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import numpy as _numpy
import cupy as _cupy
from cupy_backends.cuda.libs import cublas as _cublas
from cupy.cuda import device as _device
def gesv(a, b):
"""Solve a linear matrix equation using cusolverDn<t>getr[fs]().
Computes the solution to a system of linear equation ``ax = b``.
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)``.
Note: ``a`` and ``b`` will be overwritten.
"""
from cupy_backends.cuda.libs import cusolver as _cusolver
if a.ndim != 2:
raise ValueError('a.ndim must be 2 (actual: {})'.format(a.ndim))
if b.ndim not in (1, 2):
raise ValueError('b.ndim must be 1 or 2 (actual: {})'.format(b.ndim))
if a.shape[0] != a.shape[1]:
raise ValueError('a must be a square matrix.')
if a.shape[0] != b.shape[0]:
raise ValueError('shape mismatch (a: {}, b: {}).'.
format(a.shape, b.shape))
if a.dtype != b.dtype:
raise TypeError('dtype mismatch (a: {}, b: {})'.
format(a.dtype, b.dtype))
dtype = a.dtype
if dtype == 'f':
t = 's'
elif dtype == 'd':
t = 'd'
elif dtype == 'F':
t = 'c'
elif dtype == 'D':
t = 'z'
else:
raise TypeError('unsupported dtype (actual:{})'.format(a.dtype))
helper = getattr(_cusolver, t + 'getrf_bufferSize')
getrf = getattr(_cusolver, t + 'getrf')
getrs = getattr(_cusolver, t + 'getrs')
n = b.shape[0]
nrhs = b.shape[1] if b.ndim == 2 else 1
if a._f_contiguous:
trans = _cublas.CUBLAS_OP_N
elif a._c_contiguous:
trans = _cublas.CUBLAS_OP_T
else:
raise ValueError('a must be F-contiguous or C-contiguous.')
if not b._f_contiguous:
raise ValueError('b must be F-contiguous.')
handle = _device.get_cusolver_handle()
dipiv = _cupy.empty(n, dtype=_numpy.int32)
dinfo = _cupy.empty(1, dtype=_numpy.int32)
lwork = helper(handle, n, n, a.data.ptr, n)
dwork = _cupy.empty(lwork, dtype=a.dtype)
# LU factrization (A = L * U)
getrf(handle, n, n, a.data.ptr, n, dwork.data.ptr, dipiv.data.ptr,
dinfo.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
getrf, dinfo)
# Solves Ax = b
getrs(handle, trans, n, nrhs, a.data.ptr, n,
dipiv.data.ptr, b.data.ptr, n, dinfo.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
getrs, dinfo)
def gels(a, b):
"""Solves over/well/under-determined linear systems.
Computes least-square solution to equation ``ax = b` by QR factorization
using cusolverDn<t>geqrf().
Args:
a (cupy.ndarray): The matrix with dimension ``(M, N)``.
b (cupy.ndarray): The matrix with dimension ``(M)`` or ``(M, K)``.
Returns:
cupy.ndarray:
The matrix with dimension ``(N)`` or ``(N, K)``.
"""
from cupy_backends.cuda.libs import cusolver as _cusolver
if a.ndim != 2:
raise ValueError('a.ndim must be 2 (actual: {})'.format(a.ndim))
if b.ndim == 1:
nrhs = 1
elif b.ndim == 2:
nrhs = b.shape[1]
else:
raise ValueError('b.ndim must be 1 or 2 (actual: {})'.format(b.ndim))
if a.shape[0] != b.shape[0]:
raise ValueError('shape mismatch (a: {}, b: {}).'.
format(a.shape, b.shape))
if a.dtype != b.dtype:
raise ValueError('dtype mismatch (a: {}, b: {}).'.
