dgsvj1.c

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/* dgsvj1.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__0 = 0;
static doublereal c_b35 = 1.;

/* Subroutine */ int dgsvj1_(char *jobv, integer *m, integer *n, integer *n1, 
        doublereal *a, integer *lda, doublereal *d__, doublereal *sva, 
        integer *mv, doublereal *v, integer *ldv, doublereal *eps, doublereal 
        *sfmin, doublereal *tol, integer *nsweep, doublereal *work, integer *
        lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5, 
            i__6;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal), d_sign(doublereal *, doublereal *);

    /* Local variables */
    doublereal bigtheta;
    integer pskipped, i__, p, q;
    doublereal t, rootsfmin, cs, sn;
    integer jbc;
    doublereal big;
    integer kbl, igl, ibr, jgl, mvl, nblc;
    doublereal aapp, aapq, aaqq;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    integer nblr, ierr;
    doublereal aapp0;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal temp1, large, apoaq, aqoap;
    extern logical lsame_(char *, char *);
    doublereal theta, small;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    doublereal fastr[5];
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    logical applv, rsvec;
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *), drotm_(integer *, doublereal 
            *, integer *, doublereal *, integer *, doublereal *);
    logical rotok;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    integer ijblsk, swband, blskip;
    doublereal mxaapq;
    extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, 
            doublereal *, doublereal *);
    doublereal thsign, mxsinj;
    integer emptsw, notrot, iswrot;
    doublereal rootbig, rooteps;
    integer rowskip;
    doublereal roottol;


/*  -- LAPACK routine (version 3.2)                                    -- */

/*  -- Contributed by Zlatko Drmac of the University of Zagreb and     -- */
/*  -- Kresimir Veselic of the Fernuniversitaet Hagen                  -- */
/*  -- November 2008                                                   -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/* This routine is also part of SIGMA (version 1.23, October 23. 2008.) */
/* SIGMA is a library of algorithms for highly accurate algorithms for */
/* computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the */
/* eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. */

/*     -#- Scalar Arguments -#- */


/*     -#- Array Arguments -#- */

/*     .. */

/*  Purpose */
/*  ~~~~~~~ */
/*  DGSVJ1 is called from SGESVJ as a pre-processor and that is its main */
/*  purpose. It applies Jacobi rotations in the same way as SGESVJ does, but */
/*  it targets only particular pivots and it does not check convergence */
/*  (stopping criterion). Few tunning parameters (marked by [TP]) are */
/*  available for the implementer. */

/*  Further details */
/*  ~~~~~~~~~~~~~~~ */
/*  DGSVJ1 applies few sweeps of Jacobi rotations in the column space of */
/*  the input M-by-N matrix A. The pivot pairs are taken from the (1,2) */
/*  off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The */
/*  block-entries (tiles) of the (1,2) off-diagonal block are marked by the */
/*  [x]'s in the following scheme: */

/*     | *   *   * [x] [x] [x]| */
/*     | *   *   * [x] [x] [x]|    Row-cycling in the nblr-by-nblc [x] blocks. */
/*     | *   *   * [x] [x] [x]|    Row-cyclic pivoting inside each [x] block. */
/*     |[x] [x] [x] *   *   * | */
/*     |[x] [x] [x] *   *   * | */
/*     |[x] [x] [x] *   *   * | */

/*  In terms of the columns of A, the first N1 columns are rotated 'against' */
/*  the remaining N-N1 columns, trying to increase the angle between the */
/*  corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is */
/*  tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter. */
/*  The number of sweeps is given in NSWEEP and the orthogonality threshold */
/*  is given in TOL. */

/*  Contributors */
/*  ~~~~~~~~~~~~ */
/*  Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) */

/*  Arguments */
/*  ~~~~~~~~~ */

/*  JOBV    (input) CHARACTER*1 */
/*          Specifies whether the output from this procedure is used */
/*          to compute the matrix V: */
/*          = 'V': the product of the Jacobi rotations is accumulated */
/*                 by postmulyiplying the N-by-N array V. */
/*                (See the description of V.) */
/*          = 'A': the product of the Jacobi rotations is accumulated */
/*                 by postmulyiplying the MV-by-N array V. */
/*                (See the descriptions of MV and V.) */
/*          = 'N': the Jacobi rotations are not accumulated. */

/*  M       (input) INTEGER */
/*          The number of rows of the input matrix A.  M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the input matrix A. */
/*          M >= N >= 0. */

