ergo
template_lapack_lae2.h
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1/* Ergo, version 3.8.2, a program for linear scaling electronic structure
2 * calculations.
3 * Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4 * and Anastasia Kruchinina.
5 *
6 * This program is free software: you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation, either version 3 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
15 *
16 * You should have received a copy of the GNU General Public License
17 * along with this program. If not, see <http://www.gnu.org/licenses/>.
18 *
19 * Primary academic reference:
20 * Ergo: An open-source program for linear-scaling electronic structure
21 * calculations,
22 * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23 * Kruchinina,
24 * SoftwareX 7, 107 (2018),
25 * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26 *
27 * For further information about Ergo, see <http://www.ergoscf.org>.
28 */
29
30 /* This file belongs to the template_lapack part of the Ergo source
31 * code. The source files in the template_lapack directory are modified
32 * versions of files originally distributed as CLAPACK, see the
33 * Copyright/license notice in the file template_lapack/COPYING.
34 */
35
36
37#ifndef TEMPLATE_LAPACK_LAE2_HEADER
38#define TEMPLATE_LAPACK_LAE2_HEADER
39
40
41template<class Treal>
42int template_lapack_lae2(const Treal *a, const Treal *b, const Treal *c__,
43 Treal *rt1, Treal *rt2)
44{
45/* -- LAPACK auxiliary routine (version 3.0) --
46 Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
47 Courant Institute, Argonne National Lab, and Rice University
48 October 31, 1992
49
50
51 Purpose
52 =======
53
54 DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
55 [ A B ]
56 [ B C ].
57 On return, RT1 is the eigenvalue of larger absolute value, and RT2
58 is the eigenvalue of smaller absolute value.
59
60 Arguments
61 =========
62
63 A (input) DOUBLE PRECISION
64 The (1,1) element of the 2-by-2 matrix.
65
66 B (input) DOUBLE PRECISION
67 The (1,2) and (2,1) elements of the 2-by-2 matrix.
68
69 C (input) DOUBLE PRECISION
70 The (2,2) element of the 2-by-2 matrix.
71
72 RT1 (output) DOUBLE PRECISION
73 The eigenvalue of larger absolute value.
74
75 RT2 (output) DOUBLE PRECISION
76 The eigenvalue of smaller absolute value.
77
78 Further Details
79 ===============
80
81 RT1 is accurate to a few ulps barring over/underflow.
82
83 RT2 may be inaccurate if there is massive cancellation in the
84 determinant A*C-B*B; higher precision or correctly rounded or
85 correctly truncated arithmetic would be needed to compute RT2
86 accurately in all cases.
87
88 Overflow is possible only if RT1 is within a factor of 5 of overflow.
89 Underflow is harmless if the input data is 0 or exceeds
90 underflow_threshold / macheps.
91
92 =====================================================================
93
94
95 Compute the eigenvalues */
96 /* System generated locals */
97 Treal d__1;
98 /* Local variables */
99 Treal acmn, acmx, ab, df, tb, sm, rt, adf;
100
101
102 sm = *a + *c__;
103 df = *a - *c__;
104 adf = absMACRO(df);
105 tb = *b + *b;
106 ab = absMACRO(tb);
107 if (absMACRO(*a) > absMACRO(*c__)) {
108 acmx = *a;
109 acmn = *c__;
110 } else {
111 acmx = *c__;
112 acmn = *a;
113 }
114 if (adf > ab) {
115/* Computing 2nd power */
116 d__1 = ab / adf;
117 rt = adf * template_blas_sqrt(d__1 * d__1 + 1.);
118 } else if (adf < ab) {
119/* Computing 2nd power */
120 d__1 = adf / ab;
121 rt = ab * template_blas_sqrt(d__1 * d__1 + 1.);
122 } else {
123
124/* Includes case AB=ADF=0 */
125
126 rt = ab * template_blas_sqrt(2.);
127 }
128 if (sm < 0.) {
129 *rt1 = (sm - rt) * .5;
130
131/* Order of execution important.
132 To get fully accurate smaller eigenvalue,
133 next line needs to be executed in higher precision. */
134
135 *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
136 } else if (sm > 0.) {
137 *rt1 = (sm + rt) * .5;
138
139/* Order of execution important.
140 To get fully accurate smaller eigenvalue,
141 next line needs to be executed in higher precision. */
142
143 *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
144 } else {
145
146/* Includes case RT1 = RT2 = 0 */
147
148 *rt1 = rt * .5;
149 *rt2 = rt * -.5;
150 }
151 return 0;
152
153/* End of DLAE2 */
154
155} /* dlae2_ */
156
157#endif
Treal template_blas_sqrt(Treal x)
#define absMACRO(x)
Definition template_blas_common.h:47
int template_lapack_lae2(const Treal *a, const Treal *b, const Treal *c__, Treal *rt1, Treal *rt2)
Definition template_lapack_lae2.h:42