/* fortran/dlasd6.f -- translated by f2c (version 20200916).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"

/* Table of constant values */

static integer c__0 = 0;
static doublereal c_b7 = 1.;
static integer c__1 = 1;
static integer c_n1 = -1;

/* > \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o
nes by appending a row. Used by sbdsdc. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download DLASD6 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd6.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */
/*                          IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */
/*                          LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */
/*                          IWORK, INFO ) */

/*       .. Scalar Arguments .. */
/*       INTEGER            GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */
/*      $                   NR, SQRE */
/*       DOUBLE PRECISION   ALPHA, BETA, C, S */
/*       .. */
/*       .. Array Arguments .. */
/*       INTEGER            GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */
/*      $                   PERM( * ) */
/*       DOUBLE PRECISION   D( * ), DIFL( * ), DIFR( * ), */
/*      $                   GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
/*      $                   VF( * ), VL( * ), WORK( * ), Z( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLASD6 computes the SVD of an updated upper bidiagonal matrix B */
/* > obtained by merging two smaller ones by appending a row. This */
/* > routine is used only for the problem which requires all singular */
/* > values and optionally singular vector matrices in factored form. */
/* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
/* > A related subroutine, DLASD1, handles the case in which all singular */
/* > values and singular vectors of the bidiagonal matrix are desired. */
/* > */
/* > DLASD6 computes the SVD as follows: */
/* > */
/* >               ( D1(in)    0    0       0 ) */
/* >   B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in) */
/* >               (   0       0   D2(in)   0 ) */
/* > */
/* >     = U(out) * ( D(out) 0) * VT(out) */
/* > */
/* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */
/* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
/* > elsewhere; and the entry b is empty if SQRE = 0. */
/* > */
/* > The singular values of B can be computed using D1, D2, the first */
/* > components of all the right singular vectors of the lower block, and */
/* > the last components of all the right singular vectors of the upper */
/* > block. These components are stored and updated in VF and VL, */
/* > respectively, in DLASD6. Hence U and VT are not explicitly */
/* > referenced. */
/* > */
/* > The singular values are stored in D. The algorithm consists of two */
/* > stages: */
/* > */
/* >       The first stage consists of deflating the size of the problem */
/* >       when there are multiple singular values or if there is a zero */
/* >       in the Z vector. For each such occurrence the dimension of the */
/* >       secular equation problem is reduced by one. This stage is */
/* >       performed by the routine DLASD7. */
/* > */
/* >       The second stage consists of calculating the updated */
/* >       singular values. This is done by finding the roots of the */
/* >       secular equation via the routine DLASD4 (as called by DLASD8). */
/* >       This routine also updates VF and VL and computes the distances */
/* >       between the updated singular values and the old singular */
/* >       values. */
/* > */
/* > DLASD6 is called from DLASDA. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] ICOMPQ */
/* > \verbatim */
/* >          ICOMPQ is INTEGER */
/* >         Specifies whether singular vectors are to be computed in */
/* >         factored form: */
/* >         = 0: Compute singular values only. */
/* >         = 1: Compute singular vectors in factored form as well. */
/* > \endverbatim */
/* > */
/* > \param[in] NL */
/* > \verbatim */
/* >          NL is INTEGER */
/* >         The row dimension of the upper block.  NL >= 1. */
/* > \endverbatim */
/* > */
/* > \param[in] NR */
/* > \verbatim */
/* >          NR is INTEGER */
/* >         The row dimension of the lower block.  NR >= 1. */
/* > \endverbatim */
/* > */
/* > \param[in] SQRE */
/* > \verbatim */
/* >          SQRE is INTEGER */
/* >         = 0: the lower block is an NR-by-NR square matrix. */
/* >         = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
/* > */
/* >         The bidiagonal matrix has row dimension N = NL + NR + 1, */
/* >         and column dimension M = N + SQRE. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is DOUBLE PRECISION array, dimension ( NL+NR+1 ). */
/* >         On entry D(1:NL,1:NL) contains the singular values of the */
/* >         upper block, and D(NL+2:N) contains the singular values */
/* >         of the lower block. On exit D(1:N) contains the singular */
/* >         values of the modified matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VF */
/* > \verbatim */
/* >          VF is DOUBLE PRECISION array, dimension ( M ) */
/* >         On entry, VF(1:NL+1) contains the first components of all */
/* >         right singular vectors of the upper block; and VF(NL+2:M) */
/* >         contains the first components of all right singular vectors */
/* >         of the lower block. On exit, VF contains the first components */
/* >         of all right singular vectors of the bidiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] VL */
/* > \verbatim */
/* >          VL is DOUBLE PRECISION array, dimension ( M ) */
/* >         On entry, VL(1:NL+1) contains the  last components of all */
/* >         right singular vectors of the upper block; and VL(NL+2:M) */
/* >         contains the last components of all right singular vectors of */
/* >         the lower block. On exit, VL contains the last components of */
/* >         all right singular vectors of the bidiagonal matrix. */
/* > \endverbatim */
/* > */
/* > \param[in,out] ALPHA */
/* > \verbatim */
/* >          ALPHA is DOUBLE PRECISION */
/* >         Contains the diagonal element associated with the added row. */
/* > \endverbatim */
/* > */
