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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_quadrature/Mini.h
1
// This code conforms with the UFC specification version 2.0.0
2
// and was automatically generated by FFC version 0.9.10.
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
//
140
140
double basisvalues[3] = {0.0, 0.0, 0.0};
141
141
142
142
// Declare helper variables.
143
unsigned int rr = 0;
144
unsigned int ss = 0;
145
143
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
146
144
147
145
// Compute basisvalues.
148
146
basisvalues[0] = 1.0;
149
147
basisvalues[1] = tmp0;
150
for (unsigned int r = 0; r < 1; r++)
151
{
152
rr = (r + 1)*(r + 1 + 1)/2 + 1;
153
ss = r*(r + 1)/2;
154
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
155
}// end loop over 'r'
156
for (unsigned int r = 0; r < 2; r++)
157
{
158
for (unsigned int s = 0; s < 2 - r; s++)
159
{
160
rr = (r + s)*(r + s + 1)/2 + s;
161
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
162
}// end loop over 's'
163
}// end loop over 'r'
148
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
149
basisvalues[0] *= std::sqrt(0.5);
150
basisvalues[2] *= std::sqrt(1.0);
151
basisvalues[1] *= std::sqrt(3.0);
164
152
165
153
// Table(s) of coefficients.
166
154
static const double coefficients0[3] = \
180
168
double basisvalues[3] = {0.0, 0.0, 0.0};
181
169
182
170
// Declare helper variables.
183
unsigned int rr = 0;
184
unsigned int ss = 0;
185
171
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
186
172
187
173
// Compute basisvalues.
188
174
basisvalues[0] = 1.0;
189
175
basisvalues[1] = tmp0;
190
for (unsigned int r = 0; r < 1; r++)
191
{
192
rr = (r + 1)*(r + 1 + 1)/2 + 1;
193
ss = r*(r + 1)/2;
194
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
195
}// end loop over 'r'
196
for (unsigned int r = 0; r < 2; r++)
197
{
198
for (unsigned int s = 0; s < 2 - r; s++)
199
{
200
rr = (r + s)*(r + s + 1)/2 + s;
201
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
202
}// end loop over 's'
203
}// end loop over 'r'
176
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
177
basisvalues[0] *= std::sqrt(0.5);
178
basisvalues[2] *= std::sqrt(1.0);
179
basisvalues[1] *= std::sqrt(3.0);
204
180
205
181
// Table(s) of coefficients.
206
182
static const double coefficients0[3] = \
220
196
double basisvalues[3] = {0.0, 0.0, 0.0};
221
197
222
198
// Declare helper variables.
223
unsigned int rr = 0;
224
unsigned int ss = 0;
225
199
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
226
200
227
201
// Compute basisvalues.
228
202
basisvalues[0] = 1.0;
229
203
basisvalues[1] = tmp0;
230
for (unsigned int r = 0; r < 1; r++)
231
{
232
rr = (r + 1)*(r + 1 + 1)/2 + 1;
233
ss = r*(r + 1)/2;
234
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
235
}// end loop over 'r'
236
for (unsigned int r = 0; r < 2; r++)
237
{
238
for (unsigned int s = 0; s < 2 - r; s++)
239
{
240
rr = (r + s)*(r + s + 1)/2 + s;
241
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
242
}// end loop over 's'
243
}// end loop over 'r'
204
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
205
basisvalues[0] *= std::sqrt(0.5);
206
basisvalues[2] *= std::sqrt(1.0);
207
basisvalues[1] *= std::sqrt(3.0);
244
208
245
209
// Table(s) of coefficients.
246
210
static const double coefficients0[3] = \
260
224
double basisvalues[3] = {0.0, 0.0, 0.0};
261
225
262
226
// Declare helper variables.
263
unsigned int rr = 0;
264
unsigned int ss = 0;
265
227
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
266
228
267
229
// Compute basisvalues.
