nag_sparse_herm_precon_ssor_solve (f11jrc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_sparse_herm_precon_ssor_solve (f11jrc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sparse_herm_precon_ssor_solve (f11jrc) solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a complex sparse Hermitian matrix, represented in symmetric coordinate storage format.

2  Specification

#include <nag.h>
#include <nagf11.h>
void  nag_sparse_herm_precon_ssor_solve (Integer n, Integer nnz, const Complex a[], const Integer irow[], const Integer icol[], const double rdiag[], double omega, Nag_SparseSym_CheckData check, const Complex y[], Complex x[], NagError *fail)

3  Description

nag_sparse_herm_precon_ssor_solve (f11jrc) solves a system of equations
involving the preconditioning matrix
M=1ω2-ω D+ω L D-1 D+ω LH
corresponding to symmetric successive-over-relaxation (SSOR) (see Young (1971)) on a linear system Ax=b, where A is a sparse complex Hermitian matrix stored in symmetric coordinate storage (SCS) format (see Section 2.1.2 in the f11 Chapter Introduction).
In the definition of M given above D is the diagonal part of A, L is the strictly lower triangular part of A and ω is a user-defined relaxation argument. Note that since A is Hermitian the matrix D is necessarily real.

4  References

Young D (1971) Iterative Solution of Large Linear Systems Academic Press, New York

5  Arguments

1:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n1.
2:     nnzIntegerInput
On entry: the number of nonzero elements in the lower triangular part of the matrix A.
Constraint: 1nnzn×n+1/2.
3:     a[nnz]const ComplexInput
On entry: the nonzero elements in the lower triangular part of the matrix A, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The function nag_sparse_herm_sort (f11zpc) may be used to order the elements in this way.
4:     irow[nnz]const IntegerInput
5:     icol[nnz]const IntegerInput
On entry: the row and column indices of the nonzero elements supplied in array a.
irow and icol must satisfy the following constraints (which may be imposed by a call to nag_sparse_herm_sort (f11zpc)):
  • 1irow[i]n and 1icol[i]irow[i], for i=0,1,,nnz-1;
  • irow[i-1]<irow[i] or irow[i-1]=irow[i] and icol[i-1]<icol[i], for i=1,2,,nnz-1.
6:     rdiag[n]const doubleInput
On entry: the elements of the diagonal matrix D-1, where D is the diagonal part of A. Note that since A is Hermitian the elements of D-1 are necessarily real.
7:     omegadoubleInput
On entry: the relaxation argument ω.
Constraint: 0.0<omega<2.0.
8:     checkNag_SparseSym_CheckDataInput
On entry: specifies whether or not the input data should be checked.
Checks are carried out on the values of n, nnz, irow, icol and omega.
None of these checks are carried out.
Constraint: check=Nag_SparseSym_Check or Nag_SparseSym_NoCheck.
9:     y[n]const ComplexInput
On entry: the right-hand side vector y.
10:   x[n]ComplexOutput
On exit: the solution vector x.
11:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n1.
On entry, nnz=value.
Constraint: nnz1.
On entry, nnz=value and n=value.
Constraint: nnzn×n+1/2.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
On entry, I=value, icol[I-1]=value, irow[I-1]=value.
Constraint: 1icol[i-1]irow[i-1].
On entry, I=value, irow[I-1]=value and n=value.
Constraint: 1irow[i-1]n.
On entry, a[i-1] is out of order: i=value.
On entry, the location (irow[I-1],icol[I-1]) is a duplicate: I=value. Consider calling nag_sparse_herm_sort (f11zpc) to reorder and sum or remove duplicates.
On entry, omega=value.
Constraint: 0.0<omega<2.0.
The matrix A has no diagonal entry in row value.

7  Accuracy

The computed solution x is the exact solution of a perturbed system of equations M+δMx=y, where
cn is a modest linear function of n, and ε is the machine precision.

8  Parallelism and Performance

Not applicable.

9  Further Comments

9.1  Timing

The time taken for a call to nag_sparse_herm_precon_ssor_solve (f11jrc) is proportional to nnz.

10  Example

This example program solves the preconditioning equation Mx=y for a 9 by 9 sparse complex Hermitian matrix A, given in symmetric coordinate storage (SCS) format.

10.1  Program Text

Program Text (f11jrce.c)

10.2  Program Data

Program Data (f11jrce.d)

10.3  Program Results

Program Results (f11jrce.r)

nag_sparse_herm_precon_ssor_solve (f11jrc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014