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144 lines
3.9 KiB
144 lines
3.9 KiB
/* dlas2.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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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 3.2) -- */ |
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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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