-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcof_mk_s.f90
executable file
·333 lines (248 loc) · 9.4 KB
/
cof_mk_s.f90
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
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
!====================================================================
!====================================================================
!
! Fourier transform subroutines using MathKeisan library on IDRIS NEC
!
!====================================================================
!====================================================================
subroutine fft_initialize
! Not required for MathKeisan library
end subroutine fft_initialize
subroutine fft_free
! Not required for MathKeisan library
end subroutine fft_free
subroutine coftx (f, fk)
!====================================================================
! Calculation of the Fourier-coefficients of a real function
! along x (1st index)
! FILTERING
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = 1, jump = 1
integer :: ierr
real (kind=pr), dimension (0:nx+1, 0:ny-1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: f
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: fk
real (kind=pr) :: norm
! FFT Plan physique ---> plan spectral
!$omp parallel workshare
ft(0:nx-1,:) = f
ft(nx:nx+1,:) = 0.0
!$omp end parallel workshare
call srcfts (ft, nx, jump, ny, nx+2, iopt, ierr)
norm = 1.0 / real(nx)
!$omp parallel workshare
fk = ft(0:nx-1,:) * norm
!$omp end parallel workshare
! last mode M=NX, NX+1; mode KF left unconsidered => filtering
end subroutine coftx
subroutine cofitx (fk, f)
!====================================================================
! Calculation of a real function from its Fourier coefficients
! along x (1st index)
! FILTERING
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = -1, jump = 1
integer :: ierr
real (kind=pr), dimension (0:nx+1, 0:ny-1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: fk
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: f
real (kind=pr) :: norm
! Inverse FFT
norm = real(nx)
!$omp parallel workshare
ft(0:nx-1,:) = fk * norm
ft(nx:nx+1,:) = 0.0
!$omp end parallel workshare
call srcfts (ft, nx, jump, ny, nx+2, iopt, ierr)
!$omp parallel workshare
f = ft(0:nx-1,:)
!$omp end parallel workshare
! last mode M=NX, NX+1; mode KF left unconsidered => filtering
end subroutine cofitx
subroutine cofty (f, fk)
!====================================================================
! Calculation of the Fourier-coefficients of a real function
! along y (2nd index)
! FILTERING
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = 1, jump = 1
integer :: ierr
real (kind=pr), dimension (0:nx-1, 0:ny+1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: f
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: fk
real (kind=pr) :: norm
! FFT Plan physique ---> plan spectral
!$omp parallel workshare
ft(:,0:ny-1) = f
ft(:,ny:ny+1) = 0.0
!$omp end parallel workshare
call srcfts (ft, ny, nx, nx, jump, iopt, ierr)
norm = 1.0 / real(ny)
!$omp parallel workshare
fk = ft(:,0:ny-1) * norm
!$omp end parallel workshare
! last mode M=NY, NY+1; mode KF left unconsidered => filtering
end subroutine cofty
subroutine cofity (fk, f)
!====================================================================
! Calculation of a real function from its Fourier coefficients
! along y (2nd index)
! FILTERING
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = -1, jump = 1
integer :: ierr
real (kind=pr), dimension (0:nx-1, 0:ny+1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: fk
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: f
real (kind=pr) :: norm
! Inverse FFT
norm = real(ny)
!$omp parallel workshare
ft(:,0:ny-1) = fk * norm
ft(:,ny:ny+1) = 0.0
!$omp end parallel workshare
call srcfts (ft, ny, nx, nx, jump, iopt, ierr)
!$omp parallel workshare
f = ft(:,0:ny-1)
!$omp end parallel workshare
! last mode M=NY, NY+1; mode KF left unconsidered => filtering
end subroutine cofity
subroutine coftxy (f, fk)
!====================================================================
! Calculation of the Fourier-coefficients of a real function
! along x (1st index) and y (2nd index)
! FILTERING
! MK library is used
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = 1
