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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_LAPACK_LAE2_HEADER
#define TEMPLATE_LAPACK_LAE2_HEADER
template<class Treal>
int template_lapack_lae2(const Treal *a, const Treal *b, const Treal *c__,
Treal *rt1, Treal *rt2)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
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.
Arguments
=========
A (input) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
B (input) DOUBLE PRECISION
The (1,2) and (2,1) elements 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.
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.
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.
=====================================================================
Compute the eigenvalues */
/* System generated locals */
Treal d__1;
/* Local variables */
Treal acmn, acmx, ab, df, tb, sm, rt, adf;
sm = *a + *c__;
df = *a - *c__;
adf = absMACRO(df);
tb = *b + *b;
ab = absMACRO(tb);
if (absMACRO(*a) > absMACRO(*c__)) {
acmx = *a;
acmn = *c__;
} else {
acmx = *c__;
acmn = *a;
}
if (adf > ab) {
/* Computing 2nd power */
d__1 = ab / adf;
rt = adf * template_blas_sqrt(d__1 * d__1 + 1.);
} else if (adf < ab) {
/* Computing 2nd power */
d__1 = adf / ab;
rt = ab * template_blas_sqrt(d__1 * d__1 + 1.);
} else {
/* Includes case AB=ADF=0 */
rt = ab * template_blas_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 */
} /* dlae2_ */
#endif
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