[] add metering mode to CLI

1 files changed, 861 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dlarre.c b/contrib/libs/clapack/dlarre.c
new file mode 100644
index 0000000000..763c416234
--- /dev/null
+++ b/contrib/libs/clapack/dlarre.c
@@ -0,0 +1,861 @@
+/* dlarre.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"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__2 = 2;
+
+/* Subroutine */ int dlarre_(char *range, integer *n, doublereal *vl, 
+	doublereal *vu, integer *il, integer *iu, doublereal *d__, doublereal 
+	*e, doublereal *e2, doublereal *rtol1, doublereal *rtol2, doublereal *
+	spltol, integer *nsplit, integer *isplit, integer *m, doublereal *w, 
+	doublereal *werr, doublereal *wgap, integer *iblock, integer *indexw, 
+	doublereal *gers, doublereal *pivmin, doublereal *work, integer *
+	iwork, integer *info)
+{
+    /* System generated locals */
+    integer i__1, i__2;
+    doublereal d__1, d__2, d__3;
+
+    /* Builtin functions */
+    double sqrt(doublereal), log(doublereal);
+
+    /* Local variables */
+    integer i__, j;
+    doublereal s1, s2;
+    integer mb;
+    doublereal gl;
+    integer in, mm;
+    doublereal gu;
+    integer cnt;
+    doublereal eps, tau, tmp, rtl;
+    integer cnt1, cnt2;
+    doublereal tmp1, eabs;
+    integer iend, jblk;
+    doublereal eold;
+    integer indl;
+    doublereal dmax__, emax;
+    integer wend, idum, indu;
+    doublereal rtol;
+    integer iseed[4];
+    doublereal avgap, sigma;
+    extern logical lsame_(char *, char *);
+    integer iinfo;
+    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *);
+    logical norep;
+    extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *);
+    extern doublereal dlamch_(char *);
+    integer ibegin;
+    logical forceb;
+    integer irange;
+    doublereal sgndef;
+    extern /* Subroutine */ int dlarra_(integer *, doublereal *, doublereal *, 
+	     doublereal *, doublereal *, doublereal *, integer *, integer *, 
+	    integer *), dlarrb_(integer *, doublereal *, doublereal *, 
+	    integer *, integer *, doublereal *, doublereal *, integer *, 
+	    doublereal *, doublereal *, doublereal *, doublereal *, integer *, 
+	     doublereal *, doublereal *, integer *, integer *), dlarrc_(char *
+, integer *, doublereal *, doublereal *, doublereal *, doublereal 
+	    *, doublereal *, integer *, integer *, integer *, integer *);
+    integer wbegin;
+    extern /* Subroutine */ int dlarrd_(char *, char *, integer *, doublereal 
+	    *, doublereal *, integer *, integer *, doublereal *, doublereal *, 
+	     doublereal *, doublereal *, doublereal *, doublereal *, integer *
+, integer *, integer *, doublereal *, doublereal *, doublereal *, 
+	    doublereal *, integer *, integer *, doublereal *, integer *, 
+	    integer *);
+    doublereal safmin, spdiam;
+    extern /* Subroutine */ int dlarrk_(integer *, integer *, doublereal *, 
+	    doublereal *, doublereal *, doublereal *, doublereal *, 
+	    doublereal *, doublereal *, doublereal *, integer *);
+    logical usedqd;
+    doublereal clwdth, isleft;
+    extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *, 
+	    doublereal *);
+    doublereal isrght, bsrtol, dpivot;
+
+
+/*  -- LAPACK auxiliary routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  To find the desired eigenvalues of a given real symmetric */
+/*  tridiagonal matrix T, DLARRE sets any "small" off-diagonal */
+/*  elements to zero, and for each unreduced block T_i, it finds */
+/*  (a) a suitable shift at one end of the block's spectrum, */
+/*  (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and */
+/*  (c) eigenvalues of each L_i D_i L_i^T. */
