naginterfaces.library.linsys.real_​sparse_​fac_​solve

naginterfaces.library.linsys.real_sparse_fac_solve(a, comm, rhs, mtype)

real_sparse_fac_solve calculates the approximate solution of a set of real sparse linear equations with a single right-hand side, $Ax=b$ or $A^{T}x=b$, where $A$ has been factorized by matop.real_gen_sparse_lu or matop.real_gen_sparse_lu_reuse.

For full information please refer to the NAG Library document for f04ax

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f04/f04axf.html

Parameters

afloat, array-like, shape $\left(\text{licn}\right)$

The nonzero elements in the factorization of the matrix $A$, as returned by matop.real_gen_sparse_lu or matop.real_gen_sparse_lu_reuse.

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to matop.real_gen_sparse_lu.

rhsfloat, array-like, shape $\left(n\right)$

The right-hand side vector $b$.

mtypeint

$mtype$ specifies the task to be performed.

$mtype=1$

Solve $Ax=b$.

$mtype\ne 1$

Solve $A^{T}x=b$.

Returns

rhsfloat, ndarray, shape $\left(n\right)$

$rhs$ is overwritten by the solution vector $x$.

residfloat

The value of the maximum residual, $max\left(|b_i-{\sum }_j{a}_{ij}{x}_j|\right)$, over all the unsatisfied equations, in case matop.real_gen_sparse_lu or matop.real_gen_sparse_lu_reuse has been used to factorize a singular or rectangular matrix.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

To solve a system of real linear equations $Ax=b$ or $A^{T}x=b$, where $A$ is a general sparse matrix, $A$ must first be factorized by matop.real_gen_sparse_lu or matop.real_gen_sparse_lu_reuse. real_sparse_fac_solve then computes $x$ by block forward or backward substitution using simple forward and backward substitution within each diagonal block.

The method is fully described in Duff (1977).

A more recent method is available through solver function sparse.direct_real_gen_solve and factorization function sparse.direct_real_gen_lu.

References

Duff, I S, 1977, MA28 – a set of Fortran subroutines for sparse unsymmetric linear equations, AERE Report R8730, HMSO