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authormaxim-yurchuk <maxim-yurchuk@yandex-team.com>2024-10-09 12:29:46 +0300
committermaxim-yurchuk <maxim-yurchuk@yandex-team.com>2024-10-09 13:14:22 +0300
commit9731d8a4bb7ee2cc8554eaf133bb85498a4c7d80 (patch)
treea8fb3181d5947c0d78cf402aa56e686130179049 /contrib/libs/clapack/sla_syrcond.c
parenta44b779cd359f06c3ebbef4ec98c6b38609d9d85 (diff)
downloadydb-9731d8a4bb7ee2cc8554eaf133bb85498a4c7d80.tar.gz
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+/* sla_syrcond.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;
+
+doublereal sla_syrcond__(char *uplo, integer *n, real *a, integer *lda, real *
+ af, integer *ldaf, integer *ipiv, integer *cmode, real *c__, integer *
+ info, real *work, integer *iwork, ftnlen uplo_len)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2;
+ real ret_val, r__1;
+
+ /* Local variables */
+ integer i__, j;
+ logical up;
+ real tmp;
+ integer kase;
+ extern logical lsame_(char *, char *);
+ integer isave[3];
+ extern /* Subroutine */ int slacn2_(integer *, real *, real *, integer *,
+ real *, integer *, integer *);
+ extern doublereal slamch_(char *);
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ real ainvnm;
+ char normin[1];
+ real smlnum;
+ extern /* Subroutine */ int ssytrs_(char *, integer *, integer *, real *,
+ integer *, integer *, real *, integer *, integer *);
+
+
+/* -- LAPACK routine (version 3.2.1) -- */
+/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
+/* -- Jason Riedy of Univ. of California Berkeley. -- */
+/* -- April 2009 -- */
+
+/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
+/* -- Univ. of California Berkeley and NAG Ltd. -- */
+
+/* .. */
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) */
+/* where op2 is determined by CMODE as follows */
+/* CMODE = 1 op2(C) = C */
+/* CMODE = 0 op2(C) = I */
+/* CMODE = -1 op2(C) = inv(C) */
+/* The Skeel condition number cond(A) = norminf( |inv(A)||A| ) */
+/* is computed by computing scaling factors R such that */
+/* diag(R)*A*op2(C) is row equilibrated and computing the standard */
+/* infinity-norm condition number. */
+
+/* Arguments */
+/* ========== */
+
+/* UPLO (input) CHARACTER*1 */
+/* = 'U': Upper triangle of A is stored; */
+/* = 'L': Lower triangle of A is stored. */
+
+/* N (input) INTEGER */
+/* The number of linear equations, i.e., the order of the */
+/* matrix A. N >= 0. */
+
+/* A (input) REAL array, dimension (LDA,N) */
+/* On entry, the N-by-N matrix A. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,N). */
+
+/* AF (input) REAL array, dimension (LDAF,N) */
+/* The block diagonal matrix D and the multipliers used to */
+/* obtain the factor U or L as computed by SSYTRF. */
+
+/* LDAF (input) INTEGER */
+/* The leading dimension of the array AF. LDAF >= max(1,N). */
+
+/* IPIV (input) INTEGER array, dimension (N) */
+/* Details of the interchanges and the block structure of D */
+/* as determined by SSYTRF. */
+
+/* CMODE (input) INTEGER */
+/* Determines op2(C) in the formula op(A) * op2(C) as follows: */
+/* CMODE = 1 op2(C) = C */
+/* CMODE = 0 op2(C) = I */
+/* CMODE = -1 op2(C) = inv(C) */
+
+/* C (input) REAL array, dimension (N) */
+/* The vector C in the formula op(A) * op2(C). */
+
+/* INFO (output) INTEGER */
+/* = 0: Successful exit. */
+/* i > 0: The ith argument is invalid. */
+
+/* WORK (input) REAL array, dimension (3*N). */
+/* Workspace. */
+
+/* IWORK (input) INTEGER array, dimension (N). */
+/* Workspace. */
+
+/* ===================================================================== */
+
+/* .. Local Scalars .. */
+/* .. */
+/* .. Local Arrays .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ af_dim1 = *ldaf;
+ af_offset = 1 + af_dim1;
+ af -= af_offset;
+ --ipiv;
+ --c__;
+ --work;
+ --iwork;
+
+ /* Function Body */
+ ret_val = 0.f;
+
+ *info = 0;
+ if (*n < 0) {
+ *info = -2;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("SLA_SYRCOND", &i__1);
+ return ret_val;
+ }
+ if (*n == 0) {
+ ret_val = 1.f;
+ return ret_val;
+ }
+ up = FALSE_;
+ if (lsame_(uplo, "U")) {
+ up = TRUE_;
+ }
+
+/* Compute the equilibration matrix R such that */
+/* inv(R)*A*C has unit 1-norm. */
+
+ if (up) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ tmp = 0.f;
+ if (*cmode == 1) {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1] * c__[j], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1] * c__[j], dabs(r__1));
+ }
+ } else if (*cmode == 0) {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1], dabs(r__1));
+ }
+ } else {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1] / c__[j], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1] / c__[j], dabs(r__1));
+ }
+ }
+ work[(*n << 1) + i__] = tmp;
+ }
+ } else {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ tmp = 0.f;
+ if (*cmode == 1) {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1] * c__[j], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1] * c__[j], dabs(r__1));
+ }
+ } else if (*cmode == 0) {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1], dabs(r__1));
+ }
+ } else {
+ i__2 = i__;
+ for (j = 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[i__ + j * a_dim1] / c__[j], dabs(r__1));
+ }
+ i__2 = *n;
+ for (j = i__ + 1; j <= i__2; ++j) {
+ tmp += (r__1 = a[j + i__ * a_dim1] / c__[j], dabs(r__1));
+ }
+ }
+ work[(*n << 1) + i__] = tmp;
+ }
+ }
+
+/* Estimate the norm of inv(op(A)). */
+
+ smlnum = slamch_("Safe minimum");
+ ainvnm = 0.f;
+ *(unsigned char *)normin = 'N';
+ kase = 0;
+L10:
+ slacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
+ if (kase != 0) {
+ if (kase == 2) {
+
+/* Multiply by R. */
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] *= work[(*n << 1) + i__];
+ }
+ if (up) {
+ ssytrs_("U", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+ 1], n, info);
+ } else {
+ ssytrs_("L", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+ 1], n, info);
+ }
+
+/* Multiply by inv(C). */
+
+ if (*cmode == 1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] /= c__[i__];
+ }
+ } else if (*cmode == -1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] *= c__[i__];
+ }
+ }
+ } else {
+
+/* Multiply by inv(C'). */
+
+ if (*cmode == 1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] /= c__[i__];
+ }
+ } else if (*cmode == -1) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] *= c__[i__];
+ }
+ }
+ if (up) {
+ ssytrs_("U", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+ 1], n, info);
+ } else {
+ ssytrs_("L", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[
+ 1], n, info);
+ }
+
+/* Multiply by R. */
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ work[i__] *= work[(*n << 1) + i__];
+ }
+ }
+
+ goto L10;
+ }
+
+/* Compute the estimate of the reciprocal condition number. */
+
+ if (ainvnm != 0.f) {
+ ret_val = 1.f / ainvnm;
+ }
+
+ return ret_val;
+
+} /* sla_syrcond__ */