+/*  The representations and eigenvalues found are then used by */
+/*  DSTEMR to compute the eigenvectors of T. */
+/*  The accuracy varies depending on whether bisection is used to */
+/*  find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to */
+/*  conpute all and then discard any unwanted one. */
+/*  As an added benefit, DLARRE also outputs the n */
+/*  Gerschgorin intervals for the matrices L_i D_i L_i^T. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  RANGE   (input) CHARACTER */
+/*          = 'A': ("All")   all eigenvalues will be found. */
+/*          = 'V': ("Value") all eigenvalues in the half-open interval */
+/*                           (VL, VU] will be found. */
+/*          = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
+/*                           entire matrix) will be found. */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix. N > 0. */
+
+/*  VL      (input/output) DOUBLE PRECISION */
+/*  VU      (input/output) DOUBLE PRECISION */
+/*          If RANGE='V', the lower and upper bounds for the eigenvalues. */
+/*          Eigenvalues less than or equal to VL, or greater than VU, */
+/*          will not be returned.  VL < VU. */
+/*          If RANGE='I' or ='A', DLARRE computes bounds on the desired */
+/*          part of the spectrum. */
+
+/*  IL      (input) INTEGER */
+/*  IU      (input) INTEGER */
+/*          If RANGE='I', the indices (in ascending order) of the */
+/*          smallest and largest eigenvalues to be returned. */
+/*          1 <= IL <= IU <= N. */
+
+/*  D       (input/output) DOUBLE PRECISION array, dimension (N) */
+/*          On entry, the N diagonal elements of the tridiagonal */
+/*          matrix T. */
+/*          On exit, the N diagonal elements of the diagonal */
+/*          matrices D_i. */
+
+/*  E       (input/output) DOUBLE PRECISION array, dimension (N) */
+/*          On entry, the first (N-1) entries contain the subdiagonal */
+/*          elements of the tridiagonal matrix T; E(N) need not be set. */
+/*          On exit, E contains the subdiagonal elements of the unit */
+/*          bidiagonal matrices L_i. The entries E( ISPLIT( I ) ), */
+/*          1 <= I <= NSPLIT, contain the base points sigma_i on output. */
+
+/*  E2      (input/output) DOUBLE PRECISION array, dimension (N) */
+/*          On entry, the first (N-1) entries contain the SQUARES of the */
+/*          subdiagonal elements of the tridiagonal matrix T; */
+/*          E2(N) need not be set. */
+/*          On exit, the entries E2( ISPLIT( I ) ), */
+/*          1 <= I <= NSPLIT, have been set to zero */
+
+/*  RTOL1   (input) DOUBLE PRECISION */
+/*  RTOL2   (input) DOUBLE PRECISION */
+/*           Parameters for bisection. */
+/*           An interval [LEFT,RIGHT] has converged if */
+/*           RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
+
+/*  SPLTOL (input) DOUBLE PRECISION */
+/*          The threshold for splitting. */
+
+/*  NSPLIT  (output) INTEGER */
+/*          The number of blocks T splits into. 1 <= NSPLIT <= N. */
+
+/*  ISPLIT  (output) INTEGER array, dimension (N) */
+/*          The splitting points, at which T breaks up into blocks. */
+/*          The first block consists of rows/columns 1 to ISPLIT(1), */
+/*          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
+/*          etc., and the NSPLIT-th consists of rows/columns */
+/*          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
+
+/*  M       (output) INTEGER */
+/*          The total number of eigenvalues (of all L_i D_i L_i^T) */
+/*          found. */
+
+/*  W       (output) DOUBLE PRECISION array, dimension (N) */
