dormqr.c

来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 277 行

#include "f2c.h"
#include "netlib.h"

/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
static ftnlen cc__2 = 2;
static integer c__65 = 65;

/* Subroutine */ void dormqr_(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
const char *side, *trans;
const integer *m, *n, *k;
doublereal *a;
const integer *lda;
doublereal *tau, *c;
const integer *ldc;
doublereal *work;
integer *lwork, *info;
{
    /* System generated locals */
    address a__1[2];
    integer a_dim1, a_offset, c_dim1, c_offset, i__1;
    ftnlen i__2[2];
    char ch__1[2];

    /* Local variables */
    static logical left;
    static integer i;
    static doublereal t[4160] /* was [65][64] */;
    static integer nbmin, iinfo, i1, i2, i3;
    static integer ib, ic, jc, nb, mi, ni;
    static integer nq, nw;
    static logical notran;
    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                                                               */
/*  =======                                                               */
/*                                                                        */
/*  DORMQR overwrites the general real M-by-N matrix C with               */
/*                                                                        */
/*                  SIDE = 'L'     SIDE = 'R'                             */
/*  TRANS = 'N':      Q * C          C * Q                                */
/*  TRANS = 'T':      Q**T * C       C * Q**T                             */
/*                                                                        */
/*  where Q is a real orthogonal matrix defined as the product of k       */
/*  elementary reflectors                                                 */
/*                                                                        */
/*        Q = H(1) H(2) . . . H(k)                                        */
/*                                                                        */
/*  as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N   */
/*  if SIDE = 'R'.                                                        */
/*                                                                        */
/*  Arguments                                                             */
/*  =========                                                             */
/*                                                                        */
/*  SIDE    (input) CHARACTER*1                                           */
/*          = 'L': apply Q or Q**T from the Left;                         */
/*          = 'R': apply Q or Q**T from the Right.                        */
/*                                                                        */
/*  TRANS   (input) CHARACTER*1                                           */
/*          = 'N':  No transpose, apply Q;                                */
/*          = 'T':  Transpose, apply Q**T.                                */
/*                                                                        */
/*  M       (input) INTEGER                                               */
/*          The number of rows of the matrix C. M >= 0.                   */
/*                                                                        */
/*  N       (input) INTEGER                                               */
/*          The number of columns of the matrix C. N >= 0.                */
/*                                                                        */
/*  K       (input) INTEGER                                               */
/*          The number of elementary reflectors whose product defines     */
/*          the matrix Q.                                                 */
/*          If SIDE = 'L', M >= K >= 0;                                   */
/*          if SIDE = 'R', N >= K >= 0.                                   */
/*                                                                        */
/*  A       (input) DOUBLE PRECISION array, dimension (LDA,K)             */
/*          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.        */
/*          A is modified by the routine but restored on exit.            */
/*                                                                        */
/*  LDA     (input) INTEGER                                               */
/*          The leading dimension of the array A.                         */
/*          If SIDE = 'L', LDA >= max(1,M);                               */
/*          if SIDE = 'R', LDA >= max(1,N).                               */
/*                                                                        */
/*  TAU     (input) DOUBLE PRECISION array, dimension (K)                 */
/*          TAU(i) must contain the scalar factor of the elementary       */
/*          reflector H(i), as returned by DGEQRF.                        */
/*                                                                        */
/*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)      */
/*          On entry, the M-by-N matrix C.                                */
/*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.  */
/*                                                                        */
/*  LDC     (input) INTEGER                                               */
/*          The leading dimension of the array C. LDC >= max(1,M).        */
/*                                                                        */
/*  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.                              */
/*          If SIDE = 'L', LWORK >= max(1,N);                             */
/*          if SIDE = 'R', LWORK >= max(1,M).                             */
/*          For optimum performance LWORK >= N*NB if SIDE = 'L', and      */
/*          LWORK >= M*NB if SIDE = 'R', 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    */
/*                                                                        */
/*  ===================================================================== */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --tau;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1 * 1;
    c -= c_offset;
    --work;

/*     Test the input arguments */

    *info = 0;
    left = lsame_(side, "L");
    notran = lsame_(trans, "N");
    lquery = *lwork == -1;

/*     NQ is the order of Q and NW is the minimum dimension of WORK */

    if (left) {
        nq = *m;
        nw = *n;
    } else {
        nq = *n;
        nw = *m;
    }
    if (! left && ! lsame_(side, "R")) {
        *info = -1;
    } else if (! notran && ! lsame_(trans, "T")) {
        *info = -2;
    } else if (*m < 0) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*k < 0 || *k > nq) {
        *info = -5;
    } else if (*lda < max(1,nq)) {
        *info = -7;
    } else if (*ldc < max(1,*m)) {
        *info = -10;
    } else if (*lwork < max(1,nw) && ! lquery) {
        *info = -12;
    }

    if (*info == 0) {

/*        Determine the block size.  NB may be at most NBMAX, where NBMAX */
/*        is used to define the local array T. */

/* Writing concatenation */
        i__2[0] = 1, a__1[0] = side;
        i__2[1] = 1, a__1[1] = trans;
        s_cat(ch__1, a__1, i__2, &cc__2, (ftnlen)2);
        nb = ilaenv_(&c__1, "DORMQR", ch__1, m, n, k, &c_n1);
        nb = min(64,nb);
        lwkopt = max(1,nw) * nb;
        work[1] = (doublereal) lwkopt;
    }

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

/*     Quick return if possible */

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

    nbmin = 2;
    ldwork = nw;
    if (nb > 1 && nb < *k) {
        iws = nw * nb;
        if (*lwork < iws) {
            nb = *lwork / ldwork;
/* Writing concatenation */
            i__2[0] = 1, a__1[0] = side;
            i__2[1] = 1, a__1[1] = trans;
            s_cat(ch__1, a__1, i__2, &cc__2, (ftnlen)2);
            nbmin = ilaenv_(&c__2, "DORMQR", ch__1, m, n, k, &c_n1);
            nbmin = max(2,nbmin);
        }
    } else {
        iws = nw;
    }

    if (nb < nbmin || nb >= *k) {

/*        Use unblocked code */

        dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c[c_offset], ldc, &work[1], &iinfo);
    } else {

/*        Use blocked code */

        if ( (left && ! notran) || (! left && notran) ) {
            i1 = 1;
            i2 = *k;
            i3 = nb;
        } else {
            i1 = (*k - 1) / nb * nb + 1;
            i2 = 1;
            i3 = -nb;
        }

        if (left) {
            ni = *n;
            jc = 1;
        } else {
            mi = *m;
            ic = 1;
        }

        for (i = i1; i3 < 0 ? i >= i2 : i <= i2; i += i3) {
            ib = min(nb, *k - i + 1);

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

            i__1 = nq - i + 1;
            dlarft_("Forward", "Columnwise", &i__1, &ib, &a[i + i * a_dim1], lda, &tau[i], t, &c__65);
            if (left) {

/*              H or H' is applied to C(i:m,1:n) */

                mi = *m - i + 1;
                ic = i;
            } else {

/*              H or H' is applied to C(1:m,i:n) */

                ni = *n - i + 1;
                jc = i;
            }

/*           Apply H or H' */

            dlarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib,
                    &a[i + i * a_dim1], lda, t, &c__65, &c[ic + jc * c_dim1], ldc, &work[1], &ldwork);
        }
    }
    work[1] = (doublereal) lwkopt;

} /* dormqr_ */