C
else:
raise ValueError('unknown trans')
lu = lu.astype(dtype, order='F', copy=False)
ipiv = ipiv.astype(ipiv.dtype, order='F', copy=True)
# cuSolver uses 1-origin while SciPy uses 0-origin
ipiv += 1
b = b.astype(dtype, order='F', copy=(not overwrite_b))
if check_finite:
if lu.dtype.kind == 'f' and not cupy.isfinite(lu).all():
raise ValueError(
'array must not contain infs or NaNs.\n'
'Note that when a singular matrix is given, unlike '
'scipy.linalg.lu_factor, cupyx.scipy.linalg.lu_factor '
'returns an array containing NaN.')
if b.dtype.kind == 'f' and not cupy.isfinite(b).all():
raise ValueError(
'array must not contain infs or NaNs')
n = 1 if b.ndim == 1 else b.shape[1]
cusolver_handle = device.get_cusolver_handle()
dev_info = cupy.empty(1, dtype=numpy.int32)
# solve for the inverse
getrs(cusolver_handle,
trans,
m, n, lu.data.ptr, m, ipiv.data.ptr, b.data.ptr,
m, dev_info.data.ptr)
if dev_info[0] < 0:
raise ValueError('illegal value in %d-th argument of '
'internal getrs (lu_solve)' % -dev_info[0])
return b
