Line data Source code
1 : !--------------------------------------------------------------------------------------------------!
2 : ! CP2K: A general program to perform molecular dynamics simulations !
3 : ! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
4 : ! !
5 : ! SPDX-License-Identifier: GPL-2.0-or-later !
6 : !--------------------------------------------------------------------------------------------------!
7 :
8 : ! **************************************************************************************************
9 : !> \brief Creates the wavelet kernel for the wavelet based poisson solver.
10 : !> \author Florian Schiffmann (09.2007,fschiff)
11 : ! **************************************************************************************************
12 : MODULE ps_wavelet_kernel
13 :
14 : USE kinds, ONLY: dp
15 : USE message_passing, ONLY: mp_comm_type
16 : USE ps_wavelet_base, ONLY: scramble_unpack
17 : USE ps_wavelet_fft3d, ONLY: ctrig,&
18 : ctrig_length,&
19 : fftstp
20 : USE ps_wavelet_scaling_function, ONLY: scaling_function,&
21 : scf_recursion
22 : USE ps_wavelet_util, ONLY: F_FFT_dimensions,&
23 : S_FFT_dimensions
24 : #include "../base/base_uses.f90"
25 :
26 : IMPLICIT NONE
27 :
28 : PRIVATE
29 :
30 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'ps_wavelet_kernel'
31 :
32 : ! *** Public data types ***
33 :
34 : PUBLIC :: createKernel
35 :
36 : CONTAINS
37 :
38 : ! **************************************************************************************************
39 : !> \brief Allocate a pointer which corresponds to the zero-padded FFT slice needed for
40 : !> calculating the convolution with the kernel expressed in the interpolating scaling
41 : !> function basis. The kernel pointer is unallocated on input, allocated on output.
42 : !> \param geocode Indicates the boundary conditions (BC) of the problem:
43 : !> 'F' free BC, isolated systems.
44 : !> The program calculates the solution as if the given density is
45 : !> "alone" in R^3 space.
46 : !> 'S' surface BC, isolated in y direction, periodic in xz plane
47 : !> The given density is supposed to be periodic in the xz plane,
48 : !> so the dimensions in these direction mus be compatible with the FFT
49 : !> Beware of the fact that the isolated direction is y!
50 : !> 'P' periodic BC.
51 : !> The density is supposed to be periodic in all the three directions,
52 : !> then all the dimensions must be compatible with the FFT.
53 : !> No need for setting up the kernel.
54 : !> \param n01 dimensions of the real space grid to be hit with the Poisson Solver
55 : !> \param n02 dimensions of the real space grid to be hit with the Poisson Solver
56 : !> \param n03 dimensions of the real space grid to be hit with the Poisson Solver
57 : !> \param hx grid spacings. For the isolated BC case for the moment they are supposed to
58 : !> be equal in the three directions
59 : !> \param hy grid spacings. For the isolated BC case for the moment they are supposed to
60 : !> be equal in the three directions
61 : !> \param hz grid spacings. For the isolated BC case for the moment they are supposed to
62 : !> be equal in the three directions
63 : !> \param itype_scf order of the interpolating scaling functions used in the decomposition
64 : !> \param iproc ,nproc: number of process, number of processes
65 : !> \param nproc ...
66 : !> \param kernel pointer for the kernel FFT. Unallocated on input, allocated on output.
67 : !> Its dimensions are equivalent to the region of the FFT space for which the
68 : !> kernel is injective. This will divide by two each direction,
69 : !> since the kernel for the zero-padded convolution is real and symmetric.
70 : !> \param mpi_group ...
71 : !> \date February 2007
72 : !> \author Luigi Genovese
73 : !> \note Due to the fact that the kernel dimensions are unknown before the calling, the kernel
74 : !> must be declared as pointer in input of this routine.
75 : !> To avoid that, one can properly define the kernel dimensions by adding
76 : !> the nd1,nd2,nd3 arguments to the PS_dim4allocation routine, then eliminating the pointer
77 : !> declaration.
78 : ! **************************************************************************************************
79 752 : SUBROUTINE createKernel(geocode, n01, n02, n03, hx, hy, hz, itype_scf, iproc, nproc, kernel, mpi_group)
80 :
81 : CHARACTER(len=1), INTENT(in) :: geocode
82 : INTEGER, INTENT(in) :: n01, n02, n03
83 : REAL(KIND=dp), INTENT(in) :: hx, hy, hz
84 : INTEGER, INTENT(in) :: itype_scf, iproc, nproc
85 : REAL(KIND=dp), POINTER :: kernel(:)
86 :
87 : CLASS(mp_comm_type), INTENT(in) :: mpi_group
88 :
89 : INTEGER :: m1, m2, m3, md1, md2, md3, n1, n2, n3, &
90 : nd1, nd2, nd3, nlimd, nlimk
91 : REAL(KIND=dp) :: hgrid
92 :
93 752 : hgrid = MAX(hx, hy, hz)
94 :
95 752 : IF (geocode == 'P') THEN
96 :
97 : CALL F_FFT_dimensions(n01, n02, n03, m1, m2, m3, n1, n2, n3, &
98 294 : md1, md2, md3, nd1, nd2, nd3, nproc)
99 :
100 294 : ALLOCATE (kernel(1))
101 294 : nlimd = n2
102 588 : nlimk = 0
103 :
104 458 : ELSE IF (geocode == 'S') THEN
105 :
106 : CALL S_FFT_dimensions(n01, n02, n03, m1, m2, m3, n1, n2, n3, &
107 2 : md1, md2, md3, nd1, nd2, nd3, nproc)
108 :
109 6 : ALLOCATE (kernel(nd1*nd2*nd3/nproc))
110 :
111 : !the kernel must be built and scattered to all the processes
112 :
113 : CALL Surfaces_Kernel(n1, n2, n3, m3, nd1, nd2, nd3, hx, hz, hy, &
114 2 : itype_scf, kernel, iproc, nproc, mpi_group)
115 : !last plane calculated for the density and the kernel
116 :
117 2 : nlimd = n2
118 4 : nlimk = n3/2 + 1
119 456 : ELSE IF (geocode == 'F') THEN
120 :
121 : !Build the Kernel
122 :
123 : CALL F_FFT_dimensions(n01, n02, n03, m1, m2, m3, n1, n2, n3, &
124 456 : md1, md2, md3, nd1, nd2, nd3, nproc)
125 1368 : ALLOCATE (kernel(nd1*nd2*nd3/nproc))
126 :
127 : !the kernel must be built and scattered to all the processes
128 : CALL Free_Kernel(n01, n02, n03, n1, n2, n3, nd1, nd2, nd3, hgrid, &
129 456 : itype_scf, iproc, nproc, kernel, mpi_group)
130 :
131 : !last plane calculated for the density and the kernel
132 456 : nlimd = n2/2
133 912 : nlimk = n3/2 + 1
134 :
135 : ELSE
136 :
137 0 : CPABORT("No wavelet based poisson solver for given geometry")
138 :
139 : END IF
140 : !!! IF (iproc==0) THEN
141 : !!! write(*,*)'done.'
142 : !!! write(*,'(1x,a,i0)') 'Allocate words for kernel ',nd1*nd2*nd3/nproc
143 : !!! !print the load balancing of the different dimensions on screen
144 : !!! write(*,'(1x,a,3(i5))')'Grid Dimensions:',n01,n02,n03
145 : !!! if (nproc > 1) then
146 : !!! write(*,'(1x,a,3(i5),a,3(i5),a,3(i5))')&
147 : !!! 'Memory occ. per proc. Density',md1,md3,md2/nproc,' Kernel',nd1,nd2,nd3/nproc
148 : !!! write(*,'(1x,a)')'Load Balancing--------------------------------------------'
149 : !!! jhd=1000
150 : !!! jzd=1000
151 : !!! npd=0
152 : !!! load_balancing: do jproc=0,nproc-1
153 : !!! !print *,'jproc,jfull=',jproc,jproc*md2/nproc,(jproc+1)*md2/nproc
154 : !!! if ((jproc+1)*md2/nproc <= nlimd) then
155 : !!! jfd=jproc
156 : !!! else if (jproc*md2/nproc <= nlimd) then
157 : !!! jhd=jproc
158 : !!! npd=nint(real(nlimd-(jproc)*md2/nproc,KIND=dp)/real(md2/nproc,KIND=dp)*100._dp)
159 : !!! else
160 : !!! jzd=jproc
161 : !!! exit load_balancing
162 : !!! end if
163 : !!! end do load_balancing
164 : !!! write(*,'(1x,a,i3,a)')'LB_den : processors 0 -',jfd,' work at 100%'
165 : !!! if (jfd < nproc-1) write(*,'(1x,a,i3,a,i3,1a)')' processor ',jhd,&
166 : !!! ' work at ',npd,'%'
167 : !!! if (jhd < nproc-1) write(*,'(1x,a,i3,1a,i3,a)')' processors ',&
168 : !!! jzd,' -',nproc-1,' work at 0%'
169 : !!! jhk=1000
170 : !!! jzk=1000
171 : !!! npk=0
172 : !!! if (geocode /= 'P') then
173 : !!! load_balancingk: do jproc=0,nproc-1
174 : !!! !print *,'jproc,jfull=',jproc,jproc*nd3/nproc,(jproc+1)*nd3/nproc
175 : !!! if ((jproc+1)*nd3/nproc <= nlimk) then
176 : !!! jfk=jproc
177 : !!! else if (jproc*nd3/nproc <= nlimk) then
178 : !!! jhk=jproc
179 : !!! npk=nint(real(nlimk-(jproc)*nd3/nproc,KIND=dp)/real(nd3/nproc,KIND=dp)*100._dp)
180 : !!! else
181 : !!! jzk=jproc
182 : !!! exit load_balancingk
183 : !!! end if
184 : !!! end do load_balancingk
185 : !!! write(*,'(1x,a,i3,a)')'LB_ker : processors 0 -',jfk,' work at 100%'
186 : !!! if (jfk < nproc-1) write(*,'(1x,a,i3,a,i3,1a)')' processor ',jhk,&
187 : !!! ' work at ',npk,'%'
188 : !!! if (jhk < nproc-1) write(*,'(1x,a,i3,1a,i3,a)')' processors ',jzk,' -',nproc-1,&
189 : !!! ' work at 0%'
190 : !!! end if
191 : !!! write(*,'(1x,a)')'The LB per processor is 1/3 LB_den + 2/3 LB_ker-----------'
192 : !!! end if
193 : !!!
