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- Committer: Package Import Robot
- Author(s): Johannes Ring
- Date: 2011-10-26 17:52:20 UTC
- mfrom: (1.1.10)
- Revision ID: package-import@ubuntu.com-20111026175220-ope1dzqv4jn2b8pq
Tags: 1.0-beta2-1
* New upstream release. This release includes some performance
improvements for evaluating basis functions. It also adds support
for Bessel functions and error functions.
* debian/control: Bump version numbers for python-ufc, python-fiat,
python-instant, and python-ufl.
improvements for evaluating basis functions. It also adds support
for Bessel functions and error functions.
* debian/control: Bump version numbers for python-ufc, python-fiat,
python-instant, and python-ufl.
- files modified:
- ChangeLog
added
removed
test/regression/references/r_auto/VectorLaplaceGradCurl.h
1
// This code conforms with the UFC specification version 2.0.0
2
// and was automatically generated by FFC version 1.0-beta.
1
// This code conforms with the UFC specification version 2.0.2
2
// and was automatically generated by FFC version 1.0-beta+.
3
3
//
4
4
// This code was generated with the following parameters:
5
5
//
149
149
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
150
150
151
151
// Declare helper variables.
152
unsigned int rr = 0;
153
unsigned int ss = 0;
154
unsigned int tt = 0;
155
double tmp5 = 0.0;
156
double tmp6 = 0.0;
157
double tmp7 = 0.0;
158
152
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
159
153
double tmp1 = 0.25*(Y + Z)*(Y + Z);
160
154
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
164
158
// Compute basisvalues.
165
159
basisvalues[0] = 1.0;
166
160
basisvalues[1] = tmp0;
167
for (unsigned int r = 1; r < 2; r++)
168
{
169
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
170
ss = r*(r + 1)*(r + 2)/6;
171
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
172
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
173
}// end loop over 'r'
174
for (unsigned int r = 0; r < 2; r++)
175
{
176
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
177
ss = r*(r + 1)*(r + 2)/6;
178
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
179
}// end loop over 'r'
180
for (unsigned int r = 0; r < 1; r++)
181
{
182
for (unsigned int s = 1; s < 2 - r; s++)
183
{
184
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
185
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
186
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
187
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
188
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
189
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
190
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
191
}// end loop over 's'
192
}// end loop over 'r'
193
for (unsigned int r = 0; r < 2; r++)
194
{
195
for (unsigned int s = 0; s < 2 - r; s++)
196
{
197
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
198
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
199
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
200
}// end loop over 's'
201
}// end loop over 'r'
202
for (unsigned int r = 0; r < 1; r++)
203
{
204
for (unsigned int s = 0; s < 1 - r; s++)
205
{
206
for (unsigned int t = 1; t < 2 - r - s; t++)
207
{
208
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
209
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
210
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
211
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
212
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
213
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
214
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
215
}// end loop over 't'
216
}// end loop over 's'
217
}// end loop over 'r'
218
for (unsigned int r = 0; r < 3; r++)
219
{
220
for (unsigned int s = 0; s < 3 - r; s++)
221
{
222
for (unsigned int t = 0; t < 3 - r - s; t++)
223
{
224
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
225
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
226
}// end loop over 't'
227
}// end loop over 's'
228
}// end loop over 'r'
161
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
162
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
163
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
164
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
165
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
166
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
167
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
168
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
169
basisvalues[0] *= std::sqrt(0.75);
170
basisvalues[3] *= std::sqrt(1.25);
171
basisvalues[9] *= std::sqrt(1.75);
172
basisvalues[2] *= std::sqrt(2.5);
173
basisvalues[8] *= std::sqrt(3.5);
174
basisvalues[7] *= std::sqrt(5.25);
175
basisvalues[1] *= std::sqrt(7.5);
176
basisvalues[6] *= std::sqrt(10.5);
177
basisvalues[5] *= std::sqrt(15.75);
178
basisvalues[4] *= std::sqrt(26.25);
229
179
230
180
// Table(s) of coefficients.
231
181
static const double coefficients0[10] = \
245
195
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
246
196
247
197
// Declare helper variables.
248
unsigned int rr = 0;
249
unsigned int ss = 0;
250
unsigned int tt = 0;
251
double tmp5 = 0.0;
252
double tmp6 = 0.0;
253
double tmp7 = 0.0;
254
198
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
255
199
double tmp1 = 0.25*(Y + Z)*(Y + Z);
256
200
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
260
204
// Compute basisvalues.
261
205
basisvalues[0] = 1.0;
262
206
basisvalues[1] = tmp0;
263
for (unsigned int r = 1; r < 2; r++)
264
{
265
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
266
ss = r*(r + 1)*(r + 2)/6;
267
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
268
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
269
}// end loop over 'r'
270
for (unsigned int r = 0; r < 2; r++)
271
{
272
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
273
ss = r*(r + 1)*(r + 2)/6;
274
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
275
}// end loop over 'r'
276
for (unsigned int r = 0; r < 1; r++)
277
{
278
for (unsigned int s = 1; s < 2 - r; s++)
279
{
280
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
281
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
282
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
283
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
284
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
285
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
286
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
287
}// end loop over 's'
288
}// end loop over 'r'
289
for (unsigned int r = 0; r < 2; r++)
290
{
291
for (unsigned int s = 0; s < 2 - r; s++)
292
{
293
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
294
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
295
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
296
}// end loop over 's'
297
}// end loop over 'r'
298
for (unsigned int r = 0; r < 1; r++)
299
{
300
for (unsigned int s = 0; s < 1 - r; s++)
301
{
302
for (unsigned int t = 1; t < 2 - r - s; t++)
303
{
304
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
305
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
306
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
307
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
308
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
309
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
310
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
311
}// end loop over 't'
312
}// end loop over 's'
313
}// end loop over 'r'
314
for (unsigned int r = 0; r < 3; r++)
315
{
316
for (unsigned int s = 0; s < 3 - r; s++)
317
{
318
for (unsigned int t = 0; t < 3 - r - s; t++)
319
{
320
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
321
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
322
}// end loop over 't'
323
}// end loop over 's'
324
}// end loop over 'r'
207
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
208
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
209
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
210
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
211
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
212
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
213
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
214
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
215
basisvalues[0] *= std::sqrt(0.75);
216
basisvalues[3] *= std::sqrt(1.25);
217
basisvalues[9] *= std::sqrt(1.75);
218
basisvalues[2] *= std::sqrt(2.5);
219
basisvalues[8] *= std::sqrt(3.5);
220
basisvalues[7] *= std::sqrt(5.25);
221
basisvalues[1] *= std::sqrt(7.5);
222
basisvalues[6] *= std::sqrt(10.5);
223
basisvalues[5] *= std::sqrt(15.75);
224
basisvalues[4] *= std::sqrt(26.25);
325
225
326
226
// Table(s) of coefficients.
327
227
static const double coefficients0[10] = \
341
241
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
342
242
343
243
// Declare helper variables.
344
unsigned int rr = 0;
345
unsigned int ss = 0;
346
unsigned int tt = 0;
347
double tmp5 = 0.0;
348
double tmp6 = 0.0;
349
double tmp7 = 0.0;
350
244
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
351
245
double tmp1 = 0.25*(Y + Z)*(Y + Z);
352
246
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
356
250
// Compute basisvalues.
357
251
basisvalues[0] = 1.0;
358
252
basisvalues[1] = tmp0;
359
for (unsigned int r = 1; r < 2; r++)
360
{
361
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
362
ss = r*(r + 1)*(r + 2)/6;
363
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
364
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
365
}// end loop over 'r'
366
for (unsigned int r = 0; r < 2; r++)
367
{
368
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
369
ss = r*(r + 1)*(r + 2)/6;
370
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
371
}// end loop over 'r'
372
for (unsigned int r = 0; r < 1; r++)
373
{
374
for (unsigned int s = 1; s < 2 - r; s++)
375
{
376
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
377
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
378
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
379
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
380
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
381
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
382
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
383
}// end loop over 's'
384
}// end loop over 'r'
385
for (unsigned int r = 0; r < 2; r++)
386
{
387
for (unsigned int s = 0; s < 2 - r; s++)
388
{
389
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
390
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
391
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
392
}// end loop over 's'
393
}// end loop over 'r'
394
for (unsigned int r = 0; r < 1; r++)
395
{
396
for (unsigned int s = 0; s < 1 - r; s++)
397
{
398
for (unsigned int t = 1; t < 2 - r - s; t++)
399
{
400
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
401
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
402
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
403
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
404
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
405
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
406
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
407
}// end loop over 't'
408
}// end loop over 's'
409
}// end loop over 'r'
410
for (unsigned int r = 0; r < 3; r++)
411
{
412
for (unsigned int s = 0; s < 3 - r; s++)
413
{
414
for (unsigned int t = 0; t < 3 - r - s; t++)
415
{
416
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
417
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
418
}// end loop over 't'
419
}// end loop over 's'
420
}// end loop over 'r'
253
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
254
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
255
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
256
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
257
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
258
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
259
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
260
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
261
basisvalues[0] *= std::sqrt(0.75);
262
basisvalues[3] *= std::sqrt(1.25);
263
basisvalues[9] *= std::sqrt(1.75);
264
basisvalues[2] *= std::sqrt(2.5);
265
basisvalues[8] *= std::sqrt(3.5);
266
basisvalues[7] *= std::sqrt(5.25);
267
basisvalues[1] *= std::sqrt(7.5);
268
basisvalues[6] *= std::sqrt(10.5);
269
basisvalues[5] *= std::sqrt(15.75);
270
basisvalues[4] *= std::sqrt(26.25);
421
271
422
272
// Table(s) of coefficients.
423
273
static const double coefficients0[10] = \
437
287
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
438
288
439
289
// Declare helper variables.
440
unsigned int rr = 0;
441
unsigned int ss = 0;
442
unsigned int tt = 0;
443
double tmp5 = 0.0;
444
double tmp6 = 0.0;
445
double tmp7 = 0.0;
446
290
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
447
291
double tmp1 = 0.25*(Y + Z)*(Y + Z);
448
292
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
452
296
// Compute basisvalues.
453
297
basisvalues[0] = 1.0;
454
298
basisvalues[1] = tmp0;
455
for (unsigned int r = 1; r < 2; r++)
456
{
457
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
458
ss = r*(r + 1)*(r + 2)/6;
459
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
460
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
461
}// end loop over 'r'
462
for (unsigned int r = 0; r < 2; r++)
463
{
464
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
465
ss = r*(r + 1)*(r + 2)/6;
466
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
467
}// end loop over 'r'
468
for (unsigned int r = 0; r < 1; r++)
469
{
470
for (unsigned int s = 1; s < 2 - r; s++)
471
{
472
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
473
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
474
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
475
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
476
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
477
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
478
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
479
}// end loop over 's'
480
}// end loop over 'r'
481
for (unsigned int r = 0; r < 2; r++)
482
{
483
for (unsigned int s = 0; s < 2 - r; s++)
484
{
485
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
486
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
487
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
488
}// end loop over 's'
489
}// end loop over 'r'
490
for (unsigned int r = 0; r < 1; r++)
491
{
492
for (unsigned int s = 0; s < 1 - r; s++)
493
{
494
for (unsigned int t = 1; t < 2 - r - s; t++)
495
{
496
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
497
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
498
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
499
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
500
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
501
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
502
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
503
}// end loop over 't'
504
}// end loop over 's'
505
}// end loop over 'r'
506
for (unsigned int r = 0; r < 3; r++)
507
{
508
for (unsigned int s = 0; s < 3 - r; s++)
509
{
510
for (unsigned int t = 0; t < 3 - r - s; t++)
511
{
512
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
513
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
514
}// end loop over 't'
515
}// end loop over 's'
516
}// end loop over 'r'
299
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
300
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
301
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
302
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
303
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
304
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
305
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
306
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
307
basisvalues[0] *= std::sqrt(0.75);
308
basisvalues[3] *= std::sqrt(1.25);
309
basisvalues[9] *= std::sqrt(1.75);
310
basisvalues[2] *= std::sqrt(2.5);
311
basisvalues[8] *= std::sqrt(3.5);
312
basisvalues[7] *= std::sqrt(5.25);
313
basisvalues[1] *= std::sqrt(7.5);
314
basisvalues[6] *= std::sqrt(10.5);
315
basisvalues[5] *= std::sqrt(15.75);
316
basisvalues[4] *= std::sqrt(26.25);
517
317
518
318
// Table(s) of coefficients.
519
319
static const double coefficients0[10] = \
533
333
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
534
334
535
335
// Declare helper variables.
536
unsigned int rr = 0;
537
unsigned int ss = 0;
538
unsigned int tt = 0;
539
double tmp5 = 0.0;
540
double tmp6 = 0.0;
541
double tmp7 = 0.0;
542
336
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
543
337
double tmp1 = 0.25*(Y + Z)*(Y + Z);
544
338
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
548
342
// Compute basisvalues.
549
343
basisvalues[0] = 1.0;
550
344
basisvalues[1] = tmp0;
551
for (unsigned int r = 1; r < 2; r++)
552
{
553
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
554
ss = r*(r + 1)*(r + 2)/6;
555
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
556
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
557
}// end loop over 'r'
558
for (unsigned int r = 0; r < 2; r++)
559
{
560
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
561
ss = r*(r + 1)*(r + 2)/6;
562
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
563
}// end loop over 'r'
564
for (unsigned int r = 0; r < 1; r++)
565
{
566
for (unsigned int s = 1; s < 2 - r; s++)
567
{
568
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
569
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
570
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
571
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
572
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
573
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
574
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
575
}// end loop over 's'
576
}// end loop over 'r'
577
for (unsigned int r = 0; r < 2; r++)
578
{
579
for (unsigned int s = 0; s < 2 - r; s++)
580
{
581
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
582
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
583
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
584
}// end loop over 's'
585
}// end loop over 'r'
586
for (unsigned int r = 0; r < 1; r++)
587
{
588
for (unsigned int s = 0; s < 1 - r; s++)
589
{
590
for (unsigned int t = 1; t < 2 - r - s; t++)
591
{
592
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
593
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
594
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
595
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
596
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
597
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
598
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
599
}// end loop over 't'
600
}// end loop over 's'
601
}// end loop over 'r'
602
for (unsigned int r = 0; r < 3; r++)
603
{
604
for (unsigned int s = 0; s < 3 - r; s++)
605
{
606
for (unsigned int t = 0; t < 3 - r - s; t++)
607
{
608
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
609
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
610
}// end loop over 't'
611
}// end loop over 's'
612
}// end loop over 'r'
345
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
346
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
347
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
348
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
349
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
350
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
351
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
352
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
353
basisvalues[0] *= std::sqrt(0.75);
354
basisvalues[3] *= std::sqrt(1.25);
355
basisvalues[9] *= std::sqrt(1.75);
356
basisvalues[2] *= std::sqrt(2.5);
357
basisvalues[8] *= std::sqrt(3.5);
358
basisvalues[7] *= std::sqrt(5.25);
359
basisvalues[1] *= std::sqrt(7.5);
360
basisvalues[6] *= std::sqrt(10.5);
361
basisvalues[5] *= std::sqrt(15.75);
362
basisvalues[4] *= std::sqrt(26.25);
613
363
614
364
// Table(s) of coefficients.
615
365
static const double coefficients0[10] = \
629
379
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
630
380
631
381
// Declare helper variables.
632
unsigned int rr = 0;
633
unsigned int ss = 0;
634
unsigned int tt = 0;
635
double tmp5 = 0.0;
636
double tmp6 = 0.0;
637
double tmp7 = 0.0;
638
382
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
639
383
double tmp1 = 0.25*(Y + Z)*(Y + Z);
640
384
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
644
388
// Compute basisvalues.
645
389
basisvalues[0] = 1.0;
646
390
basisvalues[1] = tmp0;
647
for (unsigned int r = 1; r < 2; r++)
648
{
649
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
650
ss = r*(r + 1)*(r + 2)/6;
651
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
652
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
653
}// end loop over 'r'
654
for (unsigned int r = 0; r < 2; r++)
655
{
656
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
657
ss = r*(r + 1)*(r + 2)/6;
658
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
659
}// end loop over 'r'
660
for (unsigned int r = 0; r < 1; r++)
661
{
662
for (unsigned int s = 1; s < 2 - r; s++)
663
{
664
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
665
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
666
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
667
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
668
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
669
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
670
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
671
}// end loop over 's'
672
}// end loop over 'r'
673
for (unsigned int r = 0; r < 2; r++)
674
{
675
for (unsigned int s = 0; s < 2 - r; s++)
676
{
677
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
678
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
679
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
680
}// end loop over 's'
681
}// end loop over 'r'
682
for (unsigned int r = 0; r < 1; r++)
683
{
684
for (unsigned int s = 0; s < 1 - r; s++)
685
{
686
for (unsigned int t = 1; t < 2 - r - s; t++)
687
{
688
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
689
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
690
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
691
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
692
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
693
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
694
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
695
}// end loop over 't'
696
}// end loop over 's'
697
}// end loop over 'r'
698
for (unsigned int r = 0; r < 3; r++)
699
{
700
for (unsigned int s = 0; s < 3 - r; s++)
701
{
702
for (unsigned int t = 0; t < 3 - r - s; t++)
703
{
704
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
705
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
706
}// end loop over 't'
707
}// end loop over 's'
708
}// end loop over 'r'
391
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
392
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
393
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
394
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
395
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
396
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
397
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
398
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
399
basisvalues[0] *= std::sqrt(0.75);
400
basisvalues[3] *= std::sqrt(1.25);
401
basisvalues[9] *= std::sqrt(1.75);
402
basisvalues[2] *= std::sqrt(2.5);
403
basisvalues[8] *= std::sqrt(3.5);
404
basisvalues[7] *= std::sqrt(5.25);
405
basisvalues[1] *= std::sqrt(7.5);
406
basisvalues[6] *= std::sqrt(10.5);
407
basisvalues[5] *= std::sqrt(15.75);
408
basisvalues[4] *= std::sqrt(26.25);
709
409
710
410
// Table(s) of coefficients.
711
411
static const double coefficients0[10] = \
725
425
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
726
426
727
427
// Declare helper variables.
728
unsigned int rr = 0;
729
unsigned int ss = 0;
730
unsigned int tt = 0;
731
double tmp5 = 0.0;
732
double tmp6 = 0.0;
733
double tmp7 = 0.0;
734
428
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
735
429
double tmp1 = 0.25*(Y + Z)*(Y + Z);
736
430
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
740
434
// Compute basisvalues.
741
435
basisvalues[0] = 1.0;
742
436
basisvalues[1] = tmp0;
743
for (unsigned int r = 1; r < 2; r++)
744
{
745
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
746
ss = r*(r + 1)*(r + 2)/6;
747
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
748
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
749
}// end loop over 'r'
750
for (unsigned int r = 0; r < 2; r++)
751
{
752
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
753
ss = r*(r + 1)*(r + 2)/6;
754
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
755
}// end loop over 'r'
756
for (unsigned int r = 0; r < 1; r++)
757
{
758
for (unsigned int s = 1; s < 2 - r; s++)
759
{
760
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
761
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
762
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
763
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
764
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
765
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
766
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
767
}// end loop over 's'
768
}// end loop over 'r'
769
for (unsigned int r = 0; r < 2; r++)
770
{
771
for (unsigned int s = 0; s < 2 - r; s++)
772
{
773
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
774
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
775
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
776
}// end loop over 's'
777
}// end loop over 'r'
778
for (unsigned int r = 0; r < 1; r++)
779
{
780
for (unsigned int s = 0; s < 1 - r; s++)
781
{
782
for (unsigned int t = 1; t < 2 - r - s; t++)
783
{
784
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
785
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
786
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
787
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
788
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
789
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
790
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
791
}// end loop over 't'
792
}// end loop over 's'
793
}// end loop over 'r'
794
for (unsigned int r = 0; r < 3; r++)
795
{
796
for (unsigned int s = 0; s < 3 - r; s++)
797
{
798
for (unsigned int t = 0; t < 3 - r - s; t++)
799
{
800
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
801
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
802
}// end loop over 't'
803
}// end loop over 's'
804
}// end loop over 'r'
437
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
438
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
439
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
440
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
441
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
442
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
443
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
444
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
445
basisvalues[0] *= std::sqrt(0.75);
446
basisvalues[3] *= std::sqrt(1.25);
447
basisvalues[9] *= std::sqrt(1.75);
448
basisvalues[2] *= std::sqrt(2.5);
449
basisvalues[8] *= std::sqrt(3.5);
450
basisvalues[7] *= std::sqrt(5.25);
451
basisvalues[1] *= std::sqrt(7.5);
452
basisvalues[6] *= std::sqrt(10.5);
453
basisvalues[5] *= std::sqrt(15.75);
454
basisvalues[4] *= std::sqrt(26.25);
805
455
806
456
// Table(s) of coefficients.
807
457
static const double coefficients0[10] = \
821
471
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
822
472
823
473
// Declare helper variables.
824
unsigned int rr = 0;
825
unsigned int ss = 0;
826
unsigned int tt = 0;
827
double tmp5 = 0.0;
828
double tmp6 = 0.0;
829
double tmp7 = 0.0;
830
474
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
831
475
double tmp1 = 0.25*(Y + Z)*(Y + Z);
832
476
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
836
480
// Compute basisvalues.
837
481
basisvalues[0] = 1.0;
838
482
basisvalues[1] = tmp0;
839
for (unsigned int r = 1; r < 2; r++)
840
{
841
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
842
ss = r*(r + 1)*(r + 2)/6;
843
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
844
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
845
}// end loop over 'r'
846
for (unsigned int r = 0; r < 2; r++)
847
{
848
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
849
ss = r*(r + 1)*(r + 2)/6;
850
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
851
}// end loop over 'r'
852
for (unsigned int r = 0; r < 1; r++)
853
{
854
for (unsigned int s = 1; s < 2 - r; s++)
855
{
856
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
857
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
858
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
859
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
860
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
861
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
862
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
863
}// end loop over 's'
864
}// end loop over 'r'
865
for (unsigned int r = 0; r < 2; r++)
866
{
867
for (unsigned int s = 0; s < 2 - r; s++)
868
{
869
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
870
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
871
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
872
}// end loop over 's'
873
}// end loop over 'r'
874
for (unsigned int r = 0; r < 1; r++)
875
{
876
for (unsigned int s = 0; s < 1 - r; s++)
877
{
878
for (unsigned int t = 1; t < 2 - r - s; t++)
879
{
880
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
881
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
882
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
883
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
884
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
885
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
886
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
887
}// end loop over 't'
888
}// end loop over 's'
889
}// end loop over 'r'
890
for (unsigned int r = 0; r < 3; r++)
891
{
892
for (unsigned int s = 0; s < 3 - r; s++)
893
{
894
for (unsigned int t = 0; t < 3 - r - s; t++)
895
{
896
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
897
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
898
}// end loop over 't'
899
}// end loop over 's'
900
}// end loop over 'r'
483
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
484
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
485
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
486
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
487
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
488
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
489
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
490
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
491
basisvalues[0] *= std::sqrt(0.75);
492
basisvalues[3] *= std::sqrt(1.25);
493
basisvalues[9] *= std::sqrt(1.75);
494
basisvalues[2] *= std::sqrt(2.5);
495
basisvalues[8] *= std::sqrt(3.5);
496
basisvalues[7] *= std::sqrt(5.25);
497
basisvalues[1] *= std::sqrt(7.5);
498
basisvalues[6] *= std::sqrt(10.5);
499
basisvalues[5] *= std::sqrt(15.75);
500
basisvalues[4] *= std::sqrt(26.25);
901
501
902
502
// Table(s) of coefficients.
903
503
static const double coefficients0[10] = \
917
517
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
918
518
919
519
// Declare helper variables.
920
unsigned int rr = 0;
921
unsigned int ss = 0;
922
unsigned int tt = 0;
923
double tmp5 = 0.0;
924
double tmp6 = 0.0;
925
double tmp7 = 0.0;
926
520
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
927
521
double tmp1 = 0.25*(Y + Z)*(Y + Z);
928
522
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
932
526
// Compute basisvalues.
933
527
basisvalues[0] = 1.0;
934
528
basisvalues[1] = tmp0;
935
for (unsigned int r = 1; r < 2; r++)
936
{
937
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
938
ss = r*(r + 1)*(r + 2)/6;
939
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
940
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
941
}// end loop over 'r'
942
for (unsigned int r = 0; r < 2; r++)
943
{
944
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
945
ss = r*(r + 1)*(r + 2)/6;
946
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
947
}// end loop over 'r'
948
for (unsigned int r = 0; r < 1; r++)
949
{
950
for (unsigned int s = 1; s < 2 - r; s++)
951
{
952
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
953
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
954
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
955
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
956
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
957
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
958
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
959
}// end loop over 's'
960
}// end loop over 'r'
961
for (unsigned int r = 0; r < 2; r++)
962
{
963
for (unsigned int s = 0; s < 2 - r; s++)
964
{
965
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
966
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
967
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
968
}// end loop over 's'
969
}// end loop over 'r'
970
for (unsigned int r = 0; r < 1; r++)
971
{
972
for (unsigned int s = 0; s < 1 - r; s++)
973
{
974
for (unsigned int t = 1; t < 2 - r - s; t++)
975
{
976
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
977
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
978
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
979
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
980
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
981
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
982
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
983
}// end loop over 't'
984
}// end loop over 's'
985
}// end loop over 'r'
986
for (unsigned int r = 0; r < 3; r++)
987
{
988
for (unsigned int s = 0; s < 3 - r; s++)
989
{
990
for (unsigned int t = 0; t < 3 - r - s; t++)
991
{
992
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
993
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
994
}// end loop over 't'
995
}// end loop over 's'
996
}// end loop over 'r'
529
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
530
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
531
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
532
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
533
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
534
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
535
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
536
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
537
basisvalues[0] *= std::sqrt(0.75);
538
basisvalues[3] *= std::sqrt(1.25);
539
basisvalues[9] *= std::sqrt(1.75);
540
basisvalues[2] *= std::sqrt(2.5);
541
basisvalues[8] *= std::sqrt(3.5);
542
basisvalues[7] *= std::sqrt(5.25);
543
basisvalues[1] *= std::sqrt(7.5);
544
basisvalues[6] *= std::sqrt(10.5);
545
basisvalues[5] *= std::sqrt(15.75);
546
basisvalues[4] *= std::sqrt(26.25);
997
547
998
548
// Table(s) of coefficients.
999
549
static const double coefficients0[10] = \
1013
563
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1014
564
1015
565
// Declare helper variables.
1016
unsigned int rr = 0;
1017
unsigned int ss = 0;
1018
unsigned int tt = 0;
1019
double tmp5 = 0.0;
1020
double tmp6 = 0.0;
1021
double tmp7 = 0.0;
1022
566
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
1023
567
double tmp1 = 0.25*(Y + Z)*(Y + Z);
1024
568
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
1028
572
// Compute basisvalues.
1029
573
basisvalues[0] = 1.0;
1030
574
basisvalues[1] = tmp0;
1031
for (unsigned int r = 1; r < 2; r++)
1032
{
1033
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1034
ss = r*(r + 1)*(r + 2)/6;
1035
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1036
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
1037
}// end loop over 'r'
1038
for (unsigned int r = 0; r < 2; r++)
1039
{
1040
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1041
ss = r*(r + 1)*(r + 2)/6;
1042
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
1043
}// end loop over 'r'
1044
for (unsigned int r = 0; r < 1; r++)
1045
{
1046
for (unsigned int s = 1; s < 2 - r; s++)
1047
{
1048
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1049
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1050
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1051
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
1052
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1053
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1054
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1055
}// end loop over 's'
1056
}// end loop over 'r'
1057
for (unsigned int r = 0; r < 2; r++)
1058
{
1059
for (unsigned int s = 0; s < 2 - r; s++)
1060
{
1061
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1062
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1063
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
1064
}// end loop over 's'
1065
}// end loop over 'r'
1066
for (unsigned int r = 0; r < 1; r++)
1067
{
1068
for (unsigned int s = 0; s < 1 - r; s++)
1069
{
1070
for (unsigned int t = 1; t < 2 - r - s; t++)
1071
{
1072
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1073
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1074
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1075
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
1076
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1077
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1078
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1079
}// end loop over 't'
1080
}// end loop over 's'
1081
}// end loop over 'r'
1082
for (unsigned int r = 0; r < 3; r++)
1083
{
1084
for (unsigned int s = 0; s < 3 - r; s++)
1085
{
1086
for (unsigned int t = 0; t < 3 - r - s; t++)
1087
{
1088
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1089
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
1090
}// end loop over 't'
1091
}// end loop over 's'
1092
}// end loop over 'r'
575
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
576
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
577
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
578
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
579
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
580
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
581
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
582
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
583
basisvalues[0] *= std::sqrt(0.75);
584
basisvalues[3] *= std::sqrt(1.25);
585
basisvalues[9] *= std::sqrt(1.75);
586
basisvalues[2] *= std::sqrt(2.5);
587
basisvalues[8] *= std::sqrt(3.5);
588
basisvalues[7] *= std::sqrt(5.25);
589
basisvalues[1] *= std::sqrt(7.5);
590
basisvalues[6] *= std::sqrt(10.5);
591
basisvalues[5] *= std::sqrt(15.75);
592
basisvalues[4] *= std::sqrt(26.25);
1093
593
1094
594
// Table(s) of coefficients.
1095
595
static const double coefficients0[10] = \
1252
752
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1253
753
1254
754
// Declare helper variables.
1255
unsigned int rr = 0;
1256
unsigned int ss = 0;
1257
unsigned int tt = 0;
1258
double tmp5 = 0.0;
1259
double tmp6 = 0.0;
1260
double tmp7 = 0.0;
1261
755
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
1262
756
double tmp1 = 0.25*(Y + Z)*(Y + Z);
1263
757
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
1267
761
// Compute basisvalues.
1268
762
basisvalues[0] = 1.0;
1269
763
basisvalues[1] = tmp0;
1270
for (unsigned int r = 1; r < 2; r++)
1271
{
1272
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1273
ss = r*(r + 1)*(r + 2)/6;
1274
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1275
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
1276
}// end loop over 'r'
1277
for (unsigned int r = 0; r < 2; r++)
1278
{
1279
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1280
ss = r*(r + 1)*(r + 2)/6;
1281
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
1282
}// end loop over 'r'
1283
for (unsigned int r = 0; r < 1; r++)
1284
{
1285
for (unsigned int s = 1; s < 2 - r; s++)
1286
{
1287
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1288
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1289
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1290
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
1291
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1292
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1293
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1294
}// end loop over 's'
1295
}// end loop over 'r'
1296
for (unsigned int r = 0; r < 2; r++)
1297
{
1298
for (unsigned int s = 0; s < 2 - r; s++)
1299
{
1300
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1301
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1302
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
1303
}// end loop over 's'
1304
}// end loop over 'r'
1305
for (unsigned int r = 0; r < 1; r++)
1306
{
1307
for (unsigned int s = 0; s < 1 - r; s++)
1308
{
1309
for (unsigned int t = 1; t < 2 - r - s; t++)
1310
{
1311
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1312
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1313
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1314
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
1315
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1316
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1317
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1318
}// end loop over 't'
1319
}// end loop over 's'
1320
}// end loop over 'r'
1321
for (unsigned int r = 0; r < 3; r++)
1322
{
1323
for (unsigned int s = 0; s < 3 - r; s++)
1324
{
1325
for (unsigned int t = 0; t < 3 - r - s; t++)
1326
{
1327
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1328
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
1329
}// end loop over 't'
1330
}// end loop over 's'
1331
}// end loop over 'r'
764
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
765
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
766
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
767
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
768
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
769
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
770
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
771
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
772
basisvalues[0] *= std::sqrt(0.75);
773
basisvalues[3] *= std::sqrt(1.25);
774
basisvalues[9] *= std::sqrt(1.75);
775
basisvalues[2] *= std::sqrt(2.5);
776
basisvalues[8] *= std::sqrt(3.5);
777
basisvalues[7] *= std::sqrt(5.25);
778
basisvalues[1] *= std::sqrt(7.5);
779
basisvalues[6] *= std::sqrt(10.5);
780
basisvalues[5] *= std::sqrt(15.75);
781
basisvalues[4] *= std::sqrt(26.25);
1332
782
1333
783
// Table(s) of coefficients.
1334
784
static const double coefficients0[10] = \
1520
970
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1521
971
1522
972
// Declare helper variables.
1523
unsigned int rr = 0;
1524
unsigned int ss = 0;
1525
unsigned int tt = 0;
1526
double tmp5 = 0.0;
1527
double tmp6 = 0.0;
1528
double tmp7 = 0.0;
1529
973
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
1530
974
double tmp1 = 0.25*(Y + Z)*(Y + Z);
1531
975
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
1535
979
// Compute basisvalues.
1536
980
basisvalues[0] = 1.0;
1537
981
basisvalues[1] = tmp0;
1538
for (unsigned int r = 1; r < 2; r++)
1539
{
1540
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1541
ss = r*(r + 1)*(r + 2)/6;
1542
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1543
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
1544
}// end loop over 'r'
1545
for (unsigned int r = 0; r < 2; r++)
1546
{
1547
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1548
ss = r*(r + 1)*(r + 2)/6;
1549
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
1550
}// end loop over 'r'
1551
for (unsigned int r = 0; r < 1; r++)
1552
{
1553
for (unsigned int s = 1; s < 2 - r; s++)
1554
{
1555
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1556
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1557
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1558
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
1559
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1560
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1561
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1562
}// end loop over 's'
1563
}// end loop over 'r'
1564
for (unsigned int r = 0; r < 2; r++)
1565
{
1566
for (unsigned int s = 0; s < 2 - r; s++)
1567
{
1568
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1569
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1570
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
1571
}// end loop over 's'
1572
}// end loop over 'r'
1573
for (unsigned int r = 0; r < 1; r++)
1574
{
1575
for (unsigned int s = 0; s < 1 - r; s++)
1576
{
1577
for (unsigned int t = 1; t < 2 - r - s; t++)
1578
{
1579
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1580
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1581
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1582
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
1583
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1584
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1585
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1586
}// end loop over 't'
1587
}// end loop over 's'
1588
}// end loop over 'r'
1589
for (unsigned int r = 0; r < 3; r++)
1590
{
1591
for (unsigned int s = 0; s < 3 - r; s++)
1592
{
1593
for (unsigned int t = 0; t < 3 - r - s; t++)
1594
{
1595
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1596
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
1597
}// end loop over 't'
1598
}// end loop over 's'
1599
}// end loop over 'r'
982
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
983
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
984
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
985
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
986
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
987
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
988
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
989
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
990
basisvalues[0] *= std::sqrt(0.75);
991
basisvalues[3] *= std::sqrt(1.25);
992
basisvalues[9] *= std::sqrt(1.75);
993
basisvalues[2] *= std::sqrt(2.5);
994
basisvalues[8] *= std::sqrt(3.5);
995
basisvalues[7] *= std::sqrt(5.25);
996
basisvalues[1] *= std::sqrt(7.5);
997
basisvalues[6] *= std::sqrt(10.5);
998
basisvalues[5] *= std::sqrt(15.75);
999
basisvalues[4] *= std::sqrt(26.25);
1600
1000
1601
1001
// Table(s) of coefficients.
1602
1002
static const double coefficients0[10] = \
1788
1188
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1789
1189
1790
1190
// Declare helper variables.
1791
unsigned int rr = 0;
1792
unsigned int ss = 0;
1793
unsigned int tt = 0;
1794
double tmp5 = 0.0;
1795
double tmp6 = 0.0;
1796
double tmp7 = 0.0;
1797
1191
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
1798
1192
double tmp1 = 0.25*(Y + Z)*(Y + Z);
1799
1193
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
1803
1197
// Compute basisvalues.
1804
1198
basisvalues[0] = 1.0;
1805
1199
basisvalues[1] = tmp0;
1806
for (unsigned int r = 1; r < 2; r++)
1807
{
1808
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
1809
ss = r*(r + 1)*(r + 2)/6;
1810
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
1811
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
1812
}// end loop over 'r'
1813
for (unsigned int r = 0; r < 2; r++)
1814
{
1815
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
1816
ss = r*(r + 1)*(r + 2)/6;
1817
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
1818
}// end loop over 'r'
1819
for (unsigned int r = 0; r < 1; r++)
1820
{
1821
for (unsigned int s = 1; s < 2 - r; s++)
1822
{
1823
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
1824
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1825
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
1826
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
1827
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1828
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
1829
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
1830
}// end loop over 's'
1831
}// end loop over 'r'
1832
for (unsigned int r = 0; r < 2; r++)
1833
{
1834
for (unsigned int s = 0; s < 2 - r; s++)
1835
{
1836
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
1837
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
1838
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
1839
}// end loop over 's'
1840
}// end loop over 'r'
1841
for (unsigned int r = 0; r < 1; r++)
1842
{
1843
for (unsigned int s = 0; s < 1 - r; s++)
1844
{
1845
for (unsigned int t = 1; t < 2 - r - s; t++)
1846
{
1847
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
1848
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1849
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
1850
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
1851
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1852
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
1853
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
1854
}// end loop over 't'
1855
}// end loop over 's'
1856
}// end loop over 'r'
1857
for (unsigned int r = 0; r < 3; r++)
1858
{
1859
for (unsigned int s = 0; s < 3 - r; s++)
1860
{
1861
for (unsigned int t = 0; t < 3 - r - s; t++)
1862
{
1863
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
1864
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
1865
}// end loop over 't'
1866
}// end loop over 's'
1867
}// end loop over 'r'
1200
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
1201
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
1202
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
1203
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
1204
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
1205
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
1206
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
1207
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
1208
basisvalues[0] *= std::sqrt(0.75);
1209
basisvalues[3] *= std::sqrt(1.25);
1210
basisvalues[9] *= std::sqrt(1.75);
1211
basisvalues[2] *= std::sqrt(2.5);
1212
basisvalues[8] *= std::sqrt(3.5);
1213
basisvalues[7] *= std::sqrt(5.25);
1214
basisvalues[1] *= std::sqrt(7.5);
1215
basisvalues[6] *= std::sqrt(10.5);
1216
basisvalues[5] *= std::sqrt(15.75);
1217
basisvalues[4] *= std::sqrt(26.25);
1868
1218
1869
1219
// Table(s) of coefficients.
