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 |
logical, save :: haveShapeMap = .false. |
21 |
|
22 |
public :: do_shape_pair |
23 |
|
24 |
type :: ShapeList |
25 |
integer :: nLMpairs = 0 |
26 |
integer :: bigL = 0 |
27 |
integer :: bigM = 0 |
28 |
integer, allocatable, dimension(:) :: lValue |
29 |
integer, allocatable, dimension(:) :: mValue |
30 |
real(kind=dp), allocatable, dimension(:) :: contactFuncSinCoeff |
31 |
real(kind=dp), allocatable, dimension(:) :: contactFuncCosCoeff |
32 |
real(kind=dp), allocatable, dimension(:) :: rangeFuncSinCoeff |
33 |
real(kind=dp), allocatable, dimension(:) :: rangeFuncCosCoeff |
34 |
real(kind=dp), allocatable, dimension(:) :: strengthFuncSinCoeff |
35 |
real(kind=dp), allocatable, dimension(:) :: strengthFuncCosCoeff |
36 |
integer, allocatable, dimension(:) :: mValue |
37 |
logical :: isLJ = .false. |
38 |
real ( kind = dp ) :: epsilon = 0.0_dp |
39 |
real ( kind = dp ) :: sigma = 0.0_dp |
40 |
end type ShapeList |
41 |
|
42 |
type(ShapeList), dimension(:),allocatable :: ShapeMap |
43 |
|
44 |
|
45 |
contains |
46 |
|
47 |
subroutine do_shape_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
48 |
pot, A, f, t, do_pot) |
49 |
|
50 |
!! We assume that the rotation matrices have already been calculated |
51 |
!! and placed in the A array. |
52 |
|
53 |
r3 = r2*rij |
54 |
r5 = r3*r2 |
55 |
|
56 |
drdx = d(1) / rij |
57 |
drdy = d(2) / rij |
58 |
drdz = d(3) / rij |
59 |
|
60 |
#ifdef IS_MPI |
61 |
me1 = atid_Row(atom1) |
62 |
me2 = atid_Col(atom2) |
63 |
#else |
64 |
me1 = atid(atom1) |
65 |
me2 = atid(atom2) |
66 |
#endif |
67 |
|
68 |
if (ShapeMap(me1)%isLJ) then |
69 |
sigma_i = ShapeMap(me1)%sigma |
70 |
s_i = ShapeMap(me1)%sigma |
71 |
eps_i = ShapeMap(me1)%epsilon |
72 |
dsigmaidx = 0.0d0 |
73 |
dsigmaidy = 0.0d0 |
74 |
dsigmaidz = 0.0d0 |
75 |
dsigmaidux = 0.0d0 |
76 |
dsigmaiduy = 0.0d0 |
77 |
dsigmaiduz = 0.0d0 |
78 |
dsidx = 0.0d0 |
79 |
dsidy = 0.0d0 |
80 |
dsidz = 0.0d0 |
81 |
dsidux = 0.0d0 |
82 |
dsiduy = 0.0d0 |
83 |
dsiduz = 0.0d0 |
84 |
depsidx = 0.0d0 |
85 |
depsidy = 0.0d0 |
86 |
depsidz = 0.0d0 |
87 |
depsidux = 0.0d0 |
88 |
depsiduy = 0.0d0 |
89 |
depsiduz = 0.0d0 |
90 |
else |
91 |
|
92 |
#ifdef IS_MPI |
93 |
! rotate the inter-particle separation into the two different |
94 |
! body-fixed coordinate systems: |
95 |
|
96 |
xi = A_row(1,atom1)*d(1) + A_row(2,atom1)*d(2) + A_row(3,atom1)*d(3) |
97 |
yi = A_row(4,atom1)*d(1) + A_row(5,atom1)*d(2) + A_row(6,atom1)*d(3) |
98 |
zi = A_row(7,atom1)*d(1) + A_row(8,atom1)*d(2) + A_row(9,atom1)*d(3) |
99 |
|
100 |
#else |
101 |
! rotate the inter-particle separation into the two different |
102 |
! body-fixed coordinate systems: |
103 |
|
104 |
xi = a(1,atom1)*d(1) + a(2,atom1)*d(2) + a(3,atom1)*d(3) |
105 |
yi = a(4,atom1)*d(1) + a(5,atom1)*d(2) + a(6,atom1)*d(3) |
106 |
zi = a(7,atom1)*d(1) + a(8,atom1)*d(2) + a(9,atom1)*d(3) |
107 |
|
108 |
#endif |
109 |
|
110 |
xi2 = xi*xi |
111 |
yi2 = yi*yi |
112 |
zi2 = zi*zi |
113 |
|
114 |
proji = sqrt(xi2 + yi2) |
115 |
proji3 = proji*proji*proji |
116 |
|
117 |
cti = zi / rij |
118 |
dctidx = - zi * xi / r3 |
119 |
dctidy = - zi * yi / r3 |
120 |
dctidz = 1.0d0 / rij - zi2 / r3 |
121 |
dctidux = yi / rij |
122 |
dctiduy = -xi / rij |
123 |
dctiduz = 0.0d0 |
124 |
|
125 |
cpi = xi / proji |
126 |
dcpidx = 1.0d0 / proji - xi2 / proji3 |
127 |
dcpidy = - xi * yi / proji3 |
128 |
dcpidz = 0.0d0 |
129 |
dcpidux = xi * yi * zi / proji3 |
130 |
dcpiduy = -zi * (1.0d0 / proji - xi2 / proji3) |
131 |
dcpiduz = -yi * (1.0d0 / proji - xi2 / proji3) - (xi2 * yi / proji3) |
132 |
|
133 |
spi = yi / proji |
134 |
dspidx = - xi * yi / proji3 |
135 |
dspidy = 1.0d0 / proji - yi2 / proji3 |