194 : !!! END IF
195 752 : END SUBROUTINE createKernel
196 :
197 : ! **************************************************************************************************
198 : !> \brief Build the kernel of the Poisson operator with
199 : !> surfaces Boundary conditions
200 : !> in an interpolating scaling functions basis.
201 : !> Beware of the fact that the nonperiodic direction is y!
202 : !> \param n1 Dimensions for the FFT
203 : !> \param n2 Dimensions for the FFT
204 : !> \param n3 Dimensions for the FFT
205 : !> \param m3 Actual dimension in non-periodic direction
206 : !> \param nker1 Dimensions of the kernel (nker3=n3/2+1) nker(1,2)=n(1,2)/2+1
207 : !> \param nker2 Dimensions of the kernel (nker3=n3/2+1) nker(1,2)=n(1,2)/2+1
208 : !> \param nker3 Dimensions of the kernel (nker3=n3/2+1) nker(1,2)=n(1,2)/2+1
209 : !> \param h1 Mesh steps in the three dimensions
210 : !> \param h2 Mesh steps in the three dimensions
211 : !> \param h3 Mesh steps in the three dimensions
212 : !> \param itype_scf Order of the scaling function
213 : !> \param karray output array
214 : !> \param iproc Number of process
215 : !> \param nproc number of processes
216 : !> \param mpi_group ...
217 : !> \date October 2006
218 : !> \author L. Genovese
219 : ! **************************************************************************************************
220 2 : SUBROUTINE Surfaces_Kernel(n1, n2, n3, m3, nker1, nker2, nker3, h1, h2, h3, &
221 2 : itype_scf, karray, iproc, nproc, mpi_group)
222 :
223 : INTEGER, INTENT(in) :: n1, n2, n3, m3, nker1, nker2, nker3
224 : REAL(KIND=dp), INTENT(in) :: h1, h2, h3
225 : INTEGER, INTENT(in) :: itype_scf, nproc, iproc
226 : REAL(KIND=dp), &
227 : DIMENSION(nker1, nker2, nker3/nproc), &
228 : INTENT(out) :: karray
229 : TYPE(mp_comm_type), INTENT(in) :: mpi_group
230 :
231 : INTEGER, PARAMETER :: n_points = 2**6, ncache_optimal = 8*1024
232 :
233 : INTEGER :: i, i1, i2, i3, ic, iend, imu, ind1, ind2, inzee, ipolyord, ireim, istart, j2, &
234 : j2nd, j2st, jnd1, jp2, jreim, n_cell, n_range, n_scf, nact2, ncache, nfft, num_of_mus, &
235 : shift
236 2 : INTEGER, ALLOCATABLE, DIMENSION(:) :: after, before, now
237 : REAL(kind=dp) :: a, b, c, cp, d, diff, dx, feI, feR, foI, &
238 : foR, fR, mu1, pi, pion, ponx, pony, &
239 : sp, value, x
240 2 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: kernel_scf, x_scf, y_scf
241 2 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: btrig, cossinarr
242 2 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: halfft_cache, kernel
243 2 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :) :: kernel_mpi
244 : REAL(KIND=dp), DIMENSION(9, 8) :: cpol
245 :
246 : !Better if higher (1024 points are enough 10^{-14}: 2*itype_scf*n_points)
247 : ! include "perfdata.inc"
248 : !FFT arrays
249 : !coefficients for the polynomial interpolation
250 : !assign the values of the coefficients
251 :
252 45530 : karray = 0.0_dp
253 162 : cpol(:, :) = 1._dp
254 :
255 2 : cpol(1, 2) = .25_dp
256 :
257 2 : cpol(1, 3) = 1._dp/3._dp
258 :
259 2 : cpol(1, 4) = 7._dp/12._dp
260 2 : cpol(2, 4) = 8._dp/3._dp
261 :
262 2 : cpol(1, 5) = 19._dp/50._dp
263 2 : cpol(2, 5) = 3._dp/2._dp
264 :
265 2 : cpol(1, 6) = 41._dp/272._dp
266 2 : cpol(2, 6) = 27._dp/34._dp
267 2 : cpol(3, 6) = 27._dp/272._dp
268 :
269 2 : cpol(1, 7) = 751._dp/2989._dp
270 2 : cpol(2, 7) = 73._dp/61._dp
271 2 : cpol(3, 7) = 27._dp/61._dp
272 :
273 2 : cpol(1, 8) = -989._dp/4540._dp
274 2 : cpol(2, 8) = -1472._dp/1135._dp
275 2 : cpol(3, 8) = 232._dp/1135._dp
276 2 : cpol(4, 8) = -2624._dp/1135._dp
277 :
278 : !renormalize values
279 2 : cpol(1, 1) = .5_dp*cpol(1, 1)
280 6 : cpol(1:2, 2) = 2._dp/3._dp*cpol(1:2, 2)
281 6 : cpol(1:2, 3) = 3._dp/8._dp*cpol(1:2, 3)
282 8 : cpol(1:3, 4) = 2._dp/15._dp*cpol(1:3, 4)
283 8 : cpol(1:3, 5) = 25._dp/144._dp*cpol(1:3, 5)
284 10 : cpol(1:4, 6) = 34._dp/105._dp*cpol(1:4, 6)
285 10 : cpol(1:4, 7) = 2989._dp/17280._dp*cpol(1:4, 7)
286 12 : cpol(1:5, 8) = -454._dp/2835._dp*cpol(1:5, 8)
287 :
288 : !assign the complete values
289 2 : cpol(2, 1) = cpol(1, 1)
290 :
291 2 : cpol(3, 2) = cpol(1, 2)
292 :
293 2 : cpol(3, 3) = cpol(2, 3)
294 2 : cpol(4, 3) = cpol(1, 3)
295 :
296 2 : cpol(4, 4) = cpol(2, 4)
297 2 : cpol(5, 4) = cpol(1, 4)
298 :
299 2 : cpol(4, 5) = cpol(3, 5)
300 2 : cpol(5, 5) = cpol(2, 5)
301 2 : cpol(6, 5) = cpol(1, 5)
302 :
303 2 : cpol(5, 6) = cpol(3, 6)
304 2 : cpol(6, 6) = cpol(2, 6)
305 2 : cpol(7, 6) = cpol(1, 6)
306 :
307 2 : cpol(5, 7) = cpol(4, 7)
308 2 : cpol(6, 7) = cpol(3, 7)
309 2 : cpol(7, 7) = cpol(2, 7)
310 2 : cpol(8, 7) = cpol(1, 7)
311 :
312 2 : cpol(6, 8) = cpol(4, 8)
313 2 : cpol(7, 8) = cpol(3, 8)
314 2 : cpol(8, 8) = cpol(2, 8)
315 2 : cpol(9, 8) = cpol(1, 8)
316 :
317 : !Number of integration points : 2*itype_scf*n_points
318 2 : n_scf = 2*itype_scf*n_points
319 : !Allocations
320 6 : ALLOCATE (x_scf(0:n_scf))
321 6 : ALLOCATE (y_scf(0:n_scf))
322 :
323 : !Build the scaling function
324 2 : CALL scaling_function(itype_scf, n_scf, n_range, x_scf, y_scf)
325 : !Step grid for the integration
326 2 : dx = REAL(n_range, KIND=dp)/REAL(n_scf, KIND=dp)
327 : !Extend the range (no more calculations because fill in by 0._dp)
328 2 : n_cell = m3
329 2 : n_range = MAX(n_cell, n_range)
330 :
331 : !Allocations
332 2 : ncache = ncache_optimal
333 : !the HalFFT must be performed only in the third dimension,
334 : !and nker3=n3/2+1, hence
335 2 : IF (ncache <= (nker3 - 1)*4) ncache = nker3 - 1*4
336 :
337 : !enlarge the second dimension of the kernel to be compatible with nproc
338 2 : nact2 = nker2
339 0 : enlarge_ydim: DO
340 2 : IF (nproc*(nact2/nproc) /= nact2) THEN
341 0 : nact2 = nact2 + 1
342 : ELSE
343 : EXIT enlarge_ydim
344 : END IF
345 : END DO enlarge_ydim
346 :
347 : !array for the MPI procedure
348 10 : ALLOCATE (kernel(nker1, nact2/nproc, nker3))
349 12 : ALLOCATE (kernel_mpi(nker1, nact2/nproc, nker3/nproc, nproc))
350 6 : ALLOCATE (kernel_scf(n_range))
351 8 : ALLOCATE (halfft_cache(2, ncache/4, 2))
352 6 : ALLOCATE (cossinarr(2, n3/2 - 1))
353 2 : ALLOCATE (btrig(2, ctrig_length))
354 2 : ALLOCATE (after(7))
355 2 : ALLOCATE (now(7))
356 2 : ALLOCATE (before(7))
357 :
358 : !constants
359 2 : pi = 4._dp*ATAN(1._dp)
360 :
361 : !arrays for the halFFT
362 2 : CALL ctrig(n3/2, btrig, after, before, now, 1, ic)
363 :
364 : !build the phases for the HalFFT reconstruction
