146 lines
3.8 KiB
C
146 lines
3.8 KiB
C
/* slas2.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 "clapack.h"
|
|
|
|
|
|
/* Subroutine */ int slas2_(real *f, real *g, real *h__, real *ssmin, real *
|
|
ssmax)
|
|
{
|
|
/* System generated locals */
|
|
real r__1, r__2;
|
|
|
|
/* Builtin functions */
|
|
double sqrt(doublereal);
|
|
|
|
/* Local variables */
|
|
real c__, fa, ga, ha, as, at, au, fhmn, fhmx;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.2) -- */
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
|
/* November 2006 */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* SLAS2 computes the singular values of the 2-by-2 matrix */
|
|
/* [ F G ] */
|
|
/* [ 0 H ]. */
|
|
/* On return, SSMIN is the smaller singular value and SSMAX is the */
|
|
/* larger singular value. */
|
|
|
|
/* Arguments */
|
|
/* ========= */
|
|
|
|
/* F (input) REAL */
|
|
/* The (1,1) element of the 2-by-2 matrix. */
|
|
|
|
/* G (input) REAL */
|
|
/* The (1,2) element of the 2-by-2 matrix. */
|
|
|
|
/* H (input) REAL */
|
|
/* The (2,2) element of the 2-by-2 matrix. */
|
|
|
|
/* SSMIN (output) REAL */
|
|
/* The smaller singular value. */
|
|
|
|
/* SSMAX (output) REAL */
|
|
/* The larger singular value. */
|
|
|
|
/* Further Details */
|
|
/* =============== */
|
|
|
|
/* Barring over/underflow, all output quantities are correct to within */
|
|
/* a few units in the last place (ulps), even in the absence of a guard */
|
|
/* digit in addition/subtraction. */
|
|
|
|
/* In IEEE arithmetic, the code works correctly if one matrix element is */
|
|
/* infinite. */
|
|
|
|
/* Overflow will not occur unless the largest singular value itself */
|
|
/* overflows, or is within a few ulps of overflow. (On machines with */
|
|
/* partial overflow, like the Cray, overflow may occur if the largest */
|
|
/* singular value is within a factor of 2 of overflow.) */
|
|
|
|
/* Underflow is harmless if underflow is gradual. Otherwise, results */
|
|
/* may correspond to a matrix modified by perturbations of size near */
|
|
/* the underflow threshold. */
|
|
|
|
/* ==================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
|
|
|
|
fa = dabs(*f);
|
|
ga = dabs(*g);
|
|
ha = dabs(*h__);
|
|
fhmn = dmin(fa,ha);
|
|
fhmx = dmax(fa,ha);
|
|
if (fhmn == 0.f) {
|
|
*ssmin = 0.f;
|
|
if (fhmx == 0.f) {
|
|
*ssmax = ga;
|
|
} else {
|
|
/* Computing 2nd power */
|
|
r__1 = dmin(fhmx,ga) / dmax(fhmx,ga);
|
|
*ssmax = dmax(fhmx,ga) * sqrt(r__1 * r__1 + 1.f);
|
|
}
|
|
} else {
|
|
if (ga < fhmx) {
|
|
as = fhmn / fhmx + 1.f;
|
|
at = (fhmx - fhmn) / fhmx;
|
|
/* Computing 2nd power */
|
|
r__1 = ga / fhmx;
|
|
au = r__1 * r__1;
|
|
c__ = 2.f / (sqrt(as * as + au) + sqrt(at * at + au));
|
|
*ssmin = fhmn * c__;
|
|
*ssmax = fhmx / c__;
|
|
} else {
|
|
au = fhmx / ga;
|
|
if (au == 0.f) {
|
|
|
|
/* Avoid possible harmful underflow if exponent range */
|
|
/* asymmetric (true SSMIN may not underflow even if */
|
|
/* AU underflows) */
|
|
|
|
*ssmin = fhmn * fhmx / ga;
|
|
*ssmax = ga;
|
|
} else {
|
|
as = fhmn / fhmx + 1.f;
|
|
at = (fhmx - fhmn) / fhmx;
|
|
/* Computing 2nd power */
|
|
r__1 = as * au;
|
|
/* Computing 2nd power */
|
|
r__2 = at * au;
|
|
c__ = 1.f / (sqrt(r__1 * r__1 + 1.f) + sqrt(r__2 * r__2 + 1.f)
|
|
);
|
|
*ssmin = fhmn * c__ * au;
|
|
*ssmin += *ssmin;
|
|
*ssmax = ga / (c__ + c__);
|
|
}
|
|
}
|
|
}
|
|
return 0;
|
|
|
|
/* End of SLAS2 */
|
|
|
|
} /* slas2_ */
|