slasd6.c

#include "clapack.h"

/* Table of constant values */

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

/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, 
	integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta, 
	 integer *idxq, integer *perm, integer *givptr, integer *givcol, 
	integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
	difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
	work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, 
	    poles_dim1, poles_offset, i__1;
    real r__1, r__2;

    /* Local variables */
    integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), slasd7_(integer *, integer *, integer *, integer *, 
	    integer *, real *, real *, real *, real *, real *, real *, real *, 
	     real *, real *, real *, integer *, integer *, integer *, integer 
	    *, integer *, integer *, integer *, real *, integer *, real *, 
	    real *, integer *), slasd8_(integer *, integer *, real *, real *, 
	    real *, real *, real *, real *, integer *, real *, real *, 
	    integer *);
    integer isigma;
    extern /* Subroutine */ int xerbla_(char *, integer *), slascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
, real *, integer *, integer *), slamrg_(integer *, 
	    integer *, real *, integer *, integer *, integer *);
    real orgnrm;


/*  -- LAPACK auxiliary routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLASD6 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, SLASD1, handles the case in which all singular */
/*  values and singular vectors of the bidiagonal matrix are desired. */

/*  SLASD6 computes the SVD as follows: */

/*                ( D1(in)  0    0     0 ) */
/*    B = U(in) * (   Z1'   a   Z2'    b ) * VT(in) */
/*                (   0     0   D2(in) 0 ) */

/*      = U(out) * ( D(out) 0) * VT(out) */

/*  where Z' = (Z1' a Z2' b) = u' VT', 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 SLASD6. 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 occurence the dimension of the */
/*        secular equation problem is reduced by one. This stage is */
/*        performed by the routine SLASD7. */

/*        The second stage consists of calculating the updated */
/*        singular values. This is done by finding the roots of the */
/*        secular equation via the routine SLASD4 (as called by SLASD8). */
/*        This routine also updates VF and VL and computes the distances */
/*        between the updated singular values and the old singular */
/*        values. */

/*  SLASD6 is called from SLASDA. */

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

/*  ICOMPQ (input) 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. */

/*  NL     (input) INTEGER */
/*         The row dimension of the upper block.  NL >= 1. */

/*  NR     (input) INTEGER */
/*         The row dimension of the lower block.  NR >= 1. */

/*  SQRE   (input) 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. */

/*  D      (input/output) REAL 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. */

/*  VF     (input/output) REAL 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. */

/*  VL     (input/output) REAL 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. */

/*  ALPHA  (input/output) REAL */
/*         Contains the diagonal element associated with the added row. */

/*  BETA   (input/output) REAL */
/*         Contains the off-diagonal element associated with the added */
/*         row. */

/*  IDXQ   (output) 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. */

/*  PERM   (output) INTEGER array, dimension ( N ) */
/*         The permutations (from deflation and sorting) to be applied */
/*         to each block. Not referenced if ICOMPQ = 0. */

/*  GIVPTR (output) INTEGER */
/*         The number of Givens rotations which took place in this */
/*         subproblem. Not referenced if ICOMPQ = 0. */

/*  GIVCOL (output) 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. */

/*  LDGCOL (input) INTEGER */
/*         leading dimension of GIVCOL, must be at least N. */

/*  GIVNUM (output) REAL 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. */

/*  LDGNUM (input) INTEGER */
/*         The leading dimension of GIVNUM and POLES, must be at least N. */

/*  POLES  (output) REAL 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. */

/*  DIFL   (output) REAL 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. */

/*  DIFR   (output) REAL array, */
/*                  dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and */
/*                  dimension ( N ) if ICOMPQ = 0. */
/*         On exit, DIFR(I, 1) is the distance between I-th updated */
/*         (undeflated) singular value and the I+1-th (undeflated) old */
/*         singular value. */

/*         If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
/*         normalizing factors for the right singular vector matrix. */

/*         See SLASD8 for details on DIFL and DIFR. */

/*  Z      (output) REAL array, dimension ( M ) */
/*         The first elements of this array contain the components */
/*         of the deflation-adjusted updating row vector. */

/*  K      (output) INTEGER */
/*         Contains the dimension of the non-deflated matrix, */
/*         This is the order of the related secular equation. 1 <= K <=N. */

/*  C      (output) REAL */
/*         C contains garbage if SQRE =0 and the C-value of a Givens */
/*         rotation related to the right null space if SQRE = 1. */

/*  S      (output) REAL */
/*         S contains garbage if SQRE =0 and the S-value of a Givens */
/*         rotation related to the right null space if SQRE = 1. */

/*  WORK   (workspace) REAL array, dimension ( 4 * M ) */

/*  IWORK  (workspace) INTEGER array, dimension ( 3 * N ) */

/*  INFO   (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          > 0:  if INFO = 1, an singular value did not converge */

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

/*  Based on contributions by */
/*     Ming Gu and Huan Ren, Computer Science Division, University of */
/*     California at Berkeley, USA */

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

/*     .. 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_("SLASD6", &i__1);
	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 SLASD7 and SLASD8. */

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

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

/*     Scale. */

/* Computing MAX */
    r__1 = dabs(*alpha), r__2 = dabs(*beta);
    orgnrm = dmax(r__1,r__2);
    d__[*nl + 1] = 0.f;
    i__1 = n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	if ((r__1 = d__[i__], dabs(r__1)) > orgnrm) {
	    orgnrm = (r__1 = d__[i__], dabs(r__1));
	}
/* L10: */
    }
    slascl_("G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info);
    *alpha /= orgnrm;
    *beta /= orgnrm;

/*     Sort and Deflate singular values. */

    slasd7_(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. */

    slasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], 
	    ldgnum, &work[isigma], &work[iw], info);

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

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

/*     Unscale. */

    slascl_("G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info);

/*     Prepare the IDXQ sorting permutation. */

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

    return 0;

/*     End of SLASD6 */

} /* slasd6_ */