dlasd2.c

著名的LAPACK矩阵计算软件包, 是比较新的版本, 一般用到矩阵分解的朋友也许会用到

#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 {
    doublereal ops, itcnt;
} latime_;

#define latime_1 latime_

/* Table of constant values */

static integer c__1 = 1;
static doublereal c_b30 = 0.;

/* Subroutine */ int dlasd2_(integer *nl, integer *nr, integer *sqre, integer 
	*k, doublereal *d__, doublereal *z__, doublereal *alpha, doublereal *
	beta, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, 
	doublereal *dsigma, doublereal *u2, integer *ldu2, doublereal *vt2, 
	integer *ldvt2, integer *idxp, integer *idx, integer *idxc, integer *
	idxq, integer *coltyp, integer *info)
{
    /* System generated locals */
    integer u_dim1, u_offset, u2_dim1, u2_offset, vt_dim1, vt_offset, 
	    vt2_dim1, vt2_offset, i__1;
    doublereal d__1, d__2;

    /* Local variables */
    static integer idxi, idxj;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *);
    static integer ctot[4];
    static doublereal c__;
    static integer i__, j, m, n;
    static doublereal s;
    static integer idxjp;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer jprev, k2;
    static doublereal z1;
    extern doublereal dlapy2_(doublereal *, doublereal *);
    static integer ct;
    extern doublereal dlamch_(char *);
    static integer jp;
    extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, 
	    integer *, integer *, integer *), dlacpy_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *), xerbla_(char *, 
	    integer *);
    static doublereal hlftol, eps, tau, tol;
    static integer psm[4], nlp1, nlp2;


#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define u2_ref(a_1,a_2) u2[(a_2)*u2_dim1 + a_1]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define vt2_ref(a_1,a_2) vt2[(a_2)*vt2_dim1 + a_1]


/*  -- LAPACK auxiliary routine (instrumented to count ops, version 3.0) --   
       Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab,   
       Courant Institute, NAG Ltd., and Rice University   
       October 31, 1999   


    Purpose   
    =======   

    DLASD2 merges the two sets of singular values together into a single   
    sorted set.  Then it tries to deflate the size of the problem.   
    There are two ways in which deflation can occur:  when two or more   
    singular values are close together or if there is a tiny entry in the   
    Z vector.  For each such occurrence the order of the related secular   
    equation problem is reduced by one.   

    DLASD2 is called from DLASD1.   

    Arguments   
    =========   

    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 N = NL + NR + 1 rows and   
           M = N + SQRE >= N columns.   

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

    D      (input/output) DOUBLE PRECISION array, dimension(N)   
           On entry D contains the singular values of the two submatrices   
           to be combined.  On exit D contains the trailing (N-K) updated   
           singular values (those which were deflated) sorted into   
           increasing order.   

    ALPHA  (input) DOUBLE PRECISION   
           Contains the diagonal element associated with the added row.   

    BETA   (input) DOUBLE PRECISION   
           Contains the off-diagonal element associated with the added   
           row.   

    U      (input/output) DOUBLE PRECISION array, dimension(LDU,N)   
           On entry U contains the left singular vectors of two   
           submatrices in the two square blocks with corners at (1,1),   
           (NL, NL), and (NL+2, NL+2), (N,N).   
           On exit U contains the trailing (N-K) updated left singular   
           vectors (those which were deflated) in its last N-K columns.   

    LDU    (input) INTEGER   
           The leading dimension of the array U.  LDU >= N.   

    Z      (output) DOUBLE PRECISION array, dimension(N)   
           On exit Z contains the updating row vector in the secular   
           equation.   

    DSIGMA (output) DOUBLE PRECISION array, dimension (N)   
           Contains a copy of the diagonal elements (K-1 singular values   
           and one zero) in the secular equation.   

    U2     (output) DOUBLE PRECISION array, dimension(LDU2,N)   
           Contains a copy of the first K-1 left singular vectors which   
           will be used by DLASD3 in a matrix multiply (DGEMM) to solve   
           for the new left singular vectors. U2 is arranged into four   
           blocks. The first block contains a column with 1 at NL+1 and   
           zero everywhere else; the second block contains non-zero   
           entries only at and above NL; the third contains non-zero   
           entries only below NL+1; and the fourth is dense.   

    LDU2   (input) INTEGER   
           The leading dimension of the array U2.  LDU2 >= N.   

    VT     (input/output) DOUBLE PRECISION array, dimension(LDVT,M)   
           On entry VT' contains the right singular vectors of two   
           submatrices in the two square blocks with corners at (1,1),   
           (NL+1, NL+1), and (NL+2, NL+2), (M,M).   
           On exit VT' contains the trailing (N-K) updated right singular   
           vectors (those which were deflated) in its last N-K columns.   
           In case SQRE =1, the last row of VT spans the right null   
           space.   

