starpu-max/min-dgels/base/SRC/dgsvj0.c

/* dgsvj0.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_b42 = 1.;

/* Subroutine */ int dgsvj0_(char *jobv, integer *m, integer *n, 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 ir1, jbc;
    doublereal big;
    integer kbl, igl, ibr, jgl, nbl, mvl;
    doublereal aapp, aapq, aaqq;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    integer ierr;
    doublereal aapp0;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal temp1, 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, lkahead;
    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 */
/*  ~~~~~~~ */
/*  DGSVJ0 is called from DGESVJ as a pre-processor and that is its main */
/*  purpose. It applies Jacobi rotations in the same way as DGESVJ does, but */
/*  it does not check convergence (stopping criterion). Few tuning */
/*  parameters (marked by [TP]) are available for the implementer. */

/*  Further details */
/*  ~~~~~~~~~~~~~~~ */
/*  DGSVJ0 is used just to enable SGESVJ to call a simplified version of */
/*  itself to work on a submatrix of the original matrix. */

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

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

/*  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. */

/*  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 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 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 (*lda < *m) {
	*info = -5;
    } else if (*mv < 0) {
	*info = -8;
    } else if (*ldv < *m) {
	*info = -10;
    } else if (*tol <= *eps) {
	*info = -13;
    } else if (*nsweep < 0) {
	*info = -14;
    } else if (*lwork < *m) {
	*info = -16;
    } else {
	*info = 0;
    }

/*     #:( */
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DGSVJ0", &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;
    bigtheta = 1. / rooteps;
    roottol = sqrt(*tol);


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

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

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

    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. For sweeps i=1:SWBAND the procedure */
/*     ...... */
    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 + 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. */
    swband = 0;
    pskipped = 0;

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

/* Computing MIN */
	    i__4 = lkahead, i__5 = nbl - ibr;
	    i__3 = min(i__4,i__5);
	    for (ir1 = 0; ir1 <= i__3; ++ir1) {

		igl += ir1 * kbl;

/* Computing MIN */
		i__5 = igl + kbl - 1, i__6 = *n - 1;
		i__4 = min(i__5,i__6);
		for (p = igl; p <= i__4; ++p) {
/*     .. de Rijk's pivoting */
		    i__5 = *n - p + 1;
		    q = idamax_(&i__5, &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 = d__[p];
			d__[p] = d__[q];
			d__[q] = temp1;
		    }

		    if (ir1 == 0) {

/*        Column norms are periodically updated by explicit */
/*        norm computation. */
/*        Caveat: */
/*        Some BLAS implementations compute DNRM2(M,A(1,p),1) */
/*        as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may result in */
/*        overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and */
/*        undeflow 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 ) * D(p)". */

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

		    if (aapp > 0.) {

			pskipped = 0;

/* Computing MIN */
			i__6 = igl + kbl - 1;
			i__5 = min(i__6,*n);
			for (q = p + 1; q <= i__5; ++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) * 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 {
				    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) * 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) {

/*           .. rotate */
/*           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 * 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)));
					    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_b42, &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 = 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);
			      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 {
			  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);
			      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 (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 {
/*              .. have to use modified Gram-Schmidt like transformation */
					dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
						work[1], &c__1);
					dlascl_("G", &c__0, &c__0, &aapp, &
						c_b42, m, &c__1, &work[1], 
						lda, &ierr);
					dlascl_("G", &c__0, &c__0, &aaqq, &
						c_b42, 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_b42, &
						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) * 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];
					}
				    }
				    if (aapp / aapp0 <= 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;
				    }

				} else {
/*        A(:,p) and A(:,q) already numerically orthogonal */
				    if (ir1 == 0) {
					++notrot;
				    }
				    ++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__5 = igl + kbl - 1;
			    notrot = notrot + min(i__5,*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__3 = nbl;
	    for (jbc = ibr + 1; jbc <= i__3; ++jbc) {

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

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

		ijblsk = 0;
/* Computing MIN */
		i__5 = igl + kbl - 1;
		i__4 = min(i__5,*n);
		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_b42, &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_b42, m, &c__1, &work[1]
, lda, &ierr);
					    dlascl_("G", &c__0, &c__0, &aaqq, 
						    &c_b42, 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_b42, 
						     &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_b42, m, &c__1, &work[1]
, lda, &ierr);
					    dlascl_("G", &c__0, &c__0, &aapp, 
						    &c_b42, 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_b42, 
						     &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;
				    ++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__5 = jgl + kbl - 1;
			    notrot = notrot + min(i__5,*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__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: */
	    }

/* 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 comleted the given */
/*     number of iterations. */
    *info = *nsweep - 1;
    goto L1995;
L1994:
/* #:) Reaching this point means that during the i-th sweep all pivots were */
/*     below the given tolerance, 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 DGSVJ0 */
/*     .. */
} /* dgsvj0_ */