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*/
#include "f2c.h"
/* > \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
=========== DOCUMENTATION ===========
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Definition:
===========
SUBROUTINE DLAE2( A, B, C, RT1, RT2 )
DOUBLE PRECISION A, B, C, RT1, RT2
> \par Purpose:
=============
>
> \verbatim
>
> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
> [ A B ]
> [ B C ].
> On return, RT1 is the eigenvalue of larger absolute value, and RT2
> is the eigenvalue of smaller absolute value.
> \endverbatim
Arguments:
==========
> \param[in] A
> \verbatim
> A is DOUBLE PRECISION
> The (1,1) element of the 2-by-2 matrix.
> \endverbatim
>
> \param[in] B
> \verbatim
> B is DOUBLE PRECISION
> The (1,2) and (2,1) elements of the 2-by-2 matrix.
> \endverbatim
>
> \param[in] C
> \verbatim
> C is DOUBLE PRECISION
> The (2,2) element of the 2-by-2 matrix.
> \endverbatim
>
> \param[out] RT1
> \verbatim
> RT1 is DOUBLE PRECISION
> The eigenvalue of larger absolute value.
> \endverbatim
>
> \param[out] RT2
> \verbatim
> RT2 is DOUBLE PRECISION
> The eigenvalue of smaller absolute value.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERauxiliary
> \par Further Details:
=====================
>
> \verbatim
>
> 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.
>
> 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.
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdlae2_(doublereal *a, doublereal *b, doublereal *c__,
doublereal *rt1, doublereal *rt2)
{
/* System generated locals */
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal ab, df, tb, sm, rt, adf, acmn, acmx;
/* -- LAPACK auxiliary routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
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;
/* 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;
/* 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;
}
return 0;
/* End of DLAE2 */
} /* igraphdlae2_ */