dgelss.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 {
    doublereal ops, itcnt;
} latime_;

#define latime_1 latime_

struct {
    doublereal opcnt[6], timng[6];
} lstime_;

#define lstime_1 lstime_

/* Table of constant values */

static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static doublereal c_b74 = 0.;
static doublereal c_b145 = 1.;

/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, 
	doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
	s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
	 integer *info)
{
    /* Initialized data */

    static integer bdsqr = 5;
    static integer ormlq = 6;
    static integer ormqr = 2;
    static integer gebrd = 3;
    static integer gelqf = 2;
    static integer gelss = 1;
    static integer gemm = 6;
    static integer gemv = 6;
    static integer geqrf = 2;
    static integer orgbr = 4;
    static integer ormbr = 4;

    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
    doublereal d__1;

    /* Local variables */
    static doublereal anrm, bnrm;
    static integer itau;
    static doublereal vdum[1];
    static integer i__;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static integer iascl, ibscl;
    extern doublereal dopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *), drscl_(integer *, 
	    doublereal *, doublereal *, integer *);
    static integer chunk, minmn, maxmn, itaup, itauq;
    static doublereal sfmin;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer mnthr, iwork;
    static doublereal t1, t2;
    extern doublereal dopla2_(char *, char *, integer *, integer *, integer *,
	     integer *, integer *), dopbl2_(char *, integer *,
	     integer *, integer *, integer *), dopbl3_(char *, 
	    integer *, integer *, integer *);
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    static integer bl, ie, nb, il;
    extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *,
	     doublereal *, integer *, integer *);
    extern doublereal dlamch_(char *);
    static integer mm;
    extern doublereal dlange_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *);
    static integer bdspac;
    extern doublereal dsecnd_(void);
    extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dlascl_(char *, integer *, integer *, doublereal *, doublereal *, 
	    integer *, integer *, doublereal *, integer *, integer *),
	     dgeqrf_(integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
	     integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *), dlaset_(char *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *), 
	    xerbla_(char *, integer *), dbdsqr_(char *, integer *, 
	    integer *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, integer *), dorgbr_(char *, 
	    integer *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *);
    static doublereal bignum;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *), dormlq_(char *, char *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer minwrk, maxwrk;
    static doublereal smlnum;
    static logical lquery;
    static doublereal eps, thr;


#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]


/*  -- LAPACK driver 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   
       October 31, 1999   

       Common blocks to return operation counts and timings   

    Purpose   
    =======   

    DGELSS computes the minimum norm solution to a real linear least   
    squares problem:   

    Minimize 2-norm(| b - A*x |).   

    using the singular value decomposition (SVD) of A. A is an M-by-N   
    matrix which may be rank-deficient.   

    Several right hand side vectors b and solution vectors x can be   
    handled in a single call; they are stored as the columns of the   
    M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix   
    X.   

    The effective rank of A is determined by treating as zero those   
    singular values which are less than RCOND times the largest singular   
    value.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix A. M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix A. N >= 0.   

    NRHS    (input) INTEGER   
            The number of right hand sides, i.e., the number of columns   
            of the matrices B and X. NRHS >= 0.   

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, the first min(m,n) rows of A are overwritten with   
            its right singular vectors, stored rowwise.   

    LDA     (input) INTEGER   
            The leading dimension of the array A.  LDA >= max(1,M).   

    B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)   
            On entry, the M-by-NRHS right hand side matrix B.   
            On exit, B is overwritten by the N-by-NRHS solution   
            matrix X.  If m >= n and RANK = n, the residual   
            sum-of-squares for the solution in the i-th column is given   
            by the sum of squares of elements n+1:m in that column.   

    LDB     (input) INTEGER   
            The leading dimension of the array B. LDB >= max(1,max(M,N)).   

    S       (output) DOUBLE PRECISION array, dimension (min(M,N))   
            The singular values of A in decreasing order.   
            The condition number of A in the 2-norm = S(1)/S(min(m,n)).   

    RCOND   (input) DOUBLE PRECISION   
            RCOND is used to determine the effective rank of A.   
            Singular values S(i) <= RCOND*S(1) are treated as zero.   
            If RCOND < 0, machine precision is used instead.   

    RANK    (output) INTEGER   
            The effective rank of A, i.e., the number of singular values   
            which are greater than RCOND*S(1).   

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK >= 1, and also:   
            LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )   
            For good performance, LWORK should generally be larger.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            > 0:  the algorithm for computing the SVD failed to converge;   
                  if INFO = i, i off-diagonal elements of an intermediate   
                  bidiagonal form did not converge to zero.   

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

       Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --s;
    --work;

    /* Function Body   

       Test the input arguments */

    *info = 0;
    minmn = min(*m,*n);
    maxmn = max(*m,*n);
    mnthr = ilaenv_(&c__6, "DGELSS", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
	    ftnlen)1);
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*nrhs < 0) {
	*info = -3;
    } else if (*lda < max(1,*m)) {
	*info = -5;
    } else if (*ldb < max(1,maxmn)) {
	*info = -7;
    }

/*     Compute workspace   
        (Note: Comments in the code beginning "Workspace:" describe the   
         minimal amount of workspace needed at that point in the code,   
         as well as the preferred amount for good performance.   
         NB refers to the optimal block size for the immediately   
         following subroutine, as returned by ILAENV.) */

    minwrk = 1;
    if (*info == 0 && (*lwork >= 1 || lquery)) {
	maxwrk = 0;
	mm = *m;
	if (*m >= *n && *m >= mnthr) {

/*           Path 1a - overdetermined, with many more rows than columns */

	    mm = *n;
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, 
		    n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT", 
		    m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
	    maxwrk = max(i__1,i__2);
	}
	if (*m >= *n) {

/*           Path 1 - overdetermined or exactly determined   

             Compute workspace needed for DBDSQR   

   Computing MAX */
	    i__1 = 1, i__2 = *n * 5;
	    bdspac = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD"
		    , " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR", 
		    "QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORGBR",
		     "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
	    maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * *nrhs;
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2);
	    minwrk = max(i__1,bdspac);
	    maxwrk = max(minwrk,maxwrk);
	}
	if (*n > *m) {

/*           Compute workspace needed for DBDSQR   

   Computing MAX */
	    i__1 = 1, i__2 = *m * 5;
	    bdspac = max(i__1,i__2);
/* Computing MAX */
	    i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,i__2);
	    minwrk = max(i__1,bdspac);
	    if (*n >= mnthr) {

/*              Path 2a - underdetermined, with many more columns   
                than rows */

		maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, 
			&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * 
			ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (
			ftnlen)6, (ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
			c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
			ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * 
			ilaenv_(&c__1, "DORGBR", "P", m, m, m, &c_n1, (ftnlen)