1 |
module shapes |
2 |
|
3 |
use force_globals |
4 |
use definitions |
5 |
use atype_module |
6 |
use vector_class |
7 |
use simulation |
8 |
use status |
9 |
#ifdef IS_MPI |
10 |
use mpiSimulation |
11 |
#endif |
12 |
implicit none |
13 |
|
14 |
PRIVATE |
15 |
|
16 |
INTEGER, PARAMETER:: CHEBYSHEV_TN = 1 |
17 |
INTEGER, PARAMETER:: CHEBYSHEV_UN = 2 |
18 |
INTEGER, PARAMETER:: LAGUERRE = 3 |
19 |
INTEGER, PARAMETER:: HERMITE = 4 |
20 |
INTEGER, PARAMETER:: SH_COS = 0 |
21 |
INTEGER, PARAMETER:: SH_SIN = 1 |
22 |
|
23 |
logical, save :: haveShapeMap = .false. |
24 |
|
25 |
public :: do_shape_pair |
26 |
|
27 |
|
28 |
type, private :: Shape |
29 |
integer :: atid |
30 |
integer :: nContactFuncs |
31 |
integer :: nRangeFuncs |
32 |
integer :: nStrengthFuncs |
33 |
integer :: bigL |
34 |
integer :: bigM |
35 |
integer, pointer, dimension(:) :: ContactFuncLValue => null() |
36 |
integer, pointer, dimension(:) :: ContactFuncMValue => null() |
37 |
integer, pointer, dimension(:) :: ContactFunctionType => null() |
38 |
real(kind=dp), pointer, dimension(:) :: ContactFuncCoefficient => null() |
39 |
integer, pointer, dimension(:) :: RangeFuncLValue => null() |
40 |
integer, pointer, dimension(:) :: RangeFuncMValue => null() |
41 |
integer, pointer, dimension(:) :: RangeFunctionType => null() |
42 |
real(kind=dp), pointer, dimension(:) :: RangeFuncCoefficient => null() |
43 |
integer, pointer, dimension(:) :: StrengthFuncLValue => null() |
44 |
integer, pointer, dimension(:) :: StrengthFuncMValue => null() |
45 |
integer, pointer, dimension(:) :: StrengthFunctionType => null() |
46 |
real(kind=dp), pointer, dimension(:) :: StrengthFuncCoefficient => null() |
47 |
logical :: isLJ |
48 |
real ( kind = dp ) :: epsilon |
49 |
real ( kind = dp ) :: sigma |
50 |
end type Shape |
51 |
|
52 |
type, private :: ShapeList |
53 |
integer :: n_shapes = 0 |
54 |
integer :: currentShape = 0 |
55 |
type (Shape), pointer :: Shapes(:) => null() |
56 |
integer, pointer :: atidToShape(:) => null() |
57 |
end type ShapeList |
58 |
|
59 |
type(ShapeList), save :: ShapeMap |
60 |
|
61 |
integer :: lmax |
62 |
real (kind=dp), allocatable, dimension(:,:) :: plm_i, dlm_i, plm_j, dlm_j |
63 |
real (kind=dp), allocatable, dimension(:) :: tm_i, dtm_i, um_i, dum_i |
64 |
real (kind=dp), allocatable, dimension(:) :: tm_j, dtm_j, um_j, dum_j |
65 |
|
66 |
contains |
67 |
|
68 |
subroutine newShapeType(nContactFuncs, ContactFuncLValue, & |
69 |
ContactFuncMValue, ContactFunctionType, ContactFuncCoefficient, & |
70 |
nRangeFuncs, RangeFuncLValue, RangeFuncMValue, RangeFunctionType, & |
71 |
RangeFuncCoefficient, nStrengthFuncs, StrengthFuncLValue, & |
72 |
StrengthFuncMValue, StrengthFunctionType, StrengthFuncCoefficient, & |
73 |
myAtid, status) |
74 |
|
75 |
integer :: nContactFuncs |
76 |
integer :: nRangeFuncs |
77 |
integer :: nStrengthFuncs |
78 |
integer :: shape_ident |
79 |
integer :: status |
80 |
integer :: myAtid |
81 |
integer :: bigL |
82 |
integer :: bigM |
83 |
integer :: j, me, nShapeTypes, nLJTypes, ntypes, current, alloc_stat |
84 |
integer, pointer :: MatchList(:) => null() |
85 |
|
86 |
integer, dimension(nContactFuncs) :: ContactFuncLValue |
87 |
integer, dimension(nContactFuncs) :: ContactFuncMValue |
88 |
integer, dimension(nContactFuncs) :: ContactFunctionType |
89 |
real(kind=dp), dimension(nContactFuncs) :: ContactFuncCoefficient |
90 |
integer, dimension(nRangeFuncs) :: RangeFuncLValue |
91 |
integer, dimension(nRangeFuncs) :: RangeFuncMValue |
92 |
integer, dimension(nRangeFuncs) :: RangeFunctionType |
93 |
real(kind=dp), dimension(nRangeFuncs) :: RangeFuncCoefficient |
94 |
integer, dimension(nStrengthFuncs) :: StrengthFuncLValue |
95 |
integer, dimension(nStrengthFuncs) :: StrengthFuncMValue |
96 |
integer, dimension(nStrengthFuncs) :: StrengthFunctionType |
97 |
real(kind=dp), dimension(nStrengthFuncs) :: StrengthFuncCoefficient |
98 |
|
99 |
status = 0 |
100 |
! check to see if this is the first time into this routine... |
101 |
if (.not.associated(ShapeMap%Shapes)) then |
102 |
|
103 |
call getMatchingElementList(atypes, "is_Shape", .true., & |
104 |
nShapeTypes, MatchList) |
105 |
|
106 |
call getMatchingElementList(atypes, "is_LJ", .true., & |
107 |
nLJTypes, MatchList) |
108 |
|
109 |
ShapeMap%n_shapes = nShapeTypes + nLJTypes |
110 |
|
111 |
allocate(ShapeMap%Shapes(nShapeTypes + nLJTypes)) |
112 |
|
113 |
ntypes = getSize(atypes) |
114 |
|
115 |
allocate(ShapeMap%atidToShape(ntypes)) |
116 |
end if |
117 |
|
118 |
ShapeMap%currentShape = ShapeMap%currentShape + 1 |
119 |
current = ShapeMap%currentShape |
120 |
|
121 |
call allocateShape(nContactFuncs, nRangeFuncs, nStrengthFuncs, & |
122 |
ShapeMap%Shapes(current), stat=alloc_stat) |
123 |
if (alloc_stat .ne. 0) then |
124 |
status = -1 |
125 |
return |
126 |
endif |
127 |
|
128 |
call getElementProperty(atypes, myAtid, "c_ident", me) |
129 |
ShapeMap%atidToShape(me) = current |
130 |
ShapeMap%Shapes(current)%atid = me |
131 |
ShapeMap%Shapes(current)%nContactFuncs = nContactFuncs |
132 |
ShapeMap%Shapes(current)%nRangeFuncs = nRangeFuncs |
133 |
ShapeMap%Shapes(current)%nStrengthFuncs = nStrengthFuncs |
134 |
ShapeMap%Shapes(current)%ContactFuncLValue = ContactFuncLValue |
135 |
ShapeMap%Shapes(current)%ContactFuncMValue = ContactFuncMValue |
136 |
ShapeMap%Shapes(current)%ContactFunctionType = ContactFunctionType |
137 |
ShapeMap%Shapes(current)%ContactFuncCoefficient = ContactFuncCoefficient |
138 |
ShapeMap%Shapes(current)%RangeFuncLValue = RangeFuncLValue |
139 |
ShapeMap%Shapes(current)%RangeFuncMValue = RangeFuncMValue |
140 |
ShapeMap%Shapes(current)%RangeFunctionType = RangeFunctionType |
141 |
ShapeMap%Shapes(current)%RangeFuncCoefficient = RangeFuncCoefficient |
142 |
ShapeMap%Shapes(current)%StrengthFuncLValue = StrengthFuncLValue |
143 |
ShapeMap%Shapes(current)%StrengthFuncMValue = StrengthFuncMValue |
144 |
ShapeMap%Shapes(current)%StrengthFunctionType = StrengthFunctionType |
145 |
ShapeMap%Shapes(current)%StrengthFuncCoefficient = StrengthFuncCoefficient |
146 |
|
147 |
bigL = -1 |
148 |
bigM = -1 |
149 |
|
150 |
do j = 1, ShapeMap%Shapes(current)%nContactFuncs |
151 |
if (ShapeMap%Shapes(current)%ContactFuncLValue(j) .gt. bigL) then |
152 |
