text: /* clarrv.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 complex c_b1 = {0.f,0.f};
  static integer c__1 = 1;
  static integer c__2 = 2;
  static real c_b28 = 0.f;
  
  /* Subroutine */ int clarrv_(integer *n, real *vl, real *vu, real *d__, real *
  	l, real *pivmin, integer *isplit, integer *m, integer *dol, integer *
  	dou, real *minrgp, real *rtol1, real *rtol2, real *w, real *werr, 
  	real *wgap, integer *iblock, integer *indexw, real *gers, complex *
  	z__, integer *ldz, integer *isuppz, real *work, integer *iwork, 
  	integer *info)
  {
      /* System generated locals */
      integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
      real r__1, r__2;
      complex q__1;
      logical L__1;
  
      /* Builtin functions */
      double log(doublereal);
  
      /* Local variables */
      integer minwsize, i__, j, k, p, q, miniwsize, ii;
      real gl;
      integer im, in;
      real gu, gap, eps, tau, tol, tmp;
      integer zto;
      real ztz;
      integer iend, jblk;
      real lgap;
      integer done;
      real rgap, left;
      integer wend, iter;
      real bstw;
      integer itmp1, indld;
      real fudge;
      integer idone;
      real sigma;
      integer iinfo, iindr;
      real resid;
      logical eskip;
      real right;
      integer nclus, zfrom;
      extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
  	    integer *);
      real rqtol;
      integer iindc1, iindc2, indin1, indin2;
      extern /* Subroutine */ int clar1v_(integer *, integer *, integer *, real 
  	    *, real *, real *, real *, real *, real *, real *, complex *, 
  	    logical *, integer *, real *, real *, integer *, integer *, real *
  , real *, real *, real *);
      logical stp2ii;
      real lambda;
      integer ibegin, indeig;
      logical needbs;
      integer indlld;
      real sgndef, mingma;
      extern doublereal slamch_(char *);
      integer oldien, oldncl, wbegin;
      real spdiam;
      integer negcnt;
      extern /* Subroutine */ int claset_(char *, integer *, integer *, complex 
  	    *, complex *, complex *, integer *);
      integer oldcls;
      real savgap;
      integer ndepth;
      real ssigma;
      extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
  	    *);
      logical usedbs;
      integer iindwk, offset;
      real gaptol;
      extern /* Subroutine */ int slarrb_(integer *, real *, real *, integer *, 
  	    integer *, real *, real *, integer *, real *, real *, real *, 
  	    real *, integer *, real *, real *, integer *, integer *);
      integer newcls, oldfst, indwrk, windex, oldlst;
      logical usedrq;
      integer newfst, newftt, parity, windmn, windpl, isupmn, newlst, zusedl;
      real bstres;
      integer newsiz, zusedu, zusedw;
      real nrminv, rqcorr;
      logical tryrqc;
      integer isupmx;
      extern /* Subroutine */ int slarrf_(integer *, real *, real *, real *, 
  	    integer *, integer *, real *, real *, real *, real *, real *, 
  	    real *, real *, real *, real *, real *, real *, integer *);
  
  
  /*  -- LAPACK auxiliary routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  CLARRV computes the eigenvectors of the tridiagonal matrix */
  /*  T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T. */
  /*  The input eigenvalues should have been computed by SLARRE. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  N       (input) INTEGER */
  /*          The order of the matrix.  N >= 0. */
  
  /*  VL      (input) REAL */
  /*  VU      (input) REAL */
  /*          Lower and upper bounds of the interval that contains the desired */
  /*          eigenvalues. VL < VU. Needed to compute gaps on the left or right */
  /*          end of the extremal eigenvalues in the desired RANGE. */
  
  /*  D       (input/output) REAL             array, dimension (N) */
  /*          On entry, the N diagonal elements of the diagonal matrix D. */
  /*          On exit, D may be overwritten. */
  
  /*  L       (input/output) REAL             array, dimension (N) */
  /*          On entry, the (N-1) subdiagonal elements of the unit */
  /*          bidiagonal matrix L are in elements 1 to N-1 of L */
  /*          (if the matrix is not splitted.) At the end of each block */
  /*          is stored the corresponding shift as given by SLARRE. */
  /*          On exit, L is overwritten. */
  
  /*  PIVMIN  (in) DOUBLE PRECISION */
  /*          The minimum pivot allowed in the Sturm sequence. */
  
  /*  ISPLIT  (input) 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. */
  
  /*  M       (input) INTEGER */
  /*          The total number of input eigenvalues.  0 <= M <= N. */
  
  /*  DOL     (input) INTEGER */
  /*  DOU     (input) INTEGER */
  /*          If the user wants to compute only selected eigenvectors from all */
  /*          the eigenvalues supplied, he can specify an index range DOL:DOU. */
  /*          Or else the setting DOL=1, DOU=M should be applied. */
  /*          Note that DOL and DOU refer to the order in which the eigenvalues */
  /*          are stored in W. */
  /*          If the user wants to compute only selected eigenpairs, then */
  /*          the columns DOL-1 to DOU+1 of the eigenvector space Z contain the */
  /*          computed eigenvectors. All other columns of Z are set to zero. */
  
