dgesvj.c

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/* dgesvj.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 doublereal c_b17 = 0.;
static doublereal c_b18 = 1.;
static integer c__1 = 1;
static integer c__0 = 0;
static integer c__2 = 2;

/* Subroutine */ int dgesvj_(char *joba, char *jobu, char *jobv, integer *m, 
        integer *n, doublereal *a, integer *lda, doublereal *sva, integer *mv, 
         doublereal *v, integer *ldv, 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;
    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;
    integer n2, n4;
    doublereal rootsfmin;
    integer n34;
    doublereal cs, sn;
    integer ir1, jbc;
    doublereal big;
    integer kbl, igl, ibr, jgl, nbl;
    doublereal tol;
    integer mvl;
    doublereal aapp, aapq, aaqq;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    doublereal ctol;
    integer ierr;
    doublereal aapp0;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal temp1;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal scale, large, apoaq, aqoap;
    extern logical lsame_(char *, char *);
    doublereal theta, small, sfmin;
    logical lsvec;
    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 *);
    logical uctol;
    extern /* Subroutine */ int drotm_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *);
    logical lower, upper, rotok;
    extern /* Subroutine */ int dgsvj0_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, doublereal *, 
             integer *, doublereal *, integer *, integer *), dgsvj1_(
            char *, integer *, integer *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *, doublereal *, 
             integer *, integer *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *), 
            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, lkahead;
    logical goscale, noscale;
    doublereal rootbig, epsilon, 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 */
/*  ~~~~~~~ */
/*  DGESVJ computes the singular value decomposition (SVD) of a real */
/*  M-by-N matrix A, where M >= N. The SVD of A is written as */
/*                                     [++]   [xx]   [x0]   [xx] */
/*               A = U * SIGMA * V^t,  [++] = [xx] * [ox] * [xx] */
/*                                     [++]   [xx] */
/*  where SIGMA is an N-by-N diagonal matrix, U is an M-by-N orthonormal */
/*  matrix, and V is an N-by-N orthogonal matrix. The diagonal elements */
/*  of SIGMA are the singular values of A. The columns of U and V are the */
/*  left and the right singular vectors of A, respectively. */

/*  Further Details */
/*  ~~~~~~~~~~~~~~~ */
/*  The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane */
/*  rotations. The rotations are implemented as fast scaled rotations of */
/*  Anda and Park [1]. In the case of underflow of the Jacobi angle, a */
/*  modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses */
/*  column interchanges of de Rijk [2]. The relative accuracy of the computed */
/*  singular values and the accuracy of the computed singular vectors (in */
/*  angle metric) is as guaranteed by the theory of Demmel and Veselic [3]. */
/*  The condition number that determines the accuracy in the full rank case */
/*  is essentially min_{D=diag} kappa(A*D), where kappa(.) is the */
/*  spectral condition number. The best performance of this Jacobi SVD */
/*  procedure is achieved if used in an  accelerated version of Drmac and */
/*  Veselic [5,6], and it is the kernel routine in the SIGMA library [7]. */
/*  Some tunning parameters (marked with [TP]) are available for the */
/*  implementer. */
/*  The computational range for the nonzero singular values is the  machine */
/*  number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even */
/*  denormalized singular values can be computed with the corresponding */
/*  gradual loss of accurate digits. */

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

/*  References */
/*  ~~~~~~~~~~ */
/* [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. */
/*     SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. */
/* [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the */
/*     singular value decomposition on a vector computer. */
/*     SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. */
/* [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. */
/* [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular */
/*     value computation in floating point arithmetic. */
/*     SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. */
/* [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. */
/*     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. */
/*     LAPACK Working note 169. */
/* [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. */
/*     SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. */
/*     LAPACK Working note 170. */
/* [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, */
/*     QSVD, (H,K)-SVD computations. */
/*     Department of Mathematics, University of Zagreb, 2008. */

/*  Bugs, Examples and Comments */
/*  ~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
/*  Please report all bugs and send interesting test examples and comments to */
/*  drmac@math.hr. Thank you. */

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

/*  JOBA    (input) CHARACTER* 1 */
/*          Specifies the structure of A. */
/*          = 'L': The input matrix A is lower triangular; */
/*          = 'U': The input matrix A is upper triangular; */
/*          = 'G': The input matrix A is general M-by-N matrix, M >= N. */

/*  JOBU    (input) CHARACTER*1 */
/*          Specifies whether to compute the left singular vectors */
/*          (columns of U): */

/*          = 'U': The left singular vectors corresponding to the nonzero */
/*                 singular values are computed and returned in the leading */
/*                 columns of A. See more details in the description of A. */
/*                 The default numerical orthogonality threshold is set to */
/*                 approximately TOL=CTOL*EPS, CTOL=DSQRT(M), EPS=DLAMCH('E'). */
/*          = 'C': Analogous to JOBU='U', except that user can control the */
/*                 level of numerical orthogonality of the computed left */
/*                 singular vectors. TOL can be set to TOL = CTOL*EPS, where */
/*                 CTOL is given on input in the array WORK. */
/*                 No CTOL smaller than ONE is allowed. CTOL greater */
/*                 than 1 / EPS is meaningless. The option 'C' */
/*                 can be used if M*EPS is satisfactory orthogonality */
/*                 of the computed left singular vectors, so CTOL=M could */
/*                 save few sweeps of Jacobi rotations. */
/*                 See the descriptions of A and WORK(1). */
/*          = 'N': The matrix U is not computed. However, see the */
/*                 description of A. */

