ergo
template_lapack_lanhs.h
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1 /* Ergo, version 3.7, a program for linear scaling electronic structure
2  * calculations.
3  * Copyright (C) 2018 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_LANHS_HEADER
38 #define TEMPLATE_LAPACK_LANHS_HEADER
39 
40 
41 template<class Treal>
42 Treal dlanhs_(const char *norm, const integer *n, const Treal *a, const integer *lda,
43  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  DLANHS 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  Hessenberg matrix A.
57 
58  Description
59  ===========
60 
61  DLANHS returns the value
62 
63  DLANHS = ( 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 DLANHS as described
81  above.
82 
83  N (input) INTEGER
84  The order of the matrix A. N >= 0. When N = 0, DLANHS is
85  set to zero.
86 
87  A (input) DOUBLE PRECISION array, dimension (LDA,N)
88  The n by n upper Hessenberg matrix A; the part of A below the
89  first sub-diagonal is not referenced.
90 
91  LDA (input) INTEGER
92  The leading dimension of the array A. LDA >= max(N,1).
93 
94  WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
95  where LWORK >= N when NORM = 'I'; otherwise, WORK is not
96  referenced.
97 
98  =====================================================================
99 
100 
101  Parameter adjustments */
102  /* Table of constant values */
103  integer c__1 = 1;
104 
105  /* System generated locals */
106  integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
107  Treal ret_val, d__1, d__2, d__3;
108  /* Local variables */
109  integer i__, j;
110  Treal scale;
111  Treal value;
112  Treal sum;
113 #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
114 
115 
116  a_dim1 = *lda;
117  a_offset = 1 + a_dim1 * 1;
118  a -= a_offset;
119  --work;
120 
121  /* Initialization added by Elias to get rid of compiler warnings. */
122  value = 0;
123  /* Function Body */
124  if (*n == 0) {
125  value = 0.;
126  } else if (template_blas_lsame(norm, "M")) {
127 
128 /* Find max(abs(A(i,j))). */
129 
130  value = 0.;
131  i__1 = *n;
132  for (j = 1; j <= i__1; ++j) {
133 /* Computing MIN */
134  i__3 = *n, i__4 = j + 1;
135  i__2 = minMACRO(i__3,i__4);
136  for (i__ = 1; i__ <= i__2; ++i__) {
137 /* Computing MAX */
138  d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
139  value = maxMACRO(d__2,d__3);
140 /* L10: */
141  }
142 /* L20: */
143  }
144  } else if (template_blas_lsame(norm, "O") || *(unsigned char *)
145  norm == '1') {
146 
147 /* Find norm1(A). */
148 
149  value = 0.;
150  i__1 = *n;
151  for (j = 1; j <= i__1; ++j) {
152  sum = 0.;
153 /* Computing MIN */
154  i__3 = *n, i__4 = j + 1;
155  i__2 = minMACRO(i__3,i__4);
156  for (i__ = 1; i__ <= i__2; ++i__) {
157  sum += (d__1 = a_ref(i__, j), absMACRO(d__1));
158 /* L30: */
159  }
160  value = maxMACRO(value,sum);
161 /* L40: */
162  }
163  } else if (template_blas_lsame(norm, "I")) {
164 
165 /* Find normI(A). */
166 
167  i__1 = *n;
168  for (i__ = 1; i__ <= i__1; ++i__) {
169  work[i__] = 0.;
170 /* L50: */
171  }
172  i__1 = *n;
173  for (j = 1; j <= i__1; ++j) {
174 /* Computing MIN */
175  i__3 = *n, i__4 = j + 1;
176  i__2 = minMACRO(i__3,i__4);
177  for (i__ = 1; i__ <= i__2; ++i__) {
178  work[i__] += (d__1 = a_ref(i__, j), absMACRO(d__1));
179 /* L60: */
180  }
181 /* L70: */
182  }
183  value = 0.;
184  i__1 = *n;
185  for (i__ = 1; i__ <= i__1; ++i__) {
186 /* Computing MAX */
187  d__1 = value, d__2 = work[i__];
188  value = maxMACRO(d__1,d__2);
189 /* L80: */
190  }
191  } else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
192 
193 /* Find normF(A). */
194 
195  scale = 0.;
196  sum = 1.;
197  i__1 = *n;
198  for (j = 1; j <= i__1; ++j) {
199 /* Computing MIN */
200  i__3 = *n, i__4 = j + 1;
201  i__2 = minMACRO(i__3,i__4);
202  template_lapack_lassq(&i__2, &a_ref(1, j), &c__1, &scale, &sum);
203 /* L90: */
204  }
205  value = scale * template_blas_sqrt(sum);
206  }
207 
208  ret_val = value;
209  return ret_val;
210 
211 /* End of DLANHS */
212 
213 } /* dlanhs_ */
214 
215 #undef a_ref
216 
217 
218 #endif
#define absMACRO(x)
Definition: template_blas_common.h:47
#define a_ref(a_1, a_2)
int integer
Definition: template_blas_common.h:40
#define maxMACRO(a, b)
Definition: template_blas_common.h:45
#define minMACRO(a, b)
Definition: template_blas_common.h:46
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_blas_sqrt(Treal x)
logical template_blas_lsame(const char *ca, const char *cb)
Definition: template_blas_common.cc:46
Treal dlanhs_(const char *norm, const integer *n, const Treal *a, const integer *lda, Treal *work)
Definition: template_lapack_lanhs.h:42