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- /* dlarrb.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 _starpu_dlarrb_(integer *n, doublereal *d__, doublereal *lld,
- integer *ifirst, integer *ilast, doublereal *rtol1, doublereal *rtol2,
- integer *offset, doublereal *w, doublereal *wgap, doublereal *werr,
- doublereal *work, integer *iwork, doublereal *pivmin, doublereal *
- spdiam, integer *twist, integer *info)
- {
- /* System generated locals */
- integer i__1;
- doublereal d__1, d__2;
- /* Builtin functions */
- double log(doublereal);
- /* Local variables */
- integer i__, k, r__, i1, ii, ip;
- doublereal gap, mid, tmp, back, lgap, rgap, left;
- integer iter, nint, prev, next;
- doublereal cvrgd, right, width;
- extern integer _starpu_dlaneg_(integer *, doublereal *, doublereal *, doublereal *
- , doublereal *, integer *);
- integer negcnt;
- doublereal mnwdth;
- integer olnint, maxitr;
- /* -- LAPACK auxiliary routine (version 3.2) -- */
- /* 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, DLARRB */
- /* 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) DOUBLE PRECISION array, dimension (N) */
- /* The N diagonal elements of the diagonal matrix D. */
- /* LLD (input) DOUBLE PRECISION 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) DOUBLE PRECISION */
- /* RTOL2 (input) DOUBLE PRECISION */
- /* 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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.)) +
- 2;
- mnwdth = *pivmin * 2.;
- 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 = min(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 = _starpu_dlaneg_(n, &d__[1], &lld[1], &left, pivmin, &r__);
- if (negcnt > i__ - 1) {
- left -= back;
- back *= 2.;
- 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 = _starpu_dlaneg_(n, &d__[1], &lld[1], &right, pivmin, &r__);
- if (negcnt < i__) {
- right += back;
- back *= 2.;
- goto L50;
- }
- width = (d__1 = left - right, abs(d__1)) * .5;
- /* Computing MAX */
- d__1 = abs(left), d__2 = abs(right);
- tmp = max(d__1,d__2);
- /* Computing MAX */
- d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
- cvrgd = max(d__1,d__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 = min(lgap,rgap);
- next = iwork[k - 1];
- left = work[k - 1];
- right = work[k];
- mid = (left + right) * .5;
- /* semiwidth of interval */
- width = right - mid;
- /* Computing MAX */
- d__1 = abs(left), d__2 = abs(right);
- tmp = max(d__1,d__2);
- /* Computing MAX */
- d__1 = *rtol1 * gap, d__2 = *rtol2 * tmp;
- cvrgd = max(d__1,d__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 = _starpu_dlaneg_(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]) * .5;
- 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 */
- d__1 = 0., d__2 = w[ii] - werr[ii] - w[ii - 1] - werr[ii - 1];
- wgap[ii - 1] = max(d__1,d__2);
- /* L111: */
- }
- return 0;
- /* End of DLARRB */
- } /* _starpu_dlarrb_ */
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