/*  JOBV    (input) CHARACTER*1 */
/*          Specifies whether to compute the right singular vectors, that */
/*          is, the matrix V: */
/*          = 'V' : the matrix V is computed and returned in the array V */
/*          = 'A' : the Jacobi rotations are applied to the MV-by-N */
/*                  array V. In other words, the right singular vector */
/*                  matrix V is not computed explicitly, instead it is */
/*                  applied to an MV-by-N matrix initially stored in the */
/*                  first MV rows of V. */
/*          = 'N' : the matrix V is not computed and the array V is not */
/*                  referenced */

/*  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. */

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, */
/*          If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C': */
/*          ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
/*                 If INFO .EQ. 0, */
/*                 ~~~~~~~~~~~~~~~ */
/*                 RANKA orthonormal columns of U are returned in the */
/*                 leading RANKA columns of the array A. Here RANKA <= N */
/*                 is the number of computed singular values of A that are */
/*                 above the underflow threshold DLAMCH('S'). The singular */
/*                 vectors corresponding to underflowed or zero singular */
/*                 values are not computed. The value of RANKA is returned */
/*                 in the array WORK as RANKA=NINT(WORK(2)). Also see the */
/*                 descriptions of SVA and WORK. The computed columns of U */
/*                 are mutually numerically orthogonal up to approximately */
/*                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'), */
/*                 see the description of JOBU. */
/*                 If INFO .GT. 0, */
/*                 ~~~~~~~~~~~~~~~ */
/*                 the procedure DGESVJ did not converge in the given number */
/*                 of iterations (sweeps). In that case, the computed */
/*                 columns of U may not be orthogonal up to TOL. The output */
/*                 U (stored in A), SIGMA (given by the computed singular */
/*                 values in SVA(1:N)) and V is still a decomposition of the */
/*                 input matrix A in the sense that the residual */
/*                 ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. */

/*          If JOBU .EQ. 'N': */
/*          ~~~~~~~~~~~~~~~~~ */
/*                 If INFO .EQ. 0 */
/*                 ~~~~~~~~~~~~~~ */
/*                 Note that the left singular vectors are 'for free' in the */
/*                 one-sided Jacobi SVD algorithm. However, if only the */
/*                 singular values are needed, the level of numerical */
/*                 orthogonality of U is not an issue and iterations are */
/*                 stopped when the columns of the iterated matrix are */
/*                 numerically orthogonal up to approximately M*EPS. Thus, */
/*                 on exit, A contains the columns of U scaled with the */
/*                 corresponding singular values. */
/*                 If INFO .GT. 0, */
/*                 ~~~~~~~~~~~~~~~ */
/*                 the procedure DGESVJ did not converge in the given number */
/*                 of iterations (sweeps). */

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

/*  SVA     (workspace/output) REAL array, dimension (N) */
/*          On exit, */
/*          If INFO .EQ. 0, */
/*          ~~~~~~~~~~~~~~~ */
/*          depending on the value SCALE = WORK(1), we have: */
/*                 If SCALE .EQ. ONE: */
/*                 ~~~~~~~~~~~~~~~~~~ */
/*                 SVA(1:N) contains the computed singular values of A. */
/*                 During the computation SVA contains the Euclidean column */
/*                 norms of the iterated matrices in the array A. */
/*                 If SCALE .NE. ONE: */
/*                 ~~~~~~~~~~~~~~~~~~ */
/*                 The singular values of A are SCALE*SVA(1:N), and this */
/*                 factored representation is due to the fact that some of the */
/*                 singular values of A might underflow or overflow. */

/*          If INFO .GT. 0, */
/*          ~~~~~~~~~~~~~~~ */
/*          the procedure DGESVJ did not converge in the given number of */
/*          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. */

/*  MV      (input) INTEGER */
/*          If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ */
/*          is applied to the first MV rows of V. See the description of JOBV. */

/*  V       (input/output) REAL array, dimension (LDV,N) */
/*          If JOBV = 'V', then V contains on exit the N-by-N matrix of */
/*                         the right singular vectors; */
/*          If JOBV = 'A', then V contains the product of the computed right */
/*                         singular vector matrix and the initial matrix in */
/*                         the array V. */
/*          If JOBV = 'N', then V is not referenced. */

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

/*  WORK    (input/workspace/output) REAL array, dimension max(4,M+N). */
/*          On entry, */
/*          If JOBU .EQ. 'C', */
/*          ~~~~~~~~~~~~~~~~~ */
/*          WORK(1) = CTOL, where CTOL defines the threshold for convergence. */
/*                    The process stops if all columns of A are mutually */
/*                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). */
/*                    It is required that CTOL >= ONE, i.e. it is not */
/*                    allowed to force the routine to obtain orthogonality */
/*                    below EPSILON. */
/*          On exit, */
/*          WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) */
/*                    are the computed singular vcalues of A. */
/*                    (See description of SVA().) */
/*          WORK(2) = NINT(WORK(2)) is the number of the computed nonzero */
/*                    singular values. */
/*          WORK(3) = NINT(WORK(3)) is the number of the computed singular */
/*                    values that are larger than the underflow threshold. */
/*          WORK(4) = NINT(WORK(4)) is the number of sweeps of Jacobi */
/*                    rotations needed for numerical convergence. */
/*          WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep. */
/*                    This is useful information in cases when DGESVJ did */
/*                    not converge, as it can be used to estimate whether */
/*                    the output is stil useful and for post festum analysis. */
/*          WORK(6) = the largest absolute value over all sines of the */
/*                    Jacobi rotation angles in the last sweep. It can be */
/*                    useful for a post festum analysis. */

