/* fortran/dlals0.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 doublereal c_b5 = -1.;
static integer c__1 = 1;
static doublereal c_b11 = 1.;
static doublereal c_b13 = 0.;
static integer c__0 = 0;

/* > \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and c
onquer SVD approach. Used by sgelsd. */

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

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

/* > \htmlonly */
/* > Download DLALS0 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlals0.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlals0.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlals0.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */
/*                          PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */
/*                          POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */

/*       .. Scalar Arguments .. */
/*       INTEGER            GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */
/*      $                   LDGNUM, NL, NR, NRHS, SQRE */
/*       DOUBLE PRECISION   C, S */
/*       .. */
/*       .. Array Arguments .. */
/*       INTEGER            GIVCOL( LDGCOL, * ), PERM( * ) */
/*       DOUBLE PRECISION   B( LDB, * ), BX( LDBX, * ), DIFL( * ), */
/*      $                   DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */
/*      $                   POLES( LDGNUM, * ), WORK( * ), Z( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLALS0 applies back the multiplying factors of either the left or the */
/* > right singular vector matrix of a diagonal matrix appended by a row */
/* > to the right hand side matrix B in solving the least squares problem */
/* > using the divide-and-conquer SVD approach. */
/* > */
/* > For the left singular vector matrix, three types of orthogonal */
/* > matrices are involved: */
/* > */
/* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */
/* >      pairs of columns/rows they were applied to are stored in GIVCOL; */
/* >      and the C- and S-values of these rotations are stored in GIVNUM. */
/* > */
/* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
/* >      row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
/* >      J-th row. */
/* > */
/* > (3L) The left singular vector matrix of the remaining matrix. */
/* > */
/* > For the right singular vector matrix, four types of orthogonal */
/* > matrices are involved: */
/* > */
/* > (1R) The right singular vector matrix of the remaining matrix. */
/* > */
/* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */
/* >      null space. */
/* > */
/* > (3R) The inverse transformation of (2L). */
/* > */
/* > (4R) The inverse transformation of (1L). */
/* > \endverbatim */

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

/* > \param[in] ICOMPQ */
/* > \verbatim */
/* >          ICOMPQ is INTEGER */
/* >         Specifies whether singular vectors are to be computed in */
/* >         factored form: */
/* >         = 0: Left singular vector matrix. */
/* >         = 1: Right singular vector matrix. */
/* > \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] NRHS */
/* > \verbatim */
/* >          NRHS is INTEGER */
/* >         The number of columns of B and BX. NRHS must be at least 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */
/* >         On input, B contains the right hand sides of the least */
/* >         squares problem in rows 1 through M. On output, B contains */
/* >         the solution X in rows 1 through N. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >         The leading dimension of B. LDB must be at least */
/* >         max(1,MAX( M, N ) ). */
/* > \endverbatim */
/* > */
/* > \param[out] BX */
/* > \verbatim */
/* >          BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
/* > \endverbatim */
/* > */
/* > \param[in] LDBX */
/* > \verbatim */
/* >          LDBX is INTEGER */
/* >         The leading dimension of BX. */
/* > \endverbatim */
/* > */
/* > \param[in] PERM */
/* > \verbatim */
/* >          PERM is INTEGER array, dimension ( N ) */
/* >         The permutations (from deflation and sorting) applied */
/* >         to the two blocks. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVPTR */
/* > \verbatim */
/* >          GIVPTR is INTEGER */
/* >         The number of Givens rotations which took place in this */
/* >         subproblem. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVCOL */
/* > \verbatim */
/* >          GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
/* >         Each pair of numbers indicates a pair of rows/columns */
/* >         involved in a Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGCOL */
/* > \verbatim */
/* >          LDGCOL is INTEGER */
/* >         The leading dimension of GIVCOL, must be at least N. */
/* > \endverbatim */
/* > */
/* > \param[in] GIVNUM */
/* > \verbatim */
/* >          GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
/* >         Each number indicates the C or S value used in the */
/* >         corresponding Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGNUM */
/* > \verbatim */
/* >          LDGNUM is INTEGER */
/* >         The leading dimension of arrays DIFR, POLES and */
/* >         GIVNUM, must be at least K. */
/* > \endverbatim */
/* > */
/* > \param[in] POLES */
/* > \verbatim */
/* >          POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
/* >         On entry, POLES(1:K, 1) contains the new singular */
/* >         values obtained from solving the secular equation, and */
/* >         POLES(1:K, 2) is an array containing the poles in the secular */
/* >         equation. */
/* > \endverbatim */
/* > */
/* > \param[in] DIFL */
/* > \verbatim */
/* >          DIFL is DOUBLE PRECISION array, dimension ( K ). */
/* >         On entry, DIFL(I) is the distance between I-th updated */
/* >         (undeflated) singular value and the I-th (undeflated) old */
/* >         singular value. */
/* > \endverbatim */
/* > */
/* > \param[in] DIFR */
/* > \verbatim */
/* >          DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */
/* >         On entry, DIFR(I, 1) contains the distances between I-th */
/* >         updated (undeflated) singular value and the I+1-th */
/* >         (undeflated) old singular value. And DIFR(I, 2) is the */
/* >         normalizing factor for the I-th right singular vector. */
/* > \endverbatim */
/* > */
/* > \param[in] Z */
/* > \verbatim */
/* >          Z is DOUBLE PRECISION array, dimension ( K ) */
/* >         Contain the components of the deflation-adjusted updating row */
/* >         vector. */
/* > \endverbatim */
/* > */
/* > \param[in] 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[in] 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[in] 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 ( K ) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit. */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* > \endverbatim */