365 2 : pion = 2._dp*pi/REAL(n3, KIND=dp)
366 108 : DO i3 = 2, n3/2
367 106 : x = REAL(i3 - 1, KIND=dp)*pion
368 106 : cossinarr(1, i3 - 1) = COS(x)
369 108 : cossinarr(2, i3 - 1) = -SIN(x)
370 : END DO
371 :
372 : ! satisfy valgrind, init arrays to large value, even if the offending bit is (likely?) padding
373 45586 : kernel = HUGE(0._dp)
374 45590 : kernel_mpi = HUGE(0._dp)
375 :
376 : !calculate the limits of the FFT calculations
377 : !that can be performed in a row remaining inside the cache
378 2 : num_of_mus = ncache/(2*n3)
379 :
380 2 : diff = 0._dp
381 : !order of the polynomial to be used for integration (must be a power of two)
382 2 : ipolyord = 8 !this part should be incorporated inside the numerical integration
383 : !here we have to choice the piece of the x-y grid to cover
384 :
385 : !let us now calculate the fraction of mu that will be considered
386 2 : j2st = iproc*(nact2/nproc)
387 2 : j2nd = MIN((iproc + 1)*(nact2/nproc), n2/2 + 1)
388 :
389 24 : DO ind2 = (n1/2 + 1)*j2st + 1, (n1/2 + 1)*j2nd, num_of_mus
390 22 : istart = ind2
391 22 : iend = MIN(ind2 + (num_of_mus - 1), (n1/2 + 1)*j2nd)
392 22 : nfft = iend - istart + 1
393 22 : shift = 0
394 :
395 : !initialization of the interesting part of the cache array
396 270402 : halfft_cache(:, :, :) = 0._dp
397 :
398 22 : IF (istart == 1) THEN
399 : !i2=1
400 1 : shift = 1
401 :
402 : CALL calculates_green_opt_muzero(n_range, n_scf, ipolyord, x_scf, y_scf, &
403 1 : cpol(1, ipolyord), dx, kernel_scf)
404 :
405 : !copy of the first zero value
406 1 : halfft_cache(1, 1, 1) = 0._dp
407 :
408 55 : DO i3 = 1, m3
409 :
410 54 : value = 0.5_dp*h3*kernel_scf(i3)
411 : !index in where to copy the value of the kernel
412 54 : CALL indices(ireim, num_of_mus, n3/2 + i3, 1, ind1)
413 : !index in where to copy the symmetric value
414 54 : CALL indices(jreim, num_of_mus, n3/2 + 2 - i3, 1, jnd1)
415 54 : halfft_cache(ireim, ind1, 1) = value
416 55 : halfft_cache(jreim, jnd1, 1) = value
417 :
418 : END DO
419 :
420 : END IF
421 :
422 805 : loopimpulses: DO imu = istart + shift, iend
423 :
424 : !here there is the value of mu associated to hgrid
425 : !note that we have multiplicated mu for hgrid to be comparable
426 : !with mu0ref
427 :
428 : !calculate the proper value of mu taking into account the periodic dimensions
429 : !corresponding value of i1 and i2
430 783 : i1 = MOD(imu, n1/2 + 1)
431 783 : IF (i1 == 0) i1 = n1/2 + 1
432 783 : i2 = (imu - i1)/(n1/2 + 1) + 1
433 783 : ponx = REAL(i1 - 1, KIND=dp)/REAL(n1, KIND=dp)
434 783 : pony = REAL(i2 - 1, KIND=dp)/REAL(n2, KIND=dp)
435 :
436 783 : mu1 = 2._dp*pi*SQRT((ponx/h1)**2 + (pony/h2)**2)*h3
437 :
438 : CALL calculates_green_opt(n_range, n_scf, itype_scf, ipolyord, x_scf, y_scf, &
439 783 : cpol(1, ipolyord), mu1, dx, kernel_scf)
440 :
441 : !readjust the coefficient and define the final kernel
442 :
443 : !copy of the first zero value
444 783 : halfft_cache(1, imu - istart + 1, 1) = 0._dp
445 43087 : DO i3 = 1, m3
446 42282 : value = -0.5_dp*h3/mu1*kernel_scf(i3)
447 : !write(80,*)mu1,i3,kernel_scf(i03)
448 : !index in where to copy the value of the kernel
449 42282 : CALL indices(ireim, num_of_mus, n3/2 + i3, imu - istart + 1, ind1)
450 : !index in where to copy the symmetric value
451 42282 : CALL indices(jreim, num_of_mus, n3/2 + 2 - i3, imu - istart + 1, jnd1)
452 42282 : halfft_cache(ireim, ind1, 1) = value
453 43065 : halfft_cache(jreim, jnd1, 1) = value
454 : END DO
455 :
456 : END DO loopimpulses
457 :
458 : !now perform the FFT of the array in cache
459 22 : inzee = 1
460 88 : DO i = 1, ic
461 : CALL fftstp(num_of_mus, nfft, n3/2, num_of_mus, n3/2, &
462 : halfft_cache(1, 1, inzee), halfft_cache(1, 1, 3 - inzee), &
463 66 : btrig, after(i), now(i), before(i), 1)
464 88 : inzee = 3 - inzee
465 : END DO
466 : !assign the values of the FFT array
467 : !and compare with the good results
468 808 : DO imu = istart, iend
469 :
470 : !corresponding value of i1 and i2
471 784 : i1 = MOD(imu, n1/2 + 1)
472 784 : IF (i1 == 0) i1 = n1/2 + 1
473 784 : i2 = (imu - i1)/(n1/2 + 1) + 1
474 :
475 784 : j2 = i2 - j2st
476 :
477 784 : a = halfft_cache(1, imu - istart + 1, inzee)
478 784 : b = halfft_cache(2, imu - istart + 1, inzee)
479 784 : kernel(i1, j2, 1) = a + b
480 784 : kernel(i1, j2, n3/2 + 1) = a - b
481 :
482 42358 : DO i3 = 2, n3/2
483 41552 : ind1 = imu - istart + 1 + num_of_mus*(i3 - 1)
484 41552 : jnd1 = imu - istart + 1 + num_of_mus*(n3/2 + 2 - i3 - 1)
485 41552 : cp = cossinarr(1, i3 - 1)
486 41552 : sp = cossinarr(2, i3 - 1)
487 41552 : a = halfft_cache(1, ind1, inzee)
488 41552 : b = halfft_cache(2, ind1, inzee)
489 41552 : c = halfft_cache(1, jnd1, inzee)
490 41552 : d = halfft_cache(2, jnd1, inzee)
491 41552 : feR = .5_dp*(a + c)
492 41552 : feI = .5_dp*(b - d)
493 41552 : foR = .5_dp*(a - c)
494 41552 : foI = .5_dp*(b + d)
495 41552 : fR = feR + cp*foI - sp*foR
496 42336 : kernel(i1, j2, i3) = fR
497 : END DO
498 : END DO
499 :
500 : END DO
501 :
502 : !give to each processor a slice of the third dimension
503 2 : IF (nproc > 1) THEN
504 : CALL mpi_group%alltoall(kernel, &!nker1*(nact2/nproc)*(nker3/nproc), &
505 2 : kernel_mpi, nker1*(nact2/nproc)*(nker3/nproc))
506 :
507 6 : DO jp2 = 1, nproc
508 118 : DO i3 = 1, nker3/nproc
509 1684 : DO i2 = 1, nact2/nproc
510 1568 : j2 = i2 + (jp2 - 1)*(nact2/nproc)
511 1680 : IF (j2 <= nker2) THEN
512 45472 : DO i1 = 1, nker1
513 : karray(i1, j2, i3) = &
514 45472 : kernel_mpi(i1, i2, i3, jp2)
515 : END DO
516 : END IF
517 : END DO
518 : END DO
519 : END DO
520 :
521 : ELSE
522 0 : karray(1:nker1, 1:nker2, 1:nker3) = kernel(1:nker1, 1:nker2, 1:nker3)
523 : END IF
524 :
525 : !De-allocations
526 2 : DEALLOCATE (kernel)
527 2 : DEALLOCATE (kernel_mpi)
528 2 : DEALLOCATE (btrig)
529 2 : DEALLOCATE (after)
530 2 : DEALLOCATE (now)
531 2 : DEALLOCATE (before)
532 2 : DEALLOCATE (halfft_cache)
533 2 : DEALLOCATE (kernel_scf)
534 2 : DEALLOCATE (x_scf)
535 2 : DEALLOCATE (y_scf)
536 :
537 4 : END SUBROUTINE Surfaces_Kernel
538 :
539 : ! **************************************************************************************************
540 : !> \brief ...
541 : !> \param n ...
542 : !> \param n_scf ...
543 : !> \param itype_scf ...
544 : !> \param intorder ...
545 : !> \param xval ...
546 : !> \param yval ...
547 : !> \param c ...
548 : !> \param mu ...
549 : !> \param hres ...
550 : !> \param g_mu ...