bigL = ShapeMap%Shapes(current)%ContactFuncLValue(j) |
153 |
endif |
154 |
if (ShapeMap%Shapes(current)%ContactFuncMValue(j) .gt. bigM) then |
155 |
bigM = ShapeMap%Shapes(current)%ContactFuncMValue(j) |
156 |
endif |
157 |
enddo |
158 |
do j = 1, ShapeMap%Shapes(current)%nRangeFuncs |
159 |
if (ShapeMap%Shapes(current)%RangeFuncLValue(j) .gt. bigL) then |
160 |
bigL = ShapeMap%Shapes(current)%RangeFuncLValue(j) |
161 |
endif |
162 |
if (ShapeMap%Shapes(current)%RangeFuncMValue(j) .gt. bigM) then |
163 |
bigM = ShapeMap%Shapes(current)%RangeFuncMValue(j) |
164 |
endif |
165 |
enddo |
166 |
do j = 1, ShapeMap%Shapes(current)%nStrengthFuncs |
167 |
if (ShapeMap%Shapes(current)%StrengthFuncLValue(j) .gt. bigL) then |
168 |
bigL = ShapeMap%Shapes(current)%StrengthFuncLValue(j) |
169 |
endif |
170 |
if (ShapeMap%Shapes(current)%StrengthFuncMValue(j) .gt. bigM) then |
171 |
bigM = ShapeMap%Shapes(current)%StrengthFuncMValue(j) |
172 |
endif |
173 |
enddo |
174 |
|
175 |
ShapeMap%Shapes(current)%bigL = bigL |
176 |
ShapeMap%Shapes(current)%bigM = bigM |
177 |
|
178 |
end subroutine newShapeType |
179 |
|
180 |
subroutine allocateShape(nContactFuncs, nRangeFuncs, nStrengthFuncs, & |
181 |
myShape, stat) |
182 |
|
183 |
integer, intent(in) :: nContactFuncs, nRangeFuncs, nStrengthFuncs |
184 |
type(Shape), intent(inout) :: myShape |
185 |
integer, intent(out) :: stat |
186 |
integer :: alloc_stat |
187 |
|
188 |
if (associated(myShape%contactFuncLValue)) then |
189 |
deallocate(myShape%contactFuncLValue) |
190 |
endif |
191 |
allocate(myShape%contactFuncLValue(nContactFuncs), stat = alloc_stat) |
192 |
if (alloc_stat .ne. 0) then |
193 |
stat = -1 |
194 |
return |
195 |
endif |
196 |
if (associated(myShape%contactFuncMValue)) then |
197 |
deallocate(myShape%contactFuncMValue) |
198 |
endif |
199 |
allocate(myShape%contactFuncMValue(nContactFuncs), stat = alloc_stat) |
200 |
if (alloc_stat .ne. 0) then |
201 |
stat = -1 |
202 |
return |
203 |
endif |
204 |
if (associated(myShape%contactFunctionType)) then |
205 |
deallocate(myShape%contactFunctionType) |
206 |
endif |
207 |
allocate(myShape%contactFunctionType(nContactFuncs), stat = alloc_stat) |
208 |
if (alloc_stat .ne. 0) then |
209 |
stat = -1 |
210 |
return |
211 |
endif |
212 |
if (associated(myShape%contactFuncCoefficient)) then |
213 |
deallocate(myShape%contactFuncCoefficient) |
214 |
endif |
215 |
allocate(myShape%contactFuncCoefficient(nContactFuncs), stat = alloc_stat) |
216 |
if (alloc_stat .ne. 0) then |
217 |
stat = -1 |
218 |
return |
219 |
endif |
220 |
|
221 |
if (associated(myShape%rangeFuncLValue)) then |
222 |
deallocate(myShape%rangeFuncLValue) |
223 |
endif |
224 |
allocate(myShape%rangeFuncLValue(nRangeFuncs), stat = alloc_stat) |
225 |
if (alloc_stat .ne. 0) then |
226 |
stat = -1 |
227 |
return |
228 |
endif |
229 |
if (associated(myShape%rangeFuncMValue)) then |
230 |
deallocate(myShape%rangeFuncMValue) |
231 |
endif |
232 |
allocate(myShape%rangeFuncMValue(nRangeFuncs), stat = alloc_stat) |
233 |
if (alloc_stat .ne. 0) then |
234 |
stat = -1 |
235 |
return |
236 |
endif |
237 |
if (associated(myShape%rangeFunctionType)) then |
238 |
deallocate(myShape%rangeFunctionType) |
239 |
endif |
240 |
allocate(myShape%rangeFunctionType(nRangeFuncs), stat = alloc_stat) |
241 |
if (alloc_stat .ne. 0) then |
242 |
stat = -1 |
243 |
return |
244 |
endif |
245 |
if (associated(myShape%rangeFuncCoefficient)) then |
246 |
deallocate(myShape%rangeFuncCoefficient) |
247 |
endif |
248 |
allocate(myShape%rangeFuncCoefficient(nRangeFuncs), stat = alloc_stat) |
249 |
if (alloc_stat .ne. 0) then |
250 |
stat = -1 |
251 |
return |
252 |
endif |
253 |
|
254 |
if (associated(myShape%strengthFuncLValue)) then |
255 |
deallocate(myShape%strengthFuncLValue) |
256 |
endif |
257 |
allocate(myShape%strengthFuncLValue(nStrengthFuncs), stat = alloc_stat) |
258 |
if (alloc_stat .ne. 0) then |
259 |
stat = -1 |
260 |
return |
261 |
endif |
262 |
if (associated(myShape%strengthFuncMValue)) then |
263 |
deallocate(myShape%strengthFuncMValue) |
264 |
endif |
265 |
allocate(myShape%strengthFuncMValue(nStrengthFuncs), stat = alloc_stat) |
266 |
if (alloc_stat .ne. 0) then |
267 |
stat = -1 |
268 |
return |
269 |
endif |
270 |
if (associated(myShape%strengthFunctionType)) then |
271 |
deallocate(myShape%strengthFunctionType) |
272 |
endif |
273 |
allocate(myShape%strengthFunctionType(nStrengthFuncs), stat = alloc_stat) |
274 |
if (alloc_stat .ne. 0) then |
275 |
stat = -1 |
276 |
return |
277 |
endif |
278 |
if (associated(myShape%strengthFuncCoefficient)) then |
279 |
deallocate(myShape%strengthFuncCoefficient) |
280 |
endif |
281 |
allocate(myShape%strengthFuncCoefficient(nStrengthFuncs), stat=alloc_stat) |
282 |
if (alloc_stat .ne. 0) then |
283 |
stat = -1 |
284 |
return |
285 |
endif |
286 |
|
287 |
end subroutine allocateShape |
288 |
|
289 |
subroutine init_Shape_FF(status) |
290 |
integer :: status |
291 |
integer :: i, j, l, m, lm, function_type |
292 |
real(kind=dp) :: bigSigma, myBigSigma, thisSigma, coeff, Phunc, spi |
293 |
real(kind=dp) :: costheta, cpi, theta, Pi, phi, thisDP |
294 |
integer :: alloc_stat, iTheta, iPhi, nSteps, nAtypes, thisIP, current |
295 |
logical :: thisProperty |
296 |
|
297 |
Pi = 4.0d0 * datan(1.0d0) |
298 |
|
299 |
status = 0 |
300 |
if (ShapeMap%currentShape == 0) then |
301 |
call handleError("init_Shape_FF", "No members in ShapeMap") |
302 |
status = -1 |
303 |
return |
304 |
end if |
305 |
|
306 |
bigSigma = 0.0d0 |
307 |
do i = 1, ShapeMap%currentShape |
308 |
|
309 |
! Scan over theta and phi to |
310 |
! find the largest contact in any direction.... |
311 |
|
312 |
myBigSigma = 0.0d0 |
313 |
|
314 |
do iTheta = 0, nSteps |
315 |
theta = (Pi/2.0d0)*(dble(iTheta)/dble(nSteps)) |
316 |
costheta = cos(theta) |
317 |
|
318 |
call Associated_Legendre(costheta, ShapeMap%Shapes(i)%bigL, & |
319 |
ShapeMap%Shapes(i)%bigM, lmax, plm_i, dlm_i) |
320 |
|
321 |
do iPhi = 0, nSteps |
322 |
phi = -Pi + 2.0d0 * Pi * (dble(iPhi)/dble(nSteps)) |
323 |
cpi = cos(phi) |
324 |
spi = sin(phi) |
325 |
|
326 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(i)%bigM, & |
327 |
CHEBYSHEV_TN, tm_i, dtm_i) |
328 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(i)%bigM, & |
329 |