  /*  MINRGP  (input) REAL */
  
  /*  RTOL1   (input) REAL */
  /*  RTOL2   (input) REAL */
  /*           Parameters for bisection. */
  /*           An interval [LEFT,RIGHT] has converged if */
  /*           RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) */
  
  /*  W       (input/output) REAL             array, dimension (N) */
  /*          The first M elements of W contain the APPROXIMATE eigenvalues for */
  /*          which eigenvectors are to be computed.  The eigenvalues */
  /*          should be grouped by split-off block and ordered from */
  /*          smallest to largest within the block ( The output array */
  /*          W from SLARRE is expected here ). Furthermore, they are with */
  /*          respect to the shift of the corresponding root representation */
  /*          for their block. On exit, W holds the eigenvalues of the */
  /*          UNshifted matrix. */
  
  /*  WERR    (input/output) REAL             array, dimension (N) */
  /*          The first M elements contain the semiwidth of the uncertainty */
  /*          interval of the corresponding eigenvalue in W */
  
  /*  WGAP    (input/output) REAL             array, dimension (N) */
  /*          The separation from the right neighbor eigenvalue in W. */
  
  /*  IBLOCK  (input) 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  (input) 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 the second block. */
  
  /*  GERS    (input) REAL             array, dimension (2*N) */
  /*          The N Gerschgorin intervals (the i-th Gerschgorin interval */
  /*          is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should */
  /*          be computed from the original UNshifted matrix. */
  
  /*  Z       (output) COMPLEX          array, dimension (LDZ, max(1,M) ) */
  /*          If INFO = 0, the first M columns of Z contain the */
  /*          orthonormal eigenvectors of the matrix T */
  /*          corresponding to the input eigenvalues, with the i-th */
  /*          column of Z holding the eigenvector associated with W(i). */
  /*          Note: the user must ensure that at least max(1,M) columns are */
  /*          supplied in the array Z. */
  
  /*  LDZ     (input) INTEGER */
  /*          The leading dimension of the array Z.  LDZ >= 1, and if */
  /*          JOBZ = 'V', LDZ >= max(1,N). */
  
  /*  ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) ) */
  /*          The support of the eigenvectors in Z, i.e., the indices */
  /*          indicating the nonzero elements in Z. The I-th eigenvector */
  /*          is nonzero only in elements ISUPPZ( 2*I-1 ) through */
  /*          ISUPPZ( 2*I ). */
  
  /*  WORK    (workspace) REAL             array, dimension (12*N) */
  
  /*  IWORK   (workspace) INTEGER array, dimension (7*N) */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  
  /*          > 0:  A problem occured in CLARRV. */
  /*          < 0:  One of the called subroutines signaled an internal problem. */
  /*                Needs inspection of the corresponding parameter IINFO */
  /*                for further information. */
  
  /*          =-1:  Problem in SLARRB when refining a child's eigenvalues. */
  /*          =-2:  Problem in SLARRF when computing the RRR of a child. */
  /*                When a child is inside a tight cluster, it can be difficult */
  /*                to find an RRR. A partial remedy from the user's point of */
  /*                view is to make the parameter MINRGP smaller and recompile. */
  /*                However, as the orthogonality of the computed vectors is */
  /*                proportional to 1/MINRGP, the user should be aware that */
  /*                he might be trading in precision when he decreases MINRGP. */
  /*          =-3:  Problem in SLARRB when refining a single eigenvalue */
  /*                after the Rayleigh correction was rejected. */
  /*          = 5:  The Rayleigh Quotient Iteration failed to converge to */
  /*                full accuracy in MAXITR steps. */
  
  /*  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 .. */
  /*     .. */
  /*     The first N entries of WORK are reserved for the eigenvalues */
      /* Parameter adjustments */
      --d__;
      --l;
      --isplit;
      --w;
      --werr;
      --wgap;
      --iblock;
      --indexw;
      --gers;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --isuppz;
      --work;
      --iwork;
  
      /* Function Body */
      indld = *n + 1;
      indlld = (*n << 1) + 1;
      indin1 = *n * 3 + 1;
      indin2 = (*n << 2) + 1;
      indwrk = *n * 5 + 1;
      minwsize = *n * 12;
      i__1 = minwsize;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	work[i__] = 0.f;
  /* L5: */
      }
  /*     IWORK(IINDR+1:IINDR+N) hold the twist indices R for the */
  /*     factorization used to compute the FP vector */
      iindr = 0;
  /*     IWORK(IINDC1+1:IINC2+N) are used to store the clusters of the current */
  /*     layer and the one above. */
      iindc1 = *n;
      iindc2 = *n << 1;
      iindwk = *n * 3 + 1;
      miniwsize = *n * 7;
      i__1 = miniwsize;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	iwork[i__] = 0;
  /* L10: */
      }
      zusedl = 1;
      if (*dol > 1) {
  /*        Set lower bound for use of Z */
  	zusedl = *dol - 1;
      }
      zusedu = *m;
      if (*dou < *m) {
  /*        Set lower bound for use of Z */
  	zusedu = *dou + 1;
      }
  /*     The width of the part of Z that is used */
      zusedw = zusedu - zusedl + 1;
      claset_("Full", n, &zusedw, &c_b1, &c_b1, &z__[zusedl * z_dim1 + 1], ldz);
      eps = slamch_("Precision");
      rqtol = eps * 2.f;
  
