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
|
!
! Copyright (C) 2003-2005 Quantum ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!
!----------------------------------------------------------------------------
MODULE basic_algebra_routines
!----------------------------------------------------------------------------
!
! ... Written by Carlo Sbraccia ( 16/12/2003 )
!
! ... This module contains a limited number of functions and operators
! ... for vectorial algebra. Wherever possible the appropriate BLAS routine
! ... ( always the double precision version ) is used.
!
! ... List of public methods :
!
! x .dot. y dot product between vectors ( <x|y> )
! x .ext. y external (vector) product between vectors ( <x|y> )
! norm( x ) norm of a vector ( SQRT(<x|x>) )
! A .times. x matrix-vector multiplication ( A|x> )
! x .times. A vector-matrix multiplication ( <x|A )
! matrix( x, y ) vector-vector multiplication ( |x><y| )
! identity( N ) identity matrix of rank N
!
USE kinds, ONLY : DP
!
IMPLICIT NONE
!
INTERFACE OPERATOR( .dot. )
!
MODULE PROCEDURE dot_product_
!
END INTERFACE
!
INTERFACE OPERATOR( .ext. )
!
MODULE PROCEDURE external_product_
!
END INTERFACE
!
INTERFACE OPERATOR( .times. )
!
MODULE PROCEDURE matrix_times_vector, vector_times_matrix
!
END INTERFACE
!
CONTAINS
!
!-----------------------------------------------------------------------
FUNCTION dot_product_( vec1, vec2 )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec1(:), vec2(:)
REAL(DP) :: dot_product_
!
REAL(DP) :: ddot
EXTERNAL ddot
!
dot_product_ = ddot( SIZE( vec1 ), vec1, 1, vec2, 1 )
!
END FUNCTION dot_product_
!
!-----------------------------------------------------------------------
FUNCTION external_product_( vec1, vec2 )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec1(:), vec2(:)
REAL(DP) :: external_product_(SIZE( vec1 ))
!
!
external_product_(1) = + vec1(2)*vec2(3) - vec1(3)*vec2(2)
external_product_(2) = - vec1(1)*vec2(3) - vec1(3)*vec2(1)
external_product_(3) = + vec1(1)*vec2(2) - vec1(2)*vec2(1)
!
END FUNCTION external_product_
!
!-----------------------------------------------------------------------
FUNCTION norm( vec )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec(:)
REAL(DP) :: norm
!
REAL(DP) :: dnrm2
EXTERNAL dnrm2
!
norm = dnrm2( SIZE( vec ), vec, 1 )
!
END FUNCTION norm
!
!-----------------------------------------------------------------------
FUNCTION matrix_times_vector( mat, vec )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec(:)
REAL(DP), INTENT(IN) :: mat(:,:)
REAL(DP) :: matrix_times_vector(SIZE( vec ))
! gfortran hack
REAL(DP) :: aux(SIZE( vec ))
INTEGER :: dim1
!
dim1 = SIZE( vec )
!
CALL DGEMV( 'N', dim1, dim1, 1.0_DP, mat, dim1, vec, 1, 0.0_DP, &
aux, 1 )
! gfortran hack
! matrix_times_vector, 1 )
matrix_times_vector = aux
!
END FUNCTION matrix_times_vector
!
!
!-----------------------------------------------------------------------
FUNCTION vector_times_matrix( vec, mat )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec(:)
REAL(DP), INTENT(IN) :: mat(:,:)
REAL(DP) :: vector_times_matrix(SIZE( vec ))
! gfortran hack
REAL(DP) :: aux(SIZE( vec ))
INTEGER :: dim1
!
dim1 = SIZE( vec )
!
CALL DGEMV( 'T', dim1, dim1, 1.0_DP, mat, dim1, vec, 1, 0.0_DP, &
aux, 1)
! gfortran hack
! vector_times_matrix, 1 )
vector_times_matrix = aux
!
END FUNCTION vector_times_matrix
!
!
!-----------------------------------------------------------------------
FUNCTION matrix( vec1, vec2 )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
REAL(DP), INTENT(IN) :: vec1(:), vec2(:)
REAL(DP) :: matrix(SIZE( vec1 ),SIZE( vec2 ))
#ifdef __GFORTRAN
! gfortran hack - explicit preprocessing is used because this hack
! costs an additional matrix allocation, which may not be a good idea
REAL(DP) :: aux(SIZE( vec1 ),SIZE( vec2 ))
#endif
INTEGER :: dim1, dim2
!
dim1 = SIZE( vec1 )
dim2 = SIZE( vec2 )
!
#ifdef __GFORTRAN
!
aux = 0.0_DP
CALL DGER( dim1, dim2, 1.0_DP, vec1, 1, vec2, 1, aux, dim1 )
matrix = aux
#else
!
matrix = 0.0_DP
CALL DGER( dim1, dim2, 1.0_DP, vec1, 1, vec2, 1, matrix, dim1 )
!
#endif
!
END FUNCTION matrix
!
!
!-----------------------------------------------------------------------
FUNCTION identity( dim )
!-----------------------------------------------------------------------
!
IMPLICIT NONE
!
INTEGER, INTENT(IN) :: dim
REAL(DP) :: identity(dim,dim)
INTEGER :: i
!
identity = 0.0_DP
!
FORALL( i = 1:dim ) identity(i,i) = 1.0_DP
!
END FUNCTION identity
!
END MODULE basic_algebra_routines
|
