dorgqr.c

InsightToolkit-1.4.0(有大量的优化算法程序)

#include "f2c.h"
#include "netlib.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 */ void dorgqr_(m, n, k, a, lda, tau, work, lwork, info)
integer *m, *n, *k;
doublereal *a;
integer *lda;
doublereal *tau, *work;
integer *lwork, *info;
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    static integer i, j, l, nbmin, iinfo;
    static integer ib, nb, ki, kk;
    static integer nx;
    static integer ldwork, lwkopt;
    static logical lquery;
    static integer iws;

/*  -- LAPACK routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

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

/*  DORGQR generates an M-by-N real matrix Q with orthonormal columns, */
/*  which is defined as the first N columns of a product of K elementary */
/*  reflectors of order M */

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

/*  as returned by DGEQRF. */

/*  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. M >= N >= 0. */

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

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the i-th column must contain the vector which */
/*          defines the elementary reflector H(i), for i = 1,2,...,k, as */
/*          returned by DGEQRF in the first k columns 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) DOUBLE PRECISION array, dimension (K) */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i), as returned by DGEQRF. */

/*  WORK    (workspace/output) DOUBLE PRECISION 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. */

/*          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 */

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

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

/*     Test the input arguments */

    *info = 0;
    nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1);
    lwkopt = max(1,*n) * nb;
    work[1] = (doublereal) lwkopt;
    lquery = *lwork == -1;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0 || *n > *m) {
        *info = -2;
    } else if (*k < 0 || *k > *n) {
        *info = -3;
    } else if (*lda < max(1,*m)) {
        *info = -5;
    } else if (*lwork < max(1,*n) && ! lquery) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DORGQR", &i__1);
        return;
    } else if (lquery) {
        return;
    }

/*     Quick return if possible */

    if (*n <= 0) {
        work[1] = 1.;
        return;
    }

    nbmin = 2;
    nx = 0;
    iws = *n;
    if (nb > 1 && nb < *k) {

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

        nx = ilaenv_(&c__3, "DORGQR", " ", m, n, k, &c_n1);
        nx = max(0,nx);
        if (nx < *k) {

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

            ldwork = *n;
            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;
                nbmin = ilaenv_(&c__2, "DORGQR", " ", m, n, k, &c_n1);
                nbmin = max(2,nbmin);
            }
        }
    }

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

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

        ki = (*k - nx - 1) / nb * nb;
        kk = min(*k, ki + nb);

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

        for (j = kk + 1; j <= *n; ++j) {
            for (i = 1; i <= kk; ++i) {
                a[i + j * a_dim1] = 0.;
            }
        }
    } else {
        kk = 0;
    }

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

    if (kk < *n) {
        i__1 = *m - kk;
        i__2 = *n - kk;
        i__3 = *k - kk;
        dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &tau[kk + 1], &work[1], &iinfo);
    }

    if (kk > 0) {

/*        Use blocked code */

        for (i = ki + 1; nb > 0 ? i >= 1 : i <= 1; i -= nb) {
            ib = min(nb, *k - i + 1);
            if (i + ib <= *n) {

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

                i__2 = *m - i + 1;
                dlarft_("Forward", "Columnwise", &i__2, &ib, &a[i + i * a_dim1], lda, &tau[i], &work[1], &ldwork);

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

                i__2 = *m - i + 1;
                i__3 = *n - i - ib + 1;
                dlarfb_("Left", "No transpose", "Forward", "Columnwise", &i__2, &i__3,
                        &ib, &a[i + i * a_dim1], lda, &work[1], &ldwork,
                        &a[i + (i + ib) * a_dim1], lda, &work[ib + 1], &ldwork);
            }

/*           Apply H to rows i:m of current block */

            i__2 = *m - i + 1;
            dorg2r_(&i__2, &ib, &ib, &a[i + i * a_dim1], lda, &tau[i], &work[1], &iinfo);

/*           Set rows 1:i-1 of current block to zero */

            for (j = i; j < i + ib; ++j) {
                for (l = 1; l < i; ++l) {
                    a[l + j * a_dim1] = 0.;
                }
            }
        }
    }

    work[1] = (doublereal) iws;

} /* dorgqr_ */