  /*     Set expert flags for standard code. */
      tryrqc = TRUE_;
      if (*dol == 1 && *dou == *m) {
      } else {
  /*        Only selected eigenpairs are computed. Since the other evalues */
  /*        are not refined by RQ iteration, bisection has to compute to full */
  /*        accuracy. */
  	*rtol1 = eps * 4.f;
  	*rtol2 = eps * 4.f;
      }
  /*     The entries WBEGIN:WEND in W, WERR, WGAP correspond to the */
  /*     desired eigenvalues. The support of the nonzero eigenvector */
  /*     entries is contained in the interval IBEGIN:IEND. */
  /*     Remark that if k eigenpairs are desired, then the eigenvectors */
  /*     are stored in k contiguous columns of Z. */
  /*     DONE is the number of eigenvectors already computed */
      done = 0;
      ibegin = 1;
      wbegin = 1;
      i__1 = iblock[*m];
      for (jblk = 1; jblk <= i__1; ++jblk) {
  	iend = isplit[jblk];
  	sigma = l[iend];
  /*        Find the eigenvectors of the submatrix indexed IBEGIN */
  /*        through IEND. */
  	wend = wbegin - 1;
  L15:
  	if (wend < *m) {
  	    if (iblock[wend + 1] == jblk) {
  		++wend;
  		goto L15;
  	    }
  	}
  	if (wend < wbegin) {
  	    ibegin = iend + 1;
  	    goto L170;
  	} else if (wend < *dol || wbegin > *dou) {
  	    ibegin = iend + 1;
  	    wbegin = wend + 1;
  	    goto L170;
  	}
  /*        Find local spectral diameter of the block */
  	gl = gers[(ibegin << 1) - 1];
  	gu = gers[ibegin * 2];
  	i__2 = iend;
  	for (i__ = ibegin + 1; i__ <= i__2; ++i__) {
  /* Computing MIN */
  	    r__1 = gers[(i__ << 1) - 1];
  	    gl = dmin(r__1,gl);
  /* Computing MAX */
  	    r__1 = gers[i__ * 2];
  	    gu = dmax(r__1,gu);
  /* L20: */
  	}
  	spdiam = gu - gl;
  /*        OLDIEN is the last index of the previous block */
  	oldien = ibegin - 1;
  /*        Calculate the size of the current block */
  	in = iend - ibegin + 1;
  /*        The number of eigenvalues in the current block */
  	im = wend - wbegin + 1;
  /*        This is for a 1x1 block */
  	if (ibegin == iend) {
  	    ++done;
  	    i__2 = ibegin + wbegin * z_dim1;
  	    z__[i__2].r = 1.f, z__[i__2].i = 0.f;
  	    isuppz[(wbegin << 1) - 1] = ibegin;
  	    isuppz[wbegin * 2] = ibegin;
  	    w[wbegin] += sigma;
  	    work[wbegin] = w[wbegin];
  	    ibegin = iend + 1;
  	    ++wbegin;
  	    goto L170;
  	}
  /*        The desired (shifted) eigenvalues are stored in W(WBEGIN:WEND) */
  /*        Note that these can be approximations, in this case, the corresp. */
  /*        entries of WERR give the size of the uncertainty interval. */
  /*        The eigenvalue approximations will be refined when necessary as */
  /*        high relative accuracy is required for the computation of the */
  /*        corresponding eigenvectors. */
  	scopy_(&im, &w[wbegin], &c__1, &work[wbegin], &c__1);
  /*        We store in W the eigenvalue approximations w.r.t. the original */
  /*        matrix T. */
  	i__2 = im;
  	for (i__ = 1; i__ <= i__2; ++i__) {
  	    w[wbegin + i__ - 1] += sigma;
  /* L30: */
  	}
  /*        NDEPTH is the current depth of the representation tree */
  	ndepth = 0;
  /*        PARITY is either 1 or 0 */
  	parity = 1;
  /*        NCLUS is the number of clusters for the next level of the */
  /*        representation tree, we start with NCLUS = 1 for the root */
  	nclus = 1;
  	iwork[iindc1 + 1] = 1;
  	iwork[iindc1 + 2] = im;
  /*        IDONE is the number of eigenvectors already computed in the current */
  /*        block */
  	idone = 0;
  /*        loop while( IDONE.LT.IM ) */
  /*        generate the representation tree for the current block and */
  /*        compute the eigenvectors */
  L40:
  	if (idone < im) {
  /*           This is a crude protection against infinitely deep trees */
  	    if (ndepth > *m) {
  		*info = -2;
  		return 0;
  	    }
  /*           breadth first processing of the current level of the representation */
  /*           tree: OLDNCL = number of clusters on current level */
  	    oldncl = nclus;
  /*           reset NCLUS to count the number of child clusters */
  	    nclus = 0;
  
