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133 lines
3.4 KiB
C
133 lines
3.4 KiB
C
#include "clapack.h"
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/* Subroutine */ int slas2_(real *f, real *g, real *h__, real *ssmin, real *
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ssmax)
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{
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/* System generated locals */
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real r__1, r__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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real c__, fa, ga, ha, as, at, au, fhmn, fhmx;
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/* -- LAPACK auxiliary routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SLAS2 computes the singular values of the 2-by-2 matrix */
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/* [ F G ] */
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/* [ 0 H ]. */
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/* On return, SSMIN is the smaller singular value and SSMAX is the */
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/* larger singular value. */
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/* Arguments */
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/* ========= */
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/* F (input) REAL */
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/* The (1,1) element of the 2-by-2 matrix. */
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/* G (input) REAL */
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/* The (1,2) element of the 2-by-2 matrix. */
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/* H (input) REAL */
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/* The (2,2) element of the 2-by-2 matrix. */
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/* SSMIN (output) REAL */
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/* The smaller singular value. */
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/* SSMAX (output) REAL */
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/* The larger singular value. */
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/* Further Details */
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/* =============== */
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/* Barring over/underflow, all output quantities are correct to within */
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/* a few units in the last place (ulps), even in the absence of a guard */
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/* digit in addition/subtraction. */
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/* In IEEE arithmetic, the code works correctly if one matrix element is */
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/* infinite. */
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/* Overflow will not occur unless the largest singular value itself */
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/* overflows, or is within a few ulps of overflow. (On machines with */
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/* partial overflow, like the Cray, overflow may occur if the largest */
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/* singular value is within a factor of 2 of overflow.) */
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/* Underflow is harmless if underflow is gradual. Otherwise, results */
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/* may correspond to a matrix modified by perturbations of size near */
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/* the underflow threshold. */
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/* ==================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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fa = dabs(*f);
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ga = dabs(*g);
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ha = dabs(*h__);
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fhmn = dmin(fa,ha);
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fhmx = dmax(fa,ha);
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if (fhmn == 0.f) {
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*ssmin = 0.f;
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if (fhmx == 0.f) {
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*ssmax = ga;
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} else {
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/* Computing 2nd power */
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r__1 = dmin(fhmx,ga) / dmax(fhmx,ga);
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*ssmax = dmax(fhmx,ga) * sqrt(r__1 * r__1 + 1.f);
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}
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} else {
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if (ga < fhmx) {
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as = fhmn / fhmx + 1.f;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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r__1 = ga / fhmx;
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au = r__1 * r__1;
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c__ = 2.f / (sqrt(as * as + au) + sqrt(at * at + au));
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*ssmin = fhmn * c__;
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*ssmax = fhmx / c__;
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} else {
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au = fhmx / ga;
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if (au == 0.f) {
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/* Avoid possible harmful underflow if exponent range */
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/* asymmetric (true SSMIN may not underflow even if */
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/* AU underflows) */
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*ssmin = fhmn * fhmx / ga;
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*ssmax = ga;
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} else {
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as = fhmn / fhmx + 1.f;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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r__1 = as * au;
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/* Computing 2nd power */
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r__2 = at * au;
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c__ = 1.f / (sqrt(r__1 * r__1 + 1.f) + sqrt(r__2 * r__2 + 1.f)
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);
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*ssmin = fhmn * c__ * au;
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*ssmin += *ssmin;
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*ssmax = ga / (c__ + c__);
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}
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}
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}
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return 0;
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/* End of SLAS2 */
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} /* slas2_ */
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