/* ../netlib/slarre.f -- translated by f2c (version 20100827). 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 "FLA_f2c.h" /* Table of constant values */
static integer c__1 = 1;
static integer c__2 = 2;
/* > \brief \b SLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each un reduced block Ti, finds base representations and eigenvalues. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SLARRE + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarre. f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarre. f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarre. f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2, */
/* RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, */
/* W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, */
/* WORK, IWORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER RANGE */
/* INTEGER IL, INFO, IU, M, N, NSPLIT */
/* REAL PIVMIN, RTOL1, RTOL2, SPLTOL, VL, VU */
/* .. */
/* .. Array Arguments .. */
/* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ), */
/* $ INDEXW( * ) */
/* REAL D( * ), E( * ), E2( * ), GERS( * ), */
/* $ W( * ),WERR( * ), WGAP( * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > To find the desired eigenvalues of a given real symmetric */
/* > tridiagonal matrix T, SLARRE 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 */
/* > SSTEMR 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 SLASQ2) to */
/* > conpute all and then discard any unwanted one. */
/* > As an added benefit, SLARRE also outputs the n */
/* > Gerschgorin intervals for the matrices L_i D_i L_i^T. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] RANGE */
/* > \verbatim */
/* > RANGE is CHARACTER*1 */
/* > = '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. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix. N > 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VL */
/* > \verbatim */
/* > VL is REAL */
/* > \endverbatim */
/* > */
/* > \param[in,out] VU */
/* > \verbatim */
/* > VU is REAL */
/* > 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', SLARRE computes bounds on the desired */
/* > part of the spectrum. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* > IL is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* > IU is INTEGER */
/* > If RANGE='I', the indices (in ascending order) of the */
/* > smallest and largest eigenvalues to be returned. */
/* > 1 <= IL <= IU <= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is REAL 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. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* > E is REAL 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. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E2 */
/* > \verbatim */
/* > E2 is REAL 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 */
/* > \endverbatim */
/* > */
/* > \param[in] RTOL1 */
/* > \verbatim */
/* > RTOL1 is REAL */
/* > \endverbatim */
/* > */
/* > \param[in] RTOL2 */
/* > \verbatim */
/* > RTOL2 is REAL */
/* > Parameters for bisection. */
/* > An interval [LEFT,RIGHT] has converged if */
/* > RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
/* > \endverbatim */
/* > */
/* > \param[in] SPLTOL */
/* > \verbatim */
/* > SPLTOL is REAL */
/* > The threshold for splitting. */
/* > \endverbatim */
/* > */
/* > \param[out] NSPLIT */
/* > \verbatim */
/* > NSPLIT is INTEGER */
/* > The number of blocks T splits into. 1 <= NSPLIT <= N. */
/* > \endverbatim */
/* > */
/* > \param[out] ISPLIT */
/* > \verbatim */
/* > ISPLIT is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The total number of eigenvalues (of all L_i D_i L_i^T) */
/* > found. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is REAL 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 ( SLARRE may use the */
/* > remaining N-M elements as workspace). */
/* > \endverbatim */
/* > */
/* > \param[out] WERR */
/* > \verbatim */
/* > WERR is REAL array, dimension (N) */
/* > The error bound on the corresponding eigenvalue in W. */
/* > \endverbatim */
/* > */
/* > \param[out] WGAP */
/* > \verbatim */
/* > WGAP is REAL 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 */
/* > \endverbatim */
/* > */
/* > \param[out] IBLOCK */
/* > \verbatim */
/* > IBLOCK is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] INDEXW */
/* > \verbatim */
/* > INDEXW is 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 */
