X-Git-Url: http://git.maemo.org/git/?p=opencv;a=blobdiff_plain;f=3rdparty%2Flapack%2Fdlarrf.c;fp=3rdparty%2Flapack%2Fdlarrf.c;h=ef92cdd150f610051595abce5f821647c3c3b1f4;hp=0000000000000000000000000000000000000000;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hpb=454138ff8a20f6edb9b65a910101403d8b520643

diff --git a/3rdparty/lapack/dlarrf.c b/3rdparty/lapack/dlarrf.c
new file mode 100644
index 0000000..ef92cdd
--- /dev/null
+++ b/3rdparty/lapack/dlarrf.c
@@ -0,0 +1,410 @@
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* Subroutine */ int dlarrf_(integer *n, doublereal *d__, doublereal *l, 
+	doublereal *ld, integer *clstrt, integer *clend, doublereal *w, 
+	doublereal *wgap, doublereal *werr, doublereal *spdiam, doublereal *
+	clgapl, doublereal *clgapr, doublereal *pivmin, doublereal *sigma, 
+	doublereal *dplus, doublereal *lplus, doublereal *work, integer *info)
+{
+    /* System generated locals */
+    integer i__1;
+    doublereal d__1, d__2, d__3;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    integer i__;
+    doublereal s, bestshift, smlgrowth, eps, tmp, max1, max2, rrr1, rrr2, 
+	    znm2, growthbound, fail, fact, oldp;
+    integer indx;
+    doublereal prod;
+    integer ktry;
+    doublereal fail2, avgap, ldmax, rdmax;
+    integer shift;
+    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *);
+    logical dorrr1;
+    extern doublereal dlamch_(char *);
+    doublereal ldelta;
+    logical nofail;
+    doublereal mingap, lsigma, rdelta;
+    extern logical disnan_(doublereal *);
+    logical forcer;
+    doublereal rsigma, clwdth;
+    logical sawnan1, sawnan2, tryrrr1;
+
+
+/*  -- 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 initial representation L D L^T and its cluster of close */
+/*  eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... */
+/*  W( CLEND ), DLARRF finds a new relatively robust representation */
+/*  L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the */
+/*  eigenvalues of L(+) D(+) L(+)^T is relatively isolated. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix (subblock, if the matrix splitted). */
+
+/*  D       (input) DOUBLE PRECISION array, dimension (N) */
+/*          The N diagonal elements of the diagonal matrix D. */
+
+/*  L       (input) DOUBLE PRECISION array, dimension (N-1) */
+/*          The (N-1) subdiagonal elements of the unit bidiagonal */
+/*          matrix L. */
+
+/*  LD      (input) DOUBLE PRECISION array, dimension (N-1) */
+/*          The (N-1) elements L(i)*D(i). */
+
+/*  CLSTRT  (input) INTEGER */
+/*          The index of the first eigenvalue in the cluster. */
+
+/*  CLEND   (input) INTEGER */
+/*          The index of the last eigenvalue in the cluster. */
+
+/*  W       (input) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1) */
+/*          The eigenvalue APPROXIMATIONS of L D L^T in ascending order. */
+/*          W( CLSTRT ) through W( CLEND ) form the cluster of relatively */
+/*          close eigenalues. */
+
+/*  WGAP    (input/output) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1) */
+/*          The separation from the right neighbor eigenvalue in W. */
+
+/*  WERR    (input) DOUBLE PRECISION array, dimension >=  (CLEND-CLSTRT+1) */
+/*          WERR contain the semiwidth of the uncertainty */
+/*          interval of the corresponding eigenvalue APPROXIMATION in W */
+
