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350 lines
10 KiB
C
350 lines
10 KiB
C
/* slarrb.f -- translated by f2c (version 20061008).
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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 "clapack.h"
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/* Subroutine */ int slarrb_(integer *n, real *d__, real *lld, integer *
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ifirst, integer *ilast, real *rtol1, real *rtol2, integer *offset,
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real *w, real *wgap, real *werr, real *work, integer *iwork, real *
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pivmin, real *spdiam, integer *twist, integer *info)
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{
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/* System generated locals */
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integer i__1;
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real r__1, r__2;
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/* Builtin functions */
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double log(doublereal);
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/* Local variables */
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integer i__, k, r__, i1, ii, ip;
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real gap, mid, tmp, back, lgap, rgap, left;
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integer iter, nint, prev, next;
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real cvrgd, right, width;
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extern integer slaneg_(integer *, real *, real *, real *, real *, integer
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*);
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integer negcnt;
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real mnwdth;
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integer olnint, maxitr;
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/* -- LAPACK auxiliary routine (version 3.2) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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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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/* Given the relatively robust representation(RRR) L D L^T, SLARRB */
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/* does "limited" bisection to refine the eigenvalues of L D L^T, */
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/* W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial */
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/* guesses for these eigenvalues are input in W, the corresponding estimate */
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/* of the error in these guesses and their gaps are input in WERR */
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/* and WGAP, respectively. During bisection, intervals */
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/* [left, right] are maintained by storing their mid-points and */
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/* semi-widths in the arrays W and WERR respectively. */
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/* Arguments */
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/* ========= */
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/* N (input) INTEGER */
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/* The order of the matrix. */
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/* D (input) REAL array, dimension (N) */
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/* The N diagonal elements of the diagonal matrix D. */
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/* LLD (input) REAL array, dimension (N-1) */
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/* The (N-1) elements L(i)*L(i)*D(i). */
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/* IFIRST (input) INTEGER */
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/* The index of the first eigenvalue to be computed. */
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/* ILAST (input) INTEGER */
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/* The index of the last eigenvalue to be computed. */
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/* RTOL1 (input) REAL */
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/* RTOL2 (input) REAL */
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/* Tolerance for the convergence of the bisection intervals. */
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/* An interval [LEFT,RIGHT] has converged if */
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/* RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
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/* where GAP is the (estimated) distance to the nearest */
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/* eigenvalue. */
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/* OFFSET (input) INTEGER */
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/* Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET */
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/* through ILAST-OFFSET elements of these arrays are to be used. */
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/* W (input/output) REAL array, dimension (N) */
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/* On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are */
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/* estimates of the eigenvalues of L D L^T indexed IFIRST throug */
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/* ILAST. */
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/* On output, these estimates are refined. */
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/* WGAP (input/output) REAL array, dimension (N-1) */
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/* On input, the (estimated) gaps between consecutive */
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/* eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between */
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/* eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST */
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/* then WGAP(IFIRST-OFFSET) must be set to ZERO. */
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/* On output, these gaps are refined. */
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/* WERR (input/output) REAL array, dimension (N) */
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/* On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are */
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/* the errors in the estimates of the corresponding elements in W. */
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/* On output, these errors are refined. */
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/* WORK (workspace) REAL array, dimension (2*N) */
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/* Workspace. */
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/* IWORK (workspace) INTEGER array, dimension (2*N) */
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/* Workspace. */
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/* PIVMIN (input) DOUBLE PRECISION */
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/* The minimum pivot in the Sturm sequence. */
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/* SPDIAM (input) DOUBLE PRECISION */
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/* The spectral diameter of the matrix. */
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/* TWIST (input) INTEGER */
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/* The twist index for the twisted factorization that is used */
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/* for the negcount. */
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/* TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T */
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/* TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T */
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/* TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) */
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/* INFO (output) INTEGER */
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/* Error flag. */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Beresford Parlett, University of California, Berkeley, USA */
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/* Jim Demmel, University of California, Berkeley, USA */
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/* Inderjit Dhillon, University of Texas, Austin, USA */
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/* Osni Marques, LBNL/NERSC, USA */
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/* Christof Voemel, University of California, Berkeley, USA */
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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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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--iwork;
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--work;
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--werr;
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--wgap;
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--w;
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--lld;
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--d__;
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/* Function Body */
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*info = 0;
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maxitr = (integer) ((log(*spdiam + *pivmin) - log(*pivmin)) / log(2.f)) +
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2;
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mnwdth = *pivmin * 2.f;
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r__ = *twist;
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if (r__ < 1 || r__ > *n) {
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r__ = *n;
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}
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/* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. */
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/* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while */
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/* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) */
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/* for an unconverged interval is set to the index of the next unconverged */
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/* interval, and is -1 or 0 for a converged interval. Thus a linked */
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/* list of unconverged intervals is set up. */
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i1 = *ifirst;
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/* The number of unconverged intervals */
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nint = 0;
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/* The last unconverged interval found */
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prev = 0;
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rgap = wgap[i1 - *offset];
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i__1 = *ilast;
