--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int slarrb_(integer *n, real *d__, real *lld, integer *
+ ifirst, integer *ilast, real *rtol1, real *rtol2, integer *offset,
+ real *w, real *wgap, real *werr, real *work, integer *iwork, real *
+ pivmin, real *spdiam, integer *twist, integer *info)
+{
+ /* System generated locals */
+ integer i__1;
+ real r__1, r__2;
+
+ /* Builtin functions */
+ double log(doublereal);
+
+ /* Local variables */
+ integer i__, k, r__, i1, ii, ip;
+ real gap, mid, tmp, back, lgap, rgap, left;
+ integer iter, nint, prev, next;
+ real cvrgd, right, width;
+ extern integer slaneg_(integer *, real *, real *, real *, real *, integer
+ *);
+ integer negcnt;
+ real mnwdth;
+ integer olnint, maxitr;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* Given the relatively robust representation(RRR) L D L^T, SLARRB */
+/* does "limited" bisection to refine the eigenvalues of L D L^T, */
+/* W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial */
+/* guesses for these eigenvalues are input in W, the corresponding estimate */
+/* of the error in these guesses and their gaps are input in WERR */
+/* and WGAP, respectively. During bisection, intervals */
+/* [left, right] are maintained by storing their mid-points and */
+/* semi-widths in the arrays W and WERR respectively. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the matrix. */
+
+/* D (input) REAL array, dimension (N) */
+/* The N diagonal elements of the diagonal matrix D. */
+
+/* LLD (input) REAL array, dimension (N-1) */
+/* The (N-1) elements L(i)*L(i)*D(i). */
+
+/* IFIRST (input) INTEGER */
+/* The index of the first eigenvalue to be computed. */
+
+/* ILAST (input) INTEGER */
+/* The index of the last eigenvalue to be computed. */
+
+/* RTOL1 (input) REAL */
+/* RTOL2 (input) REAL */
+/* Tolerance for the convergence of the bisection intervals. */
+/* An interval [LEFT,RIGHT] has converged if */
+/* RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
+/* where GAP is the (estimated) distance to the nearest */
+/* eigenvalue. */
+
+/* OFFSET (input) INTEGER */
+/* Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET */
+/* through ILAST-OFFSET elements of these arrays are to be used. */
+
+/* W (input/output) REAL array, dimension (N) */
+/* On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are */
+/* estimates of the eigenvalues of L D L^T indexed IFIRST throug */
+/* ILAST. */
+/* On output, these estimates are refined. */
+
+/* WGAP (input/output) REAL array, dimension (N-1) */
+/* On input, the (estimated) gaps between consecutive */
+/* eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between */
+/* eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST */
+/* then WGAP(IFIRST-OFFSET) must be set to ZERO. */
+/* On output, these gaps are refined. */
+
+/* WERR (input/output) REAL array, dimension (N) */
+/* On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are */
+/* the errors in the estimates of the corresponding elements in W. */
+/* On output, these errors are refined. */
+
+/* WORK (workspace) REAL array, dimension (2*N) */
+/* Workspace. */
+
+/* IWORK (workspace) INTEGER array, dimension (2*N) */
+/* Workspace. */
+
+/* PIVMIN (input) DOUBLE PRECISION */
+/* The minimum pivot in the Sturm sequence. */
+
+/* SPDIAM (input) DOUBLE PRECISION */
+/* The spectral diameter of the matrix. */
+
+/* TWIST (input) INTEGER */
+/* The twist index for the twisted factorization that is used */
+/* for the negcount. */
+/* TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T */
+/* TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T */
+/* TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) */
+
+/* INFO (output) INTEGER */
+/* Error flag. */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Beresford Parlett, University of California, Berkeley, USA */
+/* Jim Demmel, University of California, Berkeley, USA */
+/* Inderjit Dhillon, University of Texas, Austin, USA */
+/* Osni Marques, LBNL/NERSC, USA */
+/* Christof Voemel, University of California, Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --iwork;
+ --work;
+ --werr;
+ --wgap;
+ --w;
+ --lld;
+ --d__;
+
+ /* Function Body */
+ *info = 0;
+
+ maxitr = (integer) ((log(*spdiam + *pivmin) - log(*pivmin)) / log(2.f)) +
+ 2;
+ mnwdth = *pivmin * 2.f;
+
+ r__ = *twist;
+ if (r__ < 1 || r__ > *n) {
+ r__ = *n;
+ }
+
+/* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. */
