zgelsx.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_

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

#define lstime_1 lstime_

/* Table of constant values */

static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__0 = 0;
static integer c__2 = 2;
static integer c__1 = 1;

/* Subroutine */ int zgelsx_(integer *m, integer *n, integer *nrhs, 
	doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work, 
	doublereal *rwork, integer *info)
{
    /* Initialized data */

    static integer gelsx = 1;
    static integer geqpf = 2;
    static integer latzm = 6;
    static integer unm2r = 4;
    static integer trsm = 5;
    static integer tzrqf = 3;

    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
    doublecomplex z__1;

    /* Builtin functions */
    double z_abs(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    static doublereal anrm, bnrm, smin, smax;
    static integer i__, j, k, iascl, ibscl;
    extern doublereal dopla_(char *, integer *, integer *, integer *, integer 
	    *, integer *);
    static integer ismin, ismax;
    static doublecomplex c1, c2, s1, s2, t1, t2;
    extern /* Subroutine */ int ztrsm_(char *, char *, char *, char *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, integer *,
	     doublecomplex *, integer *);
    extern doublereal dopbl3_(char *, integer *, integer *, integer *)
	    ;
    extern /* Subroutine */ int zlaic1_(integer *, integer *, doublecomplex *,
	     doublereal *, doublecomplex *, doublecomplex *, doublereal *, 
	    doublecomplex *, doublecomplex *), dlabad_(doublereal *, 
	    doublereal *);
    extern doublereal dlamch_(char *);
    static integer mn;
    extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dsecnd_(void);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    static doublereal bignum;
    extern /* Subroutine */ int zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *), zgeqpf_(integer *, integer *, 
	    doublecomplex *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublereal *, integer *), zlaset_(char *, 
	    integer *, integer *, doublecomplex *, doublecomplex *, 
	    doublecomplex *, integer *);
    static doublereal sminpr, smaxpr, smlnum;
    extern /* Subroutine */ int zlatzm_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *), ztzrqf_(
	    integer *, integer *, doublecomplex *, integer *, doublecomplex *,
	     integer *);
    static doublereal tim1, tim2;


#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   
       September 30, 1994   

       Common blocks to return operation counts and timings   

    Purpose   
    =======   

    ZGELSX computes the minimum-norm solution to a complex linear least   
    squares problem:   
        minimize || A * X - B ||   
    using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:   
        A * P = Q * [ R11 R12 ]   
                    [  0  R22 ]   
    with R11 defined as the largest leading submatrix whose estimated   
    condition number is less than 1/RCOND.  The order of R11, RANK,   
    is the effective rank of A.   

    Then, R22 is considered to be negligible, and R12 is annihilated   
    by unitary transformations from the right, arriving at the   
    complete orthogonal factorization:   
       A * P = Q * [ T11 0 ] * Z   
                   [  0  0 ]   
    The minimum-norm solution is then   
       X = P * Z' [ inv(T11)*Q1'*B ]   
                  [        0       ]   
    where Q1 consists of the first RANK columns of Q.   

    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 matrices B and X. NRHS >= 0.   

    A       (input/output) COMPLEX*16 array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, A has been overwritten by details of its   
            complete orthogonal factorization.   

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

    B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)   
            On entry, the M-by-NRHS right hand side matrix B.   
            On exit, 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).   

    JPVT    (input/output) INTEGER array, dimension (N)   
            On entry, if JPVT(i) .ne. 0, the i-th column of A is an   
            initial column, otherwise it is a free column.  Before   
            the QR factorization of A, all initial columns are   
            permuted to the leading positions; only the remaining   
            free columns are moved as a result of column pivoting   
            during the factorization.   
            On exit, if JPVT(i) = k, then the i-th column of A*P   
            was the k-th column of A.   

    RCOND   (input) DOUBLE PRECISION   
            RCOND is used to determine the effective rank of A, which   
            is defined as the order of the largest leading triangular   
            submatrix R11 in the QR factorization with pivoting of A,   
            whose estimated condition number < 1/RCOND.   

    RANK    (output) INTEGER   
            The effective rank of A, i.e., the order of the submatrix   
            R11.  This is the same as the order of the submatrix T11   
            in the complete orthogonal factorization of A.   

    WORK    (workspace) COMPLEX*16 array, dimension   
                        (min(M,N) + max( N, 2*min(M,N)+NRHS )),   

    RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value   

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

       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;
    --jpvt;
    --work;
    --rwork;

    /* Function Body */

    mn = min(*m,*n);
    ismin = mn + 1;
    ismax = (mn << 1) + 1;

/*     Test the input arguments. */

    *info = 0;
    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(complicated condition) */ {
/* Computing MAX */
	i__1 = max(1,*m);
	if (*ldb < max(i__1,*n)) {
	    *info = -7;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGELSX", &i__1);
	return 0;
    }

/*     Quick return if possible   

   Computing MIN */
    i__1 = min(*m,*n);
    if (min(i__1,*nrhs) == 0) {
	*rank = 0;
	return 0;
    }

/*     Get machine parameters */

    lstime_1.opcnt[gelsx - 1] += 2.;
    smlnum = dlamch_("S") / dlamch_("P");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);

/*     Scale A, B if max elements outside range [SMLNUM,BIGNUM] */

    anrm = zlange_("M", m, n, &a[a_offset], lda, &rwork[1]);
    iascl = 0;
    if (anrm > 0. && anrm < smlnum) {

/*        Scale matrix norm up to SMLNUM */