CHEBYSHEV_UN, um_i, dum_i) |
330 |
|
331 |
thisSigma = 0.0d0 |
332 |
|
333 |
do lm = 1, ShapeMap%Shapes(i)%nContactFuncs |
334 |
|
335 |
l = ShapeMap%Shapes(i)%ContactFuncLValue(lm) |
336 |
m = ShapeMap%Shapes(i)%ContactFuncMValue(lm) |
337 |
coeff = ShapeMap%Shapes(i)%ContactFuncCoefficient(lm) |
338 |
function_type = ShapeMap%Shapes(i)%ContactFunctionType(lm) |
339 |
|
340 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
341 |
Phunc = coeff * tm_i(m) |
342 |
else |
343 |
Phunc = coeff * spi * um_i(m-1) |
344 |
endif |
345 |
|
346 |
thisSigma = thisSigma + plm_i(l,m)*Phunc |
347 |
enddo |
348 |
|
349 |
if (thisSigma.gt.myBigSigma) myBigSigma = thisSigma |
350 |
enddo |
351 |
enddo |
352 |
|
353 |
if (myBigSigma.gt.bigSigma) bigSigma = myBigSigma |
354 |
enddo |
355 |
|
356 |
nAtypes = getSize(atypes) |
357 |
|
358 |
if (nAtypes == 0) then |
359 |
status = -1 |
360 |
return |
361 |
end if |
362 |
|
363 |
do i = 1, nAtypes |
364 |
|
365 |
call getElementProperty(atypes, i, "is_LJ", thisProperty) |
366 |
|
367 |
if (thisProperty) then |
368 |
|
369 |
ShapeMap%currentShape = ShapeMap%currentShape + 1 |
370 |
current = ShapeMap%currentShape |
371 |
|
372 |
call getElementProperty(atypes, i, "c_ident", thisIP) |
373 |
ShapeMap%atidToShape(thisIP) = current |
374 |
ShapeMap%Shapes(current)%atid = thisIP |
375 |
|
376 |
ShapeMap%Shapes(current)%isLJ = .true. |
377 |
|
378 |
call getElementProperty(atypes, i, "lj_epsilon", thisDP) |
379 |
ShapeMap%Shapes(current)%epsilon = thisDP |
380 |
|
381 |
call getElementProperty(atypes, i, "lj_sigma", thisDP) |
382 |
ShapeMap%Shapes(current)%sigma = thisDP |
383 |
if (thisDP .gt. bigSigma) bigSigma = thisDP |
384 |
|
385 |
endif |
386 |
|
387 |
end do |
388 |
|
389 |
haveShapeMap = .true. |
390 |
|
391 |
end subroutine init_Shape_FF |
392 |
|
393 |
subroutine do_shape_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
394 |
pot, A, f, t, do_pot) |
395 |
|
396 |
integer, intent(in) :: atom1, atom2 |
397 |
real (kind=dp), intent(inout) :: rij, r2 |
398 |
real (kind=dp), dimension(3), intent(in) :: d |
399 |
real (kind=dp), dimension(3), intent(inout) :: fpair |
400 |
real (kind=dp) :: pot, vpair, sw |
401 |
real (kind=dp), dimension(9,nLocal) :: A |
402 |
real (kind=dp), dimension(3,nLocal) :: f |
403 |
real (kind=dp), dimension(3,nLocal) :: t |
404 |
logical, intent(in) :: do_pot |
405 |
|
406 |
real (kind=dp) :: r3, r5, rt2, rt3, rt5, rt6, rt11, rt12, rt126 |
407 |
integer :: atid1, atid2, st1, st2 |
408 |
integer :: l, m, lm, id1, id2, localError, function_type |
409 |
real (kind=dp) :: sigma_i, s_i, eps_i, sigma_j, s_j, eps_j |
410 |
real (kind=dp) :: coeff |
411 |
|
412 |
real (kind=dp) :: dsigmaidx, dsigmaidy, dsigmaidz |
413 |
real (kind=dp) :: dsigmaidux, dsigmaiduy, dsigmaiduz |
414 |
real (kind=dp) :: dsigmajdx, dsigmajdy, dsigmajdz |
415 |
real (kind=dp) :: dsigmajdux, dsigmajduy, dsigmajduz |
416 |
|
417 |
real (kind=dp) :: dsidx, dsidy, dsidz |
418 |
real (kind=dp) :: dsidux, dsiduy, dsiduz |
419 |
real (kind=dp) :: dsjdx, dsjdy, dsjdz |
420 |
real (kind=dp) :: dsjdux, dsjduy, dsjduz |
421 |
|
422 |
real (kind=dp) :: depsidx, depsidy, depsidz |
423 |
real (kind=dp) :: depsidux, depsiduy, depsiduz |
424 |
real (kind=dp) :: depsjdx, depsjdy, depsjdz |
425 |
real (kind=dp) :: depsjdux, depsjduy, depsjduz |
426 |
|
427 |
real (kind=dp) :: xi, yi, zi, xj, yj, zj, xi2, yi2, zi2, xj2, yj2, zj2 |
428 |
|
429 |
real (kind=dp) :: proji, proji3, projj, projj3 |
430 |
real (kind=dp) :: cti, ctj, cpi, cpj, spi, spj |
431 |
real (kind=dp) :: Phunc, sigma, s, eps, rtdenom, rt |
432 |
|
433 |
real (kind=dp) :: dctidx, dctidy, dctidz |
434 |
real (kind=dp) :: dctidux, dctiduy, dctiduz |
435 |
real (kind=dp) :: dctjdx, dctjdy, dctjdz |
436 |
real (kind=dp) :: dctjdux, dctjduy, dctjduz |
437 |
|
438 |
real (kind=dp) :: dcpidx, dcpidy, dcpidz |
439 |
real (kind=dp) :: dcpidux, dcpiduy, dcpiduz |
440 |
real (kind=dp) :: dcpjdx, dcpjdy, dcpjdz |
441 |
real (kind=dp) :: dcpjdux, dcpjduy, dcpjduz |
442 |
|
443 |
real (kind=dp) :: dspidx, dspidy, dspidz |
444 |
real (kind=dp) :: dspidux, dspiduy, dspiduz |
445 |
real (kind=dp) :: dspjdx, dspjdy, dspjdz |
446 |
real (kind=dp) :: dspjdux, dspjduy, dspjduz |
447 |
|
448 |
real (kind=dp) :: dPhuncdX, dPhuncdY, dPhuncdZ |
449 |
real (kind=dp) :: dPhuncdUx, dPhuncdUy, dPhuncdUz |
450 |
|
451 |
real (kind=dp) :: dsigmadxi, dsigmadyi, dsigmadzi |
452 |
real (kind=dp) :: dsigmaduxi, dsigmaduyi, dsigmaduzi |
453 |
real (kind=dp) :: dsigmadxj, dsigmadyj, dsigmadzj |
454 |
real (kind=dp) :: dsigmaduxj, dsigmaduyj, dsigmaduzj |
455 |
|
456 |
real (kind=dp) :: dsdxi, dsdyi, dsdzi |
457 |
real (kind=dp) :: dsduxi, dsduyi, dsduzi |
458 |
real (kind=dp) :: dsdxj, dsdyj, dsdzj |
459 |
real (kind=dp) :: dsduxj, dsduyj, dsduzj |
460 |
|
461 |
real (kind=dp) :: depsdxi, depsdyi, depsdzi |
462 |
real (kind=dp) :: depsduxi, depsduyi, depsduzi |
463 |
real (kind=dp) :: depsdxj, depsdyj, depsdzj |
464 |
real (kind=dp) :: depsduxj, depsduyj, depsduzj |
465 |
|
466 |
real (kind=dp) :: drtdxi, drtdyi, drtdzi |
467 |
real (kind=dp) :: drtduxi, drtduyi, drtduzi |
468 |
real (kind=dp) :: drtdxj, drtdyj, drtdzj |
469 |
real (kind=dp) :: drtduxj, drtduyj, drtduzj |
470 |
|
471 |
real (kind=dp) :: drdxi, drdyi, drdzi |
472 |
real (kind=dp) :: drduxi, drduyi, drduzi |
473 |
real (kind=dp) :: drdxj, drdyj, drdzj |
474 |
real (kind=dp) :: drduxj, drduyj, drduzj |
475 |
|
476 |
real (kind=dp) :: dvdxi, dvdyi, dvdzi |
477 |
real (kind=dp) :: dvduxi, dvduyi, dvduzi |
478 |
real (kind=dp) :: dvdxj, dvdyj, dvdzj |
479 |
real (kind=dp) :: dvduxj, dvduyj, dvduzj |
480 |
|
481 |
real (kind=dp) :: fxi, fyi, fzi, fxj, fyj, fzj |
482 |
real (kind=dp) :: txi, tyi, tzi, txj, tyj, tzj |
483 |
real (kind=dp) :: fxii, fyii, fzii, fxij, fyij, fzij |
484 |
real (kind=dp) :: fxji, fyji, fzji, fxjj, fyjj, fzjj |
485 |
real (kind=dp) :: fxradial, fyradial, fzradial |
486 |
|
487 |
if (.not.haveShapeMap) then |
488 |
call handleError("calc_shape", "NO SHAPEMAP!!!!") |
489 |
return |
490 |
endif |
491 |
|
492 |
!! We assume that the rotation matrices have already been calculated |
493 |
!! and placed in the A array. |
494 |
|
495 |
r3 = r2*rij |
496 |
r5 = r3*r2 |
497 |
|
498 |
drdxi = -d(1) / rij |
499 |
