zgeqrf.c

来自「算断裂的」· C语言 代码 · 共 235 行

#include "f2c.h"

/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a, 
	integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
	 integer *info)
{
/*  -- LAPACK routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    ZGEQRF computes a QR factorization of a complex M-by-N matrix A:   
    A = Q * R.   

    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.   

    A       (input/output) COMPLEX*16 array, dimension (LDA,N)   
            On entry, the M-by-N matrix A.   
            On exit, the elements on and above the diagonal of the array 
  
            contain the min(M,N)-by-N upper trapezoidal matrix R (R is   
            upper triangular if m >= n); the elements below the diagonal, 
  
            with the array TAU, represent the unitary matrix Q as a   
            product of min(m,n) elementary reflectors (see Further   
            Details).   

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

    TAU     (output) COMPLEX*16 array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors (see Further 
  
            Details).   

    WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.  LWORK >= max(1,N).   
            For optimum performance LWORK >= N*NB, where NB is   
            the optimal blocksize.   

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

    Further Details   
    ===============   

    The matrix Q is represented as a product of elementary reflectors   

       Q = H(1) H(2) . . . H(k), where k = min(m,n).   

    Each H(i) has the form   

       H(i) = I - tau * v * v'   

    where tau is a complex scalar, and v is a complex vector with   
    v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), 
  
    and tau in TAU(i).   

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


       Test the input arguments   

    
   Parameter adjustments   
       Function Body */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c_n1 = -1;
    static integer c__3 = 3;
    static integer c__2 = 2;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
    /* Local variables */
    static integer i, k, nbmin, iinfo;
    extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *);
    static integer ib, nb, nx;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, 
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    static integer iws;



#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]

#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]

    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*m)) {
	*info = -4;
    } else if (*lwork < max(1,*n)) {
	*info = -7;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGEQRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

    k = min(*m,*n);
    if (k == 0) {
	WORK(1).r = 1., WORK(1).i = 0.;
	return 0;
    }

/*     Determine the block size. */

    nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, 6L, 1L);
    nbmin = 2;
    nx = 0;
    iws = *n;
    if (nb > 1 && nb < k) {

/*        Determine when to cross over from blocked to unblocked code.
   

   Computing MAX */
	i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQRF", " ", m, n, &c_n1, &c_n1, 6L,
		 1L);
	nx = max(i__1,i__2);
	if (nx < k) {

/*           Determine if workspace is large enough for blocked co
de. */

	    ldwork = *n;
	    iws = ldwork * nb;
	    if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  reduc
e NB and   
                determine the minimum value of NB. */

		nb = *lwork / ldwork;
/* Computing MAX */
		i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", m, n, &c_n1, &
			c_n1, 6L, 1L);
		nbmin = max(i__1,i__2);
	    }
	}
    }

    if (nb >= nbmin && nb < k && nx < k) {

/*        Use blocked code initially */

	i__1 = k - nx;
	i__2 = nb;
	for (i = 1; nb < 0 ? i >= k-nx : i <= k-nx; i += nb) {
/* Computing MIN */
	    i__3 = k - i + 1;
	    ib = min(i__3,nb);

/*           Compute the QR factorization of the current block   
             A(i:m,i:i+ib-1) */

	    i__3 = *m - i + 1;
	    zgeqr2_(&i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &
		    iinfo);
	    if (i + ib <= *n) {

/*              Form the triangular factor of the block reflec
tor   
                H = H(i) H(i+1) . . . H(i+ib-1) */

		i__3 = *m - i + 1;
		zlarft_("Forward", "Columnwise", &i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &ldwork);

/*              Apply H' to A(i:m,i+ib:n) from the left */

		i__3 = *m - i + 1;
		i__4 = *n - i - ib + 1;
		zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
			, &i__3, &i__4, &ib, &A(i,i), lda, &WORK(1)
			, &ldwork, &A(i,i+ib), lda, &WORK(ib + 
			1), &ldwork);
	    }
/* L10: */
	}
    } else {
	i = 1;
    }

/*     Use unblocked code to factor the last or only block. */

    if (i <= k) {
	i__2 = *m - i + 1;
	i__1 = *n - i + 1;
	zgeqr2_(&i__2, &i__1, &A(i,i), lda, &TAU(i), &WORK(1), &
		iinfo);
    }

    WORK(1).r = (doublereal) iws, WORK(1).i = 0.;
    return 0;

/*     End of ZGEQRF */

} /* zgeqrf_ */