+/*          The first M elements contain the eigenvalues. The */
+/*          eigenvalues of each of the blocks, L_i D_i L_i^T, are */
+/*          sorted in ascending order ( DLARRE may use the */
+/*          remaining N-M elements as workspace). */
+
+/*  WERR    (output) DOUBLE PRECISION array, dimension (N) */
+/*          The error bound on the corresponding eigenvalue in W. */
+
+/*  WGAP    (output) DOUBLE PRECISION array, dimension (N) */
+/*          The separation from the right neighbor eigenvalue in W. */
+/*          The gap is only with respect to the eigenvalues of the same block */
+/*          as each block has its own representation tree. */
+/*          Exception: at the right end of a block we store the left gap */
+
+/*  IBLOCK  (output) INTEGER array, dimension (N) */
+/*          The indices of the blocks (submatrices) associated with the */
+/*          corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue */
+/*          W(i) belongs to the first block from the top, =2 if W(i) */
+/*          belongs to the second block, etc. */
+
+/*  INDEXW  (output) INTEGER array, dimension (N) */
+/*          The indices of the eigenvalues within each block (submatrix); */
+/*          for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the */
+/*          i-th eigenvalue W(i) is the 10-th eigenvalue in block 2 */
+
+/*  GERS    (output) DOUBLE PRECISION array, dimension (2*N) */
+/*          The N Gerschgorin intervals (the i-th Gerschgorin interval */
+/*          is (GERS(2*i-1), GERS(2*i)). */
+
+/*  PIVMIN  (output) DOUBLE PRECISION */
+/*          The minimum pivot in the Sturm sequence for T. */
+
+/*  WORK    (workspace) DOUBLE PRECISION array, dimension (6*N) */
+/*          Workspace. */
+
+/*  IWORK   (workspace) INTEGER array, dimension (5*N) */
+/*          Workspace. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          > 0:  A problem occured in DLARRE. */
+/*          < 0:  One of the called subroutines signaled an internal problem. */
+/*                Needs inspection of the corresponding parameter IINFO */
+/*                for further information. */
+
+/*          =-1:  Problem in DLARRD. */
+/*          = 2:  No base representation could be found in MAXTRY iterations. */
+/*                Increasing MAXTRY and recompilation might be a remedy. */
+/*          =-3:  Problem in DLARRB when computing the refined root */
+/*                representation for DLASQ2. */
+/*          =-4:  Problem in DLARRB when preforming bisection on the */
+/*                desired part of the spectrum. */
+/*          =-5:  Problem in DLASQ2. */
+/*          =-6:  Problem in DLASQ2. */
+
+/*  Further Details */
+/*  The base representations are required to suffer very little */
+/*  element growth and consequently define all their eigenvalues to */
+/*  high relative accuracy. */
+/*  =============== */
+
+/*  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 .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    --iwork;
+    --work;
+    --gers;
+    --indexw;
+    --iblock;
+    --wgap;
+    --werr;
+    --w;
+    --isplit;
+    --e2;
+    --e;
+    --d__;
+
+    /* Function Body */
+    *info = 0;
+
+/*     Decode RANGE */
+
+    if (lsame_(range, "A")) {
+	irange = 1;
+    } else if (lsame_(range, "V")) {
+	irange = 3;
+    } else if (lsame_(range, "I")) {
+	irange = 2;
+    }
+    *m = 0;
+/*     Get machine constants */
+    safmin = dlamch_("S");
+    eps = dlamch_("P");
+/*     Set parameters */
+    rtl = sqrt(eps);
+    bsrtol = sqrt(eps);
+/*     Treat case of 1x1 matrix for quick return */
+    if (*n == 1) {
+	if (irange == 1 || irange == 3 && d__[1] > *vl && d__[1] <= *vu || 