1870
1220
static const double coefficients0[10] = \
2056
1406
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2057
1407
2058
1408
// Declare helper variables.
2059
unsigned int rr = 0;
2060
unsigned int ss = 0;
2061
unsigned int tt = 0;
2062
double tmp5 = 0.0;
2063
double tmp6 = 0.0;
2064
double tmp7 = 0.0;
2065
1409
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
2066
1410
double tmp1 = 0.25*(Y + Z)*(Y + Z);
2067
1411
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
2071
1415
// Compute basisvalues.
2072
1416
basisvalues[0] = 1.0;
2073
1417
basisvalues[1] = tmp0;
2074
for (unsigned int r = 1; r < 2; r++)
2075
{
2076
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2077
ss = r*(r + 1)*(r + 2)/6;
2078
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2079
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
2080
}// end loop over 'r'
2081
for (unsigned int r = 0; r < 2; r++)
2082
{
2083
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2084
ss = r*(r + 1)*(r + 2)/6;
2085
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
2086
}// end loop over 'r'
2087
for (unsigned int r = 0; r < 1; r++)
2088
{
2089
for (unsigned int s = 1; s < 2 - r; s++)
2090
{
2091
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2092
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2093
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2094
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
2095
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2096
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2097
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2098
}// end loop over 's'
2099
}// end loop over 'r'
2100
for (unsigned int r = 0; r < 2; r++)
2101
{
2102
for (unsigned int s = 0; s < 2 - r; s++)
2103
{
2104
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2105
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2106
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
2107
}// end loop over 's'
2108
}// end loop over 'r'
2109
for (unsigned int r = 0; r < 1; r++)
2110
{
2111
for (unsigned int s = 0; s < 1 - r; s++)
2112
{
2113
for (unsigned int t = 1; t < 2 - r - s; t++)
2114
{
2115
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2116
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2117
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2118
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
2119
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2120
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2121
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2122
}// end loop over 't'
2123
}// end loop over 's'
2124
}// end loop over 'r'
2125
for (unsigned int r = 0; r < 3; r++)
2126
{
2127
for (unsigned int s = 0; s < 3 - r; s++)
2128
{
2129
for (unsigned int t = 0; t < 3 - r - s; t++)
2130
{
2131
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2132
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
2133
}// end loop over 't'
2134
}// end loop over 's'
2135
}// end loop over 'r'
1418
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
1419
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
1420
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
1421
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
1422
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
1423
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
1424
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
1425
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
1426
basisvalues[0] *= std::sqrt(0.75);
1427
basisvalues[3] *= std::sqrt(1.25);
1428
basisvalues[9] *= std::sqrt(1.75);
1429
basisvalues[2] *= std::sqrt(2.5);
1430
basisvalues[8] *= std::sqrt(3.5);
1431
basisvalues[7] *= std::sqrt(5.25);
1432
basisvalues[1] *= std::sqrt(7.5);
1433
basisvalues[6] *= std::sqrt(10.5);
1434
basisvalues[5] *= std::sqrt(15.75);
1435
basisvalues[4] *= std::sqrt(26.25);
2136
1436
2137
1437
// Table(s) of coefficients.
2138
1438
static const double coefficients0[10] = \
2324
1624
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2325
1625
2326
1626
// Declare helper variables.
2327
unsigned int rr = 0;
2328
unsigned int ss = 0;
2329
unsigned int tt = 0;
2330
double tmp5 = 0.0;
2331
double tmp6 = 0.0;
2332
double tmp7 = 0.0;
2333
1627
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
2334
1628
double tmp1 = 0.25*(Y + Z)*(Y + Z);
2335
1629
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
2339
1633
// Compute basisvalues.
2340
1634
basisvalues[0] = 1.0;
2341
1635
basisvalues[1] = tmp0;
2342
for (unsigned int r = 1; r < 2; r++)
2343
{
2344
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2345
ss = r*(r + 1)*(r + 2)/6;
2346
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2347
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
2348
}// end loop over 'r'
2349
for (unsigned int r = 0; r < 2; r++)
2350
{
2351
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2352
ss = r*(r + 1)*(r + 2)/6;
2353
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
2354
}// end loop over 'r'
2355
for (unsigned int r = 0; r < 1; r++)
2356
{
2357
for (unsigned int s = 1; s < 2 - r; s++)
2358
{
2359
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2360
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2361
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2362
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
2363
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2364
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2365
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2366
}// end loop over 's'
2367
}// end loop over 'r'
2368
for (unsigned int r = 0; r < 2; r++)
2369
{
2370
for (unsigned int s = 0; s < 2 - r; s++)
2371
{
2372
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2373
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2374
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
2375
}// end loop over 's'
2376
}// end loop over 'r'
2377
for (unsigned int r = 0; r < 1; r++)
2378
{
2379
for (unsigned int s = 0; s < 1 - r; s++)
2380
{
2381
for (unsigned int t = 1; t < 2 - r - s; t++)
2382
{
2383
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2384
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2385
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2386
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
2387
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2388
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2389
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2390
}// end loop over 't'
2391
}// end loop over 's'
2392
}// end loop over 'r'
2393
for (unsigned int r = 0; r < 3; r++)
2394
{
2395
for (unsigned int s = 0; s < 3 - r; s++)
2396
{
2397
for (unsigned int t = 0; t < 3 - r - s; t++)
2398
{
2399
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2400
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
2401
}// end loop over 't'
2402
}// end loop over 's'
2403
}// end loop over 'r'
1636
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
1637
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
1638
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
1639
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
1640
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
1641
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
1642
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
1643
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
1644
basisvalues[0] *= std::sqrt(0.75);
1645
basisvalues[3] *= std::sqrt(1.25);
1646
basisvalues[9] *= std::sqrt(1.75);
1647
basisvalues[2] *= std::sqrt(2.5);
1648
basisvalues[8] *= std::sqrt(3.5);
1649
basisvalues[7] *= std::sqrt(5.25);
1650
basisvalues[1] *= std::sqrt(7.5);
1651
basisvalues[6] *= std::sqrt(10.5);
1652
basisvalues[5] *= std::sqrt(15.75);
1653
basisvalues[4] *= std::sqrt(26.25);
2404
1654
2405
1655
// Table(s) of coefficients.
2406
1656
static const double coefficients0[10] = \
2592
1842
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2593
1843
2594
1844
// Declare helper variables.
2595
unsigned int rr = 0;
2596
unsigned int ss = 0;
2597
unsigned int tt = 0;
2598
double tmp5 = 0.0;
2599
double tmp6 = 0.0;
2600
double tmp7 = 0.0;
2601
1845
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
2602
1846
double tmp1 = 0.25*(Y + Z)*(Y + Z);
2603
1847
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
2607
1851
// Compute basisvalues.
2608
1852
basisvalues[0] = 1.0;
2609
1853
basisvalues[1] = tmp0;
2610
for (unsigned int r = 1; r < 2; r++)
2611
{
2612
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2613
ss = r*(r + 1)*(r + 2)/6;
2614
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2615
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
2616
}// end loop over 'r'
2617
for (unsigned int r = 0; r < 2; r++)
2618
{
2619
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2620
ss = r*(r + 1)*(r + 2)/6;
2621
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
2622
}// end loop over 'r'
2623
for (unsigned int r = 0; r < 1; r++)
2624
{
2625
for (unsigned int s = 1; s < 2 - r; s++)
2626
{
2627
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2628
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2629
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2630
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
2631
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2632
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2633
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2634
}// end loop over 's'
2635
}// end loop over 'r'
2636
for (unsigned int r = 0; r < 2; r++)
2637
{
2638
for (unsigned int s = 0; s < 2 - r; s++)
2639
{
2640
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2641
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2642
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
2643
}// end loop over 's'
2644
}// end loop over 'r'
2645
for (unsigned int r = 0; r < 1; r++)
2646
{
2647
for (unsigned int s = 0; s < 1 - r; s++)
2648
{
2649
for (unsigned int t = 1; t < 2 - r - s; t++)
2650
{
2651
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2652
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2653
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2654
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
2655
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2656
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2657
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2658
}// end loop over 't'
2659
}// end loop over 's'
2660
}// end loop over 'r'
2661
for (unsigned int r = 0; r < 3; r++)
2662
{
2663
for (unsigned int s = 0; s < 3 - r; s++)
2664
{
2665
for (unsigned int t = 0; t < 3 - r - s; t++)
2666
{
2667
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2668
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
2669
}// end loop over 't'
2670
}// end loop over 's'
2671
}// end loop over 'r'
1854
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
1855
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
1856
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
1857
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
1858
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
1859
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
1860
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
1861
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
1862
basisvalues[0] *= std::sqrt(0.75);
1863
basisvalues[3] *= std::sqrt(1.25);
1864
basisvalues[9] *= std::sqrt(1.75);
1865
basisvalues[2] *= std::sqrt(2.5);
1866
basisvalues[8] *= std::sqrt(3.5);
1867
basisvalues[7] *= std::sqrt(5.25);
1868
basisvalues[1] *= std::sqrt(7.5);
1869
basisvalues[6] *= std::sqrt(10.5);
1870
basisvalues[5] *= std::sqrt(15.75);
1871
basisvalues[4] *= std::sqrt(26.25);
2672
1872
2673
1873
// Table(s) of coefficients.
2674
1874
static const double coefficients0[10] = \
2860
2060
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
2861
2061
2862
2062
// Declare helper variables.
2863
unsigned int rr = 0;
2864
unsigned int ss = 0;
2865
unsigned int tt = 0;
2866
double tmp5 = 0.0;
2867
double tmp6 = 0.0;
2868
double tmp7 = 0.0;
2869
2063
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
2870
2064
double tmp1 = 0.25*(Y + Z)*(Y + Z);
2871
2065
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
2875
2069
// Compute basisvalues.
2876
2070
basisvalues[0] = 1.0;
2877
2071
basisvalues[1] = tmp0;
2878
for (unsigned int r = 1; r < 2; r++)
2879
{
2880
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
2881
ss = r*(r + 1)*(r + 2)/6;
2882
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
2883
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
2884
}// end loop over 'r'
2885
for (unsigned int r = 0; r < 2; r++)
2886
{
2887
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
2888
ss = r*(r + 1)*(r + 2)/6;
2889
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
2890
}// end loop over 'r'
2891
for (unsigned int r = 0; r < 1; r++)
2892
{
2893
for (unsigned int s = 1; s < 2 - r; s++)
2894
{
2895
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
2896
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2897
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
2898
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
2899
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2900
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
2901
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
2902
}// end loop over 's'
2903
}// end loop over 'r'
2904
for (unsigned int r = 0; r < 2; r++)
2905
{
2906
for (unsigned int s = 0; s < 2 - r; s++)
2907
{
2908
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
2909
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
2910
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
2911
}// end loop over 's'
2912
}// end loop over 'r'
2913
for (unsigned int r = 0; r < 1; r++)
2914
{
2915
for (unsigned int s = 0; s < 1 - r; s++)
2916
{
2917
for (unsigned int t = 1; t < 2 - r - s; t++)
2918
{
2919
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
2920
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2921
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
2922
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
2923
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2924
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
2925
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
2926
}// end loop over 't'
2927
}// end loop over 's'
2928
}// end loop over 'r'
2929
for (unsigned int r = 0; r < 3; r++)
2930
{
2931
for (unsigned int s = 0; s < 3 - r; s++)
2932
{
2933
for (unsigned int t = 0; t < 3 - r - s; t++)
2934
{
2935
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
2936
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
2937
}// end loop over 't'
2938
}// end loop over 's'
2939
}// end loop over 'r'
2072
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
2073
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
2074
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
2075
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
2076
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
2077
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
2078
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
2079
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
2080
basisvalues[0] *= std::sqrt(0.75);
2081
basisvalues[3] *= std::sqrt(1.25);
2082
basisvalues[9] *= std::sqrt(1.75);
2083
basisvalues[2] *= std::sqrt(2.5);
2084
basisvalues[8] *= std::sqrt(3.5);
2085
basisvalues[7] *= std::sqrt(5.25);
2086
basisvalues[1] *= std::sqrt(7.5);
2087
basisvalues[6] *= std::sqrt(10.5);
2088
basisvalues[5] *= std::sqrt(15.75);
2089
basisvalues[4] *= std::sqrt(26.25);
2940
2090
2941
2091
// Table(s) of coefficients.
2942
2092
static const double coefficients0[10] = \
3128
2278
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3129
2279
3130
2280
// Declare helper variables.
3131
unsigned int rr = 0;
3132
unsigned int ss = 0;
3133
unsigned int tt = 0;
3134
double tmp5 = 0.0;
3135
double tmp6 = 0.0;
3136
double tmp7 = 0.0;
3137
2281
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
3138
2282
double tmp1 = 0.25*(Y + Z)*(Y + Z);
3139
2283
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
3143
2287
// Compute basisvalues.
3144
2288
basisvalues[0] = 1.0;
3145
2289
basisvalues[1] = tmp0;
3146
for (unsigned int r = 1; r < 2; r++)
3147
{
3148
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3149
ss = r*(r + 1)*(r + 2)/6;
3150
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3151
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
3152
}// end loop over 'r'
3153
for (unsigned int r = 0; r < 2; r++)
3154
{
3155
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3156
ss = r*(r + 1)*(r + 2)/6;
3157
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
3158
}// end loop over 'r'
3159
for (unsigned int r = 0; r < 1; r++)
3160
{
3161
for (unsigned int s = 1; s < 2 - r; s++)
3162
{
3163
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3164
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3165
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3166
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
3167
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3168
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3169
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3170
}// end loop over 's'
3171
}// end loop over 'r'
3172
for (unsigned int r = 0; r < 2; r++)
3173
{
3174
for (unsigned int s = 0; s < 2 - r; s++)
3175
{
3176
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3177
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3178
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
3179
}// end loop over 's'
3180
}// end loop over 'r'
3181
for (unsigned int r = 0; r < 1; r++)
3182
{
3183
for (unsigned int s = 0; s < 1 - r; s++)
3184
{
3185
for (unsigned int t = 1; t < 2 - r - s; t++)
3186
{
3187
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3188
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3189
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3190
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
3191
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3192
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3193
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3194
}// end loop over 't'
3195
}// end loop over 's'
3196
}// end loop over 'r'
3197
for (unsigned int r = 0; r < 3; r++)
3198
{
3199
for (unsigned int s = 0; s < 3 - r; s++)
3200
{
3201
for (unsigned int t = 0; t < 3 - r - s; t++)
3202
{
3203
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3204
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
3205
}// end loop over 't'
3206
}// end loop over 's'
3207
}// end loop over 'r'
2290
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
2291
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
2292
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
2293
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
2294
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
2295
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
2296
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
2297
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
2298
basisvalues[0] *= std::sqrt(0.75);
2299
basisvalues[3] *= std::sqrt(1.25);
2300
basisvalues[9] *= std::sqrt(1.75);
2301
basisvalues[2] *= std::sqrt(2.5);
2302
basisvalues[8] *= std::sqrt(3.5);
2303
basisvalues[7] *= std::sqrt(5.25);
2304
basisvalues[1] *= std::sqrt(7.5);
2305
basisvalues[6] *= std::sqrt(10.5);
2306
basisvalues[5] *= std::sqrt(15.75);
2307
basisvalues[4] *= std::sqrt(26.25);
3208
2308
3209
2309
// Table(s) of coefficients.
3210
2310
static const double coefficients0[10] = \
3396
2496
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3397
2497
3398
2498
// Declare helper variables.
3399
unsigned int rr = 0;
3400
unsigned int ss = 0;
3401
unsigned int tt = 0;
3402
double tmp5 = 0.0;
3403
double tmp6 = 0.0;
3404
double tmp7 = 0.0;
3405
2499
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
3406
2500
double tmp1 = 0.25*(Y + Z)*(Y + Z);
3407
2501
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
3411
2505
// Compute basisvalues.
3412
2506
basisvalues[0] = 1.0;
3413
2507
basisvalues[1] = tmp0;
3414
for (unsigned int r = 1; r < 2; r++)
3415
{
3416
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3417
ss = r*(r + 1)*(r + 2)/6;
3418
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3419
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
3420
}// end loop over 'r'
3421
for (unsigned int r = 0; r < 2; r++)
3422
{
3423
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3424
ss = r*(r + 1)*(r + 2)/6;
3425
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
3426
}// end loop over 'r'
3427
for (unsigned int r = 0; r < 1; r++)
3428
{
3429
for (unsigned int s = 1; s < 2 - r; s++)
3430
{
3431
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3432
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3433
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3434
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
3435
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3436
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3437
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3438
}// end loop over 's'
3439
}// end loop over 'r'
3440
for (unsigned int r = 0; r < 2; r++)
3441
{
3442
for (unsigned int s = 0; s < 2 - r; s++)
3443
{
3444
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3445
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3446
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
3447
}// end loop over 's'
3448
}// end loop over 'r'
3449
for (unsigned int r = 0; r < 1; r++)
3450
{
3451
for (unsigned int s = 0; s < 1 - r; s++)
3452
{
3453
for (unsigned int t = 1; t < 2 - r - s; t++)
3454
{
3455
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3456
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3457
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3458
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
3459
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3460
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3461
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3462
}// end loop over 't'
3463
}// end loop over 's'
3464
}// end loop over 'r'
3465
for (unsigned int r = 0; r < 3; r++)
3466
{
3467
for (unsigned int s = 0; s < 3 - r; s++)
3468
{
3469
for (unsigned int t = 0; t < 3 - r - s; t++)
3470
{
3471
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3472
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
3473
}// end loop over 't'
3474
}// end loop over 's'
3475
}// end loop over 'r'
2508
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
2509
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
2510
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
2511
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
2512
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
2513
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
2514
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
2515
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
2516
basisvalues[0] *= std::sqrt(0.75);
2517
basisvalues[3] *= std::sqrt(1.25);
2518
basisvalues[9] *= std::sqrt(1.75);
2519
basisvalues[2] *= std::sqrt(2.5);
2520
basisvalues[8] *= std::sqrt(3.5);
2521
basisvalues[7] *= std::sqrt(5.25);
2522
basisvalues[1] *= std::sqrt(7.5);
2523
basisvalues[6] *= std::sqrt(10.5);
2524
basisvalues[5] *= std::sqrt(15.75);
2525
basisvalues[4] *= std::sqrt(26.25);
3476
2526
3477
2527
// Table(s) of coefficients.
3478
2528
static const double coefficients0[10] = \
3664
2714
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3665
2715
3666
2716
// Declare helper variables.
3667
unsigned int rr = 0;
3668
unsigned int ss = 0;
3669
unsigned int tt = 0;
3670
double tmp5 = 0.0;
3671
double tmp6 = 0.0;
3672
double tmp7 = 0.0;
3673
2717
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
3674
2718
double tmp1 = 0.25*(Y + Z)*(Y + Z);
3675
2719
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
3679
2723
// Compute basisvalues.
3680
2724
basisvalues[0] = 1.0;
3681
2725
basisvalues[1] = tmp0;
3682
for (unsigned int r = 1; r < 2; r++)
3683
{
3684
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
3685
ss = r*(r + 1)*(r + 2)/6;
3686
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
3687
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
3688
}// end loop over 'r'
3689
for (unsigned int r = 0; r < 2; r++)
3690
{
3691
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
3692
ss = r*(r + 1)*(r + 2)/6;
3693
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
3694
}// end loop over 'r'
3695
for (unsigned int r = 0; r < 1; r++)
3696
{
3697
for (unsigned int s = 1; s < 2 - r; s++)
3698
{
3699
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
3700
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3701
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
3702
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
3703
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3704
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
3705
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
3706
}// end loop over 's'
3707
}// end loop over 'r'
3708
for (unsigned int r = 0; r < 2; r++)
3709
{
3710
for (unsigned int s = 0; s < 2 - r; s++)
3711
{
3712
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
3713
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
3714
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
3715
}// end loop over 's'
3716
}// end loop over 'r'
3717
for (unsigned int r = 0; r < 1; r++)
3718
{
3719
for (unsigned int s = 0; s < 1 - r; s++)
3720
{
3721
for (unsigned int t = 1; t < 2 - r - s; t++)
3722
{
3723
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
3724
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3725
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
3726
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
3727
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3728
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
3729
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
3730
}// end loop over 't'
3731
}// end loop over 's'
3732
}// end loop over 'r'
3733
for (unsigned int r = 0; r < 3; r++)
3734
{
3735
for (unsigned int s = 0; s < 3 - r; s++)
3736
{
3737
for (unsigned int t = 0; t < 3 - r - s; t++)
3738
{
3739
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
3740
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
3741
}// end loop over 't'
3742
}// end loop over 's'
3743
}// end loop over 'r'
2726
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
2727
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
2728
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
2729
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
2730
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
2731
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
2732
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
2733
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
2734
basisvalues[0] *= std::sqrt(0.75);
2735
basisvalues[3] *= std::sqrt(1.25);
2736
basisvalues[9] *= std::sqrt(1.75);
2737
basisvalues[2] *= std::sqrt(2.5);
2738
basisvalues[8] *= std::sqrt(3.5);
2739
basisvalues[7] *= std::sqrt(5.25);
2740
basisvalues[1] *= std::sqrt(7.5);
2741
basisvalues[6] *= std::sqrt(10.5);
2742
basisvalues[5] *= std::sqrt(15.75);
2743
basisvalues[4] *= std::sqrt(26.25);
3744
2744
3745
2745
// Table(s) of coefficients.
3746
2746
static const double coefficients0[10] = \
4311
3311
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4312
3312
4313
3313
// Declare helper variables.
4314
unsigned int rr = 0;
4315
unsigned int ss = 0;
4316
unsigned int tt = 0;
4317
double tmp5 = 0.0;
4318
double tmp6 = 0.0;
4319
double tmp7 = 0.0;
4320
3314
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4321
3315
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4322
3316
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4326
3320
// Compute basisvalues.
4327
3321
basisvalues[0] = 1.0;
4328
3322
basisvalues[1] = tmp0;
4329
for (unsigned int r = 1; r < 2; r++)
4330
{
4331
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4332
ss = r*(r + 1)*(r + 2)/6;
4333
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4334
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4335
}// end loop over 'r'
4336
for (unsigned int r = 0; r < 2; r++)
4337
{
4338
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4339
ss = r*(r + 1)*(r + 2)/6;
4340
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4341
}// end loop over 'r'
4342
for (unsigned int r = 0; r < 1; r++)
4343
{
4344
for (unsigned int s = 1; s < 2 - r; s++)
4345
{
4346
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4347
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4348
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4349
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4350
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4351
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4352
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4353
}// end loop over 's'
4354
}// end loop over 'r'
4355
for (unsigned int r = 0; r < 2; r++)
4356
{
4357
for (unsigned int s = 0; s < 2 - r; s++)
4358
{
4359
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4360
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4361
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4362
}// end loop over 's'
4363
}// end loop over 'r'
4364
for (unsigned int r = 0; r < 1; r++)
4365
{
4366
for (unsigned int s = 0; s < 1 - r; s++)
4367
{
4368
for (unsigned int t = 1; t < 2 - r - s; t++)
4369
{
4370
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4371
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4372
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4373
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4374
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4375
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4376
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4377
}// end loop over 't'
4378
}// end loop over 's'
4379
}// end loop over 'r'
4380
for (unsigned int r = 0; r < 3; r++)
4381
{
4382
for (unsigned int s = 0; s < 3 - r; s++)
4383
{
4384
for (unsigned int t = 0; t < 3 - r - s; t++)
4385
{
4386
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4387
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4388
}// end loop over 't'
4389
}// end loop over 's'
4390
}// end loop over 'r'
3323
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3324
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3325
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3326
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3327
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3328
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3329
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3330
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3331
basisvalues[0] *= std::sqrt(0.75);
3332
basisvalues[3] *= std::sqrt(1.25);
3333
basisvalues[9] *= std::sqrt(1.75);
3334
basisvalues[2] *= std::sqrt(2.5);
3335
basisvalues[8] *= std::sqrt(3.5);
3336
basisvalues[7] *= std::sqrt(5.25);
3337
basisvalues[1] *= std::sqrt(7.5);
3338
basisvalues[6] *= std::sqrt(10.5);
3339
basisvalues[5] *= std::sqrt(15.75);
3340
basisvalues[4] *= std::sqrt(26.25);
4391
3341
4392
3342
// Table(s) of coefficients.
4393
3343
static const double coefficients0[10] = \
4407
3357
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4408
3358
4409
3359
// Declare helper variables.
4410
unsigned int rr = 0;
4411
unsigned int ss = 0;
4412
unsigned int tt = 0;
4413
double tmp5 = 0.0;
4414
double tmp6 = 0.0;
4415
double tmp7 = 0.0;
4416
3360
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4417
3361
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4418
3362
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4422
3366
// Compute basisvalues.
4423
3367
basisvalues[0] = 1.0;
4424
3368
basisvalues[1] = tmp0;
4425
for (unsigned int r = 1; r < 2; r++)
4426
{
4427
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4428
ss = r*(r + 1)*(r + 2)/6;
4429
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4430
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4431
}// end loop over 'r'
4432
for (unsigned int r = 0; r < 2; r++)
4433
{
4434
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4435
ss = r*(r + 1)*(r + 2)/6;
4436
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4437
}// end loop over 'r'
4438
for (unsigned int r = 0; r < 1; r++)
4439
{
4440
for (unsigned int s = 1; s < 2 - r; s++)
4441
{
4442
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4443
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4444
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4445
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4446
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4447
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4448
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4449
}// end loop over 's'
4450
}// end loop over 'r'
4451
for (unsigned int r = 0; r < 2; r++)
4452
{
4453
for (unsigned int s = 0; s < 2 - r; s++)
4454
{
4455
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4456
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4457
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4458
}// end loop over 's'
4459
}// end loop over 'r'
4460
for (unsigned int r = 0; r < 1; r++)
4461
{
4462
for (unsigned int s = 0; s < 1 - r; s++)
4463
{
4464
for (unsigned int t = 1; t < 2 - r - s; t++)
4465
{
4466
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4467
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4468
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4469
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4470
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4471
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4472
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4473
}// end loop over 't'
4474
}// end loop over 's'
4475
}// end loop over 'r'
4476
for (unsigned int r = 0; r < 3; r++)
4477
{
4478
for (unsigned int s = 0; s < 3 - r; s++)
4479
{
4480
for (unsigned int t = 0; t < 3 - r - s; t++)
4481
{
4482
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4483
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4484
}// end loop over 't'
4485
}// end loop over 's'
4486
}// end loop over 'r'
3369
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3370
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3371
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3372
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3373
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3374
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3375
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3376
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3377
basisvalues[0] *= std::sqrt(0.75);
3378
basisvalues[3] *= std::sqrt(1.25);
3379
basisvalues[9] *= std::sqrt(1.75);
3380
basisvalues[2] *= std::sqrt(2.5);
3381
basisvalues[8] *= std::sqrt(3.5);
3382
basisvalues[7] *= std::sqrt(5.25);
3383
basisvalues[1] *= std::sqrt(7.5);
3384
basisvalues[6] *= std::sqrt(10.5);
3385
basisvalues[5] *= std::sqrt(15.75);
3386
basisvalues[4] *= std::sqrt(26.25);
4487
3387
4488
3388
// Table(s) of coefficients.
4489
3389
static const double coefficients0[10] = \
4503
3403
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4504
3404
4505
3405
// Declare helper variables.
4506
unsigned int rr = 0;
4507
unsigned int ss = 0;
4508
unsigned int tt = 0;
4509
double tmp5 = 0.0;
4510
double tmp6 = 0.0;
4511
double tmp7 = 0.0;
4512
3406
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4513
3407
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4514
3408
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4518
3412
// Compute basisvalues.
4519
3413
basisvalues[0] = 1.0;
4520
3414
basisvalues[1] = tmp0;
4521
for (unsigned int r = 1; r < 2; r++)
4522
{
4523
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4524
ss = r*(r + 1)*(r + 2)/6;
4525
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4526
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4527
}// end loop over 'r'
4528
for (unsigned int r = 0; r < 2; r++)
4529
{
4530
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4531
ss = r*(r + 1)*(r + 2)/6;
4532
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4533
}// end loop over 'r'
4534
for (unsigned int r = 0; r < 1; r++)
4535
{
4536
for (unsigned int s = 1; s < 2 - r; s++)
4537
{
4538
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4539
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4540
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4541
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4542
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4543
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4544
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4545
}// end loop over 's'
4546
}// end loop over 'r'
4547
for (unsigned int r = 0; r < 2; r++)
4548
{
4549
for (unsigned int s = 0; s < 2 - r; s++)
4550
{
4551
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4552
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4553
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4554
}// end loop over 's'
4555
}// end loop over 'r'
4556
for (unsigned int r = 0; r < 1; r++)
4557
{
4558
for (unsigned int s = 0; s < 1 - r; s++)
4559
{
4560
for (unsigned int t = 1; t < 2 - r - s; t++)
4561
{
4562
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4563
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4564
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4565
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4566
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4567
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4568
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4569
}// end loop over 't'
4570
}// end loop over 's'
4571
}// end loop over 'r'
4572
for (unsigned int r = 0; r < 3; r++)
4573
{
4574
for (unsigned int s = 0; s < 3 - r; s++)
4575
{
4576
for (unsigned int t = 0; t < 3 - r - s; t++)
4577
{
4578
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4579
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4580
}// end loop over 't'
4581
}// end loop over 's'
4582
}// end loop over 'r'
3415
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3416
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3417
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3418
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3419
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3420
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3421
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3422
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3423
basisvalues[0] *= std::sqrt(0.75);
3424
basisvalues[3] *= std::sqrt(1.25);
3425
basisvalues[9] *= std::sqrt(1.75);
3426
basisvalues[2] *= std::sqrt(2.5);
3427
basisvalues[8] *= std::sqrt(3.5);
3428
basisvalues[7] *= std::sqrt(5.25);
3429
basisvalues[1] *= std::sqrt(7.5);
3430
basisvalues[6] *= std::sqrt(10.5);
3431
basisvalues[5] *= std::sqrt(15.75);
3432
basisvalues[4] *= std::sqrt(26.25);
4583
3433
4584
3434
// Table(s) of coefficients.
4585
3435
static const double coefficients0[10] = \
4599
3449
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4600
3450
4601
3451
// Declare helper variables.
4602
unsigned int rr = 0;
4603
unsigned int ss = 0;
4604
unsigned int tt = 0;
4605
double tmp5 = 0.0;
4606
double tmp6 = 0.0;
4607
double tmp7 = 0.0;
4608
3452
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4609
3453
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4610
3454
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4614
3458
// Compute basisvalues.
4615
3459
basisvalues[0] = 1.0;
4616
3460
basisvalues[1] = tmp0;
4617
for (unsigned int r = 1; r < 2; r++)
4618
{
4619
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4620
ss = r*(r + 1)*(r + 2)/6;
4621
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4622
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4623
}// end loop over 'r'
4624
for (unsigned int r = 0; r < 2; r++)
4625
{
4626
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4627
ss = r*(r + 1)*(r + 2)/6;
4628
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4629
}// end loop over 'r'
4630
for (unsigned int r = 0; r < 1; r++)
4631
{
4632
for (unsigned int s = 1; s < 2 - r; s++)
4633
{
4634
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4635
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4636
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4637
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4638
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4639
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4640
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4641
}// end loop over 's'
4642
}// end loop over 'r'
4643
for (unsigned int r = 0; r < 2; r++)
4644
{
4645
for (unsigned int s = 0; s < 2 - r; s++)
4646
{
4647
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4648
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4649
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4650
}// end loop over 's'
4651
}// end loop over 'r'
4652
for (unsigned int r = 0; r < 1; r++)
4653
{
4654
for (unsigned int s = 0; s < 1 - r; s++)
4655
{
4656
for (unsigned int t = 1; t < 2 - r - s; t++)
4657
{
4658
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4659
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4660
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4661
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4662
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4663
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4664
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4665
}// end loop over 't'
4666
}// end loop over 's'
4667
}// end loop over 'r'
4668
for (unsigned int r = 0; r < 3; r++)
4669
{
4670
for (unsigned int s = 0; s < 3 - r; s++)
4671
{
4672
for (unsigned int t = 0; t < 3 - r - s; t++)
4673
{
4674
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4675
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4676
}// end loop over 't'
4677
}// end loop over 's'
4678
}// end loop over 'r'
3461
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3462
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3463
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3464
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3465
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3466
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3467
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3468
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3469
basisvalues[0] *= std::sqrt(0.75);
3470
basisvalues[3] *= std::sqrt(1.25);
3471
basisvalues[9] *= std::sqrt(1.75);
3472
basisvalues[2] *= std::sqrt(2.5);
3473
basisvalues[8] *= std::sqrt(3.5);
3474
basisvalues[7] *= std::sqrt(5.25);
3475
basisvalues[1] *= std::sqrt(7.5);
3476
basisvalues[6] *= std::sqrt(10.5);
3477
basisvalues[5] *= std::sqrt(15.75);
3478
basisvalues[4] *= std::sqrt(26.25);
4679
3479
4680
3480
// Table(s) of coefficients.
4681
3481
static const double coefficients0[10] = \
4695
3495
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4696
3496
4697
3497
// Declare helper variables.
4698
unsigned int rr = 0;
4699
unsigned int ss = 0;
4700
unsigned int tt = 0;
4701
double tmp5 = 0.0;
4702
double tmp6 = 0.0;
4703
double tmp7 = 0.0;
4704
3498
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4705
3499
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4706
3500
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4710
3504
// Compute basisvalues.
4711
3505
basisvalues[0] = 1.0;
4712
3506
basisvalues[1] = tmp0;
4713
for (unsigned int r = 1; r < 2; r++)
4714
{
4715
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4716
ss = r*(r + 1)*(r + 2)/6;
4717
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4718
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4719
}// end loop over 'r'
4720
for (unsigned int r = 0; r < 2; r++)
4721
{
4722
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4723
ss = r*(r + 1)*(r + 2)/6;
4724
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4725
}// end loop over 'r'
4726
for (unsigned int r = 0; r < 1; r++)
4727
{
4728
for (unsigned int s = 1; s < 2 - r; s++)
4729
{
4730
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4731
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4732
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4733
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4734
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4735
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4736
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4737
}// end loop over 's'
4738
}// end loop over 'r'
4739
for (unsigned int r = 0; r < 2; r++)
4740
{
4741
for (unsigned int s = 0; s < 2 - r; s++)
4742
{
4743
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4744
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4745
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4746
}// end loop over 's'
4747
}// end loop over 'r'
4748
for (unsigned int r = 0; r < 1; r++)
4749
{
4750
for (unsigned int s = 0; s < 1 - r; s++)
4751
{
4752
for (unsigned int t = 1; t < 2 - r - s; t++)
4753
{
4754
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4755
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4756
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4757
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4758
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4759
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4760
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4761
}// end loop over 't'
4762
}// end loop over 's'
4763
}// end loop over 'r'
4764
for (unsigned int r = 0; r < 3; r++)
4765
{
4766
for (unsigned int s = 0; s < 3 - r; s++)
4767
{
4768
for (unsigned int t = 0; t < 3 - r - s; t++)
4769
{
4770
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4771
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4772
}// end loop over 't'
4773
}// end loop over 's'
4774
}// end loop over 'r'
3507
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3508
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3509
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3510
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3511
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3512
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3513
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3514
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3515
basisvalues[0] *= std::sqrt(0.75);
3516
basisvalues[3] *= std::sqrt(1.25);
3517
basisvalues[9] *= std::sqrt(1.75);
3518
basisvalues[2] *= std::sqrt(2.5);
3519
basisvalues[8] *= std::sqrt(3.5);
3520
basisvalues[7] *= std::sqrt(5.25);
3521
basisvalues[1] *= std::sqrt(7.5);
3522
basisvalues[6] *= std::sqrt(10.5);
3523
basisvalues[5] *= std::sqrt(15.75);
3524
basisvalues[4] *= std::sqrt(26.25);
4775
3525
4776
3526
// Table(s) of coefficients.
4777
3527
static const double coefficients0[10] = \
4791
3541
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4792
3542
4793
3543
// Declare helper variables.
4794
unsigned int rr = 0;
4795
unsigned int ss = 0;
4796
unsigned int tt = 0;
4797
double tmp5 = 0.0;
4798
double tmp6 = 0.0;
4799
double tmp7 = 0.0;
4800
3544
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4801
3545
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4802
3546
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4806
3550
// Compute basisvalues.