551 : ! **************************************************************************************************
552 783 : SUBROUTINE calculates_green_opt(n, n_scf, itype_scf, intorder, xval, yval, c, mu, hres, g_mu)
553 : INTEGER, INTENT(in) :: n, n_scf, itype_scf, intorder
554 : REAL(KIND=dp), DIMENSION(0:n_scf), INTENT(in) :: xval, yval
555 : REAL(KIND=dp), DIMENSION(intorder+1), INTENT(in) :: c
556 : REAL(KIND=dp), INTENT(in) :: mu, hres
557 : REAL(KIND=dp), DIMENSION(n), INTENT(out) :: g_mu
558 :
559 : REAL(KIND=dp), PARAMETER :: mu_max = 0.2_dp
560 :
561 : INTEGER :: i, iend, ikern, ivalue, izero, n_iter, &
562 : nrec
563 : REAL(KIND=dp) :: f, filter, fl, fr, gleft, gltmp, gright, &
564 : grtmp, mu0, ratio, x, x0, x1
565 783 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: green, green1
566 :
567 43065 : g_mu = 0.0_dp
568 : !We calculate the number of iterations to go from mu0 to mu0_ref
569 783 : IF (mu <= mu_max) THEN
570 3 : n_iter = 0
571 3 : mu0 = mu
572 : ELSE
573 780 : n_iter = 1
574 2296 : loop_iter: DO
575 3076 : ratio = REAL(2**n_iter, KIND=dp)
576 3076 : mu0 = mu/ratio
577 3076 : IF (mu0 <= mu_max) THEN
578 : EXIT loop_iter
579 : END IF
580 2296 : n_iter = n_iter + 1
581 : END DO loop_iter
582 : END IF
583 :
584 : !dimension needed for the correct calculation of the recursion
585 783 : nrec = 2**n_iter*n
586 :
587 2349 : ALLOCATE (green(-nrec:nrec))
588 :
589 : !initialization of the branching value
590 652239 : ikern = 0
591 652239 : izero = 0
592 651456 : initialization: DO
593 652239 : IF (xval(izero) >= REAL(ikern, KIND=dp) .OR. izero == n_scf) EXIT initialization
594 651456 : izero = izero + 1
595 : END DO initialization
596 1474362 : green = 0._dp
597 : !now perform the interpolation in right direction
598 : ivalue = izero
599 : gright = 0._dp
600 93177 : loop_right: DO
601 93960 : IF (ivalue >= n_scf - intorder - 1) EXIT loop_right
602 931770 : DO i = 1, intorder + 1
603 838593 : x = xval(ivalue) - REAL(ikern, KIND=dp)
604 838593 : f = yval(ivalue)*EXP(-mu0*x)
605 838593 : filter = intorder*c(i)
606 838593 : gright = gright + filter*f
607 931770 : ivalue = ivalue + 1
608 : END DO
609 93177 : ivalue = ivalue - 1
610 : END DO loop_right
611 783 : iend = n_scf - ivalue
612 7047 : DO i = 1, iend
613 6264 : x = xval(ivalue) - REAL(ikern, KIND=dp)
614 6264 : f = yval(ivalue)*EXP(-mu0*x)
615 6264 : filter = intorder*c(i)
616 6264 : gright = gright + filter*f
617 7047 : ivalue = ivalue + 1
618 : END DO
619 783 : gright = hres*gright
620 :
621 : !the scaling function is symmetric, so the same for the other direction
622 783 : gleft = gright
623 :
624 783 : green(ikern) = gleft + gright
625 :
626 : !now the loop until the last value
627 252960 : DO ikern = 1, nrec
628 335124 : gltmp = 0._dp
629 335124 : grtmp = 0._dp
630 335124 : ivalue = izero
631 335124 : x0 = xval(izero)
632 82215 : loop_integration: DO
633 335124 : IF (izero == n_scf) EXIT loop_integration
634 927855 : DO i = 1, intorder + 1
635 845640 : x = xval(ivalue)
636 845640 : fl = yval(ivalue)*EXP(mu0*x)
637 845640 : fr = yval(ivalue)*EXP(-mu0*x)
638 845640 : filter = intorder*c(i)
639 845640 : gltmp = gltmp + filter*fl
640 845640 : grtmp = grtmp + filter*fr
641 845640 : ivalue = ivalue + 1
642 845640 : IF (xval(izero) >= REAL(ikern, KIND=dp) .OR. izero == n_scf) THEN
643 : x1 = xval(izero)
644 : EXIT loop_integration
645 : END IF
646 916110 : izero = izero + 1
647 : END DO
648 82215 : ivalue = ivalue - 1
649 82215 : izero = izero - 1
650 : END DO loop_integration
651 252909 : gleft = EXP(-mu0)*(gleft + hres*EXP(-mu0*REAL(ikern - 1, KIND=dp))*gltmp)
652 252909 : IF (izero == n_scf) THEN
653 : gright = 0._dp
654 : ELSE
655 10962 : gright = EXP(mu0)*(gright - hres*EXP(mu0*REAL(ikern - 1, KIND=dp))*grtmp)
656 : END IF
657 252909 : green(ikern) = gleft + gright
658 252909 : green(-ikern) = gleft + gright
659 252960 : IF (ABS(green(ikern)) <= 1.e-20_dp) THEN
660 732 : nrec = ikern
661 732 : EXIT
662 : END IF
663 : !print *,ikern,izero,n_scf,gltmp,grtmp,gleft,gright,x0,x1,green(ikern)
664 : END DO
665 : !now we must calculate the recursion
666 2349 : ALLOCATE (green1(-nrec:nrec))
667 :
668 : !Start the iteration to go from mu0 to mu
669 783 : CALL scf_recursion(itype_scf, n_iter, nrec, green(-nrec), green1(-nrec))
670 :
671 43065 : DO i = 1, MIN(n, nrec)
672 43065 : g_mu(i) = green(i - 1)
673 : END DO
674 783 : DO i = MIN(n, nrec) + 1, n
675 783 : g_mu(i) = 0._dp
676 : END DO
677 :
678 783 : DEALLOCATE (green, green1)
679 :
680 783 : END SUBROUTINE calculates_green_opt
681 :
682 : ! **************************************************************************************************
683 : !> \brief ...
684 : !> \param n ...
685 : !> \param n_scf ...
686 : !> \param intorder ...
687 : !> \param xval ...
688 : !> \param yval ...
689 : !> \param c ...
690 : !> \param hres ...
691 : !> \param green ...
692 : ! **************************************************************************************************
693 1 : SUBROUTINE calculates_green_opt_muzero(n, n_scf, intorder, xval, yval, c, hres, green)
694 : INTEGER, INTENT(in) :: n, n_scf, intorder
695 : REAL(KIND=dp), DIMENSION(0:n_scf), INTENT(in) :: xval, yval
696 : REAL(KIND=dp), DIMENSION(intorder+1), INTENT(in) :: c
697 : REAL(KIND=dp), INTENT(in) :: hres
698 : REAL(KIND=dp), DIMENSION(n), INTENT(out) :: green
699 :
700 : INTEGER :: i, iend, ikern, ivalue, izero
701 : REAL(KIND=dp) :: c0, c1, filter, gl0, gl1, gr0, gr1, x, y
702 :
703 : !initialization of the branching value
704 :
705 1 : ikern = 0
706 1 : izero = 0
707 832 : initialization: DO
708 833 : IF (xval(izero) >= REAL(ikern, KIND=dp) .OR. izero == n_scf) EXIT initialization
709 832 : izero = izero + 1
710 : END DO initialization
711 55 : green = 0._dp
712 : !first case, ikern=0
713 : !now perform the interpolation in right direction
714 : ivalue = izero
715 : gr1 = 0._dp
716 119 : loop_right: DO
717 120 : IF (ivalue >= n_scf - intorder - 1) EXIT loop_right
718 1190 : DO i = 1, intorder + 1
719 1071 : x = xval(ivalue)
720 1071 : y = yval(ivalue)
721 1071 : filter = intorder*c(i)
722 1071 : gr1 = gr1 + filter*x*y
723 1190 : ivalue = ivalue + 1
724 : END DO
725 119 : ivalue = ivalue - 1
726 : END DO loop_right
727 1 : iend = n_scf - ivalue
728 9 : DO i = 1, iend
729 8 : x = xval(ivalue)
730 8 : y = yval(ivalue)
731 8 : filter = intorder*c(i)
732 8 : gr1 = gr1 + filter*x*y
733 9 : ivalue = ivalue + 1
734 : END DO
735 1 : gr1 = hres*gr1
736 : !the scaling function is symmetric
737 1 : gl1 = -gr1
738 1 : gl0 = 0.5_dp
739 1 : gr0 = 0.5_dp
740 :
741 1 : green(1) = 2._dp*gr1
742 :
743 : !now the loop until the last value
744 54 : DO ikern = 1, n - 1
745 : c0 = 0._dp
746 : c1 = 0._dp
747 : ivalue = izero
748 105 : loop_integration: DO
749 158 : IF (izero == n_scf) EXIT loop_integration
750 1185 : DO i = 1, intorder + 1
751 1080 : x = xval(ivalue)
752 1080 : y = yval(ivalue)
753 1080 : filter = intorder*c(i)
754 1080 : c0 = c0 + filter*y
755 1080 : c1 = c1 + filter*y*x
756 1080 : ivalue = ivalue + 1
757 1080 : IF (xval(izero) >= REAL(ikern, KIND=dp) .OR. izero == n_scf) THEN
758 : EXIT loop_integration
759 : END IF
760 1170 : izero = izero + 1
761 : END DO
762 105 : ivalue = ivalue - 1
763 120 : izero = izero - 1
764 : END DO loop_integration
765 53 : c0 = hres*c0
766 53 : c1 = hres*c1
767 :
768 53 : gl0 = gl0 + c0
769 53 : gl1 = gl1 + c1
770 53 : gr0 = gr0 - c0
771 53 : gr1 = gr1 - c1
772 : !general case
773 54 : green(ikern + 1) = REAL(ikern, KIND=dp)*(gl0 - gr0) + gr1 - gl1
774 : !print *,ikern,izero,n_scf,gltmp,grtmp,gleft,gright,x0,x1,green(ikern)
775 : END DO
776 :
777 1 : END SUBROUTINE calculates_green_opt_muzero
778 :
779 : ! **************************************************************************************************
780 : !> \brief ...
781 : !> \param var_realimag ...
782 : !> \param nelem ...
783 : !> \param intrn ...
784 : !> \param extrn ...
785 : !> \param index ...
786 : ! **************************************************************************************************
787 84672 : SUBROUTINE indices(var_realimag, nelem, intrn, extrn, index)
788 :
789 : INTEGER, INTENT(out) :: var_realimag
790 : INTEGER, INTENT(in) :: nelem, intrn, extrn
791 : INTEGER, INTENT(out) :: index
792 :
793 : INTEGER :: i
794 :
795 : !real or imaginary part
796 :
797 84672 : var_realimag = 2 - MOD(intrn, 2)
798 : !actual index over half the length
799 :
800 84672 : i = (intrn + 1)/2
801 : !check
802 84672 : IF (2*(i - 1) + var_realimag /= intrn) THEN
803 0 : PRINT *, 'error, index=', intrn, 'var_realimag=', var_realimag, 'i=', i
804 : END IF
805 : !complete index to be assigned
806 84672 : index = extrn + nelem*(i - 1)
807 :
808 84672 : END SUBROUTINE indices
809 :
810 : ! **************************************************************************************************
811 : !> \brief Build the kernel of a gaussian function
812 : !> for interpolating scaling functions.
813 : !> Do the parallel HalFFT of the symmetrized function and stores into
814 : !> memory only 1/8 of the grid divided by the number of processes nproc
815 : !>
816 : !> Build the kernel (karray) of a gaussian function
817 : !> for interpolating scaling functions
818 : !> $$ K(j) = \sum_k \omega_k \int \int \phi(x) g_k(x'-x) \delta(x'- j) dx dx' $$
819 : !> \param n01 Mesh dimensions of the density
820 : !> \param n02 Mesh dimensions of the density
821 : !> \param n03 Mesh dimensions of the density
822 : !> \param nfft1 Dimensions of the FFT grid (HalFFT in the third direction)
823 : !> \param nfft2 Dimensions of the FFT grid (HalFFT in the third direction)
824 : !> \param nfft3 Dimensions of the FFT grid (HalFFT in the third direction)
825 : !> \param n1k Dimensions of the kernel FFT
826 : !> \param n2k Dimensions of the kernel FFT
827 : !> \param n3k Dimensions of the kernel FFT
828 : !> \param hgrid Mesh step
829 : !> \param itype_scf Order of the scaling function (8,14,16)
830 : !> \param iproc ...