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

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

/* > \ingroup doubleOTHERcomputational */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/* >       California at Berkeley, USA \n */
/* >     Osni Marques, LBNL/NERSC, USA \n */

/*  ===================================================================== */
/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr,
        integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal
        *bx, integer *ldbx, 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 *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset,
            difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1,
            poles_offset, i__1, i__2;
    doublereal d__1;

    /* Local variables */
    integer i__, j, m, n;
    doublereal dj;
    integer nlp1;
    doublereal temp;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
            doublereal *, integer *, doublereal *, doublereal *);
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
            integer *);
    doublereal diflj, difrj, dsigj;
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
            doublereal *, doublereal *, integer *, doublereal *, integer *,
            doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *,
            doublereal *, integer *, doublereal *, integer *);
    extern doublereal dlamc3_(doublereal *, doublereal *);
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
            doublereal *, doublereal *, integer *, integer *, doublereal *,
            integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer
            *, doublereal *, integer *, doublereal *, integer *, ftnlen),
            xerbla_(char *, integer *, ftnlen);
    doublereal dsigjp;


/*  -- LAPACK computational 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 .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    bx_dim1 = *ldbx;
    bx_offset = 1 + bx_dim1;
    bx -= bx_offset;
    --perm;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1;
    givcol -= givcol_offset;
    difr_dim1 = *ldgnum;
    difr_offset = 1 + difr_dim1;
    difr -= difr_offset;
    poles_dim1 = *ldgnum;
    poles_offset = 1 + poles_dim1;
    poles -= poles_offset;
    givnum_dim1 = *ldgnum;
    givnum_offset = 1 + givnum_dim1;
    givnum -= givnum_offset;
    --difl;
    --z__;
    --work;

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

    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 (*nrhs < 1) {
        *info = -5;
    } else if (*ldb < n) {
        *info = -7;
    } else if (*ldbx < n) {
        *info = -9;
    } else if (*givptr < 0) {
        *info = -11;
    } else if (*ldgcol < n) {
        *info = -13;
    } else if (*ldgnum < n) {
        *info = -15;
    } else if (*k < 1) {
        *info = -20;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_((char *)"DLALS0", &i__1, (ftnlen)6);
        return 0;
    }

    m = n + *sqre;
    nlp1 = *nl + 1;

    if (*icompq == 0) {

/*        Apply back orthogonal transformations from the left. */

/*        Step (1L): apply back the Givens rotations performed. */

        i__1 = *givptr;
        for (i__ = 1; i__ <= i__1; ++i__) {
            drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
                    b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
                    (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
/* L10: */
        }

/*        Step (2L): permute rows of B. */

        dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
        i__1 = n;
        for (i__ = 2; i__ <= i__1; ++i__) {
            dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
                    ldbx);
/* L20: */
        }