/*  N1      (input) INTEGER */
/*          N1 specifies the 2 x 2 block partition, the first N1 columns are */
/*          rotated 'against' the remaining N-N1 columns of A. */

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, M-by-N matrix A, such that A*diag(D) represents */
/*          the input matrix. */
/*          On exit, */
/*          A_onexit * D_onexit represents the input matrix A*diag(D) */
/*          post-multiplied by a sequence of Jacobi rotations, where the */
/*          rotation threshold and the total number of sweeps are given in */
/*          TOL and NSWEEP, respectively. */
/*          (See the descriptions of N1, D, TOL and NSWEEP.) */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,M). */

/*  D       (input/workspace/output) REAL array, dimension (N) */
/*          The array D accumulates the scaling factors from the fast scaled */
/*          Jacobi rotations. */
/*          On entry, A*diag(D) represents the input matrix. */
/*          On exit, A_onexit*diag(D_onexit) represents the input matrix */
/*          post-multiplied by a sequence of Jacobi rotations, where the */
/*          rotation threshold and the total number of sweeps are given in */
/*          TOL and NSWEEP, respectively. */
/*          (See the descriptions of N1, A, TOL and NSWEEP.) */

/*  SVA     (input/workspace/output) REAL array, dimension (N) */
/*          On entry, SVA contains the Euclidean norms of the columns of */
/*          the matrix A*diag(D). */
/*          On exit, SVA contains the Euclidean norms of the columns of */
/*          the matrix onexit*diag(D_onexit). */

/*  MV      (input) INTEGER */
/*          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a */
/*                           sequence of Jacobi rotations. */
/*          If JOBV = 'N',   then MV is not referenced. */

/*  V       (input/output) REAL array, dimension (LDV,N) */
/*          If JOBV .EQ. 'V' then N rows of V are post-multipled by a */
/*                           sequence of Jacobi rotations. */
/*          If JOBV .EQ. 'A' then MV rows of V are post-multipled by a */
/*                           sequence of Jacobi rotations. */
/*          If JOBV = 'N',   then V is not referenced. */

/*  LDV     (input) INTEGER */
/*          The leading dimension of the array V,  LDV >= 1. */
/*          If JOBV = 'V', LDV .GE. N. */
/*          If JOBV = 'A', LDV .GE. MV. */

/*  EPS     (input) INTEGER */
/*          EPS = SLAMCH('Epsilon') */

/*  SFMIN   (input) INTEGER */
/*          SFMIN = SLAMCH('Safe Minimum') */

/*  TOL     (input) REAL */
/*          TOL is the threshold for Jacobi rotations. For a pair */
/*          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is */
/*          applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. */

/*  NSWEEP  (input) INTEGER */
/*          NSWEEP is the number of sweeps of Jacobi rotations to be */
/*          performed. */

/*  WORK    (workspace) REAL array, dimension LWORK. */

/*  LWORK   (input) INTEGER */
/*          LWORK is the dimension of WORK. LWORK .GE. M. */

/*  INFO    (output) INTEGER */
/*          = 0 : successful exit. */
/*          < 0 : if INFO = -i, then the i-th argument had an illegal value */

/*     -#- Local Parameters -#- */

/*     -#- Local Scalars -#- */


/*     Local Arrays */


/*     Intrinsic Functions */


/*     External Functions */


/*     External Subroutines */



    /* Parameter adjustments */
    --sva;
    --d__;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    --work;

    /* Function Body */
    applv = lsame_(jobv, "A");
    rsvec = lsame_(jobv, "V");
    if (! (rsvec || applv || lsame_(jobv, "N"))) {
        *info = -1;
    } else if (*m < 0) {
        *info = -2;
    } else if (*n < 0 || *n > *m) {
        *info = -3;
    } else if (*n1 < 0) {
        *info = -4;
    } else if (*lda < *m) {
        *info = -6;
    } else if (*mv < 0) {
        *info = -9;
    } else if (*ldv < *m) {
        *info = -11;
    } else if (*tol <= *eps) {
        *info = -14;
    } else if (*nsweep < 0) {
        *info = -15;
    } else if (*lwork < *m) {
        *info = -17;
    } else {
        *info = 0;
    }

