# scipy.sparse.linalg.spsolve

scipy.sparse.linalg.spsolve(A, b, permc_spec=None, use_umfpack=True)

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

  Parameters
    A ndarray or sparse matrix

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

    b ndarray or sparse 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

    use_umfpack bool, optional

      if True (default) then use umfpack for the solution. This is only referenced if b is a vector and `scikit-umfpack` is installed.

  Returns
    x ndarray or sparse 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

      >>> from scipy.sparse import csc_matrix
      >>> from scipy.sparse.linalg import spsolve
      >>> A = csc_matrix([[3, 2, 0], [1, -1, 0], [0, 5, 1]], dtype=float)
      >>> B = csc_matrix([[2, 0], [-1, 0], [2, 0]], dtype=float)
      >>> x = spsolve(A, B)
      >>> np.allclose(A.dot(x).todense(), B.todense())
      True

scipy.sparse.linalg.onenormest scipy.sparse.linalg.spsolve_triangular