831 : !> \param nproc ...
832 : !> \param karray ...
833 : !> \param mpi_group ...
834 : !> \date February 2006
835 : !> \author T. Deutsch, L. Genovese
836 : ! **************************************************************************************************
837 456 : SUBROUTINE Free_Kernel(n01, n02, n03, nfft1, nfft2, nfft3, n1k, n2k, n3k, &
838 456 : hgrid, itype_scf, iproc, nproc, karray, mpi_group)
839 :
840 : INTEGER, INTENT(in) :: n01, n02, n03, nfft1, nfft2, nfft3, n1k, &
841 : n2k, n3k
842 : REAL(KIND=dp), INTENT(in) :: hgrid
843 : INTEGER, INTENT(in) :: itype_scf, iproc, nproc
844 : REAL(KIND=dp), DIMENSION(n1k, n2k, n3k/nproc), &
845 : INTENT(out) :: karray
846 : TYPE(mp_comm_type), INTENT(in) :: mpi_group
847 :
848 : INTEGER, PARAMETER :: n_gauss = 89, n_points = 2**6
849 : REAL(KIND=dp), PARAMETER :: p0_ref = 1._dp
850 :
851 : INTEGER :: i, i01, i02, i03, i1, i2, i3, i_gauss, &
852 : i_kern, iend, istart, istart1, n1h, &
853 : n2h, n3h, n_cell, n_iter, n_range, &
854 : n_scf, nker1, nker2, nker3
855 : REAL(KIND=dp) :: a1, a2, a3, a_range, absci, acc_gauss, &
856 : dr_gauss, dx, factor, factor2, kern, &
857 : p0_cell, p0gauss, pgauss, ur_gauss
858 456 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: kern_1_scf, kernel_scf, x_scf, y_scf
859 456 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: kp
860 : REAL(KIND=dp), DIMENSION(n_gauss) :: p_gauss, w_gauss
861 :
862 : !Do not touch !!!!
863 : !Better if higher (1024 points are enough 10^{-14}: 2*itype_scf*n_points)
864 : !Better p_gauss for calculation
865 : !(the support of the exponential should be inside [-n_range/2,n_range/2])
866 : !Number of integration points : 2*itype_scf*n_points
867 :
868 456 : n_scf = 2*itype_scf*n_points
869 : !Set karray
870 33412610 : karray = 0.0_dp
871 : !here we must set the dimensions for the fft part, starting from the nfft
872 : !remember that actually nfft2 is associated to n03 and viceversa
873 :
874 : !dimensions that define the center of symmetry
875 456 : n1h = nfft1/2
876 456 : n2h = nfft2/2
877 456 : n3h = nfft3/2
878 :
879 : !Auxiliary dimensions only for building the FFT part
880 456 : nker1 = nfft1
881 456 : nker2 = nfft2
882 456 : nker3 = nfft3/2 + 1
883 :
884 : !adjusting the last two dimensions to be multiples of nproc
885 0 : DO
886 456 : IF (MODULO(nker2, nproc) == 0) EXIT
887 0 : nker2 = nker2 + 1
888 : END DO
889 308 : DO
890 764 : IF (MODULO(nker3, nproc) == 0) EXIT
891 308 : nker3 = nker3 + 1
892 : END DO
893 :
894 : !this will be the array of the kernel in the real space
895 2736 : ALLOCATE (kp(n1h + 1, n3h + 1, nker2/nproc))
896 :
897 : !defining proper extremes for the calculation of the
898 : !local part of the kernel
899 :
900 456 : istart = iproc*nker2/nproc + 1
901 456 : iend = MIN((iproc + 1)*nker2/nproc, n2h + n03)
902 :
903 456 : istart1 = istart
904 456 : IF (iproc .EQ. 0) istart1 = n2h - n03 + 2
905 :
906 : !Allocations
907 1368 : ALLOCATE (x_scf(0:n_scf))
908 1368 : ALLOCATE (y_scf(0:n_scf))
909 :
910 : !Build the scaling function
911 456 : CALL scaling_function(itype_scf, n_scf, n_range, x_scf, y_scf)
912 : !Step grid for the integration
913 456 : dx = REAL(n_range, KIND=dp)/REAL(n_scf, KIND=dp)
914 : !Extend the range (no more calculations because fill in by 0._dp)
915 456 : n_cell = MAX(n01, n02, n03)
916 456 : n_range = MAX(n_cell, n_range)
917 :
918 : !Allocations
919 1368 : ALLOCATE (kernel_scf(-n_range:n_range))
920 1368 : ALLOCATE (kern_1_scf(-n_range:n_range))
921 :
922 : !Lengthes of the box (use FFT dimension)
923 456 : a1 = hgrid*REAL(n01, KIND=dp)
924 456 : a2 = hgrid*REAL(n02, KIND=dp)
925 456 : a3 = hgrid*REAL(n03, KIND=dp)
926 :
927 2322320 : x_scf(:) = hgrid*x_scf(:)
928 2322320 : y_scf(:) = 1._dp/hgrid*y_scf(:)
929 456 : dx = hgrid*dx
930 : !To have a correct integration
931 456 : p0_cell = p0_ref/(hgrid*hgrid)
932 :
933 : !Initialization of the gaussian (Beylkin)
934 456 : CALL gequad(p_gauss, w_gauss, ur_gauss, dr_gauss, acc_gauss)
935 : !In order to have a range from a_range=sqrt(a1*a1+a2*a2+a3*a3)
936 : !(biggest length in the cube)
937 : !We divide the p_gauss by a_range**2 and a_gauss by a_range
938 456 : a_range = SQRT(a1*a1 + a2*a2 + a3*a3)
939 456 : factor = 1._dp/a_range
940 : !factor2 = factor*factor
941 456 : factor2 = 1._dp/(a1*a1 + a2*a2 + a3*a3)
942 41040 : DO i_gauss = 1, n_gauss
943 41040 : p_gauss(i_gauss) = factor2*p_gauss(i_gauss)
944 : END DO
945 41040 : DO i_gauss = 1, n_gauss
946 41040 : w_gauss(i_gauss) = factor*w_gauss(i_gauss)
947 : END DO
948 :
949 64773100 : kp(:, :, :) = 0._dp
950 : !Use in this order (better for accuracy).
951 41040 : loop_gauss: DO i_gauss = n_gauss, 1, -1
952 : !Gaussian
953 40584 : pgauss = p_gauss(i_gauss)
954 :
955 : !We calculate the number of iterations to go from pgauss to p0_ref
956 40584 : n_iter = NINT((LOG(pgauss) - LOG(p0_cell))/LOG(4._dp))
957 40584 : IF (n_iter <= 0) THEN
958 8636 : n_iter = 0
959 8636 : p0gauss = pgauss
960 : ELSE
961 31948 : p0gauss = pgauss/4._dp**n_iter
962 : END IF
963 :
964 : !Stupid integration
965 : !Do the integration with the exponential centered in i_kern
966 6594188 : kernel_scf(:) = 0._dp
967 1279898 : DO i_kern = 0, n_range
968 : kern = 0._dp
969 6512054120 : DO i = 0, n_scf
970 6510777780 : absci = x_scf(i) - REAL(i_kern, KIND=dp)*hgrid
971 6510777780 : absci = absci*absci
972 6512054120 : kern = kern + y_scf(i)*EXP(-p0gauss*absci)*dx
973 : END DO
974 1276340 : kernel_scf(i_kern) = kern
975 1276340 : kernel_scf(-i_kern) = kern
976 1279898 : IF (ABS(kern) < 1.e-18_dp) THEN
977 : !Too small not useful to calculate
978 : EXIT
979 : END IF
980 : END DO
981 :
982 : !Start the iteration to go from p0gauss to pgauss
983 40584 : CALL scf_recursion(itype_scf, n_iter, n_range, kernel_scf, kern_1_scf)
984 :
985 : !Add to the kernel (only the local part)
986 :
987 2146780 : DO i3 = istart1, iend
988 2105740 : i03 = i3 - n2h - 1
989 : ! Crash if index out of range
990 : ! Without compiler bounds checking, the calculation might run successfully but
991 : ! it is also possible that the Hartree energy will blow up
992 : ! This seems to happen with large MPI processor counts if the size of the
993 : ! RS grid is not directly compatible with the allowed FFT dimensions in
994 : ! subroutine fourier_dim (ps_wavelet_fft3d.F)
995 2105740 : IF (i03 .LT. -n_range .OR. i03 .GT. n_range) THEN
996 : CALL cp_abort(__LOCATION__, "Index out of range in wavelet solver. "// &
997 : "Try decreasing the number of MPI processors, or adjust the PW_CUTOFF or cell size "// &
998 : "so that 2*(number of RS grid points) matches the allowed FFT dimensions "// &
999 0 : "(see ps_wavelet_fft3d.F) exactly.")
1000 : END IF
1001 100093049 : DO i2 = 1, n02
1002 97946725 : i02 = i2 - 1
1003 5385048774 : DO i1 = 1, n01
1004 5284996309 : i01 = i1 - 1
1005 : kp(i1, i2, i3 - istart + 1) = kp(i1, i2, i3 - istart + 1) + w_gauss(i_gauss)* &
1006 5382943034 : kernel_scf(i01)*kernel_scf(i02)*kernel_scf(i03)
1007 : END DO
1008 : END DO
1009 : END DO
1010 :
1011 : END DO loop_gauss
1012 :
1013 : !De-allocations
1014 456 : DEALLOCATE (kernel_scf)
1015 456 : DEALLOCATE (kern_1_scf)
1016 456 : DEALLOCATE (x_scf)
1017 456 : DEALLOCATE (y_scf)
1018 :
1019 : !!!!END KERNEL CONSTRUCTION
1020 :
1021 : !!$ if(iproc .eq. 0) print *,"Do a 3D PHalFFT for the kernel"
1022 :
1023 : CALL kernelfft(nfft1, nfft2, nfft3, nker1, nker2, nker3, n1k, n2k, n3k, nproc, iproc, &
1024 456 : kp, karray, mpi_group)
1025 :
1026 : !De-allocations
1027 456 : DEALLOCATE (kp)
1028 :
1029 456 : END SUBROUTINE Free_Kernel
1030 :
1031 : ! **************************************************************************************************
1032 : !> \brief ...
1033 : !> \param n1 ...
1034 : !> \param n3 ...
