starpu-max/min-dgels/base/SRC/dlapll.c

/* 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 _starpu_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 _starpu_ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    extern /* Subroutine */ int _starpu_dlas2_(doublereal *, doublereal *, doublereal 
	    *, doublereal *, doublereal *), _starpu_daxpy_(integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *);
    doublereal ssmax;
    extern /* Subroutine */ int _starpu_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 ) */

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

    c__ = -tau * _starpu_ddot_(n, &x[1], incx, &y[1], incy);
    _starpu_daxpy_(n, &c__, &x[1], incx, &y[1], incy);

    i__1 = *n - 1;
    _starpu_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. */

    _starpu_dlas2_(&a11, &a12, &a22, ssmin, &ssmax);

    return 0;

/*     End of DLAPLL */

} /* _starpu_dlapll_ */