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/*
* -- SuperLU routine (version 3.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* October 15, 2003
*
*/
/*
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
*/
/*
* File name: dgscon.c
* History: Modified from lapack routines DGECON.
*/
#include <math.h>
#include "slu_ddefs.h"
void
dgscon(char *norm, SuperMatrix *L, SuperMatrix *U,
double anorm, double *rcond, SuperLUStat_t *stat, int *info)
{
/*
Purpose
=======
DGSCON estimates the reciprocal of the condition number of a general
real matrix A, in either the 1-norm or the infinity-norm, using
the LU factorization computed by DGETRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
See supermatrix.h for the definition of 'SuperMatrix' structure.
Arguments
=========
NORM (input) char*
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
L (input) SuperMatrix*
The factor L from the factorization Pr*A*Pc=L*U as computed by
dgstrf(). Use compressed row subscripts storage for supernodes,
i.e., L has types: Stype = SLU_SC, Dtype = SLU_D, Mtype = SLU_TRLU.
U (input) SuperMatrix*
The factor U from the factorization Pr*A*Pc=L*U as computed by
dgstrf(). Use column-wise storage scheme, i.e., U has types:
Stype = SLU_NC, Dtype = SLU_D, Mtype = TRU.
ANORM (input) double
If NORM = '1' or 'O', the 1-norm of the original matrix A.
If NORM = 'I', the infinity-norm of the original matrix A.
RCOND (output) double*
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).
INFO (output) int*
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
*/
/* Local variables */
int kase, kase1, onenrm, i;
double ainvnm;
double *work;
int *iwork;
extern int drscl_(int *, double *, double *, int *);
extern int dlacon_(int *, double *, double *, int *, double *, int *);
/* Test the input parameters. */
*info = 0;
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
if (! onenrm && ! lsame_(norm, "I")) *info = -1;
else if (L->nrow < 0 || L->nrow != L->ncol ||
L->Stype != SLU_SC || L->Dtype != SLU_D || L->Mtype != SLU_TRLU)
*info = -2;
else if (U->nrow < 0 || U->nrow != U->ncol ||
U->Stype != SLU_NC || U->Dtype != SLU_D || U->Mtype != SLU_TRU)
*info = -3;
if (*info != 0) {
i = -(*info);
xerbla_("dgscon", &i);
return;
}
/* Quick return if possible */
*rcond = 0.;
if ( L->nrow == 0 || U->nrow == 0) {
*rcond = 1.;
return;
}
work = doubleCalloc( 3*L->nrow );
iwork = intMalloc( L->nrow );
if ( !work || !iwork )
ABORT("Malloc fails for work arrays in dgscon.");
/* Estimate the norm of inv(A). */
ainvnm = 0.;
if ( onenrm ) kase1 = 1;
else kase1 = 2;
kase = 0;
do {
dlacon_(&L->nrow, &work[L->nrow], &work[0], &iwork[0], &ainvnm, &kase);
if (kase == 0) break;
if (kase == kase1) {
/* Multiply by inv(L). */
sp_dtrsv("L", "No trans", "Unit", L, U, &work[0], stat, info);
/* Multiply by inv(U). */
sp_dtrsv("U", "No trans", "Non-unit", L, U, &work[0], stat, info);
} else {
/* Multiply by inv(U'). */
sp_dtrsv("U", "Transpose", "Non-unit", L, U, &work[0], stat, info);
/* Multiply by inv(L'). */
sp_dtrsv("L", "Transpose", "Unit", L, U, &work[0], stat, info);
}
} while ( kase != 0 );
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) *rcond = (1. / ainvnm) / anorm;
SUPERLU_FREE (work);
SUPERLU_FREE (iwork);
return;
} /* dgscon */
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