4807
3551
basisvalues[0] = 1.0;
4808
3552
basisvalues[1] = tmp0;
4809
for (unsigned int r = 1; r < 2; r++)
4810
{
4811
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4812
ss = r*(r + 1)*(r + 2)/6;
4813
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4814
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4815
}// end loop over 'r'
4816
for (unsigned int r = 0; r < 2; r++)
4817
{
4818
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4819
ss = r*(r + 1)*(r + 2)/6;
4820
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4821
}// end loop over 'r'
4822
for (unsigned int r = 0; r < 1; r++)
4823
{
4824
for (unsigned int s = 1; s < 2 - r; s++)
4825
{
4826
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4827
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4828
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4829
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4830
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4831
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4832
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4833
}// end loop over 's'
4834
}// end loop over 'r'
4835
for (unsigned int r = 0; r < 2; r++)
4836
{
4837
for (unsigned int s = 0; s < 2 - r; s++)
4838
{
4839
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4840
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4841
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4842
}// end loop over 's'
4843
}// end loop over 'r'
4844
for (unsigned int r = 0; r < 1; r++)
4845
{
4846
for (unsigned int s = 0; s < 1 - r; s++)
4847
{
4848
for (unsigned int t = 1; t < 2 - r - s; t++)
4849
{
4850
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4851
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4852
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4853
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4854
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4855
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4856
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4857
}// end loop over 't'
4858
}// end loop over 's'
4859
}// end loop over 'r'
4860
for (unsigned int r = 0; r < 3; r++)
4861
{
4862
for (unsigned int s = 0; s < 3 - r; s++)
4863
{
4864
for (unsigned int t = 0; t < 3 - r - s; t++)
4865
{
4866
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4867
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4868
}// end loop over 't'
4869
}// end loop over 's'
4870
}// end loop over 'r'
3553
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3554
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3555
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3556
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3557
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3558
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3559
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3560
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3561
basisvalues[0] *= std::sqrt(0.75);
3562
basisvalues[3] *= std::sqrt(1.25);
3563
basisvalues[9] *= std::sqrt(1.75);
3564
basisvalues[2] *= std::sqrt(2.5);
3565
basisvalues[8] *= std::sqrt(3.5);
3566
basisvalues[7] *= std::sqrt(5.25);
3567
basisvalues[1] *= std::sqrt(7.5);
3568
basisvalues[6] *= std::sqrt(10.5);
3569
basisvalues[5] *= std::sqrt(15.75);
3570
basisvalues[4] *= std::sqrt(26.25);
4871
3571
4872
3572
// Table(s) of coefficients.
4873
3573
static const double coefficients0[10] = \
4887
3587
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4888
3588
4889
3589
// Declare helper variables.
4890
unsigned int rr = 0;
4891
unsigned int ss = 0;
4892
unsigned int tt = 0;
4893
double tmp5 = 0.0;
4894
double tmp6 = 0.0;
4895
double tmp7 = 0.0;
4896
3590
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4897
3591
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4898
3592
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4902
3596
// Compute basisvalues.
4903
3597
basisvalues[0] = 1.0;
4904
3598
basisvalues[1] = tmp0;
4905
for (unsigned int r = 1; r < 2; r++)
4906
{
4907
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
4908
ss = r*(r + 1)*(r + 2)/6;
4909
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
4910
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
4911
}// end loop over 'r'
4912
for (unsigned int r = 0; r < 2; r++)
4913
{
4914
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
4915
ss = r*(r + 1)*(r + 2)/6;
4916
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
4917
}// end loop over 'r'
4918
for (unsigned int r = 0; r < 1; r++)
4919
{
4920
for (unsigned int s = 1; s < 2 - r; s++)
4921
{
4922
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
4923
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4924
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
4925
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
4926
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4927
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
4928
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
4929
}// end loop over 's'
4930
}// end loop over 'r'
4931
for (unsigned int r = 0; r < 2; r++)
4932
{
4933
for (unsigned int s = 0; s < 2 - r; s++)
4934
{
4935
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
4936
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
4937
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
4938
}// end loop over 's'
4939
}// end loop over 'r'
4940
for (unsigned int r = 0; r < 1; r++)
4941
{
4942
for (unsigned int s = 0; s < 1 - r; s++)
4943
{
4944
for (unsigned int t = 1; t < 2 - r - s; t++)
4945
{
4946
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
4947
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4948
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
4949
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
4950
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4951
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
4952
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
4953
}// end loop over 't'
4954
}// end loop over 's'
4955
}// end loop over 'r'
4956
for (unsigned int r = 0; r < 3; r++)
4957
{
4958
for (unsigned int s = 0; s < 3 - r; s++)
4959
{
4960
for (unsigned int t = 0; t < 3 - r - s; t++)
4961
{
4962
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
4963
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
4964
}// end loop over 't'
4965
}// end loop over 's'
4966
}// end loop over 'r'
3599
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3600
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3601
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3602
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3603
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3604
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3605
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3606
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3607
basisvalues[0] *= std::sqrt(0.75);
3608
basisvalues[3] *= std::sqrt(1.25);
3609
basisvalues[9] *= std::sqrt(1.75);
3610
basisvalues[2] *= std::sqrt(2.5);
3611
basisvalues[8] *= std::sqrt(3.5);
3612
basisvalues[7] *= std::sqrt(5.25);
3613
basisvalues[1] *= std::sqrt(7.5);
3614
basisvalues[6] *= std::sqrt(10.5);
3615
basisvalues[5] *= std::sqrt(15.75);
3616
basisvalues[4] *= std::sqrt(26.25);
4967
3617
4968
3618
// Table(s) of coefficients.
4969
3619
static const double coefficients0[10] = \
4983
3633
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4984
3634
4985
3635
// Declare helper variables.
4986
unsigned int rr = 0;
4987
unsigned int ss = 0;
4988
unsigned int tt = 0;
4989
double tmp5 = 0.0;
4990
double tmp6 = 0.0;
4991
double tmp7 = 0.0;
4992
3636
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
4993
3637
double tmp1 = 0.25*(Y + Z)*(Y + Z);
4994
3638
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
4998
3642
// Compute basisvalues.
4999
3643
basisvalues[0] = 1.0;
5000
3644
basisvalues[1] = tmp0;
5001
for (unsigned int r = 1; r < 2; r++)
5002
{
5003
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5004
ss = r*(r + 1)*(r + 2)/6;
5005
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5006
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5007
}// end loop over 'r'
5008
for (unsigned int r = 0; r < 2; r++)
5009
{
5010
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5011
ss = r*(r + 1)*(r + 2)/6;
5012
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5013
}// end loop over 'r'
5014
for (unsigned int r = 0; r < 1; r++)
5015
{
5016
for (unsigned int s = 1; s < 2 - r; s++)
5017
{
5018
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5019
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5020
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5021
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5022
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5023
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5024
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5025
}// end loop over 's'
5026
}// end loop over 'r'
5027
for (unsigned int r = 0; r < 2; r++)
5028
{
5029
for (unsigned int s = 0; s < 2 - r; s++)
5030
{
5031
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5032
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5033
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5034
}// end loop over 's'
5035
}// end loop over 'r'
5036
for (unsigned int r = 0; r < 1; r++)
5037
{
5038
for (unsigned int s = 0; s < 1 - r; s++)
5039
{
5040
for (unsigned int t = 1; t < 2 - r - s; t++)
5041
{
5042
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5043
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5044
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5045
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5046
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5047
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5048
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5049
}// end loop over 't'
5050
}// end loop over 's'
5051
}// end loop over 'r'
5052
for (unsigned int r = 0; r < 3; r++)
5053
{
5054
for (unsigned int s = 0; s < 3 - r; s++)
5055
{
5056
for (unsigned int t = 0; t < 3 - r - s; t++)
5057
{
5058
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5059
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5060
}// end loop over 't'
5061
}// end loop over 's'
5062
}// end loop over 'r'
3645
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3646
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3647
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3648
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3649
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3650
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3651
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3652
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3653
basisvalues[0] *= std::sqrt(0.75);
3654
basisvalues[3] *= std::sqrt(1.25);
3655
basisvalues[9] *= std::sqrt(1.75);
3656
basisvalues[2] *= std::sqrt(2.5);
3657
basisvalues[8] *= std::sqrt(3.5);
3658
basisvalues[7] *= std::sqrt(5.25);
3659
basisvalues[1] *= std::sqrt(7.5);
3660
basisvalues[6] *= std::sqrt(10.5);
3661
basisvalues[5] *= std::sqrt(15.75);
3662
basisvalues[4] *= std::sqrt(26.25);
5063
3663
5064
3664
// Table(s) of coefficients.
5065
3665
static const double coefficients0[10] = \
5079
3679
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5080
3680
5081
3681
// Declare helper variables.
5082
unsigned int rr = 0;
5083
unsigned int ss = 0;
5084
unsigned int tt = 0;
5085
double tmp5 = 0.0;
5086
double tmp6 = 0.0;
5087
double tmp7 = 0.0;
5088
3682
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5089
3683
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5090
3684
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5094
3688
// Compute basisvalues.
5095
3689
basisvalues[0] = 1.0;
5096
3690
basisvalues[1] = tmp0;
5097
for (unsigned int r = 1; r < 2; r++)
5098
{
5099
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5100
ss = r*(r + 1)*(r + 2)/6;
5101
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5102
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5103
}// end loop over 'r'
5104
for (unsigned int r = 0; r < 2; r++)
5105
{
5106
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5107
ss = r*(r + 1)*(r + 2)/6;
5108
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5109
}// end loop over 'r'
5110
for (unsigned int r = 0; r < 1; r++)
5111
{
5112
for (unsigned int s = 1; s < 2 - r; s++)
5113
{
5114
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5115
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5116
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5117
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5118
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5119
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5120
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5121
}// end loop over 's'
5122
}// end loop over 'r'
5123
for (unsigned int r = 0; r < 2; r++)
5124
{
5125
for (unsigned int s = 0; s < 2 - r; s++)
5126
{
5127
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5128
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5129
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5130
}// end loop over 's'
5131
}// end loop over 'r'
5132
for (unsigned int r = 0; r < 1; r++)
5133
{
5134
for (unsigned int s = 0; s < 1 - r; s++)
5135
{
5136
for (unsigned int t = 1; t < 2 - r - s; t++)
5137
{
5138
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5139
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5140
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5141
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5142
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5143
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5144
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5145
}// end loop over 't'
5146
}// end loop over 's'
5147
}// end loop over 'r'
5148
for (unsigned int r = 0; r < 3; r++)
5149
{
5150
for (unsigned int s = 0; s < 3 - r; s++)
5151
{
5152
for (unsigned int t = 0; t < 3 - r - s; t++)
5153
{
5154
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5155
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5156
}// end loop over 't'
5157
}// end loop over 's'
5158
}// end loop over 'r'
3691
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3692
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3693
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3694
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3695
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3696
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3697
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3698
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3699
basisvalues[0] *= std::sqrt(0.75);
3700
basisvalues[3] *= std::sqrt(1.25);
3701
basisvalues[9] *= std::sqrt(1.75);
3702
basisvalues[2] *= std::sqrt(2.5);
3703
basisvalues[8] *= std::sqrt(3.5);
3704
basisvalues[7] *= std::sqrt(5.25);
3705
basisvalues[1] *= std::sqrt(7.5);
3706
basisvalues[6] *= std::sqrt(10.5);
3707
basisvalues[5] *= std::sqrt(15.75);
3708
basisvalues[4] *= std::sqrt(26.25);
5159
3709
5160
3710
// Table(s) of coefficients.
5161
3711
static const double coefficients0[10] = \
5175
3725
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5176
3726
5177
3727
// Declare helper variables.
5178
unsigned int rr = 0;
5179
unsigned int ss = 0;
5180
unsigned int tt = 0;
5181
double tmp5 = 0.0;
5182
double tmp6 = 0.0;
5183
double tmp7 = 0.0;
5184
3728
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5185
3729
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5186
3730
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5190
3734
// Compute basisvalues.
5191
3735
basisvalues[0] = 1.0;
5192
3736
basisvalues[1] = tmp0;
5193
for (unsigned int r = 1; r < 2; r++)
5194
{
5195
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5196
ss = r*(r + 1)*(r + 2)/6;
5197
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5198
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5199
}// end loop over 'r'
5200
for (unsigned int r = 0; r < 2; r++)
5201
{
5202
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5203
ss = r*(r + 1)*(r + 2)/6;
5204
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5205
}// end loop over 'r'
5206
for (unsigned int r = 0; r < 1; r++)
5207
{
5208
for (unsigned int s = 1; s < 2 - r; s++)
5209
{
5210
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5211
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5212
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5213
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5214
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5215
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5216
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5217
}// end loop over 's'
5218
}// end loop over 'r'
5219
for (unsigned int r = 0; r < 2; r++)
5220
{
5221
for (unsigned int s = 0; s < 2 - r; s++)
5222
{
5223
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5224
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5225
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5226
}// end loop over 's'
5227
}// end loop over 'r'
5228
for (unsigned int r = 0; r < 1; r++)
5229
{
5230
for (unsigned int s = 0; s < 1 - r; s++)
5231
{
5232
for (unsigned int t = 1; t < 2 - r - s; t++)
5233
{
5234
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5235
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5236
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5237
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5238
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5239
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5240
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5241
}// end loop over 't'
5242
}// end loop over 's'
5243
}// end loop over 'r'
5244
for (unsigned int r = 0; r < 3; r++)
5245
{
5246
for (unsigned int s = 0; s < 3 - r; s++)
5247
{
5248
for (unsigned int t = 0; t < 3 - r - s; t++)
5249
{
5250
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5251
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5252
}// end loop over 't'
5253
}// end loop over 's'
5254
}// end loop over 'r'
3737
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3738
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3739
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3740
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3741
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3742
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3743
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3744
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3745
basisvalues[0] *= std::sqrt(0.75);
3746
basisvalues[3] *= std::sqrt(1.25);
3747
basisvalues[9] *= std::sqrt(1.75);
3748
basisvalues[2] *= std::sqrt(2.5);
3749
basisvalues[8] *= std::sqrt(3.5);
3750
basisvalues[7] *= std::sqrt(5.25);
3751
basisvalues[1] *= std::sqrt(7.5);
3752
basisvalues[6] *= std::sqrt(10.5);
3753
basisvalues[5] *= std::sqrt(15.75);
3754
basisvalues[4] *= std::sqrt(26.25);
5255
3755
5256
3756
// Table(s) of coefficients.
5257
3757
static const double coefficients0[10] = \
5271
3771
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5272
3772
5273
3773
// Declare helper variables.
5274
unsigned int rr = 0;
5275
unsigned int ss = 0;
5276
unsigned int tt = 0;
5277
double tmp5 = 0.0;
5278
double tmp6 = 0.0;
5279
double tmp7 = 0.0;
5280
3774
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5281
3775
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5282
3776
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5286
3780
// Compute basisvalues.
5287
3781
basisvalues[0] = 1.0;
5288
3782
basisvalues[1] = tmp0;
5289
for (unsigned int r = 1; r < 2; r++)
5290
{
5291
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5292
ss = r*(r + 1)*(r + 2)/6;
5293
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5294
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5295
}// end loop over 'r'
5296
for (unsigned int r = 0; r < 2; r++)
5297
{
5298
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5299
ss = r*(r + 1)*(r + 2)/6;
5300
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5301
}// end loop over 'r'
5302
for (unsigned int r = 0; r < 1; r++)
5303
{
5304
for (unsigned int s = 1; s < 2 - r; s++)
5305
{
5306
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5307
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5308
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5309
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5310
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5311
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5312
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5313
}// end loop over 's'
5314
}// end loop over 'r'
5315
for (unsigned int r = 0; r < 2; r++)
5316
{
5317
for (unsigned int s = 0; s < 2 - r; s++)
5318
{
5319
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5320
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5321
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5322
}// end loop over 's'
5323
}// end loop over 'r'
5324
for (unsigned int r = 0; r < 1; r++)
5325
{
5326
for (unsigned int s = 0; s < 1 - r; s++)
5327
{
5328
for (unsigned int t = 1; t < 2 - r - s; t++)
5329
{
5330
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5331
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5332
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5333
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5334
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5335
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5336
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5337
}// end loop over 't'
5338
}// end loop over 's'
5339
}// end loop over 'r'
5340
for (unsigned int r = 0; r < 3; r++)
5341
{
5342
for (unsigned int s = 0; s < 3 - r; s++)
5343
{
5344
for (unsigned int t = 0; t < 3 - r - s; t++)
5345
{
5346
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5347
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5348
}// end loop over 't'
5349
}// end loop over 's'
5350
}// end loop over 'r'
3783
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3784
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3785
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3786
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3787
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3788
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3789
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3790
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3791
basisvalues[0] *= std::sqrt(0.75);
3792
basisvalues[3] *= std::sqrt(1.25);
3793
basisvalues[9] *= std::sqrt(1.75);
3794
basisvalues[2] *= std::sqrt(2.5);
3795
basisvalues[8] *= std::sqrt(3.5);
3796
basisvalues[7] *= std::sqrt(5.25);
3797
basisvalues[1] *= std::sqrt(7.5);
3798
basisvalues[6] *= std::sqrt(10.5);
3799
basisvalues[5] *= std::sqrt(15.75);
3800
basisvalues[4] *= std::sqrt(26.25);
5351
3801
5352
3802
// Table(s) of coefficients.
5353
3803
static const double coefficients0[10] = \
5367
3817
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5368
3818
5369
3819
// Declare helper variables.
5370
unsigned int rr = 0;
5371
unsigned int ss = 0;
5372
unsigned int tt = 0;
5373
double tmp5 = 0.0;
5374
double tmp6 = 0.0;
5375
double tmp7 = 0.0;
5376
3820
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5377
3821
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5378
3822
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5382
3826
// Compute basisvalues.
5383
3827
basisvalues[0] = 1.0;
5384
3828
basisvalues[1] = tmp0;
5385
for (unsigned int r = 1; r < 2; r++)
5386
{
5387
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5388
ss = r*(r + 1)*(r + 2)/6;
5389
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5390
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5391
}// end loop over 'r'
5392
for (unsigned int r = 0; r < 2; r++)
5393
{
5394
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5395
ss = r*(r + 1)*(r + 2)/6;
5396
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5397
}// end loop over 'r'
5398
for (unsigned int r = 0; r < 1; r++)
5399
{
5400
for (unsigned int s = 1; s < 2 - r; s++)
5401
{
5402
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5403
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5404
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5405
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5406
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5407
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5408
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5409
}// end loop over 's'
5410
}// end loop over 'r'
5411
for (unsigned int r = 0; r < 2; r++)
5412
{
5413
for (unsigned int s = 0; s < 2 - r; s++)
5414
{
5415
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5416
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5417
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5418
}// end loop over 's'
5419
}// end loop over 'r'
5420
for (unsigned int r = 0; r < 1; r++)
5421
{
5422
for (unsigned int s = 0; s < 1 - r; s++)
5423
{
5424
for (unsigned int t = 1; t < 2 - r - s; t++)
5425
{
5426
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5427
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5428
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5429
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5430
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5431
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5432
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5433
}// end loop over 't'
5434
}// end loop over 's'
5435
}// end loop over 'r'
5436
for (unsigned int r = 0; r < 3; r++)
5437
{
5438
for (unsigned int s = 0; s < 3 - r; s++)
5439
{
5440
for (unsigned int t = 0; t < 3 - r - s; t++)
5441
{
5442
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5443
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5444
}// end loop over 't'
5445
}// end loop over 's'
5446
}// end loop over 'r'
3829
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3830
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3831
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3832
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3833
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3834
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3835
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3836
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3837
basisvalues[0] *= std::sqrt(0.75);
3838
basisvalues[3] *= std::sqrt(1.25);
3839
basisvalues[9] *= std::sqrt(1.75);
3840
basisvalues[2] *= std::sqrt(2.5);
3841
basisvalues[8] *= std::sqrt(3.5);
3842
basisvalues[7] *= std::sqrt(5.25);
3843
basisvalues[1] *= std::sqrt(7.5);
3844
basisvalues[6] *= std::sqrt(10.5);
3845
basisvalues[5] *= std::sqrt(15.75);
3846
basisvalues[4] *= std::sqrt(26.25);
5447
3847
5448
3848
// Table(s) of coefficients.
5449
3849
static const double coefficients0[10] = \
5463
3863
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5464
3864
5465
3865
// Declare helper variables.
5466
unsigned int rr = 0;
5467
unsigned int ss = 0;
5468
unsigned int tt = 0;
5469
double tmp5 = 0.0;
5470
double tmp6 = 0.0;
5471
double tmp7 = 0.0;
5472
3866
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5473
3867
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5474
3868
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5478
3872
// Compute basisvalues.
5479
3873
basisvalues[0] = 1.0;
5480
3874
basisvalues[1] = tmp0;
5481
for (unsigned int r = 1; r < 2; r++)
5482
{
5483
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5484
ss = r*(r + 1)*(r + 2)/6;
5485
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5486
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5487
}// end loop over 'r'
5488
for (unsigned int r = 0; r < 2; r++)
5489
{
5490
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5491
ss = r*(r + 1)*(r + 2)/6;
5492
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5493
}// end loop over 'r'
5494
for (unsigned int r = 0; r < 1; r++)
5495
{
5496
for (unsigned int s = 1; s < 2 - r; s++)
5497
{
5498
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5499
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5500
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5501
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5502
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5503
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5504
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5505
}// end loop over 's'
5506
}// end loop over 'r'
5507
for (unsigned int r = 0; r < 2; r++)
5508
{
5509
for (unsigned int s = 0; s < 2 - r; s++)
5510
{
5511
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5512
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5513
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5514
}// end loop over 's'
5515
}// end loop over 'r'
5516
for (unsigned int r = 0; r < 1; r++)
5517
{
5518
for (unsigned int s = 0; s < 1 - r; s++)
5519
{
5520
for (unsigned int t = 1; t < 2 - r - s; t++)
5521
{
5522
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5523
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5524
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5525
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5526
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5527
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5528
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5529
}// end loop over 't'
5530
}// end loop over 's'
5531
}// end loop over 'r'
5532
for (unsigned int r = 0; r < 3; r++)
5533
{
5534
for (unsigned int s = 0; s < 3 - r; s++)
5535
{
5536
for (unsigned int t = 0; t < 3 - r - s; t++)
5537
{
5538
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5539
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5540
}// end loop over 't'
5541
}// end loop over 's'
5542
}// end loop over 'r'
3875
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3876
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3877
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3878
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3879
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3880
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3881
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3882
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3883
basisvalues[0] *= std::sqrt(0.75);
3884
basisvalues[3] *= std::sqrt(1.25);
3885
basisvalues[9] *= std::sqrt(1.75);
3886
basisvalues[2] *= std::sqrt(2.5);
3887
basisvalues[8] *= std::sqrt(3.5);
3888
basisvalues[7] *= std::sqrt(5.25);
3889
basisvalues[1] *= std::sqrt(7.5);
3890
basisvalues[6] *= std::sqrt(10.5);
3891
basisvalues[5] *= std::sqrt(15.75);
3892
basisvalues[4] *= std::sqrt(26.25);
5543
3893
5544
3894
// Table(s) of coefficients.
5545
3895
static const double coefficients0[10] = \
5559
3909
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5560
3910
5561
3911
// Declare helper variables.
5562
unsigned int rr = 0;
5563
unsigned int ss = 0;
5564
unsigned int tt = 0;
5565
double tmp5 = 0.0;
5566
double tmp6 = 0.0;
5567
double tmp7 = 0.0;
5568
3912
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5569
3913
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5570
3914
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5574
3918
// Compute basisvalues.
5575
3919
basisvalues[0] = 1.0;
5576
3920
basisvalues[1] = tmp0;
5577
for (unsigned int r = 1; r < 2; r++)
5578
{
5579
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5580
ss = r*(r + 1)*(r + 2)/6;
5581
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5582
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5583
}// end loop over 'r'
5584
for (unsigned int r = 0; r < 2; r++)
5585
{
5586
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5587
ss = r*(r + 1)*(r + 2)/6;
5588
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5589
}// end loop over 'r'
5590
for (unsigned int r = 0; r < 1; r++)
5591
{
5592
for (unsigned int s = 1; s < 2 - r; s++)
5593
{
5594
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5595
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5596
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5597
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5598
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5599
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5600
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5601
}// end loop over 's'
5602
}// end loop over 'r'
5603
for (unsigned int r = 0; r < 2; r++)
5604
{
5605
for (unsigned int s = 0; s < 2 - r; s++)
5606
{
5607
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5608
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5609
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5610
}// end loop over 's'
5611
}// end loop over 'r'
5612
for (unsigned int r = 0; r < 1; r++)
5613
{
5614
for (unsigned int s = 0; s < 1 - r; s++)
5615
{
5616
for (unsigned int t = 1; t < 2 - r - s; t++)
5617
{
5618
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5619
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5620
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5621
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5622
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5623
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5624
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5625
}// end loop over 't'
5626
}// end loop over 's'
5627
}// end loop over 'r'
5628
for (unsigned int r = 0; r < 3; r++)
5629
{
5630
for (unsigned int s = 0; s < 3 - r; s++)
5631
{
5632
for (unsigned int t = 0; t < 3 - r - s; t++)
5633
{
5634
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5635
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5636
}// end loop over 't'
5637
}// end loop over 's'
5638
}// end loop over 'r'
3921
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3922
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3923
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3924
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3925
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3926
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3927
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3928
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3929
basisvalues[0] *= std::sqrt(0.75);
3930
basisvalues[3] *= std::sqrt(1.25);
3931
basisvalues[9] *= std::sqrt(1.75);
3932
basisvalues[2] *= std::sqrt(2.5);
3933
basisvalues[8] *= std::sqrt(3.5);
3934
basisvalues[7] *= std::sqrt(5.25);
3935
basisvalues[1] *= std::sqrt(7.5);
3936
basisvalues[6] *= std::sqrt(10.5);
3937
basisvalues[5] *= std::sqrt(15.75);
3938
basisvalues[4] *= std::sqrt(26.25);
5639
3939
5640
3940
// Table(s) of coefficients.
5641
3941
static const double coefficients0[10] = \
5655
3955
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5656
3956
5657
3957
// Declare helper variables.
5658
unsigned int rr = 0;
5659
unsigned int ss = 0;
5660
unsigned int tt = 0;
5661
double tmp5 = 0.0;
5662
double tmp6 = 0.0;
5663
double tmp7 = 0.0;
5664
3958
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5665
3959
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5666
3960
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5670
3964
// Compute basisvalues.
5671
3965
basisvalues[0] = 1.0;
5672
3966
basisvalues[1] = tmp0;
5673
for (unsigned int r = 1; r < 2; r++)
5674
{
5675
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5676
ss = r*(r + 1)*(r + 2)/6;
5677
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5678
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5679
}// end loop over 'r'
5680
for (unsigned int r = 0; r < 2; r++)
5681
{
5682
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5683
ss = r*(r + 1)*(r + 2)/6;
5684
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5685
}// end loop over 'r'
5686
for (unsigned int r = 0; r < 1; r++)
5687
{
5688
for (unsigned int s = 1; s < 2 - r; s++)
5689
{
5690
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5691
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5692
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5693
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5694
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5695
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5696
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5697
}// end loop over 's'
5698
}// end loop over 'r'
5699
for (unsigned int r = 0; r < 2; r++)
5700
{
5701
for (unsigned int s = 0; s < 2 - r; s++)
5702
{
5703
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5704
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5705
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5706
}// end loop over 's'
5707
}// end loop over 'r'
5708
for (unsigned int r = 0; r < 1; r++)
5709
{
5710
for (unsigned int s = 0; s < 1 - r; s++)
5711
{
5712
for (unsigned int t = 1; t < 2 - r - s; t++)
5713
{
5714
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5715
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5716
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5717
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5718
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5719
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5720
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5721
}// end loop over 't'
5722
}// end loop over 's'
5723
}// end loop over 'r'
5724
for (unsigned int r = 0; r < 3; r++)
5725
{
5726
for (unsigned int s = 0; s < 3 - r; s++)
5727
{
5728
for (unsigned int t = 0; t < 3 - r - s; t++)
5729
{
5730
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5731
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5732
}// end loop over 't'
5733
}// end loop over 's'
5734
}// end loop over 'r'
3967
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
3968
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
3969
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
3970
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
3971
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
3972
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
3973
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
3974
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
3975
basisvalues[0] *= std::sqrt(0.75);
3976
basisvalues[3] *= std::sqrt(1.25);
3977
basisvalues[9] *= std::sqrt(1.75);
3978
basisvalues[2] *= std::sqrt(2.5);
3979
basisvalues[8] *= std::sqrt(3.5);
3980
basisvalues[7] *= std::sqrt(5.25);
3981
basisvalues[1] *= std::sqrt(7.5);
3982
basisvalues[6] *= std::sqrt(10.5);
3983
basisvalues[5] *= std::sqrt(15.75);
3984
basisvalues[4] *= std::sqrt(26.25);
5735
3985
5736
3986
// Table(s) of coefficients.
5737
3987
static const double coefficients0[10] = \
5751
4001
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5752
4002
5753
4003
// Declare helper variables.
5754
unsigned int rr = 0;
5755
unsigned int ss = 0;
5756
unsigned int tt = 0;
5757
double tmp5 = 0.0;
5758
double tmp6 = 0.0;
5759
double tmp7 = 0.0;
5760
4004
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5761
4005
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5762
4006
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5766
4010
// Compute basisvalues.
5767
4011
basisvalues[0] = 1.0;
5768
4012
basisvalues[1] = tmp0;
5769
for (unsigned int r = 1; r < 2; r++)
5770
{
5771
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5772
ss = r*(r + 1)*(r + 2)/6;
5773
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5774
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5775
}// end loop over 'r'
5776
for (unsigned int r = 0; r < 2; r++)
5777
{
5778
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5779
ss = r*(r + 1)*(r + 2)/6;
5780
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5781
}// end loop over 'r'
5782
for (unsigned int r = 0; r < 1; r++)
5783
{
5784
for (unsigned int s = 1; s < 2 - r; s++)
5785
{
5786
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5787
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5788
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5789
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5790
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5791
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5792
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5793
}// end loop over 's'
5794
}// end loop over 'r'
5795
for (unsigned int r = 0; r < 2; r++)
5796
{
5797
for (unsigned int s = 0; s < 2 - r; s++)
5798
{
5799
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5800
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5801
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5802
}// end loop over 's'
5803
}// end loop over 'r'
5804
for (unsigned int r = 0; r < 1; r++)
5805
{
5806
for (unsigned int s = 0; s < 1 - r; s++)
5807
{
5808
for (unsigned int t = 1; t < 2 - r - s; t++)
5809
{
5810
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5811
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5812
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5813
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5814
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5815
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5816
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5817
}// end loop over 't'
5818
}// end loop over 's'
5819
}// end loop over 'r'
5820
for (unsigned int r = 0; r < 3; r++)
5821
{
5822
for (unsigned int s = 0; s < 3 - r; s++)
5823
{
5824
for (unsigned int t = 0; t < 3 - r - s; t++)
5825
{
5826
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5827
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5828
}// end loop over 't'
5829
}// end loop over 's'
5830
}// end loop over 'r'
4013
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4014
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4015
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4016
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4017
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4018
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4019
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4020
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4021
basisvalues[0] *= std::sqrt(0.75);
4022
basisvalues[3] *= std::sqrt(1.25);
4023
basisvalues[9] *= std::sqrt(1.75);
4024
basisvalues[2] *= std::sqrt(2.5);
4025
basisvalues[8] *= std::sqrt(3.5);
4026
basisvalues[7] *= std::sqrt(5.25);
4027
basisvalues[1] *= std::sqrt(7.5);
4028
basisvalues[6] *= std::sqrt(10.5);
4029
basisvalues[5] *= std::sqrt(15.75);
4030
basisvalues[4] *= std::sqrt(26.25);
5831
4031
5832
4032
// Table(s) of coefficients.
5833
4033
static const double coefficients0[10] = \
5847
4047
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5848
4048
5849
4049
// Declare helper variables.
5850
unsigned int rr = 0;
5851
unsigned int ss = 0;
5852
unsigned int tt = 0;
5853
double tmp5 = 0.0;
5854
double tmp6 = 0.0;
5855
double tmp7 = 0.0;
5856
4050
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5857
4051
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5858
4052
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5862
4056
// Compute basisvalues.
5863
4057
basisvalues[0] = 1.0;
5864
4058
basisvalues[1] = tmp0;
5865
for (unsigned int r = 1; r < 2; r++)
5866
{
5867
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5868
ss = r*(r + 1)*(r + 2)/6;
5869
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5870
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5871
}// end loop over 'r'
5872
for (unsigned int r = 0; r < 2; r++)
5873
{
5874
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5875
ss = r*(r + 1)*(r + 2)/6;
5876
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5877
}// end loop over 'r'
5878
for (unsigned int r = 0; r < 1; r++)
5879
{
5880
for (unsigned int s = 1; s < 2 - r; s++)
5881
{
5882
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5883
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5884
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5885
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5886
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5887
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5888
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5889
}// end loop over 's'
5890
}// end loop over 'r'
5891
for (unsigned int r = 0; r < 2; r++)
5892
{
5893
for (unsigned int s = 0; s < 2 - r; s++)
5894
{
5895
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5896
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5897
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5898
}// end loop over 's'
5899
}// end loop over 'r'
5900
for (unsigned int r = 0; r < 1; r++)
5901
{
5902
for (unsigned int s = 0; s < 1 - r; s++)
5903
{
5904
for (unsigned int t = 1; t < 2 - r - s; t++)
5905
{
5906
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
5907
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5908
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
5909
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
5910
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5911
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
5912
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
5913
}// end loop over 't'
5914
}// end loop over 's'
5915
}// end loop over 'r'
5916
for (unsigned int r = 0; r < 3; r++)
5917
{
5918
for (unsigned int s = 0; s < 3 - r; s++)
5919
{
5920
for (unsigned int t = 0; t < 3 - r - s; t++)
5921
{
5922
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
5923
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
5924
}// end loop over 't'
5925
}// end loop over 's'
5926
}// end loop over 'r'
4059
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4060
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4061
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4062
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4063
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4064
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4065
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4066
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4067
basisvalues[0] *= std::sqrt(0.75);
4068
basisvalues[3] *= std::sqrt(1.25);
4069
basisvalues[9] *= std::sqrt(1.75);
4070
basisvalues[2] *= std::sqrt(2.5);
4071
basisvalues[8] *= std::sqrt(3.5);
4072
basisvalues[7] *= std::sqrt(5.25);
4073
basisvalues[1] *= std::sqrt(7.5);
4074
basisvalues[6] *= std::sqrt(10.5);
4075
basisvalues[5] *= std::sqrt(15.75);
4076
basisvalues[4] *= std::sqrt(26.25);
5927
4077
5928
4078
// Table(s) of coefficients.
5929
4079
static const double coefficients0[10] = \
5943
4093
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5944
4094
5945
4095
// Declare helper variables.
5946
unsigned int rr = 0;
5947
unsigned int ss = 0;
5948
unsigned int tt = 0;
5949
double tmp5 = 0.0;
5950
double tmp6 = 0.0;
5951
double tmp7 = 0.0;
5952
4096
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
5953
4097
double tmp1 = 0.25*(Y + Z)*(Y + Z);
5954
4098
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
5958
4102
// Compute basisvalues.
5959
4103
basisvalues[0] = 1.0;
5960
4104
basisvalues[1] = tmp0;
5961
for (unsigned int r = 1; r < 2; r++)
5962
{
5963
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
5964
ss = r*(r + 1)*(r + 2)/6;
5965
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
5966
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
5967
}// end loop over 'r'
5968
for (unsigned int r = 0; r < 2; r++)
5969
{
5970
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
5971
ss = r*(r + 1)*(r + 2)/6;
5972
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
5973
}// end loop over 'r'
5974
for (unsigned int r = 0; r < 1; r++)
5975
{
5976
for (unsigned int s = 1; s < 2 - r; s++)
5977
{
5978
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
5979
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5980
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
5981
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
5982
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5983
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
5984
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
5985
}// end loop over 's'
5986
}// end loop over 'r'
5987
for (unsigned int r = 0; r < 2; r++)
5988
{
5989
for (unsigned int s = 0; s < 2 - r; s++)
5990
{
5991
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
5992
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
5993
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
5994
}// end loop over 's'
5995
}// end loop over 'r'
5996
for (unsigned int r = 0; r < 1; r++)
5997
{
5998
for (unsigned int s = 0; s < 1 - r; s++)
5999
{
6000
for (unsigned int t = 1; t < 2 - r - s; t++)
6001
{
6002
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6003
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6004
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6005
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6006
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6007
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6008
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6009
}// end loop over 't'
6010
}// end loop over 's'
6011
}// end loop over 'r'
6012
for (unsigned int r = 0; r < 3; r++)
6013
{
6014
for (unsigned int s = 0; s < 3 - r; s++)
6015
{
6016
for (unsigned int t = 0; t < 3 - r - s; t++)
6017
{
6018
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6019
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6020
}// end loop over 't'
6021
}// end loop over 's'
6022
}// end loop over 'r'
4105
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4106
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4107
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4108
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4109
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4110
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4111
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4112
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4113
basisvalues[0] *= std::sqrt(0.75);
4114
basisvalues[3] *= std::sqrt(1.25);
4115
basisvalues[9] *= std::sqrt(1.75);
4116
basisvalues[2] *= std::sqrt(2.5);
4117
basisvalues[8] *= std::sqrt(3.5);
4118
basisvalues[7] *= std::sqrt(5.25);
4119
basisvalues[1] *= std::sqrt(7.5);
4120
basisvalues[6] *= std::sqrt(10.5);
4121
basisvalues[5] *= std::sqrt(15.75);
4122
basisvalues[4] *= std::sqrt(26.25);
6023
4123
6024
4124
// Table(s) of coefficients.
6025
4125
static const double coefficients0[10] = \
6039
4139
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6040
4140
6041
4141
// Declare helper variables.
6042
unsigned int rr = 0;
6043
unsigned int ss = 0;
6044
unsigned int tt = 0;
6045
double tmp5 = 0.0;
6046
double tmp6 = 0.0;
6047
double tmp7 = 0.0;
6048
4142
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6049
4143
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6050
4144
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6054
4148
// Compute basisvalues.
