ergo
template_lapack_potf2.h
Go to the documentation of this file.
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_POTF2_HEADER
38#define TEMPLATE_LAPACK_POTF2_HEADER
39
40
41template<class Treal>
42int template_lapack_potf2(const char *uplo, const integer *n, Treal *a, const integer *
43 lda, integer *info)
44{
45/* -- LAPACK routine (version 3.0) --
46 Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
47 Courant Institute, Argonne National Lab, and Rice University
48 February 29, 1992
49
50
51 Purpose
52 =======
53
54 DPOTF2 computes the Cholesky factorization of a real symmetric
55 positive definite matrix A.
56
57 The factorization has the form
58 A = U' * U , if UPLO = 'U', or
59 A = L * L', if UPLO = 'L',
60 where U is an upper triangular matrix and L is lower triangular.
61
62 This is the unblocked version of the algorithm, calling Level 2 BLAS.
63
64 Arguments
65 =========
66
67 UPLO (input) CHARACTER*1
68 Specifies whether the upper or lower triangular part of the
69 symmetric matrix A is stored.
70 = 'U': Upper triangular
71 = 'L': Lower triangular
72
73 N (input) INTEGER
74 The order of the matrix A. N >= 0.
75
76 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
77 On entry, the symmetric matrix A. If UPLO = 'U', the leading
78 n by n upper triangular part of A contains the upper
79 triangular part of the matrix A, and the strictly lower
80 triangular part of A is not referenced. If UPLO = 'L', the
81 leading n by n lower triangular part of A contains the lower
82 triangular part of the matrix A, and the strictly upper
83 triangular part of A is not referenced.
84
85 On exit, if INFO = 0, the factor U or L from the Cholesky
86 factorization A = U'*U or A = L*L'.
87
88 LDA (input) INTEGER
89 The leading dimension of the array A. LDA >= max(1,N).
90
91 INFO (output) INTEGER
92 = 0: successful exit
93 < 0: if INFO = -k, the k-th argument had an illegal value
94 > 0: if INFO = k, the leading minor of order k is not
95 positive definite, and the factorization could not be
96 completed.
97
98 =====================================================================
99
100
101 Test the input parameters.
102
103 Parameter adjustments */
104 /* Table of constant values */
105 integer c__1 = 1;
106 Treal c_b10 = -1.;
107 Treal c_b12 = 1.;
108
109 /* System generated locals */
110 integer a_dim1, a_offset, i__1, i__2, i__3;
111 Treal d__1;
112 /* Local variables */
113 integer j;
114 logical upper;
115 Treal ajj;
116#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
117
118
119 a_dim1 = *lda;
120 a_offset = 1 + a_dim1 * 1;
121 a -= a_offset;
122
123 /* Function Body */
124 *info = 0;
125 upper = template_blas_lsame(uplo, "U");
126 if (! upper && ! template_blas_lsame(uplo, "L")) {
127 *info = -1;
128 } else if (*n < 0) {
129 *info = -2;
130 } else if (*lda < maxMACRO(1,*n)) {
131 *info = -4;
132 }
133 if (*info != 0) {
134 i__1 = -(*info);
135 template_blas_erbla("POTF2 ", &i__1);
136 return 0;
137 }
138
139/* Quick return if possible */
140
141 if (*n == 0) {
142 return 0;
143 }
144
145 if (upper) {
146
147/* Compute the Cholesky factorization A = U'*U. */
148
149 i__1 = *n;
150 for (j = 1; j <= i__1; ++j) {
151
152/* Compute U(J,J) and test for non-positive-definiteness. */
153
154 i__2 = j - 1;
155 ajj = a_ref(j, j) - template_blas_dot(&i__2, &a_ref(1, j), &c__1, &a_ref(1, j)
156 , &c__1);
157 if (ajj <= 0.) {
158 a_ref(j, j) = ajj;
159 goto L30;
160 }
161 ajj = template_blas_sqrt(ajj);
162 a_ref(j, j) = ajj;
163
164/* Compute elements J+1:N of row J. */
165
166 if (j < *n) {
167 i__2 = j - 1;
168 i__3 = *n - j;
169 template_blas_gemv("Transpose", &i__2, &i__3, &c_b10, &a_ref(1, j + 1),
170 lda, &a_ref(1, j), &c__1, &c_b12, &a_ref(j, j + 1),
171 lda);
172 i__2 = *n - j;
173 d__1 = 1. / ajj;
174 template_blas_scal(&i__2, &d__1, &a_ref(j, j + 1), lda);
175 }
176/* L10: */
177 }
178 } else {
179
180/* Compute the Cholesky factorization A = L*L'. */
181
182 i__1 = *n;
183 for (j = 1; j <= i__1; ++j) {
184
185/* Compute L(J,J) and test for non-positive-definiteness. */
186
187 i__2 = j - 1;
188 ajj = a_ref(j, j) - template_blas_dot(&i__2, &a_ref(j, 1), lda, &a_ref(j, 1),
189 lda);
190 if (ajj <= 0.) {
191 a_ref(j, j) = ajj;
192 goto L30;
193 }
194 ajj = template_blas_sqrt(ajj);
195 a_ref(j, j) = ajj;
196
197/* Compute elements J+1:N of column J. */
198
199 if (j < *n) {
200 i__2 = *n - j;
201 i__3 = j - 1;
202 template_blas_gemv("No transpose", &i__2, &i__3, &c_b10, &a_ref(j + 1, 1),
203 lda, &a_ref(j, 1), lda, &c_b12, &a_ref(j + 1, j), &
204 c__1);
205 i__2 = *n - j;
206 d__1 = 1. / ajj;
207 template_blas_scal(&i__2, &d__1, &a_ref(j + 1, j), &c__1);
208 }
209/* L20: */
210 }
211 }
212 goto L40;
213
214L30:
215 *info = j;
216
217L40:
218 return 0;
219
220/* End of DPOTF2 */
221
222} /* dpotf2_ */
223
224#undef a_ref
225
226
227#endif
Treal template_blas_sqrt(Treal x)
int template_blas_erbla(const char *srname, integer *info)
Definition template_blas_common.cc:146
logical template_blas_lsame(const char *ca, const char *cb)
Definition template_blas_common.cc:46
int integer
Definition template_blas_common.h:40
#define maxMACRO(a, b)
Definition template_blas_common.h:45
bool logical
Definition template_blas_common.h:41
Treal template_blas_dot(const integer *n, const Treal *dx, const integer *incx, const Treal *dy, const integer *incy)
Definition template_blas_dot.h:43
int template_blas_gemv(const char *trans, const integer *m, const integer *n, const Treal *alpha, const Treal *a, const integer *lda, const Treal *x, const integer *incx, const Treal *beta, Treal *y, const integer *incy)
Definition template_blas_gemv.h:43
int template_blas_scal(const integer *n, const Treal *da, Treal *dx, const integer *incx)
Definition template_blas_scal.h:43
#define a_ref(a_1, a_2)
int template_lapack_potf2(const char *uplo, const integer *n, Treal *a, const integer *lda, integer *info)
Definition template_lapack_potf2.h:42