zlalsa.c

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/* zlalsa.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static doublereal c_b9 = 1.;
static doublereal c_b10 = 0.;
static integer c__2 = 2;

/* Subroutine */ int zlalsa_(integer *icompq, integer *smlsiz, integer *n, 
        integer *nrhs, doublecomplex *b, integer *ldb, doublecomplex *bx, 
        integer *ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *
        k, doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
        poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
        perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
        rwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, 
            difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, 
            poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, 
            z_dim1, z_offset, b_dim1, b_offset, bx_dim1, bx_offset, i__1, 
            i__2, i__3, i__4, i__5, i__6;
    doublecomplex z__1;

    /* Builtin functions */
    double d_imag(doublecomplex *);
    integer pow_ii(integer *, integer *);

    /* Local variables */
    integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, 
            nlp1, lvl2, nrp1, jcol, nlvl, sqre, jrow, jimag;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *);
    integer jreal, inode, ndiml, ndimr;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zlals0_(integer *, integer *, 
            integer *, integer *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, integer *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            doublereal *, doublereal *, integer *, doublereal *, doublereal *, 
             doublereal *, integer *), dlasdt_(integer *, integer *, integer *
, integer *, integer *, integer *, integer *), xerbla_(char *, 
            integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

/*  Purpose */
/*  ======= */

/*  ZLALSA is an itermediate step in solving the least squares problem */
/*  by computing the SVD of the coefficient matrix in compact form (The */
/*  singular vectors are computed as products of simple orthorgonal */
/*  matrices.). */

/*  If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector */
/*  matrix of an upper bidiagonal matrix to the right hand side; and if */
/*  ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the */
/*  right hand side. The singular vector matrices were generated in */
/*  compact form by ZLALSA. */

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

/*  ICOMPQ (input) INTEGER */
/*         Specifies whether the left or the right singular vector */
/*         matrix is involved. */
/*         = 0: Left singular vector matrix */
/*         = 1: Right singular vector matrix */

/*  SMLSIZ (input) INTEGER */
/*         The maximum size of the subproblems at the bottom of the */
/*         computation tree. */

/*  N      (input) INTEGER */
/*         The row and column dimensions of the upper bidiagonal matrix. */

/*  NRHS   (input) INTEGER */
/*         The number of columns of B and BX. NRHS must be at least 1. */

/*  B      (input/output) COMPLEX*16 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. */

/*  LDB    (input) INTEGER */
/*         The leading dimension of B in the calling subprogram. */
/*         LDB must be at least max(1,MAX( M, N ) ). */

/*  BX     (output) COMPLEX*16 array, dimension ( LDBX, NRHS ) */
/*         On exit, the result of applying the left or right singular */
/*         vector matrix to B. */

/*  LDBX   (input) INTEGER */
/*         The leading dimension of BX. */

/*  U      (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). */
/*         On entry, U contains the left singular vector matrices of all */
/*         subproblems at the bottom level. */

/*  LDU    (input) INTEGER, LDU = > N. */
/*         The leading dimension of arrays U, VT, DIFL, DIFR, */
/*         POLES, GIVNUM, and Z. */

/*  VT     (input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). */
/*         On entry, VT' contains the right singular vector matrices of */
/*         all subproblems at the bottom level. */

/*  K      (input) INTEGER array, dimension ( N ). */

/*  DIFL   (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
/*         where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */

/*  DIFR   (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
/*         On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */
/*         distances between singular values on the I-th level and */
/*         singular values on the (I -1)-th level, and DIFR(*, 2 * I) */
/*         record the normalizing factors of the right singular vectors */
/*         matrices of subproblems on I-th level. */

/*  Z      (input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
/*         On entry, Z(1, I) contains the components of the deflation- */
/*         adjusted updating row vector for subproblems on the I-th */
/*         level. */

/*  POLES  (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
/*         On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */
/*         singular values involved in the secular equations on the I-th */
/*         level. */

/*  GIVPTR (input) INTEGER array, dimension ( N ). */
/*         On entry, GIVPTR( I ) records the number of Givens */
/*         rotations performed on the I-th problem on the computation */
/*         tree. */