/* > \endverbatim */
/* > */
/* > \param[out] GERS */
/* > \verbatim */
/* > GERS is REAL array, dimension (2*N) */
/* > The N Gerschgorin intervals (the i-th Gerschgorin interval */
/* > is (GERS(2*i-1), GERS(2*i)). */
/* > \endverbatim */
/* > */
/* > \param[out] PIVMIN */
/* > \verbatim */
/* > PIVMIN is REAL */
/* > The minimum pivot in the Sturm sequence for T. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (6*N) */
/* > Workspace. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (5*N) */
/* > Workspace. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > > 0: A problem occured in SLARRE. */
/* > < 0: One of the called subroutines signaled an internal problem. */
/* > Needs inspection of the corresponding parameter IINFO */
/* > for further information. */
/* > */
/* > =-1: Problem in SLARRD. */
/* > = 2: No base representation could be found in MAXTRY iterations. */
/* > Increasing MAXTRY and recompilation might be a remedy. */
/* > =-3: Problem in SLARRB when computing the refined root */
/* > representation for SLASQ2. */
/* > =-4: Problem in SLARRB when preforming bisection on the */
/* > desired part of the spectrum. */
/* > =-5: Problem in SLASQ2. */
/* > =-6: Problem in SLASQ2. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date September 2012 */
/* > \ingroup auxOTHERauxiliary */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The base representations are required to suffer very little */
/* > element growth and consequently define all their eigenvalues to */
/* > high relative accuracy. */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Beresford Parlett, University of California, Berkeley, USA \n */
/* > Jim Demmel, University of California, Berkeley, USA \n */
/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
/* > Osni Marques, LBNL/NERSC, USA \n */
/* > Christof Voemel, University of California, Berkeley, USA \n */
/* > */
/* ===================================================================== */
/* Subroutine */
int slarre_(char *range, integer *n, real *vl, real *vu, integer *il, integer *iu, real *d__, real *e, real *e2, real *rtol1, real *rtol2, real *spltol, integer *nsplit, integer *isplit, integer * m, real *w, real *werr, real *wgap, integer *iblock, integer *indexw, real *gers, real *pivmin, real *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer i__1, i__2;
    real r__1, r__2, r__3;
    /* Builtin functions */
    double sqrt(doublereal), log(doublereal);
    /* Local variables */
    integer i__, j;
    real s1, s2;
    integer mb;
    real gl;
    integer in, mm;
    real gu;
    integer cnt;
    real eps, tau, tmp, rtl;
    integer cnt1, cnt2;
    real tmp1, eabs;
    integer iend, jblk;
    real eold;
    integer indl;
    real dmax__, emax;
    integer wend, idum, indu;
    real rtol;
    integer iseed[4];
    real avgap, sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    logical norep;
    extern /* Subroutine */
    int scopy_(integer *, real *, integer *, real *, integer *), slasq2_(integer *, real *, integer *);
    integer ibegin;
    logical forceb;
    integer irange;
    real sgndef;
    extern real slamch_(char *);
    integer wbegin;
    real safmin, spdiam;
    extern /* Subroutine */
    int slarra_(integer *, real *, real *, real *, real *, real *, integer *, integer *, integer *);
    logical usedqd;
    real clwdth, isleft;
    extern /* Subroutine */
    int slarrb_(integer *, real *, real *, integer *, integer *, real *, real *, integer *, real *, real *, real *, real *, integer *, real *, real *, integer *, integer *), slarrc_( char *, integer *, real *, real *, real *, real *, real *, integer *, integer *, integer *, integer *), slarrd_(char *, char *, integer *, real *, real *, integer *, integer *, real * , real *, real *, real *, real *, real *, integer *, integer *, integer *, real *, real *, real *, real *, integer *, integer *, real *, integer *, integer *), slarrk_(integer *, integer *, real *, real *, real *, real *, real *, real *, real *, real *, integer *);
    real isrght, bsrtol, dpivot;
    extern /* Subroutine */
    int slarnv_(integer *, integer *, integer *, real *);
    /* -- LAPACK auxiliary routine (version 3.4.2) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* September 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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 */
