[] add metering mode to CLI

1 files changed, 1159 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dgsvj0.c b/contrib/libs/clapack/dgsvj0.c
new file mode 100644
index 0000000000..c10304ba54
--- /dev/null
+++ b/contrib/libs/clapack/dgsvj0.c
@@ -0,0 +1,1159 @@
+/* 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_ */