nag_sparse_sym_matvec (f11xec) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_sparse_sym_matvec (f11xec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sparse_sym_matvec (f11xec) computes a matrix-vector product involving a real sparse symmetric matrix stored in symmetric coordinate storage format.

2  Specification

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

3  Description

nag_sparse_sym_matvec (f11xec) computes the matrix-vector product
y=Ax
where A is an n by n symmetric sparse matrix, of arbitrary sparsity pattern, stored in symmetric coordinate storage (SCS) format (see Section 2.1.2 in the f11 Chapter Introduction). The array a stores all nonzero elements in the lower triangular part of A, while arrays irow and icol store the corresponding row and column indices respectively.
It is envisaged that a common use of nag_sparse_sym_matvec (f11xec) will be to compute the matrix-vector product required in the application of nag_sparse_sym_basic_solver (f11gec) to sparse symmetric linear systems. An illustration of this usage appears in nag_sparse_sym_precon_ssor_solve (f11jdc).

4  References

None.

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 A.
Constraint: 1nnzn×n+1/2.
3:     a[nnz]const doubleInput
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_sym_sort (f11zbc) 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.
Constraints:
irow and icol must satisfy these constraints (which may be imposed by a call to nag_sparse_sym_sort (f11zbc)):
  • 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:     checkNag_SparseSym_CheckDataInput
On entry: specifies whether or not the SCS representation of the matrix A, values of n, nnz, irow and icol should be checked.
check=Nag_SparseSym_Check
Checks are carried out on the values of n, nnz, irow and icol.
check=Nag_SparseSym_NoCheck
None of these checks are carried out.
See also Section 8.2.
Constraint: check=Nag_SparseSym_Check or Nag_SparseSym_NoCheck.
7:     x[n]const doubleInput
On entry: the vector x.
8:     y[n]doubleOutput
On exit: the vector y.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n1.
On entry, nnz=value.
Constraint: nnz1.
NE_INT_2
On entry, nnz=value and n=value.
Constraint: nnzn×n+1/2.
NE_INTERNAL_ERROR
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.
NE_INVALID_SCS
On entry, i=value, icol[i-1]=value, irow[i-1]=value.
Constraint: icol[i-1]1 and icol[i-1]irow[i-1].
On entry, i=value, irow[i-1]=value, n=value.
Constraint: irow[i-1]1 and irow[i-1]n.
NE_NOT_STRICTLY_INCREASING
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_sym_sort (f11zbc) to reorder and sum or remove duplicates.

7  Accuracy

The computed vector y satisfies the error bound
y-AxcnεAx,
where cn is a modest linear function of n, and ε is the machine precision.

8  Further Comments

8.1  Timing

The time taken for a call to nag_sparse_sym_matvec (f11xec) is proportional to nnz.

8.2  Use of check

It is expected that a common use of nag_sparse_sym_matvec (f11xec) will be to compute the matrix-vector product required in the application of nag_sparse_sym_basic_solver (f11gec) to sparse symmetric linear systems. In this situation nag_sparse_sym_matvec (f11xec) is likely to be called many times with the same matrix A. In the interests of both reliability and efficiency you are recommended to set check=Nag_SparseSym_Check for the first of such calls, and to set check=Nag_SparseSym_NoCheck for all subsequent calls.

9  Example

This example reads in a symmetric positive definite sparse matrix A and a vector x. It then calls nag_sparse_sym_matvec (f11xec) to compute the matrix-vector product y=Ax.

9.1  Program Text

Program Text (f11xece.c)

9.2  Program Data

Program Data (f11xece.d)

9.3  Program Results

Program Results (f11xece.r)


nag_sparse_sym_matvec (f11xec) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012