dlangs.c

SuperLU 2.2版本。对大型、稀疏、非对称的线性系统的直接求解

/*
 * File name:	dlangs.c
 * History:     Modified from lapack routine DLANGE
 */
#include <math.h>
#include "superlu_ddefs.h"

double dlangs_dist(char *norm, SuperMatrix *A)
{
/* 
    Purpose   
    =======   

    DLANGS_dist 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. 

   ===================================================================== 
*/
    
    /* Local variables */
    NCformat *Astore;
    double   *Aval;
    int_t    i, j, irow;
    double   value=0., sum;
    double   *rwork;

    Astore = (NCformat *) A->Store;
    Aval   = (double *) Astore->nzval;
    
    if ( SUPERLU_MIN(A->nrow, A->ncol) == 0) {
	value = 0.;
	
    } else if (lsame_(norm, "M")) {
	/* 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 (lsame_(norm, "O") || *(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 (lsame_(norm, "I")) {
	/* 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 (lsame_(norm, "F") || lsame_(norm, "E")) {
	/* Find normF(A). */
	ABORT("Not implemented.");
    } else
	ABORT("Illegal norm specified.");

    return (value);

} /* dlangs_dist */