136 |
dspidz = 0.0d0 |
137 |
dspidux = -zi * (1.0d0 / proji - yi2 / proji3) |
138 |
dspiduy = xi * yi * zi / proji3 |
139 |
dspiduz = xi * (1.0d0 / proji - yi2 / proji3) + (xi * yi2 / proji3) |
140 |
|
141 |
call Associated_Legendre(cti, ShapeMap(me1)%bigL, & |
142 |
ShapeMap(me1)%bigM, lmax, plm_i, dlm_i) |
143 |
|
144 |
call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_TN, & |
145 |
tm_i, dtm_i) |
146 |
call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_UN, & |
147 |
um_i, dum_i) |
148 |
|
149 |
sigma_i = 0.0d0 |
150 |
s_i = 0.0d0 |
151 |
eps_i = 0.0d0 |
152 |
dsigmaidx = 0.0d0 |
153 |
dsigmaidy = 0.0d0 |
154 |
dsigmaidz = 0.0d0 |
155 |
dsigmaidux = 0.0d0 |
156 |
dsigmaiduy = 0.0d0 |
157 |
dsigmaiduz = 0.0d0 |
158 |
dsidx = 0.0d0 |
159 |
dsidy = 0.0d0 |
160 |
dsidz = 0.0d0 |
161 |
dsidux = 0.0d0 |
162 |
dsiduy = 0.0d0 |
163 |
dsiduz = 0.0d0 |
164 |
depsidx = 0.0d0 |
165 |
depsidy = 0.0d0 |
166 |
depsidz = 0.0d0 |
167 |
depsidux = 0.0d0 |
168 |
depsiduy = 0.0d0 |
169 |
depsiduz = 0.0d0 |
170 |
|
171 |
do lm = 1, ShapeMap(me1)%nLMpairs |
172 |
|
173 |
l = ShapeMap(me1)%lValue(lm) |
174 |
m = ShapeMap(me1)%mValue(lm) |
175 |
|
176 |
slm = ShapeMap(me1)%contactFuncSinCoeff(lm) |
177 |
clm = ShapeMap(me1)%contactFuncCosCoeff(lm) |
178 |
|
179 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
180 |
|
181 |
dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
182 |
+ clm * dtm_i(m) * dcpidx ) |
183 |
dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
184 |
+ clm * dtm_i(m) * dcpidy ) |
185 |
dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
186 |
+ clm * dtm_i(m) * dcpidz ) |
187 |
|
188 |
dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
189 |
+ clm * dtm_i(m) * dcpidux |
190 |
dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
191 |
+ clm * dtm_i(m) * dcpiduy |
192 |
dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
193 |
+ clm * dtm_i(m) * dcpiduz |
194 |
|
195 |
sigma_i = sigma_i + plm_i(l,m)*Phunc |
196 |
|
197 |
dsigmaidx = dsigmaidx + plm_i(l,m)*dPhuncdX + & |
198 |
Phunc * dlm_i(l,m) * dctidx |
199 |
dsigmaidy = dsigmaidy + plm_i(l,m)*dPhuncdY + & |
200 |
Phunc * dlm_i(l,m) * dctidy |
201 |
dsigmaidz = dsigmaidz + plm_i(l,m)*dPhuncdZ + & |
202 |
Phunc * dlm_i(l,m) * dctidz |
203 |
|
204 |
dsigmaidux = dsigmaidux + plm_i(l,m)* dPhuncdUx + & |
205 |
Phunc * dlm_i(l,m) * dctidux |
206 |
dsigmaiduy = dsigmaiduy + plm_i(l,m)* dPhuncdUy + & |
207 |
Phunc * dlm_i(l,m) * dctiduy |
208 |
dsigmaiduz = dsigmaiduz + plm_i(l,m)* dPhuncdUz + & |
209 |
Phunc * dlm_i(l,m) * dctiduz |
210 |
|
211 |
slm = ShapeMap(me1)%rangeFuncSinCoeff(lm) |
212 |
clm = ShapeMap(me1)%rangeFuncCosCoeff(lm) |
213 |
|
214 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
215 |
|
216 |
dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
217 |
+ clm * dtm_i(m) * dcpidx ) |
218 |
dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
219 |
+ clm * dtm_i(m) * dcpidy ) |
220 |
dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
221 |
+ clm * dtm_i(m) * dcpidz ) |
222 |
|
223 |
dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
224 |
+ clm * dtm_i(m) * dcpidux |
225 |
dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
226 |
+ clm * dtm_i(m) * dcpiduy |
227 |
dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
228 |
+ clm * dtm_i(m) * dcpiduz |
229 |
|
230 |
s_i = s_i + plm_i(l,m)*Phunc |
231 |
|
232 |
dsidx = dsidx + plm_i(l,m)*dPhuncdX + & |
233 |
Phunc * dlm_i(l,m) * dctidx |
234 |
dsidy = dsidy + plm_i(l,m)*dPhuncdY + & |
235 |
Phunc * dlm_i(l,m) * dctidy |
236 |
dsidz = dsidz + plm_i(l,m)*dPhuncdZ + & |
237 |
Phunc * dlm_i(l,m) * dctidz |
238 |
|
239 |