  	    parity = 1 - parity;
  	    if (parity == 0) {
  		oldcls = iindc1;
  		newcls = iindc2;
  	    } else {
  		oldcls = iindc2;
  		newcls = iindc1;
  	    }
  /*           Process the clusters on the current level */
  	    i__2 = oldncl;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		j = oldcls + (i__ << 1);
  /*              OLDFST, OLDLST = first, last index of current cluster. */
  /*                               cluster indices start with 1 and are relative */
  /*                               to WBEGIN when accessing W, WGAP, WERR, Z */
  		oldfst = iwork[j - 1];
  		oldlst = iwork[j];
  		if (ndepth > 0) {
  /*                 Retrieve relatively robust representation (RRR) of cluster */
  /*                 that has been computed at the previous level */
  /*                 The RRR is stored in Z and overwritten once the eigenvectors */
  /*                 have been computed or when the cluster is refined */
  		    if (*dol == 1 && *dou == *m) {
  /*                    Get representation from location of the leftmost evalue */
  /*                    of the cluster */
  			j = wbegin + oldfst - 1;
  		    } else {
  			if (wbegin + oldfst - 1 < *dol) {
  /*                       Get representation from the left end of Z array */
  			    j = *dol - 1;
  			} else if (wbegin + oldfst - 1 > *dou) {
  /*                       Get representation from the right end of Z array */
  			    j = *dou;
  			} else {
  			    j = wbegin + oldfst - 1;
  			}
  		    }
  		    i__3 = in - 1;
  		    for (k = 1; k <= i__3; ++k) {
  			i__4 = ibegin + k - 1 + j * z_dim1;
  			d__[ibegin + k - 1] = z__[i__4].r;
  			i__4 = ibegin + k - 1 + (j + 1) * z_dim1;
  			l[ibegin + k - 1] = z__[i__4].r;
  /* L45: */
  		    }
  		    i__3 = iend + j * z_dim1;
  		    d__[iend] = z__[i__3].r;
  		    i__3 = iend + (j + 1) * z_dim1;
  		    sigma = z__[i__3].r;
  /*                 Set the corresponding entries in Z to zero */
  		    claset_("Full", &in, &c__2, &c_b1, &c_b1, &z__[ibegin + j 
  			    * z_dim1], ldz);
  		}
  /*              Compute DL and DLL of current RRR */
  		i__3 = iend - 1;
  		for (j = ibegin; j <= i__3; ++j) {
  		    tmp = d__[j] * l[j];
  		    work[indld - 1 + j] = tmp;
  		    work[indlld - 1 + j] = tmp * l[j];
  /* L50: */
  		}
  		if (ndepth > 0) {
  /*                 P and Q are index of the first and last eigenvalue to compute */
  /*                 within the current block */
  		    p = indexw[wbegin - 1 + oldfst];
  		    q = indexw[wbegin - 1 + oldlst];
  /*                 Offset for the arrays WORK, WGAP and WERR, i.e., th P-OFFSET */
  /*                 thru' Q-OFFSET elements of these arrays are to be used. */
  /*                  OFFSET = P-OLDFST */
  		    offset = indexw[wbegin] - 1;
  /*                 perform limited bisection (if necessary) to get approximate */
  /*                 eigenvalues to the precision needed. */
  		    slarrb_(&in, &d__[ibegin], &work[indlld + ibegin - 1], &p, 
  			     &q, rtol1, rtol2, &offset, &work[wbegin], &wgap[
  			    wbegin], &werr[wbegin], &work[indwrk], &iwork[
  			    iindwk], pivmin, &spdiam, &in, &iinfo);
  		    if (iinfo != 0) {
  			*info = -1;
  			return 0;
  		    }
  /*                 We also recompute the extremal gaps. W holds all eigenvalues */
  /*                 of the unshifted matrix and must be used for computation */
  /*                 of WGAP, the entries of WORK might stem from RRRs with */
  /*                 different shifts. The gaps from WBEGIN-1+OLDFST to */
  /*                 WBEGIN-1+OLDLST are correctly computed in SLARRB. */
  /*                 However, we only allow the gaps to become greater since */
  /*                 this is what should happen when we decrease WERR */
  		    if (oldfst > 1) {
  /* Computing MAX */
  			r__1 = wgap[wbegin + oldfst - 2], r__2 = w[wbegin + 
  				oldfst - 1] - werr[wbegin + oldfst - 1] - w[
  				wbegin + oldfst - 2] - werr[wbegin + oldfst - 
  				2];
  			wgap[wbegin + oldfst - 2] = dmax(r__1,r__2);
  		    }
  		    if (wbegin + oldlst - 1 < wend) {
  /* Computing MAX */
  			r__1 = wgap[wbegin + oldlst - 1], r__2 = w[wbegin + 
  				oldlst] - werr[wbegin + oldlst] - w[wbegin + 
  				oldlst - 1] - werr[wbegin + oldlst - 1];
  			wgap[wbegin + oldlst - 1] = dmax(r__1,r__2);
  		    }
  /*                 Each time the eigenvalues in WORK get refined, we store */
  /*                 the newly found approximation with all shifts applied in W */
  		    i__3 = oldlst;
  		    for (j = oldfst; j <= i__3; ++j) {
  			w[wbegin + j - 1] = work[wbegin + j - 1] + sigma;
  /* L53: */
  		    }
  		}
  /*              Process the current node. */
  		newfst = oldfst;
  		i__3 = oldlst;
  		for (j = oldfst; j <= i__3; ++j) {
  		    if (j == oldlst) {
  /*                    we are at the right end of the cluster, this is also the */
  /*                    boundary of the child cluster */
  			newlst = j;
  		    } else if (wgap[wbegin + j - 1] >= *minrgp * (r__1 = work[
  			    wbegin + j - 1], dabs(r__1))) {
  /*                    the right relative gap is big enough, the child cluster */
  /*                    (NEWFST,..,NEWLST) is well separated from the following */
  			newlst = j;
  		    } else {
  /*                    inside a child cluster, the relative gap is not */
  /*                    big enough. */
  			goto L140;
  		    }
  /*                 Compute size of child cluster found */
  		    newsiz = newlst - newfst + 1;
  /*                 NEWFTT is the place in Z where the new RRR or the computed */
  /*                 eigenvector is to be stored */
  		    if (*dol == 1 && *dou == *m) {
  /*                    Store representation at location of the leftmost evalue */
  /*                    of the cluster */
  			newftt = wbegin + newfst - 1;
  		    } else {
  			if (wbegin + newfst - 1 < *dol) {
  /*                       Store representation at the left end of Z array */
  			    newftt = *dol - 1;
  			} else if (wbegin + newfst - 1 > *dou) {
  /*                       Store representation at the right end of Z array */
  			    newftt = *dou;
  			} else {
  			    newftt = wbegin + newfst - 1;
  			}
  		    }
  		    if (newsiz > 1) {
  
