nag_sparse_nherm_matvec (f11xnc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_sparse_nherm_matvec (f11xnc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sparse_nherm_matvec (f11xnc) computes a matrix-vector or conjugate transposed matrix-vector product involving a complex sparse non-Hermitian matrix stored in coordinate storage format.

2  Specification

#include <nag.h>
#include <nagf11.h>
void  nag_sparse_nherm_matvec (Nag_TransType trans, Integer n, Integer nnz, const Complex a[], const Integer irow[], const Integer icol[], Nag_SparseNsym_CheckData check, const Complex x[], Complex y[], NagError *fail)

3  Description

nag_sparse_nherm_matvec (f11xnc) computes either the matrix-vector product y=Ax, or the conjugate transposed matrix-vector product y=AHx, according to the value of the argument trans, where A is a complex n by n sparse non-Hermitian matrix, of arbitrary sparsity pattern. The matrix A is stored in coordinate storage (CS) format (see Section 2.1.1 in the f11 Chapter Introduction). The array a stores all the nonzero elements 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_nherm_matvec (f11xnc) will be to compute the matrix-vector product required in the application of nag_sparse_nherm_basic_solver (f11bsc) to sparse complex linear systems. This is illustrated in Section 9 in nag_sparse_nherm_precon_ssor_solve (f11drc).

4  References

None.

5  Arguments

1:     transNag_TransTypeInput
On entry: specifies whether or not the matrix A is conjugate transposed.
trans=Nag_NoTrans
y=Ax is computed.
trans=Nag_ConjTrans
y=AHx is computed.
Constraint: trans=Nag_NoTrans or Nag_ConjTrans.
2:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n1.
3:     nnzIntegerInput
On entry: the number of nonzero elements in the matrix A.
Constraint: 1nnzn2.
4:     a[nnz]const ComplexInput
On entry: the nonzero elements in 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_nherm_sort (f11znc) may be used to order the elements in this way.
5:     irow[nnz]const IntegerInput
6:     icol[nnz]const IntegerInput
On entry: the row and column indices of the nonzero elements supplied in array a.
Constraints:
  • 1irow[i]n and 1icol[i]n, 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.
7:     checkNag_SparseNsym_CheckDataInput
On entry: specifies whether or not the CS representation of the matrix A, values of n, nnz, irow and icol should be checked.
check=Nag_SparseNsym_Check
Checks are carried on the values of n, nnz, irow and icol.
check=Nag_SparseNsym_NoCheck
None of these checks are carried out.
See also Section 8.2.
Constraint: check=Nag_SparseNsym_Check or Nag_SparseNsym_NoCheck.
8:     x[n]const ComplexInput
On entry: the vector x.
9:     y[n]ComplexOutput
On exit: the vector y.
10:   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: nnzn2.
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_CS
On entry, i=value, icol[i-1]=value, n=value.
Constraint: icol[i-1]1 and icol[i-1]n.
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_nherm_sort (f11znc) to reorder and sum or remove duplicates.

7  Accuracy

The computed vector y satisfies the error bound: 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_nherm_matvec (f11xnc) is proportional to nnz.

8.2  Use of check

It is expected that a common use of nag_sparse_nherm_matvec (f11xnc) will be to compute the matrix-vector product required in the application of nag_sparse_nherm_basic_solver (f11bsc) to sparse complex linear systems. In this situation nag_sparse_nherm_matvec (f11xnc) 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_SparseNsym_Check for the first of such calls, and to set check=Nag_SparseNsym_NoCheck for all subsequent calls.

9  Example

This example reads in a complex sparse matrix A and a vector x. It then calls nag_sparse_nherm_matvec (f11xnc) to compute the matrix-vector product y=Ax and the conjugate transposed matrix-vector product y=AHx.

9.1  Program Text

Program Text (f11xnce.c)

9.2  Program Data

Program Data (f11xnce.d)

9.3  Program Results

Program Results (f11xnce.r)


nag_sparse_nherm_matvec (f11xnc) (PDF version)
f11 Chapter Contents
f11 Chapter Introduction
NAG C Library Manual

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