drdyi = -d(2) / rij |
500 |
drdzi = -d(3) / rij |
501 |
|
502 |
drdxj = d(1) / rij |
503 |
drdyj = d(2) / rij |
504 |
drdzj = d(3) / rij |
505 |
|
506 |
! find the atom type id (atid) for each atom: |
507 |
#ifdef IS_MPI |
508 |
atid1 = atid_Row(atom1) |
509 |
atid2 = atid_Col(atom2) |
510 |
#else |
511 |
atid1 = atid(atom1) |
512 |
atid2 = atid(atom2) |
513 |
#endif |
514 |
|
515 |
! use the atid to find the shape type (st) for each atom: |
516 |
|
517 |
st1 = ShapeMap%atidToShape(atid1) |
518 |
st2 = ShapeMap%atidToShape(atid2) |
519 |
|
520 |
if (ShapeMap%Shapes(st1)%isLJ) then |
521 |
sigma_i = ShapeMap%Shapes(st1)%sigma |
522 |
s_i = ShapeMap%Shapes(st1)%sigma |
523 |
eps_i = ShapeMap%Shapes(st1)%epsilon |
524 |
dsigmaidx = 0.0d0 |
525 |
dsigmaidy = 0.0d0 |
526 |
dsigmaidz = 0.0d0 |
527 |
dsigmaidux = 0.0d0 |
528 |
dsigmaiduy = 0.0d0 |
529 |
dsigmaiduz = 0.0d0 |
530 |
dsidx = 0.0d0 |
531 |
dsidy = 0.0d0 |
532 |
dsidz = 0.0d0 |
533 |
dsidux = 0.0d0 |
534 |
dsiduy = 0.0d0 |
535 |
dsiduz = 0.0d0 |
536 |
depsidx = 0.0d0 |
537 |
depsidy = 0.0d0 |
538 |
depsidz = 0.0d0 |
539 |
depsidux = 0.0d0 |
540 |
depsiduy = 0.0d0 |
541 |
depsiduz = 0.0d0 |
542 |
else |
543 |
|
544 |
#ifdef IS_MPI |
545 |
! rotate the inter-particle separation into the two different |
546 |
! body-fixed coordinate systems: |
547 |
|
548 |
xi = A_row(1,atom1)*d(1) + A_row(2,atom1)*d(2) + A_row(3,atom1)*d(3) |
549 |
yi = A_row(4,atom1)*d(1) + A_row(5,atom1)*d(2) + A_row(6,atom1)*d(3) |
550 |
zi = A_row(7,atom1)*d(1) + A_row(8,atom1)*d(2) + A_row(9,atom1)*d(3) |
551 |
|
552 |
#else |
553 |
! rotate the inter-particle separation into the two different |
554 |
! body-fixed coordinate systems: |
555 |
|
556 |
xi = a(1,atom1)*d(1) + a(2,atom1)*d(2) + a(3,atom1)*d(3) |
557 |
yi = a(4,atom1)*d(1) + a(5,atom1)*d(2) + a(6,atom1)*d(3) |
558 |
zi = a(7,atom1)*d(1) + a(8,atom1)*d(2) + a(9,atom1)*d(3) |
559 |
|
560 |
#endif |
561 |
|
562 |
xi2 = xi*xi |
563 |
yi2 = yi*yi |
564 |
zi2 = zi*zi |
565 |
|
566 |
proji = sqrt(xi2 + yi2) |
567 |
proji3 = proji*proji*proji |
568 |
|
569 |
cti = zi / rij |
570 |
dctidx = - zi * xi / r3 |
571 |
dctidy = - zi * yi / r3 |
572 |
dctidz = 1.0d0 / rij - zi2 / r3 |
573 |
dctidux = yi / rij |
574 |
dctiduy = -xi / rij |
575 |
dctiduz = 0.0d0 |
576 |
|
577 |
cpi = xi / proji |
578 |
dcpidx = 1.0d0 / proji - xi2 / proji3 |
579 |
dcpidy = - xi * yi / proji3 |
580 |
dcpidz = 0.0d0 |
581 |
dcpidux = xi * yi * zi / proji3 |
582 |
dcpiduy = -zi * (1.0d0 / proji - xi2 / proji3) |
583 |
dcpiduz = -yi * (1.0d0 / proji - xi2 / proji3) - (xi2 * yi / proji3) |
584 |
|
585 |
spi = yi / proji |
586 |
dspidx = - xi * yi / proji3 |
587 |
dspidy = 1.0d0 / proji - yi2 / proji3 |
588 |
dspidz = 0.0d0 |
589 |
dspidux = -zi * (1.0d0 / proji - yi2 / proji3) |
590 |
dspiduy = xi * yi * zi / proji3 |
591 |
dspiduz = xi * (1.0d0 / proji - yi2 / proji3) + (xi * yi2 / proji3) |
592 |
|
593 |
call Associated_Legendre(cti, ShapeMap%Shapes(st1)%bigL, & |
594 |
ShapeMap%Shapes(st1)%bigM, lmax, plm_i, dlm_i) |
595 |
|
596 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(st1)%bigM, & |
597 |
CHEBYSHEV_TN, tm_i, dtm_i) |
598 |
call Orthogonal_Polynomial(cpi, ShapeMap%Shapes(st1)%bigM, & |
599 |
CHEBYSHEV_UN, um_i, dum_i) |
600 |
|
601 |
sigma_i = 0.0d0 |
602 |
s_i = 0.0d0 |
603 |
eps_i = 0.0d0 |
604 |
dsigmaidx = 0.0d0 |
605 |
dsigmaidy = 0.0d0 |
606 |
dsigmaidz = 0.0d0 |
607 |
dsigmaidux = 0.0d0 |
608 |
dsigmaiduy = 0.0d0 |
609 |
dsigmaiduz = 0.0d0 |
610 |
dsidx = 0.0d0 |
611 |
dsidy = 0.0d0 |
612 |
dsidz = 0.0d0 |
613 |
dsidux = 0.0d0 |
614 |
dsiduy = 0.0d0 |
615 |
dsiduz = 0.0d0 |
616 |
depsidx = 0.0d0 |
617 |
depsidy = 0.0d0 |
618 |
depsidz = 0.0d0 |
619 |
depsidux = 0.0d0 |
620 |
depsiduy = 0.0d0 |
621 |
depsiduz = 0.0d0 |
622 |
|
623 |
do lm = 1, ShapeMap%Shapes(st1)%nContactFuncs |
624 |
l = ShapeMap%Shapes(st1)%ContactFuncLValue(lm) |
625 |
m = ShapeMap%Shapes(st1)%ContactFuncMValue(lm) |
626 |
coeff = ShapeMap%Shapes(st1)%ContactFuncCoefficient(lm) |
627 |
function_type = ShapeMap%Shapes(st1)%ContactFunctionType(lm) |
628 |
|
629 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
630 |
Phunc = coeff * tm_i(m) |
631 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
632 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
633 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
634 |
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
635 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
636 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
637 |
else |
638 |
Phunc = coeff * spi * um_i(m-1) |
639 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
640 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
641 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
642 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
643 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
644 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
645 |
endif |
646 |
|
647 |
sigma_i = sigma_i + plm_i(l,m)*Phunc |
648 |
|
649 |
dsigmaidx = dsigmaidx + plm_i(l,m)*dPhuncdX + & |
650 |
Phunc * dlm_i(l,m) * dctidx |
651 |
dsigmaidy = dsigmaidy + plm_i(l,m)*dPhuncdY + & |
652 |
Phunc * dlm_i(l,m) * dctidy |
653 |
dsigmaidz = dsigmaidz + plm_i(l,m)*dPhuncdZ + & |
654 |
Phunc * dlm_i(l,m) * dctidz |
655 |
|
656 |
dsigmaidux = dsigmaidux + plm_i(l,m)* dPhuncdUx + & |
657 |
Phunc * dlm_i(l,m) * dctidux |
658 |
dsigmaiduy = dsigmaiduy + plm_i(l,m)* dPhuncdUy + & |
659 |
Phunc * dlm_i(l,m) * dctiduy |
660 |
dsigmaiduz = dsigmaiduz + plm_i(l,m)* dPhuncdUz + & |
661 |
Phunc * dlm_i(l,m) * dctiduz |
662 |
|
663 |
end do |
664 |
|
665 |
do lm = 1, ShapeMap%Shapes(st1)%nRangeFuncs |
666 |
l = ShapeMap%Shapes(st1)%RangeFuncLValue(lm) |
667 |
m = ShapeMap%Shapes(st1)%RangeFuncMValue(lm) |
668 |
coeff = ShapeMap%Shapes(st1)%RangeFuncCoefficient(lm) |
669 |
function_type = ShapeMap%Shapes(st1)%RangeFunctionType(lm) |
670 |
|
671 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
672 |
Phunc = coeff * tm_i(m) |
673 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
674 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
675 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
676 |
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