268
230
basisvalues[0] = 1.0;
269
231
basisvalues[1] = tmp0;
270
for (unsigned int r = 0; r < 1; r++)
271
{
272
rr = (r + 1)*(r + 1 + 1)/2 + 1;
273
ss = r*(r + 1)/2;
274
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
275
}// end loop over 'r'
276
for (unsigned int r = 0; r < 2; r++)
277
{
278
for (unsigned int s = 0; s < 2 - r; s++)
279
{
280
rr = (r + s)*(r + s + 1)/2 + s;
281
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
282
}// end loop over 's'
283
}// end loop over 'r'
232
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
233
basisvalues[0] *= std::sqrt(0.5);
234
basisvalues[2] *= std::sqrt(1.0);
235
basisvalues[1] *= std::sqrt(3.0);
284
236
285
237
// Table(s) of coefficients.
286
238
static const double coefficients0[3] = \
300
252
double basisvalues[3] = {0.0, 0.0, 0.0};
301
253
302
254
// Declare helper variables.
303
unsigned int rr = 0;
304
unsigned int ss = 0;
305
255
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
306
256
307
257
// Compute basisvalues.
308
258
basisvalues[0] = 1.0;
309
259
basisvalues[1] = tmp0;
310
for (unsigned int r = 0; r < 1; r++)
311
{
312
rr = (r + 1)*(r + 1 + 1)/2 + 1;
313
ss = r*(r + 1)/2;
314
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
315
}// end loop over 'r'
316
for (unsigned int r = 0; r < 2; r++)
317
{
318
for (unsigned int s = 0; s < 2 - r; s++)
319
{
320
rr = (r + s)*(r + s + 1)/2 + s;
321
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
322
}// end loop over 's'
323
}// end loop over 'r'
260
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
261
basisvalues[0] *= std::sqrt(0.5);
262
basisvalues[2] *= std::sqrt(1.0);
263
basisvalues[1] *= std::sqrt(3.0);
324
264
325
265
// Table(s) of coefficients.
326
266
static const double coefficients0[3] = \
340
280
double basisvalues[3] = {0.0, 0.0, 0.0};
341
281
342
282
// Declare helper variables.
343
unsigned int rr = 0;
344
unsigned int ss = 0;
345
283
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
346
284
347
285
// Compute basisvalues.
348
286
basisvalues[0] = 1.0;
349
287
basisvalues[1] = tmp0;
350
for (unsigned int r = 0; r < 1; r++)
351
{
352
rr = (r + 1)*(r + 1 + 1)/2 + 1;
353
ss = r*(r + 1)/2;
354
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
355
}// end loop over 'r'
356
for (unsigned int r = 0; r < 2; r++)
357
{
358
for (unsigned int s = 0; s < 2 - r; s++)
359
{
360
rr = (r + s)*(r + s + 1)/2 + s;
361
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
362
}// end loop over 's'
363
}// end loop over 'r'
288
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
289
basisvalues[0] *= std::sqrt(0.5);
290
basisvalues[2] *= std::sqrt(1.0);
291
basisvalues[1] *= std::sqrt(3.0);
364
292
365
293
// Table(s) of coefficients.
366
294
static const double coefficients0[3] = \
380
308
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
381
309
382
310
// Declare helper variables.
383
unsigned int rr = 0;
384
unsigned int ss = 0;
385
unsigned int tt = 0;
386
double tmp5 = 0.0;
387
double tmp6 = 0.0;
388
double tmp7 = 0.0;
389
311
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
390
312
double tmp1 = (1.0 - Y)/2.0;
391
313
double tmp2 = tmp1*tmp1;
393
315
// Compute basisvalues.
