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authorshmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
committershmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
commit90d450f74722da7859d6f510a869f6c6908fd12f (patch)
tree538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/slarrk.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
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+/* slarrk.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"
+
+/* Subroutine */ int slarrk_(integer *n, integer *iw, real *gl, real *gu,
+ real *d__, real *e2, real *pivmin, real *reltol, real *w, real *werr,
+ integer *info)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2;
+
+ /* Builtin functions */
+ double log(doublereal);
+
+ /* Local variables */
+ integer i__, it;
+ real mid, eps, tmp1, tmp2, left, atoli, right;
+ integer itmax;
+ real rtoli, tnorm;
+ extern doublereal slamch_(char *);
+ integer negcnt;
+
+
+/* -- LAPACK auxiliary routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLARRK computes one eigenvalue of a symmetric tridiagonal */
+/* matrix T to suitable accuracy. This is an auxiliary code to be */
+/* called from SSTEMR. */
+
+/* To avoid overflow, the matrix must be scaled so that its */
+/* largest element is no greater than overflow**(1/2) * */
+/* underflow**(1/4) in absolute value, and for greatest */
+/* accuracy, it should not be much smaller than that. */
+
+/* See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
+/* Matrix", Report CS41, Computer Science Dept., Stanford */
+/* University, July 21, 1966. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the tridiagonal matrix T. N >= 0. */
+
+/* IW (input) INTEGER */
+/* The index of the eigenvalues to be returned. */
+
+/* GL (input) REAL */
+/* GU (input) REAL */
+/* An upper and a lower bound on the eigenvalue. */
+
+/* D (input) REAL array, dimension (N) */
+/* The n diagonal elements of the tridiagonal matrix T. */
+
+/* E2 (input) REAL array, dimension (N-1) */
+/* The (n-1) squared off-diagonal elements of the tridiagonal matrix T. */
+
+/* PIVMIN (input) REAL */
+/* The minimum pivot allowed in the Sturm sequence for T. */
+
+/* RELTOL (input) REAL */
+/* The minimum relative width of an interval. When an interval */
+/* is narrower than RELTOL times the larger (in */
+/* magnitude) endpoint, then it is considered to be */
+/* sufficiently small, i.e., converged. Note: this should */
+/* always be at least radix*machine epsilon. */
+
+/* W (output) REAL */
+
+/* WERR (output) REAL */
+/* The error bound on the corresponding eigenvalue approximation */
+/* in W. */
+
+/* INFO (output) INTEGER */
+/* = 0: Eigenvalue converged */
+/* = -1: Eigenvalue did NOT converge */
+
+/* Internal Parameters */
+/* =================== */
+
+/* FUDGE REAL , default = 2 */
+/* A "fudge factor" to widen the Gershgorin intervals. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Get machine constants */
+ /* Parameter adjustments */
+ --e2;
+ --d__;
+
+ /* Function Body */
+ eps = slamch_("P");
+/* Computing MAX */
+ r__1 = dabs(*gl), r__2 = dabs(*gu);
+ tnorm = dmax(r__1,r__2);
+ rtoli = *reltol;
+ atoli = *pivmin * 4.f;
+ itmax = (integer) ((log(tnorm + *pivmin) - log(*pivmin)) / log(2.f)) + 2;
+ *info = -1;
+ left = *gl - tnorm * 2.f * eps * *n - *pivmin * 4.f;
+ right = *gu + tnorm * 2.f * eps * *n + *pivmin * 4.f;
+ it = 0;
+L10:
+
+/* Check if interval converged or maximum number of iterations reached */
+
+ tmp1 = (r__1 = right - left, dabs(r__1));
+/* Computing MAX */
+ r__1 = dabs(right), r__2 = dabs(left);
+ tmp2 = dmax(r__1,r__2);
+/* Computing MAX */
+ r__1 = max(atoli,*pivmin), r__2 = rtoli * tmp2;
+ if (tmp1 < dmax(r__1,r__2)) {
+ *info = 0;
+ goto L30;
+ }
+ if (it > itmax) {
+ goto L30;
+ }
+
+/* Count number of negative pivots for mid-point */
+
+ ++it;
+ mid = (left + right) * .5f;
+ negcnt = 0;
+ tmp1 = d__[1] - mid;
+ if (dabs(tmp1) < *pivmin) {
+ tmp1 = -(*pivmin);
+ }
+ if (tmp1 <= 0.f) {
+ ++negcnt;
+ }
+
+ i__1 = *n;
+ for (i__ = 2; i__ <= i__1; ++i__) {
+ tmp1 = d__[i__] - e2[i__ - 1] / tmp1 - mid;
+ if (dabs(tmp1) < *pivmin) {
+ tmp1 = -(*pivmin);
+ }
+ if (tmp1 <= 0.f) {
+ ++negcnt;
+ }
+/* L20: */
+ }
+ if (negcnt >= *iw) {
+ right = mid;
+ } else {
+ left = mid;
+ }
+ goto L10;
+L30:
+
+/* Converged or maximum number of iterations reached */
+
+ *w = (left + right) * .5f;
+ *werr = (r__1 = right - left, dabs(r__1)) * .5f;
+ return 0;
+
+/* End of SLARRK */
+
+} /* slarrk_ */