    irange = 0;
    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 = slamch_("S");
    eps = slamch_("P");
    /* Set parameters */
    rtl = eps * 100.f;
    /* If one were ever to ask for less initial precision in BSRTOL, */
    /* one should keep in mind that for the subset case, the extremal */
    /* eigenvalues must be at least as accurate as the current setting */
    /* (eigenvalues in the middle need not as much accuracy) */
    bsrtol = sqrt(eps) * 5e-4f;
    /* 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.f;
            wgap[1] = 0.f;
            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.f;
        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.f;
    emax = 0.f;
    e[*n] = 0.f;
    i__1 = *n;
    for (i__ = 1;
            i__ <= i__1;
            ++i__)
    {
        werr[i__] = 0.f;
        wgap[i__] = 0.f;
        eabs = (r__1 = e[i__], f2c_abs(r__1));
        if (eabs >= emax)
        {
            emax = eabs;
        }
        tmp1 = eabs + eold;
        gers[(i__ << 1) - 1] = d__[i__] - tmp1;
        /* Computing MIN */
        r__1 = gl;
        r__2 = gers[(i__ << 1) - 1]; // , expr subst
        gl = min(r__1,r__2);
        gers[i__ * 2] = d__[i__] + tmp1;
        /* Computing MAX */
        r__1 = gu;
        r__2 = gers[i__ * 2]; // , expr subst
        gu = max(r__1,r__2);
        eold = eabs;
        /* L5: */
    }
    /* The minimum pivot allowed in the Sturm sequence for T */
    /* Computing MAX */
    /* Computing 2nd power */
    r__3 = emax;
    r__1 = 1.f;
    r__2 = r__3 * r__3; // , expr subst
    *pivmin = safmin * max(r__1,r__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 */
    slarra_(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 SLARRD 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)) */
        /* SLARRD needs a WORK of size 4*N, IWORK of size 3*N */
        slarrd_(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.f;
            werr[i__] = 0.f;
            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.f;
                /* The gap for a single block doesn't matter for the later */
                /* algorithm and is assigned an arbitrary large value */
                wgap[*m] = 0.f;
                iblock[*m] = jblk;
                indexw[*m] = 1;
                ++wbegin;
            }
            /* E( IEND ) holds the shift for the initial RRR */
            e[iend] = 0.f;
            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.f;
        /* 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 */
            r__1 = gers[(i__ << 1) - 1];
            gl = min(r__1,gl);
            /* Computing MAX */
            r__1 = gers[i__ * 2];
            gu = max(r__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.f;
                ibegin = iend + 1;
                goto L170;
            }
            else
            {
                /* Decide whether dqds or bisection is more efficient */
                usedqd = (real) mb > in * .5f && ! 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.f;
                i__2 = wend - 1;
                for (i__ = wbegin;
                        i__ <= i__2;
                        ++i__)
                {
                    /* Computing MAX */
                    r__1 = 0.f;
                    r__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + werr[i__]); // , expr subst
                    wgap[i__] = max(r__1,r__2);
                    /* L30: */
                }
                /* Computing MAX */
                r__1 = 0.f;
                r__2 = *vu - sigma - (w[wend] + werr[wend]); // , expr subst
                wgap[wend] = max(r__1,r__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 */
            slarrk_(&in, &c__1, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, & rtl, &tmp, &tmp1, &iinfo);
            if (iinfo != 0)
            {
                *info = -1;
                return 0;
            }
            /* Computing MAX */
            r__2 = gl;
            r__3 = tmp - tmp1 - eps * 100.f * (r__1 = tmp - tmp1, f2c_abs(r__1)); // , expr subst
            isleft = max(r__2,r__3);
            slarrk_(&in, &in, &gl, &gu, &d__[ibegin], &e2[ibegin], pivmin, & rtl, &tmp, &tmp1, &iinfo);
            if (iinfo != 0)
            {