  /*                    Current child is not a singleton but a cluster. */
  /*                    Compute and store new representation of child. */
  
  
  /*                    Compute left and right cluster gap. */
  
  /*                    LGAP and RGAP are not computed from WORK because */
  /*                    the eigenvalue approximations may stem from RRRs */
  /*                    different shifts. However, W hold all eigenvalues */
  /*                    of the unshifted matrix. Still, the entries in WGAP */
  /*                    have to be computed from WORK since the entries */
  /*                    in W might be of the same order so that gaps are not */
  /*                    exhibited correctly for very close eigenvalues. */
  			if (newfst == 1) {
  /* Computing MAX */
  			    r__1 = 0.f, r__2 = w[wbegin] - werr[wbegin] - *vl;
  			    lgap = dmax(r__1,r__2);
  			} else {
  			    lgap = wgap[wbegin + newfst - 2];
  			}
  			rgap = wgap[wbegin + newlst - 1];
  
  /*                    Compute left- and rightmost eigenvalue of child */
  /*                    to high precision in order to shift as close */
  /*                    as possible and obtain as large relative gaps */
  /*                    as possible */
  
  			for (k = 1; k <= 2; ++k) {
  			    if (k == 1) {
  				p = indexw[wbegin - 1 + newfst];
  			    } else {
  				p = indexw[wbegin - 1 + newlst];
  			    }
  			    offset = indexw[wbegin] - 1;
  			    slarrb_(&in, &d__[ibegin], &work[indlld + ibegin 
  				    - 1], &p, &p, &rqtol, &rqtol, &offset, &
  				    work[wbegin], &wgap[wbegin], &werr[wbegin]
  , &work[indwrk], &iwork[iindwk], pivmin, &
  				    spdiam, &in, &iinfo);
  /* L55: */
  			}
  
  			if (wbegin + newlst - 1 < *dol || wbegin + newfst - 1 
  				> *dou) {
  /*                       if the cluster contains no desired eigenvalues */
  /*                       skip the computation of that branch of the rep. tree */
  
  /*                       We could skip before the refinement of the extremal */
  /*                       eigenvalues of the child, but then the representation */
  /*                       tree could be different from the one when nothing is */
  /*                       skipped. For this reason we skip at this place. */
  			    idone = idone + newlst - newfst + 1;
  			    goto L139;
  			}
  
  /*                    Compute RRR of child cluster. */
  /*                    Note that the new RRR is stored in Z */
  