format(a.dtype, b.dtype))
dtype = a.dtype
if dtype == 'f':
t = 's'
elif dtype == 'd':
t = 'd'
elif dtype == 'F':
t = 'c'
elif dtype == 'D':
t = 'z'
else:
raise ValueError('unsupported dtype (actual: {})'.format(dtype))
geqrf_helper = getattr(_cusolver, t + 'geqrf_bufferSize')
geqrf = getattr(_cusolver, t + 'geqrf')
trsm = getattr(_cublas, t + 'trsm')
if t in 'sd':
ormqr_helper = getattr(_cusolver, t + 'ormqr_bufferSize')
ormqr = getattr(_cusolver, t + 'ormqr')
else:
ormqr_helper = getattr(_cusolver, t + 'unmqr_bufferSize')
ormqr = getattr(_cusolver, t + 'unmqr')
no_trans = _cublas.CUBLAS_OP_N
if dtype.char in 'fd':
trans = _cublas.CUBLAS_OP_T
else:
trans = _cublas.CUBLAS_OP_C
m, n = a.shape
mn_min = min(m, n)
dev_info = _cupy.empty(1, dtype=_numpy.int32)
tau = _cupy.empty(mn_min, dtype=dtype)
cusolver_handle = _device.get_cusolver_handle()
cublas_handle = _device.get_cublas_handle()
one = _numpy.array(1.0, dtype=dtype)
if m >= n: # over/well-determined systems
a = a.copy(order='F')
b = b.copy(order='F')
# geqrf (QR decomposition, A = Q * R)
ws_size = geqrf_helper(cusolver_handle, m, n, a.data.ptr, m)
workspace = _cupy.empty(ws_size, dtype=dtype)
geqrf(cusolver_handle, m, n, a.data.ptr, m, tau.data.ptr,
workspace.data.ptr, ws_size, dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
geqrf, dev_info)
# ormqr (Computes Q^T * B)
ws_size = ormqr_helper(
cusolver_handle, _cublas.CUBLAS_SIDE_LEFT, trans, m, nrhs, mn_min,
a.data.ptr, m, tau.data.ptr, b.data.ptr, m)
workspace = _cupy.empty(ws_size, dtype=dtype)
ormqr(cusolver_handle, _cublas.CUBLAS_SIDE_LEFT, trans, m, nrhs,
mn_min, a.data.ptr, m, tau.data.ptr, b.data.ptr, m,
workspace.data.ptr, ws_size, dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
ormqr, dev_info)
# trsm (Solves R * X = (Q^T * B))
trsm(cublas_handle, _cublas.CUBLAS_SIDE_LEFT,
_cublas.CUBLAS_FILL_MODE_UPPER, no_trans,
_cublas.CUBLAS_DIAG_NON_UNIT, mn_min, nrhs,
one.ctypes.data, a.data.ptr, m, b.data.ptr, m)
return b[:n]
else: # under-determined systems
a = a.conj().T.copy(order='F')
bb = b
out_shape = (n,) if b.ndim == 1 else (n, nrhs)
b = _cupy.zeros(out_shape, dtype=dtype, order='F')
b[:m] = bb
# geqrf (QR decomposition, A^T = Q * R)
ws_size = geqrf_helper(cusolver_handle, n, m, a.data.ptr, n)
workspace = _cupy.empty(ws_size, dtype=dtype)
geqrf(cusolver_handle, n, m, a.data.ptr, n, tau.data.ptr,
workspace.data.ptr, ws_size, dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
geqrf, dev_info)
# trsm (Solves R^T * Z = B)
trsm(cublas_handle, _cublas.CUBLAS_SIDE_LEFT,
_cublas.CUBLAS_FILL_MODE_UPPER, trans,
_cublas.CUBLAS_DIAG_NON_UNIT, m, nrhs,
one.ctypes.data, a.data.ptr, n, b.data.ptr, n)
# ormqr (Computes Q * Z)
ws_size = ormqr_helper(
cusolver_handle, _cublas.CUBLAS_SIDE_LEFT, no_trans, n, nrhs,
mn_min, a.data.ptr, n, tau.data.ptr, b.data.ptr, n)
workspace = _cupy.empty(ws_size, dtype=dtype)
ormqr(cusolver_handle, _cublas.CUBLAS_SIDE_LEFT, no_trans, n, nrhs,
mn_min, a.data.ptr, n, tau.data.ptr, b.data.ptr, n,
workspace.data.ptr, ws_size, dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
ormqr, dev_info)
return b
def _batched_posv(a, b):
from cupy_backends.cuda.libs import cusolver as _cusolver
import cupyx.cusolver
if not cupyx.cusolver.check_availability('potrsBatched'):