dsidux = dsidux + plm_i(l,m)* dPhuncdUx + & |
240 |
Phunc * dlm_i(l,m) * dctidux |
241 |
dsiduy = dsiduy + plm_i(l,m)* dPhuncdUy + & |
242 |
Phunc * dlm_i(l,m) * dctiduy |
243 |
dsiduz = dsiduz + plm_i(l,m)* dPhuncdUz + & |
244 |
Phunc * dlm_i(l,m) * dctiduz |
245 |
|
246 |
slm = ShapeMap(me1)%strengthFuncSinCoeff(lm) |
247 |
clm = ShapeMap(me1)%strengthFuncCosCoeff(lm) |
248 |
|
249 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
250 |
|
251 |
dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
252 |
+ clm * dtm_i(m) * dcpidx ) |
253 |
dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
254 |
+ clm * dtm_i(m) * dcpidy ) |
255 |
dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
256 |
+ clm * dtm_i(m) * dcpidz ) |
257 |
|
258 |
dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
259 |
+ clm * dtm_i(m) * dcpidux |
260 |
dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
261 |
+ clm * dtm_i(m) * dcpiduy |
262 |
dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
263 |
+ clm * dtm_i(m) * dcpiduz |
264 |
|
265 |
eps_i = eps_i + plm_i(l,m)*Phunc |
266 |
|
267 |
depsidx = depsidx + plm_i(l,m)*dPhuncdX + & |
268 |
Phunc * dlm_i(l,m) * dctidx |
269 |
depsidy = depsidy + plm_i(l,m)*dPhuncdY + & |
270 |
Phunc * dlm_i(l,m) * dctidy |
271 |
depsidz = depsidz + plm_i(l,m)*dPhuncdZ + & |
272 |
Phunc * dlm_i(l,m) * dctidz |
273 |
|
274 |
depsidux = depsidux + plm_i(l,m)* dPhuncdUx + & |
275 |
Phunc * dlm_i(l,m) * dctidux |
276 |
depsiduy = depsiduy + plm_i(l,m)* dPhuncdUy + & |
277 |
Phunc * dlm_i(l,m) * dctiduy |
278 |
depsiduz = depsiduz + plm_i(l,m)* dPhuncdUz + & |
279 |
Phunc * dlm_i(l,m) * dctiduz |
280 |
|
281 |
enddo |
282 |
endif |
283 |
|
284 |
! now do j: |
285 |
|
286 |
if (ShapeMap(me2)%isLJ) then |
287 |
sigma_j = ShapeMap(me2)%sigma |
288 |
s_j = ShapeMap(me2)%sigma |
289 |
eps_j = ShapeMap(me2)%epsilon |
290 |
dsigmajdx = 0.0d0 |
291 |
dsigmajdy = 0.0d0 |
292 |
dsigmajdz = 0.0d0 |
293 |
dsigmajdux = 0.0d0 |
294 |
dsigmajduy = 0.0d0 |
295 |
dsigmajduz = 0.0d0 |
296 |
dsjdx = 0.0d0 |
297 |
dsjdy = 0.0d0 |
298 |
dsjdz = 0.0d0 |
299 |
dsjdux = 0.0d0 |
300 |
dsjduy = 0.0d0 |
301 |
dsjduz = 0.0d0 |
302 |
depsjdx = 0.0d0 |
303 |
depsjdy = 0.0d0 |
304 |
depsjdz = 0.0d0 |
305 |
depsjdux = 0.0d0 |
306 |
depsjduy = 0.0d0 |
307 |
depsjduz = 0.0d0 |
308 |
else |
309 |
|
310 |
#ifdef IS_MPI |
311 |
! rotate the inter-particle separation into the two different |
312 |
! body-fixed coordinate systems: |
313 |
! negative sign because this is the vector from j to i: |
314 |
|
315 |
xj = -(A_Col(1,atom2)*d(1) + A_Col(2,atom2)*d(2) + A_Col(3,atom2)*d(3)) |
316 |
yj = -(A_Col(4,atom2)*d(1) + A_Col(5,atom2)*d(2) + A_Col(6,atom2)*d(3)) |
317 |
zj = -(A_Col(7,atom2)*d(1) + A_Col(8,atom2)*d(2) + A_Col(9,atom2)*d(3)) |
318 |
#else |
319 |
! rotate the inter-particle separation into the two different |
320 |
! body-fixed coordinate systems: |
321 |
! negative sign because this is the vector from j to i: |
322 |
|
323 |
xj = -(a(1,atom2)*d(1) + a(2,atom2)*d(2) + a(3,atom2)*d(3)) |
324 |
yj = -(a(4,atom2)*d(1) + a(5,atom2)*d(2) + a(6,atom2)*d(3)) |
325 |
zj = -(a(7,atom2)*d(1) + a(8,atom2)*d(2) + a(9,atom2)*d(3)) |
326 |
#endif |
327 |
|
328 |
xj2 = xj*xj |
329 |
yj2 = yj*yj |
330 |
zj2 = zj*zj |
331 |
|
332 |
projj = sqrt(xj2 + yj2) |
333 |
projj3 = projj*projj*projj |
334 |
|
335 |
ctj = zj / rij |
336 |
dctjdx = - zj * xj / r3 |
337 |
dctjdy = - zj * yj / r3 |
338 |
dctjdz = 1.0d0 / rij - zj2 / r3 |
339 |
dctjdux = yj / rij |
340 |
dctjduy = -xj / rij |
341 |
dctjduz = 0.0d0 |
342 |
|
343 |
cpj = xj / projj |
344 |
dcpjdx = 1.0d0 / projj - xj2 / projj3 |
345 |
dcpjdy = - xj * yj / projj3 |
346 |
dcpjdz = 0.0d0 |
347 |
dcpjdux = xj * yj * zj / projj3 |
