dlapll.c

InsightToolkit-1.4.0(有大量的优化算法程序)

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

/* Subroutine */ void dlapll_(integer *n, doublereal *x, integer *incx, doublereal *y, integer *incy, doublereal *ssmin)
{
    /* System generated locals */
    integer i__1;

    /* Local variables */
    static doublereal c, ssmax, a11, a12, a22, tau;

/*  -- LAPACK auxiliary routine (version 2.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     March 31, 1993 */

/*  Purpose                                                               */
/*  =======                                                               */
/*                                                                        */
/*  Given two column vectors X and Y, let                                 */
/*                                                                        */
/*                       A = ( X Y ).                                     */
/*                                                                        */
/*  The subroutine first computes the QR factorization of A = Q*R,        */
/*  and then computes the SVD of the 2-by-2 upper triangular matrix R.    */
/*  The smaller singular value of R is returned in SSMIN, which is used   */
/*  as the measurement of the linear dependency of the vectors X and Y.   */
/*                                                                        */
/*  Arguments                                                             */
/*  =========                                                             */
/*                                                                        */
/*  N       (input) INTEGER                                               */
/*          The length of the vectors X and Y.                            */
/*                                                                        */
/*  X       (input/output) DOUBLE PRECISION array,                        */
/*                         dimension (1+(N-1)*INCX)                       */
/*          On entry, X contains the N-vector X.                          */
/*          On exit, X is overwritten.                                    */
/*                                                                        */
/*  INCX    (input) INTEGER                                               */
/*          The increment between successive elements of X. INCX > 0.     */
/*                                                                        */
/*  Y       (input/output) DOUBLE PRECISION array,                        */
/*                         dimension (1+(N-1)*INCY)                       */
/*          On entry, Y contains the N-vector Y.                          */
/*          On exit, Y is overwritten.                                    */
/*                                                                        */
/*  INCY    (input) INTEGER                                               */
/*          The increment between successive elements of Y. INCY > 0.     */
/*                                                                        */
/*  SSMIN   (output) DOUBLE PRECISION                                     */
/*          The smallest singular value of the N-by-2 matrix A = (X Y).   */
/*                                                                        */
/*  ===================================================================== */

/*     Quick return if possible */

    if (*n <= 1) {
        *ssmin = 0.;
        return;
    }

/*     Compute the QR factorization of the N-by-2 matrix ( X Y ) */

    dlarfg_(n, x, &x[*incx], incx, &tau);
    a11 = x[0];
    x[0] = 1.;

    c = -tau * ddot_(n, x, incx, y, incy);
    daxpy_(n, &c, x, incx, y, incy);

    i__1 = *n - 1;
    dlarfg_(&i__1, &y[*incy], &y[2 * *incy], incy, &tau);

    a12 = y[0];
    a22 = y[*incy];

/*     Compute the SVD of 2-by-2 Upper triangular matrix. */

    dlas2_(&a11, &a12, &a22, ssmin, &ssmax);

} /* dlapll_ */