1035 : !> \param lot ...
1036 : !> \param nfft ...
1037 : !> \param i1 ...
1038 : !> \param zf ...
1039 : !> \param zw ...
1040 : ! **************************************************************************************************
1041 70404 : SUBROUTINE inserthalf(n1, n3, lot, nfft, i1, zf, zw)
1042 : INTEGER, INTENT(in) :: n1, n3, lot, nfft, i1
1043 : REAL(KIND=dp), DIMENSION(n1/2+1, n3/2+1), &
1044 : INTENT(in) :: zf
1045 : REAL(KIND=dp), DIMENSION(2, lot, n3/2), &
1046 : INTENT(out) :: zw
1047 :
1048 : INTEGER :: i01, i03i, i03r, i3, l1, l3
1049 :
1050 431644212 : zw = 0.0_dp
1051 70404 : i3 = 0
1052 4421220 : DO l3 = 1, n3, 2
1053 4350816 : i3 = i3 + 1
1054 4350816 : i03r = ABS(l3 - n3/2 - 1) + 1
1055 4350816 : i03i = ABS(l3 - n3/2) + 1
1056 127033580 : DO l1 = 1, nfft
1057 122612360 : i01 = ABS(l1 - 1 + i1 - n1/2 - 1) + 1
1058 122612360 : zw(1, l1, i3) = zf(i01, i03r)
1059 126963176 : zw(2, l1, i3) = zf(i01, i03i)
1060 : END DO
1061 : END DO
1062 :
1063 70404 : END SUBROUTINE inserthalf
1064 :
1065 : ! **************************************************************************************************
1066 : !> \brief (Based on suitable modifications of S.Goedecker routines)
1067 : !> Calculates the FFT of the distributed kernel
1068 : !> \param n1 logical dimension of the transform.
1069 : !> \param n2 logical dimension of the transform.
1070 : !> \param n3 logical dimension of the transform.
1071 : !> \param nd1 Dimensions of work arrays
1072 : !> \param nd2 Dimensions of work arrays
1073 : !> \param nd3 Dimensions of work arrays
1074 : !> \param nk1 ...
1075 : !> \param nk2 ...
1076 : !> \param nk3 ...
1077 : !> \param nproc number of processors used as returned by MPI_COMM_SIZE
1078 : !> \param iproc [0:nproc-1] number of processor as returned by MPI_COMM_RANK
1079 : !> \param zf Real kernel (input)
1080 : !> zf(i1,i2,i3)
1081 : !> \param zr Distributed Kernel FFT
1082 : !> zr(2,i1,i2,i3)
1083 : !> \param mpi_group ...
1084 : !> \date February 2006
1085 : !> \par Restrictions
1086 : !> Copyright (C) Stefan Goedecker, Cornell University, Ithaca, USA, 1994
1087 : !> Copyright (C) Stefan Goedecker, MPI Stuttgart, Germany, 1999
1088 : !> Copyright (C) 2002 Stefan Goedecker, CEA Grenoble
1089 : !> This file is distributed under the terms of the
1090 : !> GNU General Public License, see http://www.gnu.org/copyleft/gpl.txt .
1091 : !> \author S. Goedecker, L. Genovese
1092 : !> \note As transform lengths
1093 : !> most products of the prime factors 2,3,5 are allowed.
1094 : !> The detailed table with allowed transform lengths can
1095 : !> be found in subroutine CTRIG
1096 : ! **************************************************************************************************
1097 456 : SUBROUTINE kernelfft(n1, n2, n3, nd1, nd2, nd3, nk1, nk2, nk3, nproc, iproc, zf, zr, mpi_group)
1098 :
1099 : INTEGER, INTENT(in) :: n1, n2, n3, nd1, nd2, nd3, nk1, nk2, &
1100 : nk3, nproc, iproc
1101 : REAL(KIND=dp), &
1102 : DIMENSION(n1/2+1, n3/2+1, nd2/nproc), &
1103 : INTENT(in) :: zf
1104 : REAL(KIND=dp), DIMENSION(nk1, nk2, nk3/nproc), &
1105 : INTENT(inout) :: zr
1106 : TYPE(mp_comm_type), INTENT(in) :: mpi_group
1107 :
1108 : INTEGER, PARAMETER :: ncache_optimal = 8*1024
1109 :
1110 : INTEGER :: i, i1, i3, ic1, ic2, ic3, inzee, j, j2, &
1111 : J2st, j3, Jp2st, lot, lzt, ma, mb, &
1112 : ncache, nfft
1113 456 : INTEGER, ALLOCATABLE, DIMENSION(:) :: after1, after2, after3, before1, &
1114 456 : before2, before3, now1, now2, now3
1115 : REAL(kind=dp) :: twopion
1116 456 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: cosinarr, trig1, trig2, trig3
1117 456 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: zt, zw
1118 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :, :) :: zmpi2
1119 : REAL(KIND=dp), ALLOCATABLE, &
1120 456 : DIMENSION(:, :, :, :, :) :: zmpi1
1121 :
1122 : ! include "perfdata.inc"
1123 : !work arrays for transpositions
1124 : !work arrays for MPI
1125 : !cache work array
1126 : !FFT work arrays
1127 : !Body
1128 : !check input
1129 :
1130 456 : CPASSERT(nd1 .GE. n1)
1131 456 : CPASSERT(nd2 .GE. n2)
1132 456 : CPASSERT(nd3 .GE. n3/2 + 1)
1133 456 : CPASSERT(MOD(nd3, nproc) .EQ. 0)
1134 456 : CPASSERT(MOD(nd2, nproc) .EQ. 0)
1135 : MARK_USED(nd1)
1136 :
1137 : !defining work arrays dimensions
1138 456 : ncache = ncache_optimal
1139 456 : IF (ncache <= MAX(n1, n2, n3/2)*4) ncache = MAX(n1, n2, n3/2)*4
1140 456 : lzt = n2
1141 456 : IF (MOD(n2, 2) .EQ. 0) lzt = lzt + 1
1142 456 : IF (MOD(n2, 4) .EQ. 0) lzt = lzt + 1
1143 :
1144 : !Allocations
1145 456 : ALLOCATE (trig1(2, ctrig_length))
1146 456 : ALLOCATE (after1(7))
1147 456 : ALLOCATE (now1(7))
1148 456 : ALLOCATE (before1(7))
1149 456 : ALLOCATE (trig2(2, ctrig_length))
1150 456 : ALLOCATE (after2(7))
1151 456 : ALLOCATE (now2(7))
1152 456 : ALLOCATE (before2(7))
1153 456 : ALLOCATE (trig3(2, ctrig_length))
1154 456 : ALLOCATE (after3(7))
1155 456 : ALLOCATE (now3(7))
1156 456 : ALLOCATE (before3(7))
1157 1824 : ALLOCATE (zw(2, ncache/4, 2))
1158 1824 : ALLOCATE (zt(2, lzt, n1))
1159 2280 : ALLOCATE (zmpi2(2, n1, nd2/nproc, nd3))
1160 1824 : ALLOCATE (cosinarr(2, n3/2))
1161 456 : IF (nproc .GT. 1) THEN
1162 1848 : ALLOCATE (zmpi1(2, n1, nd2/nproc, nd3/nproc, nproc))
1163 299651880 : zmpi1 = 0.0_dp
1164 : END IF
1165 :
1166 380542188 : zmpi2 = 0.0_dp
1167 : !calculating the FFT work arrays (beware on the HalFFT in n3 dimension)
1168 456 : CALL ctrig(n3/2, trig3, after3, before3, now3, 1, ic3)
1169 456 : CALL ctrig(n1, trig1, after1, before1, now1, 1, ic1)
1170 456 : CALL ctrig(n2, trig2, after2, before2, now2, 1, ic2)
1171 :
1172 : !Calculating array of phases for HalFFT decoding
1173 456 : twopion = 8._dp*ATAN(1._dp)/REAL(n3, KIND=dp)
1174 20224 : DO i3 = 1, n3/2
1175 19768 : cosinarr(1, i3) = COS(twopion*(i3 - 1))
1176 20224 : cosinarr(2, i3) = -SIN(twopion*(i3 - 1))
1177 : END DO
1178 :
1179 : !transform along z axis
1180 :
1181 456 : lot = ncache/(2*n3)
1182 456 : CPASSERT(lot .GE. 1)
1183 :
1184 24574 : DO j2 = 1, nd2/nproc
1185 : !this condition ensures that we manage only the interesting part for the FFT
1186 24574 : IF (iproc*(nd2/nproc) + j2 .LE. n2) THEN
1187 94522 : DO i1 = 1, n1, lot
1188 70404 : ma = i1
1189 70404 : mb = MIN(i1 + (lot - 1), n1)
1190 70404 : nfft = mb - ma + 1
1191 :
1192 : !inserting real data into complex array of half length
1193 : !input: I1,I3,J2,(Jp2)
1194 :
1195 70404 : CALL inserthalf(n1, n3, lot, nfft, i1, zf(1, 1, j2), zw(1, 1, 1))
1196 :
1197 : !performing FFT
1198 70404 : inzee = 1
1199 262256 : DO i = 1, ic3
1200 : CALL fftstp(lot, nfft, n3/2, lot, n3/2, zw(1, 1, inzee), zw(1, 1, 3 - inzee), &
1201 191852 : trig3, after3(i), now3(i), before3(i), 1)
1202 262256 : inzee = 3 - inzee
1203 : END DO
1204 : !output: I1,i3,J2,(Jp2)
1205 :
1206 : !unpacking FFT in order to restore correct result,
1207 : !while exchanging components
1208 : !input: I1,i3,J2,(Jp2)
1209 94522 : CALL scramble_unpack(i1, j2, lot, nfft, n1, n3, nd2, nproc, nd3, zw(1, 1, inzee), zmpi2, cosinarr)
