slasd6.c

提供矩阵类的函数库

#include "blaswrap.h"
/*  -- translated by f2c (version 19990503).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Common Block Declarations */

struct {
    real ops, itcnt;
} latime_;

#define latime_1 latime_

/* 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 */
    static integer idxc, idxp, ivfw, ivlw, i__, m, n;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    static integer n1, n2;
    extern /* Subroutine */ int 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 *);
    static integer iw, 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 *);
    static real orgnrm;
    static integer idx;


#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]


/*  -- LAPACK auxiliary routine (instrumented to count ops, version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    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) REAL   
           Contains the diagonal element associated with the added row.   

    BETA   (input) 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   

    =====================================================================   


       Test the input parameters.   

       Parameter adjustments */
    --d__;
    --vf;
    --vl;
    --idxq;
    --perm;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1 * 1;
    givcol -= givcol_offset;
    poles_dim1 = *ldgnum;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    givnum_dim1 = *ldgnum;
    givnum_offset = 1 + givnum_dim1 * 1;
    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: */
    }
    latime_1.ops += (real) (n + 2);
    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_ref(1, 1), &c__1);
	scopy_(k, &work[isigma], &c__1, &poles_ref(1, 2), &c__1);
    }

/*     Unscale. */

    latime_1.ops += (real) n;
    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_ */

#undef poles_ref