677 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
678 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
679 |
else |
680 |
Phunc = coeff * spi * um_i(m-1) |
681 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
682 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
683 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
684 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
685 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
686 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
687 |
endif |
688 |
|
689 |
s_i = s_i + plm_i(l,m)*Phunc |
690 |
|
691 |
dsidx = dsidx + plm_i(l,m)*dPhuncdX + & |
692 |
Phunc * dlm_i(l,m) * dctidx |
693 |
dsidy = dsidy + plm_i(l,m)*dPhuncdY + & |
694 |
Phunc * dlm_i(l,m) * dctidy |
695 |
dsidz = dsidz + plm_i(l,m)*dPhuncdZ + & |
696 |
Phunc * dlm_i(l,m) * dctidz |
697 |
|
698 |
dsidux = dsidux + plm_i(l,m)* dPhuncdUx + & |
699 |
Phunc * dlm_i(l,m) * dctidux |
700 |
dsiduy = dsiduy + plm_i(l,m)* dPhuncdUy + & |
701 |
Phunc * dlm_i(l,m) * dctiduy |
702 |
dsiduz = dsiduz + plm_i(l,m)* dPhuncdUz + & |
703 |
Phunc * dlm_i(l,m) * dctiduz |
704 |
|
705 |
end do |
706 |
|
707 |
do lm = 1, ShapeMap%Shapes(st1)%nStrengthFuncs |
708 |
l = ShapeMap%Shapes(st1)%StrengthFuncLValue(lm) |
709 |
m = ShapeMap%Shapes(st1)%StrengthFuncMValue(lm) |
710 |
coeff = ShapeMap%Shapes(st1)%StrengthFuncCoefficient(lm) |
711 |
function_type = ShapeMap%Shapes(st1)%StrengthFunctionType(lm) |
712 |
|
713 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
714 |
Phunc = coeff * tm_i(m) |
715 |
dPhuncdX = coeff * dtm_i(m) * dcpidx |
716 |
dPhuncdY = coeff * dtm_i(m) * dcpidy |
717 |
dPhuncdZ = coeff * dtm_i(m) * dcpidz |
718 |
dPhuncdUz = coeff * dtm_i(m) * dcpidux |
719 |
dPhuncdUy = coeff * dtm_i(m) * dcpiduy |
720 |
dPhuncdUz = coeff * dtm_i(m) * dcpiduz |
721 |
else |
722 |
Phunc = coeff * spi * um_i(m-1) |
723 |
dPhuncdX = coeff * (spi * dum_i(m-1) * dcpidx + dspidx *um_i(m-1)) |
724 |
dPhuncdY = coeff * (spi * dum_i(m-1) * dcpidy + dspidy *um_i(m-1)) |
725 |
dPhuncdZ = coeff * (spi * dum_i(m-1) * dcpidz + dspidz *um_i(m-1)) |
726 |
dPhuncdUx = coeff*(spi * dum_i(m-1)*dcpidux + dspidux *um_i(m-1)) |
727 |
dPhuncdUy = coeff*(spi * dum_i(m-1)*dcpiduy + dspiduy *um_i(m-1)) |
728 |
dPhuncdUz = coeff*(spi * dum_i(m-1)*dcpiduz + dspiduz *um_i(m-1)) |
729 |
endif |
730 |
|
731 |
eps_i = eps_i + plm_i(l,m)*Phunc |
732 |
|
733 |
depsidx = depsidx + plm_i(l,m)*dPhuncdX + & |
734 |
Phunc * dlm_i(l,m) * dctidx |
735 |
depsidy = depsidy + plm_i(l,m)*dPhuncdY + & |
736 |
Phunc * dlm_i(l,m) * dctidy |
737 |
depsidz = depsidz + plm_i(l,m)*dPhuncdZ + & |
738 |
Phunc * dlm_i(l,m) * dctidz |
739 |
|
740 |
depsidux = depsidux + plm_i(l,m)* dPhuncdUx + & |
741 |
Phunc * dlm_i(l,m) * dctidux |
742 |
depsiduy = depsiduy + plm_i(l,m)* dPhuncdUy + & |
743 |
Phunc * dlm_i(l,m) * dctiduy |
744 |
depsiduz = depsiduz + plm_i(l,m)* dPhuncdUz + & |
745 |
Phunc * dlm_i(l,m) * dctiduz |
746 |
|
747 |
end do |
748 |
|
749 |
endif |
750 |
|
751 |
! now do j: |
752 |
|
753 |
if (ShapeMap%Shapes(st2)%isLJ) then |
754 |
sigma_j = ShapeMap%Shapes(st2)%sigma |
755 |
s_j = ShapeMap%Shapes(st2)%sigma |
756 |
eps_j = ShapeMap%Shapes(st2)%epsilon |
757 |
dsigmajdx = 0.0d0 |
758 |
dsigmajdy = 0.0d0 |
759 |
dsigmajdz = 0.0d0 |
760 |
dsigmajdux = 0.0d0 |
761 |
dsigmajduy = 0.0d0 |
762 |
dsigmajduz = 0.0d0 |
763 |
dsjdx = 0.0d0 |
764 |
dsjdy = 0.0d0 |
765 |
dsjdz = 0.0d0 |
766 |
dsjdux = 0.0d0 |
767 |
dsjduy = 0.0d0 |
768 |
dsjduz = 0.0d0 |
769 |
depsjdx = 0.0d0 |
770 |
depsjdy = 0.0d0 |
771 |
depsjdz = 0.0d0 |
772 |
depsjdux = 0.0d0 |
773 |
depsjduy = 0.0d0 |
774 |
depsjduz = 0.0d0 |
775 |
else |
776 |
|
777 |
#ifdef IS_MPI |
778 |
! rotate the inter-particle separation into the two different |
779 |
! body-fixed coordinate systems: |
780 |
! negative sign because this is the vector from j to i: |
781 |
|
782 |
xj = -(A_Col(1,atom2)*d(1) + A_Col(2,atom2)*d(2) + A_Col(3,atom2)*d(3)) |
783 |
yj = -(A_Col(4,atom2)*d(1) + A_Col(5,atom2)*d(2) + A_Col(6,atom2)*d(3)) |
784 |
zj = -(A_Col(7,atom2)*d(1) + A_Col(8,atom2)*d(2) + A_Col(9,atom2)*d(3)) |
785 |
#else |
786 |
! rotate the inter-particle separation into the two different |
787 |
! body-fixed coordinate systems: |
788 |
! negative sign because this is the vector from j to i: |
789 |
|
790 |
xj = -(a(1,atom2)*d(1) + a(2,atom2)*d(2) + a(3,atom2)*d(3)) |
791 |
yj = -(a(4,atom2)*d(1) + a(5,atom2)*d(2) + a(6,atom2)*d(3)) |
792 |
zj = -(a(7,atom2)*d(1) + a(8,atom2)*d(2) + a(9,atom2)*d(3)) |
793 |
#endif |
794 |
|
795 |
xj2 = xj*xj |
796 |
yj2 = yj*yj |
797 |
zj2 = zj*zj |
798 |
|
799 |
projj = sqrt(xj2 + yj2) |
800 |
projj3 = projj*projj*projj |
801 |
|
802 |
ctj = zj / rij |
803 |
dctjdx = - zj * xj / r3 |
804 |
dctjdy = - zj * yj / r3 |
805 |
dctjdz = 1.0d0 / rij - zj2 / r3 |
806 |
dctjdux = yj / rij |
807 |
dctjduy = -xj / rij |
808 |
dctjduz = 0.0d0 |
809 |
|
810 |
cpj = xj / projj |
811 |
dcpjdx = 1.0d0 / projj - xj2 / projj3 |
812 |
dcpjdy = - xj * yj / projj3 |
813 |
dcpjdz = 0.0d0 |
814 |
dcpjdux = xj * yj * zj / projj3 |
815 |
dcpjduy = -zj * (1.0d0 / projj - xj2 / projj3) |
816 |
dcpjduz = -yj * (1.0d0 / projj - xj2 / projj3) - (xj2 * yj / projj3) |
817 |
|
818 |
spj = yj / projj |
819 |
dspjdx = - xj * yj / projj3 |
820 |
dspjdy = 1.0d0 / projj - yj2 / projj3 |
821 |
dspjdz = 0.0d0 |
822 |
dspjdux = -zj * (1.0d0 / projj - yj2 / projj3) |
823 |
dspjduy = xj * yj * zj / projj3 |
824 |
dspjduz = xj * (1.0d0 / projj - yi2 / projj3) + (xj * yj2 / projj3) |
825 |
|
826 |
call Associated_Legendre(ctj, ShapeMap%Shapes(st2)%bigL, & |
827 |
ShapeMap%Shapes(st2)%bigM, lmax, plm_j, dlm_j) |
828 |
|
829 |
call Orthogonal_Polynomial(cpj, ShapeMap%Shapes(st2)%bigM, & |
830 |
CHEBYSHEV_TN, tm_j, dtm_j) |
831 |
call Orthogonal_Polynomial(cpj, ShapeMap%Shapes(st2)%bigM, & |
832 |
CHEBYSHEV_UN, um_j, dum_j) |
833 |
|
834 |
sigma_j = 0.0d0 |
835 |
s_j = 0.0d0 |
836 |
eps_j = 0.0d0 |
837 |
dsigmajdx = 0.0d0 |
838 |
dsigmajdy = 0.0d0 |
839 |
dsigmajdz = 0.0d0 |
840 |
dsigmajdux = 0.0d0 |
841 |
dsigmajduy = 0.0d0 |
842 |
dsigmajduz = 0.0d0 |
843 |
dsjdx = 0.0d0 |
844 |
dsjdy = 0.0d0 |
845 |
dsjdz = 0.0d0 |
846 |
dsjdux = 0.0d0 |
847 |
dsjduy = 0.0d0 |
848 |
dsjduz = 0.0d0 |
849 |
depsjdx = 0.0d0 |
850 |
depsjdy = 0.0d0 |
851 |
