Update to 2.0.0 tree from current Fremantle build

[opencv] / 3rdparty / lapack / slas2.c

diff --git a/3rdparty/lapack/slas2.c b/3rdparty/lapack/slas2.c
new file mode 100644 (file)
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+++ b/3rdparty/lapack/slas2.c
@@ -0,0 +1,132 @@
+#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_ */