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/* ../../../dependencies/lapack/src/dlas2.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"
/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__,
doublereal *ssmin, doublereal *ssmax)
{
/* System generated locals */
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal c__, fa, ga, ha, as, at, au, fhmn, fhmx;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAS2 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) DOUBLE PRECISION */
/* The (1,1) element of the 2-by-2 matrix. */
/* G (input) DOUBLE PRECISION */
/* The (1,2) element of the 2-by-2 matrix. */
/* H (input) DOUBLE PRECISION */
/* The (2,2) element of the 2-by-2 matrix. */
/* SSMIN (output) DOUBLE PRECISION */
/* The smaller singular value. */
/* SSMAX (output) DOUBLE PRECISION */
/* 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 = abs(*f);
ga = abs(*g);
ha = abs(*h__);
fhmn = min(fa,ha);
fhmx = max(fa,ha);
if (fhmn == 0.) {
*ssmin = 0.;
if (fhmx == 0.) {
*ssmax = ga;
} else {
/* Computing 2nd power */
d__1 = min(fhmx,ga) / max(fhmx,ga);
*ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.);
}
} else {
if (ga < fhmx) {
as = fhmn / fhmx + 1.;
at = (fhmx - fhmn) / fhmx;
/* Computing 2nd power */
d__1 = ga / fhmx;
au = d__1 * d__1;
c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au));
*ssmin = fhmn * c__;
*ssmax = fhmx / c__;
} else {
au = fhmx / ga;
if (au == 0.) {
/* 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.;
at = (fhmx - fhmn) / fhmx;
/* Computing 2nd power */
d__1 = as * au;
/* Computing 2nd power */
d__2 = at * au;
c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.));
*ssmin = fhmn * c__ * au;
*ssmin += *ssmin;
*ssmax = ga / (c__ + c__);
}
}
}
return 0;
/* End of DLAS2 */
} /* dlas2_ */
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