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bundles / scipy latest / scipy / sparse / linalg / _dsolve / linsolve / spsolve

function

scipy.sparse.linalg._dsolve.linsolve:spsolve

source: /scipy/sparse/linalg/_dsolve/linsolve.py :134

Signature

def   spsolve ( A ,  b ,  permc_spec = None ,  use_umfpack = True )

Summary

Solve the sparse linear system Ax=b, where b may be a vector or a matrix.

Parameters

A : ndarray or sparse array or matrix

The square matrix A will be converted into CSC or CSR form

b : ndarray or sparse array or matrix

The matrix or vector representing the right hand side of the equation. If a vector, b.shape must be (n,) or (n, 1).

permc_spec : str, optional

How to permute the columns of the matrix for sparsity preservation. (default: 'COLAMD')

  • NATURAL: natural ordering.

  • MMD_ATA: minimum degree ordering on the structure of A^T A.

  • MMD_AT_PLUS_A: minimum degree ordering on the structure of A^T+A.

  • COLAMD: approximate minimum degree column ordering [1], [2].

use_umfpack : bool, optional

if True (default) then use UMFPACK for the solution [3], [4], [5], [6] . This is only referenced if b is a vector and scikits.umfpack is installed.

Returns

x : ndarray or sparse array or matrix

the solution of the sparse linear equation. If b is a vector, then x is a vector of size A.shape[1] If b is a matrix, then x is a matrix of size (A.shape[1], b.shape[1])

Notes

For solving the matrix expression AX = B, this solver assumes the resulting matrix X is sparse, as is often the case for very sparse inputs. If the resulting X is dense, the construction of this sparse result will be relatively expensive. In that case, consider converting A to a dense matrix and using scipy.linalg.solve or its variants.

Examples

import numpy as np
from scipy.sparse import csc_array
from scipy.sparse.linalg import spsolve
A = csc_array([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
B = csc_array([[2, 0], [-1, 0], [2, 0]], dtype=float)
x = spsolve(A, B)
np.allclose(A.dot(x).toarray(), B.toarray())
✓

Aliases

  • scipy.sparse.linalg.spsolve

Referenced by

This package