zungrq.c

Go to the documentation of this file.

/* zungrq.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 zungrq_(integer *m, integer *n, integer *k, 
        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, i__5;

    /* Local variables */
    integer i__, j, l, ib, nb, ii, kk, nx, iws, nbmin, iinfo;
    extern /* Subroutine */ int zungr2_(integer *, 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 */
/*  ======= */

/*  ZUNGRQ generates an M-by-N complex matrix Q with orthonormal rows, */
/*  which is defined as the last M rows of a product of K elementary */
/*  reflectors of order N */

/*        Q  =  H(1)' H(2)' . . . H(k)' */

/*  as returned by ZGERQF. */

/*  Arguments */
/*  ========= */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix Q. M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix Q. N >= M. */

/*  K       (input) INTEGER */
/*          The number of elementary reflectors whose product defines the */
/*          matrix Q. M >= K >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, the (m-k+i)-th row must contain the vector which */
/*          defines the elementary reflector H(i), for i = 1,2,...,k, as */
/*          returned by ZGERQF in the last k rows of its array argument */
/*          A. */
/*          On exit, the M-by-N matrix Q. */

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

/*  TAU     (input) COMPLEX*16 array, dimension (K) */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i), as returned by ZGERQF. */

/*  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 has an illegal value */

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

/*     .. Parameters .. */
/*     .. */
/*     .. 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;
    lquery = *lwork == -1;
    if (*m < 0) {
        *info = -1;
    } else if (*n < *m) {
        *info = -2;
    } else if (*k < 0 || *k > *m) {
        *info = -3;
    } else if (*lda < max(1,*m)) {
        *info = -5;
    }

    if (*info == 0) {
        if (*m <= 0) {
            lwkopt = 1;
        } else {
            nb = ilaenv_(&c__1, "ZUNGRQ", " ", m, n, k, &c_n1);
            lwkopt = *m * nb;
        }
        work[1].r = (doublereal) lwkopt, work[1].i = 0.;

        if (*lwork < max(1,*m) && ! lquery) {
            *info = -8;
        }
    }

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

/*     Quick return if possible */

    if (*m <= 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, "ZUNGRQ", " ", m, n, k, &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, "ZUNGRQ", " ", m, n, k, &c_n1);
                nbmin = max(i__1,i__2);
            }
        }
    }

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

/*        Use blocked code after the first block. */
/*        The last kk rows are handled by the block method. */

/* Computing MIN */
        i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
        kk = min(i__1,i__2);

/*        Set A(1:m-kk,n-kk+1:n) to zero. */

        i__1 = *n;
        for (j = *n - kk + 1; j <= i__1; ++j) {
            i__2 = *m - kk;
            for (i__ = 1; i__ <= i__2; ++i__) {
                i__3 = i__ + j * a_dim1;
                a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
            }
/* L20: */
        }
    } else {
        kk = 0;
    }

/*     Use unblocked code for the first or only block. */

    i__1 = *m - kk;
    i__2 = *n - kk;
    i__3 = *k - kk;
    zungr2_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
            ;

    if (kk > 0) {

/*        Use blocked code */

        i__1 = *k;
        i__2 = nb;
        for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
                i__2) {
/* Computing MIN */
            i__3 = nb, i__4 = *k - i__ + 1;
            ib = min(i__3,i__4);
            ii = *m - *k + i__;
            if (ii > 1) {

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

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

/*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */

                i__3 = ii - 1;
                i__4 = *n - *k + i__ + ib - 1;
                zlarfb_("Right", "Conjugate transpose", "Backward", "Rowwise", 
                         &i__3, &i__4, &ib, &a[ii + a_dim1], lda, &work[1], &
                        ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
            }

/*           Apply H' to columns 1:n-k+i+ib-1 of current block */

            i__3 = *n - *k + i__ + ib - 1;
            zungr2_(&ib, &i__3, &ib, &a[ii + a_dim1], lda, &tau[i__], &work[1]
, &iinfo);

/*           Set columns n-k+i+ib:n of current block to zero */

            i__3 = *n;
            for (l = *n - *k + i__ + ib; l <= i__3; ++l) {
                i__4 = ii + ib - 1;
                for (j = ii; j <= i__4; ++j) {
                    i__5 = j + l * a_dim1;
                    a[i__5].r = 0., a[i__5].i = 0.;
/* L30: */
                }
/* L40: */
            }
/* L50: */
        }
    }

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

/*     End of ZUNGRQ */

} /* zungrq_ */