mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
132 lines
3.4 KiB
132 lines
3.4 KiB
#include "clapack.h" |
|
|
|
/* 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 3.1) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
|
|
/* 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 .. */ |
|
/* .. */ |
|
/* .. Local Scalars .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
fa = dabs(*f); |
|
ga = dabs(*g); |
|
ha = dabs(*h__); |
|
fhmn = dmin(fa,ha); |
|
fhmx = dmax(fa,ha); |
|
if (fhmn == 0.f) { |
|
*ssmin = 0.f; |
|
if (fhmx == 0.f) { |
|
*ssmax = ga; |
|
} else { |
|
/* Computing 2nd power */ |
|
r__1 = dmin(fhmx,ga) / dmax(fhmx,ga); |
|
*ssmax = dmax(fhmx,ga) * sqrt(r__1 * r__1 + 1.f); |
|
} |
|
} else { |
|
if (ga < fhmx) { |
|
as = fhmn / fhmx + 1.f; |
|
at = (fhmx - fhmn) / fhmx; |
|
/* Computing 2nd power */ |
|
r__1 = ga / fhmx; |
|
au = r__1 * r__1; |
|
c__ = 2.f / (sqrt(as * as + au) + sqrt(at * at + au)); |
|
*ssmin = fhmn * c__; |
|
*ssmax = fhmx / c__; |
|
} else { |
|
au = fhmx / ga; |
|
if (au == 0.f) { |
|
|
|
/* 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.f; |
|
at = (fhmx - fhmn) / fhmx; |
|
/* Computing 2nd power */ |
|
r__1 = as * au; |
|
/* Computing 2nd power */ |
|
r__2 = at * au; |
|
c__ = 1.f / (sqrt(r__1 * r__1 + 1.f) + sqrt(r__2 * r__2 + 1.f) |
|
); |
|
*ssmin = fhmn * c__ * au; |
|
*ssmin += *ssmin; |
|
*ssmax = ga / (c__ + c__); |
|
} |
|
} |
|
} |
|
return 0; |
|
|
|
/* End of SLAS2 */ |
|
|
|
} /* slas2_ */
|
|
|