  /*                    SLARRF needs LWORK = 2*N */
  			slarrf_(&in, &d__[ibegin], &l[ibegin], &work[indld + 
  				ibegin - 1], &newfst, &newlst, &work[wbegin], 
  				&wgap[wbegin], &werr[wbegin], &spdiam, &lgap, 
  				&rgap, pivmin, &tau, &work[indin1], &work[
  				indin2], &work[indwrk], &iinfo);
  /*                    In the complex case, SLARRF cannot write */
  /*                    the new RRR directly into Z and needs an intermediate */
  /*                    workspace */
  			i__4 = in - 1;
  			for (k = 1; k <= i__4; ++k) {
  			    i__5 = ibegin + k - 1 + newftt * z_dim1;
  			    i__6 = indin1 + k - 1;
  			    q__1.r = work[i__6], q__1.i = 0.f;
  			    z__[i__5].r = q__1.r, z__[i__5].i = q__1.i;
  			    i__5 = ibegin + k - 1 + (newftt + 1) * z_dim1;
  			    i__6 = indin2 + k - 1;
  			    q__1.r = work[i__6], q__1.i = 0.f;
  			    z__[i__5].r = q__1.r, z__[i__5].i = q__1.i;
  /* L56: */
  			}
  			i__4 = iend + newftt * z_dim1;
  			i__5 = indin1 + in - 1;
  			q__1.r = work[i__5], q__1.i = 0.f;
  			z__[i__4].r = q__1.r, z__[i__4].i = q__1.i;
  			if (iinfo == 0) {
  /*                       a new RRR for the cluster was found by SLARRF */
  /*                       update shift and store it */
  			    ssigma = sigma + tau;
  			    i__4 = iend + (newftt + 1) * z_dim1;
  			    q__1.r = ssigma, q__1.i = 0.f;
  			    z__[i__4].r = q__1.r, z__[i__4].i = q__1.i;
  /*                       WORK() are the midpoints and WERR() the semi-width */
  /*                       Note that the entries in W are unchanged. */
  			    i__4 = newlst;
  			    for (k = newfst; k <= i__4; ++k) {
  				fudge = eps * 3.f * (r__1 = work[wbegin + k - 
  					1], dabs(r__1));
  				work[wbegin + k - 1] -= tau;
  				fudge += eps * 4.f * (r__1 = work[wbegin + k 
  					- 1], dabs(r__1));
  /*                          Fudge errors */
  				werr[wbegin + k - 1] += fudge;
  /*                          Gaps are not fudged. Provided that WERR is small */
  /*                          when eigenvalues are close, a zero gap indicates */
  /*                          that a new representation is needed for resolving */
  /*                          the cluster. A fudge could lead to a wrong decision */
  /*                          of judging eigenvalues 'separated' which in */
  /*                          reality are not. This could have a negative impact */
  /*                          on the orthogonality of the computed eigenvectors. */
  /* L116: */
  			    }
  			    ++nclus;
  			    k = newcls + (nclus << 1);
  			    iwork[k - 1] = newfst;
  			    iwork[k] = newlst;
  			} else {
  			    *info = -2;
  			    return 0;
  			}
  		    } else {
  
  /*                    Compute eigenvector of singleton */
  
  			iter = 0;
  
  			tol = log((real) in) * 4.f * eps;
  