394
316
basisvalues[0] = 1.0;
395
317
basisvalues[1] = tmp0;
396
for (unsigned int r = 1; r < 3; r++)
397
{
398
rr = (r + 1)*((r + 1) + 1)/2;
399
ss = r*(r + 1)/2;
400
tt = (r - 1)*((r - 1) + 1)/2;
401
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
402
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
403
}// end loop over 'r'
404
for (unsigned int r = 0; r < 3; r++)
405
{
406
rr = (r + 1)*(r + 1 + 1)/2 + 1;
407
ss = r*(r + 1)/2;
408
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
409
}// end loop over 'r'
410
for (unsigned int r = 0; r < 2; r++)
411
{
412
for (unsigned int s = 1; s < 3 - r; s++)
413
{
414
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
415
ss = (r + s)*(r + s + 1)/2 + s;
416
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
417
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));
418
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));
419
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));
420
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
421
}// end loop over 's'
422
}// end loop over 'r'
423
for (unsigned int r = 0; r < 4; r++)
424
{
425
for (unsigned int s = 0; s < 4 - r; s++)
426
{
427
rr = (r + s)*(r + s + 1)/2 + s;
428
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
429
}// end loop over 's'
430
}// end loop over 'r'
318
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
319
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
320
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
321
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
322
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
323
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
324
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
325
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
326
basisvalues[0] *= std::sqrt(0.5);
327
basisvalues[2] *= std::sqrt(1.0);
328
basisvalues[5] *= std::sqrt(1.5);
329
basisvalues[9] *= std::sqrt(2.0);
330
basisvalues[1] *= std::sqrt(3.0);
331
basisvalues[4] *= std::sqrt(4.5);
332
basisvalues[8] *= std::sqrt(6.0);
333
basisvalues[3] *= std::sqrt(7.5);
334
basisvalues[7] *= std::sqrt(10.0);
335
basisvalues[6] *= std::sqrt(14.0);
431
336
432
337
// Table(s) of coefficients.
433
338
static const double coefficients0[10] = \
447
352
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
448
353
449
354
// Declare helper variables.
450
unsigned int rr = 0;
451
unsigned int ss = 0;
452
unsigned int tt = 0;
453
double tmp5 = 0.0;
454
double tmp6 = 0.0;
455
double tmp7 = 0.0;
456
355
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
457
356
double tmp1 = (1.0 - Y)/2.0;
458
357
double tmp2 = tmp1*tmp1;
460
359
// Compute basisvalues.
461
360
basisvalues[0] = 1.0;
462
361
basisvalues[1] = tmp0;
463
for (unsigned int r = 1; r < 3; r++)
464
{
465
rr = (r + 1)*((r + 1) + 1)/2;
466
ss = r*(r + 1)/2;
467
tt = (r - 1)*((r - 1) + 1)/2;
468
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
469
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
470
}// end loop over 'r'
471
for (unsigned int r = 0; r < 3; r++)
472
{
473
rr = (r + 1)*(r + 1 + 1)/2 + 1;
474
ss = r*(r + 1)/2;
475
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
476
}// end loop over 'r'
477
for (unsigned int r = 0; r < 2; r++)
478
{
479
for (unsigned int s = 1; s < 3 - r; s++)
480
{
481
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
482
ss = (r + s)*(r + s + 1)/2 + s;
483
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
484
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));
485
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));
486
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));
487
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
488
}// end loop over 's'
489
}// end loop over 'r'
490
for (unsigned int r = 0; r < 4; r++)
491
{
492
for (unsigned int s = 0; s < 4 - r; s++)
493
{
494
rr = (r + s)*(r + s + 1)/2 + s;
495
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
496
}// end loop over 's'
497
}// end loop over 'r'
362
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
363
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
364
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
365
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
366
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
367
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
368
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
369
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
370
basisvalues[0] *= std::sqrt(0.5);
371
basisvalues[2] *= std::sqrt(1.0);
372
basisvalues[5] *= std::sqrt(1.5);
373
basisvalues[9] *= std::sqrt(2.0);
374
basisvalues[1] *= std::sqrt(3.0);
375
basisvalues[4] *= std::sqrt(4.5);
376
basisvalues[8] *= std::sqrt(6.0);
377
basisvalues[3] *= std::sqrt(7.5);
378
basisvalues[7] *= std::sqrt(10.0);
379
basisvalues[6] *= std::sqrt(14.0);
498
380
499
381
// Table(s) of coefficients.