/*     #:( */
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGSVJ1", &i__1);
        return 0;
    }

    if (rsvec) {
        mvl = *n;
    } else if (applv) {
        mvl = *mv;
    }
    rsvec = rsvec || applv;
    rooteps = sqrt(*eps);
    rootsfmin = sqrt(*sfmin);
    small = *sfmin / *eps;
    big = 1. / *sfmin;
    rootbig = 1. / rootsfmin;
    large = big / sqrt((doublereal) (*m * *n));
    bigtheta = 1. / rooteps;
    roottol = sqrt(*tol);

/*     -#- Initialize the right singular vector matrix -#- */

/*     RSVEC = LSAME( JOBV, 'Y' ) */

    emptsw = *n1 * (*n - *n1);
    notrot = 0;
    fastr[0] = 0.;

/*     -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- */

    kbl = min(8,*n);
    nblr = *n1 / kbl;
    if (nblr * kbl != *n1) {
        ++nblr;
    }
/*     .. the tiling is nblr-by-nblc [tiles] */
    nblc = (*n - *n1) / kbl;
    if (nblc * kbl != *n - *n1) {
        ++nblc;
    }
/* Computing 2nd power */
    i__1 = kbl;
    blskip = i__1 * i__1 + 1;
/* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
    rowskip = min(5,kbl);
/* [TP] ROWSKIP is a tuning parameter. */
    swband = 0;
/* [TP] SWBAND is a tuning parameter. It is meaningful and effective */
/*     if SGESVJ is used as a computational routine in the preconditioned */
/*     Jacobi SVD algorithm SGESVJ. */


/*     | *   *   * [x] [x] [x]| */
/*     | *   *   * [x] [x] [x]|    Row-cycling in the nblr-by-nblc [x] blocks. */
/*     | *   *   * [x] [x] [x]|    Row-cyclic pivoting inside each [x] block. */
/*     |[x] [x] [x] *   *   * | */
/*     |[x] [x] [x] *   *   * | */
/*     |[x] [x] [x] *   *   * | */


    i__1 = *nsweep;
    for (i__ = 1; i__ <= i__1; ++i__) {
/*     .. go go go ... */

        mxaapq = 0.;
        mxsinj = 0.;
        iswrot = 0;

        notrot = 0;
        pskipped = 0;

        i__2 = nblr;
        for (ibr = 1; ibr <= i__2; ++ibr) {
            igl = (ibr - 1) * kbl + 1;


/* ........................................................ */
/* ... go to the off diagonal blocks */
            igl = (ibr - 1) * kbl + 1;
            i__3 = nblc;
            for (jbc = 1; jbc <= i__3; ++jbc) {
                jgl = *n1 + (jbc - 1) * kbl + 1;
/*        doing the block at ( ibr, jbc ) */
                ijblsk = 0;
/* Computing MIN */
                i__5 = igl + kbl - 1;
                i__4 = min(i__5,*n1);
                for (p = igl; p <= i__4; ++p) {
                    aapp = sva[p];
                    if (aapp > 0.) {
                        pskipped = 0;
/* Computing MIN */
                        i__6 = jgl + kbl - 1;
                        i__5 = min(i__6,*n);
                        for (q = jgl; q <= i__5; ++q) {

                            aaqq = sva[q];
                            if (aaqq > 0.) {
                                aapp0 = aapp;

/*     -#- M x 2 Jacobi SVD -#- */

/*        -#- Safe Gram matrix computation -#- */

                                if (aaqq >= 1.) {
                                    if (aapp >= aaqq) {
                                        rotok = small * aapp <= aaqq;
                                    } else {
                                        rotok = small * aaqq <= aapp;
                                    }
                                    if (aapp < big / aaqq) {
                                        aapq = ddot_(m, &a[p * a_dim1 + 1], &
                                                c__1, &a[q * a_dim1 + 1], &
                                                c__1) * d__[p] * d__[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
                                                work[1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aapp, &
                                                d__[p], m, &c__1, &work[1], 
                                                lda, &ierr);
                                        aapq = ddot_(m, &work[1], &c__1, &a[q 
                                                * a_dim1 + 1], &c__1) * d__[q]
                                                 / aaqq;
                                    }
                                } else {
                                    if (aapp >= aaqq) {
                                        rotok = aapp <= aaqq / small;
                                    } else {
                                        rotok = aaqq <= aapp / small;
                                    }
                                    if (aapp > small / aaqq) {
                                        aapq = ddot_(m, &a[p * a_dim1 + 1], &
                                                c__1, &a[q * a_dim1 + 1], &
                                                c__1) * d__[p] * d__[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
                                                work[1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aaqq, &
                                                d__[q], m, &c__1, &work[1], 
                                                lda, &ierr);
                                        aapq = ddot_(m, &work[1], &c__1, &a[p 
                                                * a_dim1 + 1], &c__1) * d__[p]
                                                 / aapp;
                                    }
                                }
/* Computing MAX */
                                d__1 = mxaapq, d__2 = abs(aapq);
                                mxaapq = max(d__1,d__2);
/*        TO rotate or NOT to rotate, THAT is the question ... */

