dlangs.c

/*! \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 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 */