500
382
static const double coefficients0[10] = \
636
518
double basisvalues[3] = {0.0, 0.0, 0.0};
637
519
638
520
// Declare helper variables.
639
unsigned int rr = 0;
640
unsigned int ss = 0;
641
521
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
642
522
643
523
// Compute basisvalues.
644
524
basisvalues[0] = 1.0;
645
525
basisvalues[1] = tmp0;
646
for (unsigned int r = 0; r < 1; r++)
647
{
648
rr = (r + 1)*(r + 1 + 1)/2 + 1;
649
ss = r*(r + 1)/2;
650
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
651
}// end loop over 'r'
652
for (unsigned int r = 0; r < 2; r++)
653
{
654
for (unsigned int s = 0; s < 2 - r; s++)
655
{
656
rr = (r + s)*(r + s + 1)/2 + s;
657
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
658
}// end loop over 's'
659
}// end loop over 'r'
526
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
527
basisvalues[0] *= std::sqrt(0.5);
528
basisvalues[2] *= std::sqrt(1.0);
529
basisvalues[1] *= std::sqrt(3.0);
660
530
661
531
// Table(s) of coefficients.
662
532
static const double coefficients0[3] = \
794
664
double basisvalues[3] = {0.0, 0.0, 0.0};
795
665
796
666
// Declare helper variables.
797
unsigned int rr = 0;
798
unsigned int ss = 0;
799
667
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
800
668
801
669
// Compute basisvalues.
802
670
basisvalues[0] = 1.0;
803
671
basisvalues[1] = tmp0;
804
for (unsigned int r = 0; r < 1; r++)
805
{
806
rr = (r + 1)*(r + 1 + 1)/2 + 1;
807
ss = r*(r + 1)/2;
808
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
809
}// end loop over 'r'
810
for (unsigned int r = 0; r < 2; r++)
811
{
812
for (unsigned int s = 0; s < 2 - r; s++)
813
{
814
rr = (r + s)*(r + s + 1)/2 + s;
815
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
816
}// end loop over 's'
817
}// end loop over 'r'
672
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
673
basisvalues[0] *= std::sqrt(0.5);
674
basisvalues[2] *= std::sqrt(1.0);
675
basisvalues[1] *= std::sqrt(3.0);
818
676
819
677
// Table(s) of coefficients.
820
678
static const double coefficients0[3] = \
952
810
double basisvalues[3] = {0.0, 0.0, 0.0};
953
811
954
812
// Declare helper variables.
955
unsigned int rr = 0;
956
unsigned int ss = 0;
957
813
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
958
814
959
815
// Compute basisvalues.
960
816
basisvalues[0] = 1.0;
961
817
basisvalues[1] = tmp0;
962
for (unsigned int r = 0; r < 1; r++)
963
{
964
rr = (r + 1)*(r + 1 + 1)/2 + 1;
965
ss = r*(r + 1)/2;
966
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
967
}// end loop over 'r'
968
for (unsigned int r = 0; r < 2; r++)
969
{
970
for (unsigned int s = 0; s < 2 - r; s++)
971
{
972
rr = (r + s)*(r + s + 1)/2 + s;
973
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
974
}// end loop over 's'
975
}// end loop over 'r'
818
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
819
basisvalues[0] *= std::sqrt(0.5);
820
basisvalues[2] *= std::sqrt(1.0);
821
basisvalues[1] *= std::sqrt(3.0);
976
822
977
823
// Table(s) of coefficients.
978
824
static const double coefficients0[3] = \
1110
956
double basisvalues[3] = {0.0, 0.0, 0.0};
1111
957
1112
958
// Declare helper variables.
1113
unsigned int rr = 0;
1114
unsigned int ss = 0;
1115
959
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1116
960
1117
961
// Compute basisvalues.