/*  LWORK   length of WORK, WORK >= MAX(6,M+N) */

/*  INFO    (output) INTEGER */
/*          = 0 : successful exit. */
/*          < 0 : if INFO = -i, then the i-th argument had an illegal value */
/*          > 0 : DGESVJ did not converge in the maximal allowed number (30) */
/*                of sweeps. The output may still be useful. See the */
/*                description of WORK. */

/*     Local Parameters */


/*     Local Scalars */


/*     Local Arrays */


/*     Intrinsic Functions */


/*     External Functions */
/*     .. from BLAS */
/*     .. from LAPACK */

/*     External Subroutines */
/*     .. from BLAS */
/*     .. from LAPACK */


/*     Test the input arguments */

    /* Parameter adjustments */
    --sva;
    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 */
    lsvec = lsame_(jobu, "U");
    uctol = lsame_(jobu, "C");
    rsvec = lsame_(jobv, "V");
    applv = lsame_(jobv, "A");
    upper = lsame_(joba, "U");
    lower = lsame_(joba, "L");

    if (! (upper || lower || lsame_(joba, "G"))) {
        *info = -1;
    } else if (! (lsvec || uctol || lsame_(jobu, "N"))) 
            {
        *info = -2;
    } else if (! (rsvec || applv || lsame_(jobv, "N"))) 
            {
        *info = -3;
    } else if (*m < 0) {
        *info = -4;
    } else if (*n < 0 || *n > *m) {
        *info = -5;
    } else if (*lda < *m) {
        *info = -7;
    } else if (*mv < 0) {
        *info = -9;
    } else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
        *info = -11;
    } else if (uctol && work[1] <= 1.) {
        *info = -12;
    } else /* if(complicated condition) */ {
/* Computing MAX */
        i__1 = *m + *n;
        if (*lwork < max(i__1,6)) {
            *info = -13;
        } else {
            *info = 0;
        }
    }

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

/* #:) Quick return for void matrix */

    if (*m == 0 || *n == 0) {
        return 0;
    }

/*     Set numerical parameters */
/*     The stopping criterion for Jacobi rotations is */

/*     max_{i<>j}|A(:,i)^T * A(:,j)|/(||A(:,i)||*||A(:,j)||) < CTOL*EPS */

/*     where EPS is the round-off and CTOL is defined as follows: */

    if (uctol) {
/*        ... user controlled */
        ctol = work[1];
    } else {
/*        ... default */
        if (lsvec || rsvec || applv) {
            ctol = sqrt((doublereal) (*m));
        } else {
            ctol = (doublereal) (*m);
        }
    }
/*     ... and the machine dependent parameters are */
/* [!]  (Make sure that DLAMCH() works properly on the target machine.) */

    epsilon = dlamch_("Epsilon");
    rooteps = sqrt(epsilon);
    sfmin = dlamch_("SafeMinimum");
    rootsfmin = sqrt(sfmin);
    small = sfmin / epsilon;
    big = dlamch_("Overflow");
/*     BIG         = ONE    / SFMIN */
    rootbig = 1. / rootsfmin;
    large = big / sqrt((doublereal) (*m * *n));
    bigtheta = 1. / rooteps;

    tol = ctol * epsilon;
    roottol = sqrt(tol);

    if ((doublereal) (*m) * epsilon >= 1.) {
        *info = -5;
        i__1 = -(*info);
        xerbla_("DGESVJ", &i__1);
        return 0;
    }

/*     Initialize the right singular vector matrix. */

    if (rsvec) {
        mvl = *n;
        dlaset_("A", &mvl, n, &c_b17, &c_b18, &v[v_offset], ldv);
    } else if (applv) {
        mvl = *mv;
    }
    rsvec = rsvec || applv;

/*     Initialize SVA( 1:N ) = ( ||A e_i||_2, i = 1:N ) */
/* (!)  If necessary, scale A to protect the largest singular value */
/*     from overflow. It is possible that saving the largest singular */
/*     value destroys the information about the small ones. */
/*     This initial scaling is almost minimal in the sense that the */
/*     goal is to make sure that no column norm overflows, and that */
/*     DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries */
/*     in A are detected, the procedure returns with INFO=-6. */

    scale = 1. / sqrt((doublereal) (*m) * (doublereal) (*n));
    noscale = TRUE_;
    goscale = TRUE_;

