ergo
template_lapack_lange.h
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1/* Ergo, version 3.8, a program for linear scaling electronic structure
2 * calculations.
3 * Copyright (C) 2019 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_LANGE_HEADER
38#define TEMPLATE_LAPACK_LANGE_HEADER
39
40
41template<class Treal>
42Treal template_lapack_lange(const char *norm, const integer *m, 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 DLANGE 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 matrix A.
57
58 Description
59 ===========
60
61 DLANGE returns the value
62
63 DLANGE = ( maxMACRO(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 maxMACRO(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 DLANGE as described
81 above.
82
83 M (input) INTEGER
84 The number of rows of the matrix A. M >= 0. When M = 0,
85 DLANGE is set to zero.
86
87 N (input) INTEGER
88 The number of columns of the matrix A. N >= 0. When N = 0,
89 DLANGE is set to zero.
90
91 A (input) DOUBLE PRECISION array, dimension (LDA,N)
92 The m by n matrix A.
93
94 LDA (input) INTEGER
95 The leading dimension of the array A. LDA >= maxMACRO(M,1).
96
97 WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
98 where LWORK >= M when NORM = 'I'; otherwise, WORK is not
99 referenced.
100
101 =====================================================================
102
103
104 Parameter adjustments */
105 /* Table of constant values */
106 integer c__1 = 1;
107
108 /* System generated locals */
109 integer a_dim1, a_offset, i__1, i__2;
110 Treal ret_val, d__1, d__2, d__3;
111 /* Local variables */
112 integer i__, j;
113 Treal scale;
114 Treal value;
115 Treal sum;
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 --work;
123
124 /* Initialization added by Elias to get rid of compiler warnings. */
125 value = 0;
126 /* Function Body */
127 if (minMACRO(*m,*n) == 0) {
128 value = 0.;
129 } else if (template_blas_lsame(norm, "M")) {
130
131/* Find maxMACRO(abs(A(i,j))). */
132
133 value = 0.;
134 i__1 = *n;
135 for (j = 1; j <= i__1; ++j) {
136 i__2 = *m;
137 for (i__ = 1; i__ <= i__2; ++i__) {
138/* Computing MAX */
139 d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
140 value = maxMACRO(d__2,d__3);
141/* L10: */
142 }
143/* L20: */
144 }
145 } else if (template_blas_lsame(norm, "O") || *(unsigned char *)
146 norm == '1') {
147
148/* Find norm1(A). */
149
150 value = 0.;
151 i__1 = *n;
152 for (j = 1; j <= i__1; ++j) {
153 sum = 0.;
154 i__2 = *m;
155 for (i__ = 1; i__ <= i__2; ++i__) {
156 sum += (d__1 = a_ref(i__, j), absMACRO(d__1));
157/* L30: */
158 }
159 value = maxMACRO(value,sum);
160/* L40: */
161 }
162 } else if (template_blas_lsame(norm, "I")) {
163
164/* Find normI(A). */
165
166 i__1 = *m;
167 for (i__ = 1; i__ <= i__1; ++i__) {
168 work[i__] = 0.;
169/* L50: */
170 }
171 i__1 = *n;
172 for (j = 1; j <= i__1; ++j) {
173 i__2 = *m;
174 for (i__ = 1; i__ <= i__2; ++i__) {
175 work[i__] += (d__1 = a_ref(i__, j), absMACRO(d__1));
176/* L60: */
177 }
178/* L70: */
179 }
180 value = 0.;
181 i__1 = *m;
182 for (i__ = 1; i__ <= i__1; ++i__) {
183/* Computing MAX */
184 d__1 = value, d__2 = work[i__];
185 value = maxMACRO(d__1,d__2);
186/* L80: */
187 }
188 } else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
189
190/* Find normF(A). */
191
192 scale = 0.;
193 sum = 1.;
194 i__1 = *n;
195 for (j = 1; j <= i__1; ++j) {
196 template_lapack_lassq(m, &a_ref(1, j), &c__1, &scale, &sum);
197/* L90: */
198 }
199 value = scale * template_blas_sqrt(sum);
200 }
201
202 ret_val = value;
203 return ret_val;
204
205/* End of DLANGE */
206
207} /* dlange_ */
208
209#undef a_ref
210
211
212#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 minMACRO(a, b)
Definition: template_blas_common.h:46
#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
Treal template_lapack_lange(const char *norm, const integer *m, const integer *n, const Treal *a, const integer *lda, Treal *work)
Definition: template_lapack_lange.h:42
#define a_ref(a_1, a_2)