1118
962
basisvalues[0] = 1.0;
1119
963
basisvalues[1] = tmp0;
1120
for (unsigned int r = 0; r < 1; r++)
1121
{
1122
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1123
ss = r*(r + 1)/2;
1124
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
1125
}// end loop over 'r'
1126
for (unsigned int r = 0; r < 2; r++)
1127
{
1128
for (unsigned int s = 0; s < 2 - r; s++)
1129
{
1130
rr = (r + s)*(r + s + 1)/2 + s;
1131
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
1132
}// end loop over 's'
1133
}// end loop over 'r'
964
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
965
basisvalues[0] *= std::sqrt(0.5);
966
basisvalues[2] *= std::sqrt(1.0);
967
basisvalues[1] *= std::sqrt(3.0);
1134
968
1135
969
// Table(s) of coefficients.
1136
970
static const double coefficients0[3] = \
1268
1102
double basisvalues[3] = {0.0, 0.0, 0.0};
1269
1103
1270
1104
// Declare helper variables.
1271
unsigned int rr = 0;
1272
unsigned int ss = 0;
1273
1105
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1274
1106
1275
1107
// Compute basisvalues.
1276
1108
basisvalues[0] = 1.0;
1277
1109
basisvalues[1] = tmp0;
1278
for (unsigned int r = 0; r < 1; r++)
1279
{
1280
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1281
ss = r*(r + 1)/2;
1282
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
1283
}// end loop over 'r'
1284
for (unsigned int r = 0; r < 2; r++)
1285
{
1286
for (unsigned int s = 0; s < 2 - r; s++)
1287
{
1288
rr = (r + s)*(r + s + 1)/2 + s;
1289
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
1290
}// end loop over 's'
1291
}// end loop over 'r'
1110
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
1111
basisvalues[0] *= std::sqrt(0.5);
1112
basisvalues[2] *= std::sqrt(1.0);
1113
basisvalues[1] *= std::sqrt(3.0);
1292
1114
1293
1115
// Table(s) of coefficients.
1294
1116
static const double coefficients0[3] = \
1426
1248
double basisvalues[3] = {0.0, 0.0, 0.0};
1427
1249
1428
1250
// Declare helper variables.
1429
unsigned int rr = 0;
1430
unsigned int ss = 0;
1431
1251
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1432
1252
1433
1253
// Compute basisvalues.
1434
1254
basisvalues[0] = 1.0;
1435
1255
basisvalues[1] = tmp0;
1436
for (unsigned int r = 0; r < 1; r++)
1437
{
1438
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1439
ss = r*(r + 1)/2;
1440
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
1441
}// end loop over 'r'
1442
for (unsigned int r = 0; r < 2; r++)
1443
{
1444
for (unsigned int s = 0; s < 2 - r; s++)
1445
{
1446
rr = (r + s)*(r + s + 1)/2 + s;
1447
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
1448
}// end loop over 's'
1449
}// end loop over 'r'
1256
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
1257
basisvalues[0] *= std::sqrt(0.5);
1258
basisvalues[2] *= std::sqrt(1.0);
1259
basisvalues[1] *= std::sqrt(3.0);
1450
1260
1451
1261
// Table(s) of coefficients.
1452
1262
static const double coefficients0[3] = \
1584
1394
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1585
1395
1586
1396
// Declare helper variables.
1587
unsigned int rr = 0;
1588
unsigned int ss = 0;
1589
unsigned int tt = 0;
1590
double tmp5 = 0.0;
1591
double tmp6 = 0.0;
1592
double tmp7 = 0.0;
1593
1397
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1594
1398
double tmp1 = (1.0 - Y)/2.0;
1595
1399
double tmp2 = tmp1*tmp1;
1597
1401
// Compute basisvalues.
