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/* lapack/single/slapll.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/*< SUBROUTINE SLAPLL( N, X, INCX, Y, INCY, SSMIN ) >*/
/* Subroutine */ int slapll_(integer *n, real *x, integer *incx, real *y,
integer *incy, real *ssmin)
{
/* System generated locals */
integer i__1;
/* Local variables */
real c__, a11, a12, a22, tau;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
extern /* Subroutine */ int slas2_(real *, real *, real *, real *, real *)
;
real ssmax;
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
real *, integer *), slarfg_(integer *, real *, real *, integer *,
real *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* March 31, 1993 */
/* .. Scalar Arguments .. */
/*< INTEGER INCX, INCY, N >*/
/*< REAL SSMIN >*/
/* .. */
/* .. Array Arguments .. */
/*< REAL X( * ), Y( * ) >*/
/* .. */
/* 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 ). */
/* ===================================================================== */
/* .. Parameters .. */
/*< REAL ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< REAL A11, A12, A22, C, SSMAX, TAU >*/
/* .. */
/* .. External Functions .. */
/*< REAL SDOT >*/
/*< EXTERNAL SDOT >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL SAXPY, SLARFG, SLAS2 >*/
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/*< IF( N.LE.1 ) THEN >*/
/* Parameter adjustments */
--y;
--x;
/* Function Body */
if (*n <= 1) {
/*< SSMIN = ZERO >*/
*ssmin = (float)0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Compute the QR factorization of the N-by-2 matrix ( X Y ) */
/*< CALL SLARFG( N, X( 1 ), X( 1+INCX ), INCX, TAU ) >*/
slarfg_(n, &x[1], &x[*incx + 1], incx, &tau);
/*< A11 = X( 1 ) >*/
a11 = x[1];
/*< X( 1 ) = ONE >*/
x[1] = (float)1.;
/*< C = -TAU*SDOT( N, X, INCX, Y, INCY ) >*/
c__ = -tau * sdot_(n, &x[1], incx, &y[1], incy);
/*< CALL SAXPY( N, C, X, INCX, Y, INCY ) >*/
saxpy_(n, &c__, &x[1], incx, &y[1], incy);
/*< CALL SLARFG( N-1, Y( 1+INCY ), Y( 1+2*INCY ), INCY, TAU ) >*/
i__1 = *n - 1;
slarfg_(&i__1, &y[*incy + 1], &y[(*incy << 1) + 1], incy, &tau);
/*< A12 = Y( 1 ) >*/
a12 = y[1];
/*< A22 = Y( 1+INCY ) >*/
a22 = y[*incy + 1];
/* Compute the SVD of 2-by-2 Upper triangular matrix. */
/*< CALL SLAS2( A11, A12, A22, SSMIN, SSMAX ) >*/
slas2_(&a11, &a12, &a22, ssmin, &ssmax);
/*< RETURN >*/
return 0;
/* End of SLAPLL */
/*< END >*/
} /* slapll_ */
#ifdef __cplusplus
}
#endif
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