                *info = -1;
                return 0;
            }
            /* Computing MIN */
            r__2 = gu;
            r__3 = tmp + tmp1 + eps * 100.f * (r__1 = tmp + tmp1, f2c_abs(r__1)); // , expr subst
            isrght = min(r__2,r__3);
            /* Improve the estimate of the spectral diameter */
            spdiam = isrght - isleft;
        }
        else
        {
            /* Case of bisection */
            /* Find approximations to the wanted extremal eigenvalues */
            /* Computing MAX */
            r__2 = gl;
            r__3 = w[wbegin] - werr[wbegin] - eps * 100.f * (r__1 = w[wbegin] - werr[wbegin], f2c_abs(r__1)); // , expr subst
            isleft = max(r__2,r__3);
            /* Computing MIN */
            r__2 = gu;
            r__3 = w[wend] + werr[wend] + eps * 100.f * (r__1 = w[ wend] + werr[wend], f2c_abs(r__1)); // , expr subst
            isrght = min(r__2,r__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 SLARRE 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 * .25f;
            s2 = isrght - spdiam * .25f;
        }
        else
        {
            /* SLARRD has computed IBLOCK and INDEXW for each eigenvalue */
            /* approximation. */
            /* choose sigma */
            if (usedqd)
            {
                s1 = isleft + spdiam * .25f;
                s2 = isrght - spdiam * .25f;
            }
            else
            {
                tmp = min(isrght,*vu) - max(isleft,*vl);
                s1 = max(isleft,*vl) + tmp * .25f;
                s2 = min(isrght,*vu) - tmp * .25f;
            }
        }
        /* Compute the negcount at the 1/4 and 3/4 points */
        if (mb > 1)
        {
            slarrc_("T", &in, &s1, &s2, &d__[ibegin], &e[ibegin], pivmin, & cnt, &cnt1, &cnt2, &iinfo);
        }
        if (mb == 1)
        {
            sigma = gl;
            sgndef = 1.f;
        }
        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.f;
        }
        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.f;
        }
        /* 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.f;
            /* Computing MAX */
            r__1 = tau;
            r__2 = eps * 2.f * f2c_abs(sigma); // , expr subst
            tau = max(r__1,r__2);
        }
        else
        {
            if (mb > 1)
            {
                clwdth = w[wend] + werr[wend] - w[wbegin] - werr[wbegin];
                avgap = (r__1 = clwdth / (real) (wend - wbegin), f2c_abs(r__1));
                if (sgndef == 1.f)
                {
                    /* Computing MAX */
                    r__1 = wgap[wbegin];
                    tau = max(r__1,avgap) * .5f;
                    /* Computing MAX */
                    r__1 = tau;
                    r__2 = werr[wbegin]; // , expr subst
                    tau = max(r__1,r__2);
                }
                else
                {
                    /* Computing MAX */
                    r__1 = wgap[wend - 1];
                    tau = max(r__1,avgap) * .5f;
                    /* Computing MAX */
                    r__1 = tau;
                    r__2 = werr[wend]; // , expr subst
                    tau = max(r__1,r__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__ = f2c_abs(work[1]);
            j = ibegin;
            i__2 = in - 1;
            for (i__ = 1;
                    i__ <= i__2;
                    ++i__)
            {
                work[(in << 1) + i__] = 1.f / 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 */
                r__1 = dmax__;
                r__2 = f2c_abs(dpivot); // , expr subst
                dmax__ = max(r__1,r__2);
                ++j;
                /* L70: */
            }
            /* check for element growth */
            if (dmax__ > spdiam * 64.f)
            {
                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.f)
                    {
                        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.f)
                    {
                        /* The fudged Gerschgorin shift should succeed */
                        sigma = gl - spdiam * 2.f * eps * *n - *pivmin * 4.f;
                    }
                    else
                    {
                        sigma = gu + spdiam * 2.f * eps * *n + *pivmin * 4.f;
                    }
                }