depsjdz = 0.0d0 |
852 |
depsjdux = 0.0d0 |
853 |
depsjduy = 0.0d0 |
854 |
depsjduz = 0.0d0 |
855 |
|
856 |
do lm = 1, ShapeMap%Shapes(st2)%nContactFuncs |
857 |
l = ShapeMap%Shapes(st2)%ContactFuncLValue(lm) |
858 |
m = ShapeMap%Shapes(st2)%ContactFuncMValue(lm) |
859 |
coeff = ShapeMap%Shapes(st2)%ContactFuncCoefficient(lm) |
860 |
function_type = ShapeMap%Shapes(st2)%ContactFunctionType(lm) |
861 |
|
862 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
863 |
Phunc = coeff * tm_j(m) |
864 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
865 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
866 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
867 |
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
868 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
869 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
870 |
else |
871 |
Phunc = coeff * spj * um_j(m-1) |
872 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
873 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
874 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
875 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
876 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
877 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
878 |
endif |
879 |
|
880 |
sigma_j = sigma_j + plm_j(l,m)*Phunc |
881 |
|
882 |
dsigmajdx = dsigmajdx + plm_j(l,m)*dPhuncdX + & |
883 |
Phunc * dlm_j(l,m) * dctjdx |
884 |
dsigmajdy = dsigmajdy + plm_j(l,m)*dPhuncdY + & |
885 |
Phunc * dlm_j(l,m) * dctjdy |
886 |
dsigmajdz = dsigmajdz + plm_j(l,m)*dPhuncdZ + & |
887 |
Phunc * dlm_j(l,m) * dctjdz |
888 |
|
889 |
dsigmajdux = dsigmajdux + plm_j(l,m)* dPhuncdUx + & |
890 |
Phunc * dlm_j(l,m) * dctjdux |
891 |
dsigmajduy = dsigmajduy + plm_j(l,m)* dPhuncdUy + & |
892 |
Phunc * dlm_j(l,m) * dctjduy |
893 |
dsigmajduz = dsigmajduz + plm_j(l,m)* dPhuncdUz + & |
894 |
Phunc * dlm_j(l,m) * dctjduz |
895 |
|
896 |
end do |
897 |
|
898 |
do lm = 1, ShapeMap%Shapes(st2)%nRangeFuncs |
899 |
l = ShapeMap%Shapes(st2)%RangeFuncLValue(lm) |
900 |
m = ShapeMap%Shapes(st2)%RangeFuncMValue(lm) |
901 |
coeff = ShapeMap%Shapes(st2)%RangeFuncCoefficient(lm) |
902 |
function_type = ShapeMap%Shapes(st2)%RangeFunctionType(lm) |
903 |
|
904 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
905 |
Phunc = coeff * tm_j(m) |
906 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
907 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
908 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
909 |
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
910 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
911 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
912 |
else |
913 |
Phunc = coeff * spj * um_j(m-1) |
914 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
915 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
916 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
917 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
918 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
919 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
920 |
endif |
921 |
|
922 |
s_j = s_j + plm_j(l,m)*Phunc |
923 |
|
924 |
dsjdx = dsjdx + plm_j(l,m)*dPhuncdX + & |
925 |
Phunc * dlm_j(l,m) * dctjdx |
926 |
dsjdy = dsjdy + plm_j(l,m)*dPhuncdY + & |
927 |
Phunc * dlm_j(l,m) * dctjdy |
928 |
dsjdz = dsjdz + plm_j(l,m)*dPhuncdZ + & |
929 |
Phunc * dlm_j(l,m) * dctjdz |
930 |
|
931 |
dsjdux = dsjdux + plm_j(l,m)* dPhuncdUx + & |
932 |
Phunc * dlm_j(l,m) * dctjdux |
933 |
dsjduy = dsjduy + plm_j(l,m)* dPhuncdUy + & |
934 |
Phunc * dlm_j(l,m) * dctjduy |
935 |
dsjduz = dsjduz + plm_j(l,m)* dPhuncdUz + & |
936 |
Phunc * dlm_j(l,m) * dctjduz |
937 |
|
938 |
end do |
939 |
|
940 |
do lm = 1, ShapeMap%Shapes(st2)%nStrengthFuncs |
941 |
l = ShapeMap%Shapes(st2)%StrengthFuncLValue(lm) |
942 |
m = ShapeMap%Shapes(st2)%StrengthFuncMValue(lm) |
943 |
coeff = ShapeMap%Shapes(st2)%StrengthFuncCoefficient(lm) |
944 |
function_type = ShapeMap%Shapes(st2)%StrengthFunctionType(lm) |
945 |
|
946 |
if ((function_type .eq. SH_COS).or.(m.eq.0)) then |
947 |
Phunc = coeff * tm_j(m) |
948 |
dPhuncdX = coeff * dtm_j(m) * dcpjdx |
949 |
dPhuncdY = coeff * dtm_j(m) * dcpjdy |
950 |
dPhuncdZ = coeff * dtm_j(m) * dcpjdz |
951 |
dPhuncdUz = coeff * dtm_j(m) * dcpjdux |
952 |
dPhuncdUy = coeff * dtm_j(m) * dcpjduy |
953 |
dPhuncdUz = coeff * dtm_j(m) * dcpjduz |
954 |
else |
955 |
Phunc = coeff * spj * um_j(m-1) |
956 |
dPhuncdX = coeff * (spj * dum_j(m-1) * dcpjdx + dspjdx *um_j(m-1)) |
957 |
dPhuncdY = coeff * (spj * dum_j(m-1) * dcpjdy + dspjdy *um_j(m-1)) |
958 |
dPhuncdZ = coeff * (spj * dum_j(m-1) * dcpjdz + dspjdz *um_j(m-1)) |
959 |
dPhuncdUx = coeff*(spj * dum_j(m-1)*dcpjdux + dspjdux *um_j(m-1)) |
960 |
dPhuncdUy = coeff*(spj * dum_j(m-1)*dcpjduy + dspjduy *um_j(m-1)) |
961 |
dPhuncdUz = coeff*(spj * dum_j(m-1)*dcpjduz + dspjduz *um_j(m-1)) |
962 |
endif |
963 |
|
964 |
eps_j = eps_j + plm_j(l,m)*Phunc |
965 |
|
966 |
depsjdx = depsjdx + plm_j(l,m)*dPhuncdX + & |
967 |
Phunc * dlm_j(l,m) * dctjdx |
968 |
depsjdy = depsjdy + plm_j(l,m)*dPhuncdY + & |
969 |
Phunc * dlm_j(l,m) * dctjdy |
970 |
depsjdz = depsjdz + plm_j(l,m)*dPhuncdZ + & |
971 |
Phunc * dlm_j(l,m) * dctjdz |
972 |
|
973 |
depsjdux = depsjdux + plm_j(l,m)* dPhuncdUx + & |
974 |
Phunc * dlm_j(l,m) * dctjdux |
975 |
depsjduy = depsjduy + plm_j(l,m)* dPhuncdUy + & |
976 |
Phunc * dlm_j(l,m) * dctjduy |
977 |
depsjduz = depsjduz + plm_j(l,m)* dPhuncdUz + & |
978 |
Phunc * dlm_j(l,m) * dctjduz |
979 |
|
980 |
end do |
981 |
|
982 |
endif |
983 |
|
984 |
! phew, now let's assemble the potential energy: |
985 |
|
986 |
sigma = 0.5*(sigma_i + sigma_j) |
987 |
|
988 |
dsigmadxi = 0.5*dsigmaidx |
989 |
dsigmadyi = 0.5*dsigmaidy |
990 |
dsigmadzi = 0.5*dsigmaidz |
991 |
dsigmaduxi = 0.5*dsigmaidux |
992 |
dsigmaduyi = 0.5*dsigmaiduy |
993 |
dsigmaduzi = 0.5*dsigmaiduz |
994 |
|
995 |
dsigmadxj = 0.5*dsigmajdx |
996 |
dsigmadyj = 0.5*dsigmajdy |
997 |
dsigmadzj = 0.5*dsigmajdz |
998 |
dsigmaduxj = 0.5*dsigmajdux |
999 |
dsigmaduyj = 0.5*dsigmajduy |
1000 |
dsigmaduzj = 0.5*dsigmajduz |
1001 |
|
1002 |
s = 0.5*(s_i + s_j) |
1003 |
|
1004 |
dsdxi = 0.5*dsidx |
1005 |
dsdyi = 0.5*dsidy |
1006 |
dsdzi = 0.5*dsidz |
1007 |
dsduxi = 0.5*dsidux |