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for (i__ = i1; i__ <= i__1; ++i__) {
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k = i__ << 1;
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ii = i__ - *offset;
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left = w[ii] - werr[ii];
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right = w[ii] + werr[ii];
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lgap = rgap;
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rgap = wgap[ii];
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gap = dmin(lgap,rgap);
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/* Make sure that [LEFT,RIGHT] contains the desired eigenvalue */
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/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - LEFT */
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/* Do while( NEGCNT(LEFT).GT.I-1 ) */
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back = werr[ii];
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L20:
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negcnt = slaneg_(n, &d__[1], &lld[1], &left, pivmin, &r__);
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if (negcnt > i__ - 1) {
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left -= back;
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back *= 2.f;
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goto L20;
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}
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/* Do while( NEGCNT(RIGHT).LT.I ) */
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/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT */
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back = werr[ii];
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L50:
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negcnt = slaneg_(n, &d__[1], &lld[1], &right, pivmin, &r__);
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if (negcnt < i__) {
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right += back;
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back *= 2.f;
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goto L50;
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}
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width = (r__1 = left - right, dabs(r__1)) * .5f;
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/* Computing MAX */
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r__1 = dabs(left), r__2 = dabs(right);
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tmp = dmax(r__1,r__2);
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/* Computing MAX */
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r__1 = *rtol1 * gap, r__2 = *rtol2 * tmp;
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cvrgd = dmax(r__1,r__2);
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if (width <= cvrgd || width <= mnwdth) {
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/* This interval has already converged and does not need refinement. */
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/* (Note that the gaps might change through refining the */
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/* eigenvalues, however, they can only get bigger.) */
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/* Remove it from the list. */
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iwork[k - 1] = -1;
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/* Make sure that I1 always points to the first unconverged interval */
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if (i__ == i1 && i__ < *ilast) {
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i1 = i__ + 1;
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}
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if (prev >= i1 && i__ <= *ilast) {
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iwork[(prev << 1) - 1] = i__ + 1;
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}
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} else {
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/* unconverged interval found */
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prev = i__;
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++nint;
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iwork[k - 1] = i__ + 1;
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iwork[k] = negcnt;
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}
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work[k - 1] = left;
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work[k] = right;
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/* L75: */
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}
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/* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals */
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/* and while (ITER.LT.MAXITR) */
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iter = 0;
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L80:
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prev = i1 - 1;
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i__ = i1;
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olnint = nint;
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i__1 = olnint;
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for (ip = 1; ip <= i__1; ++ip) {
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k = i__ << 1;
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ii = i__ - *offset;
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rgap = wgap[ii];
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lgap = rgap;
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if (ii > 1) {
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lgap = wgap[ii - 1];
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}
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gap = dmin(lgap,rgap);
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next = iwork[k - 1];
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left = work[k - 1];
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right = work[k];
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mid = (left + right) * .5f;
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/* semiwidth of interval */
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width = right - mid;
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/* Computing MAX */
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r__1 = dabs(left), r__2 = dabs(right);
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tmp = dmax(r__1,r__2);
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/* Computing MAX */
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r__1 = *rtol1 * gap, r__2 = *rtol2 * tmp;
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cvrgd = dmax(r__1,r__2);
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if (width <= cvrgd || width <= mnwdth || iter == maxitr) {
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/* reduce number of unconverged intervals */
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--nint;
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/* Mark interval as converged. */
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iwork[k - 1] = 0;
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if (i1 == i__) {
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i1 = next;
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} else {
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/* Prev holds the last unconverged interval previously examined */
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if (prev >= i1) {
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iwork[(prev << 1) - 1] = next;
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}
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}
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i__ = next;
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goto L100;
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}
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prev = i__;
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/* Perform one bisection step */
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negcnt = slaneg_(n, &d__[1], &lld[1], &mid, pivmin, &r__);
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if (negcnt <= i__ - 1) {
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work[k - 1] = mid;
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} else {
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work[k] = mid;
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}
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i__ = next;
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L100:
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;
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}
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++iter;
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/* do another loop if there are still unconverged intervals */
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/* However, in the last iteration, all intervals are accepted */
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/* since this is the best we can do. */
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if (nint > 0 && iter <= maxitr) {
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goto L80;
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}
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/* At this point, all the intervals have converged */
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i__1 = *ilast;
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for (i__ = *ifirst; i__ <= i__1; ++i__) {
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k = i__ << 1;
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ii = i__ - *offset;
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/* All intervals marked by '0' have been refined. */
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if (iwork[k - 1] == 0) {
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w[ii] = (work[k - 1] + work[k]) * .5f;
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werr[ii] = work[k] - w[ii];
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}
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/* L110: */
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}
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i__1 = *ilast;
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for (i__ = *ifirst + 1; i__ <= i__1; ++i__) {
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k = i__ << 1;
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ii = i__ - *offset;
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/* Computing MAX */
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r__1 = 0.f, r__2 = w[ii] - werr[ii] - w[ii - 1] - werr[ii - 1];
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wgap[ii - 1] = dmax(r__1,r__2);
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/* L111: */
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}
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return 0;
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/* End of SLARRB */
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} /* slarrb_ */
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