1210 : !output: I1,J2,i3,(Jp2)
1211 : END DO
1212 : END IF
1213 : END DO
1214 :
1215 : !Interprocessor data transposition
1216 : !input: I1,J2,j3,jp3,(Jp2)
1217 456 : IF (nproc .GT. 1) THEN
1218 : !communication scheduling
1219 : CALL mpi_group%alltoall(zmpi2, &!2*n1*(nd2/nproc)*(nd3/nproc), &
1220 308 : zmpi1, 2*n1*(nd2/nproc)*(nd3/nproc))
1221 : ! output: I1,J2,j3,Jp2,(jp3)
1222 : END IF
1223 :
1224 13154 : DO j3 = 1, nd3/nproc
1225 : !this condition ensures that we manage only the interesting part for the FFT
1226 13154 : IF (iproc*(nd3/nproc) + j3 .LE. n3/2 + 1) THEN
1227 12544 : Jp2st = 1
1228 12544 : J2st = 1
1229 :
1230 : !transform along x axis
1231 12544 : lot = ncache/(4*n1)
1232 12544 : CPASSERT(lot .GE. 1)
1233 :
1234 81544 : DO j = 1, n2, lot
1235 69000 : ma = j
1236 69000 : mb = MIN(j + (lot - 1), n2)
1237 69000 : nfft = mb - ma + 1
1238 :
1239 : !reverse ordering
1240 : !input: I1,J2,j3,Jp2,(jp3)
1241 69000 : IF (nproc .EQ. 1) THEN
1242 16092 : CALL mpiswitch(j3, nfft, Jp2st, J2st, lot, n1, nd2, nd3, nproc, zmpi2, zw(1, 1, 1))
1243 : ELSE
1244 52908 : CALL mpiswitch(j3, nfft, Jp2st, J2st, lot, n1, nd2, nd3, nproc, zmpi1, zw(1, 1, 1))
1245 : END IF
1246 : !output: J2,Jp2,I1,j3,(jp3)
1247 :
1248 : !performing FFT
1249 : !input: I2,I1,j3,(jp3)
1250 69000 : inzee = 1
1251 225230 : DO i = 1, ic1 - 1
1252 : CALL fftstp(lot, nfft, n1, lot, n1, zw(1, 1, inzee), zw(1, 1, 3 - inzee), &
1253 156230 : trig1, after1(i), now1(i), before1(i), 1)
1254 225230 : inzee = 3 - inzee
1255 : END DO
1256 : !storing the last step into zt
1257 69000 : i = ic1
1258 : CALL fftstp(lot, nfft, n1, lzt, n1, zw(1, 1, inzee), zt(1, j, 1), &
1259 81544 : trig1, after1(i), now1(i), before1(i), 1)
1260 : !output: I2,i1,j3,(jp3)
1261 : END DO
1262 :
1263 : !transform along y axis, and taking only the first half
1264 12544 : lot = ncache/(4*n2)
1265 12544 : CPASSERT(lot .GE. 1)
1266 :
1267 52323 : DO j = 1, nk1, lot
1268 39779 : ma = j
1269 39779 : mb = MIN(j + (lot - 1), nk1)
1270 39779 : nfft = mb - ma + 1
1271 :
1272 : !reverse ordering
1273 : !input: I2,i1,j3,(jp3)
1274 39779 : CALL switch(nfft, n2, lot, n1, lzt, zt(1, 1, j), zw(1, 1, 1))
1275 : !output: i1,I2,j3,(jp3)
1276 :
1277 : !performing FFT
1278 : !input: i1,I2,j3,(jp3)
1279 39779 : inzee = 1
1280 170769 : DO i = 1, ic2
1281 : CALL fftstp(lot, nfft, n2, lot, n2, zw(1, 1, inzee), zw(1, 1, 3 - inzee), &
1282 130990 : trig2, after2(i), now2(i), before2(i), 1)
1283 170769 : inzee = 3 - inzee
1284 : END DO
1285 :
1286 52323 : CALL realcopy(lot, nfft, n2, nk1, nk2, zw(1, 1, inzee), zr(j, 1, j3))
1287 :
1288 : END DO
1289 : !output: i1,i2,j3,(jp3)
1290 : END IF
1291 : END DO
1292 :
1293 : !De-allocations
1294 456 : DEALLOCATE (trig1)
1295 456 : DEALLOCATE (after1)
1296 456 : DEALLOCATE (now1)
1297 456 : DEALLOCATE (before1)
1298 456 : DEALLOCATE (trig2)
1299 456 : DEALLOCATE (after2)
1300 456 : DEALLOCATE (now2)
1301 456 : DEALLOCATE (before2)
1302 456 : DEALLOCATE (trig3)
1303 456 : DEALLOCATE (after3)
1304 456 : DEALLOCATE (now3)
1305 456 : DEALLOCATE (before3)
1306 456 : DEALLOCATE (zmpi2)
1307 456 : DEALLOCATE (zw)
1308 456 : DEALLOCATE (zt)
1309 456 : DEALLOCATE (cosinarr)
1310 456 : IF (nproc .GT. 1) DEALLOCATE (zmpi1)
1311 :
1312 456 : END SUBROUTINE kernelfft
1313 :
1314 : ! **************************************************************************************************
1315 : !> \brief ...
1316 : !> \param lot ...
1317 : !> \param nfft ...
1318 : !> \param n2 ...
1319 : !> \param nk1 ...
1320 : !> \param nk2 ...
1321 : !> \param zin ...
1322 : !> \param zout ...
1323 : ! **************************************************************************************************
1324 39779 : SUBROUTINE realcopy(lot, nfft, n2, nk1, nk2, zin, zout)
1325 : INTEGER, INTENT(in) :: lot, nfft, n2, nk1, nk2
1326 : REAL(KIND=dp), DIMENSION(2, lot, n2), INTENT(in) :: zin
1327 : REAL(KIND=dp), DIMENSION(nk1, nk2), INTENT(inout) :: zout
1328 :
1329 : INTEGER :: i, j
1330 :
1331 2490921 : DO i = 1, nk2
1332 34877728 : DO j = 1, nfft
1333 34837949 : zout(j, i) = zin(1, j, i)
1334 : END DO
1335 : END DO
1336 :
1337 39779 : END SUBROUTINE realcopy
1338 :
1339 : ! **************************************************************************************************
1340 : !> \brief ...
1341 : !> \param nfft ...
1342 : !> \param n2 ...
1343 : !> \param lot ...
1344 : !> \param n1 ...
1345 : !> \param lzt ...
1346 : !> \param zt ...
1347 : !> \param zw ...
1348 : ! **************************************************************************************************
1349 39779 : SUBROUTINE switch(nfft, n2, lot, n1, lzt, zt, zw)
1350 : INTEGER :: nfft, n2, lot, n1, lzt
1351 : REAL(KIND=dp) :: zt(2, lzt, n1), zw(2, lot, n2)
1352 :
1353 : INTEGER :: i, j
1354 :
1355 632152 : DO 200, j = 1, nfft
1356 64181241 : DO 100, i = 1, n2
1357 63588868 : zw(1, j, i) = zt(1, i, j)
1358 63588868 : zw(2, j, i) = zt(2, i, j)
1359 592373 : 100 CONTINUE
1360 39779 : 200 CONTINUE
1361 39779 : RETURN
1362 : END SUBROUTINE switch
1363 :
1364 : ! **************************************************************************************************
1365 : !> \brief ...
1366 : !> \param j3 ...
1367 : !> \param nfft ...
1368 : !> \param Jp2st ...
1369 : !> \param J2st ...
1370 : !> \param lot ...
1371 : !> \param n1 ...
1372 : !> \param nd2 ...
1373 : !> \param nd3 ...
1374 : !> \param nproc ...
1375 : !> \param zmpi1 ...
1376 : !> \param zw ...
1377 : ! **************************************************************************************************
1378 69000 : SUBROUTINE mpiswitch(j3, nfft, Jp2st, J2st, lot, n1, nd2, nd3, nproc, zmpi1, zw)
1379 : INTEGER :: j3, nfft, Jp2st, J2st, lot, n1, nd2, &
1380 : nd3, nproc
1381 : REAL(KIND=dp) :: zmpi1(2, n1, nd2/nproc, nd3/nproc, nproc), zw(2, lot, n1)
1382 :
1383 : INTEGER :: I1, J2, JP2, mfft
1384 :
1385 69000 : mfft = 0
1386 89224 : DO 300, Jp2 = Jp2st, nproc
1387 1236338 : DO 200, J2 = J2st, nd2/nproc
1388 1216114 : mfft = mfft + 1
1389 1216114 : IF (mfft .GT. nfft) THEN
1390 56456 : Jp2st = Jp2
1391 56456 : J2st = J2
1392 56456 : RETURN
1393 : END IF
1394 126018078 : DO 100, I1 = 1, n1
1395 124858420 : zw(1, mfft, I1) = zmpi1(1, I1, J2, j3, Jp2)
1396 124858420 : zw(2, mfft, I1) = zmpi1(2, I1, J2, j3, Jp2)
1397 1159658 : 100 CONTINUE
1398 20224 : 200 CONTINUE
1399 20224 : J2st = 1
1400 12544 : 300 CONTINUE
1401 : END SUBROUTINE mpiswitch
1402 :
1403 : ! **************************************************************************************************
1404 : !> \brief ...
1405 : !> \param p ...
1406 : !> \param w ...
1407 : !> \param urange ...
1408 : !> \param drange ...
1409 : !> \param acc ...
1410 : ! **************************************************************************************************
1411 456 : SUBROUTINE gequad(p, w, urange, drange, acc)
1412 : !
1413 : REAL(KIND=dp) :: p(*), w(*), urange, drange, acc
1414 :
1415 : !
1416 : !
1417 : ! range [10^(-9),1] and accuracy ~10^(-8);
1418 : !
1419 : !
