zgelqf.c

Go to the documentation of this file.

/* zgelqf.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;

/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a, 
        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, 
         integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;

    /* Local variables */
    integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
    extern /* Subroutine */ int zgelq2_(integer *, integer *, doublecomplex *, 
             integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
            char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, 
            integer *, integer *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *);
    integer ldwork;
    extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
            integer *);
    integer lwkopt;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZGELQF computes an LQ factorization of a complex M-by-N matrix A: */
/*  A = L * 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. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, the elements on and below the diagonal of the array */
/*          contain the m-by-min(m,n) lower trapezoidal matrix L (L is */
/*          lower triangular if m <= n); the elements above the diagonal, */
/*          with the array TAU, represent the unitary matrix Q as a */
/*          product of 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 (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

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

/*          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 */

/*  Further Details */
/*  =============== */

/*  The matrix Q is represented as a product of elementary reflectors */

/*     Q = H(k)' . . . H(2)' H(1)', 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; conjg(v(i+1:n)) is stored on exit in */
/*  A(i,i+1:n), and tau in TAU(i). */

/*  ===================================================================== */

/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    nb = ilaenv_(&c__1, "ZGELQF", " ", m, n, &c_n1, &c_n1);
    lwkopt = *m * nb;
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    lquery = *lwork == -1;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*m)) {
        *info = -4;
    } else if (*lwork < max(1,*m) && ! lquery) {
        *info = -7;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGELQF", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible */

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

    nbmin = 2;
    nx = 0;
    iws = *m;
    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, "ZGELQF", " ", m, n, &c_n1, &c_n1);
        nx = max(i__1,i__2);
        if (nx < k) {

/*           Determine if workspace is large enough for blocked code. */

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

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

                nb = *lwork / ldwork;
/* Computing MAX */
                i__1 = 2, i__2 = ilaenv_(&c__2, "ZGELQF", " ", m, n, &c_n1, &
                        c_n1);
                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; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
            i__3 = k - i__ + 1;
            ib = min(i__3,nb);

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

            i__3 = *n - i__ + 1;
            zgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
                    1], &iinfo);
            if (i__ + ib <= *m) {

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

                i__3 = *n - i__ + 1;
                zlarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ * 
                        a_dim1], lda, &tau[i__], &work[1], &ldwork);

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

                i__3 = *m - i__ - ib + 1;
                i__4 = *n - i__ + 1;
                zlarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3, 
                        &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
                        ldwork, &a[i__ + ib + i__ * a_dim1], 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;
        zgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
    }

    work[1].r = (doublereal) iws, work[1].i = 0.;
    return 0;

/*     End of ZGELQF */

} /* zgelqf_ */