+		irange == 2 && *il == 1 && *iu == 1) {
+	    *m = 1;
+	    w[1] = d__[1];
+/*           The computation error of the eigenvalue is zero */
+	    werr[1] = 0.;
+	    wgap[1] = 0.;
+	    iblock[1] = 1;
+	    indexw[1] = 1;
+	    gers[1] = d__[1];
+	    gers[2] = d__[1];
+	}
+/*        store the shift for the initial RRR, which is zero in this case */
+	e[1] = 0.;
+	return 0;
+    }
+/*     General case: tridiagonal matrix of order > 1 */
+
+/*     Init WERR, WGAP. Compute Gerschgorin intervals and spectral diameter. */
+/*     Compute maximum off-diagonal entry and pivmin. */
+    gl = d__[1];
+    gu = d__[1];
+    eold = 0.;
+    emax = 0.;
+    e[*n] = 0.;
+    i__1 = *n;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	werr[i__] = 0.;
+	wgap[i__] = 0.;
+	eabs = (d__1 = e[i__], abs(d__1));
+	if (eabs >= emax) {
+	    emax = eabs;
+	}
+	tmp1 = eabs + eold;
+	gers[(i__ << 1) - 1] = d__[i__] - tmp1;
+/* Computing MIN */
+	d__1 = gl, d__2 = gers[(i__ << 1) - 1];
+	gl = min(d__1,d__2);
+	gers[i__ * 2] = d__[i__] + tmp1;
+/* Computing MAX */
+	d__1 = gu, d__2 = gers[i__ * 2];
+	gu = max(d__1,d__2);
+	eold = eabs;
+/* L5: */
+    }
+/*     The minimum pivot allowed in the Sturm sequence for T */
+/* Computing MAX */
+/* Computing 2nd power */
+    d__3 = emax;
+    d__1 = 1., d__2 = d__3 * d__3;
+    *pivmin = safmin * max(d__1,d__2);
+/*     Compute spectral diameter. The Gerschgorin bounds give an */
+/*     estimate that is wrong by at most a factor of SQRT(2) */
+    spdiam = gu - gl;
+/*     Compute splitting points */
+    dlarra_(n, &d__[1], &e[1], &e2[1], spltol, &spdiam, nsplit, &isplit[1], &
+	    iinfo);
+/*     Can force use of bisection instead of faster DQDS. */
+/*     Option left in the code for future multisection work. */
+    forceb = FALSE_;
+/*     Initialize USEDQD, DQDS should be used for ALLRNG unless someone */
+/*     explicitly wants bisection. */
+    usedqd = irange == 1 && ! forceb;
+    if (irange == 1 && ! forceb) {
+/*        Set interval [VL,VU] that contains all eigenvalues */
+	*vl = gl;
+	*vu = gu;
+    } else {
+/*        We call DLARRD to find crude approximations to the eigenvalues */
+/*        in the desired range. In case IRANGE = INDRNG, we also obtain the */
+/*        interval (VL,VU] that contains all the wanted eigenvalues. */
+/*        An interval [LEFT,RIGHT] has converged if */
+/*        RIGHT-LEFT.LT.RTOL*MAX(ABS(LEFT),ABS(RIGHT)) */
+/*        DLARRD needs a WORK of size 4*N, IWORK of size 3*N */
+	dlarrd_(range, "B", n, vl, vu, il, iu, &gers[1], &bsrtol, &d__[1], &e[
+		1], &e2[1], pivmin, nsplit, &isplit[1], &mm, &w[1], &werr[1], 
+		vl, vu, &iblock[1], &indexw[1], &work[1], &iwork[1], &iinfo);
+	if (iinfo != 0) {
+	    *info = -1;
+	    return 0;
+	}
+/*        Make sure that the entries M+1 to N in W, WERR, IBLOCK, INDEXW are 0 */
+	i__1 = *n;
+	for (i__ = mm + 1; i__ <= i__1; ++i__) {
+	    w[i__] = 0.;
+	    werr[i__] = 0.;
+	    iblock[i__] = 0;
+	    indexw[i__] = 0;
+/* L14: */
+	}
+    }
+/* ** */
+/*     Loop over unreduced blocks */
+    ibegin = 1;
+    wbegin = 1;
+    i__1 = *nsplit;
+    for (jblk = 1; jblk <= i__1; ++jblk) {
+	iend = isplit[jblk];
+	in = iend - ibegin + 1;
+/*        1 X 1 block */
+	if (in == 1) {
+	    if (irange == 1 || irange == 3 && d__[ibegin] > *vl && d__[ibegin]
+		     <= *vu || irange == 2 && iblock[wbegin] == jblk) {
+		++(*m);
+		w[*m] = d__[ibegin];
+		werr[*m] = 0.;
+/*              The gap for a single block doesn't matter for the later */
+/*              algorithm and is assigned an arbitrary large value */
+		wgap[*m] = 0.;
+		iblock[*m] = jblk;
+		indexw[*m] = 1;
+		++wbegin;
+	    }
