X-Git-Url: https://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdlarrb.c;fp=3rdparty%2Flapack%2Fdlarrb.c;h=13f6a42f9b2c45eef2f40523cdedd820e63add3b;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv

diff --git a/3rdparty/lapack/dlarrb.c b/3rdparty/lapack/dlarrb.c
new file mode 100644
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+++ b/3rdparty/lapack/dlarrb.c
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+#include "clapack.h"
+
+/* Subroutine */ int 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 dlaneg_(integer *, doublereal *, doublereal *, doublereal *
+, doublereal *, integer *);
+    integer negcnt;
+    doublereal 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, 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 = 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 = 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 = 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 */
+
+} /* dlarrb_ */