    if (lower) {
/*        the input matrix is M-by-N lower triangular (trapezoidal) */
        i__1 = *n;
        for (p = 1; p <= i__1; ++p) {
            aapp = 0.;
            aaqq = 0.;
            i__2 = *m - p + 1;
            dlassq_(&i__2, &a[p + p * a_dim1], &c__1, &aapp, &aaqq);
            if (aapp > big) {
                *info = -6;
                i__2 = -(*info);
                xerbla_("DGESVJ", &i__2);
                return 0;
            }
            aaqq = sqrt(aaqq);
            if (aapp < big / aaqq && noscale) {
                sva[p] = aapp * aaqq;
            } else {
                noscale = FALSE_;
                sva[p] = aapp * (aaqq * scale);
                if (goscale) {
                    goscale = FALSE_;
                    i__2 = p - 1;
                    for (q = 1; q <= i__2; ++q) {
                        sva[q] *= scale;
/* L1873: */
                    }
                }
            }
/* L1874: */
        }
    } else if (upper) {
/*        the input matrix is M-by-N upper triangular (trapezoidal) */
        i__1 = *n;
        for (p = 1; p <= i__1; ++p) {
            aapp = 0.;
            aaqq = 0.;
            dlassq_(&p, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
            if (aapp > big) {
                *info = -6;
                i__2 = -(*info);
                xerbla_("DGESVJ", &i__2);
                return 0;
            }
            aaqq = sqrt(aaqq);
            if (aapp < big / aaqq && noscale) {
                sva[p] = aapp * aaqq;
            } else {
                noscale = FALSE_;
                sva[p] = aapp * (aaqq * scale);
                if (goscale) {
                    goscale = FALSE_;
                    i__2 = p - 1;
                    for (q = 1; q <= i__2; ++q) {
                        sva[q] *= scale;
/* L2873: */
                    }
                }
            }
/* L2874: */
        }
    } else {
/*        the input matrix is M-by-N general dense */
        i__1 = *n;
        for (p = 1; p <= i__1; ++p) {
            aapp = 0.;
            aaqq = 0.;
            dlassq_(m, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
            if (aapp > big) {
                *info = -6;
                i__2 = -(*info);
                xerbla_("DGESVJ", &i__2);
                return 0;
            }
            aaqq = sqrt(aaqq);
            if (aapp < big / aaqq && noscale) {
                sva[p] = aapp * aaqq;
            } else {
                noscale = FALSE_;
                sva[p] = aapp * (aaqq * scale);
                if (goscale) {
                    goscale = FALSE_;
                    i__2 = p - 1;
                    for (q = 1; q <= i__2; ++q) {
                        sva[q] *= scale;
/* L3873: */
                    }
                }
            }
/* L3874: */
        }
    }

    if (noscale) {
        scale = 1.;
    }

/*     Move the smaller part of the spectrum from the underflow threshold */
/* (!)  Start by determining the position of the nonzero entries of the */
/*     array SVA() relative to ( SFMIN, BIG ). */

    aapp = 0.;
    aaqq = big;
    i__1 = *n;
    for (p = 1; p <= i__1; ++p) {
        if (sva[p] != 0.) {
/* Computing MIN */
            d__1 = aaqq, d__2 = sva[p];
            aaqq = min(d__1,d__2);
        }
/* Computing MAX */
        d__1 = aapp, d__2 = sva[p];
        aapp = max(d__1,d__2);
/* L4781: */
    }

/* #:) Quick return for zero matrix */

    if (aapp == 0.) {
        if (lsvec) {
            dlaset_("G", m, n, &c_b17, &c_b18, &a[a_offset], lda);
        }
        work[1] = 1.;
        work[2] = 0.;
        work[3] = 0.;
        work[4] = 0.;
        work[5] = 0.;
        work[6] = 0.;
        return 0;
    }

/* #:) Quick return for one-column matrix */

    if (*n == 1) {
        if (lsvec) {
            dlascl_("G", &c__0, &c__0, &sva[1], &scale, m, &c__1, &a[a_dim1 + 
                    1], lda, &ierr);
        }
        work[1] = 1. / scale;
        if (sva[1] >= sfmin) {
            work[2] = 1.;
        } else {
            work[2] = 0.;
        }
        work[3] = 0.;
        work[4] = 0.;
        work[5] = 0.;
        work[6] = 0.;
        return 0;
    }

/*     Protect small singular values from underflow, and try to */
/*     avoid underflows/overflows in computing Jacobi rotations. */

    sn = sqrt(sfmin / epsilon);
    temp1 = sqrt(big / (doublereal) (*n));
    if (aapp <= sn || aaqq >= temp1 || sn <= aaqq && aapp <= temp1) {
/* Computing MIN */
        d__1 = big, d__2 = temp1 / aapp;
        temp1 = min(d__1,d__2);
/*         AAQQ  = AAQQ*TEMP1 */
/*         AAPP  = AAPP*TEMP1 */
    } else if (aaqq <= sn && aapp <= temp1) {
/* Computing MIN */
        d__1 = sn / aaqq, d__2 = big / (aapp * sqrt((doublereal) (*n)));
        temp1 = min(d__1,d__2);
/*         AAQQ  = AAQQ*TEMP1 */
/*         AAPP  = AAPP*TEMP1 */
    } else if (aaqq >= sn && aapp >= temp1) {
/* Computing MAX */
        d__1 = sn / aaqq, d__2 = temp1 / aapp;
        temp1 = max(d__1,d__2);
/*         AAQQ  = AAQQ*TEMP1 */
/*         AAPP  = AAPP*TEMP1 */
    } else if (aaqq <= sn && aapp >= temp1) {
/* Computing MIN */
        d__1 = sn / aaqq, d__2 = big / (sqrt((doublereal) (*n)) * aapp);
        temp1 = min(d__1,d__2);
/*         AAQQ  = AAQQ*TEMP1 */
/*         AAPP  = AAPP*TEMP1 */
    } else {
        temp1 = 1.;
    }

/*     Scale, if necessary */

    if (temp1 != 1.) {
        dlascl_("G", &c__0, &c__0, &c_b18, &temp1, n, &c__1, &sva[1], n, &
                ierr);
    }
    scale = temp1 * scale;
    if (scale != 1.) {
        dlascl_(joba, &c__0, &c__0, &c_b18, &scale, m, n, &a[a_offset], lda, &
                ierr);
        scale = 1. / scale;
    }

/*     Row-cyclic Jacobi SVD algorithm with column pivoting */

    emptsw = *n * (*n - 1) / 2;
    notrot = 0;
    fastr[0] = 0.;