+/*           E( IEND ) holds the shift for the initial RRR */
+	    e[iend] = 0.;
+	    ibegin = iend + 1;
+	    goto L170;
+	}
+
+/*        Blocks of size larger than 1x1 */
+
+/*        E( IEND ) will hold the shift for the initial RRR, for now set it =0 */
+	e[iend] = 0.;
+
+/*        Find local outer bounds GL,GU for the block */
+	gl = d__[ibegin];
+	gu = d__[ibegin];
+	i__2 = iend;
+	for (i__ = ibegin; i__ <= i__2; ++i__) {
+/* Computing MIN */
+	    d__1 = gers[(i__ << 1) - 1];
+	    gl = min(d__1,gl);
+/* Computing MAX */
+	    d__1 = gers[i__ * 2];
+	    gu = max(d__1,gu);
+/* L15: */
+	}
+	spdiam = gu - gl;
+	if (! (irange == 1 && ! forceb)) {
+/*           Count the number of eigenvalues in the current block. */
+	    mb = 0;
+	    i__2 = mm;
+	    for (i__ = wbegin; i__ <= i__2; ++i__) {
+		if (iblock[i__] == jblk) {
+		    ++mb;
+		} else {
+		    goto L21;
+		}
+/* L20: */
+	    }
+L21:
+	    if (mb == 0) {
+/*              No eigenvalue in the current block lies in the desired range */
+/*              E( IEND ) holds the shift for the initial RRR */
+		e[iend] = 0.;
+		ibegin = iend + 1;
+		goto L170;
+	    } else {
+/*              Decide whether dqds or bisection is more efficient */
+		usedqd = (doublereal) mb > in * .5 && ! forceb;
+		wend = wbegin + mb - 1;
+/*              Calculate gaps for the current block */
+/*              In later stages, when representations for individual */
+/*              eigenvalues are different, we use SIGMA = E( IEND ). */
+		sigma = 0.;
+		i__2 = wend - 1;
+		for (i__ = wbegin; i__ <= i__2; ++i__) {
+/* Computing MAX */
+		    d__1 = 0., d__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + 
+			    werr[i__]);
+		    wgap[i__] = max(d__1,d__2);
+/* L30: */
+		}
+/* Computing MAX */
+		d__1 = 0., d__2 = *vu - sigma - (w[wend] + werr[wend]);
+		wgap[wend] = max(d__1,d__2);
+/*              Find local index of the first and last desired evalue. */
+		indl = indexw[wbegin];
+		indu = indexw[wend];
+	    }
+	}
+	if (irange == 1 && ! forceb || usedqd) {
+/*           Case of DQDS */
+/*           Find approximations to the extremal eigenvalues of the block */
+	    dlarrk_(&in, &c__1, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, &
+		    rtl, &tmp, &tmp1, &iinfo);
+	    if (iinfo != 0) {
+		*info = -1;
+		return 0;
+	    }
+/* Computing MAX */
+	    d__2 = gl, d__3 = tmp - tmp1 - eps * 100. * (d__1 = tmp - tmp1, 
+		    abs(d__1));
+	    isleft = max(d__2,d__3);
+	    dlarrk_(&in, &in, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, &
+		    rtl, &tmp, &tmp1, &iinfo);
+	    if (iinfo != 0) {
+		*info = -1;
+		return 0;
+	    }
+/* Computing MIN */
+	    d__2 = gu, d__3 = tmp + tmp1 + eps * 100. * (d__1 = tmp + tmp1, 
+		    abs(d__1));
+	    isrght = min(d__2,d__3);
+/*           Improve the estimate of the spectral diameter */
+	    spdiam = isrght - isleft;
+	} else {
+/*           Case of bisection */
+/*           Find approximations to the wanted extremal eigenvalues */
+/* Computing MAX */
+	    d__2 = gl, d__3 = w[wbegin] - werr[wbegin] - eps * 100. * (d__1 = 
+		    w[wbegin] - werr[wbegin], abs(d__1));
+	    isleft = max(d__2,d__3);
+/* Computing MIN */
+	    d__2 = gu, d__3 = w[wend] + werr[wend] + eps * 100. * (d__1 = w[
+		    wend] + werr[wend], abs(d__1));
+	    isrght = min(d__2,d__3);
+	}
+/*        Decide whether the base representation for the current block */
+/*        L_JBLK D_JBLK L_JBLK^T = T_JBLK - sigma_JBLK I */
+/*        should be on the left or the right end of the current block. */
+/*        The strategy is to shift to the end which is "more populated" */
+/*        Furthermore, decide whether to use DQDS for the computation of */
