dlasda.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__0 = 0;
static doublereal c_b11 = 0.;
static doublereal c_b12 = 1.;
static integer c__1 = 1;
static integer c__2 = 2;

/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, 
	integer *sqre, doublereal *d__, doublereal *e, 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 *work, 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, i__1, i__2;

    /* Builtin functions */
    integer pow_ii(integer *, integer *);

    /* Local variables */
    static doublereal beta;
    static integer idxq, nlvl, i__, j, m;
    static doublereal alpha;
    static integer inode, ndiml, ndimr, idxqi, itemp;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer sqrei, i1;
    extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *);
    static integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;
    extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer 
	    *, integer *, integer *, doublereal *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *), dlasdt_(integer *, integer *, 
	    integer *, integer *, integer *, integer *, integer *), dlaset_(
	    char *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *), xerbla_(char *, integer *);
    static integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, 
	    nlp1, lvl2, nrp1;


#define difl_ref(a_1,a_2) difl[(a_2)*difl_dim1 + a_1]
#define difr_ref(a_1,a_2) difr[(a_2)*difr_dim1 + a_1]
#define perm_ref(a_1,a_2) perm[(a_2)*perm_dim1 + a_1]
#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define poles_ref(a_1,a_2) poles[(a_2)*poles_dim1 + a_1]
#define vt_ref(a_1,a_2) vt[(a_2)*vt_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*givcol_dim1 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*givnum_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   
    =======   

    Using a divide and conquer approach, DLASDA computes the singular   
    value decomposition (SVD) of a real upper bidiagonal N-by-M matrix   
    B with diagonal D and offdiagonal E, where M = N + SQRE. The   
    algorithm computes the singular values in the SVD B = U * S * VT.   
    The orthogonal matrices U and VT are optionally computed in   
    compact form.   

    A related subroutine, DLASD0, computes the singular values and   
    the singular vectors in explicit form.   

    Arguments   
    =========   

    ICOMPQ (input) INTEGER   
           Specifies whether singular vectors are to be computed   
           in compact form, as follows   
           = 0: Compute singular values only.   
           = 1: Compute singular vectors of upper bidiagonal   
                matrix in compact form.   

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

    N      (input) INTEGER   
           The row dimension of the upper bidiagonal matrix. This is   
           also the dimension of the main diagonal array D.   

    SQRE   (input) INTEGER   
           Specifies the column dimension of the bidiagonal matrix.   
           = 0: The bidiagonal matrix has column dimension M = N;   
           = 1: The bidiagonal matrix has column dimension M = N + 1.   

    D      (input/output) DOUBLE PRECISION array, dimension ( N )   
           On entry D contains the main diagonal of the bidiagonal   
           matrix. On exit D, if INFO = 0, contains its singular values.   

    E      (input) DOUBLE PRECISION array, dimension ( M-1 )   
           Contains the subdiagonal entries of the bidiagonal matrix.   
           On exit, E has been destroyed.   

    U      (output) DOUBLE PRECISION array,   
           dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced   
           if ICOMPQ = 0. If ICOMPQ = 1, on exit, 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     (output) DOUBLE PRECISION array,   
           dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced   
           if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right   
           singular vector matrices of all subproblems at the bottom   
           level.   

    K      (output) INTEGER array,   
           dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.   
           If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th   
           secular equation on the computation tree.   

    DIFL   (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),   
           where NLVL = floor(log_2 (N/SMLSIZ))).   

    DIFR   (output) DOUBLE PRECISION array,   
                    dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and   
                    dimension ( N ) if ICOMPQ = 0.   
           If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)   
           record distances between singular values on the I-th   
           level and singular values on the (I -1)-th level, and   
           DIFR(1:N, 2 * I ) contains the normalizing factors for   
           the right singular vector matrix. See DLASD8 for details.   

    Z      (output) DOUBLE PRECISION array,   
                    dimension ( LDU, NLVL ) if ICOMPQ = 1 and   
                    dimension ( N ) if ICOMPQ = 0.   
           The first K elements of Z(1, I) contain the components of   
           the deflation-adjusted updating row vector for subproblems   
           on the I-th level.   

    POLES  (output) DOUBLE PRECISION array,   
           dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced   
           if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and   
           POLES(1, 2*I) contain  the new and old singular values   
           involved in the secular equations on the I-th level.   

    GIVPTR (output) INTEGER array,   
           dimension ( N ) if ICOMPQ = 1, and not referenced if   
           ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records   
           the number of Givens rotations performed on the I-th   
           problem on the computation tree.   

    GIVCOL (output) INTEGER array,   
           dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not   
           referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,   
           GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record 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   (output) INTEGER array,   
           dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced   
           if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records   
           permutations done on the I-th level of the computation tree.   

    GIVNUM (output) DOUBLE PRECISION array,   
           dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not   
           referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,   
           GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-   
           values of Givens rotations performed on the I-th level on   
           the computation tree.   

    C      (output) DOUBLE PRECISION array,   
           dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.   
           If ICOMPQ = 1 and the I-th subproblem is not square, on exit,   
           C( I ) contains the C-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    S      (output) DOUBLE PRECISION array, dimension ( N ) if   
           ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1   
           and the I-th subproblem is not square, on exit, S( I )   
           contains the S-value of a Givens rotation related to   
           the right null space of the I-th subproblem.   

    WORK   (workspace) DOUBLE PRECISION array   
           If ICOMPQ = 0 its dimension must be at least   
           (2 * N + max(4 * N, (SMLSIZ + 4)*(SMLSIZ + 1))).   
           and if ICOMPQ = 1, dimension must be at least (6 * N).   

    IWORK  (workspace) INTEGER array.   
           Dimension must be at least (7 * 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__;
    --e;
    givnum_dim1 = *ldu;
    givnum_offset = 1 + givnum_dim1 * 1;
    givnum -= givnum_offset;
    poles_dim1 = *ldu;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;