                                if (abs(aapq) > *tol) {
                                    notrot = 0;
/*           ROTATED  = ROTATED + 1 */
                                    pskipped = 0;
                                    ++iswrot;

                                    if (rotok) {

                                        aqoap = aaqq / aapp;
                                        apoaq = aapp / aaqq;
                                        theta = (d__1 = aqoap - apoaq, abs(
                                                d__1)) * -.5 / aapq;
                                        if (aaqq > aapp0) {
                                            theta = -theta;
                                        }
                                        if (abs(theta) > bigtheta) {
                                            t = .5 / theta;
                                            fastr[2] = t * d__[p] / d__[q];
                                            fastr[3] = -t * d__[q] / d__[p];
                                            drotm_(m, &a[p * a_dim1 + 1], &
                                                    c__1, &a[q * a_dim1 + 1], 
                                                    &c__1, fastr);
                                            if (rsvec) {
                          drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * 
                                  v_dim1 + 1], &c__1, fastr);
                                            }
/* Computing MAX */
                                            d__1 = 0., d__2 = t * apoaq * 
                                                    aapq + 1.;
                                            sva[q] = aaqq * sqrt((max(d__1,
                                                    d__2)));
/* Computing MAX */
                                            d__1 = 0., d__2 = 1. - t * aqoap *
                                                     aapq;
                                            aapp *= sqrt((max(d__1,d__2)));
/* Computing MAX */
                                            d__1 = mxsinj, d__2 = abs(t);
                                            mxsinj = max(d__1,d__2);
                                        } else {

/*                 .. choose correct signum for THETA and rotate */

                                            thsign = -d_sign(&c_b35, &aapq);
                                            if (aaqq > aapp0) {
                          thsign = -thsign;
                                            }
                                            t = 1. / (theta + thsign * sqrt(
                                                    theta * theta + 1.));
                                            cs = sqrt(1. / (t * t + 1.));
                                            sn = t * cs;
/* Computing MAX */
                                            d__1 = mxsinj, d__2 = abs(sn);
                                            mxsinj = max(d__1,d__2);
/* Computing MAX */
                                            d__1 = 0., d__2 = t * apoaq * 
                                                    aapq + 1.;
                                            sva[q] = aaqq * sqrt((max(d__1,
                                                    d__2)));
                                            aapp *= sqrt(1. - t * aqoap * 
                                                    aapq);
                                            apoaq = d__[p] / d__[q];
                                            aqoap = d__[q] / d__[p];
                                            if (d__[p] >= 1.) {

