1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
|
/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 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_LANGE_HEADER
#define TEMPLATE_LAPACK_LANGE_HEADER
template<class Treal>
Treal template_lapack_lange(const char *norm, const integer *m, const integer *n, const Treal *a, const integer
*lda, Treal *work)
{
/* -- 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
=======
DLANGE returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real matrix A.
Description
===========
DLANGE returns the value
DLANGE = ( maxMACRO(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that maxMACRO(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in DLANGE as described
above.
M (input) INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
DLANGE is set to zero.
N (input) INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
DLANGE is set to zero.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The m by n matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= maxMACRO(M,1).
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
=====================================================================
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
Treal ret_val, d__1, d__2, d__3;
/* Local variables */
integer i__, j;
Treal scale;
Treal value;
Treal sum;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
/* Initialization added by Elias to get rid of compiler warnings. */
value = 0;
/* Function Body */
if (minMACRO(*m,*n) == 0) {
value = 0.;
} else if (template_blas_lsame(norm, "M")) {
/* Find maxMACRO(abs(A(i,j))). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
value = maxMACRO(d__2,d__3);
/* L10: */
}
/* L20: */
}
} else if (template_blas_lsame(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += (d__1 = a_ref(i__, j), absMACRO(d__1));
/* L30: */
}
value = maxMACRO(value,sum);
/* L40: */
}
} else if (template_blas_lsame(norm, "I")) {
/* Find normI(A). */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L50: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += (d__1 = a_ref(i__, j), absMACRO(d__1));
/* L60: */
}
/* L70: */
}
value = 0.;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = maxMACRO(d__1,d__2);
/* L80: */
}
} else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
template_lapack_lassq(m, &a_ref(1, j), &c__1, &scale, &sum);
/* L90: */
}
value = scale * template_blas_sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANGE */
} /* dlange_ */
#undef a_ref
#endif
|