1008 |
dsduyi = 0.5*dsiduy |
1009 |
dsduzi = 0.5*dsiduz |
1010 |
|
1011 |
dsdxj = 0.5*dsjdx |
1012 |
dsdyj = 0.5*dsjdy |
1013 |
dsdzj = 0.5*dsjdz |
1014 |
dsduxj = 0.5*dsjdux |
1015 |
dsduyj = 0.5*dsjduy |
1016 |
dsduzj = 0.5*dsjduz |
1017 |
|
1018 |
eps = sqrt(eps_i * eps_j) |
1019 |
|
1020 |
depsdxi = eps_j * depsidx / (2.0d0 * eps) |
1021 |
depsdyi = eps_j * depsidy / (2.0d0 * eps) |
1022 |
depsdzi = eps_j * depsidz / (2.0d0 * eps) |
1023 |
depsduxi = eps_j * depsidux / (2.0d0 * eps) |
1024 |
depsduyi = eps_j * depsiduy / (2.0d0 * eps) |
1025 |
depsduzi = eps_j * depsiduz / (2.0d0 * eps) |
1026 |
|
1027 |
depsdxj = eps_i * depsjdx / (2.0d0 * eps) |
1028 |
depsdyj = eps_i * depsjdy / (2.0d0 * eps) |
1029 |
depsdzj = eps_i * depsjdz / (2.0d0 * eps) |
1030 |
depsduxj = eps_i * depsjdux / (2.0d0 * eps) |
1031 |
depsduyj = eps_i * depsjduy / (2.0d0 * eps) |
1032 |
depsduzj = eps_i * depsjduz / (2.0d0 * eps) |
1033 |
|
1034 |
rtdenom = rij-sigma+s |
1035 |
rt = s / rtdenom |
1036 |
|
1037 |
drtdxi = (dsdxi + rt * (drdxi - dsigmadxi + dsdxi)) / rtdenom |
1038 |
drtdyi = (dsdyi + rt * (drdyi - dsigmadyi + dsdyi)) / rtdenom |
1039 |
drtdzi = (dsdzi + rt * (drdzi - dsigmadzi + dsdzi)) / rtdenom |
1040 |
drtduxi = (dsduxi + rt * (drduxi - dsigmaduxi + dsduxi)) / rtdenom |
1041 |
drtduyi = (dsduyi + rt * (drduyi - dsigmaduyi + dsduyi)) / rtdenom |
1042 |
drtduzi = (dsduzi + rt * (drduzi - dsigmaduzi + dsduzi)) / rtdenom |
1043 |
drtdxj = (dsdxj + rt * (drdxj - dsigmadxj + dsdxj)) / rtdenom |
1044 |
drtdyj = (dsdyj + rt * (drdyj - dsigmadyj + dsdyj)) / rtdenom |
1045 |
drtdzj = (dsdzj + rt * (drdzj - dsigmadzj + dsdzj)) / rtdenom |
1046 |
drtduxj = (dsduxj + rt * (drduxj - dsigmaduxj + dsduxj)) / rtdenom |
1047 |
drtduyj = (dsduyj + rt * (drduyj - dsigmaduyj + dsduyj)) / rtdenom |
1048 |
drtduzj = (dsduzj + rt * (drduzj - dsigmaduzj + dsduzj)) / rtdenom |
1049 |
|
1050 |
rt2 = rt*rt |
1051 |
rt3 = rt2*rt |
1052 |
rt5 = rt2*rt3 |
1053 |
rt6 = rt3*rt3 |
1054 |
rt11 = rt5*rt6 |
1055 |
rt12 = rt6*rt6 |
1056 |
rt126 = rt12 - rt6 |
1057 |
|
1058 |
if (do_pot) then |
1059 |
#ifdef IS_MPI |
1060 |
pot_row(atom1) = pot_row(atom1) + 2.0d0*eps*rt126*sw |
1061 |
pot_col(atom2) = pot_col(atom2) + 2.0d0*eps*rt126*sw |
1062 |
#else |
1063 |
pot = pot + 4.0d0*eps*rt126*sw |
1064 |
#endif |
1065 |
endif |
1066 |
|
1067 |
dvdxi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdxi + 4.0d0*depsdxi*rt126 |
1068 |
dvdyi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdyi + 4.0d0*depsdyi*rt126 |
1069 |
dvdzi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdzi + 4.0d0*depsdzi*rt126 |
1070 |
dvduxi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduxi + 4.0d0*depsduxi*rt126 |
1071 |
dvduyi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduyi + 4.0d0*depsduyi*rt126 |
1072 |
dvduzi = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduzi + 4.0d0*depsduzi*rt126 |
1073 |
|
1074 |
dvdxj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdxj + 4.0d0*depsdxj*rt126 |
1075 |
dvdyj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdyj + 4.0d0*depsdyj*rt126 |
1076 |
dvdzj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtdzj + 4.0d0*depsdzj*rt126 |
1077 |
dvduxj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduxj + 4.0d0*depsduxj*rt126 |
1078 |
dvduyj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduyj + 4.0d0*depsduyj*rt126 |
1079 |
dvduzj = 24.0d0*eps*(2.0d0*rt11 - rt5)*drtduzj + 4.0d0*depsduzj*rt126 |
1080 |
|
1081 |
! do the torques first since they are easy: |
1082 |
! remember that these are still in the body fixed axes |
1083 |
|
1084 |
txi = dvduxi * sw |
1085 |
tyi = dvduyi * sw |
1086 |
tzi = dvduzi * sw |
1087 |
|
1088 |
txj = dvduxj * sw |
1089 |
tyj = dvduyj * sw |
1090 |
tzj = dvduzj * sw |
1091 |
|
1092 |
! go back to lab frame using transpose of rotation matrix: |
1093 |
|
1094 |
#ifdef IS_MPI |
1095 |
t_Row(1,atom1) = t_Row(1,atom1) + a_Row(1,atom1)*txi + & |
1096 |
a_Row(4,atom1)*tyi + a_Row(7,atom1)*tzi |
1097 |
t_Row(2,atom1) = t_Row(2,atom1) + a_Row(2,atom1)*txi + & |
1098 |
a_Row(5,atom1)*tyi + a_Row(8,atom1)*tzi |
1099 |
t_Row(3,atom1) = t_Row(3,atom1) + a_Row(3,atom1)*txi + & |
1100 |
a_Row(6,atom1)*tyi + a_Row(9,atom1)*tzi |
1101 |
|
1102 |
t_Col(1,atom2) = t_Col(1,atom2) + a_Col(1,atom2)*txj + & |
1103 |
a_Col(4,atom2)*tyj + a_Col(7,atom2)*tzj |
1104 |
t_Col(2,atom2) = t_Col(2,atom2) + a_Col(2,atom2)*txj + & |
1105 |
a_Col(5,atom2)*tyj + a_Col(8,atom2)*tzj |
1106 |
t_Col(3,atom2) = t_Col(3,atom2) + a_Col(3,atom2)*txj + & |
1107 |
a_Col(6,atom2)*tyj + a_Col(9,atom2)*tzj |
1108 |
#else |
1109 |
t(1,atom1) = t(1,atom1) + a(1,atom1)*txi + a(4,atom1)*tyi + a(7,atom1)*tzi |
1110 |
t(2,atom1) = t(2,atom1) + a(2,atom1)*txi + a(5,atom1)*tyi + a(8,atom1)*tzi |
1111 |
t(3,atom1) = t(3,atom1) + a(3,atom1)*txi + a(6,atom1)*tyi + a(9,atom1)*tzi |
1112 |
|
1113 |
t(1,atom2) = t(1,atom2) + a(1,atom2)*txj + a(4,atom2)*tyj + a(7,atom2)*tzj |
1114 |
t(2,atom2) = t(2,atom2) + a(2,atom2)*txj + a(5,atom2)*tyj + a(8,atom2)*tzj |
1115 |
t(3,atom2) = t(3,atom2) + a(3,atom2)*txj + a(6,atom2)*tyj + a(9,atom2)*tzj |
1116 |
#endif |
1117 |
! Now, on to the forces: |
1118 |
|
1119 |
! first rotate the i terms back into the lab frame: |
1120 |
|
1121 |
fxi = dvdxi * sw |
1122 |
fyi = dvdyi * sw |
1123 |
fzi = dvdzi * sw |
1124 |
|
1125 |
fxj = dvdxj * sw |
1126 |
fyj = dvdyj * sw |
1127 |
fzj = dvdzj * sw |
1128 |
|
1129 |
#ifdef IS_MPI |
1130 |
fxii = a_Row(1,atom1)*fxi + a_Row(4,atom1)*fyi + a_Row(7,atom1)*fzi |
1131 |
fyii = a_Row(2,atom1)*fxi + a_Row(5,atom1)*fyi + a_Row(8,atom1)*fzi |
1132 |
fzii = a_Row(3,atom1)*fxi + a_Row(6,atom1)*fyi + a_Row(9,atom1)*fzi |
1133 |
|
1134 |
fxjj = a_Col(1,atom2)*fxj + a_Col(4,atom2)*fyj + a_Col(7,atom2)*fzj |
1135 |
fyjj = a_Col(2,atom2)*fxj + a_Col(5,atom2)*fyj + a_Col(8,atom2)*fzj |
1136 |
fzjj = a_Col(3,atom2)*fxj + a_Col(6,atom2)*fyj + a_Col(9,atom2)*fzj |
1137 |
#else |
1138 |
fxii = a(1,atom1)*fxi + a(4,atom1)*fyi + a(7,atom1)*fzi |
1139 |
fyii = a(2,atom1)*fxi + a(5,atom1)*fyi + a(8,atom1)*fzi |
1140 |
fzii = a(3,atom1)*fxi + a(6,atom1)*fyi + a(9,atom1)*fzi |
1141 |
|
1142 |
fxjj = a(1,atom2)*fxj + a(4,atom2)*fyj + a(7,atom2)*fzj |
1143 |
fyjj = a(2,atom2)*fxj + a(5,atom2)*fyj + a(8,atom2)*fzj |
