132 lines
3.4 KiB
C
132 lines
3.4 KiB
C
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#include "clapack.h"
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/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__,
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doublereal *ssmin, doublereal *ssmax)
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{
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/* System generated locals */
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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doublereal 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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/* DLAS2 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) DOUBLE PRECISION */
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/* The (1,1) element of the 2-by-2 matrix. */
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/* G (input) DOUBLE PRECISION */
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/* The (1,2) element of the 2-by-2 matrix. */
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/* H (input) DOUBLE PRECISION */
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/* The (2,2) element of the 2-by-2 matrix. */
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/* SSMIN (output) DOUBLE PRECISION */
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/* The smaller singular value. */
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/* SSMAX (output) DOUBLE PRECISION */
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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 = abs(*f);
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ga = abs(*g);
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ha = abs(*h__);
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fhmn = min(fa,ha);
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fhmx = max(fa,ha);
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if (fhmn == 0.) {
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*ssmin = 0.;
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if (fhmx == 0.) {
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*ssmax = ga;
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} else {
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/* Computing 2nd power */
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d__1 = min(fhmx,ga) / max(fhmx,ga);
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*ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.);
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}
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} else {
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if (ga < fhmx) {
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as = fhmn / fhmx + 1.;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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d__1 = ga / fhmx;
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au = d__1 * d__1;
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c__ = 2. / (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.) {
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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.;
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at = (fhmx - fhmn) / fhmx;
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/* Computing 2nd power */
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d__1 = as * au;
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/* Computing 2nd power */
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d__2 = at * au;
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c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.));
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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 DLAS2 */
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} /* dlas2_ */
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