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/* dlapll.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int dlapll_(integer *n, doublereal *x, integer *incx,
doublereal *y, integer *incy, doublereal *ssmin)
{
/* System generated locals */
integer i__1;
/* Local variables */
doublereal c__, a11, a12, a22, tau;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal
*, doublereal *, doublereal *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
doublereal ssmax;
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* 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 ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
--y;
--x;
/* Function Body */
if (*n <= 1) {
*ssmin = 0.;
return 0;
}
/* Compute the QR factorization of the N-by-2 matrix ( X Y ) */
dlarfg_(n, &x[1], &x[*incx + 1], incx, &tau);
a11 = x[1];
x[1] = 1.;
c__ = -tau * ddot_(n, &x[1], incx, &y[1], incy);
daxpy_(n, &c__, &x[1], incx, &y[1], incy);
i__1 = *n - 1;
dlarfg_(&i__1, &y[*incy + 1], &y[(*incy << 1) + 1], incy, &tau);
a12 = y[1];
a22 = y[*incy + 1];
/* Compute the SVD of 2-by-2 Upper triangular matrix. */
dlas2_(&a11, &a12, &a22, ssmin, &ssmax);
return 0;
/* End of DLAPLL */
} /* dlapll_ */
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