/*  GIVCOL (input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */
/*         On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */
/*         locations of Givens rotations performed on the I-th level on */
/*         the computation tree. */

/*  LDGCOL (input) INTEGER, LDGCOL = > N. */
/*         The leading dimension of arrays GIVCOL and PERM. */

/*  PERM   (input) INTEGER array, dimension ( LDGCOL, NLVL ). */
/*         On entry, PERM(*, I) records permutations done on the I-th */
/*         level of the computation tree. */

/*  GIVNUM (input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
/*         On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */
/*         values of Givens rotations performed on the I-th level on the */
/*         computation tree. */

/*  C      (input) DOUBLE PRECISION array, dimension ( N ). */
/*         On entry, if the I-th subproblem is not square, */
/*         C( I ) contains the C-value of a Givens rotation related to */
/*         the right null space of the I-th subproblem. */

/*  S      (input) DOUBLE PRECISION array, dimension ( N ). */
/*         On entry, if the I-th subproblem is not square, */
/*         S( I ) contains the S-value of a Givens rotation related to */
/*         the right null space of the I-th subproblem. */

/*  RWORK  (workspace) DOUBLE PRECISION array, dimension at least */
/*         max ( N, (SMLSZ+1)*NRHS*3 ). */

/*  IWORK  (workspace) INTEGER array. */
/*         The dimension must be at least 3 * N */

/*  INFO   (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Ming Gu and Ren-Cang Li, Computer Science Division, University of */
/*       California at Berkeley, USA */
/*     Osni Marques, LBNL/NERSC, USA */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. 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;
    givnum_dim1 = *ldu;
    givnum_offset = 1 + givnum_dim1;
    givnum -= givnum_offset;
    poles_dim1 = *ldu;
    poles_offset = 1 + poles_dim1;
    poles -= poles_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    difr_dim1 = *ldu;
    difr_offset = 1 + difr_dim1;
    difr -= difr_offset;
    difl_dim1 = *ldu;
    difl_offset = 1 + difl_dim1;
    difl -= difl_offset;
    vt_dim1 = *ldu;
    vt_offset = 1 + vt_dim1;
    vt -= vt_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    --k;
    --givptr;
    perm_dim1 = *ldgcol;
    perm_offset = 1 + perm_dim1;
    perm -= perm_offset;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1;
    givcol -= givcol_offset;
    --c__;
    --s;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
        *info = -1;
    } else if (*smlsiz < 3) {
        *info = -2;
    } else if (*n < *smlsiz) {
        *info = -3;
    } else if (*nrhs < 1) {
        *info = -4;
    } else if (*ldb < *n) {
        *info = -6;
    } else if (*ldbx < *n) {
        *info = -8;
    } else if (*ldu < *n) {
        *info = -10;
    } else if (*ldgcol < *n) {
        *info = -19;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZLALSA", &i__1);
        return 0;
    }

/*     Book-keeping and  setting up the computation tree. */

    inode = 1;
    ndiml = inode + *n;
    ndimr = ndiml + *n;

    dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 
            smlsiz);

/*     The following code applies back the left singular vector factors. */
/*     For applying back the right singular vector factors, go to 170. */

    if (*icompq == 1) {
        goto L170;
    }

/*     The nodes on the bottom level of the tree were solved */
/*     by DLASDQ. The corresponding left and right singular vector */
/*     matrices are in explicit form. First apply back the left */
/*     singular vector matrices. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node */
/*        NL : number of rows of left  subproblem */
/*        NR : number of rows of right subproblem */
/*        NLF: starting row of the left   subproblem */
/*        NRF: starting row of the right  subproblem */

        i1 = i__ - 1;
        ic = iwork[inode + i1];
        nl = iwork[ndiml + i1];
        nr = iwork[ndimr + i1];
        nlf = ic - nl;
        nrf = ic + 1;

/*        Since B and BX are complex, the following call to DGEMM */
/*        is performed in two steps (real and imaginary parts). */