raise RuntimeError('potrsBatched is not available')
dtype = _numpy.promote_types(a.dtype, b.dtype)
dtype = _numpy.promote_types(dtype, 'f')
if dtype == 'f':
potrfBatched = _cusolver.spotrfBatched
potrsBatched = _cusolver.spotrsBatched
elif dtype == 'd':
potrfBatched = _cusolver.dpotrfBatched
potrsBatched = _cusolver.dpotrsBatched
elif dtype == 'F':
potrfBatched = _cusolver.cpotrfBatched
potrsBatched = _cusolver.cpotrsBatched
elif dtype == 'D':
potrfBatched = _cusolver.zpotrfBatched
potrsBatched = _cusolver.zpotrsBatched
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
a = a.astype(dtype, order='C', copy=True)
ap = _cupy._core._mat_ptrs(a)
lda, n = a.shape[-2:]
batch_size = int(_numpy.prod(a.shape[:-2]))
handle = _device.get_cusolver_handle()
uplo = _cublas.CUBLAS_FILL_MODE_LOWER
dev_info = _cupy.empty(batch_size, dtype=_numpy.int32)
# Cholesky factorization
potrfBatched(handle, uplo, n, ap.data.ptr, lda, dev_info.data.ptr,
batch_size)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrfBatched, dev_info)
b_shape = b.shape
b = b.conj().reshape(batch_size, n, -1).astype(dtype, order='C', copy=True)
bp = _cupy._core._mat_ptrs(b)
ldb, nrhs = b.shape[-2:]
dev_info = _cupy.empty(1, dtype=_numpy.int32)
# NOTE: potrsBatched does not currently support nrhs > 1 (CUDA v10.2)
# Solve: A[i] * X[i] = B[i]
potrsBatched(handle, uplo, n, nrhs, ap.data.ptr, lda, bp.data.ptr, ldb,
dev_info.data.ptr, batch_size)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrsBatched, dev_info)
# TODO: check if conj() is necessary when nrhs > 1
return b.conj().reshape(b_shape)
def posv(a, b):
"""Solve the linear equations A x = b via Cholesky factorization of A,
where A is a real symmetric or complex Hermitian positive-definite matrix.
If matrix ``A`` is not positive definite, Cholesky factorization fails
and it raises an error.
Note: For batch input, NRHS > 1 is not currently supported.
Args:
a (cupy.ndarray): Array of real symmetric or complex hermitian
matrices with dimension (..., N, N).
b (cupy.ndarray): right-hand side (..., N) or (..., N, NRHS).
Returns:
x (cupy.ndarray): The solution (shape matches b).
"""
from cupy_backends.cuda.libs import cusolver as _cusolver
_util = _cupy.linalg._util
_util._assert_cupy_array(a, b)
_util._assert_stacked_2d(a)
_util._assert_stacked_square(a)
if a.ndim > 2:
return _batched_posv(a, b)
dtype = _numpy.promote_types(a.dtype, b.dtype)
dtype = _numpy.promote_types(dtype, 'f')
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)
a = a.astype(dtype, order='F', copy=True)
lda, n = a.shape
handle = _device.get_cusolver_handle()
uplo = _cublas.CUBLAS_FILL_MODE_LOWER
dev_info = _cupy.empty(1, dtype=_numpy.int32)
worksize = potrf_bufferSize(handle, uplo, n, a.data.ptr, lda)
workspace = _cupy.empty(worksize, dtype=dtype)
# Cholesky factorization
potrf(handle, uplo, n, a.data.ptr, lda, workspace.data.ptr,
worksize, dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrf, dev_info)
b_shape = b.shape
b = b.reshape(n, -1).astype(dtype, order='F', copy=True)
ldb, nrhs = b.shape
# Solve: A * X = B
potrs(handle, uplo, n, nrhs, a.data.ptr, lda, b.data.ptr, ldb,
dev_info.data.ptr)
_cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrs, dev_info)
return _cupy.ascontiguousarray(b.reshape(b_shape))
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