+/*        the eigenvalue approximations at the end of DLARRE or bisection. */
+/*        dqds is chosen if all eigenvalues are desired or the number of */
+/*        eigenvalues to be computed is large compared to the blocksize. */
+	if (irange == 1 && ! forceb) {
+/*           If all the eigenvalues have to be computed, we use dqd */
+	    usedqd = TRUE_;
+/*           INDL is the local index of the first eigenvalue to compute */
+	    indl = 1;
+	    indu = in;
+/*           MB =  number of eigenvalues to compute */
+	    mb = in;
+	    wend = wbegin + mb - 1;
+/*           Define 1/4 and 3/4 points of the spectrum */
+	    s1 = isleft + spdiam * .25;
+	    s2 = isrght - spdiam * .25;
+	} else {
+/*           DLARRD has computed IBLOCK and INDEXW for each eigenvalue */
+/*           approximation. */
+/*           choose sigma */
+	    if (usedqd) {
+		s1 = isleft + spdiam * .25;
+		s2 = isrght - spdiam * .25;
+	    } else {
+		tmp = min(isrght,*vu) - max(isleft,*vl);
+		s1 = max(isleft,*vl) + tmp * .25;
+		s2 = min(isrght,*vu) - tmp * .25;
+	    }
+	}
+/*        Compute the negcount at the 1/4 and 3/4 points */
+	if (mb > 1) {
+	    dlarrc_("T", &in, &s1, &s2, &d__[ibegin], &e[ibegin], pivmin, &
+		    cnt, &cnt1, &cnt2, &iinfo);
+	}
+	if (mb == 1) {
+	    sigma = gl;
+	    sgndef = 1.;
+	} else if (cnt1 - indl >= indu - cnt2) {
+	    if (irange == 1 && ! forceb) {
+		sigma = max(isleft,gl);
+	    } else if (usedqd) {
+/*              use Gerschgorin bound as shift to get pos def matrix */
+/*              for dqds */
+		sigma = isleft;
+	    } else {
+/*              use approximation of the first desired eigenvalue of the */
+/*              block as shift */
+		sigma = max(isleft,*vl);
+	    }
+	    sgndef = 1.;
+	} else {
+	    if (irange == 1 && ! forceb) {
+		sigma = min(isrght,gu);
+	    } else if (usedqd) {
+/*              use Gerschgorin bound as shift to get neg def matrix */
+/*              for dqds */
+		sigma = isrght;
+	    } else {
+/*              use approximation of the first desired eigenvalue of the */
+/*              block as shift */
+		sigma = min(isrght,*vu);
+	    }
+	    sgndef = -1.;
+	}
+/*        An initial SIGMA has been chosen that will be used for computing */
+/*        T - SIGMA I = L D L^T */
+/*        Define the increment TAU of the shift in case the initial shift */
+/*        needs to be refined to obtain a factorization with not too much */
+/*        element growth. */
+	if (usedqd) {
+/*           The initial SIGMA was to the outer end of the spectrum */
+/*           the matrix is definite and we need not retreat. */
+	    tau = spdiam * eps * *n + *pivmin * 2.;
+	} else {
+	    if (mb > 1) {
+		clwdth = w[wend] + werr[wend] - w[wbegin] - werr[wbegin];
+		avgap = (d__1 = clwdth / (doublereal) (wend - wbegin), abs(
+			d__1));
+		if (sgndef == 1.) {
+/* Computing MAX */
+		    d__1 = wgap[wbegin];
+		    tau = max(d__1,avgap) * .5;
+/* Computing MAX */
+		    d__1 = tau, d__2 = werr[wbegin];
+		    tau = max(d__1,d__2);
+		} else {
+/* Computing MAX */
+		    d__1 = wgap[wend - 1];
+		    tau = max(d__1,avgap) * .5;
+/* Computing MAX */
+		    d__1 = tau, d__2 = werr[wend];
+		    tau = max(d__1,d__2);
+		}
+	    } else {
+		tau = werr[wbegin];
+	    }
+	}
+
+	for (idum = 1; idum <= 6; ++idum) {
+/*           Compute L D L^T factorization of tridiagonal matrix T - sigma I. */
+/*           Store D in WORK(1:IN), L in WORK(IN+1:2*IN), and reciprocals of */
+/*           pivots in WORK(2*IN+1:3*IN) */
+	    dpivot = d__[ibegin] - sigma;
+	    work[1] = dpivot;
+	    dmax__ = abs(work[1]);
+	    j = ibegin;