                else
                {
                    sigma -= sgndef * tau;
                    tau *= 2.f;
                }
            }
            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. */
        scopy_(&in, &work[1], &c__1, &d__[ibegin], &c__1);
        i__2 = in - 1;
        scopy_(&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;
            slarnv_(&c__2, iseed, &i__2, &work[1]);
            i__2 = in - 1;
            for (i__ = 1;
                    i__ <= i__2;
                    ++i__)
            {
                d__[ibegin + i__ - 1] *= eps * 4.f * work[i__] + 1.f;
                e[ibegin + i__ - 1] *= eps * 4.f * work[in + i__] + 1.f;
                /* L125: */
            }
            d__[iend] *= eps * 4.f * work[in] + 1.f;
        }
        /* Don't update the Gerschgorin intervals because keeping track */
        /* of the updates would be too much work in SLARRV. */
        /* 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 SLARRD has been used, shift the eigenvalue approximations */
            /* according to their representation. This is necessary for */
            /* a uniform SLARRV since dqds computes eigenvalues of the */
            /* shifted representation. In SLARRV, W will always hold the */
            /* UNshifted eigenvalue approximation. */
            i__2 = wend;
            for (j = wbegin;
                    j <= i__2;
                    ++j)
            {
                w[j] -= sigma;
                werr[j] += (r__1 = w[j], f2c_abs(r__1)) * eps;
                /* L134: */
            }
            /* call SLARRB to reduce eigenvalue error of the approximations */
            /* from SLARRD */
            i__2 = iend - 1;
            for (i__ = ibegin;
                    i__ <= i__2;
                    ++i__)
            {
                /* Computing 2nd power */
                r__1 = e[i__];
                work[i__] = d__[i__] * (r__1 * r__1);
                /* L135: */
            }
            /* use bisection to find EV from INDL to INDU */
            i__2 = indl - 1;
            slarrb_(&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;
            }
            /* SLARRB computes all gaps correctly except for the last one */
            /* Record distance to VU/GU */
            /* Computing MAX */
            r__1 = 0.f;
            r__2 = *vu - sigma - (w[wend] + werr[wend]); // , expr subst
            wgap[wend] = max(r__1,r__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 SLASQ2 */
            /* 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((real) in) * 4.f * eps;
            j = ibegin;
            i__2 = in - 1;
            for (i__ = 1;
                    i__ <= i__2;
                    ++i__)
            {
                work[(i__ << 1) - 1] = (r__1 = d__[j], f2c_abs(r__1));
                work[i__ * 2] = e[j] * e[j] * work[(i__ << 1) - 1];
                ++j;
                /* L140: */
            }
            work[(in << 1) - 1] = (r__1 = d__[iend], f2c_abs(r__1));
            work[in * 2] = 0.f;
            slasq2_(&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.f)
                    {
                        *info = -6;
                        return 0;
                    }
                    /* L149: */
                }
            }
            if (sgndef > 0.f)
            {
                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 SLASQ2 */
                werr[i__] = rtol * (r__1 = w[i__], f2c_abs(r__1));
                /* L165: */
            }
            i__2 = *m - 1;
            for (i__ = *m - mb + 1;
                    i__ <= i__2;
                    ++i__)
            {
                /* compute the right gap between the intervals */
                /* Computing MAX */
                r__1 = 0.f;
                r__2 = w[i__ + 1] - werr[i__ + 1] - (w[i__] + werr[i__]); // , expr subst
                wgap[i__] = max(r__1,r__2);
                /* L166: */
            }
            /* Computing MAX */
            r__1 = 0.f;
            r__2 = *vu - sigma - (w[*m] + werr[*m]); // , expr subst
            wgap[*m] = max(r__1,r__2);
        }
        /* proceed with next block */
        ibegin = iend + 1;
        wbegin = wend + 1;
L170:
        ;
    }
    return 0;
    /* end of SLARRE */
}
/* slarre_ */
