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/* lapack/single/slas2.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 SLAS2( F, G, H, SSMIN, SSMAX ) >*/
/* 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 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/*< REAL F, G, H, SSMAX, SSMIN >*/
/* .. */
/* 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 .. */
/*< REAL ZERO >*/
/*< PARAMETER ( ZERO = 0.0E0 ) >*/
/*< REAL ONE >*/
/*< PARAMETER ( ONE = 1.0E0 ) >*/
/*< REAL TWO >*/
/*< PARAMETER ( TWO = 2.0E0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< REAL AS, AT, AU, C, FA, FHMN, FHMX, GA, HA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX, MIN, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/*< FA = ABS( F ) >*/
fa = dabs(*f);
/*< GA = ABS( G ) >*/
ga = dabs(*g);
/*< HA = ABS( H ) >*/
ha = dabs(*h__);
/*< FHMN = MIN( FA, HA ) >*/
fhmn = dmin(fa,ha);
/*< FHMX = MAX( FA, HA ) >*/
fhmx = dmax(fa,ha);
/*< IF( FHMN.EQ.ZERO ) THEN >*/
if (fhmn == (float)0.) {
/*< SSMIN = ZERO >*/
*ssmin = (float)0.;
/*< IF( FHMX.EQ.ZERO ) THEN >*/
if (fhmx == (float)0.) {
/*< SSMAX = GA >*/
*ssmax = ga;
/*< ELSE >*/
} else {
/*< >*/
/* Computing 2nd power */
r__1 = dmin(fhmx,ga) / dmax(fhmx,ga);
*ssmax = dmax(fhmx,ga) * sqrt(r__1 * r__1 + (float)1.);
/*< END IF >*/
}
/*< ELSE >*/
} else {
/*< IF( GA.LT.FHMX ) THEN >*/
if (ga < fhmx) {
/*< AS = ONE + FHMN / FHMX >*/
as = fhmn / fhmx + (float)1.;
/*< AT = ( FHMX-FHMN ) / FHMX >*/
at = (fhmx - fhmn) / fhmx;
/*< AU = ( GA / FHMX )**2 >*/
/* Computing 2nd power */
r__1 = ga / fhmx;
au = r__1 * r__1;
/*< C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) ) >*/
c__ = (float)2. / (sqrt(as * as + au) + sqrt(at * at + au));
/*< SSMIN = FHMN*C >*/
*ssmin = fhmn * c__;
/*< SSMAX = FHMX / C >*/
*ssmax = fhmx / c__;
/*< ELSE >*/
} else {
/*< AU = FHMX / GA >*/
au = fhmx / ga;
/*< IF( AU.EQ.ZERO ) THEN >*/
if (au == (float)0.) {
/* Avoid possible harmful underflow if exponent range */
/* asymmetric (true SSMIN may not underflow even if */
/* AU underflows) */
/*< SSMIN = ( FHMN*FHMX ) / GA >*/
*ssmin = fhmn * fhmx / ga;
/*< SSMAX = GA >*/
*ssmax = ga;
/*< ELSE >*/
} else {
/*< AS = ONE + FHMN / FHMX >*/
as = fhmn / fhmx + (float)1.;
/*< AT = ( FHMX-FHMN ) / FHMX >*/
at = (fhmx - fhmn) / fhmx;
/*< >*/
/* Computing 2nd power */
r__1 = as * au;
/* Computing 2nd power */
r__2 = at * au;
c__ = (float)1. / (sqrt(r__1 * r__1 + (float)1.) + sqrt(r__2 *
r__2 + (float)1.));
/*< SSMIN = ( FHMN*C )*AU >*/
*ssmin = fhmn * c__ * au;
/*< SSMIN = SSMIN + SSMIN >*/
*ssmin += *ssmin;
/*< SSMAX = GA / ( C+C ) >*/
*ssmax = ga / (c__ + c__);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of SLAS2 */
/*< END >*/
} /* slas2_ */
#ifdef __cplusplus
}
#endif
|