6055
4149
basisvalues[0] = 1.0;
6056
4150
basisvalues[1] = tmp0;
6057
for (unsigned int r = 1; r < 2; r++)
6058
{
6059
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6060
ss = r*(r + 1)*(r + 2)/6;
6061
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6062
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6063
}// end loop over 'r'
6064
for (unsigned int r = 0; r < 2; r++)
6065
{
6066
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6067
ss = r*(r + 1)*(r + 2)/6;
6068
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6069
}// end loop over 'r'
6070
for (unsigned int r = 0; r < 1; r++)
6071
{
6072
for (unsigned int s = 1; s < 2 - r; s++)
6073
{
6074
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6075
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6076
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6077
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6078
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6079
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6080
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6081
}// end loop over 's'
6082
}// end loop over 'r'
6083
for (unsigned int r = 0; r < 2; r++)
6084
{
6085
for (unsigned int s = 0; s < 2 - r; s++)
6086
{
6087
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6088
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6089
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6090
}// end loop over 's'
6091
}// end loop over 'r'
6092
for (unsigned int r = 0; r < 1; r++)
6093
{
6094
for (unsigned int s = 0; s < 1 - r; s++)
6095
{
6096
for (unsigned int t = 1; t < 2 - r - s; t++)
6097
{
6098
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6099
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6100
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6101
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6102
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6103
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6104
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6105
}// end loop over 't'
6106
}// end loop over 's'
6107
}// end loop over 'r'
6108
for (unsigned int r = 0; r < 3; r++)
6109
{
6110
for (unsigned int s = 0; s < 3 - r; s++)
6111
{
6112
for (unsigned int t = 0; t < 3 - r - s; t++)
6113
{
6114
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6115
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6116
}// end loop over 't'
6117
}// end loop over 's'
6118
}// end loop over 'r'
4151
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4152
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4153
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4154
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4155
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4156
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4157
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4158
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4159
basisvalues[0] *= std::sqrt(0.75);
4160
basisvalues[3] *= std::sqrt(1.25);
4161
basisvalues[9] *= std::sqrt(1.75);
4162
basisvalues[2] *= std::sqrt(2.5);
4163
basisvalues[8] *= std::sqrt(3.5);
4164
basisvalues[7] *= std::sqrt(5.25);
4165
basisvalues[1] *= std::sqrt(7.5);
4166
basisvalues[6] *= std::sqrt(10.5);
4167
basisvalues[5] *= std::sqrt(15.75);
4168
basisvalues[4] *= std::sqrt(26.25);
6119
4169
6120
4170
// Table(s) of coefficients.
6121
4171
static const double coefficients0[10] = \
6135
4185
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6136
4186
6137
4187
// Declare helper variables.
6138
unsigned int rr = 0;
6139
unsigned int ss = 0;
6140
unsigned int tt = 0;
6141
double tmp5 = 0.0;
6142
double tmp6 = 0.0;
6143
double tmp7 = 0.0;
6144
4188
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6145
4189
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6146
4190
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6150
4194
// Compute basisvalues.
6151
4195
basisvalues[0] = 1.0;
6152
4196
basisvalues[1] = tmp0;
6153
for (unsigned int r = 1; r < 2; r++)
6154
{
6155
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6156
ss = r*(r + 1)*(r + 2)/6;
6157
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6158
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6159
}// end loop over 'r'
6160
for (unsigned int r = 0; r < 2; r++)
6161
{
6162
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6163
ss = r*(r + 1)*(r + 2)/6;
6164
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6165
}// end loop over 'r'
6166
for (unsigned int r = 0; r < 1; r++)
6167
{
6168
for (unsigned int s = 1; s < 2 - r; s++)
6169
{
6170
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6171
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6172
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6173
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6174
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6175
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6176
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6177
}// end loop over 's'
6178
}// end loop over 'r'
6179
for (unsigned int r = 0; r < 2; r++)
6180
{
6181
for (unsigned int s = 0; s < 2 - r; s++)
6182
{
6183
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6184
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6185
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6186
}// end loop over 's'
6187
}// end loop over 'r'
6188
for (unsigned int r = 0; r < 1; r++)
6189
{
6190
for (unsigned int s = 0; s < 1 - r; s++)
6191
{
6192
for (unsigned int t = 1; t < 2 - r - s; t++)
6193
{
6194
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6195
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6196
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6197
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6198
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6199
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6200
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6201
}// end loop over 't'
6202
}// end loop over 's'
6203
}// end loop over 'r'
6204
for (unsigned int r = 0; r < 3; r++)
6205
{
6206
for (unsigned int s = 0; s < 3 - r; s++)
6207
{
6208
for (unsigned int t = 0; t < 3 - r - s; t++)
6209
{
6210
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6211
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6212
}// end loop over 't'
6213
}// end loop over 's'
6214
}// end loop over 'r'
4197
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4198
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4199
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4200
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4201
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4202
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4203
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4204
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4205
basisvalues[0] *= std::sqrt(0.75);
4206
basisvalues[3] *= std::sqrt(1.25);
4207
basisvalues[9] *= std::sqrt(1.75);
4208
basisvalues[2] *= std::sqrt(2.5);
4209
basisvalues[8] *= std::sqrt(3.5);
4210
basisvalues[7] *= std::sqrt(5.25);
4211
basisvalues[1] *= std::sqrt(7.5);
4212
basisvalues[6] *= std::sqrt(10.5);
4213
basisvalues[5] *= std::sqrt(15.75);
4214
basisvalues[4] *= std::sqrt(26.25);
6215
4215
6216
4216
// Table(s) of coefficients.
6217
4217
static const double coefficients0[10] = \
6231
4231
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6232
4232
6233
4233
// Declare helper variables.
6234
unsigned int rr = 0;
6235
unsigned int ss = 0;
6236
unsigned int tt = 0;
6237
double tmp5 = 0.0;
6238
double tmp6 = 0.0;
6239
double tmp7 = 0.0;
6240
4234
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6241
4235
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6242
4236
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6246
4240
// Compute basisvalues.
6247
4241
basisvalues[0] = 1.0;
6248
4242
basisvalues[1] = tmp0;
6249
for (unsigned int r = 1; r < 2; r++)
6250
{
6251
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6252
ss = r*(r + 1)*(r + 2)/6;
6253
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6254
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6255
}// end loop over 'r'
6256
for (unsigned int r = 0; r < 2; r++)
6257
{
6258
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6259
ss = r*(r + 1)*(r + 2)/6;
6260
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6261
}// end loop over 'r'
6262
for (unsigned int r = 0; r < 1; r++)
6263
{
6264
for (unsigned int s = 1; s < 2 - r; s++)
6265
{
6266
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6267
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6268
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6269
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6270
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6271
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6272
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6273
}// end loop over 's'
6274
}// end loop over 'r'
6275
for (unsigned int r = 0; r < 2; r++)
6276
{
6277
for (unsigned int s = 0; s < 2 - r; s++)
6278
{
6279
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6280
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6281
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6282
}// end loop over 's'
6283
}// end loop over 'r'
6284
for (unsigned int r = 0; r < 1; r++)
6285
{
6286
for (unsigned int s = 0; s < 1 - r; s++)
6287
{
6288
for (unsigned int t = 1; t < 2 - r - s; t++)
6289
{
6290
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6291
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6292
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6293
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6294
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6295
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6296
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6297
}// end loop over 't'
6298
}// end loop over 's'
6299
}// end loop over 'r'
6300
for (unsigned int r = 0; r < 3; r++)
6301
{
6302
for (unsigned int s = 0; s < 3 - r; s++)
6303
{
6304
for (unsigned int t = 0; t < 3 - r - s; t++)
6305
{
6306
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6307
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6308
}// end loop over 't'
6309
}// end loop over 's'
6310
}// end loop over 'r'
4243
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4244
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4245
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4246
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4247
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4248
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4249
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4250
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4251
basisvalues[0] *= std::sqrt(0.75);
4252
basisvalues[3] *= std::sqrt(1.25);
4253
basisvalues[9] *= std::sqrt(1.75);
4254
basisvalues[2] *= std::sqrt(2.5);
4255
basisvalues[8] *= std::sqrt(3.5);
4256
basisvalues[7] *= std::sqrt(5.25);
4257
basisvalues[1] *= std::sqrt(7.5);
4258
basisvalues[6] *= std::sqrt(10.5);
4259
basisvalues[5] *= std::sqrt(15.75);
4260
basisvalues[4] *= std::sqrt(26.25);
6311
4261
6312
4262
// Table(s) of coefficients.
6313
4263
static const double coefficients0[10] = \
6327
4277
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6328
4278
6329
4279
// Declare helper variables.
6330
unsigned int rr = 0;
6331
unsigned int ss = 0;
6332
unsigned int tt = 0;
6333
double tmp5 = 0.0;
6334
double tmp6 = 0.0;
6335
double tmp7 = 0.0;
6336
4280
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6337
4281
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6338
4282
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6342
4286
// Compute basisvalues.
6343
4287
basisvalues[0] = 1.0;
6344
4288
basisvalues[1] = tmp0;
6345
for (unsigned int r = 1; r < 2; r++)
6346
{
6347
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6348
ss = r*(r + 1)*(r + 2)/6;
6349
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6350
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6351
}// end loop over 'r'
6352
for (unsigned int r = 0; r < 2; r++)
6353
{
6354
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6355
ss = r*(r + 1)*(r + 2)/6;
6356
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6357
}// end loop over 'r'
6358
for (unsigned int r = 0; r < 1; r++)
6359
{
6360
for (unsigned int s = 1; s < 2 - r; s++)
6361
{
6362
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6363
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6364
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6365
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6366
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6367
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6368
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6369
}// end loop over 's'
6370
}// end loop over 'r'
6371
for (unsigned int r = 0; r < 2; r++)
6372
{
6373
for (unsigned int s = 0; s < 2 - r; s++)
6374
{
6375
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6376
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6377
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6378
}// end loop over 's'
6379
}// end loop over 'r'
6380
for (unsigned int r = 0; r < 1; r++)
6381
{
6382
for (unsigned int s = 0; s < 1 - r; s++)
6383
{
6384
for (unsigned int t = 1; t < 2 - r - s; t++)
6385
{
6386
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6387
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6388
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6389
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6390
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6391
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6392
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6393
}// end loop over 't'
6394
}// end loop over 's'
6395
}// end loop over 'r'
6396
for (unsigned int r = 0; r < 3; r++)
6397
{
6398
for (unsigned int s = 0; s < 3 - r; s++)
6399
{
6400
for (unsigned int t = 0; t < 3 - r - s; t++)
6401
{
6402
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6403
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6404
}// end loop over 't'
6405
}// end loop over 's'
6406
}// end loop over 'r'
4289
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4290
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4291
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4292
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4293
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4294
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4295
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4296
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4297
basisvalues[0] *= std::sqrt(0.75);
4298
basisvalues[3] *= std::sqrt(1.25);
4299
basisvalues[9] *= std::sqrt(1.75);
4300
basisvalues[2] *= std::sqrt(2.5);
4301
basisvalues[8] *= std::sqrt(3.5);
4302
basisvalues[7] *= std::sqrt(5.25);
4303
basisvalues[1] *= std::sqrt(7.5);
4304
basisvalues[6] *= std::sqrt(10.5);
4305
basisvalues[5] *= std::sqrt(15.75);
4306
basisvalues[4] *= std::sqrt(26.25);
6407
4307
6408
4308
// Table(s) of coefficients.
6409
4309
static const double coefficients0[10] = \
6423
4323
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6424
4324
6425
4325
// Declare helper variables.
6426
unsigned int rr = 0;
6427
unsigned int ss = 0;
6428
unsigned int tt = 0;
6429
double tmp5 = 0.0;
6430
double tmp6 = 0.0;
6431
double tmp7 = 0.0;
6432
4326
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6433
4327
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6434
4328
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6438
4332
// Compute basisvalues.
6439
4333
basisvalues[0] = 1.0;
6440
4334
basisvalues[1] = tmp0;
6441
for (unsigned int r = 1; r < 2; r++)
6442
{
6443
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6444
ss = r*(r + 1)*(r + 2)/6;
6445
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6446
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6447
}// end loop over 'r'
6448
for (unsigned int r = 0; r < 2; r++)
6449
{
6450
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6451
ss = r*(r + 1)*(r + 2)/6;
6452
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6453
}// end loop over 'r'
6454
for (unsigned int r = 0; r < 1; r++)
6455
{
6456
for (unsigned int s = 1; s < 2 - r; s++)
6457
{
6458
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6459
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6460
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6461
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6462
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6463
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6464
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6465
}// end loop over 's'
6466
}// end loop over 'r'
6467
for (unsigned int r = 0; r < 2; r++)
6468
{
6469
for (unsigned int s = 0; s < 2 - r; s++)
6470
{
6471
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6472
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6473
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6474
}// end loop over 's'
6475
}// end loop over 'r'
6476
for (unsigned int r = 0; r < 1; r++)
6477
{
6478
for (unsigned int s = 0; s < 1 - r; s++)
6479
{
6480
for (unsigned int t = 1; t < 2 - r - s; t++)
6481
{
6482
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6483
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6484
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6485
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6486
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6487
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6488
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6489
}// end loop over 't'
6490
}// end loop over 's'
6491
}// end loop over 'r'
6492
for (unsigned int r = 0; r < 3; r++)
6493
{
6494
for (unsigned int s = 0; s < 3 - r; s++)
6495
{
6496
for (unsigned int t = 0; t < 3 - r - s; t++)
6497
{
6498
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6499
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6500
}// end loop over 't'
6501
}// end loop over 's'
6502
}// end loop over 'r'
4335
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4336
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4337
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4338
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4339
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4340
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4341
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4342
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4343
basisvalues[0] *= std::sqrt(0.75);
4344
basisvalues[3] *= std::sqrt(1.25);
4345
basisvalues[9] *= std::sqrt(1.75);
4346
basisvalues[2] *= std::sqrt(2.5);
4347
basisvalues[8] *= std::sqrt(3.5);
4348
basisvalues[7] *= std::sqrt(5.25);
4349
basisvalues[1] *= std::sqrt(7.5);
4350
basisvalues[6] *= std::sqrt(10.5);
4351
basisvalues[5] *= std::sqrt(15.75);
4352
basisvalues[4] *= std::sqrt(26.25);
6503
4353
6504
4354
// Table(s) of coefficients.
6505
4355
static const double coefficients0[10] = \
6519
4369
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6520
4370
6521
4371
// Declare helper variables.
6522
unsigned int rr = 0;
6523
unsigned int ss = 0;
6524
unsigned int tt = 0;
6525
double tmp5 = 0.0;
6526
double tmp6 = 0.0;
6527
double tmp7 = 0.0;
6528
4372
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6529
4373
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6530
4374
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6534
4378
// Compute basisvalues.
6535
4379
basisvalues[0] = 1.0;
6536
4380
basisvalues[1] = tmp0;
6537
for (unsigned int r = 1; r < 2; r++)
6538
{
6539
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6540
ss = r*(r + 1)*(r + 2)/6;
6541
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6542
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6543
}// end loop over 'r'
6544
for (unsigned int r = 0; r < 2; r++)
6545
{
6546
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6547
ss = r*(r + 1)*(r + 2)/6;
6548
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6549
}// end loop over 'r'
6550
for (unsigned int r = 0; r < 1; r++)
6551
{
6552
for (unsigned int s = 1; s < 2 - r; s++)
6553
{
6554
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6555
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6556
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6557
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6558
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6559
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6560
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6561
}// end loop over 's'
6562
}// end loop over 'r'
6563
for (unsigned int r = 0; r < 2; r++)
6564
{
6565
for (unsigned int s = 0; s < 2 - r; s++)
6566
{
6567
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6568
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6569
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6570
}// end loop over 's'
6571
}// end loop over 'r'
6572
for (unsigned int r = 0; r < 1; r++)
6573
{
6574
for (unsigned int s = 0; s < 1 - r; s++)
6575
{
6576
for (unsigned int t = 1; t < 2 - r - s; t++)
6577
{
6578
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6579
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6580
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6581
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6582
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6583
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6584
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6585
}// end loop over 't'
6586
}// end loop over 's'
6587
}// end loop over 'r'
6588
for (unsigned int r = 0; r < 3; r++)
6589
{
6590
for (unsigned int s = 0; s < 3 - r; s++)
6591
{
6592
for (unsigned int t = 0; t < 3 - r - s; t++)
6593
{
6594
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6595
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6596
}// end loop over 't'
6597
}// end loop over 's'
6598
}// end loop over 'r'
4381
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4382
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4383
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4384
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4385
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4386
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4387
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4388
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4389
basisvalues[0] *= std::sqrt(0.75);
4390
basisvalues[3] *= std::sqrt(1.25);
4391
basisvalues[9] *= std::sqrt(1.75);
4392
basisvalues[2] *= std::sqrt(2.5);
4393
basisvalues[8] *= std::sqrt(3.5);
4394
basisvalues[7] *= std::sqrt(5.25);
4395
basisvalues[1] *= std::sqrt(7.5);
4396
basisvalues[6] *= std::sqrt(10.5);
4397
basisvalues[5] *= std::sqrt(15.75);
4398
basisvalues[4] *= std::sqrt(26.25);
6599
4399
6600
4400
// Table(s) of coefficients.
6601
4401
static const double coefficients0[10] = \
6615
4415
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6616
4416
6617
4417
// Declare helper variables.
6618
unsigned int rr = 0;
6619
unsigned int ss = 0;
6620
unsigned int tt = 0;
6621
double tmp5 = 0.0;
6622
double tmp6 = 0.0;
6623
double tmp7 = 0.0;
6624
4418
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6625
4419
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6626
4420
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6630
4424
// Compute basisvalues.
6631
4425
basisvalues[0] = 1.0;
6632
4426
basisvalues[1] = tmp0;
6633
for (unsigned int r = 1; r < 2; r++)
6634
{
6635
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6636
ss = r*(r + 1)*(r + 2)/6;
6637
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6638
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6639
}// end loop over 'r'
6640
for (unsigned int r = 0; r < 2; r++)
6641
{
6642
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6643
ss = r*(r + 1)*(r + 2)/6;
6644
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6645
}// end loop over 'r'
6646
for (unsigned int r = 0; r < 1; r++)
6647
{
6648
for (unsigned int s = 1; s < 2 - r; s++)
6649
{
6650
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6651
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6652
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6653
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6654
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6655
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6656
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6657
}// end loop over 's'
6658
}// end loop over 'r'
6659
for (unsigned int r = 0; r < 2; r++)
6660
{
6661
for (unsigned int s = 0; s < 2 - r; s++)
6662
{
6663
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6664
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6665
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6666
}// end loop over 's'
6667
}// end loop over 'r'
6668
for (unsigned int r = 0; r < 1; r++)
6669
{
6670
for (unsigned int s = 0; s < 1 - r; s++)
6671
{
6672
for (unsigned int t = 1; t < 2 - r - s; t++)
6673
{
6674
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6675
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6676
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6677
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6678
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6679
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6680
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6681
}// end loop over 't'
6682
}// end loop over 's'
6683
}// end loop over 'r'
6684
for (unsigned int r = 0; r < 3; r++)
6685
{
6686
for (unsigned int s = 0; s < 3 - r; s++)
6687
{
6688
for (unsigned int t = 0; t < 3 - r - s; t++)
6689
{
6690
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6691
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6692
}// end loop over 't'
6693
}// end loop over 's'
6694
}// end loop over 'r'
4427
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4428
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4429
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4430
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4431
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4432
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4433
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4434
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4435
basisvalues[0] *= std::sqrt(0.75);
4436
basisvalues[3] *= std::sqrt(1.25);
4437
basisvalues[9] *= std::sqrt(1.75);
4438
basisvalues[2] *= std::sqrt(2.5);
4439
basisvalues[8] *= std::sqrt(3.5);
4440
basisvalues[7] *= std::sqrt(5.25);
4441
basisvalues[1] *= std::sqrt(7.5);
4442
basisvalues[6] *= std::sqrt(10.5);
4443
basisvalues[5] *= std::sqrt(15.75);
4444
basisvalues[4] *= std::sqrt(26.25);
6695
4445
6696
4446
// Table(s) of coefficients.
6697
4447
static const double coefficients0[10] = \
6711
4461
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6712
4462
6713
4463
// Declare helper variables.
6714
unsigned int rr = 0;
6715
unsigned int ss = 0;
6716
unsigned int tt = 0;
6717
double tmp5 = 0.0;
6718
double tmp6 = 0.0;
6719
double tmp7 = 0.0;
6720
4464
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6721
4465
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6722
4466
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6726
4470
// Compute basisvalues.
6727
4471
basisvalues[0] = 1.0;
6728
4472
basisvalues[1] = tmp0;
6729
for (unsigned int r = 1; r < 2; r++)
6730
{
6731
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6732
ss = r*(r + 1)*(r + 2)/6;
6733
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6734
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6735
}// end loop over 'r'
6736
for (unsigned int r = 0; r < 2; r++)
6737
{
6738
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6739
ss = r*(r + 1)*(r + 2)/6;
6740
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6741
}// end loop over 'r'
6742
for (unsigned int r = 0; r < 1; r++)
6743
{
6744
for (unsigned int s = 1; s < 2 - r; s++)
6745
{
6746
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6747
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6748
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6749
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6750
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6751
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6752
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6753
}// end loop over 's'
6754
}// end loop over 'r'
6755
for (unsigned int r = 0; r < 2; r++)
6756
{
6757
for (unsigned int s = 0; s < 2 - r; s++)
6758
{
6759
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6760
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6761
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6762
}// end loop over 's'
6763
}// end loop over 'r'
6764
for (unsigned int r = 0; r < 1; r++)
6765
{
6766
for (unsigned int s = 0; s < 1 - r; s++)
6767
{
6768
for (unsigned int t = 1; t < 2 - r - s; t++)
6769
{
6770
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6771
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6772
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6773
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6774
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6775
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6776
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6777
}// end loop over 't'
6778
}// end loop over 's'
6779
}// end loop over 'r'
6780
for (unsigned int r = 0; r < 3; r++)
6781
{
6782
for (unsigned int s = 0; s < 3 - r; s++)
6783
{
6784
for (unsigned int t = 0; t < 3 - r - s; t++)
6785
{
6786
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6787
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6788
}// end loop over 't'
6789
}// end loop over 's'
6790
}// end loop over 'r'
4473
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4474
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4475
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4476
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4477
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4478
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4479
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4480
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4481
basisvalues[0] *= std::sqrt(0.75);
4482
basisvalues[3] *= std::sqrt(1.25);
4483
basisvalues[9] *= std::sqrt(1.75);
4484
basisvalues[2] *= std::sqrt(2.5);
4485
basisvalues[8] *= std::sqrt(3.5);
4486
basisvalues[7] *= std::sqrt(5.25);
4487
basisvalues[1] *= std::sqrt(7.5);
4488
basisvalues[6] *= std::sqrt(10.5);
4489
basisvalues[5] *= std::sqrt(15.75);
4490
basisvalues[4] *= std::sqrt(26.25);
6791
4491
6792
4492
// Table(s) of coefficients.
6793
4493
static const double coefficients0[10] = \
6807
4507
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6808
4508
6809
4509
// Declare helper variables.
6810
unsigned int rr = 0;
6811
unsigned int ss = 0;
6812
unsigned int tt = 0;
6813
double tmp5 = 0.0;
6814
double tmp6 = 0.0;
6815
double tmp7 = 0.0;
6816
4510
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6817
4511
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6818
4512
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6822
4516
// Compute basisvalues.
6823
4517
basisvalues[0] = 1.0;
6824
4518
basisvalues[1] = tmp0;
6825
for (unsigned int r = 1; r < 2; r++)
6826
{
6827
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6828
ss = r*(r + 1)*(r + 2)/6;
6829
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6830
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6831
}// end loop over 'r'
6832
for (unsigned int r = 0; r < 2; r++)
6833
{
6834
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6835
ss = r*(r + 1)*(r + 2)/6;
6836
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6837
}// end loop over 'r'
6838
for (unsigned int r = 0; r < 1; r++)
6839
{
6840
for (unsigned int s = 1; s < 2 - r; s++)
6841
{
6842
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6843
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6844
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6845
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6846
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6847
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6848
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6849
}// end loop over 's'
6850
}// end loop over 'r'
6851
for (unsigned int r = 0; r < 2; r++)
6852
{
6853
for (unsigned int s = 0; s < 2 - r; s++)
6854
{
6855
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6856
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6857
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6858
}// end loop over 's'
6859
}// end loop over 'r'
6860
for (unsigned int r = 0; r < 1; r++)
6861
{
6862
for (unsigned int s = 0; s < 1 - r; s++)
6863
{
6864
for (unsigned int t = 1; t < 2 - r - s; t++)
6865
{
6866
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6867
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6868
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6869
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6870
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6871
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6872
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6873
}// end loop over 't'
6874
}// end loop over 's'
6875
}// end loop over 'r'
6876
for (unsigned int r = 0; r < 3; r++)
6877
{
6878
for (unsigned int s = 0; s < 3 - r; s++)
6879
{
6880
for (unsigned int t = 0; t < 3 - r - s; t++)
6881
{
6882
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6883
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6884
}// end loop over 't'
6885
}// end loop over 's'
6886
}// end loop over 'r'
4519
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4520
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4521
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4522
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4523
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4524
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4525
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4526
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4527
basisvalues[0] *= std::sqrt(0.75);
4528
basisvalues[3] *= std::sqrt(1.25);
4529
basisvalues[9] *= std::sqrt(1.75);
4530
basisvalues[2] *= std::sqrt(2.5);
4531
basisvalues[8] *= std::sqrt(3.5);
4532
basisvalues[7] *= std::sqrt(5.25);
4533
basisvalues[1] *= std::sqrt(7.5);
4534
basisvalues[6] *= std::sqrt(10.5);
4535
basisvalues[5] *= std::sqrt(15.75);
4536
basisvalues[4] *= std::sqrt(26.25);
6887
4537
6888
4538
// Table(s) of coefficients.
6889
4539
static const double coefficients0[10] = \
6903
4553
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
6904
4554
6905
4555
// Declare helper variables.
6906
unsigned int rr = 0;
6907
unsigned int ss = 0;
6908
unsigned int tt = 0;
6909
double tmp5 = 0.0;
6910
double tmp6 = 0.0;
6911
double tmp7 = 0.0;
6912
4556
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
6913
4557
double tmp1 = 0.25*(Y + Z)*(Y + Z);
6914
4558
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
6918
4562
// Compute basisvalues.
6919
4563
basisvalues[0] = 1.0;
6920
4564
basisvalues[1] = tmp0;
6921
for (unsigned int r = 1; r < 2; r++)
6922
{
6923
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
6924
ss = r*(r + 1)*(r + 2)/6;
6925
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
6926
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
6927
}// end loop over 'r'
6928
for (unsigned int r = 0; r < 2; r++)
6929
{
6930
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
6931
ss = r*(r + 1)*(r + 2)/6;
6932
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
6933
}// end loop over 'r'
6934
for (unsigned int r = 0; r < 1; r++)
6935
{
6936
for (unsigned int s = 1; s < 2 - r; s++)
6937
{
6938
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
6939
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6940
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
6941
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
6942
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6943
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
6944
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
6945
}// end loop over 's'
6946
}// end loop over 'r'
6947
for (unsigned int r = 0; r < 2; r++)
6948
{
6949
for (unsigned int s = 0; s < 2 - r; s++)
6950
{
6951
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
6952
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
6953
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
6954
}// end loop over 's'
6955
}// end loop over 'r'
6956
for (unsigned int r = 0; r < 1; r++)
6957
{
6958
for (unsigned int s = 0; s < 1 - r; s++)
6959
{
6960
for (unsigned int t = 1; t < 2 - r - s; t++)
6961
{
6962
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
6963
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6964
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
6965
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
6966
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6967
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
6968
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
6969
}// end loop over 't'
6970
}// end loop over 's'
6971
}// end loop over 'r'
6972
for (unsigned int r = 0; r < 3; r++)
6973
{
6974
for (unsigned int s = 0; s < 3 - r; s++)
6975
{
6976
for (unsigned int t = 0; t < 3 - r - s; t++)
6977
{
6978
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
6979
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
6980
}// end loop over 't'
6981
}// end loop over 's'
6982
}// end loop over 'r'
4565
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4566
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4567
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4568
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4569
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4570
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4571
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4572
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4573
basisvalues[0] *= std::sqrt(0.75);
4574
basisvalues[3] *= std::sqrt(1.25);
4575
basisvalues[9] *= std::sqrt(1.75);
4576
basisvalues[2] *= std::sqrt(2.5);
4577
basisvalues[8] *= std::sqrt(3.5);
4578
basisvalues[7] *= std::sqrt(5.25);
4579
basisvalues[1] *= std::sqrt(7.5);
4580
basisvalues[6] *= std::sqrt(10.5);
4581
basisvalues[5] *= std::sqrt(15.75);
4582
basisvalues[4] *= std::sqrt(26.25);
6983
4583
6984
4584
// Table(s) of coefficients.
6985
4585
static const double coefficients0[10] = \
6999
4599
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7000
4600
7001
4601
// Declare helper variables.
7002
unsigned int rr = 0;
7003
unsigned int ss = 0;
7004
unsigned int tt = 0;
7005
double tmp5 = 0.0;
7006
double tmp6 = 0.0;
7007
double tmp7 = 0.0;
7008
4602
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
7009
4603
double tmp1 = 0.25*(Y + Z)*(Y + Z);
7010
4604
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
7014
4608
// Compute basisvalues.
7015
4609
basisvalues[0] = 1.0;
7016
4610
basisvalues[1] = tmp0;
7017
for (unsigned int r = 1; r < 2; r++)
7018
{
7019
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7020
ss = r*(r + 1)*(r + 2)/6;
7021
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7022
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
7023
}// end loop over 'r'
7024
for (unsigned int r = 0; r < 2; r++)
7025
{
7026
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7027
ss = r*(r + 1)*(r + 2)/6;
7028
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
7029
}// end loop over 'r'
7030
for (unsigned int r = 0; r < 1; r++)
7031
{
7032
for (unsigned int s = 1; s < 2 - r; s++)
7033
{
7034
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7035
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7036
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7037
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
7038
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7039
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7040
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7041
}// end loop over 's'
7042
}// end loop over 'r'
7043
for (unsigned int r = 0; r < 2; r++)
7044
{
7045
for (unsigned int s = 0; s < 2 - r; s++)
7046
{
7047
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7048
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7049
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
7050
}// end loop over 's'
7051
}// end loop over 'r'
7052
for (unsigned int r = 0; r < 1; r++)
7053
{
7054
for (unsigned int s = 0; s < 1 - r; s++)
7055
{
7056
for (unsigned int t = 1; t < 2 - r - s; t++)
7057
{
7058
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7059
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7060
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7061
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
7062
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7063
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7064
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7065
}// end loop over 't'
7066
}// end loop over 's'
7067
}// end loop over 'r'
7068
for (unsigned int r = 0; r < 3; r++)
7069
{
7070
for (unsigned int s = 0; s < 3 - r; s++)
7071
{
7072
for (unsigned int t = 0; t < 3 - r - s; t++)
7073
{
7074
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7075
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
7076
}// end loop over 't'
7077
}// end loop over 's'
7078
}// end loop over 'r'
4611
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4612
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4613
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4614
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4615
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4616
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4617
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4618
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4619
basisvalues[0] *= std::sqrt(0.75);
4620
basisvalues[3] *= std::sqrt(1.25);
4621
basisvalues[9] *= std::sqrt(1.75);
4622
basisvalues[2] *= std::sqrt(2.5);
4623
basisvalues[8] *= std::sqrt(3.5);
4624
basisvalues[7] *= std::sqrt(5.25);
4625
basisvalues[1] *= std::sqrt(7.5);
4626
basisvalues[6] *= std::sqrt(10.5);
4627
basisvalues[5] *= std::sqrt(15.75);
4628
basisvalues[4] *= std::sqrt(26.25);
7079
4629
7080
4630
// Table(s) of coefficients.
7081
4631
static const double coefficients0[10] = \
7095
4645
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7096
4646
7097
4647
// Declare helper variables.
7098
unsigned int rr = 0;
7099
unsigned int ss = 0;
7100
unsigned int tt = 0;
7101
double tmp5 = 0.0;
7102
double tmp6 = 0.0;
7103
double tmp7 = 0.0;
7104
4648
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
7105
4649
double tmp1 = 0.25*(Y + Z)*(Y + Z);
7106
4650
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
7110
4654
// Compute basisvalues.
7111
4655
basisvalues[0] = 1.0;
7112
4656
basisvalues[1] = tmp0;
7113
for (unsigned int r = 1; r < 2; r++)
7114
{
7115
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7116
ss = r*(r + 1)*(r + 2)/6;
7117
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7118
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
7119
}// end loop over 'r'
7120
for (unsigned int r = 0; r < 2; r++)
7121
{
7122
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7123
ss = r*(r + 1)*(r + 2)/6;
7124
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
7125
}// end loop over 'r'
7126
for (unsigned int r = 0; r < 1; r++)
7127
{
7128
for (unsigned int s = 1; s < 2 - r; s++)
7129
{
7130
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7131
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7132
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7133
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
7134
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7135
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7136
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7137
}// end loop over 's'
7138
}// end loop over 'r'
7139
for (unsigned int r = 0; r < 2; r++)
7140
{
7141
for (unsigned int s = 0; s < 2 - r; s++)
7142
{
7143
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7144
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7145
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
7146
}// end loop over 's'
7147
}// end loop over 'r'
7148
for (unsigned int r = 0; r < 1; r++)
7149
{
7150
for (unsigned int s = 0; s < 1 - r; s++)
7151
{
7152
for (unsigned int t = 1; t < 2 - r - s; t++)
7153
{
7154
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7155
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7156
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7157
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
7158
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7159
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7160
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7161
}// end loop over 't'
7162
}// end loop over 's'
7163
}// end loop over 'r'
7164
for (unsigned int r = 0; r < 3; r++)
7165
{
7166
for (unsigned int s = 0; s < 3 - r; s++)
7167
{
7168
for (unsigned int t = 0; t < 3 - r - s; t++)
7169
{
7170
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7171
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
7172
}// end loop over 't'
7173
}// end loop over 's'
7174
}// end loop over 'r'
4657
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4658
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4659
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4660
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4661
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4662
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4663
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4664
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4665
basisvalues[0] *= std::sqrt(0.75);
4666
basisvalues[3] *= std::sqrt(1.25);
4667
basisvalues[9] *= std::sqrt(1.75);
4668
basisvalues[2] *= std::sqrt(2.5);
4669
basisvalues[8] *= std::sqrt(3.5);
4670
basisvalues[7] *= std::sqrt(5.25);
4671
basisvalues[1] *= std::sqrt(7.5);
4672
basisvalues[6] *= std::sqrt(10.5);
4673
basisvalues[5] *= std::sqrt(15.75);
4674
basisvalues[4] *= std::sqrt(26.25);
7175
4675
7176
4676
// Table(s) of coefficients.
7177
4677
static const double coefficients0[10] = \
7337
4837
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7338
4838
7339
4839
// Declare helper variables.
7340
unsigned int rr = 0;
7341
unsigned int ss = 0;
7342
unsigned int tt = 0;
7343
double tmp5 = 0.0;
7344
double tmp6 = 0.0;
7345
double tmp7 = 0.0;
7346
4840
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
7347
4841
double tmp1 = 0.25*(Y + Z)*(Y + Z);
7348
4842
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
7352
4846
// Compute basisvalues.
7353
4847
basisvalues[0] = 1.0;
7354
4848
basisvalues[1] = tmp0;
7355
for (unsigned int r = 1; r < 2; r++)
7356
{
7357
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7358
ss = r*(r + 1)*(r + 2)/6;
7359
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7360
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
7361
}// end loop over 'r'
7362
for (unsigned int r = 0; r < 2; r++)
7363
{
7364
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7365
ss = r*(r + 1)*(r + 2)/6;
7366
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
7367
}// end loop over 'r'
7368
for (unsigned int r = 0; r < 1; r++)
7369
{
7370
for (unsigned int s = 1; s < 2 - r; s++)
7371
{
7372
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7373
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7374
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7375
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
7376
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7377
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7378
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7379
}// end loop over 's'
7380
}// end loop over 'r'
7381
for (unsigned int r = 0; r < 2; r++)
7382
{
7383
for (unsigned int s = 0; s < 2 - r; s++)
7384
{
7385
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7386
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7387
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
7388
}// end loop over 's'
7389
}// end loop over 'r'
7390
for (unsigned int r = 0; r < 1; r++)
7391
{
7392
for (unsigned int s = 0; s < 1 - r; s++)
7393
{
7394
for (unsigned int t = 1; t < 2 - r - s; t++)
7395
{
7396
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7397
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7398
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7399
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
7400
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7401
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7402
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7403
}// end loop over 't'
7404
}// end loop over 's'
7405
}// end loop over 'r'
7406
for (unsigned int r = 0; r < 3; r++)
7407
{
7408
for (unsigned int s = 0; s < 3 - r; s++)
7409
{
7410
for (unsigned int t = 0; t < 3 - r - s; t++)
7411
{
7412
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7413
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
7414
}// end loop over 't'
7415
}// end loop over 's'
7416
}// end loop over 'r'
4849
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
4850
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
4851
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
4852
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
4853
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
4854
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
4855
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
4856
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
4857
basisvalues[0] *= std::sqrt(0.75);
4858
basisvalues[3] *= std::sqrt(1.25);
4859
basisvalues[9] *= std::sqrt(1.75);
4860
basisvalues[2] *= std::sqrt(2.5);
4861
basisvalues[8] *= std::sqrt(3.5);
4862
basisvalues[7] *= std::sqrt(5.25);
4863
basisvalues[1] *= std::sqrt(7.5);
4864
basisvalues[6] *= std::sqrt(10.5);
4865
basisvalues[5] *= std::sqrt(15.75);
4866
basisvalues[4] *= std::sqrt(26.25);
7417
4867
7418
4868
// Table(s) of coefficients.
7419
4869
static const double coefficients0[10] = \
7605
5055
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7606
5056
7607
5057
// Declare helper variables.