+/*  SPDIAM (input) estimate of the spectral diameter obtained from the */
+/*          Gerschgorin intervals */
+
+/*  CLGAPL, CLGAPR (input) absolute gap on each end of the cluster. */
+/*          Set by the calling routine to protect against shifts too close */
+/*          to eigenvalues outside the cluster. */
+
+/*  PIVMIN  (input) DOUBLE PRECISION */
+/*          The minimum pivot allowed in the Sturm sequence. */
+
+/*  SIGMA   (output) DOUBLE PRECISION */
+/*          The shift used to form L(+) D(+) L(+)^T. */
+
+/*  DPLUS   (output) DOUBLE PRECISION array, dimension (N) */
+/*          The N diagonal elements of the diagonal matrix D(+). */
+
+/*  LPLUS   (output) DOUBLE PRECISION array, dimension (N-1) */
+/*          The first (N-1) elements of LPLUS contain the subdiagonal */
+/*          elements of the unit bidiagonal matrix L(+). */
+
+/*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N) */
+/*          Workspace. */
+
+/*  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 .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    --work;
+    --lplus;
+    --dplus;
+    --werr;
+    --wgap;
+    --w;
+    --ld;
+    --l;
+    --d__;
+
+    /* Function Body */
+    *info = 0;
+    fact = 2.;
+    eps = dlamch_("Precision");
+    shift = 0;
+    forcer = FALSE_;
+/*     Note that we cannot guarantee that for any of the shifts tried, */
+/*     the factorization has a small or even moderate element growth. */
+/*     There could be Ritz values at both ends of the cluster and despite */
+/*     backing off, there are examples where all factorizations tried */
+/*     (in IEEE mode, allowing zero pivots & infinities) have INFINITE */
+/*     element growth. */
+/*     For this reason, we should use PIVMIN in this subroutine so that at */
+/*     least the L D L^T factorization exists. It can be checked afterwards */
+/*     whether the element growth caused bad residuals/orthogonality. */
+/*     Decide whether the code should accept the best among all */
+/*     representations despite large element growth or signal INFO=1 */
+    nofail = TRUE_;
+
+/*     Compute the average gap length of the cluster */
+    clwdth = (d__1 = w[*clend] - w[*clstrt], abs(d__1)) + werr[*clend] + werr[
+	    *clstrt];
+    avgap = clwdth / (doublereal) (*clend - *clstrt);
+    mingap = min(*clgapl,*clgapr);
+/*     Initial values for shifts to both ends of cluster */
+/* Computing MIN */
+    d__1 = w[*clstrt], d__2 = w[*clend];
+    lsigma = min(d__1,d__2) - werr[*clstrt];
+/* Computing MAX */
+    d__1 = w[*clstrt], d__2 = w[*clend];
+    rsigma = max(d__1,d__2) + werr[*clend];
+/*     Use a small fudge to make sure that we really shift to the outside */
+    lsigma -= abs(lsigma) * 4. * eps;
+    rsigma += abs(rsigma) * 4. * eps;
+/*     Compute upper bounds for how much to back off the initial shifts */
+    ldmax = mingap * .25 + *pivmin * 2.;
+    rdmax = mingap * .25 + *pivmin * 2.;
+/* Computing MAX */
+    d__1 = avgap, d__2 = wgap[*clstrt];
+    ldelta = max(d__1,d__2) / fact;
+/* Computing MAX */
+    d__1 = avgap, d__2 = wgap[*clend - 1];
+    rdelta = max(d__1,d__2) / fact;
+
+/*     Initialize the record of the best representation found */
+
+    s = dlamch_("S");
+    smlgrowth = 1. / s;
+    fail = (doublereal) (*n - 1) * mingap / (*spdiam * eps);
+    fail2 = (doublereal) (*n - 1) * mingap / (*spdiam * sqrt(eps));