1144 |
fzjj = a(3,atom2)*fxj + a(6,atom2)*fyj + a(9,atom2)*fzj |
1145 |
#endif |
1146 |
|
1147 |
fxij = -fxii |
1148 |
fyij = -fyii |
1149 |
fzij = -fzii |
1150 |
|
1151 |
fxji = -fxjj |
1152 |
fyji = -fyjj |
1153 |
fzji = -fzjj |
1154 |
|
1155 |
fxradial = fxii + fxji |
1156 |
fyradial = fyii + fyji |
1157 |
fzradial = fzii + fzji |
1158 |
|
1159 |
#ifdef IS_MPI |
1160 |
f_Row(1,atom1) = f_Row(1,atom1) + fxradial |
1161 |
f_Row(2,atom1) = f_Row(2,atom1) + fyradial |
1162 |
f_Row(3,atom1) = f_Row(3,atom1) + fzradial |
1163 |
|
1164 |
f_Col(1,atom2) = f_Col(1,atom2) - fxradial |
1165 |
f_Col(2,atom2) = f_Col(2,atom2) - fyradial |
1166 |
f_Col(3,atom2) = f_Col(3,atom2) - fzradial |
1167 |
#else |
1168 |
f(1,atom1) = f(1,atom1) + fxradial |
1169 |
f(2,atom1) = f(2,atom1) + fyradial |
1170 |
f(3,atom1) = f(3,atom1) + fzradial |
1171 |
|
1172 |
f(1,atom2) = f(1,atom2) - fxradial |
1173 |
f(2,atom2) = f(2,atom2) - fyradial |
1174 |
f(3,atom2) = f(3,atom2) - fzradial |
1175 |
#endif |
1176 |
|
1177 |
#ifdef IS_MPI |
1178 |
id1 = AtomRowToGlobal(atom1) |
1179 |
id2 = AtomColToGlobal(atom2) |
1180 |
#else |
1181 |
id1 = atom1 |
1182 |
id2 = atom2 |
1183 |
#endif |
1184 |
|
1185 |
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
1186 |
|
1187 |
fpair(1) = fpair(1) + fxradial |
1188 |
fpair(2) = fpair(2) + fyradial |
1189 |
fpair(3) = fpair(3) + fzradial |
1190 |
|
1191 |
endif |
1192 |
|
1193 |
end subroutine do_shape_pair |
1194 |
|
1195 |
SUBROUTINE Associated_Legendre(x, l, m, lmax, plm, dlm) |
1196 |
|
1197 |
! Purpose: Compute the associated Legendre functions |
1198 |
! Plm(x) and their derivatives Plm'(x) |
1199 |
! Input : x --- Argument of Plm(x) |
1200 |
! l --- Order of Plm(x), l = 0,1,2,...,n |
1201 |
! m --- Degree of Plm(x), m = 0,1,2,...,N |
1202 |
! lmax --- Physical dimension of PLM and DLM |
1203 |
! Output: PLM(l,m) --- Plm(x) |
1204 |
! DLM(l,m) --- Plm'(x) |
1205 |
! |
1206 |
! adapted from the routines in |
1207 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
1208 |
! ISBN 0-471-11963-6 |
1209 |
! |
1210 |
! The original Fortran77 codes can be found here: |
1211 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
1212 |
|
1213 |
real (kind=8), intent(in) :: x |
1214 |
integer, intent(in) :: l, m, lmax |
1215 |
real (kind=8), dimension(0:lmax,0:m), intent(out) :: PLM, DLM |
1216 |
integer :: i, j, ls |
1217 |
real (kind=8) :: xq, xs |
1218 |
|
1219 |
! zero out both arrays: |
1220 |
DO I = 0, m |
1221 |
DO J = 0, l |
1222 |
PLM(J,I) = 0.0D0 |
1223 |
DLM(J,I) = 0.0D0 |
1224 |
end DO |
1225 |
end DO |
1226 |
|
1227 |
! start with 0,0: |
1228 |
PLM(0,0) = 1.0D0 |
1229 |
|
1230 |
! x = +/- 1 functions are easy: |
1231 |
IF (abs(X).EQ.1.0D0) THEN |
1232 |
DO I = 1, m |
1233 |
PLM(0, I) = X**I |
1234 |
DLM(0, I) = 0.5D0*I*(I+1.0D0)*X**(I+1) |
1235 |
end DO |
1236 |
DO J = 1, m |
1237 |
DO I = 1, l |
1238 |
IF (I.EQ.1) THEN |
1239 |
DLM(I, J) = 1.0D+300 |
1240 |
ELSE IF (I.EQ.2) THEN |
1241 |
DLM(I, J) = -0.25D0*(J+2)*(J+1)*J*(J-1)*X**(J+1) |
1242 |
ENDIF |
1243 |
end DO |
1244 |
end DO |
1245 |
RETURN |
1246 |
ENDIF |
1247 |
|
1248 |
LS = 1 |
1249 |
IF (abs(X).GT.1.0D0) LS = -1 |
1250 |
XQ = sqrt(LS*(1.0D0-X*X)) |
1251 |
XS = LS*(1.0D0-X*X) |
1252 |
|
1253 |
DO I = 1, l |
1254 |
PLM(I, I) = -LS*(2.0D0*I-1.0D0)*XQ*PLM(I-1, I-1) |
1255 |
enddo |
1256 |
|
1257 |
DO I = 0, l |
1258 |
PLM(I, I+1)=(2.0D0*I+1.0D0)*X*PLM(I, I) |
1259 |
enddo |
1260 |
|
1261 |
DO I = 0, l |
1262 |
DO J = I+2, m |
1263 |
PLM(I, J)=((2.0D0*J-1.0D0)*X*PLM(I,J-1) - & |
1264 |
(I+J-1.0D0)*PLM(I,J-2))/(J-I) |
1265 |
end DO |
1266 |
end DO |
1267 |
|
1268 |
DLM(0, 0)=0.0D0 |
1269 |
|
1270 |
DO J = 1, m |
1271 |
DLM(0, J)=LS*J*(PLM(0,J-1)-X*PLM(0,J))/XS |
1272 |
end DO |
1273 |
|
1274 |
DO I = 1, l |
1275 |
DO J = I, m |
1276 |
DLM(I,J) = LS*I*X*PLM(I, J)/XS + (J+I)*(J-I+1.0D0)/XQ*PLM(I-1, J) |
1277 |
end DO |
1278 |
end DO |
1279 |
|
1280 |
RETURN |
1281 |
END SUBROUTINE Associated_Legendre |
1282 |
|
1283 |
|
1284 |
subroutine Orthogonal_Polynomial(x, m, function_type, pl, dpl) |
1285 |
|
1286 |
! Purpose: Compute orthogonal polynomials: Tn(x) or Un(x), |
1287 |
! or Ln(x) or Hn(x), and their derivatives |
1288 |
! Input : function_type --- Function code |
1289 |
! =1 for Chebyshev polynomial Tn(x) |
1290 |
! =2 for Chebyshev polynomial Un(x) |
1291 |
! =3 for Laguerre polynomial Ln(x) |
1292 |
! =4 for Hermite polynomial Hn(x) |
1293 |
! n --- Order of orthogonal polynomials |
1294 |
! x --- Argument of orthogonal polynomials |
1295 |
! Output: PL(n) --- Tn(x) or Un(x) or Ln(x) or Hn(x) |
1296 |
! DPL(n)--- Tn'(x) or Un'(x) or Ln'(x) or Hn'(x) |
1297 |
! |
1298 |
! adapted from the routines in |
1299 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
1300 |
! ISBN 0-471-11963-6 |
1301 |
! |
1302 |
! The original Fortran77 codes can be found here: |
1303 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
1304 |
|
1305 |
real(kind=8), intent(in) :: x |
1306 |
integer, intent(in):: m |
1307 |
integer, intent(in):: function_type |
1308 |
real(kind=8), dimension(0:m), intent(inout) :: pl, dpl |
1309 |
|
1310 |
real(kind=8) :: a, b, c, y0, y1, dy0, dy1, yn, dyn |
1311 |
integer :: k |
1312 |
|
1313 |
A = 2.0D0 |
1314 |
B = 0.0D0 |
1315 |
C = 1.0D0 |
1316 |
Y0 = 1.0D0 |
1317 |
Y1 = 2.0D0*X |
1318 |
DY0 = 0.0D0 |
1319 |
DY1 = 2.0D0 |
1320 |
PL(0) = 1.0D0 |
1321 |
PL(1) = 2.0D0*X |
1322 |
DPL(0) = 0.0D0 |
1323 |
DPL(1) = 2.0D0 |
1324 |
IF (function_type.EQ.CHEBYSHEV_TN) THEN |
1325 |
Y1 = X |
1326 |
DY1 = 1.0D0 |
1327 |
PL(1) = X |
1328 |
DPL(1) = 1.0D0 |
1329 |
ELSE IF (function_type.EQ.LAGUERRE) THEN |
1330 |
Y1 = 1.0D0-X |
1331 |
DY1 = -1.0D0 |
1332 |
PL(1) = 1.0D0-X |
1333 |
DPL(1) = -1.0D0 |
1334 |
ENDIF |
1335 |
DO K = 2, m |
1336 |
IF (function_type.EQ.LAGUERRE) THEN |
1337 |
A = -1.0D0/K |
1338 |
B = 2.0D0+A |
1339 |
C = 1.0D0+A |
1340 |
ELSE IF (function_type.EQ.HERMITE) THEN |
1341 |
C = 2.0D0*(K-1.0D0) |
1342 |
ENDIF |
1343 |
YN = (A*X+B)*Y1-C*Y0 |
1344 |
DYN = A*Y1+(A*X+B)*DY1-C*DY0 |
1345 |
PL(K) = YN |
1346 |
DPL(K) = DYN |
1347 |
Y0 = Y1 |
1348 |
Y1 = YN |
1349 |
DY0 = DY1 |
1350 |
DY1 = DYN |
1351 |
end DO |
1352 |
RETURN |
1353 |
|
1354 |
end subroutine Orthogonal_Polynomial |
1355 |
|
1356 |
end module shapes |