def connected_components(csgraph, directed=True, connection='weak', return_labels=True): """Analyzes the connected components of a sparse graph Args: csgraph (cupy.ndarray of cupyx.scipy.sparse.csr_matrix): The adjacency matrix representing connectivity among nodes. directed (bool): If ``True``, it operates on a directed graph. If ``False``, it operates on an undirected graph. connection (str): ``'weak'`` or ``'strong'``. For directed graphs, the type of connection to use. Nodes i and j are "strongly" connected only when a path exists both from i to j and from j to i. If ``directed`` is ``False``, this argument is ignored. return_labels (bool): If ``True``, it returns the labels for each of the connected components. Returns: tuple of int and cupy.ndarray, or int: If ``return_labels`` == ``True``, returns a tuple ``(n, labels)``, where ``n`` is the number of connected components and ``labels`` is labels of each connected components. Otherwise, returns ``n``. .. seealso:: :func:`scipy.sparse.csgraph.connected_components` """ if not _cugraph_available: raise RuntimeError('cugraph is not available') connection = connection.lower() if connection not in ('weak', 'strong'): raise ValueError("connection must be 'weak' or 'strong'") if not directed: connection = 'weak' if not cupyx.scipy.sparse.isspmatrix_csr(csgraph): csgraph = cupyx.scipy.sparse.csr_matrix(csgraph) _util._assert_nd_squareness(csgraph) m = csgraph.shape[0] if csgraph.nnz == 0: return m, cupy.arange(m, dtype=csgraph.indices.dtype) labels = cupy.empty(m, dtype=csgraph.indices.dtype) if connection == 'strong': cugraph.strongly_connected_components(csgraph, labels) else: csgraph += csgraph.T if not cupyx.scipy.sparse.isspmatrix_csr(csgraph): csgraph = cupyx.scipy.sparse.csr_matrix(csgraph) cugraph.weakly_connected_components(csgraph, labels) # Note: In the case of weak connection, cuGraph creates labels with a # start number of 1, so decrement the label number. labels -= 1 count = cupy.zeros((1, ), dtype=csgraph.indices.dtype) root_labels = cupy.empty((m, ), dtype=csgraph.indices.dtype) _cupy_count_components(labels, count, root_labels, size=m) n = int(count[0]) if not return_labels: return n _cupy_adjust_labels(n, cupy.sort(root_labels[:n]), labels) return n, labels
def _batched_inv(a): assert(a.ndim >= 3) _util._assert_cupy_array(a) _util._assert_nd_squareness(a) dtype, out_dtype = _util.linalg_common_type(a) if dtype == cupy.float32: getrf = cupy.cuda.cublas.sgetrfBatched getri = cupy.cuda.cublas.sgetriBatched elif dtype == cupy.float64: getrf = cupy.cuda.cublas.dgetrfBatched getri = cupy.cuda.cublas.dgetriBatched elif dtype == cupy.complex64: getrf = cupy.cuda.cublas.cgetrfBatched getri = cupy.cuda.cublas.cgetriBatched elif dtype == cupy.complex128: getrf = cupy.cuda.cublas.zgetrfBatched getri = cupy.cuda.cublas.zgetriBatched else: msg = ('dtype must be float32, float64, complex64 or complex128' ' (actual: {})'.format(a.dtype)) raise ValueError(msg) if 0 in a.shape: return cupy.empty_like(a, dtype=out_dtype) a_shape = a.shape # copy is necessary to present `a` to be overwritten. a = a.astype(dtype, order='C').reshape(-1, a_shape[-2], a_shape[-1]) handle = device.get_cublas_handle() batch_size = a.shape[0] n = a.shape[1] lda = n step = n * lda * a.itemsize start = a.data.ptr stop = start + step * batch_size a_array = cupy.arange(start, stop, step, dtype=cupy.uintp) pivot_array = cupy.empty((batch_size, n), dtype=cupy.int32) info_array = cupy.empty((batch_size,), dtype=cupy.int32) getrf(handle, n, a_array.data.ptr, lda, pivot_array.data.ptr, info_array.data.ptr, batch_size) cupy.linalg._util._check_cublas_info_array_if_synchronization_allowed( getrf, info_array) c = cupy.empty_like(a) ldc = lda step = n * ldc * c.itemsize start = c.data.ptr stop = start + step * batch_size c_array = cupy.arange(start, stop, step, dtype=cupy.uintp) getri(handle, n, a_array.data.ptr, lda, pivot_array.data.ptr, c_array.data.ptr, ldc, info_array.data.ptr, batch_size) cupy.linalg._util._check_cublas_info_array_if_synchronization_allowed( getri, info_array) return c.reshape(a_shape).astype(out_dtype, copy=False)