348 |
dcpjduy = -zj * (1.0d0 / projj - xj2 / projj3) |
349 |
dcpjduz = -yj * (1.0d0 / projj - xj2 / projj3) - (xj2 * yj / projj3) |
350 |
|
351 |
spj = yj / projj |
352 |
dspjdx = - xj * yj / projj3 |
353 |
dspjdy = 1.0d0 / projj - yj2 / projj3 |
354 |
dspjdz = 0.0d0 |
355 |
dspjdux = -zj * (1.0d0 / projj - yj2 / projj3) |
356 |
dspjduy = xj * yj * zj / projj3 |
357 |
dspjduz = xj * (1.0d0 / projj - yi2 / projj3) + (xj * yj2 / projj3) |
358 |
|
359 |
call Associated_Legendre(ctj, ShapeMap(me2)%bigL, & |
360 |
ShapeMap(me2)%bigM, lmax, plm_j, dlm_j) |
361 |
|
362 |
call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_TN, & |
363 |
tm_j, dtm_j) |
364 |
call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_UN, & |
365 |
um_j, dum_j) |
366 |
|
367 |
sigma_j = 0.0d0 |
368 |
s_j = 0.0d0 |
369 |
eps_j = 0.0d0 |
370 |
dsigmajdx = 0.0d0 |
371 |
dsigmajdy = 0.0d0 |
372 |
dsigmajdz = 0.0d0 |
373 |
dsigmajdux = 0.0d0 |
374 |
dsigmajduy = 0.0d0 |
375 |
dsigmajduz = 0.0d0 |
376 |
dsjdx = 0.0d0 |
377 |
dsjdy = 0.0d0 |
378 |
dsjdz = 0.0d0 |
379 |
dsjdux = 0.0d0 |
380 |
dsjduy = 0.0d0 |
381 |
dsjduz = 0.0d0 |
382 |
depsjdx = 0.0d0 |
383 |
depsjdy = 0.0d0 |
384 |
depsjdz = 0.0d0 |
385 |
depsjdux = 0.0d0 |
386 |
depsjduy = 0.0d0 |
387 |
depsjduz = 0.0d0 |
388 |
|
389 |
do lm = 1, ShapeMap(me2)%nLMpairs |
390 |
|
391 |
l = ShapeMap(me2)%lValue(lm) |
392 |
m = ShapeMap(me2)%mValue(lm) |
393 |
|
394 |
slm = ShapeMap(me2)%contactFuncSinCoeff(lm) |
395 |
clm = ShapeMap(me2)%contactFuncCosCoeff(lm) |
396 |
|
397 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
398 |
|
399 |
dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
400 |
+ clm * dtm_j(m) * dcpjdx ) |
401 |
dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
402 |
+ clm * dtm_j(m) * dcpjdy ) |
403 |
dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
404 |
+ clm * dtm_j(m) * dcpjdz ) |
405 |
|
406 |
dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
407 |
+ clm * dtm_j(m) * dcpjdux |
408 |
dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
409 |
+ clm * dtm_j(m) * dcpjduy |
410 |
dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
411 |
+ clm * dtm_j(m) * dcpjduz |
412 |
|
413 |
sigma_j = sigma_j + plm_j(l,m)*Phunc |
414 |
|
415 |
dsigmajdx = dsigmajdx + plm_j(l,m)*dPhuncdX + & |
416 |
Phunc * dlm_j(l,m) * dctjdx |
417 |
dsigmajdy = dsigmajdy + plm_j(l,m)*dPhuncdY + & |
418 |
Phunc * dlm_j(l,m) * dctjdy |
419 |
dsigmajdz = dsigmajdz + plm_j(l,m)*dPhuncdZ + & |
420 |
Phunc * dlm_j(l,m) * dctjdz |
421 |
|
422 |
dsigmajdux = dsigmajdux + plm_j(l,m)* dPhuncdUx + & |
423 |
Phunc * dlm_j(l,m) * dctjdux |
424 |
dsigmajduy = dsigmajduy + plm_j(l,m)* dPhuncdUy + & |
425 |
Phunc * dlm_j(l,m) * dctjduy |
426 |
dsigmajduz = dsigmajduz + plm_j(l,m)* dPhuncdUz + & |
427 |
Phunc * dlm_j(l,m) * dctjduz |
428 |
|
429 |
slm = ShapeMap(me2)%rangeFuncSinCoeff(lm) |
430 |
clm = ShapeMap(me2)%rangeFuncCosCoeff(lm) |
431 |
|
432 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
433 |
|
434 |
dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
435 |
+ clm * dtm_j(m) * dcpjdx ) |
436 |
dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
437 |
+ clm * dtm_j(m) * dcpjdy ) |
438 |
dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
439 |
+ clm * dtm_j(m) * dcpjdz ) |
440 |
|
441 |
dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
442 |
+ clm * dtm_j(m) * dcpjdux |
443 |
dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
444 |
+ clm * dtm_j(m) * dcpjduy |
445 |
dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
446 |
+ clm * dtm_j(m) * dcpjduz |
447 |
|
448 |
s_j = s_j + plm_j(l,m)*Phunc |
449 |
|
450 |
dsjdx = dsjdx + plm_j(l,m)*dPhuncdX + & |
