cgelss.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_

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

#define lstime_1 lstime_

/* Table of constant values */

static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__6 = 6;
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static real c_b78 = 0.f;

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

    static integer bdsqr = 5;
    static integer unmlq = 6;
    static integer unmqr = 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 ungbr = 4;
    static integer unmbr = 4;

    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    real r__1;

    /* Local variables */
    static real anrm, bnrm;
    static integer itau;
    static complex vdum[1];
    static integer i__;
    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
	    integer *, complex *, complex *, integer *, complex *, integer *, 
	    complex *, complex *, integer *);
    static integer iascl, ibscl;
    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
	    , complex *, integer *, complex *, integer *, complex *, complex *
	    , integer *);
    static integer chunk;
    static real sfmin;
    static integer minmn, maxmn, itaup, itauq, mnthr;
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *);
    extern doublereal sopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    static integer iwork;
    static real t1, t2;
    extern doublereal sopla2_(char *, char *, integer *, integer *, integer *,
	     integer *, integer *), sopbl2_(char *, integer *,
	     integer *, integer *, integer *), sopbl3_(char *, 
	    integer *, integer *, integer *);
    static integer bl, ie, nb, il;
    extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *, 
	    integer *, real *, real *, complex *, complex *, complex *, 
	    integer *, integer *), slabad_(real *, real *);
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    static integer mm;
    extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, 
	    integer *, complex *, complex *, integer *, integer *), clascl_(
	    char *, integer *, integer *, real *, real *, integer *, integer *
	    , complex *, integer *, integer *), cgeqrf_(integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), claset_(char *, 
	    integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *), cbdsqr_(char *, 
	    integer *, integer *, integer *, integer *, real *, real *, 
	    complex *, integer *, complex *, integer *, complex *, integer *, 
	    real *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static real bignum;
    extern /* Subroutine */ int cungbr_(char *, integer *, integer *, integer 
	    *, complex *, integer *, complex *, complex *, integer *, integer 
	    *), slascl_(char *, integer *, integer *, real *, real *, 
	    integer *, integer *, real *, integer *, integer *);
    extern doublereal second_(void);
    extern /* Subroutine */ int cunmbr_(char *, char *, char *, integer *, 
	    integer *, integer *, complex *, integer *, complex *, complex *, 
	    integer *, complex *, integer *, integer *), csrscl_(integer *, real *, complex *, integer *), 
	    slaset_(char *, integer *, integer *, real *, real *, real *, 
	    integer *), cunmlq_(char *, char *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *, integer *);
    static integer minwrk, maxwrk;
    static real smlnum;
    static integer irwork;
    static logical lquery;
    static real eps, thr;


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


/*  -- 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   
    =======   

    CGELSS computes the minimum norm solution to a complex 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) COMPLEX 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) COMPLEX 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,M,N).   

    S       (output) REAL 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) REAL   
            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) COMPLEX 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 >=  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.   

    RWORK   (workspace) REAL array, dimension (5*min(M,N))   

    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;
    --rwork;

    /* Function Body   

       Test the input arguments */

    *info = 0;
    minmn = min(*m,*n);
    maxmn = max(*m,*n);
    mnthr = ilaenv_(&c__6, "CGELSS", " ", 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.   
         CWorkspace refers to complex workspace, and RWorkspace refers   
         to real workspace. 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   

             Space needed for CBDSQR is BDSPAC = 5*N */

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

/*           Path 1 - overdetermined or exactly determined   

             Space needed for CBDSQR is BDSPC = 7*N+12   

   Computing MAX */
	    i__1 = maxwrk, i__2 = (*n << 1) + (mm + *n) * ilaenv_(&c__1, 
		    "CGEBRD", " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1)
		    ;
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = (*n << 1) + *nrhs * ilaenv_(&c__1, "CUNMBR",
		     "QLC", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "CUN"
		    "GBR", "P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    maxwrk = max(i__1,i__2);
/* Computing MAX */
	    i__1 = maxwrk, i__2 = *n * *nrhs;
	    maxwrk = max(i__1,i__2);
	    minwrk = (*n << 1) + max(*nrhs,*m);
	}
	if (*n > *m) {
	    minwrk = (*m << 1) + max(*nrhs,*n);
	    if (*n >= mnthr) {

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

                Space needed for CBDSQR is BDSPAC = 5*M */

		maxwrk = *m + *m * ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, 
			&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * *m + (*m << 1) * ilaenv_(&
			c__1, "CGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)6, (
			ftnlen)1);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * *m + *nrhs * ilaenv_(&
			c__1, "CUNMBR", "QLC", m, nrhs, m, &c_n1, (ftnlen)6, (
			ftnlen)3);
		maxwrk = max(i__1,i__2);
/* Computing MAX */
		i__1 = maxwrk, i__2 = *m * 3 + *m * *m + (*m - 1) * ilaenv_(&
			c__1, "CUNGBR", "P", m, m, m, &c_n1, (ftnlen)6, (
			ftnlen)1);
		maxwrk = max(i__1,i__2);
		if (*nrhs > 1) {
/* Computing MAX */
		    i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;