Update to 2.0.0 tree from current Fremantle build

[opencv] / 3rdparty / lapack / dlaev2.c

diff --git a/3rdparty/lapack/dlaev2.c b/3rdparty/lapack/dlaev2.c
new file mode 100644 (file)
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+++ b/3rdparty/lapack/dlaev2.c
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+#include "clapack.h"
+
+/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, 
+       doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1)
+{
+    /* System generated locals */
+    doublereal d__1;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    doublereal ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
+    integer sgn1, sgn2;
+    doublereal acmn, acmx;
+
+
+/*  -- LAPACK auxiliary routine (version 3.1) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */
+/*     [  A   B  ] */
+/*     [  B   C  ]. */
+/*  On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */
+/*  eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */
+/*  eigenvector for RT1, giving the decomposition */
+
+/*     [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ] */
+/*     [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ]. */
+
+/*  Arguments */
+/*  ========= */
+
+/*  A       (input) DOUBLE PRECISION */
+/*          The (1,1) element of the 2-by-2 matrix. */
+
+/*  B       (input) DOUBLE PRECISION */
+/*          The (1,2) element and the conjugate of the (2,1) element of */
+/*          the 2-by-2 matrix. */
+
+/*  C       (input) DOUBLE PRECISION */
+/*          The (2,2) element of the 2-by-2 matrix. */
+
+/*  RT1     (output) DOUBLE PRECISION */
+/*          The eigenvalue of larger absolute value. */
+
+/*  RT2     (output) DOUBLE PRECISION */
+/*          The eigenvalue of smaller absolute value. */
+
+/*  CS1     (output) DOUBLE PRECISION */
+/*  SN1     (output) DOUBLE PRECISION */
+/*          The vector (CS1, SN1) is a unit right eigenvector for RT1. */
+
+/*  Further Details */
+/*  =============== */
+
+/*  RT1 is accurate to a few ulps barring over/underflow. */
+
+/*  RT2 may be inaccurate if there is massive cancellation in the */
+/*  determinant A*C-B*B; higher precision or correctly rounded or */
+/*  correctly truncated arithmetic would be needed to compute RT2 */
+/*  accurately in all cases. */
+
+/*  CS1 and SN1 are accurate to a few ulps barring over/underflow. */
+
+/*  Overflow is possible only if RT1 is within a factor of 5 of overflow. */
+/*  Underflow is harmless if the input data is 0 or exceeds */
+/*     underflow_threshold / macheps. */
+
+/* ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Compute the eigenvalues */
+
+    sm = *a + *c__;
+    df = *a - *c__;
+    adf = abs(df);
+    tb = *b + *b;
+    ab = abs(tb);
+    if (abs(*a) > abs(*c__)) {
+       acmx = *a;
+       acmn = *c__;
+    } else {
+       acmx = *c__;
+       acmn = *a;
+    }
+    if (adf > ab) {
+/* Computing 2nd power */
+       d__1 = ab / adf;
+       rt = adf * sqrt(d__1 * d__1 + 1.);
+    } else if (adf < ab) {
+/* Computing 2nd power */
+       d__1 = adf / ab;
+       rt = ab * sqrt(d__1 * d__1 + 1.);
+    } else {
+
+/*        Includes case AB=ADF=0 */
+
+       rt = ab * sqrt(2.);
+    }
+    if (sm < 0.) {
+       *rt1 = (sm - rt) * .5;
+       sgn1 = -1;
+
+/*        Order of execution important. */
+/*        To get fully accurate smaller eigenvalue, */
+/*        next line needs to be executed in higher precision. */
+
+       *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
+    } else if (sm > 0.) {
+       *rt1 = (sm + rt) * .5;
+       sgn1 = 1;
+
+/*        Order of execution important. */
+/*        To get fully accurate smaller eigenvalue, */
+/*        next line needs to be executed in higher precision. */
+
+       *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
+    } else {
+
+/*        Includes case RT1 = RT2 = 0 */
+
+       *rt1 = rt * .5;
+       *rt2 = rt * -.5;
+       sgn1 = 1;
+    }
+
+/*     Compute the eigenvector */
+
+    if (df >= 0.) {
+       cs = df + rt;
+       sgn2 = 1;
+    } else {
+       cs = df - rt;
+       sgn2 = -1;
+    }
+    acs = abs(cs);
+    if (acs > ab) {
+       ct = -tb / cs;
+       *sn1 = 1. / sqrt(ct * ct + 1.);
+       *cs1 = ct * *sn1;
+    } else {
+       if (ab == 0.) {
+           *cs1 = 1.;
+           *sn1 = 0.;
+       } else {
+           tn = -cs / tb;
+           *cs1 = 1. / sqrt(tn * tn + 1.);
+           *sn1 = tn * *cs1;
+       }
+    }
+    if (sgn1 == sgn2) {
+       tn = *cs1;
+       *cs1 = -(*sn1);
+       *sn1 = tn;
+    }
+    return 0;
+
+/*     End of DLAEV2 */
+
+} /* dlaev2_ */