1420 :
1421 456 : p(1) = 4.96142640560223544e19_dp
1422 456 : p(2) = 1.37454269147978052e19_dp
1423 456 : p(3) = 7.58610013441204679e18_dp
1424 456 : p(4) = 4.42040691347806996e18_dp
1425 456 : p(5) = 2.61986077948367892e18_dp
1426 456 : p(6) = 1.56320138155496681e18_dp
1427 456 : p(7) = 9.35645215863028402e17_dp
1428 456 : p(8) = 5.60962910452691703e17_dp
1429 456 : p(9) = 3.3666225119686761e17_dp
1430 456 : p(10) = 2.0218253197947866e17_dp
1431 456 : p(11) = 1.21477756091902017e17_dp
1432 456 : p(12) = 7.3012982513608503e16_dp
1433 456 : p(13) = 4.38951893556421099e16_dp
1434 456 : p(14) = 2.63949482512262325e16_dp
1435 456 : p(15) = 1.58742054072786174e16_dp
1436 456 : p(16) = 9.54806587737665531e15_dp
1437 456 : p(17) = 5.74353712364571709e15_dp
1438 456 : p(18) = 3.455214877389445e15_dp
1439 456 : p(19) = 2.07871658520326804e15_dp
1440 456 : p(20) = 1.25064667315629928e15_dp
1441 456 : p(21) = 7.52469429541933745e14_dp
1442 456 : p(22) = 4.5274603337253175e14_dp
1443 456 : p(23) = 2.72414006900059548e14_dp
1444 456 : p(24) = 1.63912168349216752e14_dp
1445 456 : p(25) = 9.86275802590865738e13_dp
1446 456 : p(26) = 5.93457701624974985e13_dp
1447 456 : p(27) = 3.5709554322296296e13_dp
1448 456 : p(28) = 2.14872890367310454e13_dp
1449 456 : p(29) = 1.29294719957726902e13_dp
1450 456 : p(30) = 7.78003375426361016e12_dp
1451 456 : p(31) = 4.68148199759876704e12_dp
1452 456 : p(32) = 2.8169955024829868e12_dp
1453 456 : p(33) = 1.69507790481958464e12_dp
1454 456 : p(34) = 1.01998486064607581e12_dp
1455 456 : p(35) = 6.13759486539856459e11_dp
1456 456 : p(36) = 3.69320183828682544e11_dp
1457 456 : p(37) = 2.22232783898905102e11_dp
1458 456 : p(38) = 1.33725247623668682e11_dp
1459 456 : p(39) = 8.0467192739036288e10_dp
1460 456 : p(40) = 4.84199582415144143e10_dp
1461 456 : p(41) = 2.91360091170559564e10_dp
1462 456 : p(42) = 1.75321747475309216e10_dp
1463 456 : p(43) = 1.0549735552210995e10_dp
1464 456 : p(44) = 6.34815321079006586e9_dp
1465 456 : p(45) = 3.81991113733594231e9_dp
1466 456 : p(46) = 2.29857747533101109e9_dp
1467 456 : p(47) = 1.38313653595483694e9_dp
1468 456 : p(48) = 8.32282908580025358e8_dp
1469 456 : p(49) = 5.00814519374587467e8_dp
1470 456 : p(50) = 3.01358090773319025e8_dp
1471 456 : p(51) = 1.81337994217503535e8_dp
1472 456 : p(52) = 1.09117589961086823e8_dp
1473 456 : p(53) = 6.56599771718640323e7_dp
1474 456 : p(54) = 3.95099693638497164e7_dp
1475 456 : p(55) = 2.37745694710665991e7_dp
1476 456 : p(56) = 1.43060135285912813e7_dp
1477 456 : p(57) = 8.60844290313506695e6_dp
1478 456 : p(58) = 5.18000974075383424e6_dp
1479 456 : p(59) = 3.116998193057466e6_dp
1480 456 : p(60) = 1.87560993870024029e6_dp
1481 456 : p(61) = 1.12862197183979562e6_dp
1482 456 : p(62) = 679132.441326077231_dp
1483 456 : p(63) = 408658.421279877969_dp
1484 456 : p(64) = 245904.473450669789_dp
1485 456 : p(65) = 147969.568088321005_dp
1486 456 : p(66) = 89038.612357311147_dp
1487 456 : p(67) = 53577.7362552358895_dp
1488 456 : p(68) = 32239.6513926914668_dp
1489 456 : p(69) = 19399.7580852362791_dp
1490 456 : p(70) = 11673.5323603058634_dp
1491 456 : p(71) = 7024.38438577707758_dp
1492 456 : p(72) = 4226.82479307685999_dp
1493 456 : p(73) = 2543.43254175354295_dp
1494 456 : p(74) = 1530.47486269122675_dp
1495 456 : p(75) = 920.941785160749482_dp
1496 456 : p(76) = 554.163803906291646_dp
1497 456 : p(77) = 333.46029740785694_dp
1498 456 : p(78) = 200.6550575335041_dp
1499 456 : p(79) = 120.741366914147284_dp
1500 456 : p(80) = 72.6544243200329916_dp
1501 456 : p(81) = 43.7187810415471025_dp
1502 456 : p(82) = 26.3071631447061043_dp
1503 456 : p(83) = 15.8299486353816329_dp
1504 456 : p(84) = 9.52493152341244004_dp
1505 456 : p(85) = 5.72200417067776041_dp
1506 456 : p(86) = 3.36242234070940928_dp
1507 456 : p(87) = 1.75371394604499472_dp
1508 456 : p(88) = 0.64705932650658966_dp
1509 456 : p(89) = 0.072765905943708247_dp
1510 : !
1511 456 : w(1) = 47.67445484528304247e10_dp
1512 456 : w(2) = 11.37485774750442175e9_dp
1513 456 : w(3) = 78.64340976880190239e8_dp
1514 456 : w(4) = 46.27335788759590498e8_dp
1515 456 : w(5) = 24.7380464827152951e8_dp
1516 456 : w(6) = 13.62904116438987719e8_dp
1517 456 : w(7) = 92.79560029045882433e8_dp
1518 456 : w(8) = 52.15931216254660251e8_dp
1519 456 : w(9) = 31.67018011061666244e8_dp
1520 456 : w(10) = 1.29291036801493046e8_dp
1521 456 : w(11) = 1.00139319988015862e8_dp
1522 456 : w(12) = 7.75892350510188341e7_dp
1523 456 : w(13) = 6.01333567950731271e7_dp
1524 456 : w(14) = 4.66141178654796875e7_dp
1525 456 : w(15) = 3.61398903394911448e7_dp
1526 456 : w(16) = 2.80225846672956389e7_dp
1527 456 : w(17) = 2.1730509180930247e7_dp
1528 456 : w(18) = 1.68524482625876965e7_dp
1529 456 : w(19) = 1.30701489345870338e7_dp
1530 456 : w(20) = 1.01371784832269282e7_dp
1531 456 : w(21) = 7.86264116300379329e6_dp
1532 456 : w(22) = 6.09861667912273717e6_dp
1533 456 : w(23) = 4.73045784039455683e6_dp
1534 456 : w(24) = 3.66928949951594161e6_dp
1535 456 : w(25) = 2.8462050836230259e6_dp
1536 456 : w(26) = 2.20777394798527011e6_dp
1537 456 : w(27) = 1.71256191589205524e6_dp
1538 456 : w(28) = 1.32843556197737076e6_dp
1539 456 : w(29) = 1.0304731275955989e6_dp
1540 456 : w(30) = 799345.206572271448_dp
1541 456 : w(31) = 620059.354143595343_dp
1542 456 : w(32) = 480986.704107449333_dp
1543 456 : w(33) = 373107.167700228515_dp
1544 456 : w(34) = 289424.08337412132_dp
1545 456 : w(35) = 224510.248231581788_dp
1546 456 : w(36) = 174155.825690028966_dp
1547 456 : w(37) = 135095.256919654065_dp
1548 456 : w(38) = 104795.442776800312_dp
1549 456 : w(39) = 81291.4458222430418_dp
1550 456 : w(40) = 63059.0493649328682_dp
1551 456 : w(41) = 48915.9040455329689_dp
1552 456 : w(42) = 37944.8484018048756_dp
1553 456 : w(43) = 29434.4290473253969_dp
1554 456 : w(44) = 22832.7622054490044_dp
1555 456 : w(45) = 17711.743950151233_dp
1556 456 : w(46) = 13739.287867104177_dp
1557 456 : w(47) = 10657.7895710752585_dp
1558 456 : w(48) = 8267.42141053961834_dp
1559 456 : w(49) = 6413.17397520136448_dp
1560 456 : w(50) = 4974.80402838654277_dp
1561 456 : w(51) = 3859.03698188553047_dp
1562 456 : w(52) = 2993.51824493299154_dp
1563 456 : w(53) = 2322.1211966811754_dp
1564 456 : w(54) = 1801.30750964719641_dp
1565 456 : w(55) = 1397.30379659817038_dp
1566 456 : w(56) = 1083.91149143250697_dp
1567 456 : w(57) = 840.807939169209188_dp
1568 456 : w(58) = 652.228524366749422_dp
1569 456 : w(59) = 505.944376983506128_dp
1570 456 : w(60) = 392.469362317941064_dp
1571 456 : w(61) = 304.444930257324312_dp
1572 456 : w(62) = 236.162932842453601_dp
1573 456 : w(63) = 183.195466078603525_dp
1574 456 : w(64) = 142.107732186551471_dp
1575 456 : w(65) = 110.23530215723992_dp
1576 456 : w(66) = 85.5113346705382257_dp
1577 456 : w(67) = 66.3325469806696621_dp
1578 456 : w(68) = 51.4552463353841373_dp
1579 456 : w(69) = 39.9146798429449273_dp
1580 456 : w(70) = 30.9624728409162095_dp
1581 456 : w(71) = 24.018098812215013_dp
1582 456 : w(72) = 18.6312338024296588_dp
1583 456 : w(73) = 14.4525541233150501_dp
1584 456 : w(74) = 11.2110836519105938_dp
1585 456 : w(75) = 8.69662175848497178_dp
1586 456 : w(76) = 6.74611236165731961_dp
1587 456 : w(77) = 5.23307018057529994_dp
1588 456 : w(78) = 4.05937850501539556_dp
1589 456 : w(79) = 3.14892659076635714_dp
1590 456 : w(80) = 2.44267408211071604_dp
1591 456 : w(81) = 1.89482240522855261_dp
1592 456 : w(82) = 1.46984505907050079_dp
1593 456 : w(83) = 1.14019261330527007_dp
1594 456 : w(84) = 0.884791217422925293_dp
1595 456 : w(85) = 0.692686387080616483_dp
1596 456 : w(86) = 0.585244576897023282_dp
1597 456 : w(87) = 0.576182522545327589_dp
1598 456 : w(88) = 0.596688817388997178_dp
1599 456 : w(89) = 0.607879901151108771_dp
1600 : !
1601 : !
1602 456 : urange = 1._dp
1603 456 : drange = 1e-08_dp
1604 456 : acc = 1e-08_dp
1605 : !
1606 456 : RETURN
1607 : END SUBROUTINE gequad
1608 :
1609 : END MODULE ps_wavelet_kernel
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