451 |
Phunc * dlm_j(l,m) * dctjdx |
452 |
dsjdy = dsjdy + plm_j(l,m)*dPhuncdY + & |
453 |
Phunc * dlm_j(l,m) * dctjdy |
454 |
dsjdz = dsjdz + plm_j(l,m)*dPhuncdZ + & |
455 |
Phunc * dlm_j(l,m) * dctjdz |
456 |
|
457 |
dsjdux = dsjdux + plm_j(l,m)* dPhuncdUx + & |
458 |
Phunc * dlm_j(l,m) * dctjdux |
459 |
dsjduy = dsjduy + plm_j(l,m)* dPhuncdUy + & |
460 |
Phunc * dlm_j(l,m) * dctjduy |
461 |
dsjduz = dsjduz + plm_j(l,m)* dPhuncdUz + & |
462 |
Phunc * dlm_j(l,m) * dctjduz |
463 |
|
464 |
slm = ShapeMap(me2)%strengthFuncSinCoeff(lm) |
465 |
clm = ShapeMap(me2)%strengthFuncCosCoeff(lm) |
466 |
|
467 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
468 |
|
469 |
dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
470 |
+ clm * dtm_j(m) * dcpjdx ) |
471 |
dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
472 |
+ clm * dtm_j(m) * dcpjdy ) |
473 |
dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
474 |
+ clm * dtm_j(m) * dcpjdz ) |
475 |
|
476 |
dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
477 |
+ clm * dtm_j(m) * dcpjdux |
478 |
dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
479 |
+ clm * dtm_j(m) * dcpjduy |
480 |
dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
481 |
+ clm * dtm_j(m) * dcpjduz |
482 |
|
483 |
eps_j = eps_j + plm_j(l,m)*Phunc |
484 |
|
485 |
depsjdx = depsjdx + plm_j(l,m)*dPhuncdX + & |
486 |
Phunc * dlm_j(l,m) * dctjdx |
487 |
depsjdy = depsjdy + plm_j(l,m)*dPhuncdY + & |
488 |
Phunc * dlm_j(l,m) * dctjdy |
489 |
depsjdz = depsjdz + plm_j(l,m)*dPhuncdZ + & |
490 |
Phunc * dlm_j(l,m) * dctjdz |
491 |
|
492 |
depsjdux = depsjdux + plm_j(l,m)* dPhuncdUx + & |
493 |
Phunc * dlm_j(l,m) * dctjdux |
494 |
depsjduy = depsjduy + plm_j(l,m)* dPhuncdUy + & |
495 |
Phunc * dlm_j(l,m) * dctjduy |
496 |
depsjduz = depsjduz + plm_j(l,m)* dPhuncdUz + & |
497 |
Phunc * dlm_j(l,m) * dctjduz |
498 |
|
499 |
enddo |
500 |
endif |
501 |
|
502 |
! phew, now let's assemble the potential energy: |
503 |
|
504 |
|
505 |
sigma = 0.5*(sigma_i + sigma_j) |
506 |
|
507 |
dsigmadxi = 0.5*dsigmaidx |
508 |
dsigmadyi = 0.5*dsigmaidy |
509 |
dsigmadzi = 0.5*dsigmaidz |
510 |
dsigmaduxi = 0.5*dsigmaidux |
511 |
dsigmaduyi = 0.5*dsigmaiduy |
512 |
dsigmaduzi = 0.5*dsigmaiduz |
513 |
|
514 |
dsigmadxj = 0.5*dsigmajdx |
515 |
dsigmadyj = 0.5*dsigmajdy |
516 |
dsigmadzj = 0.5*dsigmajdz |
517 |
dsigmaduxj = 0.5*dsigmajdux |
518 |
dsigmaduyj = 0.5*dsigmajduy |
519 |
dsigmaduzj = 0.5*dsigmajduz |
520 |
|
521 |
s = 0.5*(s_i + s_j) |
522 |
|
523 |
dsdxi = 0.5*dsidx |
524 |
dsdyi = 0.5*dsidy |
525 |
dsdzi = 0.5*dsidz |
526 |
dsduxi = 0.5*dsidux |
527 |
dsduyi = 0.5*dsiduy |
528 |
dsduzi = 0.5*dsiduz |
529 |
|
530 |
dsdxj = 0.5*dsjdx |
531 |
dsdyj = 0.5*dsjdy |
532 |
dsdzj = 0.5*dsjdz |
533 |
dsduxj = 0.5*dsjdux |
534 |
dsduyj = 0.5*dsjduy |
535 |
dsduzj = 0.5*dsjduz |
536 |
|
537 |
eps = sqrt(eps_i * eps_j) |
538 |
|
539 |
depsdxi = eps_j * depsidx / (2.0d0 * eps) |
540 |
depsdyi = eps_j * depsidy / (2.0d0 * eps) |
541 |
depsdzi = eps_j * depsidz / (2.0d0 * eps) |
542 |
depsduxi = eps_j * depsidux / (2.0d0 * eps) |
543 |
depsduyi = eps_j * depsiduy / (2.0d0 * eps) |
544 |
depsduzi = eps_j * depsiduz / (2.0d0 * eps) |
545 |
|
546 |
depsdxj = eps_i * depsjdx / (2.0d0 * eps) |
547 |
depsdyj = eps_i * depsjdy / (2.0d0 * eps) |
548 |
depsdzj = eps_i * depsjdz / (2.0d0 * eps) |
549 |
depsduxj = eps_i * depsjdux / (2.0d0 * eps) |
550 |
depsduyj = eps_i * depsjduy / (2.0d0 * eps) |
551 |
depsduzj = eps_i * depsjduz / (2.0d0 * eps) |
552 |
|
553 |
rtdenom = r-sigma+s |
554 |
rt = s / rtdenom |
555 |
|
556 |
drtdxi = (dsdxi + rt * (drdxi - dsigmadxi + dsdxi)) / rtdenom |
557 |