/*     A is represented in factored form A = A * diag(WORK), where diag(WORK) */
/*     is initialized to identity. WORK is updated during fast scaled */
/*     rotations. */

    i__1 = *n;
    for (q = 1; q <= i__1; ++q) {
        work[q] = 1.;
/* L1868: */
    }


    swband = 3;
/* [TP] SWBAND is a tuning parameter [TP]. It is meaningful and effective */
/*     if DGESVJ is used as a computational routine in the preconditioned */
/*     Jacobi SVD algorithm DGESVJ. For sweeps i=1:SWBAND the procedure */
/*     works on pivots inside a band-like region around the diagonal. */
/*     The boundaries are determined dynamically, based on the number of */
/*     pivots above a threshold. */

    kbl = min(8,*n);
/* [TP] KBL is a tuning parameter that defines the tile size in the */
/*     tiling of the p-q loops of pivot pairs. In general, an optimal */
/*     value of KBL depends on the matrix dimensions and on the */
/*     parameters of the computer's memory. */

    nbl = *n / kbl;
    if (nbl * kbl != *n) {
        ++nbl;
    }

/* Computing 2nd power */
    i__1 = kbl;
    blskip = i__1 * i__1;
/* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */

    rowskip = min(5,kbl);
/* [TP] ROWSKIP is a tuning parameter. */

    lkahead = 1;
/* [TP] LKAHEAD is a tuning parameter. */

/*     Quasi block transformations, using the lower (upper) triangular */
/*     structure of the input matrix. The quasi-block-cycling usually */
/*     invokes cubic convergence. Big part of this cycle is done inside */
/*     canonical subspaces of dimensions less than M. */

/* Computing MAX */
    i__1 = 64, i__2 = kbl << 2;
    if ((lower || upper) && *n > max(i__1,i__2)) {
/* [TP] The number of partition levels and the actual partition are */
/*     tuning parameters. */
        n4 = *n / 4;
        n2 = *n / 2;
        n34 = n4 * 3;
        if (applv) {
            q = 0;
        } else {
            q = 1;
        }

        if (lower) {

/*     This works very well on lower triangular matrices, in particular */
/*     in the framework of the preconditioned Jacobi SVD (xGEJSV). */
/*     The idea is simple: */
/*     [+ 0 0 0]   Note that Jacobi transformations of [0 0] */
/*     [+ + 0 0]                                       [0 0] */
/*     [+ + x 0]   actually work on [x 0]              [x 0] */
/*     [+ + x x]                    [x x].             [x x] */

            i__1 = *m - n34;
            i__2 = *n - n34;
            i__3 = *lwork - *n;
            dgsvj0_(jobv, &i__1, &i__2, &a[n34 + 1 + (n34 + 1) * a_dim1], lda, 
                     &work[n34 + 1], &sva[n34 + 1], &mvl, &v[n34 * q + 1 + (
                    n34 + 1) * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__2, &
                    work[*n + 1], &i__3, &ierr);

            i__1 = *m - n2;
            i__2 = n34 - n2;
            i__3 = *lwork - *n;
            dgsvj0_(jobv, &i__1, &i__2, &a[n2 + 1 + (n2 + 1) * a_dim1], lda, &
                    work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1)
                     * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__2, &work[*n 
                    + 1], &i__3, &ierr);

            i__1 = *m - n2;
            i__2 = *n - n2;
            i__3 = *lwork - *n;
            dgsvj1_(jobv, &i__1, &i__2, &n4, &a[n2 + 1 + (n2 + 1) * a_dim1], 
                    lda, &work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (
                    n2 + 1) * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &
                    work[*n + 1], &i__3, &ierr);

            i__1 = *m - n4;
            i__2 = n2 - n4;
            i__3 = *lwork - *n;
            dgsvj0_(jobv, &i__1, &i__2, &a[n4 + 1 + (n4 + 1) * a_dim1], lda, &
                    work[n4 + 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1)
                     * v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n 
                    + 1], &i__3, &ierr);

            i__1 = *lwork - *n;
            dgsvj0_(jobv, m, &n4, &a[a_offset], lda, &work[1], &sva[1], &mvl, 
                    &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*
                    n + 1], &i__1, &ierr);

            i__1 = *lwork - *n;
            dgsvj1_(jobv, m, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1], &
                    mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &
                    work[*n + 1], &i__1, &ierr);


        } else if (upper) {


            i__1 = *lwork - *n;
            dgsvj0_(jobv, &n4, &n4, &a[a_offset], lda, &work[1], &sva[1], &
                    mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__2, &
                    work[*n + 1], &i__1, &ierr);

            i__1 = *lwork - *n;
            dgsvj0_(jobv, &n2, &n4, &a[(n4 + 1) * a_dim1 + 1], lda, &work[n4 
                    + 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1) * 
                    v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n + 1]
, &i__1, &ierr);

            i__1 = *lwork - *n;
            dgsvj1_(jobv, &n2, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1], 
                     &mvl, &v[v_offset], ldv, &epsilon, &sfmin, &tol, &c__1, &
                    work[*n + 1], &i__1, &ierr);

            i__1 = n2 + n4;
            i__2 = *lwork - *n;
            dgsvj0_(jobv, &i__1, &n4, &a[(n2 + 1) * a_dim1 + 1], lda, &work[
                    n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1) * 
                    v_dim1], ldv, &epsilon, &sfmin, &tol, &c__1, &work[*n + 1]
, &i__2, &ierr);
        }

    }

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

    for (i__ = 1; i__ <= 30; ++i__) {

/*     .. go go go ... */

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

        notrot = 0;
        pskipped = 0;

