def lsqr(A, b):
"""Solves linear system with QR decomposition.
Find the solution to a large, sparse, linear system of equations.
The function solves ``Ax = b``. Given two-dimensional matrix ``A`` is
decomposed into ``Q * R``.
Args:
A (cupy.ndarray or cupyx.scipy.sparse.csr_matrix): The input matrix
with dimension ``(N, N)``
b (cupy.ndarray): Right-hand side vector.
Returns:
tuple:
Its length must be ten. It has same type elements
as SciPy. Only the first element, the solution vector ``x``, is
available and other elements are expressed as ``None`` because
the implementation of cuSOLVER is different from the one of SciPy.
You can easily calculate the fourth element by ``norm(b - Ax)``
and the ninth element by ``norm(x)``.
.. seealso:: :func:`scipy.sparse.linalg.lsqr`
"""
if runtime.is_hip:
raise RuntimeError('HIP does not support lsqr')
if not sparse.isspmatrix_csr(A):
A = sparse.csr_matrix(A)
# csr_matrix is 2d
_util._assert_stacked_square(A)
_util._assert_cupy_array(b)
m = A.shape[0]
if b.ndim != 1 or len(b) != m:
raise ValueError('b must be 1-d array whose size is same as A')
# Cast to float32 or float64
if A.dtype == 'f' or A.dtype == 'd':
dtype = A.dtype
else:
dtype = numpy.promote_types(A.dtype, 'f')
handle = device.get_cusolver_sp_handle()
nnz = A.nnz
tol = 1.0
reorder = 1
x = cupy.empty(m, dtype=dtype)
singularity = numpy.empty(1, numpy.int32)
if dtype == 'f':
csrlsvqr = cusolver.scsrlsvqr
else:
csrlsvqr = cusolver.dcsrlsvqr
csrlsvqr(
handle, m, nnz, A._descr.descriptor, A.data.data.ptr,
A.indptr.data.ptr, A.indices.data.ptr, b.data.ptr, tol, reorder,
x.data.ptr, singularity.ctypes.data)
# The return type of SciPy is always float64. Therefore, x must be casted.
x = x.astype(numpy.float64)
ret = (x, None, None, None, None, None, None, None, None, None)
return ret
def csrlsvqr(A, b, tol=0, reorder=1):
"""Solves the linear system ``Ax = b`` using QR factorization.
Args:
A (cupyx.scipy.sparse.csr_matrix): Sparse matrix with dimension
``(M, M)``.
b (cupy.ndarray): Dense vector with dimension ``(M,)``.
tol (float): Tolerance to decide if singular or not.
reorder (int): Reordering scheme to reduce zero fill-in.
1: symrcm is used.
2: symamd is used.
3: csrmetisnd is used.
else: no reordering.
"""
if not check_availability('csrlsvqr'):
raise RuntimeError('csrlsvqr is not available.')
if not _cupyx.scipy.sparse.isspmatrix_csr(A):
raise ValueError('A must be CSR sparse matrix')
if not isinstance(b, _cupy.ndarray):
raise ValueError('b must be cupy.ndarray')
if b.ndim != 1:
raise ValueError('b.ndim must be 1 (actual: {})'.format(b.ndim))
if not (A.shape[0] == A.shape[1] == b.shape[0]):
raise ValueError('invalid shape')
if A.dtype != b.dtype:
raise TypeError('dtype mismatch')
dtype = A.dtype
if dtype.char == 'f':
t = 's'
elif dtype.char == 'd':
t = 'd'
elif dtype.char == 'F':
t = 'c'
elif dtype.char == 'D':
t = 'z'
else:
raise TypeError('Invalid dtype (actual: {})'.format(dtype))
solve = getattr(_cusolver, t + 'csrlsvqr')
tol = max(tol, 0)
m = A.shape[0]
x = _cupy.empty((m,), dtype=dtype)
singularity = _numpy.empty((1,), _numpy.int32)
handle = _device.get_cusolver_sp_handle()
solve(handle, m, A.nnz, A._descr.descriptor, A.data.data.ptr,
A.indptr.data.ptr, A.indices.data.ptr, b.data.ptr, tol, reorder,
x.data.ptr, singularity.ctypes.data)
if singularity[0] >= 0:
_warnings.warn('A is not positive definite or near singular under '
'tolerance {} (singularity: {})'.
format(tol, singularity))
return x
def lschol(A, b):
"""Solves linear system with cholesky decomposition.
Find the solution to a large, sparse, linear system of equations.
The function solves ``Ax = b``. Given two-dimensional matrix ``A`` is
decomposed into ``L * L^*``.
Args:
A (cupy.ndarray or cupy.sparse.csr_matrix): The input matrix with
dimension ``(N, N)``. Must be positive-definite input matrix.
Only symmetric real matrix is supported currently.
b (cupy.ndarray): Right-hand side vector.
Returns:
ret (cupy.ndarray): The solution vector ``x``.
"""
if not cuda.cusolver_enabled:
raise RuntimeError('Current cupy only supports cusolver in CUDA 8.0')
if not cupy.sparse.isspmatrix_csr(A):
A = cupy.sparse.csr_matrix(A)
util._assert_nd_squareness(A)
util._assert_cupy_array(b)
m = A.shape[0]
if b.ndim != 1 or len(b) != m:
raise ValueError('b must be 1-d array whose size is same as A')
# Cast to float32 or float64
if A.dtype == 'f' or A.dtype == 'd':
dtype = A.dtype
else:
dtype = numpy.find_common_type((A.dtype, 'f'), ())
handle = device.get_cusolver_sp_handle()
nnz = A.nnz
tol = 1.0
reorder = 1
x = cupy.empty(m, dtype=dtype)
singularity = numpy.empty(1, numpy.int32)
if dtype == 'f':
csrlsvchol = cusolver.scsrlsvchol
else:
csrlsvchol = cusolver.dcsrlsvchol
csrlsvchol(handle, m, nnz, A._descr.descriptor, A.data.data.ptr,
A.indptr.data.ptr, A.indices.data.ptr, b.data.ptr, tol, reorder,
x.data.ptr, singularity.ctypes.data)
# The return type of SciPy is always float64.
x = x.astype(numpy.float64)
return x