drtdyi = (dsdyi + rt * (drdyi - dsigmadyi + dsdyi)) / rtdenom |
558 |
drtdzi = (dsdzi + rt * (drdzi - dsigmadzi + dsdzi)) / rtdenom |
559 |
drtduxi = (dsduxi + rt * (drduxi - dsigmaduxi + dsduxi)) / rtdenom |
560 |
drtduyi = (dsduyi + rt * (drduyi - dsigmaduyi + dsduyi)) / rtdenom |
561 |
drtduzi = (dsduzi + rt * (drduzi - dsigmaduzi + dsduzi)) / rtdenom |
562 |
drtdxj = (dsdxj + rt * (drdxj - dsigmadxj + dsdxj)) / rtdenom |
563 |
drtdyj = (dsdyj + rt * (drdyj - dsigmadyj + dsdyj)) / rtdenom |
564 |
drtdzj = (dsdzj + rt * (drdzj - dsigmadzj + dsdzj)) / rtdenom |
565 |
drtduxj = (dsduxj + rt * (drduxj - dsigmaduxj + dsduxj)) / rtdenom |
566 |
drtduyj = (dsduyj + rt * (drduyj - dsigmaduyj + dsduyj)) / rtdenom |
567 |
drtduzj = (dsduzj + rt * (drduzj - dsigmaduzj + dsduzj)) / rtdenom |
568 |
|
569 |
rt2 = rt*rt |
570 |
rt3 = rt2*rt |
571 |
rt5 = rt2*rt3 |
572 |
rt6 = rt3*rt3 |
573 |
rt11 = rt5*rt6 |
574 |
rt12 = rt6*rt6 |
575 |
rt126 = rt12 - rt6 |
576 |
|
577 |
if (do_pot) then |
578 |
#ifdef IS_MPI |
579 |
pot_row(atom1) = pot_row(atom1) + 2.0d0*eps*rt126*sw |
580 |
pot_col(atom2) = pot_col(atom2) + 2.0d0*eps*rt126*sw |
581 |
#else |
582 |
pot = pot + 4.0d0*eps*rt126*sw |
583 |
endif |
584 |
|
585 |
dvdxi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdxi + 4.0d0*depsdxi*rt126 |
586 |
dvdyi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdyi + 4.0d0*depsdyi*rt126 |
587 |
dvdzi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdzi + 4.0d0*depsdzi*rt126 |
588 |
dvduxi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduxi + 4.0d0*depsduxi*rt126 |
589 |
dvduyi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduyi + 4.0d0*depsduyi*rt126 |
590 |
dvduzi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduzi + 4.0d0*depsduzi*rt126 |
591 |
|
592 |
dvdxj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdxj + 4.0d0*depsdxj*rt126 |
593 |
dvdyj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdyj + 4.0d0*depsdyj*rt126 |
594 |
dvdzj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdzj + 4.0d0*depsdzj*rt126 |
595 |
dvduxj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduxj + 4.0d0*depsduxj*rt126 |
596 |
dvduyj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduyj + 4.0d0*depsduyj*rt126 |
597 |
dvduzj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduzj + 4.0d0*depsduzj*rt126 |
598 |
|
599 |
! do the torques first since they are easy: |
600 |
! remember that these are still in the body fixed axes |
601 |
|
602 |
txi = dvduxi * sw |
603 |
tyi = dvduyi * sw |
604 |
tzi = dvduzi * sw |
605 |
|
606 |
txj = dvduxj * sw |
607 |
tyj = dvduyj * sw |
608 |
tzj = dvduzj * sw |
609 |
|
610 |
! go back to lab frame using transpose of rotation matrix: |
611 |
|
612 |
#ifdef IS_MPI |
613 |
t_Row(1,atom1) = t_Row(1,atom1) + a_Row(1,atom1)*txi + & |
614 |
a_Row(4,atom1)*tyi + a_Row(7,atom1)*tzi |
615 |
t_Row(2,atom1) = t_Row(2,atom1) + a_Row(2,atom1)*txi + & |
616 |
a_Row(5,atom1)*tyi + a_Row(8,atom1)*tzi |
617 |
t_Row(3,atom1) = t_Row(3,atom1) + a_Row(3,atom1)*txi + & |
618 |
a_Row(6,atom1)*tyi + a_Row(9,atom1)*tzi |
619 |
|
620 |
t_Col(1,atom2) = t_Col(1,atom2) + a_Col(1,atom2)*txj + & |
621 |
a_Col(4,atom2)*tyj + a_Col(7,atom2)*tzj |
622 |
t_Col(2,atom2) = t_Col(2,atom2) + a_Col(2,atom2)*txj + & |
623 |
a_Col(5,atom2)*tyj + a_Col(8,atom2)*tzj |
624 |
t_Col(3,atom2) = t_Col(3,atom2) + a_Col(3,atom2)*txj + & |
625 |
a_Col(6,atom2)*tyj + a_Col(9,atom2)*tzj |
626 |
#else |
627 |
t(1,atom1) = t(1,atom1) + a(1,atom1)*txi + a(4,atom1)*tyi + a(7,atom1)*tzi |
628 |
t(2,atom1) = t(2,atom1) + a(2,atom1)*txi + a(5,atom1)*tyi + a(8,atom1)*tzi |
629 |
t(3,atom1) = t(3,atom1) + a(3,atom1)*txi + a(6,atom1)*tyi + a(9,atom1)*tzi |
630 |
|
631 |