  			k = newfst;
  			windex = wbegin + k - 1;
  /* Computing MAX */
  			i__4 = windex - 1;
  			windmn = max(i__4,1);
  /* Computing MIN */
  			i__4 = windex + 1;
  			windpl = min(i__4,*m);
  			lambda = work[windex];
  			++done;
  /*                    Check if eigenvector computation is to be skipped */
  			if (windex < *dol || windex > *dou) {
  			    eskip = TRUE_;
  			    goto L125;
  			} else {
  			    eskip = FALSE_;
  			}
  			left = work[windex] - werr[windex];
  			right = work[windex] + werr[windex];
  			indeig = indexw[windex];
  /*                    Note that since we compute the eigenpairs for a child, */
  /*                    all eigenvalue approximations are w.r.t the same shift. */
  /*                    In this case, the entries in WORK should be used for */
  /*                    computing the gaps since they exhibit even very small */
  /*                    differences in the eigenvalues, as opposed to the */
  /*                    entries in W which might "look" the same. */
  			if (k == 1) {
  /*                       In the case RANGE='I' and with not much initial */
  /*                       accuracy in LAMBDA and VL, the formula */
  /*                       LGAP = MAX( ZERO, (SIGMA - VL) + LAMBDA ) */
  /*                       can lead to an overestimation of the left gap and */
  /*                       thus to inadequately early RQI 'convergence'. */
  /*                       Prevent this by forcing a small left gap. */
  /* Computing MAX */
  			    r__1 = dabs(left), r__2 = dabs(right);
  			    lgap = eps * dmax(r__1,r__2);
  			} else {
  			    lgap = wgap[windmn];
  			}
  			if (k == im) {
  /*                       In the case RANGE='I' and with not much initial */
  /*                       accuracy in LAMBDA and VU, the formula */
  /*                       can lead to an overestimation of the right gap and */
  /*                       thus to inadequately early RQI 'convergence'. */
  /*                       Prevent this by forcing a small right gap. */
  /* Computing MAX */
  			    r__1 = dabs(left), r__2 = dabs(right);
  			    rgap = eps * dmax(r__1,r__2);
  			} else {
  			    rgap = wgap[windex];
  			}
  			gap = dmin(lgap,rgap);
  			if (k == 1 || k == im) {
  /*                       The eigenvector support can become wrong */
  /*                       because significant entries could be cut off due to a */
  /*                       large GAPTOL parameter in LAR1V. Prevent this. */
  			    gaptol = 0.f;
  			} else {
  			    gaptol = gap * eps;
  			}
  			isupmn = in;
  			isupmx = 1;
  /*                    Update WGAP so that it holds the minimum gap */
  /*                    to the left or the right. This is crucial in the */
  /*                    case where bisection is used to ensure that the */
  /*                    eigenvalue is refined up to the required precision. */
  /*                    The correct value is restored afterwards. */
  			savgap = wgap[windex];
  			wgap[windex] = gap;
  /*                    We want to use the Rayleigh Quotient Correction */
  /*                    as often as possible since it converges quadratically */
  /*                    when we are close enough to the desired eigenvalue. */
  /*                    However, the Rayleigh Quotient can have the wrong sign */
  /*                    and lead us away from the desired eigenvalue. In this */
  /*                    case, the best we can do is to use bisection. */
  			usedbs = FALSE_;
  			usedrq = FALSE_;
  /*                    Bisection is initially turned off unless it is forced */
  			needbs = ! tryrqc;
  L120:
  /*                    Check if bisection should be used to refine eigenvalue */
  			if (needbs) {
  /*                       Take the bisection as new iterate */
  			    usedbs = TRUE_;
  			    itmp1 = iwork[iindr + windex];
  			    offset = indexw[wbegin] - 1;
  			    r__1 = eps * 2.f;
  			    slarrb_(&in, &d__[ibegin], &work[indlld + ibegin 
  				    - 1], &indeig, &indeig, &c_b28, &r__1, &
  				    offset, &work[wbegin], &wgap[wbegin], &
  				    werr[wbegin], &work[indwrk], &iwork[
  				    iindwk], pivmin, &spdiam, &itmp1, &iinfo);
  			    if (iinfo != 0) {
  				*info = -3;
  				return 0;
  			    }
  			    lambda = work[windex];
  /*                       Reset twist index from inaccurate LAMBDA to */
  /*                       force computation of true MINGMA */
  			    iwork[iindr + windex] = 0;
  			}
  /*                    Given LAMBDA, compute the eigenvector. */
  			L__1 = ! usedbs;
  			clar1v_(&in, &c__1, &in, &lambda, &d__[ibegin], &l[
  				ibegin], &work[indld + ibegin - 1], &work[
  				indlld + ibegin - 1], pivmin, &gaptol, &z__[
  				ibegin + windex * z_dim1], &L__1, &negcnt, &
  				ztz, &mingma, &iwork[iindr + windex], &isuppz[
  				(windex << 1) - 1], &nrminv, &resid, &rqcorr, 
  				&work[indwrk]);
  			if (iter == 0) {
  			    bstres = resid;
  			    bstw = lambda;
  			} else if (resid < bstres) {
  			    bstres = resid;
  			    bstw = lambda;
  			}
  /* Computing MIN */
  			i__4 = isupmn, i__5 = isuppz[(windex << 1) - 1];
  			isupmn = min(i__4,i__5);
  /* Computing MAX */
  			i__4 = isupmx, i__5 = isuppz[windex * 2];
  			isupmx = max(i__4,i__5);
  			++iter;
  /*                    sin alpha <= |resid|/gap */
  /*                    Note that both the residual and the gap are */
  /*                    proportional to the matrix, so ||T|| doesn't play */
  /*                    a role in the quotient */
  
  /*                    Convergence test for Rayleigh-Quotient iteration */
  /*                    (omitted when Bisection has been used) */
  