+    bestshift = lsigma;
+
+/*     while (KTRY <= KTRYMAX) */
+    ktry = 0;
+    growthbound = *spdiam * 8.;
+L5:
+    sawnan1 = FALSE_;
+    sawnan2 = FALSE_;
+/*     Ensure that we do not back off too much of the initial shifts */
+    ldelta = min(ldmax,ldelta);
+    rdelta = min(rdmax,rdelta);
+/*     Compute the element growth when shifting to both ends of the cluster */
+/*     accept the shift if there is no element growth at one of the two ends */
+/*     Left end */
+    s = -lsigma;
+    dplus[1] = d__[1] + s;
+    if (abs(dplus[1]) < *pivmin) {
+	dplus[1] = -(*pivmin);
+/*        Need to set SAWNAN1 because refined RRR test should not be used */
+/*        in this case */
+	sawnan1 = TRUE_;
+    }
+    max1 = abs(dplus[1]);
+    i__1 = *n - 1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	lplus[i__] = ld[i__] / dplus[i__];
+	s = s * lplus[i__] * l[i__] - lsigma;
+	dplus[i__ + 1] = d__[i__ + 1] + s;
+	if ((d__1 = dplus[i__ + 1], abs(d__1)) < *pivmin) {
+	    dplus[i__ + 1] = -(*pivmin);
+/*           Need to set SAWNAN1 because refined RRR test should not be used */
+/*           in this case */
+	    sawnan1 = TRUE_;
+	}
+/* Computing MAX */
+	d__2 = max1, d__3 = (d__1 = dplus[i__ + 1], abs(d__1));
+	max1 = max(d__2,d__3);
+/* L6: */
+    }
+    sawnan1 = sawnan1 || disnan_(&max1);
+    if (forcer || max1 <= growthbound && ! sawnan1) {
+	*sigma = lsigma;
+	shift = 1;
+	goto L100;
+    }
+/*     Right end */
+    s = -rsigma;
+    work[1] = d__[1] + s;
+    if (abs(work[1]) < *pivmin) {
+	work[1] = -(*pivmin);
+/*        Need to set SAWNAN2 because refined RRR test should not be used */
+/*        in this case */
+	sawnan2 = TRUE_;
+    }
+    max2 = abs(work[1]);
+    i__1 = *n - 1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	work[*n + i__] = ld[i__] / work[i__];
+	s = s * work[*n + i__] * l[i__] - rsigma;
+	work[i__ + 1] = d__[i__ + 1] + s;
+	if ((d__1 = work[i__ + 1], abs(d__1)) < *pivmin) {
+	    work[i__ + 1] = -(*pivmin);
+/*           Need to set SAWNAN2 because refined RRR test should not be used */
+/*           in this case */
+	    sawnan2 = TRUE_;
+	}
+/* Computing MAX */
+	d__2 = max2, d__3 = (d__1 = work[i__ + 1], abs(d__1));
+	max2 = max(d__2,d__3);
+/* L7: */
+    }
+    sawnan2 = sawnan2 || disnan_(&max2);
+    if (forcer || max2 <= growthbound && ! sawnan2) {
+	*sigma = rsigma;
+	shift = 2;
+	goto L100;
+    }
+/*     If we are at this point, both shifts led to too much element growth */
+/*     Record the better of the two shifts (provided it didn't lead to NaN) */
+    if (sawnan1 && sawnan2) {
+/*        both MAX1 and MAX2 are NaN */
+	goto L50;
+    } else {
+	if (! sawnan1) {
+	    indx = 1;
+	    if (max1 <= smlgrowth) {
+		smlgrowth = max1;
+		bestshift = lsigma;
+	    }
+	}
+	if (! sawnan2) {
+	    if (sawnan1 || max2 <= max1) {
+		indx = 2;
+	    }
+	    if (max2 <= smlgrowth) {
+		smlgrowth = max2;
+		bestshift = rsigma;
+	    }
+	}
+    }
+/*     If we are here, both the left and the right shift led to */
+/*     element growth. If the element growth is moderate, then */
+/*     we may still accept the representation, if it passes a */
+/*     refined test for RRR. This test supposes that no NaN occurred. */
+/*     Moreover, we use the refined RRR test only for isolated clusters. */
+    if (clwdth < mingap / 128. && min(max1,max2) < fail2 && ! sawnan1 && ! 