/*     Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
/*     1 <= p < q <= N. This is the first step toward a blocked implementation */
/*     of the rotations. New implementation, based on block transformations, */
/*     is under development. */

        i__1 = nbl;
        for (ibr = 1; ibr <= i__1; ++ibr) {

            igl = (ibr - 1) * kbl + 1;

/* Computing MIN */
            i__3 = lkahead, i__4 = nbl - ibr;
            i__2 = min(i__3,i__4);
            for (ir1 = 0; ir1 <= i__2; ++ir1) {

                igl += ir1 * kbl;

/* Computing MIN */
                i__4 = igl + kbl - 1, i__5 = *n - 1;
                i__3 = min(i__4,i__5);
                for (p = igl; p <= i__3; ++p) {

/*     .. de Rijk's pivoting */

                    i__4 = *n - p + 1;
                    q = idamax_(&i__4, &sva[p], &c__1) + p - 1;
                    if (p != q) {
                        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);
                        }
                        temp1 = sva[p];
                        sva[p] = sva[q];
                        sva[q] = temp1;
                        temp1 = work[p];
                        work[p] = work[q];
                        work[q] = temp1;
                    }

                    if (ir1 == 0) {

/*        Column norms are periodically updated by explicit */
/*        norm computation. */
/*        Caveat: */
/*        Unfortunately, some BLAS implementations compute DNRM2(M,A(1,p),1) */
/*        as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may cause the result to */
/*        overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and to */
/*        underflow for ||A(:,p)||_2 < DSQRT(underflow_threshold). */
/*        Hence, DNRM2 cannot be trusted, not even in the case when */
/*        the true norm is far from the under(over)flow boundaries. */
/*        If properly implemented DNRM2 is available, the IF-THEN-ELSE */
/*        below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". */

                        if (sva[p] < rootbig && sva[p] > rootsfmin) {
                            sva[p] = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) * 
                                    work[p];
                        } else {
                            temp1 = 0.;
                            aapp = 0.;
                            dlassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
                                    aapp);
                            sva[p] = temp1 * sqrt(aapp) * work[p];
                        }
                        aapp = sva[p];
                    } else {
                        aapp = sva[p];
                    }

                    if (aapp > 0.) {

                        pskipped = 0;

/* Computing MIN */
                        i__5 = igl + kbl - 1;
                        i__4 = min(i__5,*n);
                        for (q = p + 1; q <= i__4; ++q) {

                            aaqq = sva[q];

                            if (aaqq > 0.) {

                                aapp0 = aapp;
                                if (aaqq >= 1.) {
                                    rotok = small * aapp <= aaqq;
                                    if (aapp < big / aaqq) {
                                        aapq = ddot_(m, &a[p * a_dim1 + 1], &
                                                c__1, &a[q * a_dim1 + 1], &
                                                c__1) * work[p] * work[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
                                                work[*n + 1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aapp, &
                                                work[p], m, &c__1, &work[*n + 
                                                1], lda, &ierr);
                                        aapq = ddot_(m, &work[*n + 1], &c__1, 
                                                &a[q * a_dim1 + 1], &c__1) * 
                                                work[q] / aaqq;
                                    }
                                } else {
                                    rotok = aapp <= aaqq / small;
                                    if (aapp > small / aaqq) {
                                        aapq = ddot_(m, &a[p * a_dim1 + 1], &
                                                c__1, &a[q * a_dim1 + 1], &
                                                c__1) * work[p] * work[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
                                                work[*n + 1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aaqq, &
                                                work[q], m, &c__1, &work[*n + 
                                                1], lda, &ierr);
                                        aapq = ddot_(m, &work[*n + 1], &c__1, 
                                                &a[p * a_dim1 + 1], &c__1) * 
                                                work[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) {

/*           .. rotate */
/* [RTD]      ROTATED = ROTATED + ONE */

                                    if (ir1 == 0) {
                                        notrot = 0;
                                        pskipped = 0;
                                        ++iswrot;
                                    }

                                    if (rotok) {

                                        aqoap = aaqq / aapp;
                                        apoaq = aapp / aaqq;
                                        theta = (d__1 = aqoap - apoaq, abs(
                                                d__1)) * -.5 / aapq;

                                        if (abs(theta) > bigtheta) {

                                            t = .5 / theta;
                                            fastr[2] = t * work[p] / work[q];
                                            fastr[3] = -t * work[q] / work[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)));
                                            aapp *= sqrt(1. - t * aqoap * 
                                                    aapq);
/* 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_b18, &aapq);
                                            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)));
/* Computing MAX */
                                            d__1 = 0., d__2 = 1. - t * aqoap *
                                                     aapq;
                                            aapp *= sqrt((max(d__1,d__2)));

                                            apoaq = work[p] / work[q];
                                            aqoap = work[q] / work[p];
                                            if (work[p] >= 1.) {
                          if (work[q] >= 1.) {
                              fastr[2] = t * apoaq;
                              fastr[3] = -t * aqoap;
                              work[p] *= cs;
                              work[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);
                              work[p] *= cs;
                              work[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 {
                          if (work[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);
                              work[p] /= cs;
                              work[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 (work[p] >= work[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);
                                  work[p] *= cs;
                                  work[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);
                                  work[p] /= cs;
                                  work[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 {
/*              .. have to use modified Gram-Schmidt like transformation */
                                        dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
                                                work[*n + 1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aapp, &
                                                c_b18, m, &c__1, &work[*n + 1]
, lda, &ierr);
                                        dlascl_("G", &c__0, &c__0, &aaqq, &
                                                c_b18, m, &c__1, &a[q * 
                                                a_dim1 + 1], lda, &ierr);
                                        temp1 = -aapq * work[p] / work[q];
                                        daxpy_(m, &temp1, &work[*n + 1], &
                                                c__1, &a[q * a_dim1 + 1], &
                                                c__1);
                                        dlascl_("G", &c__0, &c__0, &c_b18, &
                                                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);
                                    }
/*           END IF ROTOK THEN ... ELSE */