    LDVT   (input) INTEGER   
           The leading dimension of the array VT.  LDVT >= M.   

    VT2    (output) DOUBLE PRECISION array, dimension(LDVT2,N)   
           VT2' contains a copy of the first K right singular vectors   
           which will be used by DLASD3 in a matrix multiply (DGEMM) to   
           solve for the new right singular vectors. VT2 is arranged into   
           three blocks. The first block contains a row that corresponds   
           to the special 0 diagonal element in SIGMA; the second block   
           contains non-zeros only at and before NL +1; the third block   
           contains non-zeros only at and after  NL +2.   

    LDVT2  (input) INTEGER   
           The leading dimension of the array VT2.  LDVT2 >= M.   

    IDXP   (workspace) INTEGER array, dimension(N)   
           This will contain the permutation used to place deflated   
           values of D at the end of the array. On output IDXP(2:K)   
           points to the nondeflated D-values and IDXP(K+1:N)   
           points to the deflated singular values.   

    IDX    (workspace) INTEGER array, dimension(N)   
           This will contain the permutation used to sort the contents of   
           D into ascending order.   

    IDXC   (output) INTEGER array, dimension(N)   
           This will contain the permutation used to arrange the columns   
           of the deflated U matrix into three groups:  the first group   
           contains non-zero entries only at and above NL, the second   
           contains non-zero entries only below NL+2, and the third is   
           dense.   

    COLTYP (workspace/output) INTEGER array, dimension(N)   
           As workspace, this will contain a label which will indicate   
           which of the following types a column in the U2 matrix or a   
           row in the VT2 matrix is:   
           1 : non-zero in the upper half only   
           2 : non-zero in the lower half only   
           3 : dense   
           4 : deflated   

           On exit, it is an array of dimension 4, with COLTYP(I) being   
           the dimension of the I-th type columns.   

    IDXQ   (input) INTEGER array, dimension(N)   
           This contains the permutation which separately sorts the two   
           sub-problems in D into ascending order.  Note that entries in   
           the first hlaf of this permutation must first be moved one   
           position backward; and entries in the second half   
           must first have NL+1 added to their values.   

    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 Huan Ren, Computer Science Division, University of   
       California at Berkeley, USA   

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


       Test the input parameters.   

       Parameter adjustments */
    --d__;
    --z__;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    vt_dim1 = *ldvt;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    --dsigma;
    u2_dim1 = *ldu2;
    u2_offset = 1 + u2_dim1 * 1;
    u2 -= u2_offset;
    vt2_dim1 = *ldvt2;
    vt2_offset = 1 + vt2_dim1 * 1;
    vt2 -= vt2_offset;
    --idxp;
    --idx;
    --idxc;
    --idxq;
    --coltyp;

    /* Function Body */
    *info = 0;

    if (*nl < 1) {
	*info = -1;
    } else if (*nr < 1) {
	*info = -2;
    } else if (*sqre != 1 && *sqre != 0) {
	*info = -3;
    }

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

    if (*ldu < n) {
	*info = -10;
    } else if (*ldvt < m) {
	*info = -12;
    } else if (*ldu2 < n) {
	*info = -15;
    } else if (*ldvt2 < m) {
	*info = -17;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DLASD2", &i__1);
	return 0;
    }

    nlp1 = *nl + 1;
    nlp2 = *nl + 2;

/*     Generate the first part of the vector Z; and move the singular   
       values in the first part of D one position backward. */

    latime_1.ops += (doublereal) (*nl + 1);
    z1 = *alpha * vt_ref(nlp1, nlp1);
    z__[1] = z1;
    for (i__ = *nl; i__ >= 1; --i__) {
	z__[i__ + 1] = *alpha * vt_ref(i__, nlp1);
	d__[i__ + 1] = d__[i__];
	idxq[i__ + 1] = idxq[i__] + 1;
/* L10: */
    }

/*     Generate the second part of the vector Z. */

    latime_1.ops += (doublereal) (m - nlp2 + 1);
    i__1 = m;
    for (i__ = nlp2; i__ <= i__1; ++i__) {
	z__[i__] = *beta * vt_ref(i__, nlp2);
/* L20: */
    }

/*     Initialize some reference arrays. */

    i__1 = nlp1;
    for (i__ = 2; i__ <= i__1; ++i__) {
	coltyp[i__] = 1;
/* L30: */
    }
    i__1 = n;
    for (i__ = nlp2; i__ <= i__1; ++i__) {
	coltyp[i__] = 2;
/* L40: */
    }