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/*! @file dlangs.c
* \brief Returns the value of the one norm
*
* <pre>
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
* Modified from lapack routine DLANGE
* </pre>
*/
/*
* File name: dlangs.c
* History: Modified from lapack routine DLANGE
*/
#include <math.h>
#include "slu_ddefs.h"
/*! \brief
*
* <pre>
* Purpose
* =======
*
* DLANGS returns the value of the one norm, or the Frobenius norm, or
* the infinity norm, or the element of largest absolute value of a
* real matrix A.
*
* Description
* ===========
*
* DLANGE returns the value
*
* DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
* (
* ( norm1(A), NORM = '1', 'O' or 'o'
* (
* ( normI(A), NORM = 'I' or 'i'
* (
* ( normF(A), NORM = 'F', 'f', 'E' or 'e'
*
* where norm1 denotes the one norm of a matrix (maximum column sum),
* normI denotes the infinity norm of a matrix (maximum row sum) and
* normF denotes the Frobenius norm of a matrix (square root of sum of
* squares). Note that max(abs(A(i,j))) is not a matrix norm.
*
* Arguments
* =========
*
* NORM (input) CHARACTER*1
* Specifies the value to be returned in DLANGE as described above.
* A (input) SuperMatrix*
* The M by N sparse matrix A.
*
* =====================================================================
* </pre>
*/
double dlangs(char *norm, SuperMatrix *A)
{
/* Local variables */
NCformat *Astore;
double *Aval;
int i, j, irow;
double value, sum;
double *rwork;
Astore = A->Store;
Aval = Astore->nzval;
if ( SUPERLU_MIN(A->nrow, A->ncol) == 0) {
value = 0.;
} else if (strncmp(norm, "M", 1)==0) {
/* Find max(abs(A(i,j))). */
value = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
value = SUPERLU_MAX( value, fabs( Aval[i]) );
} else if (strncmp(norm, "O", 1)==0 || *(unsigned char *)norm == '1') {
/* Find norm1(A). */
value = 0.;
for (j = 0; j < A->ncol; ++j) {
sum = 0.;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
sum += fabs(Aval[i]);
value = SUPERLU_MAX(value,sum);
}
} else if (strncmp(norm, "I", 1)==0) {
/* Find normI(A). */
if ( !(rwork = (double *) SUPERLU_MALLOC(A->nrow * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for rwork.");
for (i = 0; i < A->nrow; ++i) rwork[i] = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++) {
irow = Astore->rowind[i];
rwork[irow] += fabs(Aval[i]);
}
value = 0.;
for (i = 0; i < A->nrow; ++i)
value = SUPERLU_MAX(value, rwork[i]);
SUPERLU_FREE (rwork);
} else if (strncmp(norm, "F", 1)==0 || strncmp(norm, "E", 1)==0) {
/* Find normF(A). */
ABORT("Not implemented.");
} else
ABORT("Illegal norm specified.");
return (value);
} /* dlangs */
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