t(1,atom2) = t(1,atom2) + a(1,atom2)*txj + a(4,atom2)*tyj + a(7,atom2)*tzj |
632 |
t(2,atom2) = t(2,atom2) + a(2,atom2)*txj + a(5,atom2)*tyj + a(8,atom2)*tzj |
633 |
t(3,atom2) = t(3,atom2) + a(3,atom2)*txj + a(6,atom2)*tyj + a(9,atom2)*tzj |
634 |
#endif |
635 |
! Now, on to the forces: |
636 |
|
637 |
! first rotate the i terms back into the lab frame: |
638 |
|
639 |
fxi = dvdxi * sw |
640 |
fyi = dvdyi * sw |
641 |
fzi = dvdzi * sw |
642 |
|
643 |
fxj = dvdxj * sw |
644 |
fyj = dvdyj * sw |
645 |
fzj = dvdzj * sw |
646 |
|
647 |
#ifdef IS_MPI |
648 |
fxii = a_Row(1,atom1)*fxi + a_Row(4,atom1)*fyi + a_Row(7,atom1)*fzi |
649 |
fyii = a_Row(2,atom1)*fxi + a_Row(5,atom1)*fyi + a_Row(8,atom1)*fzi |
650 |
fzii = a_Row(3,atom1)*fxi + a_Row(6,atom1)*fyi + a_Row(9,atom1)*fzi |
651 |
|
652 |
fxjj = a_Col(1,atom2)*fxj + a_Col(4,atom2)*fyj + a_Col(7,atom2)*fzj |
653 |
fyjj = a_Col(2,atom2)*fxj + a_Col(5,atom2)*fyj + a_Col(8,atom2)*fzj |
654 |
fzjj = a_Col(3,atom2)*fxj + a_Col(6,atom2)*fyj + a_Col(9,atom2)*fzj |
655 |
#else |
656 |
fxii = a(1,atom1)*fxi + a(4,atom1)*fyi + a(7,atom1)*fzi |
657 |
fyii = a(2,atom1)*fxi + a(5,atom1)*fyi + a(8,atom1)*fzi |
658 |
fzii = a(3,atom1)*fxi + a(6,atom1)*fyi + a(9,atom1)*fzi |
659 |
|
660 |
fxjj = a(1,atom2)*fxj + a(4,atom2)*fyj + a(7,atom2)*fzj |
661 |
fyjj = a(2,atom2)*fxj + a(5,atom2)*fyj + a(8,atom2)*fzj |
662 |
fzjj = a(3,atom2)*fxj + a(6,atom2)*fyj + a(9,atom2)*fzj |
663 |
#endif |
664 |
|
665 |
fxij = -fxii |
666 |
fyij = -fyii |
667 |
fzij = -fzii |
668 |
|
669 |
fxji = -fxjj |
670 |
fyji = -fyjj |
671 |
fzji = -fzjj |
672 |
|
673 |
fxradial = fxii + fxji |
674 |
fyradial = fyii + fyji |
675 |
fzradial = fzii + fzji |
676 |
|
677 |
#ifdef IS_MPI |
678 |
f_Row(1,atom1) = f_Row(1,atom1) + fxradial |
679 |
f_Row(2,atom1) = f_Row(2,atom1) + fyradial |
680 |
f_Row(3,atom1) = f_Row(3,atom1) + fzradial |
681 |
|
682 |
f_Col(1,atom2) = f_Col(1,atom2) - fxradial |
683 |
f_Col(2,atom2) = f_Col(2,atom2) - fyradial |
684 |
f_Col(3,atom2) = f_Col(3,atom2) - fzradial |
685 |
#else |
686 |
f(1,atom1) = f(1,atom1) + fxradial |
687 |
f(2,atom1) = f(2,atom1) + fyradial |
688 |
f(3,atom1) = f(3,atom1) + fzradial |
689 |
|
690 |
f(1,atom2) = f(1,atom2) - fxradial |
691 |
f(2,atom2) = f(2,atom2) - fyradial |
692 |
f(3,atom2) = f(3,atom2) - fzradial |
693 |
#endif |
694 |
|
695 |
#ifdef IS_MPI |
696 |
id1 = AtomRowToGlobal(atom1) |
697 |
id2 = AtomColToGlobal(atom2) |
698 |
#else |
699 |
id1 = atom1 |
700 |
id2 = atom2 |
701 |
#endif |
702 |
|
703 |
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
704 |
|
705 |
fpair(1) = fpair(1) + fxradial |
706 |
fpair(2) = fpair(2) + fyradial |
707 |
fpair(3) = fpair(3) + fzradial |
708 |
|
709 |
endif |
710 |
|
711 |
end subroutine do_shape_pair |
712 |
|
713 |
SUBROUTINE Associated_Legendre(x, l, m, lmax, plm, dlm) |
714 |
|
715 |
! Purpose: Compute the associated Legendre functions |
716 |
! Plm(x) and their derivatives Plm'(x) |
717 |
! Input : x --- Argument of Plm(x) |
718 |
! l --- Order of Plm(x), l = 0,1,2,...,n |
719 |
! m --- Degree of Plm(x), m = 0,1,2,...,N |
720 |
! lmax --- Physical dimension of PLM and DLM |
721 |
! Output: PLM(l,m) --- Plm(x) |
722 |
! DLM(l,m) --- Plm'(x) |
723 |
! |
724 |
! adapted from the routines in |
725 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
726 |
! ISBN 0-471-11963-6 |
727 |
! |
728 |
! The original Fortran77 codes can be found here: |
729 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
730 |
|
731 |
real (kind=8), intent(in) :: x |
732 |
integer, intent(in) :: l, m, lmax |
733 |
real (kind=8), dimension(0:lmax,0:m), intent(out) :: PLM, DLM |
734 |
integer :: i, j, ls |
735 |
real (kind=8) :: xq, xs |
736 |
|