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 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` """ _util._assert_cupy_array(a) _util._assert_nd_squareness(a) if a.ndim > 2: return _potrf_batched(a) dtype, out_dtype = _util.linalg_common_type(a) 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.astype(out_dtype, copy=False)
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 not sparse.isspmatrix_csr(A): A = 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.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 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)') dtype = numpy.promote_types(a.dtype, b.dtype) dtype = numpy.promote_types(dtype, 'f') 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 # prevent 'a' to be overwritten a = a.astype(dtype, copy=True, order='C') x = cupy.empty_like(b) 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 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 cupyx.scipy.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 sparse.isspmatrix_csr(A): A = 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.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': 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
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 eigvalsh(a, UPLO='L'): """Calculates eigenvalues of a symmetric matrix. This method calculates eigenvalues a given symmetric matrix. Note that :func:`cupy.linalg.eigh` calculates both eigenvalues and eigenvectors. Args: a (cupy.ndarray): A symmetric 2-D square matrix ``(M, M)`` or a batch of symmetric 2-D square matrices ``(..., M, M)``. UPLO (str): Select from ``'L'`` or ``'U'``. It specifies which part of ``a`` is used. ``'L'`` uses the lower triangular part of ``a``, and ``'U'`` uses the upper triangular part of ``a``. Returns: cupy.ndarray: Returns eigenvalues as a vector ``w``. For batch input, ``w[k]`` is a vector of eigenvalues of matrix ``a[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.eigvalsh` """ if a.ndim < 2: raise ValueError('Array must be at least two-dimensional') _util._assert_nd_squareness(a) if a.ndim > 2: return cupy.cusolver.syevj(a, UPLO, False) else: return _syevd(a, UPLO, False)[0]
def slogdet(a): """Returns sign and logarithm of the determinant of an array. It calculates the natural logarithm of the determinant of a given value. Args: a (cupy.ndarray): The input matrix with dimension ``(..., N, N)``. Returns: tuple of :class:`~cupy.ndarray`: It returns a tuple ``(sign, logdet)``. ``sign`` represents each sign of the determinant as a real number ``0``, ``1`` or ``-1``. 'logdet' represents the natural logarithm of the absolute of the determinant. If the determinant is zero, ``sign`` will be ``0`` and ``logdet`` will be ``-inf``. The shapes of both ``sign`` and ``logdet`` are equal to ``a.shape[:-2]``. .. 