/*           In the case of cancellation in updating SVA(q), SVA(p) */
/*           recompute SVA(q), SVA(p). */

/* 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) * work[q];
                                        } else {
                                            t = 0.;
                                            aaqq = 0.;
                                            dlassq_(m, &a[q * a_dim1 + 1], &
                                                    c__1, &t, &aaqq);
                                            sva[q] = t * sqrt(aaqq) * work[q];
                                        }
                                    }
                                    if (aapp / aapp0 <= rooteps) {
                                        if (aapp < rootbig && aapp > 
                                                rootsfmin) {
                                            aapp = dnrm2_(m, &a[p * a_dim1 + 
                                                    1], &c__1) * work[p];
                                        } else {
                                            t = 0.;
                                            aapp = 0.;
                                            dlassq_(m, &a[p * a_dim1 + 1], &
                                                    c__1, &t, &aapp);
                                            aapp = t * sqrt(aapp) * work[p];
                                        }
                                        sva[p] = aapp;
                                    }

                                } else {
/*        A(:,p) and A(:,q) already numerically orthogonal */
                                    if (ir1 == 0) {
                                        ++notrot;
                                    }
/* [RTD]      SKIPPED  = SKIPPED  + 1 */
                                    ++pskipped;
                                }
                            } else {
/*        A(:,q) is zero column */
                                if (ir1 == 0) {
                                    ++notrot;
                                }
                                ++pskipped;
                            }

                            if (i__ <= swband && pskipped > rowskip) {
                                if (ir1 == 0) {
                                    aapp = -aapp;
                                }
                                notrot = 0;
                                goto L2103;
                            }

/* L2002: */
                        }
/*     END q-LOOP */

L2103:
/*     bailed out of q-loop */

                        sva[p] = aapp;

                    } else {
                        sva[p] = aapp;
                        if (ir1 == 0 && aapp == 0.) {
/* Computing MIN */
                            i__4 = igl + kbl - 1;
                            notrot = notrot + min(i__4,*n) - p;
                        }
                    }

/* L2001: */
                }
/*     end of the p-loop */
/*     end of doing the block ( ibr, ibr ) */
/* L1002: */
            }
/*     end of ir1-loop */

/* ... go to the off diagonal blocks */

            igl = (ibr - 1) * kbl + 1;

            i__2 = nbl;
            for (jbc = ibr + 1; jbc <= i__2; ++jbc) {

                jgl = (jbc - 1) * kbl + 1;

/*        doing the block at ( ibr, jbc ) */

                ijblsk = 0;
/* Computing MIN */
                i__4 = igl + kbl - 1;
                i__3 = min(i__4,*n);
                for (p = igl; p <= i__3; ++p) {

                    aapp = sva[p];
                    if (aapp > 0.) {

                        pskipped = 0;

/* Computing MIN */
                        i__5 = jgl + kbl - 1;
                        i__4 = min(i__5,*n);
                        for (q = jgl; q <= i__4; ++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) * work[p] * work[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
                                                work[*n + 1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aapp, &
                                                work[p], m, &c__1, &work[*n + 
                                                1], lda, &ierr);
                                        aapq = ddot_(m, &work[*n + 1], &c__1, 
                                                &a[q * a_dim1 + 1], &c__1) * 
                                                work[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) * work[p] * work[q] / 
                                                aaqq / aapp;
                                    } else {
                                        dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
                                                work[*n + 1], &c__1);
                                        dlascl_("G", &c__0, &c__0, &aaqq, &
                                                work[q], m, &c__1, &work[*n + 
                                                1], lda, &ierr);
                                        aapq = ddot_(m, &work[*n + 1], &c__1, 
                                                &a[p * a_dim1 + 1], &c__1) * 
                                                work[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;
/* [RTD]      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 * work[p] / work[q];
                                            fastr[3] = -t * work[q] / work[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_b18, &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 = work[p] / work[q];
                                            aqoap = work[q] / work[p];
                                            if (work[p] >= 1.) {