                          if (d__[q] >= 1.) {
                              fastr[2] = t * apoaq;
                              fastr[3] = -t * aqoap;
                              d__[p] *= cs;
                              d__[q] *= cs;
                              drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q * 
                                      a_dim1 + 1], &c__1, fastr);
                              if (rsvec) {
                                  drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
                                          q * v_dim1 + 1], &c__1, fastr);
                              }
                          } else {
                              d__1 = -t * aqoap;
                              daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
                                      p * a_dim1 + 1], &c__1);
                              d__1 = cs * sn * apoaq;
                              daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
                                      q * a_dim1 + 1], &c__1);
                              if (rsvec) {
                                  d__1 = -t * aqoap;
                                  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
                                          c__1, &v[p * v_dim1 + 1], &c__1);
                                  d__1 = cs * sn * apoaq;
                                  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
                                          c__1, &v[q * v_dim1 + 1], &c__1);
                              }
                              d__[p] *= cs;
                              d__[q] /= cs;
                          }
                                            } else {
                          if (d__[q] >= 1.) {
                              d__1 = t * apoaq;
                              daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
                                      q * a_dim1 + 1], &c__1);
                              d__1 = -cs * sn * aqoap;
                              daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
                                      p * a_dim1 + 1], &c__1);
                              if (rsvec) {
                                  d__1 = t * apoaq;
                                  daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
                                          c__1, &v[q * v_dim1 + 1], &c__1);
                                  d__1 = -cs * sn * aqoap;
                                  daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
                                          c__1, &v[p * v_dim1 + 1], &c__1);
                              }
                              d__[p] /= cs;
                              d__[q] *= cs;
                          } else {
                              if (d__[p] >= d__[q]) {
                                  d__1 = -t * aqoap;
                                  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
                                          &a[p * a_dim1 + 1], &c__1);
                                  d__1 = cs * sn * apoaq;
                                  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
                                          &a[q * a_dim1 + 1], &c__1);
                                  d__[p] *= cs;
                                  d__[q] /= cs;
                                  if (rsvec) {
                                      d__1 = -t * aqoap;
                                      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
                                              &c__1, &v[p * v_dim1 + 1], &
                                              c__1);
                                      d__1 = cs * sn * apoaq;
                                      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
                                              &c__1, &v[q * v_dim1 + 1], &
                                              c__1);
                                  }
                              } else {
                                  d__1 = t * apoaq;
                                  daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, 
                                          &a[q * a_dim1 + 1], &c__1);
                                  d__1 = -cs * sn * aqoap;
                                  daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, 
                                          &a[p * a_dim1 + 1], &c__1);
                                  d__[p] /= cs;
                                  d__[q] *= cs;
                                  if (rsvec) {
                                      d__1 = t * apoaq;
                                      daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], 
                                              &c__1, &v[q * v_dim1 + 1], &
                                              c__1);
                                      d__1 = -cs * sn * aqoap;
                                      daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], 
                                              &c__1, &v[p * v_dim1 + 1], &
                                              c__1);
                                  }
                              }
                          }
                                            }
                                        }
                                    } else {
                                        if (aapp > aaqq) {
                                            dcopy_(m, &a[p * a_dim1 + 1], &
                                                    c__1, &work[1], &c__1);
                                            dlascl_("G", &c__0, &c__0, &aapp, 
                                                    &c_b35, m, &c__1, &work[1]
, lda, &ierr);
                                            dlascl_("G", &c__0, &c__0, &aaqq, 
                                                    &c_b35, m, &c__1, &a[q * 
                                                    a_dim1 + 1], lda, &ierr);
                                            temp1 = -aapq * d__[p] / d__[q];
                                            daxpy_(m, &temp1, &work[1], &c__1, 
                                                     &a[q * a_dim1 + 1], &
                                                    c__1);
                                            dlascl_("G", &c__0, &c__0, &c_b35, 
                                                     &aaqq, m, &c__1, &a[q * 
                                                    a_dim1 + 1], lda, &ierr);
/* Computing MAX */
                                            d__1 = 0., d__2 = 1. - aapq * 
                                                    aapq;
                                            sva[q] = aaqq * sqrt((max(d__1,
                                                    d__2)));
                                            mxsinj = max(mxsinj,*sfmin);
                                        } else {
                                            dcopy_(m, &a[q * a_dim1 + 1], &
                                                    c__1, &work[1], &c__1);
                                            dlascl_("G", &c__0, &c__0, &aaqq, 
                                                    &c_b35, m, &c__1, &work[1]
, lda, &ierr);
                                            dlascl_("G", &c__0, &c__0, &aapp, 
                                                    &c_b35, m, &c__1, &a[p * 
                                                    a_dim1 + 1], lda, &ierr);
                                            temp1 = -aapq * d__[q] / d__[p];
                                            daxpy_(m, &temp1, &work[1], &c__1, 
                                                     &a[p * a_dim1 + 1], &
                                                    c__1);
                                            dlascl_("G", &c__0, &c__0, &c_b35, 
                                                     &aapp, m, &c__1, &a[p * 
                                                    a_dim1 + 1], lda, &ierr);
/* Computing MAX */
                                            d__1 = 0., d__2 = 1. - aapq * 
                                                    aapq;
                                            sva[p] = aapp * sqrt((max(d__1,
                                                    d__2)));
                                            mxsinj = max(mxsinj,*sfmin);
                                        }
                                    }
/*           END IF ROTOK THEN ... ELSE */