/* > \param[in,out] BETA */
/* > \verbatim */
/* >          BETA is DOUBLE PRECISION */
/* >         Contains the off-diagonal element associated with the added */
/* >         row. */
/* > \endverbatim */
/* > */
/* > \param[in,out] IDXQ */
/* > \verbatim */
/* >          IDXQ is INTEGER array, dimension ( N ) */
/* >         This contains the permutation which will reintegrate the */
/* >         subproblem just solved back into sorted order, i.e. */
/* >         D( IDXQ( I = 1, N ) ) will be in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[out] PERM */
/* > \verbatim */
/* >          PERM is INTEGER array, dimension ( N ) */
/* >         The permutations (from deflation and sorting) to be applied */
/* >         to each block. Not referenced if ICOMPQ = 0. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVPTR */
/* > \verbatim */
/* >          GIVPTR is INTEGER */
/* >         The number of Givens rotations which took place in this */
/* >         subproblem. Not referenced if ICOMPQ = 0. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVCOL */
/* > \verbatim */
/* >          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
/* >         Each pair of numbers indicates a pair of columns to take place */
/* >         in a Givens rotation. Not referenced if ICOMPQ = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGCOL */
/* > \verbatim */
/* >          LDGCOL is INTEGER */
/* >         leading dimension of GIVCOL, must be at least N. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVNUM */
/* > \verbatim */
/* >          GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
/* >         Each number indicates the C or S value to be used in the */
/* >         corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGNUM */
/* > \verbatim */
/* >          LDGNUM is INTEGER */
/* >         The leading dimension of GIVNUM and POLES, must be at least N. */
/* > \endverbatim */
/* > */
/* > \param[out] POLES */
/* > \verbatim */
/* >          POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
/* >         On exit, POLES(1,*) is an array containing the new singular */
/* >         values obtained from solving the secular equation, and */
/* >         POLES(2,*) is an array containing the poles in the secular */
/* >         equation. Not referenced if ICOMPQ = 0. */
/* > \endverbatim */
/* > */
/* > \param[out] DIFL */
/* > \verbatim */
/* >          DIFL is DOUBLE PRECISION array, dimension ( N ) */
/* >         On exit, DIFL(I) is the distance between I-th updated */
/* >         (undeflated) singular value and the I-th (undeflated) old */
/* >         singular value. */
/* > \endverbatim */
/* > */
/* > \param[out] DIFR */
/* > \verbatim */
/* >          DIFR is DOUBLE PRECISION array, */
/* >                   dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */
/* >                   dimension ( K ) if ICOMPQ = 0. */
/* >          On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */
/* >          defined and will not be referenced. */
/* > */
/* >          If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
/* >          normalizing factors for the right singular vector matrix. */
/* > */
/* >         See DLASD8 for details on DIFL and DIFR. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION array, dimension ( M ) */
/* >         The first elements of this array contain the components */
/* >         of the deflation-adjusted updating row vector. */
/* > \endverbatim */
/* > */
/* > \param[out] K */
/* > \verbatim */
/* >          K is INTEGER */
/* >         Contains the dimension of the non-deflated matrix, */
/* >         This is the order of the related secular equation. 1 <= K <=N. */
/* > \endverbatim */
/* > */
/* > \param[out] C */
/* > \verbatim */
/* >          C is DOUBLE PRECISION */
/* >         C contains garbage if SQRE =0 and the C-value of a Givens */
/* >         rotation related to the right null space if SQRE = 1. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* >          S is DOUBLE PRECISION */
/* >         S contains garbage if SQRE =0 and the S-value of a Givens */
/* >         rotation related to the right null space if SQRE = 1. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension ( 4 * M ) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension ( 3 * N ) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit. */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* >          > 0:  if INFO = 1, a singular value did not converge */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Huan Ren, Computer Science Division, University of */
/* >     California at Berkeley, USA */
/* > */
/*  ===================================================================== */
/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr,
        integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl,
        doublereal *alpha, doublereal *beta, integer *idxq, integer *perm,
        integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
         integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
        difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s,
        doublereal *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
            poles_dim1, poles_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
            doublereal *, integer *), dlasd7_(integer *, integer *, integer *,
             integer *, integer *, doublereal *, doublereal *, doublereal *,
            doublereal *, doublereal *, doublereal *, doublereal *,
            doublereal *, doublereal *, doublereal *, integer *, integer *,
            integer *, integer *, integer *, integer *, integer *, doublereal
            *, integer *, doublereal *, doublereal *, integer *), dlasd8_(
            integer *, integer *, doublereal *, doublereal *, doublereal *,
            doublereal *, doublereal *, doublereal *, integer *, doublereal *,
             doublereal *, integer *), dlascl_(char *, integer *, integer *,
            doublereal *, doublereal *, integer *, integer *, doublereal *,
            integer *, integer *, ftnlen), dlamrg_(integer *, integer *,
            doublereal *, integer *, integer *, integer *);
    integer isigma;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    doublereal orgnrm;