+	    i__2 = in - 1;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		work[(in << 1) + i__] = 1. / work[i__];
+		tmp = e[j] * work[(in << 1) + i__];
+		work[in + i__] = tmp;
+		dpivot = d__[j + 1] - sigma - tmp * e[j];
+		work[i__ + 1] = dpivot;
+/* Computing MAX */
+		d__1 = dmax__, d__2 = abs(dpivot);
+		dmax__ = max(d__1,d__2);
+		++j;
+/* L70: */
+	    }
+/*           check for element growth */
+	    if (dmax__ > spdiam * 64.) {
+		norep = TRUE_;
+	    } else {
+		norep = FALSE_;
+	    }
+	    if (usedqd && ! norep) {
+/*              Ensure the definiteness of the representation */
+/*              All entries of D (of L D L^T) must have the same sign */
+		i__2 = in;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    tmp = sgndef * work[i__];
+		    if (tmp < 0.) {
+			norep = TRUE_;
+		    }
+/* L71: */
+		}
+	    }
+	    if (norep) {
+/*              Note that in the case of IRANGE=ALLRNG, we use the Gerschgorin */
+/*              shift which makes the matrix definite. So we should end up */
+/*              here really only in the case of IRANGE = VALRNG or INDRNG. */
+		if (idum == 5) {
+		    if (sgndef == 1.) {
+/*                    The fudged Gerschgorin shift should succeed */
+			sigma = gl - spdiam * 2. * eps * *n - *pivmin * 4.;
+		    } else {
+			sigma = gu + spdiam * 2. * eps * *n + *pivmin * 4.;
+		    }
+		} else {
+		    sigma -= sgndef * tau;
+		    tau *= 2.;
+		}
+	    } else {
+/*              an initial RRR is found */
+		goto L83;
+	    }
+/* L80: */
+	}
+/*        if the program reaches this point, no base representation could be */
+/*        found in MAXTRY iterations. */
+	*info = 2;
+	return 0;
+L83:
+/*        At this point, we have found an initial base representation */
+/*        T - SIGMA I = L D L^T with not too much element growth. */
+/*        Store the shift. */
+	e[iend] = sigma;
+/*        Store D and L. */
+	dcopy_(&in, &work[1], &c__1, &d__[ibegin], &c__1);
+	i__2 = in - 1;
+	dcopy_(&i__2, &work[in + 1], &c__1, &e[ibegin], &c__1);
+	if (mb > 1) {
+
+/*           Perturb each entry of the base representation by a small */
+/*           (but random) relative amount to overcome difficulties with */
+/*           glued matrices. */
+
+	    for (i__ = 1; i__ <= 4; ++i__) {
+		iseed[i__ - 1] = 1;
+/* L122: */
+	    }
+	    i__2 = (in << 1) - 1;
+	    dlarnv_(&c__2, iseed, &i__2, &work[1]);
+	    i__2 = in - 1;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		d__[ibegin + i__ - 1] *= eps * 8. * work[i__] + 1.;
+		e[ibegin + i__ - 1] *= eps * 8. * work[in + i__] + 1.;
+/* L125: */
+	    }
+	    d__[iend] *= eps * 4. * work[in] + 1.;
+
+	}
+
+/*        Don't update the Gerschgorin intervals because keeping track */
+/*        of the updates would be too much work in DLARRV. */
+/*        We update W instead and use it to locate the proper Gerschgorin */
+/*        intervals. */
+/*        Compute the required eigenvalues of L D L' by bisection or dqds */
+	if (! usedqd) {
+/*           If DLARRD has been used, shift the eigenvalue approximations */
+/*           according to their representation. This is necessary for */
+/*           a uniform DLARRV since dqds computes eigenvalues of the */
+/*           shifted representation. In DLARRV, W will always hold the */
+/*           UNshifted eigenvalue approximation. */
+	    i__2 = wend;
+	    for (j = wbegin; j <= i__2; ++j) {
+		w[j] -= sigma;
+		werr[j] += (d__1 = w[j], abs(d__1)) * eps;
+/* L134: */
+	    }
+/*           call DLARRB to reduce eigenvalue error of the approximations */
+/*           from DLARRD */
+	    i__2 = iend - 1;
+	    for (i__ = ibegin; i__ <= i__2; ++i__) {
+/* Computing 2nd power */