1598
1402
basisvalues[0] = 1.0;
1599
1403
basisvalues[1] = tmp0;
1600
for (unsigned int r = 1; r < 3; r++)
1601
{
1602
rr = (r + 1)*((r + 1) + 1)/2;
1603
ss = r*(r + 1)/2;
1604
tt = (r - 1)*((r - 1) + 1)/2;
1605
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
1606
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
1607
}// end loop over 'r'
1608
for (unsigned int r = 0; r < 3; r++)
1609
{
1610
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1611
ss = r*(r + 1)/2;
1612
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
1613
}// end loop over 'r'
1614
for (unsigned int r = 0; r < 2; r++)
1615
{
1616
for (unsigned int s = 1; s < 3 - r; s++)
1617
{
1618
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1619
ss = (r + s)*(r + s + 1)/2 + s;
1620
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1621
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));
1622
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));
1623
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));
1624
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1625
}// end loop over 's'
1626
}// end loop over 'r'
1627
for (unsigned int r = 0; r < 4; r++)
1628
{
1629
for (unsigned int s = 0; s < 4 - r; s++)
1630
{
1631
rr = (r + s)*(r + s + 1)/2 + s;
1632
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
1633
}// end loop over 's'
1634
}// end loop over 'r'
1404
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1405
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
1406
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
1407
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
1408
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
1409
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
1410
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
1411
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
1412
basisvalues[0] *= std::sqrt(0.5);
1413
basisvalues[2] *= std::sqrt(1.0);
1414
basisvalues[5] *= std::sqrt(1.5);
1415
basisvalues[9] *= std::sqrt(2.0);
1416
basisvalues[1] *= std::sqrt(3.0);
1417
basisvalues[4] *= std::sqrt(4.5);
1418
basisvalues[8] *= std::sqrt(6.0);
1419
basisvalues[3] *= std::sqrt(7.5);
1420
basisvalues[7] *= std::sqrt(10.0);
1421
basisvalues[6] *= std::sqrt(14.0);
1635
1422
1636
1423
// Table(s) of coefficients.
1637
1424
static const double coefficients0[10] = \
1797
1584
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
1798
1585
1799
1586
// Declare helper variables.
1800
unsigned int rr = 0;
1801
unsigned int ss = 0;
1802
unsigned int tt = 0;
1803
double tmp5 = 0.0;
1804
double tmp6 = 0.0;
1805
double tmp7 = 0.0;
1806
1587
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
1807
1588
double tmp1 = (1.0 - Y)/2.0;
1808
1589
double tmp2 = tmp1*tmp1;
1810
1591
// Compute basisvalues.
1811
1592
basisvalues[0] = 1.0;
1812
1593
basisvalues[1] = tmp0;
1813
for (unsigned int r = 1; r < 3; r++)
1814
{
1815
rr = (r + 1)*((r + 1) + 1)/2;
1816
ss = r*(r + 1)/2;
1817
tt = (r - 1)*((r - 1) + 1)/2;
1818
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
1819
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
1820
}// end loop over 'r'
1821
for (unsigned int r = 0; r < 3; r++)
1822
{
1823
rr = (r + 1)*(r + 1 + 1)/2 + 1;
1824
ss = r*(r + 1)/2;
1825
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
1826
}// end loop over 'r'
1827
for (unsigned int r = 0; r < 2; r++)
1828
{
1829
for (unsigned int s = 1; s < 3 - r; s++)
1830
{
1831
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
1832
ss = (r + s)*(r + s + 1)/2 + s;
1833
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
1834
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));
1835
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));
1836
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));
1837
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
1838
}// end loop over 's'
1839
}// end loop over 'r'
1840
for (unsigned int r = 0; r < 4; r++)
1841
{
1842
for (unsigned int s = 0; s < 4 - r; s++)
1843
{
1844
rr = (r + s)*(r + s + 1)/2 + s;
1845
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
1846
}// end loop over 's'
1847
}// end loop over 'r'
1594
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
1595
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
1596
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
1597
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
1598
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
1599
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
1600
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
1601
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
1602
basisvalues[0] *= std::sqrt(0.5);
1603
basisvalues[2] *= std::sqrt(1.0);
1604
basisvalues[5] *= std::sqrt(1.5);
1605
basisvalues[9] *= std::sqrt(2.0);
1606
basisvalues[1] *= std::sqrt(3.0);
1607
basisvalues[4] *= std::sqrt(4.5);
1608
basisvalues[8] *= std::sqrt(6.0);
1609
basisvalues[3] *= std::sqrt(7.5);
1610
basisvalues[7] *= std::sqrt(10.0);
1611
basisvalues[6] *= std::sqrt(14.0);
1848
1612
1849
1613
// Table(s) of coefficients.
