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references/igraph-1.0.1/vendor/lapack/dlaev2.c
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/* -- translated by f2c (version 20240504).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* > \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLAEV2 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaev2.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaev2.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaev2.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1
> \par Purpose:
=============
>
> \verbatim
>
> 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 ].
> \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) element and the conjugate of the (2,1) element 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
>
> \param[out] CS1
> \verbatim
> CS1 is DOUBLE PRECISION
> \endverbatim
>
> \param[out] SN1
> \verbatim
> SN1 is DOUBLE PRECISION
> The vector (CS1, SN1) is a unit right eigenvector for RT1.
> \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.
>
> 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.
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdlaev2_(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 3.4.2) --
-- 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;
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 */
} /* igraphdlaev2_ */