7608
unsigned int rr = 0;
7609
unsigned int ss = 0;
7610
unsigned int tt = 0;
7611
double tmp5 = 0.0;
7612
double tmp6 = 0.0;
7613
double tmp7 = 0.0;
7614
5058
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
7615
5059
double tmp1 = 0.25*(Y + Z)*(Y + Z);
7616
5060
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
7620
5064
// Compute basisvalues.
7621
5065
basisvalues[0] = 1.0;
7622
5066
basisvalues[1] = tmp0;
7623
for (unsigned int r = 1; r < 2; r++)
7624
{
7625
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7626
ss = r*(r + 1)*(r + 2)/6;
7627
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7628
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
7629
}// end loop over 'r'
7630
for (unsigned int r = 0; r < 2; r++)
7631
{
7632
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7633
ss = r*(r + 1)*(r + 2)/6;
7634
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
7635
}// end loop over 'r'
7636
for (unsigned int r = 0; r < 1; r++)
7637
{
7638
for (unsigned int s = 1; s < 2 - r; s++)
7639
{
7640
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7641
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7642
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7643
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
7644
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7645
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7646
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7647
}// end loop over 's'
7648
}// end loop over 'r'
7649
for (unsigned int r = 0; r < 2; r++)
7650
{
7651
for (unsigned int s = 0; s < 2 - r; s++)
7652
{
7653
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7654
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7655
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
7656
}// end loop over 's'
7657
}// end loop over 'r'
7658
for (unsigned int r = 0; r < 1; r++)
7659
{
7660
for (unsigned int s = 0; s < 1 - r; s++)
7661
{
7662
for (unsigned int t = 1; t < 2 - r - s; t++)
7663
{
7664
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7665
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7666
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7667
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
7668
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7669
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7670
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7671
}// end loop over 't'
7672
}// end loop over 's'
7673
}// end loop over 'r'
7674
for (unsigned int r = 0; r < 3; r++)
7675
{
7676
for (unsigned int s = 0; s < 3 - r; s++)
7677
{
7678
for (unsigned int t = 0; t < 3 - r - s; t++)
7679
{
7680
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7681
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
7682
}// end loop over 't'
7683
}// end loop over 's'
7684
}// end loop over 'r'
5067
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
5068
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
5069
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
5070
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
5071
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
5072
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
5073
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
5074
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
5075
basisvalues[0] *= std::sqrt(0.75);
5076
basisvalues[3] *= std::sqrt(1.25);
5077
basisvalues[9] *= std::sqrt(1.75);
5078
basisvalues[2] *= std::sqrt(2.5);
5079
basisvalues[8] *= std::sqrt(3.5);
5080
basisvalues[7] *= std::sqrt(5.25);
5081
basisvalues[1] *= std::sqrt(7.5);
5082
basisvalues[6] *= std::sqrt(10.5);
5083
basisvalues[5] *= std::sqrt(15.75);
5084
basisvalues[4] *= std::sqrt(26.25);
7685
5085
7686
5086
// Table(s) of coefficients.
7687
5087
static const double coefficients0[10] = \
7873
5273
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
7874
5274
7875
5275
// Declare helper variables.
7876
unsigned int rr = 0;
7877
unsigned int ss = 0;
7878
unsigned int tt = 0;
7879
double tmp5 = 0.0;
7880
double tmp6 = 0.0;
7881
double tmp7 = 0.0;
7882
5276
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
7883
5277
double tmp1 = 0.25*(Y + Z)*(Y + Z);
7884
5278
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
7888
5282
// Compute basisvalues.
7889
5283
basisvalues[0] = 1.0;
7890
5284
basisvalues[1] = tmp0;
7891
for (unsigned int r = 1; r < 2; r++)
7892
{
7893
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
7894
ss = r*(r + 1)*(r + 2)/6;
7895
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
7896
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
7897
}// end loop over 'r'
7898
for (unsigned int r = 0; r < 2; r++)
7899
{
7900
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
7901
ss = r*(r + 1)*(r + 2)/6;
7902
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
7903
}// end loop over 'r'
7904
for (unsigned int r = 0; r < 1; r++)
7905
{
7906
for (unsigned int s = 1; s < 2 - r; s++)
7907
{
7908
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
7909
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7910
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
7911
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
7912
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7913
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
7914
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
7915
}// end loop over 's'
7916
}// end loop over 'r'
7917
for (unsigned int r = 0; r < 2; r++)
7918
{
7919
for (unsigned int s = 0; s < 2 - r; s++)
7920
{
7921
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
7922
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
7923
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
7924
}// end loop over 's'
7925
}// end loop over 'r'
7926
for (unsigned int r = 0; r < 1; r++)
7927
{
7928
for (unsigned int s = 0; s < 1 - r; s++)
7929
{
7930
for (unsigned int t = 1; t < 2 - r - s; t++)
7931
{
7932
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
7933
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7934
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
7935
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
7936
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7937
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
7938
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
7939
}// end loop over 't'
7940
}// end loop over 's'
7941
}// end loop over 'r'
7942
for (unsigned int r = 0; r < 3; r++)
7943
{
7944
for (unsigned int s = 0; s < 3 - r; s++)
7945
{
7946
for (unsigned int t = 0; t < 3 - r - s; t++)
7947
{
7948
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
7949
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
7950
}// end loop over 't'
7951
}// end loop over 's'
7952
}// end loop over 'r'
5285
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
5286
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
5287
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
5288
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
5289
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
5290
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
5291
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
5292
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
5293
basisvalues[0] *= std::sqrt(0.75);
5294
basisvalues[3] *= std::sqrt(1.25);
5295
basisvalues[9] *= std::sqrt(1.75);
5296
basisvalues[2] *= std::sqrt(2.5);
5297
basisvalues[8] *= std::sqrt(3.5);
5298
basisvalues[7] *= std::sqrt(5.25);
5299
basisvalues[1] *= std::sqrt(7.5);
5300
basisvalues[6] *= std::sqrt(10.5);
5301
basisvalues[5] *= std::sqrt(15.75);
5302
basisvalues[4] *= std::sqrt(26.25);
7953
5303
7954
5304
// Table(s) of coefficients.
7955
5305
static const double coefficients0[10] = \
8141
5491
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8142
5492
8143
5493
// Declare helper variables.
8144
unsigned int rr = 0;
8145
unsigned int ss = 0;
8146
unsigned int tt = 0;
8147
double tmp5 = 0.0;
8148
double tmp6 = 0.0;
8149
double tmp7 = 0.0;
8150
5494
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
8151
5495
double tmp1 = 0.25*(Y + Z)*(Y + Z);
8152
5496
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
8156
5500
// Compute basisvalues.
8157
5501
basisvalues[0] = 1.0;
8158
5502
basisvalues[1] = tmp0;
8159
for (unsigned int r = 1; r < 2; r++)
8160
{
8161
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8162
ss = r*(r + 1)*(r + 2)/6;
8163
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8164
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
8165
}// end loop over 'r'
8166
for (unsigned int r = 0; r < 2; r++)
8167
{
8168
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8169
ss = r*(r + 1)*(r + 2)/6;
8170
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
8171
}// end loop over 'r'
8172
for (unsigned int r = 0; r < 1; r++)
8173
{
8174
for (unsigned int s = 1; s < 2 - r; s++)
8175
{
8176
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8177
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8178
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8179
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
8180
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8181
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8182
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8183
}// end loop over 's'
8184
}// end loop over 'r'
8185
for (unsigned int r = 0; r < 2; r++)
8186
{
8187
for (unsigned int s = 0; s < 2 - r; s++)
8188
{
8189
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8190
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8191
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
8192
}// end loop over 's'
8193
}// end loop over 'r'
8194
for (unsigned int r = 0; r < 1; r++)
8195
{
8196
for (unsigned int s = 0; s < 1 - r; s++)
8197
{
8198
for (unsigned int t = 1; t < 2 - r - s; t++)
8199
{
8200
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8201
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8202
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8203
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
8204
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8205
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8206
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8207
}// end loop over 't'
8208
}// end loop over 's'
8209
}// end loop over 'r'
8210
for (unsigned int r = 0; r < 3; r++)
8211
{
8212
for (unsigned int s = 0; s < 3 - r; s++)
8213
{
8214
for (unsigned int t = 0; t < 3 - r - s; t++)
8215
{
8216
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8217
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
8218
}// end loop over 't'
8219
}// end loop over 's'
8220
}// end loop over 'r'
5503
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
5504
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
5505
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
5506
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
5507
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
5508
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
5509
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
5510
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
5511
basisvalues[0] *= std::sqrt(0.75);
5512
basisvalues[3] *= std::sqrt(1.25);
5513
basisvalues[9] *= std::sqrt(1.75);
5514
basisvalues[2] *= std::sqrt(2.5);
5515
basisvalues[8] *= std::sqrt(3.5);
5516
basisvalues[7] *= std::sqrt(5.25);
5517
basisvalues[1] *= std::sqrt(7.5);
5518
basisvalues[6] *= std::sqrt(10.5);
5519
basisvalues[5] *= std::sqrt(15.75);
5520
basisvalues[4] *= std::sqrt(26.25);
8221
5521
8222
5522
// Table(s) of coefficients.
8223
5523
static const double coefficients0[10] = \
8409
5709
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8410
5710
8411
5711
// Declare helper variables.
8412
unsigned int rr = 0;
8413
unsigned int ss = 0;
8414
unsigned int tt = 0;
8415
double tmp5 = 0.0;
8416
double tmp6 = 0.0;
8417
double tmp7 = 0.0;
8418
5712
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
8419
5713
double tmp1 = 0.25*(Y + Z)*(Y + Z);
8420
5714
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
8424
5718
// Compute basisvalues.
8425
5719
basisvalues[0] = 1.0;
8426
5720
basisvalues[1] = tmp0;
8427
for (unsigned int r = 1; r < 2; r++)
8428
{
8429
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8430
ss = r*(r + 1)*(r + 2)/6;
8431
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8432
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
8433
}// end loop over 'r'
8434
for (unsigned int r = 0; r < 2; r++)
8435
{
8436
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8437
ss = r*(r + 1)*(r + 2)/6;
8438
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
8439
}// end loop over 'r'
8440
for (unsigned int r = 0; r < 1; r++)
8441
{
8442
for (unsigned int s = 1; s < 2 - r; s++)
8443
{
8444
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8445
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8446
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8447
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
8448
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8449
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8450
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8451
}// end loop over 's'
8452
}// end loop over 'r'
8453
for (unsigned int r = 0; r < 2; r++)
8454
{
8455
for (unsigned int s = 0; s < 2 - r; s++)
8456
{
8457
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8458
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8459
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
8460
}// end loop over 's'
8461
}// end loop over 'r'
8462
for (unsigned int r = 0; r < 1; r++)
8463
{
8464
for (unsigned int s = 0; s < 1 - r; s++)
8465
{
8466
for (unsigned int t = 1; t < 2 - r - s; t++)
8467
{
8468
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8469
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8470
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8471
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
8472
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8473
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8474
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8475
}// end loop over 't'
8476
}// end loop over 's'
8477
}// end loop over 'r'
8478
for (unsigned int r = 0; r < 3; r++)
8479
{
8480
for (unsigned int s = 0; s < 3 - r; s++)
8481
{
8482
for (unsigned int t = 0; t < 3 - r - s; t++)
8483
{
8484
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8485
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
8486
}// end loop over 't'
8487
}// end loop over 's'
8488
}// end loop over 'r'
5721
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
5722
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
5723
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
5724
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
5725
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
5726
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
5727
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
5728
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
5729
basisvalues[0] *= std::sqrt(0.75);
5730
basisvalues[3] *= std::sqrt(1.25);
5731
basisvalues[9] *= std::sqrt(1.75);
5732
basisvalues[2] *= std::sqrt(2.5);
5733
basisvalues[8] *= std::sqrt(3.5);
5734
basisvalues[7] *= std::sqrt(5.25);
5735
basisvalues[1] *= std::sqrt(7.5);
5736
basisvalues[6] *= std::sqrt(10.5);
5737
basisvalues[5] *= std::sqrt(15.75);
5738
basisvalues[4] *= std::sqrt(26.25);
8489
5739
8490
5740
// Table(s) of coefficients.
8491
5741
static const double coefficients0[10] = \
8677
5927
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8678
5928
8679
5929
// Declare helper variables.
8680
unsigned int rr = 0;
8681
unsigned int ss = 0;
8682
unsigned int tt = 0;
8683
double tmp5 = 0.0;
8684
double tmp6 = 0.0;
8685
double tmp7 = 0.0;
8686
5930
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
8687
5931
double tmp1 = 0.25*(Y + Z)*(Y + Z);
8688
5932
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
8692
5936
// Compute basisvalues.
8693
5937
basisvalues[0] = 1.0;
8694
5938
basisvalues[1] = tmp0;
8695
for (unsigned int r = 1; r < 2; r++)
8696
{
8697
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8698
ss = r*(r + 1)*(r + 2)/6;
8699
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8700
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
8701
}// end loop over 'r'
8702
for (unsigned int r = 0; r < 2; r++)
8703
{
8704
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8705
ss = r*(r + 1)*(r + 2)/6;
8706
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
8707
}// end loop over 'r'
8708
for (unsigned int r = 0; r < 1; r++)
8709
{
8710
for (unsigned int s = 1; s < 2 - r; s++)
8711
{
8712
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8713
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8714
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8715
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
8716
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8717
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8718
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8719
}// end loop over 's'
8720
}// end loop over 'r'
8721
for (unsigned int r = 0; r < 2; r++)
8722
{
8723
for (unsigned int s = 0; s < 2 - r; s++)
8724
{
8725
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8726
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8727
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
8728
}// end loop over 's'
8729
}// end loop over 'r'
8730
for (unsigned int r = 0; r < 1; r++)
8731
{
8732
for (unsigned int s = 0; s < 1 - r; s++)
8733
{
8734
for (unsigned int t = 1; t < 2 - r - s; t++)
8735
{
8736
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
8737
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8738
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
8739
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
8740
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8741
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
8742
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
8743
}// end loop over 't'
8744
}// end loop over 's'
8745
}// end loop over 'r'
8746
for (unsigned int r = 0; r < 3; r++)
8747
{
8748
for (unsigned int s = 0; s < 3 - r; s++)
8749
{
8750
for (unsigned int t = 0; t < 3 - r - s; t++)
8751
{
8752
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
8753
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
8754
}// end loop over 't'
8755
}// end loop over 's'
8756
}// end loop over 'r'
5939
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
5940
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
5941
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
5942
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
5943
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
5944
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
5945
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
5946
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
5947
basisvalues[0] *= std::sqrt(0.75);
5948
basisvalues[3] *= std::sqrt(1.25);
5949
basisvalues[9] *= std::sqrt(1.75);
5950
basisvalues[2] *= std::sqrt(2.5);
5951
basisvalues[8] *= std::sqrt(3.5);
5952
basisvalues[7] *= std::sqrt(5.25);
5953
basisvalues[1] *= std::sqrt(7.5);
5954
basisvalues[6] *= std::sqrt(10.5);
5955
basisvalues[5] *= std::sqrt(15.75);
5956
basisvalues[4] *= std::sqrt(26.25);
8757
5957
8758
5958
// Table(s) of coefficients.
8759
5959
static const double coefficients0[10] = \
8945
6145
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
8946
6146
8947
6147
// Declare helper variables.
8948
unsigned int rr = 0;
8949
unsigned int ss = 0;
8950
unsigned int tt = 0;
8951
double tmp5 = 0.0;
8952
double tmp6 = 0.0;
8953
double tmp7 = 0.0;
8954
6148
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
8955
6149
double tmp1 = 0.25*(Y + Z)*(Y + Z);
8956
6150
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
8960
6154
// Compute basisvalues.
8961
6155
basisvalues[0] = 1.0;
8962
6156
basisvalues[1] = tmp0;
8963
for (unsigned int r = 1; r < 2; r++)
8964
{
8965
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
8966
ss = r*(r + 1)*(r + 2)/6;
8967
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
8968
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
8969
}// end loop over 'r'
8970
for (unsigned int r = 0; r < 2; r++)
8971
{
8972
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
8973
ss = r*(r + 1)*(r + 2)/6;
8974
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
8975
}// end loop over 'r'
8976
for (unsigned int r = 0; r < 1; r++)
8977
{
8978
for (unsigned int s = 1; s < 2 - r; s++)
8979
{
8980
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
8981
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8982
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
8983
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
8984
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8985
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
8986
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
8987
}// end loop over 's'
8988
}// end loop over 'r'
8989
for (unsigned int r = 0; r < 2; r++)
8990
{
8991
for (unsigned int s = 0; s < 2 - r; s++)
8992
{
8993
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
8994
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
8995
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
8996
}// end loop over 's'
8997
}// end loop over 'r'
8998
for (unsigned int r = 0; r < 1; r++)
8999
{
9000
for (unsigned int s = 0; s < 1 - r; s++)
9001
{
9002
for (unsigned int t = 1; t < 2 - r - s; t++)
9003
{
9004
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9005
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9006
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9007
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
9008
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9009
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9010
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9011
}// end loop over 't'
9012
}// end loop over 's'
9013
}// end loop over 'r'
9014
for (unsigned int r = 0; r < 3; r++)
9015
{
9016
for (unsigned int s = 0; s < 3 - r; s++)
9017
{
9018
for (unsigned int t = 0; t < 3 - r - s; t++)
9019
{
9020
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9021
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
9022
}// end loop over 't'
9023
}// end loop over 's'
9024
}// end loop over 'r'
6157
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
6158
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
6159
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
6160
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
6161
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
6162
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
6163
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
6164
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
6165
basisvalues[0] *= std::sqrt(0.75);
6166
basisvalues[3] *= std::sqrt(1.25);
6167
basisvalues[9] *= std::sqrt(1.75);
6168
basisvalues[2] *= std::sqrt(2.5);
6169
basisvalues[8] *= std::sqrt(3.5);
6170
basisvalues[7] *= std::sqrt(5.25);
6171
basisvalues[1] *= std::sqrt(7.5);
6172
basisvalues[6] *= std::sqrt(10.5);
6173
basisvalues[5] *= std::sqrt(15.75);
6174
basisvalues[4] *= std::sqrt(26.25);
9025
6175
9026
6176
// Table(s) of coefficients.
9027
6177
static const double coefficients0[10] = \
9213
6363
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9214
6364
9215
6365
// Declare helper variables.
9216
unsigned int rr = 0;
9217
unsigned int ss = 0;
9218
unsigned int tt = 0;
9219
double tmp5 = 0.0;
9220
double tmp6 = 0.0;
9221
double tmp7 = 0.0;
9222
6366
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
9223
6367
double tmp1 = 0.25*(Y + Z)*(Y + Z);
9224
6368
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
9228
6372
// Compute basisvalues.
9229
6373
basisvalues[0] = 1.0;
9230
6374
basisvalues[1] = tmp0;
9231
for (unsigned int r = 1; r < 2; r++)
9232
{
9233
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9234
ss = r*(r + 1)*(r + 2)/6;
9235
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9236
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
9237
}// end loop over 'r'
9238
for (unsigned int r = 0; r < 2; r++)
9239
{
9240
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9241
ss = r*(r + 1)*(r + 2)/6;
9242
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
9243
}// end loop over 'r'
9244
for (unsigned int r = 0; r < 1; r++)
9245
{
9246
for (unsigned int s = 1; s < 2 - r; s++)
9247
{
9248
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9249
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9250
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9251
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
9252
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9253
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9254
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9255
}// end loop over 's'
9256
}// end loop over 'r'
9257
for (unsigned int r = 0; r < 2; r++)
9258
{
9259
for (unsigned int s = 0; s < 2 - r; s++)
9260
{
9261
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9262
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9263
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
9264
}// end loop over 's'
9265
}// end loop over 'r'
9266
for (unsigned int r = 0; r < 1; r++)
9267
{
9268
for (unsigned int s = 0; s < 1 - r; s++)
9269
{
9270
for (unsigned int t = 1; t < 2 - r - s; t++)
9271
{
9272
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9273
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9274
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9275
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
9276
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9277
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9278
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9279
}// end loop over 't'
9280
}// end loop over 's'
9281
}// end loop over 'r'
9282
for (unsigned int r = 0; r < 3; r++)
9283
{
9284
for (unsigned int s = 0; s < 3 - r; s++)
9285
{
9286
for (unsigned int t = 0; t < 3 - r - s; t++)
9287
{
9288
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9289
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
9290
}// end loop over 't'
9291
}// end loop over 's'
9292
}// end loop over 'r'
6375
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
6376
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
6377
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
6378
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
6379
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
6380
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
6381
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
6382
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
6383
basisvalues[0] *= std::sqrt(0.75);
6384
basisvalues[3] *= std::sqrt(1.25);
6385
basisvalues[9] *= std::sqrt(1.75);
6386
basisvalues[2] *= std::sqrt(2.5);
6387
basisvalues[8] *= std::sqrt(3.5);
6388
basisvalues[7] *= std::sqrt(5.25);
6389
basisvalues[1] *= std::sqrt(7.5);
6390
basisvalues[6] *= std::sqrt(10.5);
6391
basisvalues[5] *= std::sqrt(15.75);
6392
basisvalues[4] *= std::sqrt(26.25);
9293
6393
9294
6394
// Table(s) of coefficients.
9295
6395
static const double coefficients0[10] = \
9481
6581
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9482
6582
9483
6583
// Declare helper variables.
9484
unsigned int rr = 0;
9485
unsigned int ss = 0;
9486
unsigned int tt = 0;
9487
double tmp5 = 0.0;
9488
double tmp6 = 0.0;
9489
double tmp7 = 0.0;
9490
6584
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
9491
6585
double tmp1 = 0.25*(Y + Z)*(Y + Z);
9492
6586
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
9496
6590
// Compute basisvalues.
9497
6591
basisvalues[0] = 1.0;
9498
6592
basisvalues[1] = tmp0;
9499
for (unsigned int r = 1; r < 2; r++)
9500
{
9501
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9502
ss = r*(r + 1)*(r + 2)/6;
9503
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9504
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
9505
}// end loop over 'r'
9506
for (unsigned int r = 0; r < 2; r++)
9507
{
9508
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9509
ss = r*(r + 1)*(r + 2)/6;
9510
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
9511
}// end loop over 'r'
9512
for (unsigned int r = 0; r < 1; r++)
9513
{
9514
for (unsigned int s = 1; s < 2 - r; s++)
9515
{
9516
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9517
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9518
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9519
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
9520
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9521
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9522
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9523
}// end loop over 's'
9524
}// end loop over 'r'
9525
for (unsigned int r = 0; r < 2; r++)
9526
{
9527
for (unsigned int s = 0; s < 2 - r; s++)
9528
{
9529
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9530
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9531
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
9532
}// end loop over 's'
9533
}// end loop over 'r'
9534
for (unsigned int r = 0; r < 1; r++)
9535
{
9536
for (unsigned int s = 0; s < 1 - r; s++)
9537
{
9538
for (unsigned int t = 1; t < 2 - r - s; t++)
9539
{
9540
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9541
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9542
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9543
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
9544
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9545
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9546
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9547
}// end loop over 't'
9548
}// end loop over 's'
9549
}// end loop over 'r'
9550
for (unsigned int r = 0; r < 3; r++)
9551
{
9552
for (unsigned int s = 0; s < 3 - r; s++)
9553
{
9554
for (unsigned int t = 0; t < 3 - r - s; t++)
9555
{
9556
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9557
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
9558
}// end loop over 't'
9559
}// end loop over 's'
9560
}// end loop over 'r'
6593
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
6594
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
6595
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
6596
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
6597
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
6598
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
6599
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
6600
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
6601
basisvalues[0] *= std::sqrt(0.75);
6602
basisvalues[3] *= std::sqrt(1.25);
6603
basisvalues[9] *= std::sqrt(1.75);
6604
basisvalues[2] *= std::sqrt(2.5);
6605
basisvalues[8] *= std::sqrt(3.5);
6606
basisvalues[7] *= std::sqrt(5.25);
6607
basisvalues[1] *= std::sqrt(7.5);
6608
basisvalues[6] *= std::sqrt(10.5);
6609
basisvalues[5] *= std::sqrt(15.75);
6610
basisvalues[4] *= std::sqrt(26.25);
9561
6611
9562
6612
// Table(s) of coefficients.
9563
6613
static const double coefficients0[10] = \
9749
6799
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
9750
6800
9751
6801
// Declare helper variables.
9752
unsigned int rr = 0;
9753
unsigned int ss = 0;
9754
unsigned int tt = 0;
9755
double tmp5 = 0.0;
9756
double tmp6 = 0.0;
9757
double tmp7 = 0.0;
9758
6802
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
9759
6803
double tmp1 = 0.25*(Y + Z)*(Y + Z);
9760
6804
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
9764
6808
// Compute basisvalues.
9765
6809
basisvalues[0] = 1.0;
9766
6810
basisvalues[1] = tmp0;
9767
for (unsigned int r = 1; r < 2; r++)
9768
{
9769
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
9770
ss = r*(r + 1)*(r + 2)/6;
9771
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
9772
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
9773
}// end loop over 'r'
9774
for (unsigned int r = 0; r < 2; r++)
9775
{
9776
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
9777
ss = r*(r + 1)*(r + 2)/6;
9778
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
9779
}// end loop over 'r'
9780
for (unsigned int r = 0; r < 1; r++)
9781
{
9782
for (unsigned int s = 1; s < 2 - r; s++)
9783
{
9784
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
9785
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9786
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
9787
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
9788
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9789
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
9790
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
9791
}// end loop over 's'
9792
}// end loop over 'r'
9793
for (unsigned int r = 0; r < 2; r++)
9794
{
9795
for (unsigned int s = 0; s < 2 - r; s++)
9796
{
9797
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
9798
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
9799
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
9800
}// end loop over 's'
9801
}// end loop over 'r'
9802
for (unsigned int r = 0; r < 1; r++)
9803
{
9804
for (unsigned int s = 0; s < 1 - r; s++)
9805
{
9806
for (unsigned int t = 1; t < 2 - r - s; t++)
9807
{
9808
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
9809
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9810
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
9811
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
9812
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9813
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
9814
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
9815
}// end loop over 't'
9816
}// end loop over 's'
9817
}// end loop over 'r'
9818
for (unsigned int r = 0; r < 3; r++)
9819
{
9820
for (unsigned int s = 0; s < 3 - r; s++)
9821
{
9822
for (unsigned int t = 0; t < 3 - r - s; t++)
9823
{
9824
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
9825
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
9826
}// end loop over 't'
9827
}// end loop over 's'
9828
}// end loop over 'r'
6811
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
6812
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
6813
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
6814
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
6815
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
6816
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
6817
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
6818
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
6819
basisvalues[0] *= std::sqrt(0.75);
6820
basisvalues[3] *= std::sqrt(1.25);
6821
basisvalues[9] *= std::sqrt(1.75);
6822
basisvalues[2] *= std::sqrt(2.5);
6823
basisvalues[8] *= std::sqrt(3.5);
6824
basisvalues[7] *= std::sqrt(5.25);
6825
basisvalues[1] *= std::sqrt(7.5);
6826
basisvalues[6] *= std::sqrt(10.5);
6827
basisvalues[5] *= std::sqrt(15.75);
6828
basisvalues[4] *= std::sqrt(26.25);
9829
6829
9830
6830
// Table(s) of coefficients.
9831
6831
static const double coefficients0[10] = \
10017
7017
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10018
7018
10019
7019
// Declare helper variables.
10020
unsigned int rr = 0;
10021
unsigned int ss = 0;
10022
unsigned int tt = 0;
10023
double tmp5 = 0.0;
10024
double tmp6 = 0.0;
10025
double tmp7 = 0.0;
10026
7020
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
10027
7021
double tmp1 = 0.25*(Y + Z)*(Y + Z);
10028
7022
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
10032
7026
// Compute basisvalues.
10033
7027
basisvalues[0] = 1.0;
10034
7028
basisvalues[1] = tmp0;
10035
for (unsigned int r = 1; r < 2; r++)
10036
{
10037
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10038
ss = r*(r + 1)*(r + 2)/6;
10039
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10040
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
10041
}// end loop over 'r'
10042
for (unsigned int r = 0; r < 2; r++)
10043
{
10044
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10045
ss = r*(r + 1)*(r + 2)/6;
10046
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
10047
}// end loop over 'r'
10048
for (unsigned int r = 0; r < 1; r++)
10049
{
10050
for (unsigned int s = 1; s < 2 - r; s++)
10051
{
10052
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10053
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10054
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10055
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
10056
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10057
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10058
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10059
}// end loop over 's'
10060
}// end loop over 'r'
10061
for (unsigned int r = 0; r < 2; r++)
10062
{
10063
for (unsigned int s = 0; s < 2 - r; s++)
10064
{
10065
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10066
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10067
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
10068
}// end loop over 's'
10069
}// end loop over 'r'
10070
for (unsigned int r = 0; r < 1; r++)
10071
{
10072
for (unsigned int s = 0; s < 1 - r; s++)
10073
{
10074
for (unsigned int t = 1; t < 2 - r - s; t++)
10075
{
10076
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10077
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10078
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10079
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
10080
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10081
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10082
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10083
}// end loop over 't'
10084
}// end loop over 's'
10085
}// end loop over 'r'
10086
for (unsigned int r = 0; r < 3; r++)
10087
{
10088
for (unsigned int s = 0; s < 3 - r; s++)
10089
{
10090
for (unsigned int t = 0; t < 3 - r - s; t++)
10091
{
10092
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10093
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
10094
}// end loop over 't'
10095
}// end loop over 's'
10096
}// end loop over 'r'
7029
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
7030
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
7031
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
7032
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
7033
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
7034
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
7035
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
7036
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
7037
basisvalues[0] *= std::sqrt(0.75);
7038
basisvalues[3] *= std::sqrt(1.25);
7039
basisvalues[9] *= std::sqrt(1.75);
7040
basisvalues[2] *= std::sqrt(2.5);
7041
basisvalues[8] *= std::sqrt(3.5);
7042
basisvalues[7] *= std::sqrt(5.25);
7043
basisvalues[1] *= std::sqrt(7.5);
7044
basisvalues[6] *= std::sqrt(10.5);
7045
basisvalues[5] *= std::sqrt(15.75);
7046
basisvalues[4] *= std::sqrt(26.25);
10097
7047
10098
7048
// Table(s) of coefficients.
10099
7049
static const double coefficients0[10] = \
10285
7235
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10286
7236
10287
7237
// Declare helper variables.
10288
unsigned int rr = 0;
10289
unsigned int ss = 0;
10290
unsigned int tt = 0;
10291
double tmp5 = 0.0;
10292
double tmp6 = 0.0;
10293
double tmp7 = 0.0;
10294
7238
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
10295
7239
double tmp1 = 0.25*(Y + Z)*(Y + Z);
10296
7240
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
10300
7244
// Compute basisvalues.
10301
7245
basisvalues[0] = 1.0;
10302
7246
basisvalues[1] = tmp0;
10303
for (unsigned int r = 1; r < 2; r++)
10304
{
10305
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10306
ss = r*(r + 1)*(r + 2)/6;
10307
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10308
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
10309
}// end loop over 'r'
10310
for (unsigned int r = 0; r < 2; r++)
10311
{
10312
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10313
ss = r*(r + 1)*(r + 2)/6;
10314
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
10315
}// end loop over 'r'
10316
for (unsigned int r = 0; r < 1; r++)
10317
{
10318
for (unsigned int s = 1; s < 2 - r; s++)
10319
{
10320
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10321
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10322
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10323
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
10324
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10325
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10326
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10327
}// end loop over 's'
10328
}// end loop over 'r'
10329
for (unsigned int r = 0; r < 2; r++)
10330
{
10331
for (unsigned int s = 0; s < 2 - r; s++)
10332
{
10333
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10334
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10335
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
10336
}// end loop over 's'
10337
}// end loop over 'r'
10338
for (unsigned int r = 0; r < 1; r++)
10339
{
10340
for (unsigned int s = 0; s < 1 - r; s++)
10341
{
10342
for (unsigned int t = 1; t < 2 - r - s; t++)
10343
{
10344
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10345
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10346
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10347
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
10348
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10349
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10350
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10351
}// end loop over 't'
10352
}// end loop over 's'
10353
}// end loop over 'r'
10354
for (unsigned int r = 0; r < 3; r++)
10355
{
10356
for (unsigned int s = 0; s < 3 - r; s++)
10357
{
10358
for (unsigned int t = 0; t < 3 - r - s; t++)
10359
{
10360
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10361
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
10362
}// end loop over 't'
10363
}// end loop over 's'
10364
}// end loop over 'r'
7247
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
7248
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
7249
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
7250
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
7251
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
7252
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
7253
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
7254
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
7255
basisvalues[0] *= std::sqrt(0.75);
7256
basisvalues[3] *= std::sqrt(1.25);
7257
basisvalues[9] *= std::sqrt(1.75);
7258
basisvalues[2] *= std::sqrt(2.5);
7259
basisvalues[8] *= std::sqrt(3.5);
7260
basisvalues[7] *= std::sqrt(5.25);
7261
basisvalues[1] *= std::sqrt(7.5);
7262
basisvalues[6] *= std::sqrt(10.5);
7263
basisvalues[5] *= std::sqrt(15.75);
7264
basisvalues[4] *= std::sqrt(26.25);
10365
7265
10366
7266
// Table(s) of coefficients.
10367
7267
static const double coefficients0[10] = \
10553
7453
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10554
7454
10555
7455
// Declare helper variables.
10556
unsigned int rr = 0;
10557
unsigned int ss = 0;
10558
unsigned int tt = 0;
10559
double tmp5 = 0.0;
10560
double tmp6 = 0.0;
10561
double tmp7 = 0.0;
10562
7456
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
10563
7457
double tmp1 = 0.25*(Y + Z)*(Y + Z);
10564
7458
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
10568
7462
// Compute basisvalues.
10569
7463
basisvalues[0] = 1.0;
10570
7464
basisvalues[1] = tmp0;
10571
for (unsigned int r = 1; r < 2; r++)
10572
{
10573
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10574
ss = r*(r + 1)*(r + 2)/6;
10575
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10576
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
10577
}// end loop over 'r'
10578
for (unsigned int r = 0; r < 2; r++)
10579
{
10580
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10581
ss = r*(r + 1)*(r + 2)/6;
10582
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
10583
}// end loop over 'r'
10584
for (unsigned int r = 0; r < 1; r++)
10585
{
10586
for (unsigned int s = 1; s < 2 - r; s++)
10587
{
10588
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10589
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10590
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10591
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
10592
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10593
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10594
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10595
}// end loop over 's'
10596
}// end loop over 'r'
10597
for (unsigned int r = 0; r < 2; r++)
10598
{
10599
for (unsigned int s = 0; s < 2 - r; s++)
10600
{
10601
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10602
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10603
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
10604
}// end loop over 's'
10605
}// end loop over 'r'
10606
for (unsigned int r = 0; r < 1; r++)
10607
{
10608
for (unsigned int s = 0; s < 1 - r; s++)
10609
{
10610
for (unsigned int t = 1; t < 2 - r - s; t++)
10611
{
10612
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10613
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10614
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10615
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
10616
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10617
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10618
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10619
}// end loop over 't'
10620
}// end loop over 's'
10621
}// end loop over 'r'
10622
for (unsigned int r = 0; r < 3; r++)
10623
{
10624
for (unsigned int s = 0; s < 3 - r; s++)
10625
{
10626
for (unsigned int t = 0; t < 3 - r - s; t++)
10627
{
10628
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10629
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
10630
}// end loop over 't'
10631
}// end loop over 's'
10632
}// end loop over 'r'
7465
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
7466
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
7467
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
7468
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
7469
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
7470
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
7471
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
7472
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
7473
basisvalues[0] *= std::sqrt(0.75);
7474
basisvalues[3] *= std::sqrt(1.25);
7475
basisvalues[9] *= std::sqrt(1.75);
7476
basisvalues[2] *= std::sqrt(2.5);
7477
basisvalues[8] *= std::sqrt(3.5);
7478
basisvalues[7] *= std::sqrt(5.25);
7479
basisvalues[1] *= std::sqrt(7.5);
7480
basisvalues[6] *= std::sqrt(10.5);
7481
basisvalues[5] *= std::sqrt(15.75);
7482
basisvalues[4] *= std::sqrt(26.25);
10633
7483
10634
7484
// Table(s) of coefficients.
10635
7485
static const double coefficients0[10] = \
10821
7671
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
10822
7672
10823
7673
// Declare helper variables.
10824
unsigned int rr = 0;
10825
unsigned int ss = 0;
10826
unsigned int tt = 0;
10827
double tmp5 = 0.0;
10828
double tmp6 = 0.0;
10829
double tmp7 = 0.0;
10830
7674
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
10831
7675
double tmp1 = 0.25*(Y + Z)*(Y + Z);
10832
7676
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
10836
7680
// Compute basisvalues.
