slapll.c

来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 83 行

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

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

    /* Local variables */
    static real 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) REAL 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) REAL 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) REAL                                               */
/*          The smallest singular value of the N-by-2 matrix A = (X Y). */
/*                                                                      */
/* ===================================================================== */

/*     Quick return if possible */

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

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

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

    c = -tau * sdot_(n, x, incx, y, incy);
    saxpy_(n, &c, x, incx, y, incy);

    i__1 = *n - 1;
    slarfg_(&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. */

    slas2_(&a11, &a12, &a22, ssmin, &ssmax);

} /* slapll_ */