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`. .. warning:: To produce the same results as :func:`numpy.linalg.slogdet` for singular inputs, set the `linalg` configuration to `raise`. .. seealso:: :func:`numpy.linalg.slogdet` """ if a.ndim < 2: msg = ('%d-dimensional array given. ' 'Array must be at least two-dimensional' % a.ndim) raise linalg.LinAlgError(msg) _util._assert_nd_squareness(a) dtype = numpy.promote_types(a.dtype.char, 'f') real_dtype = numpy.dtype(dtype.char.lower()) if dtype not in (numpy.float32, numpy.float64, numpy.complex64, numpy.complex128): msg = ('dtype must be float32, float64, complex64, or complex128' ' (actual: {})'.format(a.dtype)) raise ValueError(msg) a_shape = a.shape shape = a_shape[:-2] n = a_shape[-2] if a.size == 0: # empty batch (result is empty, too) or empty matrices det([[]]) == 1 sign = cupy.ones(shape, dtype) logdet = cupy.zeros(shape, real_dtype) return sign, logdet lu, ipiv, dev_info = _decomposition._lu_factor(a, dtype) # dev_info < 0 means illegal value (in dimensions, strides, and etc.) that # should never happen even if the matrix contains nan or inf. # TODO(kataoka): assert dev_info >= 0 if synchronization is allowed for # debugging purposes. diag = cupy.diagonal(lu, axis1=-2, axis2=-1) logdet = cupy.log(cupy.abs(diag)).sum(axis=-1) # ipiv is 1-origin non_zero = cupy.count_nonzero(ipiv != cupy.arange(1, n + 1), axis=-1) if dtype.kind == "f": non_zero += cupy.count_nonzero(diag < 0, axis=-1) # Note: sign == -1 ** (non_zero % 2) sign = (non_zero % 2) * -2 + 1 if dtype.kind == "c": sign = sign * cupy.prod(diag / cupy.abs(diag), axis=-1) singular = dev_info > 0 return ( cupy.where(singular, dtype.type(0), sign.astype(dtype)).reshape(shape), cupy.where(singular, real_dtype.type('-inf'), logdet).reshape(shape), )
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 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 batched_gesv(a, b): """Solves multiple linear matrix equations using cublas<t>getr[fs]Batched(). Computes the solution to 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)``. """ _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)') dtype = numpy.promote_types(a.dtype.char, 'f') if dtype == 'f': t = 's' elif dtype == 'd': t = 'd' elif dtype == 'F': t = 'c' elif dtype == 'D': t = 'z' else: raise TypeError('invalid dtype') getrf = getattr(cublas, t + 'getrfBatched') getrs = getattr(cublas, t + 'getrsBatched') bs = numpy.prod(a.shape[:-2]) if a.ndim > 2 else 1 n = a.shape[-1] nrhs = b.shape[-1] if a.ndim == b.ndim else 1 b_shape = b.shape a_data_ptr = a.data.ptr b_data_ptr = b.data.ptr a = cupy.ascontiguousarray(a.reshape(bs, n, n).transpose(0, 2, 1), dtype=dtype) b = cupy.ascontiguousarray(b.reshape(bs, n, nrhs).transpose(0, 2, 1), dtype=dtype) if a.data.ptr == a_data_ptr: a = a.copy() if b.data.ptr == b_data_ptr: b = b.copy() if n > get_batched_gesv_limit(): warnings.warn('The matrix size ({}) exceeds the set limit ({})'.format( n, get_batched_gesv_limit())) handle = device.get_cublas_handle() lda = n a_step = lda * n * a.itemsize a_array = cupy.arange(a.data.ptr, a.data.ptr + a_step * bs, a_step, dtype=cupy.uintp) ldb = n b_step = ldb * nrhs * b.itemsize b_array = cupy.arange(b.data.ptr, b.data.ptr + b_step * bs, b_step, dtype=cupy.uintp) pivot = cupy.empty((bs, n), dtype=numpy.int32) dinfo = cupy.empty((bs, ), dtype=numpy.int32) info = numpy.empty((1, ), dtype=numpy.int32) # LU factorization (A = L * U) getrf(handle, n, a_array.data.ptr, lda, pivot.data.ptr, dinfo.data.ptr, bs) _util._check_cublas_info_array_if_synchronization_allowed(getrf, dinfo) # Solves Ax = b getrs(handle, cublas.CUBLAS_OP_N, n, nrhs, a_array.data.ptr, lda, pivot.data.ptr, b_array.data.ptr, ldb, info.ctypes.data, bs) if info[0] != 0: msg = 'Error reported by {} in cuBLAS. '.format(getrs.__name__) if info[0] < 0: msg += 'The {}-th parameter had an illegal value.'.format(-info[0]) raise linalg.LinAlgError(msg) return b.transpose(0, 2, 1).reshape(b_shape)
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