10837
7681
basisvalues[0] = 1.0;
10838
7682
basisvalues[1] = tmp0;
10839
for (unsigned int r = 1; r < 2; r++)
10840
{
10841
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
10842
ss = r*(r + 1)*(r + 2)/6;
10843
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
10844
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
10845
}// end loop over 'r'
10846
for (unsigned int r = 0; r < 2; r++)
10847
{
10848
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
10849
ss = r*(r + 1)*(r + 2)/6;
10850
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
10851
}// end loop over 'r'
10852
for (unsigned int r = 0; r < 1; r++)
10853
{
10854
for (unsigned int s = 1; s < 2 - r; s++)
10855
{
10856
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
10857
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10858
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
10859
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
10860
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10861
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
10862
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
10863
}// end loop over 's'
10864
}// end loop over 'r'
10865
for (unsigned int r = 0; r < 2; r++)
10866
{
10867
for (unsigned int s = 0; s < 2 - r; s++)
10868
{
10869
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
10870
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
10871
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
10872
}// end loop over 's'
10873
}// end loop over 'r'
10874
for (unsigned int r = 0; r < 1; r++)
10875
{
10876
for (unsigned int s = 0; s < 1 - r; s++)
10877
{
10878
for (unsigned int t = 1; t < 2 - r - s; t++)
10879
{
10880
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
10881
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10882
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
10883
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
10884
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10885
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
10886
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
10887
}// end loop over 't'
10888
}// end loop over 's'
10889
}// end loop over 'r'
10890
for (unsigned int r = 0; r < 3; r++)
10891
{
10892
for (unsigned int s = 0; s < 3 - r; s++)
10893
{
10894
for (unsigned int t = 0; t < 3 - r - s; t++)
10895
{
10896
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
10897
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
10898
}// end loop over 't'
10899
}// end loop over 's'
10900
}// end loop over 'r'
7683
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
7684
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
7685
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
7686
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
7687
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
7688
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
7689
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
7690
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
7691
basisvalues[0] *= std::sqrt(0.75);
7692
basisvalues[3] *= std::sqrt(1.25);
7693
basisvalues[9] *= std::sqrt(1.75);
7694
basisvalues[2] *= std::sqrt(2.5);
7695
basisvalues[8] *= std::sqrt(3.5);
7696
basisvalues[7] *= std::sqrt(5.25);
7697
basisvalues[1] *= std::sqrt(7.5);
7698
basisvalues[6] *= std::sqrt(10.5);
7699
basisvalues[5] *= std::sqrt(15.75);
7700
basisvalues[4] *= std::sqrt(26.25);
10901
7701
10902
7702
// Table(s) of coefficients.
10903
7703
static const double coefficients0[10] = \
11089
7889
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11090
7890
11091
7891
// Declare helper variables.
11092
unsigned int rr = 0;
11093
unsigned int ss = 0;
11094
unsigned int tt = 0;
11095
double tmp5 = 0.0;
11096
double tmp6 = 0.0;
11097
double tmp7 = 0.0;
11098
7892
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
11099
7893
double tmp1 = 0.25*(Y + Z)*(Y + Z);
11100
7894
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
11104
7898
// Compute basisvalues.
11105
7899
basisvalues[0] = 1.0;
11106
7900
basisvalues[1] = tmp0;
11107
for (unsigned int r = 1; r < 2; r++)
11108
{
11109
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11110
ss = r*(r + 1)*(r + 2)/6;
11111
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11112
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
11113
}// end loop over 'r'
11114
for (unsigned int r = 0; r < 2; r++)
11115
{
11116
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11117
ss = r*(r + 1)*(r + 2)/6;
11118
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
11119
}// end loop over 'r'
11120
for (unsigned int r = 0; r < 1; r++)
11121
{
11122
for (unsigned int s = 1; s < 2 - r; s++)
11123
{
11124
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11125
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11126
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11127
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
11128
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11129
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11130
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11131
}// end loop over 's'
11132
}// end loop over 'r'
11133
for (unsigned int r = 0; r < 2; r++)
11134
{
11135
for (unsigned int s = 0; s < 2 - r; s++)
11136
{
11137
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11138
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11139
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
11140
}// end loop over 's'
11141
}// end loop over 'r'
11142
for (unsigned int r = 0; r < 1; r++)
11143
{
11144
for (unsigned int s = 0; s < 1 - r; s++)
11145
{
11146
for (unsigned int t = 1; t < 2 - r - s; t++)
11147
{
11148
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11149
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11150
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11151
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
11152
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11153
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11154
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11155
}// end loop over 't'
11156
}// end loop over 's'
11157
}// end loop over 'r'
11158
for (unsigned int r = 0; r < 3; r++)
11159
{
11160
for (unsigned int s = 0; s < 3 - r; s++)
11161
{
11162
for (unsigned int t = 0; t < 3 - r - s; t++)
11163
{
11164
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11165
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
11166
}// end loop over 't'
11167
}// end loop over 's'
11168
}// end loop over 'r'
7901
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
7902
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
7903
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
7904
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
7905
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
7906
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
7907
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
7908
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
7909
basisvalues[0] *= std::sqrt(0.75);
7910
basisvalues[3] *= std::sqrt(1.25);
7911
basisvalues[9] *= std::sqrt(1.75);
7912
basisvalues[2] *= std::sqrt(2.5);
7913
basisvalues[8] *= std::sqrt(3.5);
7914
basisvalues[7] *= std::sqrt(5.25);
7915
basisvalues[1] *= std::sqrt(7.5);
7916
basisvalues[6] *= std::sqrt(10.5);
7917
basisvalues[5] *= std::sqrt(15.75);
7918
basisvalues[4] *= std::sqrt(26.25);
11169
7919
11170
7920
// Table(s) of coefficients.
11171
7921
static const double coefficients0[10] = \
11357
8107
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11358
8108
11359
8109
// Declare helper variables.
11360
unsigned int rr = 0;
11361
unsigned int ss = 0;
11362
unsigned int tt = 0;
11363
double tmp5 = 0.0;
11364
double tmp6 = 0.0;
11365
double tmp7 = 0.0;
11366
8110
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
11367
8111
double tmp1 = 0.25*(Y + Z)*(Y + Z);
11368
8112
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
11372
8116
// Compute basisvalues.
11373
8117
basisvalues[0] = 1.0;
11374
8118
basisvalues[1] = tmp0;
11375
for (unsigned int r = 1; r < 2; r++)
11376
{
11377
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11378
ss = r*(r + 1)*(r + 2)/6;
11379
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11380
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
11381
}// end loop over 'r'
11382
for (unsigned int r = 0; r < 2; r++)
11383
{
11384
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11385
ss = r*(r + 1)*(r + 2)/6;
11386
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
11387
}// end loop over 'r'
11388
for (unsigned int r = 0; r < 1; r++)
11389
{
11390
for (unsigned int s = 1; s < 2 - r; s++)
11391
{
11392
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11393
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11394
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11395
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
11396
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11397
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11398
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11399
}// end loop over 's'
11400
}// end loop over 'r'
11401
for (unsigned int r = 0; r < 2; r++)
11402
{
11403
for (unsigned int s = 0; s < 2 - r; s++)
11404
{
11405
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11406
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11407
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
11408
}// end loop over 's'
11409
}// end loop over 'r'
11410
for (unsigned int r = 0; r < 1; r++)
11411
{
11412
for (unsigned int s = 0; s < 1 - r; s++)
11413
{
11414
for (unsigned int t = 1; t < 2 - r - s; t++)
11415
{
11416
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11417
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11418
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11419
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
11420
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11421
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11422
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11423
}// end loop over 't'
11424
}// end loop over 's'
11425
}// end loop over 'r'
11426
for (unsigned int r = 0; r < 3; r++)
11427
{
11428
for (unsigned int s = 0; s < 3 - r; s++)
11429
{
11430
for (unsigned int t = 0; t < 3 - r - s; t++)
11431
{
11432
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11433
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
11434
}// end loop over 't'
11435
}// end loop over 's'
11436
}// end loop over 'r'
8119
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
8120
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
8121
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
8122
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
8123
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
8124
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
8125
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
8126
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
8127
basisvalues[0] *= std::sqrt(0.75);
8128
basisvalues[3] *= std::sqrt(1.25);
8129
basisvalues[9] *= std::sqrt(1.75);
8130
basisvalues[2] *= std::sqrt(2.5);
8131
basisvalues[8] *= std::sqrt(3.5);
8132
basisvalues[7] *= std::sqrt(5.25);
8133
basisvalues[1] *= std::sqrt(7.5);
8134
basisvalues[6] *= std::sqrt(10.5);
8135
basisvalues[5] *= std::sqrt(15.75);
8136
basisvalues[4] *= std::sqrt(26.25);
11437
8137
11438
8138
// Table(s) of coefficients.
11439
8139
static const double coefficients0[10] = \
11625
8325
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11626
8326
11627
8327
// Declare helper variables.
11628
unsigned int rr = 0;
11629
unsigned int ss = 0;
11630
unsigned int tt = 0;
11631
double tmp5 = 0.0;
11632
double tmp6 = 0.0;
11633
double tmp7 = 0.0;
11634
8328
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
11635
8329
double tmp1 = 0.25*(Y + Z)*(Y + Z);
11636
8330
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
11640
8334
// Compute basisvalues.
11641
8335
basisvalues[0] = 1.0;
11642
8336
basisvalues[1] = tmp0;
11643
for (unsigned int r = 1; r < 2; r++)
11644
{
11645
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11646
ss = r*(r + 1)*(r + 2)/6;
11647
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11648
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
11649
}// end loop over 'r'
11650
for (unsigned int r = 0; r < 2; r++)
11651
{
11652
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11653
ss = r*(r + 1)*(r + 2)/6;
11654
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
11655
}// end loop over 'r'
11656
for (unsigned int r = 0; r < 1; r++)
11657
{
11658
for (unsigned int s = 1; s < 2 - r; s++)
11659
{
11660
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11661
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11662
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11663
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
11664
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11665
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11666
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11667
}// end loop over 's'
11668
}// end loop over 'r'
11669
for (unsigned int r = 0; r < 2; r++)
11670
{
11671
for (unsigned int s = 0; s < 2 - r; s++)
11672
{
11673
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11674
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11675
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
11676
}// end loop over 's'
11677
}// end loop over 'r'
11678
for (unsigned int r = 0; r < 1; r++)
11679
{
11680
for (unsigned int s = 0; s < 1 - r; s++)
11681
{
11682
for (unsigned int t = 1; t < 2 - r - s; t++)
11683
{
11684
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11685
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11686
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11687
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
11688
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11689
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11690
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11691
}// end loop over 't'
11692
}// end loop over 's'
11693
}// end loop over 'r'
11694
for (unsigned int r = 0; r < 3; r++)
11695
{
11696
for (unsigned int s = 0; s < 3 - r; s++)
11697
{
11698
for (unsigned int t = 0; t < 3 - r - s; t++)
11699
{
11700
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11701
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
11702
}// end loop over 't'
11703
}// end loop over 's'
11704
}// end loop over 'r'
8337
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
8338
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
8339
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
8340
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
8341
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
8342
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
8343
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
8344
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
8345
basisvalues[0] *= std::sqrt(0.75);
8346
basisvalues[3] *= std::sqrt(1.25);
8347
basisvalues[9] *= std::sqrt(1.75);
8348
basisvalues[2] *= std::sqrt(2.5);
8349
basisvalues[8] *= std::sqrt(3.5);
8350
basisvalues[7] *= std::sqrt(5.25);
8351
basisvalues[1] *= std::sqrt(7.5);
8352
basisvalues[6] *= std::sqrt(10.5);
8353
basisvalues[5] *= std::sqrt(15.75);
8354
basisvalues[4] *= std::sqrt(26.25);
11705
8355
11706
8356
// Table(s) of coefficients.
11707
8357
static const double coefficients0[10] = \
11893
8543
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
11894
8544
11895
8545
// Declare helper variables.
11896
unsigned int rr = 0;
11897
unsigned int ss = 0;
11898
unsigned int tt = 0;
11899
double tmp5 = 0.0;
11900
double tmp6 = 0.0;
11901
double tmp7 = 0.0;
11902
8546
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
11903
8547
double tmp1 = 0.25*(Y + Z)*(Y + Z);
11904
8548
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
11908
8552
// Compute basisvalues.
11909
8553
basisvalues[0] = 1.0;
11910
8554
basisvalues[1] = tmp0;
11911
for (unsigned int r = 1; r < 2; r++)
11912
{
11913
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
11914
ss = r*(r + 1)*(r + 2)/6;
11915
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
11916
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
11917
}// end loop over 'r'
11918
for (unsigned int r = 0; r < 2; r++)
11919
{
11920
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
11921
ss = r*(r + 1)*(r + 2)/6;
11922
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
11923
}// end loop over 'r'
11924
for (unsigned int r = 0; r < 1; r++)
11925
{
11926
for (unsigned int s = 1; s < 2 - r; s++)
11927
{
11928
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
11929
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11930
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
11931
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
11932
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11933
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
11934
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
11935
}// end loop over 's'
11936
}// end loop over 'r'
11937
for (unsigned int r = 0; r < 2; r++)
11938
{
11939
for (unsigned int s = 0; s < 2 - r; s++)
11940
{
11941
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
11942
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
11943
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
11944
}// end loop over 's'
11945
}// end loop over 'r'
11946
for (unsigned int r = 0; r < 1; r++)
11947
{
11948
for (unsigned int s = 0; s < 1 - r; s++)
11949
{
11950
for (unsigned int t = 1; t < 2 - r - s; t++)
11951
{
11952
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
11953
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11954
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
11955
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
11956
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11957
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
11958
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
11959
}// end loop over 't'
11960
}// end loop over 's'
11961
}// end loop over 'r'
11962
for (unsigned int r = 0; r < 3; r++)
11963
{
11964
for (unsigned int s = 0; s < 3 - r; s++)
11965
{
11966
for (unsigned int t = 0; t < 3 - r - s; t++)
11967
{
11968
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
11969
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
11970
}// end loop over 't'
11971
}// end loop over 's'
11972
}// end loop over 'r'
8555
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
8556
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
8557
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
8558
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
8559
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
8560
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
8561
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
8562
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
8563
basisvalues[0] *= std::sqrt(0.75);
8564
basisvalues[3] *= std::sqrt(1.25);
8565
basisvalues[9] *= std::sqrt(1.75);
8566
basisvalues[2] *= std::sqrt(2.5);
8567
basisvalues[8] *= std::sqrt(3.5);
8568
basisvalues[7] *= std::sqrt(5.25);
8569
basisvalues[1] *= std::sqrt(7.5);
8570
basisvalues[6] *= std::sqrt(10.5);
8571
basisvalues[5] *= std::sqrt(15.75);
8572
basisvalues[4] *= std::sqrt(26.25);
11973
8573
11974
8574
// Table(s) of coefficients.
11975
8575
static const double coefficients0[10] = \
12161
8761
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12162
8762
12163
8763
// Declare helper variables.
12164
unsigned int rr = 0;
12165
unsigned int ss = 0;
12166
unsigned int tt = 0;
12167
double tmp5 = 0.0;
12168
double tmp6 = 0.0;
12169
double tmp7 = 0.0;
12170
8764
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
12171
8765
double tmp1 = 0.25*(Y + Z)*(Y + Z);
12172
8766
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
12176
8770
// Compute basisvalues.
12177
8771
basisvalues[0] = 1.0;
12178
8772
basisvalues[1] = tmp0;
12179
for (unsigned int r = 1; r < 2; r++)
12180
{
12181
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12182
ss = r*(r + 1)*(r + 2)/6;
12183
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12184
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
12185
}// end loop over 'r'
12186
for (unsigned int r = 0; r < 2; r++)
12187
{
12188
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12189
ss = r*(r + 1)*(r + 2)/6;
12190
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
12191
}// end loop over 'r'
12192
for (unsigned int r = 0; r < 1; r++)
12193
{
12194
for (unsigned int s = 1; s < 2 - r; s++)
12195
{
12196
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12197
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12198
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12199
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
12200
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12201
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12202
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12203
}// end loop over 's'
12204
}// end loop over 'r'
12205
for (unsigned int r = 0; r < 2; r++)
12206
{
12207
for (unsigned int s = 0; s < 2 - r; s++)
12208
{
12209
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12210
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12211
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
12212
}// end loop over 's'
12213
}// end loop over 'r'
12214
for (unsigned int r = 0; r < 1; r++)
12215
{
12216
for (unsigned int s = 0; s < 1 - r; s++)
12217
{
12218
for (unsigned int t = 1; t < 2 - r - s; t++)
12219
{
12220
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12221
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12222
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12223
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
12224
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12225
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12226
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12227
}// end loop over 't'
12228
}// end loop over 's'
12229
}// end loop over 'r'
12230
for (unsigned int r = 0; r < 3; r++)
12231
{
12232
for (unsigned int s = 0; s < 3 - r; s++)
12233
{
12234
for (unsigned int t = 0; t < 3 - r - s; t++)
12235
{
12236
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12237
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
12238
}// end loop over 't'
12239
}// end loop over 's'
12240
}// end loop over 'r'
8773
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
8774
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
8775
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
8776
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
8777
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
8778
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
8779
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
8780
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
8781
basisvalues[0] *= std::sqrt(0.75);
8782
basisvalues[3] *= std::sqrt(1.25);
8783
basisvalues[9] *= std::sqrt(1.75);
8784
basisvalues[2] *= std::sqrt(2.5);
8785
basisvalues[8] *= std::sqrt(3.5);
8786
basisvalues[7] *= std::sqrt(5.25);
8787
basisvalues[1] *= std::sqrt(7.5);
8788
basisvalues[6] *= std::sqrt(10.5);
8789
basisvalues[5] *= std::sqrt(15.75);
8790
basisvalues[4] *= std::sqrt(26.25);
12241
8791
12242
8792
// Table(s) of coefficients.
12243
8793
static const double coefficients0[10] = \
12429
8979
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12430
8980
12431
8981
// Declare helper variables.
12432
unsigned int rr = 0;
12433
unsigned int ss = 0;
12434
unsigned int tt = 0;
12435
double tmp5 = 0.0;
12436
double tmp6 = 0.0;
12437
double tmp7 = 0.0;
12438
8982
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
12439
8983
double tmp1 = 0.25*(Y + Z)*(Y + Z);
12440
8984
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
12444
8988
// Compute basisvalues.
12445
8989
basisvalues[0] = 1.0;
12446
8990
basisvalues[1] = tmp0;
12447
for (unsigned int r = 1; r < 2; r++)
12448
{
12449
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12450
ss = r*(r + 1)*(r + 2)/6;
12451
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12452
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
12453
}// end loop over 'r'
12454
for (unsigned int r = 0; r < 2; r++)
12455
{
12456
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12457
ss = r*(r + 1)*(r + 2)/6;
12458
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
12459
}// end loop over 'r'
12460
for (unsigned int r = 0; r < 1; r++)
12461
{
12462
for (unsigned int s = 1; s < 2 - r; s++)
12463
{
12464
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12465
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12466
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12467
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
12468
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12469
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12470
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12471
}// end loop over 's'
12472
}// end loop over 'r'
12473
for (unsigned int r = 0; r < 2; r++)
12474
{
12475
for (unsigned int s = 0; s < 2 - r; s++)
12476
{
12477
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12478
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12479
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
12480
}// end loop over 's'
12481
}// end loop over 'r'
12482
for (unsigned int r = 0; r < 1; r++)
12483
{
12484
for (unsigned int s = 0; s < 1 - r; s++)
12485
{
12486
for (unsigned int t = 1; t < 2 - r - s; t++)
12487
{
12488
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12489
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12490
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12491
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
12492
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12493
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12494
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12495
}// end loop over 't'
12496
}// end loop over 's'
12497
}// end loop over 'r'
12498
for (unsigned int r = 0; r < 3; r++)
12499
{
12500
for (unsigned int s = 0; s < 3 - r; s++)
12501
{
12502
for (unsigned int t = 0; t < 3 - r - s; t++)
12503
{
12504
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12505
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
12506
}// end loop over 't'
12507
}// end loop over 's'
12508
}// end loop over 'r'
8991
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
8992
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
8993
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
8994
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
8995
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
8996
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
8997
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
8998
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
8999
basisvalues[0] *= std::sqrt(0.75);
9000
basisvalues[3] *= std::sqrt(1.25);
9001
basisvalues[9] *= std::sqrt(1.75);
9002
basisvalues[2] *= std::sqrt(2.5);
9003
basisvalues[8] *= std::sqrt(3.5);
9004
basisvalues[7] *= std::sqrt(5.25);
9005
basisvalues[1] *= std::sqrt(7.5);
9006
basisvalues[6] *= std::sqrt(10.5);
9007
basisvalues[5] *= std::sqrt(15.75);
9008
basisvalues[4] *= std::sqrt(26.25);
12509
9009
12510
9010
// Table(s) of coefficients.
12511
9011
static const double coefficients0[10] = \
12697
9197
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12698
9198
12699
9199
// Declare helper variables.
12700
unsigned int rr = 0;
12701
unsigned int ss = 0;
12702
unsigned int tt = 0;
12703
double tmp5 = 0.0;
12704
double tmp6 = 0.0;
12705
double tmp7 = 0.0;
12706
9200
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
12707
9201
double tmp1 = 0.25*(Y + Z)*(Y + Z);
12708
9202
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
12712
9206
// Compute basisvalues.
12713
9207
basisvalues[0] = 1.0;
12714
9208
basisvalues[1] = tmp0;
12715
for (unsigned int r = 1; r < 2; r++)
12716
{
12717
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12718
ss = r*(r + 1)*(r + 2)/6;
12719
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12720
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
12721
}// end loop over 'r'
12722
for (unsigned int r = 0; r < 2; r++)
12723
{
12724
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12725
ss = r*(r + 1)*(r + 2)/6;
12726
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
12727
}// end loop over 'r'
12728
for (unsigned int r = 0; r < 1; r++)
12729
{
12730
for (unsigned int s = 1; s < 2 - r; s++)
12731
{
12732
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
12733
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12734
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
12735
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
12736
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12737
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
12738
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
12739
}// end loop over 's'
12740
}// end loop over 'r'
12741
for (unsigned int r = 0; r < 2; r++)
12742
{
12743
for (unsigned int s = 0; s < 2 - r; s++)
12744
{
12745
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
12746
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
12747
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
12748
}// end loop over 's'
12749
}// end loop over 'r'
12750
for (unsigned int r = 0; r < 1; r++)
12751
{
12752
for (unsigned int s = 0; s < 1 - r; s++)
12753
{
12754
for (unsigned int t = 1; t < 2 - r - s; t++)
12755
{
12756
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
12757
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12758
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
12759
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
12760
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12761
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
12762
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
12763
}// end loop over 't'
12764
}// end loop over 's'
12765
}// end loop over 'r'
12766
for (unsigned int r = 0; r < 3; r++)
12767
{
12768
for (unsigned int s = 0; s < 3 - r; s++)
12769
{
12770
for (unsigned int t = 0; t < 3 - r - s; t++)
12771
{
12772
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
12773
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
12774
}// end loop over 't'
12775
}// end loop over 's'
12776
}// end loop over 'r'
9209
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
9210
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
9211
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
9212
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
9213
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
9214
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
9215
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
9216
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
9217
basisvalues[0] *= std::sqrt(0.75);
9218
basisvalues[3] *= std::sqrt(1.25);
9219
basisvalues[9] *= std::sqrt(1.75);
9220
basisvalues[2] *= std::sqrt(2.5);
9221
basisvalues[8] *= std::sqrt(3.5);
9222
basisvalues[7] *= std::sqrt(5.25);
9223
basisvalues[1] *= std::sqrt(7.5);
9224
basisvalues[6] *= std::sqrt(10.5);
9225
basisvalues[5] *= std::sqrt(15.75);
9226
basisvalues[4] *= std::sqrt(26.25);
12777
9227
12778
9228
// Table(s) of coefficients.
12779
9229
static const double coefficients0[10] = \
12965
9415
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
12966
9416
12967
9417
// Declare helper variables.
12968
unsigned int rr = 0;
12969
unsigned int ss = 0;
12970
unsigned int tt = 0;
12971
double tmp5 = 0.0;
12972
double tmp6 = 0.0;
12973
double tmp7 = 0.0;
12974
9418
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
12975
9419
double tmp1 = 0.25*(Y + Z)*(Y + Z);
12976
9420
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
12980
9424
// Compute basisvalues.
12981
9425
basisvalues[0] = 1.0;
12982
9426
basisvalues[1] = tmp0;
12983
for (unsigned int r = 1; r < 2; r++)
12984
{
12985
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
12986
ss = r*(r + 1)*(r + 2)/6;
12987
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
12988
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
12989
}// end loop over 'r'
12990
for (unsigned int r = 0; r < 2; r++)
12991
{
12992
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
12993
ss = r*(r + 1)*(r + 2)/6;
12994
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
12995
}// end loop over 'r'
12996
for (unsigned int r = 0; r < 1; r++)
12997
{
12998
for (unsigned int s = 1; s < 2 - r; s++)
12999
{
13000
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13001
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13002
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13003
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
13004
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13005
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13006
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13007
}// end loop over 's'
13008
}// end loop over 'r'
13009
for (unsigned int r = 0; r < 2; r++)
13010
{
13011
for (unsigned int s = 0; s < 2 - r; s++)
13012
{
13013
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13014
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13015
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
13016
}// end loop over 's'
13017
}// end loop over 'r'
13018
for (unsigned int r = 0; r < 1; r++)
13019
{
13020
for (unsigned int s = 0; s < 1 - r; s++)
13021
{
13022
for (unsigned int t = 1; t < 2 - r - s; t++)
13023
{
13024
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13025
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13026
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13027
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
13028
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13029
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13030
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13031
}// end loop over 't'
13032
}// end loop over 's'
13033
}// end loop over 'r'
13034
for (unsigned int r = 0; r < 3; r++)
13035
{
13036
for (unsigned int s = 0; s < 3 - r; s++)
13037
{
13038
for (unsigned int t = 0; t < 3 - r - s; t++)
13039
{
13040
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13041
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
13042
}// end loop over 't'
13043
}// end loop over 's'
13044
}// end loop over 'r'
9427
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
9428
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
9429
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
9430
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
9431
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
9432
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
9433
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
9434
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
9435
basisvalues[0] *= std::sqrt(0.75);
9436
basisvalues[3] *= std::sqrt(1.25);
9437
basisvalues[9] *= std::sqrt(1.75);
9438
basisvalues[2] *= std::sqrt(2.5);
9439
basisvalues[8] *= std::sqrt(3.5);
9440
basisvalues[7] *= std::sqrt(5.25);
9441
basisvalues[1] *= std::sqrt(7.5);
9442
basisvalues[6] *= std::sqrt(10.5);
9443
basisvalues[5] *= std::sqrt(15.75);
9444
basisvalues[4] *= std::sqrt(26.25);
13045
9445
13046
9446
// Table(s) of coefficients.
13047
9447
static const double coefficients0[10] = \
13233
9633
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13234
9634
13235
9635
// Declare helper variables.
13236
unsigned int rr = 0;
13237
unsigned int ss = 0;
13238
unsigned int tt = 0;
13239
double tmp5 = 0.0;
13240
double tmp6 = 0.0;
13241
double tmp7 = 0.0;
13242
9636
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
13243
9637
double tmp1 = 0.25*(Y + Z)*(Y + Z);
13244
9638
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
13248
9642
// Compute basisvalues.
13249
9643
basisvalues[0] = 1.0;
13250
9644
basisvalues[1] = tmp0;
13251
for (unsigned int r = 1; r < 2; r++)
13252
{
13253
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13254
ss = r*(r + 1)*(r + 2)/6;
13255
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13256
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
13257
}// end loop over 'r'
13258
for (unsigned int r = 0; r < 2; r++)
13259
{
13260
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13261
ss = r*(r + 1)*(r + 2)/6;
13262
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
13263
}// end loop over 'r'
13264
for (unsigned int r = 0; r < 1; r++)
13265
{
13266
for (unsigned int s = 1; s < 2 - r; s++)
13267
{
13268
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13269
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13270
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13271
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
13272
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13273
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13274
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13275
}// end loop over 's'
13276
}// end loop over 'r'
13277
for (unsigned int r = 0; r < 2; r++)
13278
{
13279
for (unsigned int s = 0; s < 2 - r; s++)
13280
{
13281
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13282
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13283
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
13284
}// end loop over 's'
13285
}// end loop over 'r'
13286
for (unsigned int r = 0; r < 1; r++)
13287
{
13288
for (unsigned int s = 0; s < 1 - r; s++)
13289
{
13290
for (unsigned int t = 1; t < 2 - r - s; t++)
13291
{
13292
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13293
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13294
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13295
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
13296
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13297
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13298
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13299
}// end loop over 't'
13300
}// end loop over 's'
13301
}// end loop over 'r'
13302
for (unsigned int r = 0; r < 3; r++)
13303
{
13304
for (unsigned int s = 0; s < 3 - r; s++)
13305
{
13306
for (unsigned int t = 0; t < 3 - r - s; t++)
13307
{
13308
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13309
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
13310
}// end loop over 't'
13311
}// end loop over 's'
13312
}// end loop over 'r'
9645
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
9646
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
9647
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
9648
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
9649
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
9650
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
9651
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
9652
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
9653
basisvalues[0] *= std::sqrt(0.75);
9654
basisvalues[3] *= std::sqrt(1.25);
9655
basisvalues[9] *= std::sqrt(1.75);
9656
basisvalues[2] *= std::sqrt(2.5);
9657
basisvalues[8] *= std::sqrt(3.5);
9658
basisvalues[7] *= std::sqrt(5.25);
9659
basisvalues[1] *= std::sqrt(7.5);
9660
basisvalues[6] *= std::sqrt(10.5);
9661
basisvalues[5] *= std::sqrt(15.75);
9662
basisvalues[4] *= std::sqrt(26.25);
13313
9663
13314
9664
// Table(s) of coefficients.
13315
9665
static const double coefficients0[10] = \
13501
9851
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13502
9852
13503
9853
// Declare helper variables.
13504
unsigned int rr = 0;
13505
unsigned int ss = 0;
13506
unsigned int tt = 0;
13507
double tmp5 = 0.0;
13508
double tmp6 = 0.0;
13509
double tmp7 = 0.0;
13510
9854
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
13511
9855
double tmp1 = 0.25*(Y + Z)*(Y + Z);
13512
9856
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
13516
9860
// Compute basisvalues.
13517
9861
basisvalues[0] = 1.0;
13518
9862
basisvalues[1] = tmp0;
13519
for (unsigned int r = 1; r < 2; r++)
13520
{
13521
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13522
ss = r*(r + 1)*(r + 2)/6;
13523
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13524
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
13525
}// end loop over 'r'
13526
for (unsigned int r = 0; r < 2; r++)
13527
{
13528
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13529
ss = r*(r + 1)*(r + 2)/6;
13530
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
13531
}// end loop over 'r'
13532
for (unsigned int r = 0; r < 1; r++)
13533
{
13534
for (unsigned int s = 1; s < 2 - r; s++)
13535
{
13536
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13537
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13538
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13539
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
13540
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13541
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13542
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13543
}// end loop over 's'
13544
}// end loop over 'r'
13545
for (unsigned int r = 0; r < 2; r++)
13546
{
13547
for (unsigned int s = 0; s < 2 - r; s++)
13548
{
13549
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13550
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13551
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
13552
}// end loop over 's'
13553
}// end loop over 'r'
13554
for (unsigned int r = 0; r < 1; r++)
13555
{
13556
for (unsigned int s = 0; s < 1 - r; s++)
13557
{
13558
for (unsigned int t = 1; t < 2 - r - s; t++)
13559
{
13560
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13561
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13562
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13563
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
13564
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13565
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13566
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13567
}// end loop over 't'
13568
}// end loop over 's'
13569
}// end loop over 'r'
13570
for (unsigned int r = 0; r < 3; r++)
13571
{
13572
for (unsigned int s = 0; s < 3 - r; s++)
13573
{
13574
for (unsigned int t = 0; t < 3 - r - s; t++)
13575
{
13576
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13577
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
13578
}// end loop over 't'
13579
}// end loop over 's'
13580
}// end loop over 'r'
9863
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
9864
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
9865
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
9866
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
9867
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
9868
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
9869
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
9870
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
9871
basisvalues[0] *= std::sqrt(0.75);
9872
basisvalues[3] *= std::sqrt(1.25);
9873
basisvalues[9] *= std::sqrt(1.75);
9874
basisvalues[2] *= std::sqrt(2.5);
9875
basisvalues[8] *= std::sqrt(3.5);
9876
basisvalues[7] *= std::sqrt(5.25);
9877
basisvalues[1] *= std::sqrt(7.5);
9878
basisvalues[6] *= std::sqrt(10.5);
9879
basisvalues[5] *= std::sqrt(15.75);
9880
basisvalues[4] *= std::sqrt(26.25);
13581
9881
13582
9882
// Table(s) of coefficients.
13583
9883
static const double coefficients0[10] = \
13769
10069
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
13770
10070
13771
10071
// Declare helper variables.
13772
unsigned int rr = 0;
13773
unsigned int ss = 0;
13774
unsigned int tt = 0;
13775
double tmp5 = 0.0;
13776
double tmp6 = 0.0;
13777
double tmp7 = 0.0;
13778
10072
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
13779
10073
double tmp1 = 0.25*(Y + Z)*(Y + Z);
13780
10074
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
13784
10078
// Compute basisvalues.
13785
10079
basisvalues[0] = 1.0;
13786
10080
basisvalues[1] = tmp0;
13787
for (unsigned int r = 1; r < 2; r++)
13788
{
13789
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
13790
ss = r*(r + 1)*(r + 2)/6;
13791
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
13792
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
13793
}// end loop over 'r'
13794
for (unsigned int r = 0; r < 2; r++)
13795
{
13796
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
13797
ss = r*(r + 1)*(r + 2)/6;
13798
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
13799
}// end loop over 'r'
13800
for (unsigned int r = 0; r < 1; r++)
13801
{
13802
for (unsigned int s = 1; s < 2 - r; s++)
13803
{
13804
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
13805
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13806
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
13807
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
13808
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13809
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
13810
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
13811
}// end loop over 's'
13812
}// end loop over 'r'
13813
for (unsigned int r = 0; r < 2; r++)
13814
{
13815
for (unsigned int s = 0; s < 2 - r; s++)
13816
{
13817
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
13818
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
13819
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
13820
}// end loop over 's'
13821
}// end loop over 'r'
13822
for (unsigned int r = 0; r < 1; r++)
13823
{
13824
for (unsigned int s = 0; s < 1 - r; s++)
13825
{
13826
for (unsigned int t = 1; t < 2 - r - s; t++)
13827
{
13828
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
13829
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13830
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
13831
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
13832
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13833
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
13834
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
13835
}// end loop over 't'
13836
}// end loop over 's'
13837
}// end loop over 'r'
13838
for (unsigned int r = 0; r < 3; r++)
13839
{
13840
for (unsigned int s = 0; s < 3 - r; s++)
13841
{
13842
for (unsigned int t = 0; t < 3 - r - s; t++)
13843
{
13844
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
13845
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
13846
}// end loop over 't'
13847
}// end loop over 's'
13848
}// end loop over 'r'
10081
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
10082
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
10083
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
10084
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
10085
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
10086
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
10087
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
10088
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
10089
basisvalues[0] *= std::sqrt(0.75);
10090
basisvalues[3] *= std::sqrt(1.25);
10091
basisvalues[9] *= std::sqrt(1.75);
10092
basisvalues[2] *= std::sqrt(2.5);
10093
basisvalues[8] *= std::sqrt(3.5);
10094
basisvalues[7] *= std::sqrt(5.25);
10095
basisvalues[1] *= std::sqrt(7.5);
10096
basisvalues[6] *= std::sqrt(10.5);
10097
basisvalues[5] *= std::sqrt(15.75);
10098
basisvalues[4] *= std::sqrt(26.25);
13849
10099
13850
10100
// Table(s) of coefficients.
13851
10101
static const double coefficients0[10] = \
14037
10287
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14038
10288
14039
10289
// Declare helper variables.
14040
unsigned int rr = 0;
14041
unsigned int ss = 0;
14042
unsigned int tt = 0;
14043
double tmp5 = 0.0;
14044
double tmp6 = 0.0;
14045
double tmp7 = 0.0;
14046
10290
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
14047
10291
double tmp1 = 0.25*(Y + Z)*(Y + Z);
14048
10292
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
14052
10296
// Compute basisvalues.
14053
10297
basisvalues[0] = 1.0;
14054
10298
basisvalues[1] = tmp0;
14055
for (unsigned int r = 1; r < 2; r++)
14056
{
14057
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14058
ss = r*(r + 1)*(r + 2)/6;
14059
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14060
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
14061
}// end loop over 'r'
14062
for (unsigned int r = 0; r < 2; r++)
14063
{
14064
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14065
ss = r*(r + 1)*(r + 2)/6;
14066
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
14067
}// end loop over 'r'
14068
for (unsigned int r = 0; r < 1; r++)
14069
{
14070
for (unsigned int s = 1; s < 2 - r; s++)
14071
{
14072
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14073
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14074
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14075
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
14076
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14077
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14078
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14079
}// end loop over 's'
14080
}// end loop over 'r'
14081
for (unsigned int r = 0; r < 2; r++)
14082
{
14083
for (unsigned int s = 0; s < 2 - r; s++)
14084
{
14085
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14086
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14087
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
14088
}// end loop over 's'
14089
}// end loop over 'r'
14090
for (unsigned int r = 0; r < 1; r++)
14091
{
14092
for (unsigned int s = 0; s < 1 - r; s++)
14093
{
14094
for (unsigned int t = 1; t < 2 - r - s; t++)
14095
{
14096
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14097
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14098
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14099
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
14100
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14101
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14102
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14103
}// end loop over 't'
14104
}// end loop over 's'
14105
}// end loop over 'r'
14106
for (unsigned int r = 0; r < 3; r++)
14107
{
14108
for (unsigned int s = 0; s < 3 - r; s++)
14109
{
14110
for (unsigned int t = 0; t < 3 - r - s; t++)
14111
{
14112
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14113
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
14114
}// end loop over 't'
14115
}// end loop over 's'
14116
}// end loop over 'r'
10299
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
10300
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
10301
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
10302
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
10303
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
10304
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
10305
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
10306
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
10307
basisvalues[0] *= std::sqrt(0.75);
10308
basisvalues[3] *= std::sqrt(1.25);
10309
basisvalues[9] *= std::sqrt(1.75);
10310
basisvalues[2] *= std::sqrt(2.5);
10311
basisvalues[8] *= std::sqrt(3.5);
10312
basisvalues[7] *= std::sqrt(5.25);
10313
basisvalues[1] *= std::sqrt(7.5);
10314
basisvalues[6] *= std::sqrt(10.5);
10315
basisvalues[5] *= std::sqrt(15.75);
10316
basisvalues[4] *= std::sqrt(26.25);
14117
10317
14118
10318
// Table(s) of coefficients.