+	    sawnan2) {
+	dorrr1 = TRUE_;
+    } else {
+	dorrr1 = FALSE_;
+    }
+    tryrrr1 = TRUE_;
+    if (tryrrr1 && dorrr1) {
+	if (indx == 1) {
+	    tmp = (d__1 = dplus[*n], abs(d__1));
+	    znm2 = 1.;
+	    prod = 1.;
+	    oldp = 1.;
+	    for (i__ = *n - 1; i__ >= 1; --i__) {
+		if (prod <= eps) {
+		    prod = dplus[i__ + 1] * work[*n + i__ + 1] / (dplus[i__] *
+			     work[*n + i__]) * oldp;
+		} else {
+		    prod *= (d__1 = work[*n + i__], abs(d__1));
+		}
+		oldp = prod;
+/* Computing 2nd power */
+		d__1 = prod;
+		znm2 += d__1 * d__1;
+/* Computing MAX */
+		d__2 = tmp, d__3 = (d__1 = dplus[i__] * prod, abs(d__1));
+		tmp = max(d__2,d__3);
+/* L15: */
+	    }
+	    rrr1 = tmp / (*spdiam * sqrt(znm2));
+	    if (rrr1 <= 8.) {
+		*sigma = lsigma;
+		shift = 1;
+		goto L100;
+	    }
+	} else if (indx == 2) {
+	    tmp = (d__1 = work[*n], abs(d__1));
+	    znm2 = 1.;
+	    prod = 1.;
+	    oldp = 1.;
+	    for (i__ = *n - 1; i__ >= 1; --i__) {
+		if (prod <= eps) {
+		    prod = work[i__ + 1] * lplus[i__ + 1] / (work[i__] * 
+			    lplus[i__]) * oldp;
+		} else {
+		    prod *= (d__1 = lplus[i__], abs(d__1));
+		}
+		oldp = prod;
+/* Computing 2nd power */
+		d__1 = prod;
+		znm2 += d__1 * d__1;
+/* Computing MAX */
+		d__2 = tmp, d__3 = (d__1 = work[i__] * prod, abs(d__1));
+		tmp = max(d__2,d__3);
+/* L16: */
+	    }
+	    rrr2 = tmp / (*spdiam * sqrt(znm2));
+	    if (rrr2 <= 8.) {
+		*sigma = rsigma;
+		shift = 2;
+		goto L100;
+	    }
+	}
+    }
+L50:
+    if (ktry < 1) {
+/*        If we are here, both shifts failed also the RRR test. */
+/*        Back off to the outside */
+/* Computing MAX */
+	d__1 = lsigma - ldelta, d__2 = lsigma - ldmax;
+	lsigma = max(d__1,d__2);
+/* Computing MIN */
+	d__1 = rsigma + rdelta, d__2 = rsigma + rdmax;
+	rsigma = min(d__1,d__2);
+	ldelta *= 2.;
+	rdelta *= 2.;
+	++ktry;
+	goto L5;
+    } else {
+/*        None of the representations investigated satisfied our */
+/*        criteria. Take the best one we found. */
+	if (smlgrowth < fail || nofail) {
+	    lsigma = bestshift;
+	    rsigma = bestshift;
+	    forcer = TRUE_;
+	    goto L5;
+	} else {
+	    *info = 1;
+	    return 0;
+	}
+    }
+L100:
+    if (shift == 1) {
+    } else if (shift == 2) {
+/*        store new L and D back into DPLUS, LPLUS */
+	dcopy_(n, &work[1], &c__1, &dplus[1], &c__1);
+	i__1 = *n - 1;
+	dcopy_(&i__1, &work[*n + 1], &c__1, &lplus[1], &c__1);
+    }
+    return 0;
+
+/*     End of DLARRF */
+
+} /* dlarrf_ */