/*        Step (3L): apply the inverse of the left singular vector */
/*        matrix to BX. */

        if (*k == 1) {
            dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
            if (z__[1] < 0.) {
                dscal_(nrhs, &c_b5, &b[b_offset], ldb);
            }
        } else {
            i__1 = *k;
            for (j = 1; j <= i__1; ++j) {
                diflj = difl[j];
                dj = poles[j + poles_dim1];
                dsigj = -poles[j + (poles_dim1 << 1)];
                if (j < *k) {
                    difrj = -difr[j + difr_dim1];
                    dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
                }
                if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) {
                    work[j] = 0.;
                } else {
                    work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
                             (poles[j + (poles_dim1 << 1)] + dj);
                }
                i__2 = j - 1;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
                            0.) {
                        work[i__] = 0.;
                    } else {
                        work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
                                / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
                                dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
                                1)] + dj);
                    }
/* L30: */
                }
                i__2 = *k;
                for (i__ = j + 1; i__ <= i__2; ++i__) {
                    if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
                            0.) {
                        work[i__] = 0.;
                    } else {
                        work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
                                / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
                                dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
                                 1)] + dj);
                    }
/* L40: */
                }
                work[1] = -1.;
                temp = dnrm2_(k, &work[1], &c__1);
                dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
                        c__1, &c_b13, &b[j + b_dim1], ldb, (ftnlen)1);
                dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j +
                        b_dim1], ldb, info, (ftnlen)1);
/* L50: */
            }
        }

/*        Move the deflated rows of BX to B also. */

        if (*k < max(m,n)) {
            i__1 = n - *k;
            dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
                    + b_dim1], ldb, (ftnlen)1);
        }
    } else {

/*        Apply back the right orthogonal transformations. */

/*        Step (1R): apply back the new right singular vector matrix */
/*        to B. */

        if (*k == 1) {
            dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
        } else {
            i__1 = *k;
            for (j = 1; j <= i__1; ++j) {
                dsigj = poles[j + (poles_dim1 << 1)];
                if (z__[j] == 0.) {
                    work[j] = 0.;
                } else {
                    work[j] = -z__[j] / difl[j] / (dsigj + poles[j +
                            poles_dim1]) / difr[j + (difr_dim1 << 1)];
                }
                i__2 = j - 1;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    if (z__[j] == 0.) {
                        work[i__] = 0.;
                    } else {
                        d__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
                        work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
                                i__ + difr_dim1]) / (dsigj + poles[i__ +
                                poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
                    }
/* L60: */
                }
                i__2 = *k;
                for (i__ = j + 1; i__ <= i__2; ++i__) {
                    if (z__[j] == 0.) {
                        work[i__] = 0.;
                    } else {
                        d__1 = -poles[i__ + (poles_dim1 << 1)];
                        work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
                                i__]) / (dsigj + poles[i__ + poles_dim1]) /
                                difr[i__ + (difr_dim1 << 1)];
                    }
/* L70: */
                }
                dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
                        c__1, &c_b13, &bx[j + bx_dim1], ldbx, (ftnlen)1);
/* L80: */
            }
        }

/*        Step (2R): if SQRE = 1, apply back the rotation that is */
/*        related to the right null space of the subproblem. */

        if (*sqre == 1) {
            dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
            drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
                    s);
        }
        if (*k < max(m,n)) {
            i__1 = n - *k;
            dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
                    bx_dim1], ldbx, (ftnlen)1);
        }

/*        Step (3R): permute rows of B. */

        dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
        if (*sqre == 1) {
            dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
        }
        i__1 = n;
        for (i__ = 2; i__ <= i__1; ++i__) {
            dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
                    ldb);
/* L90: */
        }

/*        Step (4R): apply back the Givens rotations performed. */

        for (i__ = *givptr; i__ >= 1; --i__) {
            d__1 = -givnum[i__ + givnum_dim1];
            drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
                    b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
                    (givnum_dim1 << 1)], &d__1);
/* L100: */
        }
    }

    return 0;

/*     End of DLALS0 */

} /* dlals0_ */

#ifdef __cplusplus
        }
#endif