14119
10319
static const double coefficients0[10] = \
14305
10505
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14306
10506
14307
10507
// Declare helper variables.
14308
unsigned int rr = 0;
14309
unsigned int ss = 0;
14310
unsigned int tt = 0;
14311
double tmp5 = 0.0;
14312
double tmp6 = 0.0;
14313
double tmp7 = 0.0;
14314
10508
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
14315
10509
double tmp1 = 0.25*(Y + Z)*(Y + Z);
14316
10510
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
14320
10514
// Compute basisvalues.
14321
10515
basisvalues[0] = 1.0;
14322
10516
basisvalues[1] = tmp0;
14323
for (unsigned int r = 1; r < 2; r++)
14324
{
14325
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14326
ss = r*(r + 1)*(r + 2)/6;
14327
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14328
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
14329
}// end loop over 'r'
14330
for (unsigned int r = 0; r < 2; r++)
14331
{
14332
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14333
ss = r*(r + 1)*(r + 2)/6;
14334
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
14335
}// end loop over 'r'
14336
for (unsigned int r = 0; r < 1; r++)
14337
{
14338
for (unsigned int s = 1; s < 2 - r; s++)
14339
{
14340
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14341
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14342
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14343
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
14344
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14345
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14346
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14347
}// end loop over 's'
14348
}// end loop over 'r'
14349
for (unsigned int r = 0; r < 2; r++)
14350
{
14351
for (unsigned int s = 0; s < 2 - r; s++)
14352
{
14353
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14354
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14355
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
14356
}// end loop over 's'
14357
}// end loop over 'r'
14358
for (unsigned int r = 0; r < 1; r++)
14359
{
14360
for (unsigned int s = 0; s < 1 - r; s++)
14361
{
14362
for (unsigned int t = 1; t < 2 - r - s; t++)
14363
{
14364
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14365
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14366
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14367
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
14368
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14369
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14370
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14371
}// end loop over 't'
14372
}// end loop over 's'
14373
}// end loop over 'r'
14374
for (unsigned int r = 0; r < 3; r++)
14375
{
14376
for (unsigned int s = 0; s < 3 - r; s++)
14377
{
14378
for (unsigned int t = 0; t < 3 - r - s; t++)
14379
{
14380
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14381
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
14382
}// end loop over 't'
14383
}// end loop over 's'
14384
}// end loop over 'r'
10517
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
10518
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
10519
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
10520
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
10521
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
10522
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
10523
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
10524
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
10525
basisvalues[0] *= std::sqrt(0.75);
10526
basisvalues[3] *= std::sqrt(1.25);
10527
basisvalues[9] *= std::sqrt(1.75);
10528
basisvalues[2] *= std::sqrt(2.5);
10529
basisvalues[8] *= std::sqrt(3.5);
10530
basisvalues[7] *= std::sqrt(5.25);
10531
basisvalues[1] *= std::sqrt(7.5);
10532
basisvalues[6] *= std::sqrt(10.5);
10533
basisvalues[5] *= std::sqrt(15.75);
10534
basisvalues[4] *= std::sqrt(26.25);
14385
10535
14386
10536
// Table(s) of coefficients.
14387
10537
static const double coefficients0[10] = \
14573
10723
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14574
10724
14575
10725
// Declare helper variables.
14576
unsigned int rr = 0;
14577
unsigned int ss = 0;
14578
unsigned int tt = 0;
14579
double tmp5 = 0.0;
14580
double tmp6 = 0.0;
14581
double tmp7 = 0.0;
14582
10726
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
14583
10727
double tmp1 = 0.25*(Y + Z)*(Y + Z);
14584
10728
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
14588
10732
// Compute basisvalues.
14589
10733
basisvalues[0] = 1.0;
14590
10734
basisvalues[1] = tmp0;
14591
for (unsigned int r = 1; r < 2; r++)
14592
{
14593
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14594
ss = r*(r + 1)*(r + 2)/6;
14595
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14596
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
14597
}// end loop over 'r'
14598
for (unsigned int r = 0; r < 2; r++)
14599
{
14600
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14601
ss = r*(r + 1)*(r + 2)/6;
14602
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
14603
}// end loop over 'r'
14604
for (unsigned int r = 0; r < 1; r++)
14605
{
14606
for (unsigned int s = 1; s < 2 - r; s++)
14607
{
14608
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14609
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14610
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14611
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
14612
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14613
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14614
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14615
}// end loop over 's'
14616
}// end loop over 'r'
14617
for (unsigned int r = 0; r < 2; r++)
14618
{
14619
for (unsigned int s = 0; s < 2 - r; s++)
14620
{
14621
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14622
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14623
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
14624
}// end loop over 's'
14625
}// end loop over 'r'
14626
for (unsigned int r = 0; r < 1; r++)
14627
{
14628
for (unsigned int s = 0; s < 1 - r; s++)
14629
{
14630
for (unsigned int t = 1; t < 2 - r - s; t++)
14631
{
14632
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14633
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14634
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14635
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
14636
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14637
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14638
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14639
}// end loop over 't'
14640
}// end loop over 's'
14641
}// end loop over 'r'
14642
for (unsigned int r = 0; r < 3; r++)
14643
{
14644
for (unsigned int s = 0; s < 3 - r; s++)
14645
{
14646
for (unsigned int t = 0; t < 3 - r - s; t++)
14647
{
14648
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14649
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
14650
}// end loop over 't'
14651
}// end loop over 's'
14652
}// end loop over 'r'
10735
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
10736
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
10737
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
10738
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
10739
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
10740
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
10741
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
10742
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
10743
basisvalues[0] *= std::sqrt(0.75);
10744
basisvalues[3] *= std::sqrt(1.25);
10745
basisvalues[9] *= std::sqrt(1.75);
10746
basisvalues[2] *= std::sqrt(2.5);
10747
basisvalues[8] *= std::sqrt(3.5);
10748
basisvalues[7] *= std::sqrt(5.25);
10749
basisvalues[1] *= std::sqrt(7.5);
10750
basisvalues[6] *= std::sqrt(10.5);
10751
basisvalues[5] *= std::sqrt(15.75);
10752
basisvalues[4] *= std::sqrt(26.25);
14653
10753
14654
10754
// Table(s) of coefficients.
14655
10755
static const double coefficients0[10] = \
14841
10941
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
14842
10942
14843
10943
// Declare helper variables.
14844
unsigned int rr = 0;
14845
unsigned int ss = 0;
14846
unsigned int tt = 0;
14847
double tmp5 = 0.0;
14848
double tmp6 = 0.0;
14849
double tmp7 = 0.0;
14850
10944
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
14851
10945
double tmp1 = 0.25*(Y + Z)*(Y + Z);
14852
10946
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
14856
10950
// Compute basisvalues.
14857
10951
basisvalues[0] = 1.0;
14858
10952
basisvalues[1] = tmp0;
14859
for (unsigned int r = 1; r < 2; r++)
14860
{
14861
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
14862
ss = r*(r + 1)*(r + 2)/6;
14863
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
14864
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
14865
}// end loop over 'r'
14866
for (unsigned int r = 0; r < 2; r++)
14867
{
14868
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
14869
ss = r*(r + 1)*(r + 2)/6;
14870
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
14871
}// end loop over 'r'
14872
for (unsigned int r = 0; r < 1; r++)
14873
{
14874
for (unsigned int s = 1; s < 2 - r; s++)
14875
{
14876
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
14877
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14878
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
14879
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
14880
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14881
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
14882
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
14883
}// end loop over 's'
14884
}// end loop over 'r'
14885
for (unsigned int r = 0; r < 2; r++)
14886
{
14887
for (unsigned int s = 0; s < 2 - r; s++)
14888
{
14889
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
14890
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
14891
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
14892
}// end loop over 's'
14893
}// end loop over 'r'
14894
for (unsigned int r = 0; r < 1; r++)
14895
{
14896
for (unsigned int s = 0; s < 1 - r; s++)
14897
{
14898
for (unsigned int t = 1; t < 2 - r - s; t++)
14899
{
14900
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
14901
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14902
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
14903
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
14904
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14905
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
14906
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
14907
}// end loop over 't'
14908
}// end loop over 's'
14909
}// end loop over 'r'
14910
for (unsigned int r = 0; r < 3; r++)
14911
{
14912
for (unsigned int s = 0; s < 3 - r; s++)
14913
{
14914
for (unsigned int t = 0; t < 3 - r - s; t++)
14915
{
14916
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
14917
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
14918
}// end loop over 't'
14919
}// end loop over 's'
14920
}// end loop over 'r'
10953
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
10954
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
10955
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
10956
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
10957
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
10958
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
10959
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
10960
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
10961
basisvalues[0] *= std::sqrt(0.75);
10962
basisvalues[3] *= std::sqrt(1.25);
10963
basisvalues[9] *= std::sqrt(1.75);
10964
basisvalues[2] *= std::sqrt(2.5);
10965
basisvalues[8] *= std::sqrt(3.5);
10966
basisvalues[7] *= std::sqrt(5.25);
10967
basisvalues[1] *= std::sqrt(7.5);
10968
basisvalues[6] *= std::sqrt(10.5);
10969
basisvalues[5] *= std::sqrt(15.75);
10970
basisvalues[4] *= std::sqrt(26.25);
14921
10971
14922
10972
// Table(s) of coefficients.
14923
10973
static const double coefficients0[10] = \
15109
11159
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
15110
11160
15111
11161
// Declare helper variables.
15112
unsigned int rr = 0;
15113
unsigned int ss = 0;
15114
unsigned int tt = 0;
15115
double tmp5 = 0.0;
15116
double tmp6 = 0.0;
15117
double tmp7 = 0.0;
15118
11162
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
15119
11163
double tmp1 = 0.25*(Y + Z)*(Y + Z);
15120
11164
double tmp2 = 0.5*(1.0 + Z + 2.0*Y);
15124
11168
// Compute basisvalues.
15125
11169
basisvalues[0] = 1.0;
15126
11170
basisvalues[1] = tmp0;
15127
for (unsigned int r = 1; r < 2; r++)
15128
{
15129
rr = (r + 1)*((r + 1) + 1)*((r + 1) + 2)/6;
15130
ss = r*(r + 1)*(r + 2)/6;
15131
tt = (r - 1)*((r - 1) + 1)*((r - 1) + 2)/6;
15132
basisvalues[rr] = (basisvalues[ss]*tmp0*(1.0 + 2.0*r)/(1.0 + r) - basisvalues[tt]*tmp1*r/(1.0 + r));
15133
}// end loop over 'r'
15134
for (unsigned int r = 0; r < 2; r++)
15135
{
15136
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
15137
ss = r*(r + 1)*(r + 2)/6;
15138
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
15139
}// end loop over 'r'
15140
for (unsigned int r = 0; r < 1; r++)
15141
{
15142
for (unsigned int s = 1; s < 2 - r; s++)
15143
{
15144
rr = (r + (s + 1))*(r + (s + 1) + 1)*(r + (s + 1) + 2)/6 + (s + 1)*((s + 1) + 1)/2;
15145
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
15146
tt = (r + (s - 1))*(r + (s - 1) + 1)*(r + (s - 1) + 2)/6 + (s - 1)*((s - 1) + 1)/2;
15147
tmp5 = (2.0 + 2.0*r + 2.0*s)*(3.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + s)*(2.0 + s + 2.0*r));
15148
tmp6 = (1.0 + 4.0*r*r + 4.0*r)*(2.0 + 2.0*r + 2.0*s)/(2.0*(1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
15149
tmp7 = (1.0 + s + 2.0*r)*(3.0 + 2.0*r + 2.0*s)*s/((1.0 + 2.0*r + 2.0*s)*(1.0 + s)*(2.0 + s + 2.0*r));
15150
basisvalues[rr] = (basisvalues[ss]*(tmp2*tmp5 + tmp3*tmp6) - basisvalues[tt]*tmp4*tmp7);
15151
}// end loop over 's'
15152
}// end loop over 'r'
15153
for (unsigned int r = 0; r < 2; r++)
15154
{
15155
for (unsigned int s = 0; s < 2 - r; s++)
15156
{
15157
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
15158
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
15159
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
15160
}// end loop over 's'
15161
}// end loop over 'r'
15162
for (unsigned int r = 0; r < 1; r++)
15163
{
15164
for (unsigned int s = 0; s < 1 - r; s++)
15165
{
15166
for (unsigned int t = 1; t < 2 - r - s; t++)
15167
{
15168
rr = (r + s + t + 1)*(r + s + t + 1 + 1)*(r + s + t + 1 + 2)/6 + (s + t + 1)*(s + t + 1 + 1)/2 + t + 1;
15169
ss = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
15170
tt = (r + s + t - 1)*(r + s + t - 1 + 1)*(r + s + t - 1 + 2)/6 + (s + t - 1)*(s + t - 1 + 1)/2 + t - 1;
15171
tmp5 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 2.0*r + 2.0*s + 2.0*t)/(2.0*(1.0 + t)*(3.0 + t + 2.0*r + 2.0*s));
15172
tmp6 = (3.0 + 2.0*r + 2.0*s + 2.0*t)*(4.0 + 4.0*r*r + 4.0*s*s + 8.0*r*s + 8.0*r + 8.0*s)/(2.0*(1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
15173
tmp7 = (2.0 + t + 2.0*r + 2.0*s)*(4.0 + 2.0*r + 2.0*s + 2.0*t)*t/((1.0 + t)*(2.0 + 2.0*r + 2.0*s + 2.0*t)*(3.0 + t + 2.0*r + 2.0*s));
15174
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Z*tmp5) - basisvalues[tt]*tmp7);
15175
}// end loop over 't'
15176
}// end loop over 's'
15177
}// end loop over 'r'
15178
for (unsigned int r = 0; r < 3; r++)
15179
{
15180
for (unsigned int s = 0; s < 3 - r; s++)
15181
{
15182
for (unsigned int t = 0; t < 3 - r - s; t++)
15183
{
15184
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
15185
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
15186
}// end loop over 't'
15187
}// end loop over 's'
15188
}// end loop over 'r'
11171
basisvalues[4] = 1.5*tmp0*basisvalues[1] - 0.5*tmp1*basisvalues[0];
11172
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
11173
basisvalues[5] = (0.5*(2.0 + 3.0*Y + Z) + 1.0*(1.0 + Y))*basisvalues[1];
11174
basisvalues[7] = (1.6666667*tmp2 + 0.11111111*tmp3)*basisvalues[2] - 0.55555556*tmp4*basisvalues[0];
11175
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
11176
basisvalues[8] = (3.0*Z + 2.0)*basisvalues[2];
11177
basisvalues[6] = (3.0*Z + 2.0)*basisvalues[1];
11178
basisvalues[9] = basisvalues[3]*(0.3125 + 1.875*Z) - 0.5625*basisvalues[0];
11179
basisvalues[0] *= std::sqrt(0.75);
11180
basisvalues[3] *= std::sqrt(1.25);
11181
basisvalues[9] *= std::sqrt(1.75);
11182
basisvalues[2] *= std::sqrt(2.5);
11183
basisvalues[8] *= std::sqrt(3.5);
11184
basisvalues[7] *= std::sqrt(5.25);
11185
basisvalues[1] *= std::sqrt(7.5);
11186
basisvalues[6] *= std::sqrt(10.5);
11187
basisvalues[5] *= std::sqrt(15.75);
11188
basisvalues[4] *= std::sqrt(26.25);
15189
11189
15190
11190
// Table(s) of coefficients.
15191
11191
static const double coefficients0[10] = \
16054
12054
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16055
12055
16056
12056
// Declare helper variables.
16057
unsigned int rr = 0;
16058
unsigned int ss = 0;
16059
12057
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16060
12058
16061
12059
// Compute basisvalues.
16062
12060
basisvalues[0] = 1.0;
16063
12061
basisvalues[1] = tmp0;
16064
for (unsigned int r = 0; r < 1; r++)
16065
{
16066
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16067
ss = r*(r + 1)*(r + 2)/6;
16068
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16069
}// end loop over 'r'
16070
for (unsigned int r = 0; r < 1; r++)
16071
{
16072
for (unsigned int s = 0; s < 1 - r; s++)
16073
{
16074
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16075
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16076
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16077
}// end loop over 's'
16078
}// end loop over 'r'
16079
for (unsigned int r = 0; r < 2; r++)
16080
{
16081
for (unsigned int s = 0; s < 2 - r; s++)
16082
{
16083
for (unsigned int t = 0; t < 2 - r - s; t++)
16084
{
16085
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16086
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16087
}// end loop over 't'
16088
}// end loop over 's'
16089
}// end loop over 'r'
12062
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12063
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12064
basisvalues[0] *= std::sqrt(0.75);
12065
basisvalues[3] *= std::sqrt(1.25);
12066
basisvalues[2] *= std::sqrt(2.5);
12067
basisvalues[1] *= std::sqrt(7.5);
16090
12068
16091
12069
// Table(s) of coefficients.
16092
12070
static const double coefficients0[4] = \
16106
12084
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16107
12085
16108
12086
// Declare helper variables.
16109
unsigned int rr = 0;
16110
unsigned int ss = 0;
16111
12087
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16112
12088
16113
12089
// Compute basisvalues.
16114
12090
basisvalues[0] = 1.0;
16115
12091
basisvalues[1] = tmp0;
16116
for (unsigned int r = 0; r < 1; r++)
16117
{
16118
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16119
ss = r*(r + 1)*(r + 2)/6;
16120
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16121
}// end loop over 'r'
16122
for (unsigned int r = 0; r < 1; r++)
16123
{
16124
for (unsigned int s = 0; s < 1 - r; s++)
16125
{
16126
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16127
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16128
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16129
}// end loop over 's'
16130
}// end loop over 'r'
16131
for (unsigned int r = 0; r < 2; r++)
16132
{
16133
for (unsigned int s = 0; s < 2 - r; s++)
16134
{
16135
for (unsigned int t = 0; t < 2 - r - s; t++)
16136
{
16137
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16138
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16139
}// end loop over 't'
16140
}// end loop over 's'
16141
}// end loop over 'r'
12092
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12093
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12094
basisvalues[0] *= std::sqrt(0.75);
12095
basisvalues[3] *= std::sqrt(1.25);
12096
basisvalues[2] *= std::sqrt(2.5);
12097
basisvalues[1] *= std::sqrt(7.5);
16142
12098
16143
12099
// Table(s) of coefficients.
16144
12100
static const double coefficients0[4] = \
16158
12114
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16159
12115
16160
12116
// Declare helper variables.
16161
unsigned int rr = 0;
16162
unsigned int ss = 0;
16163
12117
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16164
12118
16165
12119
// Compute basisvalues.
16166
12120
basisvalues[0] = 1.0;
16167
12121
basisvalues[1] = tmp0;
16168
for (unsigned int r = 0; r < 1; r++)
16169
{
16170
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16171
ss = r*(r + 1)*(r + 2)/6;
16172
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16173
}// end loop over 'r'
16174
for (unsigned int r = 0; r < 1; r++)
16175
{
16176
for (unsigned int s = 0; s < 1 - r; s++)
16177
{
16178
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16179
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16180
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16181
}// end loop over 's'
16182
}// end loop over 'r'
16183
for (unsigned int r = 0; r < 2; r++)
16184
{
16185
for (unsigned int s = 0; s < 2 - r; s++)
16186
{
16187
for (unsigned int t = 0; t < 2 - r - s; t++)
16188
{
16189
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16190
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16191
}// end loop over 't'
16192
}// end loop over 's'
16193
}// end loop over 'r'
12122
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12123
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12124
basisvalues[0] *= std::sqrt(0.75);
12125
basisvalues[3] *= std::sqrt(1.25);
12126
basisvalues[2] *= std::sqrt(2.5);
12127
basisvalues[1] *= std::sqrt(7.5);
16194
12128
16195
12129
// Table(s) of coefficients.
16196
12130
static const double coefficients0[4] = \
16210
12144
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16211
12145
16212
12146
// Declare helper variables.
16213
unsigned int rr = 0;
16214
unsigned int ss = 0;
16215
12147
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16216
12148
16217
12149
// Compute basisvalues.
16218
12150
basisvalues[0] = 1.0;
16219
12151
basisvalues[1] = tmp0;
16220
for (unsigned int r = 0; r < 1; r++)
16221
{
16222
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16223
ss = r*(r + 1)*(r + 2)/6;
16224
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16225
}// end loop over 'r'
16226
for (unsigned int r = 0; r < 1; r++)
16227
{
16228
for (unsigned int s = 0; s < 1 - r; s++)
16229
{
16230
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16231
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16232
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16233
}// end loop over 's'
16234
}// end loop over 'r'
16235
for (unsigned int r = 0; r < 2; r++)
16236
{
16237
for (unsigned int s = 0; s < 2 - r; s++)
16238
{
16239
for (unsigned int t = 0; t < 2 - r - s; t++)
16240
{
16241
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16242
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16243
}// end loop over 't'
16244
}// end loop over 's'
16245
}// end loop over 'r'
12152
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12153
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12154
basisvalues[0] *= std::sqrt(0.75);
12155
basisvalues[3] *= std::sqrt(1.25);
12156
basisvalues[2] *= std::sqrt(2.5);
12157
basisvalues[1] *= std::sqrt(7.5);
16246
12158
16247
12159
// Table(s) of coefficients.
16248
12160
static const double coefficients0[4] = \
16405
12317
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16406
12318
16407
12319
// Declare helper variables.
16408
unsigned int rr = 0;
16409
unsigned int ss = 0;
16410
12320
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16411
12321
16412
12322
// Compute basisvalues.
16413
12323
basisvalues[0] = 1.0;
16414
12324
basisvalues[1] = tmp0;
16415
for (unsigned int r = 0; r < 1; r++)
16416
{
16417
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16418
ss = r*(r + 1)*(r + 2)/6;
16419
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16420
}// end loop over 'r'
16421
for (unsigned int r = 0; r < 1; r++)
16422
{
16423
for (unsigned int s = 0; s < 1 - r; s++)
16424
{
16425
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16426
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16427
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16428
}// end loop over 's'
16429
}// end loop over 'r'
16430
for (unsigned int r = 0; r < 2; r++)
16431
{
16432
for (unsigned int s = 0; s < 2 - r; s++)
16433
{
16434
for (unsigned int t = 0; t < 2 - r - s; t++)
16435
{
16436
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16437
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16438
}// end loop over 't'
16439
}// end loop over 's'
16440
}// end loop over 'r'
12325
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12326
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12327
basisvalues[0] *= std::sqrt(0.75);
12328
basisvalues[3] *= std::sqrt(1.25);
12329
basisvalues[2] *= std::sqrt(2.5);
12330
basisvalues[1] *= std::sqrt(7.5);
16441
12331
16442
12332
// Table(s) of coefficients.
16443
12333
static const double coefficients0[4] = \
16599
12489
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16600
12490
16601
12491
// Declare helper variables.
16602
unsigned int rr = 0;
16603
unsigned int ss = 0;
16604
12492
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16605
12493
16606
12494
// Compute basisvalues.
16607
12495
basisvalues[0] = 1.0;
16608
12496
basisvalues[1] = tmp0;
16609
for (unsigned int r = 0; r < 1; r++)
16610
{
16611
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16612
ss = r*(r + 1)*(r + 2)/6;
16613
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16614
}// end loop over 'r'
16615
for (unsigned int r = 0; r < 1; r++)
16616
{
16617
for (unsigned int s = 0; s < 1 - r; s++)
16618
{
16619
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16620
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16621
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16622
}// end loop over 's'
16623
}// end loop over 'r'
16624
for (unsigned int r = 0; r < 2; r++)
16625
{
16626
for (unsigned int s = 0; s < 2 - r; s++)
16627
{
16628
for (unsigned int t = 0; t < 2 - r - s; t++)
16629
{
16630
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16631
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16632
}// end loop over 't'
16633
}// end loop over 's'
16634
}// end loop over 'r'
12497
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12498
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12499
basisvalues[0] *= std::sqrt(0.75);
12500
basisvalues[3] *= std::sqrt(1.25);
12501
basisvalues[2] *= std::sqrt(2.5);
12502
basisvalues[1] *= std::sqrt(7.5);
16635
12503
16636
12504
// Table(s) of coefficients.
16637
12505
static const double coefficients0[4] = \
16793
12661
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16794
12662
16795
12663
// Declare helper variables.
16796
unsigned int rr = 0;
16797
unsigned int ss = 0;
16798
12664
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16799
12665
16800
12666
// Compute basisvalues.
16801
12667
basisvalues[0] = 1.0;
16802
12668
basisvalues[1] = tmp0;
16803
for (unsigned int r = 0; r < 1; r++)
16804
{
16805
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
16806
ss = r*(r + 1)*(r + 2)/6;
16807
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
16808
}// end loop over 'r'
16809
for (unsigned int r = 0; r < 1; r++)
16810
{
16811
for (unsigned int s = 0; s < 1 - r; s++)
16812
{
16813
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
16814
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
16815
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
16816
}// end loop over 's'
16817
}// end loop over 'r'
16818
for (unsigned int r = 0; r < 2; r++)
16819
{
16820
for (unsigned int s = 0; s < 2 - r; s++)
16821
{
16822
for (unsigned int t = 0; t < 2 - r - s; t++)
16823
{
16824
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
16825
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
16826
}// end loop over 't'
16827
}// end loop over 's'
16828
}// end loop over 'r'
12669
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12670
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12671
basisvalues[0] *= std::sqrt(0.75);
12672
basisvalues[3] *= std::sqrt(1.25);
12673
basisvalues[2] *= std::sqrt(2.5);
12674
basisvalues[1] *= std::sqrt(7.5);
16829
12675
16830
12676
// Table(s) of coefficients.
16831
12677
static const double coefficients0[4] = \
16987
12833
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
16988
12834
16989
12835
// Declare helper variables.
16990
unsigned int rr = 0;
16991
unsigned int ss = 0;
16992
12836
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
16993
12837
16994
12838
// Compute basisvalues.
16995
12839
basisvalues[0] = 1.0;
16996
12840
basisvalues[1] = tmp0;
16997
for (unsigned int r = 0; r < 1; r++)
16998
{
16999
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17000
ss = r*(r + 1)*(r + 2)/6;
17001
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17002
}// end loop over 'r'
17003
for (unsigned int r = 0; r < 1; r++)
17004
{
17005
for (unsigned int s = 0; s < 1 - r; s++)
17006
{
17007
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17008
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17009
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17010
}// end loop over 's'
17011
}// end loop over 'r'
17012
for (unsigned int r = 0; r < 2; r++)
17013
{
17014
for (unsigned int s = 0; s < 2 - r; s++)
17015
{
17016
for (unsigned int t = 0; t < 2 - r - s; t++)
17017
{
17018
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17019
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17020
}// end loop over 't'
17021
}// end loop over 's'
17022
}// end loop over 'r'
12841
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
12842
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
12843
basisvalues[0] *= std::sqrt(0.75);
12844
basisvalues[3] *= std::sqrt(1.25);
12845
basisvalues[2] *= std::sqrt(2.5);
12846
basisvalues[1] *= std::sqrt(7.5);
17023
12847
17024
12848
// Table(s) of coefficients.
17025
12849
static const double coefficients0[4] = \
17485
13309
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17486
13310
17487
13311
// Declare helper variables.
17488
unsigned int rr = 0;
17489
unsigned int ss = 0;
17490
13312
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17491
13313
17492
13314
// Compute basisvalues.
17493
13315
basisvalues[0] = 1.0;
17494
13316
basisvalues[1] = tmp0;
17495
for (unsigned int r = 0; r < 1; r++)
17496
{
17497
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17498
ss = r*(r + 1)*(r + 2)/6;
17499
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17500
}// end loop over 'r'
17501
for (unsigned int r = 0; r < 1; r++)
17502
{
17503
for (unsigned int s = 0; s < 1 - r; s++)
17504
{
17505
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17506
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17507
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17508
}// end loop over 's'
17509
}// end loop over 'r'
17510
for (unsigned int r = 0; r < 2; r++)
17511
{
17512
for (unsigned int s = 0; s < 2 - r; s++)
17513
{
17514
for (unsigned int t = 0; t < 2 - r - s; t++)
17515
{
17516
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17517
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17518
}// end loop over 't'
17519
}// end loop over 's'
17520
}// end loop over 'r'
13317
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13318
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13319
basisvalues[0] *= std::sqrt(0.75);
13320
basisvalues[3] *= std::sqrt(1.25);
13321
basisvalues[2] *= std::sqrt(2.5);
13322
basisvalues[1] *= std::sqrt(7.5);
17521
13323
17522
13324
// Table(s) of coefficients.
17523
13325
static const double coefficients0[4] = \
17553
13355
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17554
13356
17555
13357
// Declare helper variables.
17556
unsigned int rr = 0;
17557
unsigned int ss = 0;
17558
13358
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17559
13359
17560
13360
// Compute basisvalues.
17561
13361
basisvalues[0] = 1.0;
17562
13362
basisvalues[1] = tmp0;
17563
for (unsigned int r = 0; r < 1; r++)
17564
{
17565
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17566
ss = r*(r + 1)*(r + 2)/6;
17567
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17568
}// end loop over 'r'
17569
for (unsigned int r = 0; r < 1; r++)
17570
{
17571
for (unsigned int s = 0; s < 1 - r; s++)
17572
{
17573
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17574
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17575
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17576
}// end loop over 's'
17577
}// end loop over 'r'
17578
for (unsigned int r = 0; r < 2; r++)
17579
{
17580
for (unsigned int s = 0; s < 2 - r; s++)
17581
{
17582
for (unsigned int t = 0; t < 2 - r - s; t++)
17583
{
17584
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17585
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17586
}// end loop over 't'
17587
}// end loop over 's'
17588
}// end loop over 'r'
13363
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13364
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13365
basisvalues[0] *= std::sqrt(0.75);
13366
basisvalues[3] *= std::sqrt(1.25);
13367
basisvalues[2] *= std::sqrt(2.5);
13368
basisvalues[1] *= std::sqrt(7.5);
17589
13369
17590
13370
// Table(s) of coefficients.
17591
13371
static const double coefficients0[4] = \
17621
13401
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17622
13402
17623
13403
// Declare helper variables.
17624
unsigned int rr = 0;
17625
unsigned int ss = 0;
17626
13404
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17627
13405
17628
13406
// Compute basisvalues.
17629
13407
basisvalues[0] = 1.0;
17630
13408
basisvalues[1] = tmp0;
17631
for (unsigned int r = 0; r < 1; r++)
17632
{
17633
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17634
ss = r*(r + 1)*(r + 2)/6;
17635
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17636
}// end loop over 'r'
17637
for (unsigned int r = 0; r < 1; r++)
17638
{
17639
for (unsigned int s = 0; s < 1 - r; s++)
17640
{
17641
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17642
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17643
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17644
}// end loop over 's'
17645
}// end loop over 'r'
17646
for (unsigned int r = 0; r < 2; r++)
17647
{
17648
for (unsigned int s = 0; s < 2 - r; s++)
17649
{
17650
for (unsigned int t = 0; t < 2 - r - s; t++)
17651
{
17652
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17653
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17654
}// end loop over 't'
17655
}// end loop over 's'
17656
}// end loop over 'r'
13409
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13410
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13411
basisvalues[0] *= std::sqrt(0.75);
13412
basisvalues[3] *= std::sqrt(1.25);
13413
basisvalues[2] *= std::sqrt(2.5);
13414
basisvalues[1] *= std::sqrt(7.5);
17657
13415
17658
13416
// Table(s) of coefficients.
17659
13417
static const double coefficients0[4] = \
17689
13447
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17690
13448
17691
13449
// Declare helper variables.
17692
unsigned int rr = 0;
17693
unsigned int ss = 0;
17694
13450
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17695
13451
17696
13452
// Compute basisvalues.
17697
13453
basisvalues[0] = 1.0;
17698
13454
basisvalues[1] = tmp0;
17699
for (unsigned int r = 0; r < 1; r++)
17700
{
17701
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17702
ss = r*(r + 1)*(r + 2)/6;
17703
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17704
}// end loop over 'r'
17705
for (unsigned int r = 0; r < 1; r++)
17706
{
17707
for (unsigned int s = 0; s < 1 - r; s++)
17708
{
17709
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17710
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17711
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17712
}// end loop over 's'
17713
}// end loop over 'r'
17714
for (unsigned int r = 0; r < 2; r++)
17715
{
17716
for (unsigned int s = 0; s < 2 - r; s++)
17717
{
17718
for (unsigned int t = 0; t < 2 - r - s; t++)
17719
{
17720
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17721
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17722
}// end loop over 't'
17723
}// end loop over 's'
17724
}// end loop over 'r'
13455
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13456
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13457
basisvalues[0] *= std::sqrt(0.75);
13458
basisvalues[3] *= std::sqrt(1.25);
13459
basisvalues[2] *= std::sqrt(2.5);
13460
basisvalues[1] *= std::sqrt(7.5);
17725
13461
17726
13462
// Table(s) of coefficients.
17727
13463
static const double coefficients0[4] = \
17757
13493
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17758
13494
17759
13495
// Declare helper variables.
17760
unsigned int rr = 0;
17761
unsigned int ss = 0;
17762
13496
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17763
13497
17764
13498
// Compute basisvalues.
17765
13499
basisvalues[0] = 1.0;
17766
13500
basisvalues[1] = tmp0;
17767
for (unsigned int r = 0; r < 1; r++)
17768
{
17769
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17770
ss = r*(r + 1)*(r + 2)/6;
17771
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17772
}// end loop over 'r'
17773
for (unsigned int r = 0; r < 1; r++)
17774
{
17775
for (unsigned int s = 0; s < 1 - r; s++)
17776
{
17777
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17778
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17779
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17780
}// end loop over 's'
17781
}// end loop over 'r'
17782
for (unsigned int r = 0; r < 2; r++)
17783
{
17784
for (unsigned int s = 0; s < 2 - r; s++)
17785
{
17786
for (unsigned int t = 0; t < 2 - r - s; t++)
17787
{
17788
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17789
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17790
}// end loop over 't'
17791
}// end loop over 's'
17792
}// end loop over 'r'
13501
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13502
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13503
basisvalues[0] *= std::sqrt(0.75);
13504
basisvalues[3] *= std::sqrt(1.25);
13505
basisvalues[2] *= std::sqrt(2.5);
13506
basisvalues[1] *= std::sqrt(7.5);
17793
13507
17794
13508
// Table(s) of coefficients.
17795
13509
static const double coefficients0[4] = \
17825
13539
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
17826
13540
17827
13541
// Declare helper variables.
17828
unsigned int rr = 0;
17829
unsigned int ss = 0;
17830
13542
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
17831
13543
17832
13544
// Compute basisvalues.
17833
13545
basisvalues[0] = 1.0;
17834
13546
basisvalues[1] = tmp0;
17835
for (unsigned int r = 0; r < 1; r++)
17836
{
17837
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
17838
ss = r*(r + 1)*(r + 2)/6;
17839
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
17840
}// end loop over 'r'
17841
for (unsigned int r = 0; r < 1; r++)
17842
{
17843
for (unsigned int s = 0; s < 1 - r; s++)
17844
{
17845
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
17846
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
17847
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
17848
}// end loop over 's'
17849
}// end loop over 'r'
17850
for (unsigned int r = 0; r < 2; r++)
17851
{
17852
for (unsigned int s = 0; s < 2 - r; s++)
17853
{
17854
for (unsigned int t = 0; t < 2 - r - s; t++)
17855
{
17856
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
17857
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
17858
}// end loop over 't'
17859
}// end loop over 's'
17860
}// end loop over 'r'
13547
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13548
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13549
basisvalues[0] *= std::sqrt(0.75);
13550
basisvalues[3] *= std::sqrt(1.25);
13551
basisvalues[2] *= std::sqrt(2.5);
13552
basisvalues[1] *= std::sqrt(7.5);
17861
13553
17862
13554
// Table(s) of coefficients.
17863
13555
static const double coefficients0[4] = \
18039
13731
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
18040
13732
18041
13733
// Declare helper variables.
18042
unsigned int rr = 0;
18043
unsigned int ss = 0;
18044
13734
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
18045
13735
18046
13736
// Compute basisvalues.
18047
13737
basisvalues[0] = 1.0;
18048
13738
basisvalues[1] = tmp0;
18049
for (unsigned int r = 0; r < 1; r++)
18050
{
18051
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18052
ss = r*(r + 1)*(r + 2)/6;
18053
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
18054
}// end loop over 'r'
18055
for (unsigned int r = 0; r < 1; r++)
18056
{
18057
for (unsigned int s = 0; s < 1 - r; s++)
18058
{
18059
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18060
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18061
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
18062
}// end loop over 's'
18063
}// end loop over 'r'
18064
for (unsigned int r = 0; r < 2; r++)
18065
{
18066
for (unsigned int s = 0; s < 2 - r; s++)
18067
{
18068
for (unsigned int t = 0; t < 2 - r - s; t++)
18069
{
18070
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18071
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
18072
}// end loop over 't'
18073
}// end loop over 's'
18074
}// end loop over 'r'
13739
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13740
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13741
basisvalues[0] *= std::sqrt(0.75);
13742
basisvalues[3] *= std::sqrt(1.25);
13743
basisvalues[2] *= std::sqrt(2.5);
13744
basisvalues[1] *= std::sqrt(7.5);
18075
13745
18076
13746
// Table(s) of coefficients.
18077
13747
static const double coefficients0[4] = \
18251
13921
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
18252
13922
18253
13923
// Declare helper variables.
