/* dpocon.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int dpocon_(char *uplo, integer *n, doublereal *a, integer *
lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer *
iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
doublereal d__1;
/* Local variables */
integer ix, kase;
doublereal scale;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *,
integer *);
logical upper;
extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
doublereal scalel;
extern integer idamax_(integer *, doublereal *, integer *);
doublereal scaleu;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal ainvnm;
extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
char normin[1];
doublereal smlnum;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DPOCON estimates the reciprocal of the condition number (in the */
/* 1-norm) of a real symmetric positive definite matrix using the */
/* Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF. */
/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**T*U or A = L*L**T, as computed by DPOTRF. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* ANORM (input) DOUBLE PRECISION */
/* The 1-norm (or infinity-norm) of the symmetric matrix A. */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/* estimate of the 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*anorm < 0.) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DPOCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm == 0.) {
return 0;
}
smlnum = dlamch_("Safe minimum");
/* Estimate the 1-norm of inv(A). */
kase = 0;
*(unsigned char *)normin = 'N';
L10:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (upper) {
/* Multiply by inv(U'). */
dlatrs_("Upper", "Transpose", "Non-unit", normin, n, &a[a_offset],
lda, &work[1], &scalel, &work[(*n << 1) + 1], info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(U). */
dlatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[
a_offset], lda, &work[1], &scaleu, &work[(*n << 1) + 1],
info);
} else {
/* Multiply by inv(L). */
dlatrs_("Lower", "No transpose", "Non-unit", normin, n, &a[
a_offset], lda, &work[1], &scalel, &work[(*n << 1) + 1],
info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(L'). */
dlatrs_("Lower", "Transpose", "Non-unit", normin, n, &a[a_offset],
lda, &work[1], &scaleu, &work[(*n << 1) + 1], info);
}
/* Multiply by 1/SCALE if doing so will not cause overflow. */
scale = scalel * scaleu;
if (scale != 1.) {
ix = idamax_(n, &work[1], &c__1);
if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.)
{
goto L20;
}
drscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
L20:
return 0;
/* End of DPOCON */
} /* dpocon_ */
