# Source code for dolfinx.la

# Copyright (C) 2017-2021 Garth N. Wells
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
"""Linear algebra functionality"""

import numpy as np

from dolfinx import cpp as _cpp
from dolfinx.cpp.la import Norm, ScatterMode
from dolfinx.cpp.la.petsc import create_vector as create_petsc_vector

__all__ = ["orthonormalize", "is_orthonormal", "create_petsc_vector", "matrix_csr", "vector",
"MatrixCSRMetaClass", "Norm", "ScatterMode", "VectorMetaClass", ]

[docs]def orthonormalize(basis): """Orthogoalise set of PETSc vectors in-place""" for i, x in enumerate(basis): for y in basis[:i]: alpha = x.dot(y) x.axpy(-alpha, y) x.normalize()
[docs]def is_orthonormal(basis, eps: float = 1.0e-12) -> bool: """Check that list of PETSc vectors are orthonormal""" for x in basis: if abs(x.norm() - 1.0) > eps: return False for i, x in enumerate(basis[:-1]): for y in basis[i + 1:]: if abs(x.dot(y)) > eps: return False return True
[docs]class MatrixCSRMetaClass: def __init__(self, sp): """A distributed sparse matrix that uses compressed sparse row storage. Args: sp: The sparsity pattern that defines the nonzero structure of the matrix the parallel distribution of the matrix Note: Objects of this type should be created using :func:`matrix_csr` and not created using the class initialiser. """ super().__init__(sp)
[docs]def matrix_csr(sp, dtype=np.float64) -> MatrixCSRMetaClass: """Create a distributed sparse matrix. The matrix uses compressed sparse row storage. Args: sp: The sparsity pattern that defines the nonzero structure of the matrix the parallel distribution of the matrix. dtype: The scalar type. Returns: A sparse matrix. """ if dtype == np.float32: ftype = _cpp.la.MatrixCSR_float32 elif dtype == np.float64: ftype = _cpp.la.MatrixCSR_float64 elif dtype == np.complex64: ftype = _cpp.la.MatrixCSR_complex64 elif dtype == np.complex128: ftype = _cpp.la.MatrixCSR_complex128 else: raise NotImplementedError(f"Type {dtype} not supported.") matrixcls = type("MatrixCSR", (MatrixCSRMetaClass, ftype), {}) return matrixcls(sp)
[docs]class VectorMetaClass: def __init__(self, map, bs): """A distributed vector object. Args: map: Index map the describes the size and distribution of the vector bs: Block size Note: Objects of this type should be created using :func:`vector` and not created using the class initialiser. """ super().__init__(map, bs) # type: ignore @property def array(self) -> np.ndarray: return super().array # type: ignore
[docs]def vector(map, bs=1, dtype=np.float64) -> VectorMetaClass: """Create a distributed vector. Args: map: Index map the describes the size and distribution of the vector. bs: Block size. dtype: The scalar type. Returns: A distributed vector. """ if dtype == np.float32: vtype = _cpp.la.Vector_float32 elif dtype == np.float64: vtype = _cpp.la.Vector_float64 elif dtype == np.complex64: vtype = _cpp.la.Vector_complex64 elif dtype == np.complex128: vtype = _cpp.la.Vector_complex128 else: raise NotImplementedError(f"Type {dtype} not supported.") vectorcls = type("Vector", (VectorMetaClass, vtype), {}) return vectorcls(map, bs)