18254
unsigned int rr = 0;
18255
unsigned int ss = 0;
18256
13924
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
18257
13925
18258
13926
// Compute basisvalues.
18259
13927
basisvalues[0] = 1.0;
18260
13928
basisvalues[1] = tmp0;
18261
for (unsigned int r = 0; r < 1; r++)
18262
{
18263
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18264
ss = r*(r + 1)*(r + 2)/6;
18265
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
18266
}// end loop over 'r'
18267
for (unsigned int r = 0; r < 1; r++)
18268
{
18269
for (unsigned int s = 0; s < 1 - r; s++)
18270
{
18271
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18272
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18273
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
18274
}// end loop over 's'
18275
}// end loop over 'r'
18276
for (unsigned int r = 0; r < 2; r++)
18277
{
18278
for (unsigned int s = 0; s < 2 - r; s++)
18279
{
18280
for (unsigned int t = 0; t < 2 - r - s; t++)
18281
{
18282
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18283
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
18284
}// end loop over 't'
18285
}// end loop over 's'
18286
}// end loop over 'r'
13929
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
13930
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
13931
basisvalues[0] *= std::sqrt(0.75);
13932
basisvalues[3] *= std::sqrt(1.25);
13933
basisvalues[2] *= std::sqrt(2.5);
13934
basisvalues[1] *= std::sqrt(7.5);
18287
13935
18288
13936
// Table(s) of coefficients.
18289
13937
static const double coefficients0[4] = \
18463
14111
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
18464
14112
18465
14113
// Declare helper variables.
18466
unsigned int rr = 0;
18467
unsigned int ss = 0;
18468
14114
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
18469
14115
18470
14116
// Compute basisvalues.
18471
14117
basisvalues[0] = 1.0;
18472
14118
basisvalues[1] = tmp0;
18473
for (unsigned int r = 0; r < 1; r++)
18474
{
18475
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18476
ss = r*(r + 1)*(r + 2)/6;
18477
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
18478
}// end loop over 'r'
18479
for (unsigned int r = 0; r < 1; r++)
18480
{
18481
for (unsigned int s = 0; s < 1 - r; s++)
18482
{
18483
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18484
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18485
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
18486
}// end loop over 's'
18487
}// end loop over 'r'
18488
for (unsigned int r = 0; r < 2; r++)
18489
{
18490
for (unsigned int s = 0; s < 2 - r; s++)
18491
{
18492
for (unsigned int t = 0; t < 2 - r - s; t++)
18493
{
18494
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18495
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
18496
}// end loop over 't'
18497
}// end loop over 's'
18498
}// end loop over 'r'
14119
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
14120
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
14121
basisvalues[0] *= std::sqrt(0.75);
14122
basisvalues[3] *= std::sqrt(1.25);
14123
basisvalues[2] *= std::sqrt(2.5);
14124
basisvalues[1] *= std::sqrt(7.5);
18499
14125
18500
14126
// Table(s) of coefficients.
18501
14127
static const double coefficients0[4] = \
18675
14301
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
18676
14302
18677
14303
// Declare helper variables.
18678
unsigned int rr = 0;
18679
unsigned int ss = 0;
18680
14304
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
18681
14305
18682
14306
// Compute basisvalues.
18683
14307
basisvalues[0] = 1.0;
18684
14308
basisvalues[1] = tmp0;
18685
for (unsigned int r = 0; r < 1; r++)
18686
{
18687
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18688
ss = r*(r + 1)*(r + 2)/6;
18689
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
18690
}// end loop over 'r'
18691
for (unsigned int r = 0; r < 1; r++)
18692
{
18693
for (unsigned int s = 0; s < 1 - r; s++)
18694
{
18695
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18696
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18697
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
18698
}// end loop over 's'
18699
}// end loop over 'r'
18700
for (unsigned int r = 0; r < 2; r++)
18701
{
18702
for (unsigned int s = 0; s < 2 - r; s++)
18703
{
18704
for (unsigned int t = 0; t < 2 - r - s; t++)
18705
{
18706
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18707
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
18708
}// end loop over 't'
18709
}// end loop over 's'
18710
}// end loop over 'r'
14309
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
14310
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
14311
basisvalues[0] *= std::sqrt(0.75);
14312
basisvalues[3] *= std::sqrt(1.25);
14313
basisvalues[2] *= std::sqrt(2.5);
14314
basisvalues[1] *= std::sqrt(7.5);
18711
14315
18712
14316
// Table(s) of coefficients.
18713
14317
static const double coefficients0[4] = \
18887
14491
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
18888
14492
18889
14493
// Declare helper variables.
18890
unsigned int rr = 0;
18891
unsigned int ss = 0;
18892
14494
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
18893
14495
18894
14496
// Compute basisvalues.
18895
14497
basisvalues[0] = 1.0;
18896
14498
basisvalues[1] = tmp0;
18897
for (unsigned int r = 0; r < 1; r++)
18898
{
18899
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
18900
ss = r*(r + 1)*(r + 2)/6;
18901
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
18902
}// end loop over 'r'
18903
for (unsigned int r = 0; r < 1; r++)
18904
{
18905
for (unsigned int s = 0; s < 1 - r; s++)
18906
{
18907
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
18908
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
18909
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
18910
}// end loop over 's'
18911
}// end loop over 'r'
18912
for (unsigned int r = 0; r < 2; r++)
18913
{
18914
for (unsigned int s = 0; s < 2 - r; s++)
18915
{
18916
for (unsigned int t = 0; t < 2 - r - s; t++)
18917
{
18918
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
18919
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
18920
}// end loop over 't'
18921
}// end loop over 's'
18922
}// end loop over 'r'
14499
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
14500
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
14501
basisvalues[0] *= std::sqrt(0.75);
14502
basisvalues[3] *= std::sqrt(1.25);
14503
basisvalues[2] *= std::sqrt(2.5);
14504
basisvalues[1] *= std::sqrt(7.5);
18923
14505
18924
14506
// Table(s) of coefficients.
18925
14507
static const double coefficients0[4] = \
19099
14681
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19100
14682
19101
14683
// Declare helper variables.
19102
unsigned int rr = 0;
19103
unsigned int ss = 0;
19104
14684
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19105
14685
19106
14686
// Compute basisvalues.
19107
14687
basisvalues[0] = 1.0;
19108
14688
basisvalues[1] = tmp0;
19109
for (unsigned int r = 0; r < 1; r++)
19110
{
19111
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19112
ss = r*(r + 1)*(r + 2)/6;
19113
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19114
}// end loop over 'r'
19115
for (unsigned int r = 0; r < 1; r++)
19116
{
19117
for (unsigned int s = 0; s < 1 - r; s++)
19118
{
19119
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19120
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19121
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19122
}// end loop over 's'
19123
}// end loop over 'r'
19124
for (unsigned int r = 0; r < 2; r++)
19125
{
19126
for (unsigned int s = 0; s < 2 - r; s++)
19127
{
19128
for (unsigned int t = 0; t < 2 - r - s; t++)
19129
{
19130
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19131
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19132
}// end loop over 't'
19133
}// end loop over 's'
19134
}// end loop over 'r'
14689
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
14690
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
14691
basisvalues[0] *= std::sqrt(0.75);
14692
basisvalues[3] *= std::sqrt(1.25);
14693
basisvalues[2] *= std::sqrt(2.5);
14694
basisvalues[1] *= std::sqrt(7.5);
19135
14695
19136
14696
// Table(s) of coefficients.
19137
14697
static const double coefficients0[4] = \
19726
15286
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19727
15287
19728
15288
// Declare helper variables.
19729
unsigned int rr = 0;
19730
unsigned int ss = 0;
19731
15289
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19732
15290
19733
15291
// Compute basisvalues.
19734
15292
basisvalues[0] = 1.0;
19735
15293
basisvalues[1] = tmp0;
19736
for (unsigned int r = 0; r < 1; r++)
19737
{
19738
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19739
ss = r*(r + 1)*(r + 2)/6;
19740
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19741
}// end loop over 'r'
19742
for (unsigned int r = 0; r < 1; r++)
19743
{
19744
for (unsigned int s = 0; s < 1 - r; s++)
19745
{
19746
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19747
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19748
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19749
}// end loop over 's'
19750
}// end loop over 'r'
19751
for (unsigned int r = 0; r < 2; r++)
19752
{
19753
for (unsigned int s = 0; s < 2 - r; s++)
19754
{
19755
for (unsigned int t = 0; t < 2 - r - s; t++)
19756
{
19757
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19758
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19759
}// end loop over 't'
19760
}// end loop over 's'
19761
}// end loop over 'r'
15294
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15295
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15296
basisvalues[0] *= std::sqrt(0.75);
15297
basisvalues[3] *= std::sqrt(1.25);
15298
basisvalues[2] *= std::sqrt(2.5);
15299
basisvalues[1] *= std::sqrt(7.5);
19762
15300
19763
15301
// Table(s) of coefficients.
19764
15302
static const double coefficients0[4] = \
19778
15316
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19779
15317
19780
15318
// Declare helper variables.
19781
unsigned int rr = 0;
19782
unsigned int ss = 0;
19783
15319
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19784
15320
19785
15321
// Compute basisvalues.
19786
15322
basisvalues[0] = 1.0;
19787
15323
basisvalues[1] = tmp0;
19788
for (unsigned int r = 0; r < 1; r++)
19789
{
19790
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19791
ss = r*(r + 1)*(r + 2)/6;
19792
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19793
}// end loop over 'r'
19794
for (unsigned int r = 0; r < 1; r++)
19795
{
19796
for (unsigned int s = 0; s < 1 - r; s++)
19797
{
19798
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19799
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19800
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19801
}// end loop over 's'
19802
}// end loop over 'r'
19803
for (unsigned int r = 0; r < 2; r++)
19804
{
19805
for (unsigned int s = 0; s < 2 - r; s++)
19806
{
19807
for (unsigned int t = 0; t < 2 - r - s; t++)
19808
{
19809
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19810
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19811
}// end loop over 't'
19812
}// end loop over 's'
19813
}// end loop over 'r'
15324
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15325
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15326
basisvalues[0] *= std::sqrt(0.75);
15327
basisvalues[3] *= std::sqrt(1.25);
15328
basisvalues[2] *= std::sqrt(2.5);
15329
basisvalues[1] *= std::sqrt(7.5);
19814
15330
19815
15331
// Table(s) of coefficients.
19816
15332
static const double coefficients0[4] = \
19830
15346
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19831
15347
19832
15348
// Declare helper variables.
19833
unsigned int rr = 0;
19834
unsigned int ss = 0;
19835
15349
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19836
15350
19837
15351
// Compute basisvalues.
19838
15352
basisvalues[0] = 1.0;
19839
15353
basisvalues[1] = tmp0;
19840
for (unsigned int r = 0; r < 1; r++)
19841
{
19842
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19843
ss = r*(r + 1)*(r + 2)/6;
19844
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19845
}// end loop over 'r'
19846
for (unsigned int r = 0; r < 1; r++)
19847
{
19848
for (unsigned int s = 0; s < 1 - r; s++)
19849
{
19850
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19851
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19852
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19853
}// end loop over 's'
19854
}// end loop over 'r'
19855
for (unsigned int r = 0; r < 2; r++)
19856
{
19857
for (unsigned int s = 0; s < 2 - r; s++)
19858
{
19859
for (unsigned int t = 0; t < 2 - r - s; t++)
19860
{
19861
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19862
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19863
}// end loop over 't'
19864
}// end loop over 's'
19865
}// end loop over 'r'
15354
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15355
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15356
basisvalues[0] *= std::sqrt(0.75);
15357
basisvalues[3] *= std::sqrt(1.25);
15358
basisvalues[2] *= std::sqrt(2.5);
15359
basisvalues[1] *= std::sqrt(7.5);
19866
15360
19867
15361
// Table(s) of coefficients.
19868
15362
static const double coefficients0[4] = \
19882
15376
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19883
15377
19884
15378
// Declare helper variables.
19885
unsigned int rr = 0;
19886
unsigned int ss = 0;
19887
15379
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19888
15380
19889
15381
// Compute basisvalues.
19890
15382
basisvalues[0] = 1.0;
19891
15383
basisvalues[1] = tmp0;
19892
for (unsigned int r = 0; r < 1; r++)
19893
{
19894
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19895
ss = r*(r + 1)*(r + 2)/6;
19896
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19897
}// end loop over 'r'
19898
for (unsigned int r = 0; r < 1; r++)
19899
{
19900
for (unsigned int s = 0; s < 1 - r; s++)
19901
{
19902
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19903
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19904
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19905
}// end loop over 's'
19906
}// end loop over 'r'
19907
for (unsigned int r = 0; r < 2; r++)
19908
{
19909
for (unsigned int s = 0; s < 2 - r; s++)
19910
{
19911
for (unsigned int t = 0; t < 2 - r - s; t++)
19912
{
19913
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19914
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19915
}// end loop over 't'
19916
}// end loop over 's'
19917
}// end loop over 'r'
15384
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15385
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15386
basisvalues[0] *= std::sqrt(0.75);
15387
basisvalues[3] *= std::sqrt(1.25);
15388
basisvalues[2] *= std::sqrt(2.5);
15389
basisvalues[1] *= std::sqrt(7.5);
19918
15390
19919
15391
// Table(s) of coefficients.
19920
15392
static const double coefficients0[4] = \
19934
15406
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
19935
15407
19936
15408
// Declare helper variables.
19937
unsigned int rr = 0;
19938
unsigned int ss = 0;
19939
15409
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
19940
15410
19941
15411
// Compute basisvalues.
19942
15412
basisvalues[0] = 1.0;
19943
15413
basisvalues[1] = tmp0;
19944
for (unsigned int r = 0; r < 1; r++)
19945
{
19946
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
19947
ss = r*(r + 1)*(r + 2)/6;
19948
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
19949
}// end loop over 'r'
19950
for (unsigned int r = 0; r < 1; r++)
19951
{
19952
for (unsigned int s = 0; s < 1 - r; s++)
19953
{
19954
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
19955
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
19956
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
19957
}// end loop over 's'
19958
}// end loop over 'r'
19959
for (unsigned int r = 0; r < 2; r++)
19960
{
19961
for (unsigned int s = 0; s < 2 - r; s++)
19962
{
19963
for (unsigned int t = 0; t < 2 - r - s; t++)
19964
{
19965
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
19966
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
19967
}// end loop over 't'
19968
}// end loop over 's'
19969
}// end loop over 'r'
15414
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15415
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15416
basisvalues[0] *= std::sqrt(0.75);
15417
basisvalues[3] *= std::sqrt(1.25);
15418
basisvalues[2] *= std::sqrt(2.5);
15419
basisvalues[1] *= std::sqrt(7.5);
19970
15420
19971
15421
// Table(s) of coefficients.
19972
15422
static const double coefficients0[4] = \
20002
15452
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20003
15453
20004
15454
// Declare helper variables.
20005
unsigned int rr = 0;
20006
unsigned int ss = 0;
20007
15455
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20008
15456
20009
15457
// Compute basisvalues.
20010
15458
basisvalues[0] = 1.0;
20011
15459
basisvalues[1] = tmp0;
20012
for (unsigned int r = 0; r < 1; r++)
20013
{
20014
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20015
ss = r*(r + 1)*(r + 2)/6;
20016
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20017
}// end loop over 'r'
20018
for (unsigned int r = 0; r < 1; r++)
20019
{
20020
for (unsigned int s = 0; s < 1 - r; s++)
20021
{
20022
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20023
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20024
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20025
}// end loop over 's'
20026
}// end loop over 'r'
20027
for (unsigned int r = 0; r < 2; r++)
20028
{
20029
for (unsigned int s = 0; s < 2 - r; s++)
20030
{
20031
for (unsigned int t = 0; t < 2 - r - s; t++)
20032
{
20033
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20034
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20035
}// end loop over 't'
20036
}// end loop over 's'
20037
}// end loop over 'r'
15460
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15461
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15462
basisvalues[0] *= std::sqrt(0.75);
15463
basisvalues[3] *= std::sqrt(1.25);
15464
basisvalues[2] *= std::sqrt(2.5);
15465
basisvalues[1] *= std::sqrt(7.5);
20038
15466
20039
15467
// Table(s) of coefficients.
20040
15468
static const double coefficients0[4] = \
20070
15498
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20071
15499
20072
15500
// Declare helper variables.
20073
unsigned int rr = 0;
20074
unsigned int ss = 0;
20075
15501
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20076
15502
20077
15503
// Compute basisvalues.
20078
15504
basisvalues[0] = 1.0;
20079
15505
basisvalues[1] = tmp0;
20080
for (unsigned int r = 0; r < 1; r++)
20081
{
20082
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20083
ss = r*(r + 1)*(r + 2)/6;
20084
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20085
}// end loop over 'r'
20086
for (unsigned int r = 0; r < 1; r++)
20087
{
20088
for (unsigned int s = 0; s < 1 - r; s++)
20089
{
20090
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20091
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20092
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20093
}// end loop over 's'
20094
}// end loop over 'r'
20095
for (unsigned int r = 0; r < 2; r++)
20096
{
20097
for (unsigned int s = 0; s < 2 - r; s++)
20098
{
20099
for (unsigned int t = 0; t < 2 - r - s; t++)
20100
{
20101
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20102
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20103
}// end loop over 't'
20104
}// end loop over 's'
20105
}// end loop over 'r'
15506
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15507
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15508
basisvalues[0] *= std::sqrt(0.75);
15509
basisvalues[3] *= std::sqrt(1.25);
15510
basisvalues[2] *= std::sqrt(2.5);
15511
basisvalues[1] *= std::sqrt(7.5);
20106
15512
20107
15513
// Table(s) of coefficients.
20108
15514
static const double coefficients0[4] = \
20138
15544
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20139
15545
20140
15546
// Declare helper variables.
20141
unsigned int rr = 0;
20142
unsigned int ss = 0;
20143
15547
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20144
15548
20145
15549
// Compute basisvalues.
20146
15550
basisvalues[0] = 1.0;
20147
15551
basisvalues[1] = tmp0;
20148
for (unsigned int r = 0; r < 1; r++)
20149
{
20150
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20151
ss = r*(r + 1)*(r + 2)/6;
20152
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20153
}// end loop over 'r'
20154
for (unsigned int r = 0; r < 1; r++)
20155
{
20156
for (unsigned int s = 0; s < 1 - r; s++)
20157
{
20158
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20159
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20160
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20161
}// end loop over 's'
20162
}// end loop over 'r'
20163
for (unsigned int r = 0; r < 2; r++)
20164
{
20165
for (unsigned int s = 0; s < 2 - r; s++)
20166
{
20167
for (unsigned int t = 0; t < 2 - r - s; t++)
20168
{
20169
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20170
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20171
}// end loop over 't'
20172
}// end loop over 's'
20173
}// end loop over 'r'
15552
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15553
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15554
basisvalues[0] *= std::sqrt(0.75);
15555
basisvalues[3] *= std::sqrt(1.25);
15556
basisvalues[2] *= std::sqrt(2.5);
15557
basisvalues[1] *= std::sqrt(7.5);
20174
15558
20175
15559
// Table(s) of coefficients.
20176
15560
static const double coefficients0[4] = \
20206
15590
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20207
15591
20208
15592
// Declare helper variables.
20209
unsigned int rr = 0;
20210
unsigned int ss = 0;
20211
15593
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20212
15594
20213
15595
// Compute basisvalues.
20214
15596
basisvalues[0] = 1.0;
20215
15597
basisvalues[1] = tmp0;
20216
for (unsigned int r = 0; r < 1; r++)
20217
{
20218
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20219
ss = r*(r + 1)*(r + 2)/6;
20220
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20221
}// end loop over 'r'
20222
for (unsigned int r = 0; r < 1; r++)
20223
{
20224
for (unsigned int s = 0; s < 1 - r; s++)
20225
{
20226
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20227
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20228
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20229
}// end loop over 's'
20230
}// end loop over 'r'
20231
for (unsigned int r = 0; r < 2; r++)
20232
{
20233
for (unsigned int s = 0; s < 2 - r; s++)
20234
{
20235
for (unsigned int t = 0; t < 2 - r - s; t++)
20236
{
20237
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20238
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20239
}// end loop over 't'
20240
}// end loop over 's'
20241
}// end loop over 'r'
15598
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15599
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15600
basisvalues[0] *= std::sqrt(0.75);
15601
basisvalues[3] *= std::sqrt(1.25);
15602
basisvalues[2] *= std::sqrt(2.5);
15603
basisvalues[1] *= std::sqrt(7.5);
20242
15604
20243
15605
// Table(s) of coefficients.
20244
15606
static const double coefficients0[4] = \
20274
15636
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20275
15637
20276
15638
// Declare helper variables.
20277
unsigned int rr = 0;
20278
unsigned int ss = 0;
20279
15639
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20280
15640
20281
15641
// Compute basisvalues.
20282
15642
basisvalues[0] = 1.0;
20283
15643
basisvalues[1] = tmp0;
20284
for (unsigned int r = 0; r < 1; r++)
20285
{
20286
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20287
ss = r*(r + 1)*(r + 2)/6;
20288
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20289
}// end loop over 'r'
20290
for (unsigned int r = 0; r < 1; r++)
20291
{
20292
for (unsigned int s = 0; s < 1 - r; s++)
20293
{
20294
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20295
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20296
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20297
}// end loop over 's'
20298
}// end loop over 'r'
20299
for (unsigned int r = 0; r < 2; r++)
20300
{
20301
for (unsigned int s = 0; s < 2 - r; s++)
20302
{
20303
for (unsigned int t = 0; t < 2 - r - s; t++)
20304
{
20305
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20306
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20307
}// end loop over 't'
20308
}// end loop over 's'
20309
}// end loop over 'r'
15644
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15645
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15646
basisvalues[0] *= std::sqrt(0.75);
15647
basisvalues[3] *= std::sqrt(1.25);
15648
basisvalues[2] *= std::sqrt(2.5);
15649
basisvalues[1] *= std::sqrt(7.5);
20310
15650
20311
15651
// Table(s) of coefficients.
20312
15652
static const double coefficients0[4] = \
20488
15828
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20489
15829
20490
15830
// Declare helper variables.
20491
unsigned int rr = 0;
20492
unsigned int ss = 0;
20493
15831
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20494
15832
20495
15833
// Compute basisvalues.
20496
15834
basisvalues[0] = 1.0;
20497
15835
basisvalues[1] = tmp0;
20498
for (unsigned int r = 0; r < 1; r++)
20499
{
20500
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20501
ss = r*(r + 1)*(r + 2)/6;
20502
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20503
}// end loop over 'r'
20504
for (unsigned int r = 0; r < 1; r++)
20505
{
20506
for (unsigned int s = 0; s < 1 - r; s++)
20507
{
20508
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20509
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20510
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20511
}// end loop over 's'
20512
}// end loop over 'r'
20513
for (unsigned int r = 0; r < 2; r++)
20514
{
20515
for (unsigned int s = 0; s < 2 - r; s++)
20516
{
20517
for (unsigned int t = 0; t < 2 - r - s; t++)
20518
{
20519
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20520
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20521
}// end loop over 't'
20522
}// end loop over 's'
20523
}// end loop over 'r'
15836
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
15837
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
15838
basisvalues[0] *= std::sqrt(0.75);
15839
basisvalues[3] *= std::sqrt(1.25);
15840
basisvalues[2] *= std::sqrt(2.5);
15841
basisvalues[1] *= std::sqrt(7.5);
20524
15842
20525
15843
// Table(s) of coefficients.
20526
15844
static const double coefficients0[4] = \
20682
16000
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20683
16001
20684
16002
// Declare helper variables.
20685
unsigned int rr = 0;
20686
unsigned int ss = 0;
20687
16003
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20688
16004
20689
16005
// Compute basisvalues.
20690
16006
basisvalues[0] = 1.0;
20691
16007
basisvalues[1] = tmp0;
20692
for (unsigned int r = 0; r < 1; r++)
20693
{
20694
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20695
ss = r*(r + 1)*(r + 2)/6;
20696
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20697
}// end loop over 'r'
20698
for (unsigned int r = 0; r < 1; r++)
20699
{
20700
for (unsigned int s = 0; s < 1 - r; s++)
20701
{
20702
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20703
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20704
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20705
}// end loop over 's'
20706
}// end loop over 'r'
20707
for (unsigned int r = 0; r < 2; r++)
20708
{
20709
for (unsigned int s = 0; s < 2 - r; s++)
20710
{
20711
for (unsigned int t = 0; t < 2 - r - s; t++)
20712
{
20713
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20714
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20715
}// end loop over 't'
20716
}// end loop over 's'
20717
}// end loop over 'r'
16008
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16009
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16010
basisvalues[0] *= std::sqrt(0.75);
16011
basisvalues[3] *= std::sqrt(1.25);
16012
basisvalues[2] *= std::sqrt(2.5);
16013
basisvalues[1] *= std::sqrt(7.5);
20718
16014
20719
16015
// Table(s) of coefficients.
20720
16016
static const double coefficients0[4] = \
20876
16172
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
20877
16173
20878
16174
// Declare helper variables.
20879
unsigned int rr = 0;
20880
unsigned int ss = 0;
20881
16175
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
20882
16176
20883
16177
// Compute basisvalues.
20884
16178
basisvalues[0] = 1.0;
20885
16179
basisvalues[1] = tmp0;
20886
for (unsigned int r = 0; r < 1; r++)
20887
{
20888
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
20889
ss = r*(r + 1)*(r + 2)/6;
20890
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
20891
}// end loop over 'r'
20892
for (unsigned int r = 0; r < 1; r++)
20893
{
20894
for (unsigned int s = 0; s < 1 - r; s++)
20895
{
20896
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
20897
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
20898
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
20899
}// end loop over 's'
20900
}// end loop over 'r'
20901
for (unsigned int r = 0; r < 2; r++)
20902
{
20903
for (unsigned int s = 0; s < 2 - r; s++)
20904
{
20905
for (unsigned int t = 0; t < 2 - r - s; t++)
20906
{
20907
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
20908
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
20909
}// end loop over 't'
20910
}// end loop over 's'
20911
}// end loop over 'r'
16180
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16181
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16182
basisvalues[0] *= std::sqrt(0.75);
16183
basisvalues[3] *= std::sqrt(1.25);
16184
basisvalues[2] *= std::sqrt(2.5);
16185
basisvalues[1] *= std::sqrt(7.5);
20912
16186
20913
16187
// Table(s) of coefficients.
20914
16188
static const double coefficients0[4] = \
21070
16344
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
21071
16345
21072
16346
// Declare helper variables.
21073
unsigned int rr = 0;
21074
unsigned int ss = 0;
21075
16347
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
21076
16348
21077
16349
// Compute basisvalues.
21078
16350
basisvalues[0] = 1.0;
21079
16351
basisvalues[1] = tmp0;
21080
for (unsigned int r = 0; r < 1; r++)
21081
{
21082
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21083
ss = r*(r + 1)*(r + 2)/6;
21084
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
21085
}// end loop over 'r'
21086
for (unsigned int r = 0; r < 1; r++)
21087
{
21088
for (unsigned int s = 0; s < 1 - r; s++)
21089
{
21090
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21091
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21092
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
21093
}// end loop over 's'
21094
}// end loop over 'r'
21095
for (unsigned int r = 0; r < 2; r++)
21096
{
21097
for (unsigned int s = 0; s < 2 - r; s++)
21098
{
21099
for (unsigned int t = 0; t < 2 - r - s; t++)
21100
{
21101
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21102
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
21103
}// end loop over 't'
21104
}// end loop over 's'
21105
}// end loop over 'r'
16352
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16353
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16354
basisvalues[0] *= std::sqrt(0.75);
16355
basisvalues[3] *= std::sqrt(1.25);
16356
basisvalues[2] *= std::sqrt(2.5);
16357
basisvalues[1] *= std::sqrt(7.5);
21106
16358
21107
16359
// Table(s) of coefficients.
21108
16360
static const double coefficients0[4] = \
21264
16516
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
21265
16517
21266
16518
// Declare helper variables.
21267
unsigned int rr = 0;
21268
unsigned int ss = 0;
21269
16519
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
21270
16520
21271
16521
// Compute basisvalues.
21272
16522
basisvalues[0] = 1.0;
21273
16523
basisvalues[1] = tmp0;
21274
for (unsigned int r = 0; r < 1; r++)
21275
{
21276
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21277
ss = r*(r + 1)*(r + 2)/6;
21278
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
21279
}// end loop over 'r'
21280
for (unsigned int r = 0; r < 1; r++)
21281
{
21282
for (unsigned int s = 0; s < 1 - r; s++)
21283
{
21284
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21285
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21286
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
21287
}// end loop over 's'
21288
}// end loop over 'r'
21289
for (unsigned int r = 0; r < 2; r++)
21290
{
21291
for (unsigned int s = 0; s < 2 - r; s++)
21292
{
21293
for (unsigned int t = 0; t < 2 - r - s; t++)
21294
{
21295
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21296
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
21297
}// end loop over 't'
21298
}// end loop over 's'
21299
}// end loop over 'r'
16524
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16525
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16526
basisvalues[0] *= std::sqrt(0.75);
16527
basisvalues[3] *= std::sqrt(1.25);
16528
basisvalues[2] *= std::sqrt(2.5);
16529
basisvalues[1] *= std::sqrt(7.5);
21300
16530
21301
16531
// Table(s) of coefficients.
21302
16532
static const double coefficients0[4] = \
21476
16706
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
21477
16707
21478
16708
// Declare helper variables.
21479
unsigned int rr = 0;
21480
unsigned int ss = 0;
21481
16709
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
21482
16710
21483
16711
// Compute basisvalues.
21484
16712
basisvalues[0] = 1.0;
21485
16713
basisvalues[1] = tmp0;
21486
for (unsigned int r = 0; r < 1; r++)
21487
{
21488
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21489
ss = r*(r + 1)*(r + 2)/6;
21490
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
21491
}// end loop over 'r'
21492
for (unsigned int r = 0; r < 1; r++)
21493
{
21494
for (unsigned int s = 0; s < 1 - r; s++)
21495
{
21496
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21497
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21498
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
21499
}// end loop over 's'
21500
}// end loop over 'r'
21501
for (unsigned int r = 0; r < 2; r++)
21502
{
21503
for (unsigned int s = 0; s < 2 - r; s++)
21504
{
21505
for (unsigned int t = 0; t < 2 - r - s; t++)
21506
{
21507
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21508
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
21509
}// end loop over 't'
21510
}// end loop over 's'
21511
}// end loop over 'r'
16714
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16715
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16716
basisvalues[0] *= std::sqrt(0.75);
16717
basisvalues[3] *= std::sqrt(1.25);
16718
basisvalues[2] *= std::sqrt(2.5);
16719
basisvalues[1] *= std::sqrt(7.5);
21512
16720
21513
16721
// Table(s) of coefficients.
21514
16722
static const double coefficients0[4] = \
21688
16896
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
21689
16897
21690
16898
// Declare helper variables.
21691
unsigned int rr = 0;
21692
unsigned int ss = 0;
21693
16899
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
21694
16900
21695
16901
// Compute basisvalues.
21696
16902
basisvalues[0] = 1.0;
21697
16903
basisvalues[1] = tmp0;
21698
for (unsigned int r = 0; r < 1; r++)
21699
{
21700
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21701
ss = r*(r + 1)*(r + 2)/6;
21702
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
21703
}// end loop over 'r'
21704
for (unsigned int r = 0; r < 1; r++)
21705
{
21706
for (unsigned int s = 0; s < 1 - r; s++)
21707
{
21708
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21709
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21710
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
21711
}// end loop over 's'
21712
}// end loop over 'r'
21713
for (unsigned int r = 0; r < 2; r++)
21714
{
21715
for (unsigned int s = 0; s < 2 - r; s++)
21716
{
21717
for (unsigned int t = 0; t < 2 - r - s; t++)
21718
{
21719
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21720
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
21721
}// end loop over 't'
21722
}// end loop over 's'
21723
}// end loop over 'r'
16904
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
16905
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
16906
basisvalues[0] *= std::sqrt(0.75);
16907
basisvalues[3] *= std::sqrt(1.25);
16908
basisvalues[2] *= std::sqrt(2.5);
16909
basisvalues[1] *= std::sqrt(7.5);
21724
16910
21725
16911
// Table(s) of coefficients.
21726
16912
static const double coefficients0[4] = \
21900
17086
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
21901
17087
21902
17088
// Declare helper variables.
21903
unsigned int rr = 0;
21904
unsigned int ss = 0;
21905
17089
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
21906
17090
21907
17091
// Compute basisvalues.
21908
17092
basisvalues[0] = 1.0;
21909
17093
basisvalues[1] = tmp0;
21910
for (unsigned int r = 0; r < 1; r++)
21911
{
21912
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
21913
ss = r*(r + 1)*(r + 2)/6;
21914
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
21915
}// end loop over 'r'
21916
for (unsigned int r = 0; r < 1; r++)
21917
{
21918
for (unsigned int s = 0; s < 1 - r; s++)
21919
{
21920
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
21921
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
21922
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
21923
}// end loop over 's'
21924
}// end loop over 'r'
21925
for (unsigned int r = 0; r < 2; r++)
21926
{
21927
for (unsigned int s = 0; s < 2 - r; s++)
21928
{
21929
for (unsigned int t = 0; t < 2 - r - s; t++)
21930
{
21931
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
21932
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
21933
}// end loop over 't'
21934
}// end loop over 's'
21935
}// end loop over 'r'
17094
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
17095
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
17096
basisvalues[0] *= std::sqrt(0.75);
17097
basisvalues[3] *= std::sqrt(1.25);
17098
basisvalues[2] *= std::sqrt(2.5);
17099
basisvalues[1] *= std::sqrt(7.5);
21936
17100
21937
17101
// Table(s) of coefficients.
21938
17102
static const double coefficients0[4] = \
22112
17276
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
22113
17277
22114
17278
// Declare helper variables.
22115
unsigned int rr = 0;
22116
unsigned int ss = 0;
22117
17279
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
22118
17280
22119
17281
// Compute basisvalues.
22120
17282
basisvalues[0] = 1.0;
22121
17283
basisvalues[1] = tmp0;
22122
for (unsigned int r = 0; r < 1; r++)
22123
{
22124
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
22125
ss = r*(r + 1)*(r + 2)/6;
22126
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
22127
}// end loop over 'r'
22128
for (unsigned int r = 0; r < 1; r++)
22129
{
22130
for (unsigned int s = 0; s < 1 - r; s++)
22131
{
22132
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
22133
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
22134
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
22135
}// end loop over 's'
22136
}// end loop over 'r'
22137
for (unsigned int r = 0; r < 2; r++)
22138
{
22139
for (unsigned int s = 0; s < 2 - r; s++)
22140
{
22141
for (unsigned int t = 0; t < 2 - r - s; t++)
22142
{
22143
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
22144
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
22145
}// end loop over 't'
22146
}// end loop over 's'
22147
}// end loop over 'r'
17284
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
17285
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
17286
basisvalues[0] *= std::sqrt(0.75);
17287
basisvalues[3] *= std::sqrt(1.25);
17288
basisvalues[2] *= std::sqrt(2.5);
17289
basisvalues[1] *= std::sqrt(7.5);
22148
17290
22149
17291
// Table(s) of coefficients.
22150
17292
static const double coefficients0[4] = \
22324
17466
double basisvalues[4] = {0.0, 0.0, 0.0, 0.0};
22325
17467
22326
17468
// Declare helper variables.
22327
unsigned int rr = 0;
22328
unsigned int ss = 0;
22329
17469
double tmp0 = 0.5*(2.0 + Y + Z + 2.0*X);
22330
17470
22331
17471
// Compute basisvalues.
22332
17472
basisvalues[0] = 1.0;
22333
17473
basisvalues[1] = tmp0;
22334
for (unsigned int r = 0; r < 1; r++)
22335
{
22336
rr = (r + 1)*(r + 1 + 1)*(r + 1 + 2)/6 + 1*(1 + 1)/2;
22337
ss = r*(r + 1)*(r + 2)/6;
22338
basisvalues[rr] = basisvalues[ss]*(r*(1.0 + Y) + (2.0 + Z + 3.0*Y)/2.0);
22339
}// end loop over 'r'
22340
for (unsigned int r = 0; r < 1; r++)
22341
{
22342
for (unsigned int s = 0; s < 1 - r; s++)
22343
{
22344
rr = (r + s + 1)*(r + s + 1 + 1)*(r + s + 1 + 2)/6 + (s + 1)*(s + 1 + 1)/2 + 1;
22345
ss = (r + s)*(r + s + 1)*(r + s + 2)/6 + s*(s + 1)/2;
22346
basisvalues[rr] = basisvalues[ss]*(1.0 + r + s + Z*(2.0 + r + s));
22347
}// end loop over 's'
22348
}// end loop over 'r'
22349
for (unsigned int r = 0; r < 2; r++)
22350
{
22351
for (unsigned int s = 0; s < 2 - r; s++)
22352
{
22353
for (unsigned int t = 0; t < 2 - r - s; t++)
22354
{
22355
rr = (r + s + t)*(r + s + t + 1)*(r + s + t + 2)/6 + (s + t)*(s + t + 1)/2 + t;
22356
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s)*(1.5 + r + s + t));
22357
}// end loop over 't'
22358
}// end loop over 's'
22359
}// end loop over 'r'
17474
basisvalues[2] = 0.5*(2.0 + 3.0*Y + Z)*basisvalues[0];
17475
basisvalues[3] = (2.0*Z + 1.0)*basisvalues[0];
17476
basisvalues[0] *= std::sqrt(0.75);
17477
basisvalues[3] *= std::sqrt(1.25);
17478
basisvalues[2] *= std::sqrt(2.5);
17479
basisvalues[1] *= std::sqrt(7.5);
22360
17480
22361
17481
// Table(s) of coefficients.
22362
17482
static const double coefficients0[4] = \
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