/*           In the case of cancellation in updating SVA(q) */
/*           .. recompute SVA(q) */
/* Computing 2nd power */
                                    d__1 = sva[q] / aaqq;
                                    if (d__1 * d__1 <= rooteps) {
                                        if (aaqq < rootbig && aaqq > 
                                                rootsfmin) {
                                            sva[q] = dnrm2_(m, &a[q * a_dim1 
                                                    + 1], &c__1) * d__[q];
                                        } else {
                                            t = 0.;
                                            aaqq = 0.;
                                            dlassq_(m, &a[q * a_dim1 + 1], &
                                                    c__1, &t, &aaqq);
                                            sva[q] = t * sqrt(aaqq) * d__[q];
                                        }
                                    }
/* Computing 2nd power */
                                    d__1 = aapp / aapp0;
                                    if (d__1 * d__1 <= rooteps) {
                                        if (aapp < rootbig && aapp > 
                                                rootsfmin) {
                                            aapp = dnrm2_(m, &a[p * a_dim1 + 
                                                    1], &c__1) * d__[p];
                                        } else {
                                            t = 0.;
                                            aapp = 0.;
                                            dlassq_(m, &a[p * a_dim1 + 1], &
                                                    c__1, &t, &aapp);
                                            aapp = t * sqrt(aapp) * d__[p];
                                        }
                                        sva[p] = aapp;
                                    }
/*              end of OK rotation */
                                } else {
                                    ++notrot;
/*           SKIPPED  = SKIPPED  + 1 */
                                    ++pskipped;
                                    ++ijblsk;
                                }
                            } else {
                                ++notrot;
                                ++pskipped;
                                ++ijblsk;
                            }
/*      IF ( NOTROT .GE. EMPTSW )  GO TO 2011 */
                            if (i__ <= swband && ijblsk >= blskip) {
                                sva[p] = aapp;
                                notrot = 0;
                                goto L2011;
                            }
                            if (i__ <= swband && pskipped > rowskip) {
                                aapp = -aapp;
                                notrot = 0;
                                goto L2203;
                            }

/* L2200: */
                        }
/*        end of the q-loop */
L2203:
                        sva[p] = aapp;

                    } else {
                        if (aapp == 0.) {
/* Computing MIN */
                            i__5 = jgl + kbl - 1;
                            notrot = notrot + min(i__5,*n) - jgl + 1;
                        }
                        if (aapp < 0.) {
                            notrot = 0;
                        }
/* **      IF ( NOTROT .GE. EMPTSW )  GO TO 2011 */
                    }
/* L2100: */
                }
/*     end of the p-loop */
/* L2010: */
            }
/*     end of the jbc-loop */
L2011:
/* 2011 bailed out of the jbc-loop */
/* Computing MIN */
            i__4 = igl + kbl - 1;
            i__3 = min(i__4,*n);
            for (p = igl; p <= i__3; ++p) {
                sva[p] = (d__1 = sva[p], abs(d__1));
/* L2012: */
            }
/* **   IF ( NOTROT .GE. EMPTSW ) GO TO 1994 */
/* L2000: */
        }
/* 2000 :: end of the ibr-loop */

/*     .. update SVA(N) */
        if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
            sva[*n] = dnrm2_(m, &a[*n * a_dim1 + 1], &c__1) * d__[*n];
        } else {
            t = 0.;
            aapp = 0.;
            dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
            sva[*n] = t * sqrt(aapp) * d__[*n];
        }

/*     Additional steering devices */

        if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
            swband = i__;
        }
        if (i__ > swband + 1 && mxaapq < (doublereal) (*n) * *tol && (
                doublereal) (*n) * mxaapq * mxsinj < *tol) {
            goto L1994;
        }

        if (notrot >= emptsw) {
            goto L1994;
        }
/* L1993: */
    }
/*     end i=1:NSWEEP loop */
/* #:) Reaching this point means that the procedure has completed the given */
/*     number of sweeps. */
    *info = *nsweep - 1;
    goto L1995;
L1994:
/* #:) Reaching this point means that during the i-th sweep all pivots were */
/*     below the given threshold, causing early exit. */
    *info = 0;
/* #:) INFO = 0 confirms successful iterations. */
L1995:

/*     Sort the vector D */

    i__1 = *n - 1;
    for (p = 1; p <= i__1; ++p) {
        i__2 = *n - p + 1;
        q = idamax_(&i__2, &sva[p], &c__1) + p - 1;
        if (p != q) {
            temp1 = sva[p];
            sva[p] = sva[q];
            sva[q] = temp1;
            temp1 = d__[p];
            d__[p] = d__[q];
            d__[q] = temp1;
            dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
            if (rsvec) {
                dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &
                        c__1);
            }
        }
/* L5991: */
    }

    return 0;
/*     .. */
/*     .. END OF DGSVJ1 */
/*     .. */
} /* dgsvj1_ */