+/* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while */
+/* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) */
+/* for an unconverged interval is set to the index of the next unconverged */
+/* interval, and is -1 or 0 for a converged interval. Thus a linked */
+/* list of unconverged intervals is set up. */
+
+ i1 = *ifirst;
+/* The number of unconverged intervals */
+ nint = 0;
+/* The last unconverged interval found */
+ prev = 0;
+ rgap = wgap[i1 - *offset];
+ i__1 = *ilast;
+ for (i__ = i1; i__ <= i__1; ++i__) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+ left = w[ii] - werr[ii];
+ right = w[ii] + werr[ii];
+ lgap = rgap;
+ rgap = wgap[ii];
+ gap = dmin(lgap,rgap);
+/* Make sure that [LEFT,RIGHT] contains the desired eigenvalue */
+/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - LEFT */
+
+/* Do while( NEGCNT(LEFT).GT.I-1 ) */
+
+ back = werr[ii];
+L20:
+ negcnt = slaneg_(n, &d__[1], &lld[1], &left, pivmin, &r__);
+ if (negcnt > i__ - 1) {
+ left -= back;
+ back *= 2.f;
+ goto L20;
+ }
+
+/* Do while( NEGCNT(RIGHT).LT.I ) */
+/* Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT */
+
+ back = werr[ii];
+L50:
+ negcnt = slaneg_(n, &d__[1], &lld[1], &right, pivmin, &r__);
+ if (negcnt < i__) {
+ right += back;
+ back *= 2.f;
+ goto L50;
+ }
+ width = (r__1 = left - right, dabs(r__1)) * .5f;
+/* Computing MAX */
+ r__1 = dabs(left), r__2 = dabs(right);
+ tmp = dmax(r__1,r__2);
+/* Computing MAX */
+ r__1 = *rtol1 * gap, r__2 = *rtol2 * tmp;
+ cvrgd = dmax(r__1,r__2);
+ if (width <= cvrgd || width <= mnwdth) {
+/* This interval has already converged and does not need refinement. */
+/* (Note that the gaps might change through refining the */
+/* eigenvalues, however, they can only get bigger.) */
+/* Remove it from the list. */
+ iwork[k - 1] = -1;
+/* Make sure that I1 always points to the first unconverged interval */
+ if (i__ == i1 && i__ < *ilast) {
+ i1 = i__ + 1;
+ }
+ if (prev >= i1 && i__ <= *ilast) {
+ iwork[(prev << 1) - 1] = i__ + 1;
+ }
+ } else {
+/* unconverged interval found */
+ prev = i__;
+ ++nint;
+ iwork[k - 1] = i__ + 1;
+ iwork[k] = negcnt;
+ }
+ work[k - 1] = left;
+ work[k] = right;
+/* L75: */
+ }
+
+/* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals */
+/* and while (ITER.LT.MAXITR) */
+
+ iter = 0;
+L80:
+ prev = i1 - 1;
+ i__ = i1;
+ olnint = nint;
+ i__1 = olnint;
+ for (ip = 1; ip <= i__1; ++ip) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+ rgap = wgap[ii];
+ lgap = rgap;
+ if (ii > 1) {
+ lgap = wgap[ii - 1];
+ }
+ gap = dmin(lgap,rgap);
+ next = iwork[k - 1];
+ left = work[k - 1];
+ right = work[k];
+ mid = (left + right) * .5f;
+/* semiwidth of interval */
+ width = right - mid;
+/* Computing MAX */
+ r__1 = dabs(left), r__2 = dabs(right);
+ tmp = dmax(r__1,r__2);
+/* Computing MAX */
+ r__1 = *rtol1 * gap, r__2 = *rtol2 * tmp;
+ cvrgd = dmax(r__1,r__2);
+ if (width <= cvrgd || width <= mnwdth || iter == maxitr) {
+/* reduce number of unconverged intervals */
+ --nint;
+/* Mark interval as converged. */
+ iwork[k - 1] = 0;
+ if (i1 == i__) {
+ i1 = next;
+ } else {
+/* Prev holds the last unconverged interval previously examined */
+ if (prev >= i1) {
+ iwork[(prev << 1) - 1] = next;
+ }
+ }
+ i__ = next;
+ goto L100;
+ }
+ prev = i__;
+
+/* Perform one bisection step */
+
+ negcnt = slaneg_(n, &d__[1], &lld[1], &mid, pivmin, &r__);
+ if (negcnt <= i__ - 1) {
+ work[k - 1] = mid;
+ } else {
+ work[k] = mid;
+ }
+ i__ = next;
+L100:
+ ;
+ }
+ ++iter;
+/* do another loop if there are still unconverged intervals */
+/* However, in the last iteration, all intervals are accepted */
+/* since this is the best we can do. */
+ if (nint > 0 && iter <= maxitr) {
+ goto L80;
+ }
+
+
+/* At this point, all the intervals have converged */
+ i__1 = *ilast;
+ for (i__ = *ifirst; i__ <= i__1; ++i__) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+/* All intervals marked by '0' have been refined. */
+ if (iwork[k - 1] == 0) {
+ w[ii] = (work[k - 1] + work[k]) * .5f;
+ werr[ii] = work[k] - w[ii];
+ }
+/* L110: */
+ }
+
+ i__1 = *ilast;
+ for (i__ = *ifirst + 1; i__ <= i__1; ++i__) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+/* Computing MAX */
+ r__1 = 0.f, r__2 = w[ii] - werr[ii] - w[ii - 1] - werr[ii - 1];
+ wgap[ii - 1] = dmax(r__1,r__2);
+/* L111: */
+ }
+ return 0;
+
+/* End of SLARRB */
+
+} /* slarrb_ */
projects / opencv / blobdiff