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/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/
/*! @file zlangs.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 ZLANGE
* </pre>
*/
/*
* File name: zlangs.c
* History: Modified from lapack routine ZLANGE
*/
#include <math.h>
#include "slu_zdefs.h"
/*! \brief
*
* <pre>
* Purpose
* =======
*
* ZLANGS 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
* ===========
*
* ZLANGE returns the value
*
* ZLANGE = ( 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 ZLANGE as described above.
* A (input) SuperMatrix*
* The M by N sparse matrix A.
*
* =====================================================================
* </pre>
*/
double zlangs(char *norm, SuperMatrix *A)
{
/* Local variables */
NCformat *Astore;
doublecomplex *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, z_abs( &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 += z_abs( &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] += z_abs( &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);
} /* zlangs */
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