integer :: ierr
complex (kind=pr), dimension (0:nx, 0:ny-1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: f
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: fk
real (kind=pr) :: norm
! FFT Plan physique ---> plan spectral
!$omp parallel workshare
ft(0:nx-1,:) = cmplx( f, 0.0, pr )
ft(nx,:) = 0.0
!$omp end parallel workshare
! call real-to-complex 2d fft
! complex array is used for storage (redundant but faster)
call crc2ft (ft, nx, ny, nx+1, iopt, ierr)
! normalization
norm = 1.0 / ( real(nx) * real(ny) )
! complex 2d Fourier coefficients are used to
! compute coefficients before sin and cos (Temperton style)
!$omp parallel workshare
fk(0:nx-2:2,0) = real( ft(0:nx/2-1,0) )
fk(1:nx-1:2,0) = imag( ft(0:nx/2-1,0) )
fk(:,1) = 0.0
fk(0:nx-2:2,2:ny-2:2) = 0.5 * ( real( ft(0:nx/2-1,1:ny/2-1)) &
+ real( ft(0:nx/2-1,ny-1:ny/2+1:-1)) )
fk(0:nx-2:2,3:ny-1:2) = 0.5 * ( imag( ft(0:nx/2-1,1:ny/2-1)) &
- imag( ft(0:nx/2-1,ny-1:ny/2+1:-1)) )
fk(1:nx-1:2,2:ny-2:2) = 0.5 * ( imag( ft(0:nx/2-1,1:ny/2-1)) &
+ imag( ft(0:nx/2-1,ny-1:ny/2+1:-1)) )
fk(1:nx-1:2,3:ny-1:2) = 0.5 * ( - real( ft(0:nx/2-1,1:ny/2-1)) &
+ real( ft(0:nx/2-1,ny-1:ny/2+1:-1)) )
fk = fk * norm
!$omp end parallel workshare
! mode KF left unconsidered => filtering
end subroutine coftxy
subroutine cofitxy (fk, f)
!====================================================================
! Calculation of a real function from its Fourier coefficients
! along x (1st index) and y (2nd index)
! FILTERING
! MK library is used
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = -1
integer :: ierr
complex (kind=pr), dimension (0:nx, 0:ny-1) :: ft
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (in) :: fk
real (kind=pr), dimension (0:nx-1, 0:ny-1), intent (out) :: f
real (kind=pr) :: norm
! Inverse FFT
norm = real(nx) * real(ny)
!$omp parallel workshare
ft = 0.0
ft(0:nx/2-1,0) = cmplx( fk(0:nx-2:2,0), fk(1:nx-1:2,0), pr )
ft(0:nx/2-1,1:ny/2-1) = cmplx( fk(0:nx-2:2,2:ny-2:2) - fk(1:nx-1:2,3:ny-1:2), &
fk(0:nx-2:2,3:ny-1:2) + fk(1:nx-1:2,2:ny-2:2) )
ft(0:nx/2-1,ny-1:ny/2+1:-1) = cmplx( fk(0:nx-2:2,2:ny-2:2) + fk(1:nx-1:2,3:ny-1:2), &
-fk(0:nx-2:2,3:ny-1:2) + fk(1:nx-1:2,2:ny-2:2) )
ft = ft * norm
!$omp end parallel workshare
call crc2ft (ft, nx, ny, nx+1, iopt, ierr)
!$omp parallel workshare
f = real( ft(0:nx-1,:) )
!$omp end parallel workshare
! mode KF left unconsidered => filtering
end subroutine cofitxy
subroutine cofts (f, fk, L, n)
!====================================================================
! Calculation of the Fourier coefficients of n real functions
! aligned in columns
! FILTERING
! MK library is used
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = 1, jump = 1
integer, intent (in) :: l, n
integer :: ierr
real (kind=pr), dimension (0:L+1, 0:n-1) :: ft
real (kind=pr), dimension (0:L-1, 0:n-1), intent (in) :: f
real (kind=pr), dimension (0:L-1, 0:n-1), intent (out) :: fk
real (kind=pr) :: norm
! FFT Plan physique ---> plan spectral
!$omp parallel workshare
ft(0:L-1,:) = f
ft(L:L+1,:) = 0.0
!$omp end parallel workshare
call srcfts (ft, L, jump, n, L+2, iopt, ierr)
norm = 1.0 / real(L)
!$omp parallel workshare
fk = ft(0:L-1,:) * norm
!$omp end parallel workshare
! last mode M=L, L+1; mode KF left unconsidered => filtering
end subroutine cofts
subroutine cofits (fk, f, L, n)
!====================================================================
! Calculation of n real functions from their Fourier coefficients
! aligned in columns
! FILTERING
! MK library is used
!====================================================================
use share_vars
implicit none
integer, parameter :: iopt = -1, jump = 1
integer, intent (in) :: L, n ! length of the array and number of arrays
integer :: ierr
real (kind=pr), dimension (0:L+1, 0:n-1) :: ft
real (kind=pr), dimension (0:L-1, 0:n-1), intent (in) :: fk
real (kind=pr), dimension (0:L-1, 0:n-1), intent (out) :: f
real (kind=pr) :: norm
! Inverse FFT
norm = real(L)
!$omp parallel workshare
ft(0:L-1,:) = fk * norm
ft(L:L+1,:) = 0.0
!$omp end parallel workshare
call srcfts (ft, L, jump, n, L+2, iopt, ierr)
!$omp parallel workshare
f = ft(0:L-1,:)
!$omp end parallel workshare
! last mode M=L, L+1; mode KF left unconsidered => filtering
end subroutine cofits