Abdelrahman Said
250 lines
6.5 KiB
C
250 lines
6.5 KiB
C
/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* > \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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> \htmlonly
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> Download DLAEV2 + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaev2.
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f">
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> [TGZ]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaev2.
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f">
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> [ZIP]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaev2.
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f">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
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DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1
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> \par Purpose:
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=============
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>
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> \verbatim
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>
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> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
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> [ A B ]
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> [ B C ].
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> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
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> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
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> eigenvector for RT1, giving the decomposition
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>
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> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
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> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
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> \endverbatim
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Arguments:
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==========
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> \param[in] A
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> \verbatim
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> A is DOUBLE PRECISION
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> The (1,1) element of the 2-by-2 matrix.
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> \endverbatim
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>
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> \param[in] B
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> \verbatim
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> B is DOUBLE PRECISION
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> The (1,2) element and the conjugate of the (2,1) element of
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> the 2-by-2 matrix.
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> \endverbatim
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>
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> \param[in] C
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> \verbatim
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> C is DOUBLE PRECISION
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> The (2,2) element of the 2-by-2 matrix.
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> \endverbatim
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>
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> \param[out] RT1
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> \verbatim
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> RT1 is DOUBLE PRECISION
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> The eigenvalue of larger absolute value.
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> \endverbatim
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>
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> \param[out] RT2
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> \verbatim
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> RT2 is DOUBLE PRECISION
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> The eigenvalue of smaller absolute value.
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> \endverbatim
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>
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> \param[out] CS1
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> \verbatim
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> CS1 is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[out] SN1
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> \verbatim
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> SN1 is DOUBLE PRECISION
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> The vector (CS1, SN1) is a unit right eigenvector for RT1.
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date September 2012
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> \ingroup auxOTHERauxiliary
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> \par Further Details:
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=====================
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>
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> \verbatim
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>
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> RT1 is accurate to a few ulps barring over/underflow.
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>
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> RT2 may be inaccurate if there is massive cancellation in the
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> determinant A*C-B*B; higher precision or correctly rounded or
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> correctly truncated arithmetic would be needed to compute RT2
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> accurately in all cases.
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>
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> CS1 and SN1 are accurate to a few ulps barring over/underflow.
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>
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> Overflow is possible only if RT1 is within a factor of 5 of overflow.
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> Underflow is harmless if the input data is 0 or exceeds
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> underflow_threshold / macheps.
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> \endverbatim
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>
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=====================================================================
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Subroutine */ int igraphdlaev2_(doublereal *a, doublereal *b, doublereal *c__,
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doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1)
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{
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/* System generated locals */
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doublereal d__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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doublereal ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
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integer sgn1, sgn2;
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doublereal acmn, acmx;
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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September 2012
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=====================================================================
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Compute the eigenvalues */
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sm = *a + *c__;
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df = *a - *c__;
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adf = abs(df);
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tb = *b + *b;
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ab = abs(tb);
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if (abs(*a) > abs(*c__)) {
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acmx = *a;
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acmn = *c__;
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} else {
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acmx = *c__;
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acmn = *a;
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}
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if (adf > ab) {
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/* Computing 2nd power */
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d__1 = ab / adf;
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rt = adf * sqrt(d__1 * d__1 + 1.);
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} else if (adf < ab) {
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/* Computing 2nd power */
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d__1 = adf / ab;
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rt = ab * sqrt(d__1 * d__1 + 1.);
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} else {
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/* Includes case AB=ADF=0 */
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rt = ab * sqrt(2.);
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}
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if (sm < 0.) {
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*rt1 = (sm - rt) * .5;
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sgn1 = -1;
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/* Order of execution important.
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To get fully accurate smaller eigenvalue,
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next line needs to be executed in higher precision. */
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*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
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} else if (sm > 0.) {
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*rt1 = (sm + rt) * .5;
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sgn1 = 1;
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/* Order of execution important.
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To get fully accurate smaller eigenvalue,
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next line needs to be executed in higher precision. */
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*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
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} else {
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/* Includes case RT1 = RT2 = 0 */
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*rt1 = rt * .5;
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*rt2 = rt * -.5;
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sgn1 = 1;
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}
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/* Compute the eigenvector */
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if (df >= 0.) {
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cs = df + rt;
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sgn2 = 1;
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} else {
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cs = df - rt;
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sgn2 = -1;
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}
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acs = abs(cs);
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if (acs > ab) {
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ct = -tb / cs;
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*sn1 = 1. / sqrt(ct * ct + 1.);
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*cs1 = ct * *sn1;
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} else {
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if (ab == 0.) {
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*cs1 = 1.;
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*sn1 = 0.;
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} else {
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tn = -cs / tb;
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*cs1 = 1. / sqrt(tn * tn + 1.);
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*sn1 = tn * *cs1;
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}
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}
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if (sgn1 == sgn2) {
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tn = *cs1;
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*cs1 = -(*sn1);
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*sn1 = tn;
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}
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return 0;
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/* End of DLAEV2 */
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} /* igraphdlaev2_ */
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