737 |
! zero out both arrays: |
738 |
DO I = 0, m |
739 |
DO J = 0, l |
740 |
PLM(J,I) = 0.0D0 |
741 |
DLM(J,I) = 0.0D0 |
742 |
end DO |
743 |
end DO |
744 |
|
745 |
! start with 0,0: |
746 |
PLM(0,0) = 1.0D0 |
747 |
|
748 |
! x = +/- 1 functions are easy: |
749 |
IF (abs(X).EQ.1.0D0) THEN |
750 |
DO I = 1, m |
751 |
PLM(0, I) = X**I |
752 |
DLM(0, I) = 0.5D0*I*(I+1.0D0)*X**(I+1) |
753 |
end DO |
754 |
DO J = 1, m |
755 |
DO I = 1, l |
756 |
IF (I.EQ.1) THEN |
757 |
DLM(I, J) = 1.0D+300 |
758 |
ELSE IF (I.EQ.2) THEN |
759 |
DLM(I, J) = -0.25D0*(J+2)*(J+1)*J*(J-1)*X**(J+1) |
760 |
ENDIF |
761 |
end DO |
762 |
end DO |
763 |
RETURN |
764 |
ENDIF |
765 |
|
766 |
LS = 1 |
767 |
IF (abs(X).GT.1.0D0) LS = -1 |
768 |
XQ = sqrt(LS*(1.0D0-X*X)) |
769 |
XS = LS*(1.0D0-X*X) |
770 |
|
771 |
DO I = 1, l |
772 |
PLM(I, I) = -LS*(2.0D0*I-1.0D0)*XQ*PLM(I-1, I-1) |
773 |
enddo |
774 |
|
775 |
DO I = 0, l |
776 |
PLM(I, I+1)=(2.0D0*I+1.0D0)*X*PLM(I, I) |
777 |
enddo |
778 |
|
779 |
DO I = 0, l |
780 |
DO J = I+2, m |
781 |
PLM(I, J)=((2.0D0*J-1.0D0)*X*PLM(I,J-1) - & |
782 |
(I+J-1.0D0)*PLM(I,J-2))/(J-I) |
783 |
end DO |
784 |
end DO |
785 |
|
786 |
DLM(0, 0)=0.0D0 |
787 |
|
788 |
DO J = 1, m |
789 |
DLM(0, J)=LS*J*(PLM(0,J-1)-X*PLM(0,J))/XS |
790 |
end DO |
791 |
|
792 |
DO I = 1, l |
793 |
DO J = I, m |
794 |
DLM(I,J) = LS*I*X*PLM(I, J)/XS + (J+I)*(J-I+1.0D0)/XQ*PLM(I-1, J) |
795 |
end DO |
796 |
end DO |
797 |
|
798 |
RETURN |
799 |
END SUBROUTINE Associated_Legendre |
800 |
|
801 |
|
802 |
subroutine Orthogonal_Polynomial(x, m, function_type, pl, dpl) |
803 |
|
804 |
! Purpose: Compute orthogonal polynomials: Tn(x) or Un(x), |
805 |
! or Ln(x) or Hn(x), and their derivatives |
806 |
! Input : function_type --- Function code |
807 |
! =1 for Chebyshev polynomial Tn(x) |
808 |
! =2 for Chebyshev polynomial Un(x) |
809 |
! =3 for Laguerre polynomial Ln(x) |
810 |
! =4 for Hermite polynomial Hn(x) |
811 |
! n --- Order of orthogonal polynomials |
812 |
! x --- Argument of orthogonal polynomials |
813 |
! Output: PL(n) --- Tn(x) or Un(x) or Ln(x) or Hn(x) |
814 |
! DPL(n)--- Tn'(x) or Un'(x) or Ln'(x) or Hn'(x) |
815 |
! |
816 |
! adapted from the routines in |
817 |
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
818 |
! ISBN 0-471-11963-6 |
819 |
! |
820 |
! The original Fortran77 codes can be found here: |
821 |
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
822 |
|
823 |
real(kind=8), intent(in) :: x |
824 |
integer, intent(in):: m |
825 |
integer, intent(in):: function_type |
826 |
real(kind=8), dimension(0:m), intent(inout) :: pl, dpl |
827 |
|
828 |
real(kind=8) :: a, b, c, y0, y1, dy0, dy1, yn, dyn |
829 |
integer :: k |
830 |
|
831 |
A = 2.0D0 |
832 |
B = 0.0D0 |
833 |
C = 1.0D0 |
834 |
Y0 = 1.0D0 |
835 |
Y1 = 2.0D0*X |
836 |
DY0 = 0.0D0 |
837 |
DY1 = 2.0D0 |
838 |
PL(0) = 1.0D0 |
839 |
PL(1) = 2.0D0*X |
840 |
DPL(0) = 0.0D0 |
841 |
DPL(1) = 2.0D0 |
842 |
IF (function_type.EQ.CHEBYSHEV_TN) THEN |
843 |
Y1 = X |
844 |
DY1 = 1.0D0 |
845 |
PL(1) = X |
846 |
DPL(1) = 1.0D0 |
847 |
ELSE IF (function_type.EQ.LAGUERRE) THEN |
848 |
Y1 = 1.0D0-X |
849 |
DY1 = -1.0D0 |
850 |
PL(1) = 1.0D0-X |
851 |
DPL(1) = -1.0D0 |
852 |
ENDIF |
853 |
DO K = 2, m |
854 |
IF (function_type.EQ.LAGUERRE) THEN |
855 |
A = -1.0D0/K |
856 |
B = 2.0D0+A |
857 |
C = 1.0D0+A |
858 |
ELSE IF (function_type.EQ.HERMITE) THEN |
859 |
C = 2.0D0*(K-1.0D0) |
860 |
ENDIF |
861 |
YN = (A*X+B)*Y1-C*Y0 |
862 |
DYN = A*Y1+(A*X+B)*DY1-C*DY0 |
863 |
PL(K) = YN |
864 |
DPL(K) = DYN |
865 |
Y0 = Y1 |
866 |
Y1 = YN |
867 |
DY0 = DY1 |
868 |
DY1 = DYN |
869 |
end DO |
870 |
RETURN |
871 |
|
872 |
end subroutine Orthogonal_Polynomial |
873 |
|
874 |
end module shapes |