sgerq2.c

InsightToolkit-1.4.0(有大量的优化算法程序)

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

/* Subroutine */ void sgerq2_(const integer *m, const integer *n, real *a, const integer *lda,
                              real *tau, real *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    static integer i, k;
    static real aii;

/*  -- LAPACK routine (version 2.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     February 29, 1992 */

/*  Purpose                                                               */
/*  =======                                                               */
/*                                                                        */
/*  SGERQ2 computes an RQ factorization of a real m by n matrix A:        */
/*  A = R * 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) REAL array, dimension (LDA,N)                  */
/*          On entry, the m by n matrix A.                                */
/*          On exit, if m <= n, the upper triangle of the subarray        */
/*          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; */
/*          if m >= n, the elements on and above the (m-n)-th subdiagonal */
/*          contain the m by n upper trapezoidal matrix R; the remaining  */
/*          elements, with the array TAU, represent the orthogonal 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) REAL array, dimension (min(M,N))                     */
/*          The scalar factors of the elementary reflectors (see Further  */
/*          Details).                                                     */
/*                                                                        */
/*  WORK    (workspace) REAL array, dimension (M)                         */
/*                                                                        */
/*  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 real scalar, and v is a real vector with               */
/*  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in  */
/*  A(m-k+i,1:n-k+i-1), and tau in TAU(i).                                */
/*                                                                        */
/*  ===================================================================== */

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

/*     Test the input arguments */

    *info = 0;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*m)) {
        *info = -4;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SGERQ2", &i__1);
        return;
    }

    k = min(*m,*n);

    for (i = k; i >= 1; --i) {

/*        Generate elementary reflector H(i) to annihilate */
/*        A(m-k+i,1:n-k+i-1) */

        i__1 = *n - k + i;
        slarfg_(&i__1, &a[*m - k + i + (*n - k + i) * a_dim1], &a[*m - k + i + a_dim1], lda, &tau[i]);

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

        aii = a[*m - k + i + (*n - k + i) * a_dim1];
        a[*m - k + i + (*n - k + i) * a_dim1] = 1.f;
        i__1 = *m - k + i - 1;
        i__2 = *n - k + i;
        slarf_("Right", &i__1, &i__2, &a[*m - k + i + a_dim1], lda, &tau[i], &a[a_offset], lda, &work[1]);
        a[*m - k + i + (*n - k + i) * a_dim1] = aii;
    }
} /* sgerq2_ */