  			if (resid > tol * gap && dabs(rqcorr) > rqtol * dabs(
  				lambda) && ! usedbs) {
  /*                       We need to check that the RQCORR update doesn't */
  /*                       move the eigenvalue away from the desired one and */
  /*                       towards a neighbor. -> protection with bisection */
  			    if (indeig <= negcnt) {
  /*                          The wanted eigenvalue lies to the left */
  				sgndef = -1.f;
  			    } else {
  /*                          The wanted eigenvalue lies to the right */
  				sgndef = 1.f;
  			    }
  /*                       We only use the RQCORR if it improves the */
  /*                       the iterate reasonably. */
  			    if (rqcorr * sgndef >= 0.f && lambda + rqcorr <= 
  				    right && lambda + rqcorr >= left) {
  				usedrq = TRUE_;
  /*                          Store new midpoint of bisection interval in WORK */
  				if (sgndef == 1.f) {
  /*                             The current LAMBDA is on the left of the true */
  /*                             eigenvalue */
  				    left = lambda;
  /*                             We prefer to assume that the error estimate */
  /*                             is correct. We could make the interval not */
  /*                             as a bracket but to be modified if the RQCORR */
  /*                             chooses to. In this case, the RIGHT side should */
  /*                             be modified as follows: */
  /*                              RIGHT = MAX(RIGHT, LAMBDA + RQCORR) */
  				} else {
  /*                             The current LAMBDA is on the right of the true */
  /*                             eigenvalue */
  				    right = lambda;
  /*                             See comment about assuming the error estimate is */
  /*                             correct above. */
  /*                              LEFT = MIN(LEFT, LAMBDA + RQCORR) */
  				}
  				work[windex] = (right + left) * .5f;
  /*                          Take RQCORR since it has the correct sign and */
  /*                          improves the iterate reasonably */
  				lambda += rqcorr;
  /*                          Update width of error interval */
  				werr[windex] = (right - left) * .5f;
  			    } else {
  				needbs = TRUE_;
  			    }
  			    if (right - left < rqtol * dabs(lambda)) {
  /*                             The eigenvalue is computed to bisection accuracy */
  /*                             compute eigenvector and stop */
  				usedbs = TRUE_;
  				goto L120;
  			    } else if (iter < 10) {
  				goto L120;
  			    } else if (iter == 10) {
  				needbs = TRUE_;
  				goto L120;
  			    } else {
  				*info = 5;
  				return 0;
  			    }
  			} else {
  			    stp2ii = FALSE_;
  			    if (usedrq && usedbs && bstres <= resid) {
  				lambda = bstw;
  				stp2ii = TRUE_;
  			    }
  			    if (stp2ii) {
  /*                          improve error angle by second step */
  				L__1 = ! usedbs;
  				clar1v_(&in, &c__1, &in, &lambda, &d__[ibegin]
  , &l[ibegin], &work[indld + ibegin - 
  					1], &work[indlld + ibegin - 1], 
  					pivmin, &gaptol, &z__[ibegin + windex 
  					* z_dim1], &L__1, &negcnt, &ztz, &
  					mingma, &iwork[iindr + windex], &
  					isuppz[(windex << 1) - 1], &nrminv, &
  					resid, &rqcorr, &work[indwrk]);
  			    }
  			    work[windex] = lambda;
  			}
  
  /*                    Compute FP-vector support w.r.t. whole matrix */
  
  			isuppz[(windex << 1) - 1] += oldien;
  			isuppz[windex * 2] += oldien;
  			zfrom = isuppz[(windex << 1) - 1];
  			zto = isuppz[windex * 2];
  			isupmn += oldien;
  			isupmx += oldien;
  /*                    Ensure vector is ok if support in the RQI has changed */
  			if (isupmn < zfrom) {
  			    i__4 = zfrom - 1;
  			    for (ii = isupmn; ii <= i__4; ++ii) {
  				i__5 = ii + windex * z_dim1;
  				z__[i__5].r = 0.f, z__[i__5].i = 0.f;
  /* L122: */
  			    }
  			}
  			if (isupmx > zto) {
  			    i__4 = isupmx;
  			    for (ii = zto + 1; ii <= i__4; ++ii) {
  				i__5 = ii + windex * z_dim1;
  				z__[i__5].r = 0.f, z__[i__5].i = 0.f;
  /* L123: */
  			    }
  			}
  			i__4 = zto - zfrom + 1;
  			csscal_(&i__4, &nrminv, &z__[zfrom + windex * z_dim1], 
  				 &c__1);
  L125:
  /*                    Update W */
  			w[windex] = lambda + sigma;
  /*                    Recompute the gaps on the left and right */
  /*                    But only allow them to become larger and not */
  /*                    smaller (which can only happen through "bad" */
  /*                    cancellation and doesn't reflect the theory */
  /*                    where the initial gaps are underestimated due */
  /*                    to WERR being too crude.) */
  			if (! eskip) {
  			    if (k > 1) {
  /* Computing MAX */
  				r__1 = wgap[windmn], r__2 = w[windex] - werr[
  					windex] - w[windmn] - werr[windmn];
  				wgap[windmn] = dmax(r__1,r__2);
  			    }
  			    if (windex < wend) {
  /* Computing MAX */
  				r__1 = savgap, r__2 = w[windpl] - werr[windpl]
  					 - w[windex] - werr[windex];
  				wgap[windex] = dmax(r__1,r__2);
  			    }
  			}
  			++idone;
  		    }
  /*                 here ends the code for the current child */
  
  L139:
  /*                 Proceed to any remaining child nodes */
  		    newfst = j + 1;
  L140:
  		    ;
  		}
  /* L150: */
  	    }
  	    ++ndepth;
  	    goto L40;
  	}
  	ibegin = iend + 1;
  	wbegin = wend + 1;
  L170:
  	;
      }
  
      return 0;
  
  /*     End of CLARRV */
  
  } /* clarrv_ */
  