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

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --vf;
    --vl;
    --idxq;
    --perm;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1;
    givcol -= givcol_offset;
    poles_dim1 = *ldgnum;
    poles_offset = 1 + poles_dim1;
    poles -= poles_offset;
    givnum_dim1 = *ldgnum;
    givnum_offset = 1 + givnum_dim1;
    givnum -= givnum_offset;
    --difl;
    --difr;
    --z__;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    n = *nl + *nr + 1;
    m = n + *sqre;

    if (*icompq < 0 || *icompq > 1) {
        *info = -1;
    } else if (*nl < 1) {
        *info = -2;
    } else if (*nr < 1) {
        *info = -3;
    } else if (*sqre < 0 || *sqre > 1) {
        *info = -4;
    } else if (*ldgcol < n) {
        *info = -14;
    } else if (*ldgnum < n) {
        *info = -16;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_((char *)"DLASD6", &i__1, (ftnlen)6);
        return 0;
    }

/*     The following values are for bookkeeping purposes only.  They are */
/*     integer pointers which indicate the portion of the workspace */
/*     used by a particular array in DLASD7 and DLASD8. */

    isigma = 1;
    iw = isigma + n;
    ivfw = iw + m;
    ivlw = ivfw + m;

    idx = 1;
    idxc = idx + n;
    idxp = idxc + n;

/*     Scale. */

/* Computing MAX */
    d__1 = abs(*alpha), d__2 = abs(*beta);
    orgnrm = max(d__1,d__2);
    d__[*nl + 1] = 0.;
    i__1 = n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
            orgnrm = (d__1 = d__[i__], abs(d__1));
        }
/* L10: */
    }
    dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, (
            ftnlen)1);
    *alpha /= orgnrm;
    *beta /= orgnrm;

/*     Sort and Deflate singular values. */

    dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
            work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
            iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
            givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
            info);

/*     Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */

    dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
            ldgnum, &work[isigma], &work[iw], info);

/*     Report the possible convergence failure. */

    if (*info != 0) {
        return 0;
    }

/*     Save the poles if ICOMPQ = 1. */

    if (*icompq == 1) {
        dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
        dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
    }

/*     Unscale. */

    dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, (
            ftnlen)1);

/*     Prepare the IDXQ sorting permutation. */

    n1 = *k;
    n2 = n - *k;
    dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);

    return 0;

/*     End of DLASD6 */

} /* dlasd6_ */

#ifdef __cplusplus
        }
#endif