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template_lapack_lansy.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_LANSY_HEADER
38#define TEMPLATE_LAPACK_LANSY_HEADER
39
40
41template<class Treal>
42Treal template_lapack_lansy(const char *norm, const char *uplo, const integer *n, const Treal *a, const integer
43 *lda, Treal *work)
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 DLANSY returns the value of the one norm, or the Frobenius norm, or
55 the infinity norm, or the element of largest absolute value of a
56 real symmetric matrix A.
57
58 Description
59 ===========
60
61 DLANSY returns the value
62
63 DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
64 (
65 ( norm1(A), NORM = '1', 'O' or 'o'
66 (
67 ( normI(A), NORM = 'I' or 'i'
68 (
69 ( normF(A), NORM = 'F', 'f', 'E' or 'e'
70
71 where norm1 denotes the one norm of a matrix (maximum column sum),
72 normI denotes the infinity norm of a matrix (maximum row sum) and
73 normF denotes the Frobenius norm of a matrix (square root of sum of
74 squares). Note that max(abs(A(i,j))) is not a matrix norm.
75
76 Arguments
77 =========
78
79 NORM (input) CHARACTER*1
80 Specifies the value to be returned in DLANSY as described
81 above.
82
83 UPLO (input) CHARACTER*1
84 Specifies whether the upper or lower triangular part of the
85 symmetric matrix A is to be referenced.
86 = 'U': Upper triangular part of A is referenced
87 = 'L': Lower triangular part of A is referenced
88
89 N (input) INTEGER
90 The order of the matrix A. N >= 0. When N = 0, DLANSY is
91 set to zero.
92
93 A (input) DOUBLE PRECISION array, dimension (LDA,N)
94 The symmetric matrix A. If UPLO = 'U', the leading n by n
95 upper triangular part of A contains the upper triangular part
96 of the matrix A, and the strictly lower triangular part of A
97 is not referenced. If UPLO = 'L', the leading n by n lower
98 triangular part of A contains the lower triangular part of
99 the matrix A, and the strictly upper triangular part of A is
100 not referenced.
101
102 LDA (input) INTEGER
103 The leading dimension of the array A. LDA >= max(N,1).
104
105 WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
106 where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
107 WORK is not referenced.
108
109 =====================================================================
110
111
112 Parameter adjustments */
113 /* Table of constant values */
114 integer c__1 = 1;
115
116 /* System generated locals */
117 integer a_dim1, a_offset, i__1, i__2;
118 Treal ret_val, d__1, d__2, d__3;
119 /* Local variables */
120 Treal absa;
121 integer i__, j;
122 Treal scale;
123 Treal value;
124 Treal sum;
125#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
126
127
128 a_dim1 = *lda;
129 a_offset = 1 + a_dim1 * 1;
130 a -= a_offset;
131 --work;
132
133 /* Initialization added by Elias to get rid of compiler warnings. */
134 value = 0;
135 /* Function Body */
136 if (*n == 0) {
137 value = 0.;
138 } else if (template_blas_lsame(norm, "M")) {
139
140/* Find max(abs(A(i,j))). */
141
142 value = 0.;
143 if (template_blas_lsame(uplo, "U")) {
144 i__1 = *n;
145 for (j = 1; j <= i__1; ++j) {
146 i__2 = j;
147 for (i__ = 1; i__ <= i__2; ++i__) {
148/* Computing MAX */
149 d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
150 value = maxMACRO(d__2,d__3);
151/* L10: */
152 }
153/* L20: */
154 }
155 } else {
156 i__1 = *n;
157 for (j = 1; j <= i__1; ++j) {
158 i__2 = *n;
159 for (i__ = j; i__ <= i__2; ++i__) {
160/* Computing MAX */
161 d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
162 value = maxMACRO(d__2,d__3);
163/* L30: */
164 }
165/* L40: */
166 }
167 }
168 } else if (template_blas_lsame(norm, "I") || template_blas_lsame(norm, "O") || *(unsigned char *)norm == '1') {
169
170/* Find normI(A) ( = norm1(A), since A is symmetric). */
171
172 value = 0.;
173 if (template_blas_lsame(uplo, "U")) {
174 i__1 = *n;
175 for (j = 1; j <= i__1; ++j) {
176 sum = 0.;
177 i__2 = j - 1;
178 for (i__ = 1; i__ <= i__2; ++i__) {
179 absa = (d__1 = a_ref(i__, j), absMACRO(d__1));
180 sum += absa;
181 work[i__] += absa;
182/* L50: */
183 }
184 work[j] = sum + (d__1 = a_ref(j, j), absMACRO(d__1));
185/* L60: */
186 }
187 i__1 = *n;
188 for (i__ = 1; i__ <= i__1; ++i__) {
189/* Computing MAX */
190 d__1 = value, d__2 = work[i__];
191 value = maxMACRO(d__1,d__2);
192/* L70: */
193 }
194 } else {
195 i__1 = *n;
196 for (i__ = 1; i__ <= i__1; ++i__) {
197 work[i__] = 0.;
198/* L80: */
199 }
200 i__1 = *n;
201 for (j = 1; j <= i__1; ++j) {
202 sum = work[j] + (d__1 = a_ref(j, j), absMACRO(d__1));
203 i__2 = *n;
204 for (i__ = j + 1; i__ <= i__2; ++i__) {
205 absa = (d__1 = a_ref(i__, j), absMACRO(d__1));
206 sum += absa;
207 work[i__] += absa;
208/* L90: */
209 }
210 value = maxMACRO(value,sum);
211/* L100: */
212 }
213 }
214 } else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
215
216/* Find normF(A). */
217
218 scale = 0.;
219 sum = 1.;
220 if (template_blas_lsame(uplo, "U")) {
221 i__1 = *n;
222 for (j = 2; j <= i__1; ++j) {
223 i__2 = j - 1;
224 template_lapack_lassq(&i__2, &a_ref(1, j), &c__1, &scale, &sum);
225/* L110: */
226 }
227 } else {
228 i__1 = *n - 1;
229 for (j = 1; j <= i__1; ++j) {
230 i__2 = *n - j;
231 template_lapack_lassq(&i__2, &a_ref(j + 1, j), &c__1, &scale, &sum);
232/* L120: */
233 }
234 }
235 sum *= 2;
236 i__1 = *lda + 1;
237 template_lapack_lassq(n, &a[a_offset], &i__1, &scale, &sum);
238 value = scale * template_blas_sqrt(sum);
239 }
240
241 ret_val = value;
242 return ret_val;
243
244/* End of DLANSY */
245
246} /* dlansy_ */
247
248#undef a_ref
249
250
251#endif
Treal template_blas_sqrt(Treal x)
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 absMACRO(x)
Definition: template_blas_common.h:47
#define maxMACRO(a, b)
Definition: template_blas_common.h:45
int template_lapack_lassq(const integer *n, const Treal *x, const integer *incx, Treal *scale, Treal *sumsq)
Definition: template_lapack_lamch.h:73
#define a_ref(a_1, a_2)
Treal template_lapack_lansy(const char *norm, const char *uplo, const integer *n, const Treal *a, const integer *lda, Treal *work)
Definition: template_lapack_lansy.h:42