/*        CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU, */
/*     $               B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */

        j = nl * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nl - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++j;
                i__4 = jrow + jcol * b_dim1;
                rwork[j] = b[i__4].r;
/* L10: */
            }
/* L20: */
        }
        dgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u[nlf + u_dim1], ldu, &rwork[
                (nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[1], &nl);
        j = nl * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nl - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++j;
                rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L30: */
            }
/* L40: */
        }
        dgemm_("T", "N", &nl, nrhs, &nl, &c_b9, &u[nlf + u_dim1], ldu, &rwork[
                (nl * *nrhs << 1) + 1], &nl, &c_b10, &rwork[nl * *nrhs + 1], &
                nl);
        jreal = 0;
        jimag = nl * *nrhs;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nl - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++jreal;
                ++jimag;
                i__4 = jrow + jcol * bx_dim1;
                i__5 = jreal;
                i__6 = jimag;
                z__1.r = rwork[i__5], z__1.i = rwork[i__6];
                bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L50: */
            }
/* L60: */
        }

/*        Since B and BX are complex, the following call to DGEMM */
/*        is performed in two steps (real and imaginary parts). */

/*        CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU, */
/*    $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */

        j = nr * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nr - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++j;
                i__4 = jrow + jcol * b_dim1;
                rwork[j] = b[i__4].r;
/* L70: */
            }
/* L80: */
        }
        dgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u[nrf + u_dim1], ldu, &rwork[
                (nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[1], &nr);
        j = nr * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nr - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++j;
                rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L90: */
            }
/* L100: */
        }
        dgemm_("T", "N", &nr, nrhs, &nr, &c_b9, &u[nrf + u_dim1], ldu, &rwork[
                (nr * *nrhs << 1) + 1], &nr, &c_b10, &rwork[nr * *nrhs + 1], &
                nr);
        jreal = 0;
        jimag = nr * *nrhs;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nr - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++jreal;
                ++jimag;
                i__4 = jrow + jcol * bx_dim1;
                i__5 = jreal;
                i__6 = jimag;
                z__1.r = rwork[i__5], z__1.i = rwork[i__6];
                bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L110: */
            }
/* L120: */
        }

/* L130: */
    }

/*     Next copy the rows of B that correspond to unchanged rows */
/*     in the bidiagonal matrix to BX. */

    i__1 = nd;
    for (i__ = 1; i__ <= i__1; ++i__) {
        ic = iwork[inode + i__ - 1];
        zcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx);
/* L140: */
    }

/*     Finally go through the left singular vector matrices of all */
/*     the other subproblems bottom-up on the tree. */

    j = pow_ii(&c__2, &nlvl);
    sqre = 0;

    for (lvl = nlvl; lvl >= 1; --lvl) {
        lvl2 = (lvl << 1) - 1;

/*        find the first node LF and last node LL on */
/*        the current level LVL */

        if (lvl == 1) {
            lf = 1;
            ll = 1;
        } else {
            i__1 = lvl - 1;
            lf = pow_ii(&c__2, &i__1);
            ll = (lf << 1) - 1;
        }
        i__1 = ll;
        for (i__ = lf; i__ <= i__1; ++i__) {
            im1 = i__ - 1;
            ic = iwork[inode + im1];
            nl = iwork[ndiml + im1];
            nr = iwork[ndimr + im1];
            nlf = ic - nl;
            nrf = ic + 1;
            --j;
            zlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &
                    b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], &
                    givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
                    givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
                     poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + 
                    lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
                    j], &s[j], &rwork[1], info);
/* L150: */
        }
/* L160: */
    }
    goto L330;

/*     ICOMPQ = 1: applying back the right singular vector factors. */

L170:

/*     First now go through the right singular vector matrices of all */
/*     the tree nodes top-down. */

    j = 0;
    i__1 = nlvl;
    for (lvl = 1; lvl <= i__1; ++lvl) {
        lvl2 = (lvl << 1) - 1;

