naginterfaces.library.sparse.direct_​real_​gen_​solve

naginterfaces.library.sparse.direct_real_gen_solve(trans, iprm, il, lval, iu, uval, b)

direct_real_gen_solve solves a real sparse system of linear equations with multiple right-hand sides given an $LU$ factorization of the sparse matrix computed by direct_real_gen_lu().

For full information please refer to the NAG Library document for f11mf

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f11/f11mff.html

Parameters

transstr, length 1

Specifies whether $AX=B$ or $A^{T}X=B$ is solved.

$trans=\text{'N'}$

$AX=B$ is solved.

$trans=\text{'T'}$

$A^{T}X=B$ is solved.

iprmint, array-like, shape $(7\times n)$

The column permutation which defines $P_c$, the row permutation which defines $P_r$, plus associated data structures as computed by direct_real_gen_lu().

ilint, array-like, shape $(:)$

Records the sparsity pattern of matrix $L$ as computed by direct_real_gen_lu().

lvalfloat, array-like, shape $(:)$

Records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by direct_real_gen_lu().

iuint, array-like, shape $(:)$

Records the sparsity pattern of matrix $U$ as computed by direct_real_gen_lu().

uvalfloat, array-like, shape $(:)$

Records some nonzero values of matrix $U$ as computed by direct_real_gen_lu().

bfloat, array-like, shape $(n,\text{nrhs})$

The $n\times \text{nrhs}$ right-hand side matrix $B$.

Returns

bfloat, ndarray, shape $(n,\text{nrhs})$

The $n\times \text{nrhs}$ solution matrix $X$.

Raises

NagValueError

(errno $1$)

On entry, $\text{nrhs}=⟨value⟩$.

Constraint: $\text{nrhs}\ge 0$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $1$)

On entry, $trans=⟨value⟩$.

Constraint: $trans=\text{'N'}$ or $\text{'T'}$.

(errno $2$)

Incorrect row permutations in array $iprm$.

(errno $3$)

Incorrect column permutations in array $iprm$.

Notes

direct_real_gen_solve solves a real system of linear equations with multiple right-hand sides $AX=B$ or $A^{T}X=B$, according to the value of the argument $trans$, where the matrix factorization $P_{r}A{P}_c=LU$ corresponds to an $LU$ decomposition of a sparse matrix stored in compressed column (Harwell–Boeing) format, as computed by direct_real_gen_lu().

In the above decomposition $L$ is a lower triangular sparse matrix with unit diagonal elements and $U$ is an upper triangular sparse matrix; $P_r$ and $P_c$ are permutation matrices.