144c6b23bd
Added lapack routines for calculation of condition number and to fill out the QR factorization capability.
228 lines
6.4 KiB
C
228 lines
6.4 KiB
C
/* dgecon.f -- translated by f2c (version 20031025).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer *
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lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer *
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iwork, integer *info, ftnlen norm_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1;
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doublereal d__1;
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/* Local variables */
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static doublereal sl;
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static integer ix;
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static doublereal su;
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static integer kase, kase1;
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static doublereal scale;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *,
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integer *);
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extern doublereal dlamch_(char *, ftnlen);
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extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *);
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extern integer idamax_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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static doublereal ainvnm;
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extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
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static logical onenrm;
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static char normin[1];
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static doublereal smlnum;
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/* -- LAPACK routine (version 3.0) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
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/* Courant Institute, Argonne National Lab, and Rice University */
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/* February 29, 1992 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DGECON estimates the reciprocal of the condition number of a general */
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/* real matrix A, in either the 1-norm or the infinity-norm, using */
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/* the LU factorization computed by DGETRF. */
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/* An estimate is obtained for norm(inv(A)), and the reciprocal of the */
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/* condition number is computed as */
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/* RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
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/* Arguments */
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/* ========= */
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/* NORM (input) CHARACTER*1 */
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/* Specifies whether the 1-norm condition number or the */
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/* infinity-norm condition number is required: */
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/* = '1' or 'O': 1-norm; */
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/* = 'I': Infinity-norm. */
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/* N (input) INTEGER */
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/* The order of the matrix A. N >= 0. */
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/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
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/* The factors L and U from the factorization A = P*L*U */
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/* as computed by DGETRF. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,N). */
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/* ANORM (input) DOUBLE PRECISION */
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/* If NORM = '1' or 'O', the 1-norm of the original matrix A. */
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/* If NORM = 'I', the infinity-norm of the original matrix A. */
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/* RCOND (output) DOUBLE PRECISION */
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/* The reciprocal of the condition number of the matrix A, */
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/* computed as RCOND = 1/(norm(A) * norm(inv(A))). */
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/* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */
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/* IWORK (workspace) INTEGER array, dimension (N) */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -i, the i-th argument had an illegal value */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O", (ftnlen)1, (
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ftnlen)1);
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if (! onenrm && ! lsame_(norm, "I", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -4;
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} else if (*anorm < 0.) {
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*info = -5;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGECON", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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*rcond = 0.;
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if (*n == 0) {
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*rcond = 1.;
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return 0;
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} else if (*anorm == 0.) {
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return 0;
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}
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smlnum = dlamch_("Safe minimum", (ftnlen)12);
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/* Estimate the norm of inv(A). */
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ainvnm = 0.;
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*(unsigned char *)normin = 'N';
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if (onenrm) {
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kase1 = 1;
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} else {
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kase1 = 2;
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}
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kase = 0;
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L10:
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dlacon_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase);
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if (kase != 0) {
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if (kase == kase1) {
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/* Multiply by inv(L). */
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dlatrs_("Lower", "No transpose", "Unit", normin, n, &a[a_offset],
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lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5,
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(ftnlen)12, (ftnlen)4, (ftnlen)1);
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/* Multiply by inv(U). */
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dlatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[
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a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info, (
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ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1);
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} else {
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/* Multiply by inv(U'). */
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dlatrs_("Upper", "Transpose", "Non-unit", normin, n, &a[a_offset],
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lda, &work[1], &su, &work[*n * 3 + 1], info, (ftnlen)5, (
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ftnlen)9, (ftnlen)8, (ftnlen)1);
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/* Multiply by inv(L'). */
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dlatrs_("Lower", "Transpose", "Unit", normin, n, &a[a_offset],
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lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5,
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(ftnlen)9, (ftnlen)4, (ftnlen)1);
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}
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/* Divide X by 1/(SL*SU) if doing so will not cause overflow. */
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scale = sl * su;
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*(unsigned char *)normin = 'Y';
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if (scale != 1.) {
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ix = idamax_(n, &work[1], &c__1);
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if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.)
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{
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goto L20;
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}
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drscl_(n, &scale, &work[1], &c__1);
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}
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goto L10;
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}
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/* Compute the estimate of the reciprocal condition number. */
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if (ainvnm != 0.) {
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*rcond = 1. / ainvnm / *anorm;
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}
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L20:
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return 0;
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/* End of DGECON */
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} /* dgecon_ */
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