/*        Find the first node LF and last node LL on */
/*        the current level LVL. */

        if (lvl == 1) {
            lf = 1;
            ll = 1;
        } else {
            i__2 = lvl - 1;
            lf = pow_ii(&c__2, &i__2);
            ll = (lf << 1) - 1;
        }
        i__2 = lf;
        for (i__ = ll; i__ >= i__2; --i__) {
            im1 = i__ - 1;
            ic = iwork[inode + im1];
            nl = iwork[ndiml + im1];
            nr = iwork[ndimr + im1];
            nlf = ic - nl;
            nrf = ic + 1;
            if (i__ == ll) {
                sqre = 0;
            } else {
                sqre = 1;
            }
            ++j;
            zlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[
                    nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], &
                    givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
                    givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
                     poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + 
                    lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
                    j], &s[j], &rwork[1], info);
/* L180: */
        }
/* L190: */
    }

/*     The nodes on the bottom level of the tree were solved */
/*     by DLASDQ. The corresponding right singular vector */
/*     matrices are in explicit form. Apply them back. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {
        i1 = i__ - 1;
        ic = iwork[inode + i1];
        nl = iwork[ndiml + i1];
        nr = iwork[ndimr + i1];
        nlp1 = nl + 1;
        if (i__ == nd) {
            nrp1 = nr;
        } else {
            nrp1 = nr + 1;
        }
        nlf = ic - nl;
        nrf = ic + 1;

/*        Since B and BX are complex, the following call to DGEMM is */
/*        performed in two steps (real and imaginary parts). */

/*        CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU, */
/*    $               B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) */

        j = nlp1 * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nlp1 - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++j;
                i__4 = jrow + jcol * b_dim1;
                rwork[j] = b[i__4].r;
/* L200: */
            }
/* L210: */
        }
        dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt[nlf + vt_dim1], ldu, &
                rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[1], &
                nlp1);
        j = nlp1 * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nlp1 - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++j;
                rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L220: */
            }
/* L230: */
        }
        dgemm_("T", "N", &nlp1, nrhs, &nlp1, &c_b9, &vt[nlf + vt_dim1], ldu, &
                rwork[(nlp1 * *nrhs << 1) + 1], &nlp1, &c_b10, &rwork[nlp1 * *
                nrhs + 1], &nlp1);
        jreal = 0;
        jimag = nlp1 * *nrhs;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nlf + nlp1 - 1;
            for (jrow = nlf; jrow <= i__3; ++jrow) {
                ++jreal;
                ++jimag;
                i__4 = jrow + jcol * bx_dim1;
                i__5 = jreal;
                i__6 = jimag;
                z__1.r = rwork[i__5], z__1.i = rwork[i__6];
                bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L240: */
            }
/* L250: */
        }

/*        Since B and BX are complex, the following call to DGEMM is */
/*        performed in two steps (real and imaginary parts). */

/*        CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU, */
/*    $               B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) */

        j = nrp1 * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nrp1 - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++j;
                i__4 = jrow + jcol * b_dim1;
                rwork[j] = b[i__4].r;
/* L260: */
            }
/* L270: */
        }
        dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt[nrf + vt_dim1], ldu, &
                rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[1], &
                nrp1);
        j = nrp1 * *nrhs << 1;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nrp1 - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++j;
                rwork[j] = d_imag(&b[jrow + jcol * b_dim1]);
/* L280: */
            }
/* L290: */
        }
        dgemm_("T", "N", &nrp1, nrhs, &nrp1, &c_b9, &vt[nrf + vt_dim1], ldu, &
                rwork[(nrp1 * *nrhs << 1) + 1], &nrp1, &c_b10, &rwork[nrp1 * *
                nrhs + 1], &nrp1);
        jreal = 0;
        jimag = nrp1 * *nrhs;
        i__2 = *nrhs;
        for (jcol = 1; jcol <= i__2; ++jcol) {
            i__3 = nrf + nrp1 - 1;
            for (jrow = nrf; jrow <= i__3; ++jrow) {
                ++jreal;
                ++jimag;
                i__4 = jrow + jcol * bx_dim1;
                i__5 = jreal;
                i__6 = jimag;
                z__1.r = rwork[i__5], z__1.i = rwork[i__6];
                bx[i__4].r = z__1.r, bx[i__4].i = z__1.i;
/* L300: */
            }
/* L310: */
        }

/* L320: */
    }

L330:

    return 0;

/*     End of ZLALSA */

} /* zlalsa_ */