                          if (work[q] >= 1.) {
                              fastr[2] = t * apoaq;
                              fastr[3] = -t * aqoap;
                              work[p] *= cs;
                              work[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);
                              }
                              work[p] *= cs;
                              work[q] /= cs;
                          }
                                            } else {
                          if (work[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);
                              }
                              work[p] /= cs;
                              work[q] *= cs;
                          } else {
                              if (work[p] >= work[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);
                                  work[p] *= cs;
                                  work[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);
                                  work[p] /= cs;
                                  work[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[*n + 1], &
                                                    c__1);
                                            dlascl_("G", &c__0, &c__0, &aapp, 
                                                    &c_b18, m, &c__1, &work[*
                                                    n + 1], lda, &ierr);
                                            dlascl_("G", &c__0, &c__0, &aaqq, 
                                                    &c_b18, m, &c__1, &a[q * 
                                                    a_dim1 + 1], lda, &ierr);
                                            temp1 = -aapq * work[p] / work[q];
                                            daxpy_(m, &temp1, &work[*n + 1], &
                                                    c__1, &a[q * a_dim1 + 1], 
                                                    &c__1);
                                            dlascl_("G", &c__0, &c__0, &c_b18, 
                                                     &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[*n + 1], &
                                                    c__1);
                                            dlascl_("G", &c__0, &c__0, &aaqq, 
                                                    &c_b18, m, &c__1, &work[*
                                                    n + 1], lda, &ierr);
                                            dlascl_("G", &c__0, &c__0, &aapp, 
                                                    &c_b18, m, &c__1, &a[p * 
                                                    a_dim1 + 1], lda, &ierr);
                                            temp1 = -aapq * work[q] / work[p];
                                            daxpy_(m, &temp1, &work[*n + 1], &
                                                    c__1, &a[p * a_dim1 + 1], 
                                                    &c__1);
                                            dlascl_("G", &c__0, &c__0, &c_b18, 
                                                     &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) * work[q];
                                        } else {
                                            t = 0.;
                                            aaqq = 0.;
                                            dlassq_(m, &a[q * a_dim1 + 1], &
                                                    c__1, &t, &aaqq);
                                            sva[q] = t * sqrt(aaqq) * work[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) * work[p];
                                        } else {
                                            t = 0.;
                                            aapp = 0.;
                                            dlassq_(m, &a[p * a_dim1 + 1], &
                                                    c__1, &t, &aapp);
                                            aapp = t * sqrt(aapp) * work[p];
                                        }
                                        sva[p] = aapp;
                                    }
/*              end of OK rotation */
                                } else {
                                    ++notrot;
/* [RTD]      SKIPPED  = SKIPPED  + 1 */
                                    ++pskipped;
                                    ++ijblsk;
                                }
                            } else {
                                ++notrot;
                                ++pskipped;
                                ++ijblsk;
                            }

                            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__4 = jgl + kbl - 1;
                            notrot = notrot + min(i__4,*n) - jgl + 1;
                        }
                        if (aapp < 0.) {
                            notrot = 0;
                        }

                    }

/* L2100: */
                }
/*     end of the p-loop */
/* L2010: */
            }
/*     end of the jbc-loop */
L2011:
/* 2011 bailed out of the jbc-loop */
/* Computing MIN */
            i__3 = igl + kbl - 1;
            i__2 = min(i__3,*n);
            for (p = igl; p <= i__2; ++p) {
                sva[p] = (d__1 = sva[p], abs(d__1));
/* L2012: */
            }
/* ** */
/* 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) * work[*n];
        } else {
            t = 0.;
            aapp = 0.;
            dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
            sva[*n] = t * sqrt(aapp) * work[*n];
        }

/*     Additional steering devices */

        if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
            swband = i__;
        }

        if (i__ > swband + 1 && mxaapq < sqrt((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 not converged. */
    *info = 29;
    goto L1995;

L1994:
/* #:) Reaching this point means numerical convergence after the i-th */
/*     sweep. */

    *info = 0;
/* #:) INFO = 0 confirms successful iterations. */
L1995:

/*     Sort the singular values and find how many are above */
/*     the underflow threshold. */

    n2 = 0;
    n4 = 0;
    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 = work[p];
            work[p] = work[q];
            work[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);
            }
        }
        if (sva[p] != 0.) {
            ++n4;
            if (sva[p] * scale > sfmin) {
                ++n2;
            }
        }
/* L5991: */
    }
    if (sva[*n] != 0.) {
        ++n4;
        if (sva[*n] * scale > sfmin) {
            ++n2;
        }
    }

/*     Normalize the left singular vectors. */

    if (lsvec || uctol) {
        i__1 = n2;
        for (p = 1; p <= i__1; ++p) {
            d__1 = work[p] / sva[p];
            dscal_(m, &d__1, &a[p * a_dim1 + 1], &c__1);
/* L1998: */
        }
    }

/*     Scale the product of Jacobi rotations (assemble the fast rotations). */

    if (rsvec) {
        if (applv) {
            i__1 = *n;
            for (p = 1; p <= i__1; ++p) {
                dscal_(&mvl, &work[p], &v[p * v_dim1 + 1], &c__1);
/* L2398: */
            }
        } else {
            i__1 = *n;
            for (p = 1; p <= i__1; ++p) {
                temp1 = 1. / dnrm2_(&mvl, &v[p * v_dim1 + 1], &c__1);
                dscal_(&mvl, &temp1, &v[p * v_dim1 + 1], &c__1);
/* L2399: */
            }
        }
    }

/*     Undo scaling, if necessary (and possible). */
    if (scale > 1. && sva[1] < big / scale || scale < 1. && sva[n2] > sfmin / 
            scale) {
        i__1 = *n;
        for (p = 1; p <= i__1; ++p) {
            sva[p] = scale * sva[p];
/* L2400: */
        }
        scale = 1.;
    }

    work[1] = scale;
/*     The singular values of A are SCALE*SVA(1:N). If SCALE.NE.ONE */
/*     then some of the singular values may overflow or underflow and */
/*     the spectrum is given in this factored representation. */

    work[2] = (doublereal) n4;
/*     N4 is the number of computed nonzero singular values of A. */

    work[3] = (doublereal) n2;
/*     N2 is the number of singular values of A greater than SFMIN. */
/*     If N2<N, SVA(N2:N) contains ZEROS and/or denormalized numbers */
/*     that may carry some information. */

    work[4] = (doublereal) i__;
/*     i is the index of the last sweep before declaring convergence. */

    work[5] = mxaapq;
/*     MXAAPQ is the largest absolute value of scaled pivots in the */
/*     last sweep */

    work[6] = mxsinj;
/*     MXSINJ is the largest absolute value of the sines of Jacobi angles */
/*     in the last sweep */

    return 0;
/*     .. */
/*     .. END OF DGESVJ */
/*     .. */
} /* dgesvj_ */