+		d__1 = e[i__];
+		work[i__] = d__[i__] * (d__1 * d__1);
+/* L135: */
+	    }
+/*           use bisection to find EV from INDL to INDU */
+	    i__2 = indl - 1;
+	    dlarrb_(&in, &d__[ibegin], &work[ibegin], &indl, &indu, rtol1, 
+		    rtol2, &i__2, &w[wbegin], &wgap[wbegin], &werr[wbegin], &
+		    work[(*n << 1) + 1], &iwork[1], pivmin, &spdiam, &in, &
+		    iinfo);
+	    if (iinfo != 0) {
+		*info = -4;
+		return 0;
+	    }
+/*           DLARRB computes all gaps correctly except for the last one */
+/*           Record distance to VU/GU */
+/* Computing MAX */
+	    d__1 = 0., d__2 = *vu - sigma - (w[wend] + werr[wend]);
+	    wgap[wend] = max(d__1,d__2);
+	    i__2 = indu;
+	    for (i__ = indl; i__ <= i__2; ++i__) {
+		++(*m);
+		iblock[*m] = jblk;
+		indexw[*m] = i__;
+/* L138: */
+	    }
+	} else {
+/*           Call dqds to get all eigs (and then possibly delete unwanted */
+/*           eigenvalues). */
+/*           Note that dqds finds the eigenvalues of the L D L^T representation */
+/*           of T to high relative accuracy. High relative accuracy */
+/*           might be lost when the shift of the RRR is subtracted to obtain */
+/*           the eigenvalues of T. However, T is not guaranteed to define its */
+/*           eigenvalues to high relative accuracy anyway. */
+/*           Set RTOL to the order of the tolerance used in DLASQ2 */
+/*           This is an ESTIMATED error, the worst case bound is 4*N*EPS */
+/*           which is usually too large and requires unnecessary work to be */
+/*           done by bisection when computing the eigenvectors */
+	    rtol = log((doublereal) in) * 4. * eps;
+	    j = ibegin;
+	    i__2 = in - 1;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		work[(i__ << 1) - 1] = (d__1 = d__[j], abs(d__1));
+		work[i__ * 2] = e[j] * e[j] * work[(i__ << 1) - 1];
+		++j;
+/* L140: */
+	    }
+	    work[(in << 1) - 1] = (d__1 = d__[iend], abs(d__1));
+	    work[in * 2] = 0.;
+	    dlasq2_(&in, &work[1], &iinfo);
+	    if (iinfo != 0) {
+/*              If IINFO = -5 then an index is part of a tight cluster */
+/*              and should be changed. The index is in IWORK(1) and the */
+/*              gap is in WORK(N+1) */
+		*info = -5;
+		return 0;
+	    } else {
+/*              Test that all eigenvalues are positive as expected */
+		i__2 = in;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    if (work[i__] < 0.) {
+			*info = -6;
+			return 0;
+		    }
+/* L149: */
+		}
+	    }
+	    if (sgndef > 0.) {
+		i__2 = indu;
+		for (i__ = indl; i__ <= i__2; ++i__) {
+		    ++(*m);
+		    w[*m] = work[in - i__ + 1];
+		    iblock[*m] = jblk;
+		    indexw[*m] = i__;
+/* L150: */
+		}
+	    } else {
+		i__2 = indu;
+		for (i__ = indl; i__ <= i__2; ++i__) {
+		    ++(*m);
+		    w[*m] = -work[i__];
+		    iblock[*m] = jblk;
+		    indexw[*m] = i__;
+/* L160: */
+		}
+	    }
+	    i__2 = *m;
+	    for (i__ = *m - mb + 1; i__ <= i__2; ++i__) {
+/*              the value of RTOL below should be the tolerance in DLASQ2 */
+		werr[i__] = rtol * (d__1 = w[i__], abs(d__1));
+/* L165: */
+	    }
+	    i__2 = *m - 1;
+	    for (i__ = *m - mb + 1; i__ <= i__2; ++i__) {
+/*              compute the right gap between the intervals */
+/* Computing MAX */
+		d__1 = 0., d__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + werr[
+			i__]);
+		wgap[i__] = max(d__1,d__2);
+/* L166: */
+	    }
+/* Computing MAX */
+	    d__1 = 0., d__2 = *vu - sigma - (w[*m] + werr[*m]);
+	    wgap[*m] = max(d__1,d__2);
+	}
+/*        proceed with next block */
+	ibegin = iend + 1;
+	wbegin = wend + 1;
+L170:
+	;
+    }
+
+    return 0;
+
+/*     end of DLARRE */
+
+} /* dlarre_ */