1850
1614
static const double coefficients0[10] = \
2317
2081
double basisvalues[3] = {0.0, 0.0, 0.0};
2318
2082
2319
2083
// Declare helper variables.
2320
unsigned int rr = 0;
2321
unsigned int ss = 0;
2322
2084
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2323
2085
2324
2086
// Compute basisvalues.
2325
2087
basisvalues[0] = 1.0;
2326
2088
basisvalues[1] = tmp0;
2327
for (unsigned int r = 0; r < 1; r++)
2328
{
2329
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2330
ss = r*(r + 1)/2;
2331
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2332
}// end loop over 'r'
2333
for (unsigned int r = 0; r < 2; r++)
2334
{
2335
for (unsigned int s = 0; s < 2 - r; s++)
2336
{
2337
rr = (r + s)*(r + s + 1)/2 + s;
2338
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2339
}// end loop over 's'
2340
}// end loop over 'r'
2089
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2090
basisvalues[0] *= std::sqrt(0.5);
2091
basisvalues[2] *= std::sqrt(1.0);
2092
basisvalues[1] *= std::sqrt(3.0);
2341
2093
2342
2094
// Table(s) of coefficients.
2343
2095
static const double coefficients0[3] = \
2357
2109
double basisvalues[3] = {0.0, 0.0, 0.0};
2358
2110
2359
2111
// Declare helper variables.
2360
unsigned int rr = 0;
2361
unsigned int ss = 0;
2362
2112
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2363
2113
2364
2114
// Compute basisvalues.
2365
2115
basisvalues[0] = 1.0;
2366
2116
basisvalues[1] = tmp0;
2367
for (unsigned int r = 0; r < 1; r++)
2368
{
2369
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2370
ss = r*(r + 1)/2;
2371
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2372
}// end loop over 'r'
2373
for (unsigned int r = 0; r < 2; r++)
2374
{
2375
for (unsigned int s = 0; s < 2 - r; s++)
2376
{
2377
rr = (r + s)*(r + s + 1)/2 + s;
2378
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2379
}// end loop over 's'
2380
}// end loop over 'r'
2117
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2118
basisvalues[0] *= std::sqrt(0.5);
2119
basisvalues[2] *= std::sqrt(1.0);
2120
basisvalues[1] *= std::sqrt(3.0);
2381
2121
2382
2122
// Table(s) of coefficients.
2383
2123
static const double coefficients0[3] = \
2397
2137
double basisvalues[3] = {0.0, 0.0, 0.0};
2398
2138
2399
2139
// Declare helper variables.
2400
unsigned int rr = 0;
2401
unsigned int ss = 0;
2402
2140
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2403
2141
2404
2142
// Compute basisvalues.
2405
2143
basisvalues[0] = 1.0;
2406
2144
basisvalues[1] = tmp0;
2407
for (unsigned int r = 0; r < 1; r++)
2408
{
2409
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2410
ss = r*(r + 1)/2;
2411
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2412
}// end loop over 'r'
2413
for (unsigned int r = 0; r < 2; r++)
2414
{
2415
for (unsigned int s = 0; s < 2 - r; s++)
2416
{
2417
rr = (r + s)*(r + s + 1)/2 + s;
2418
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2419
}// end loop over 's'
2420
}// end loop over 'r'
2145
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2146
basisvalues[0] *= std::sqrt(0.5);
2147
basisvalues[2] *= std::sqrt(1.0);
2148
basisvalues[1] *= std::sqrt(3.0);
2421
2149
2422
2150
// Table(s) of coefficients.
2423
2151
static const double coefficients0[3] = \
2556
2284
double basisvalues[3] = {0.0, 0.0, 0.0};
2557
2285
2558
2286
// Declare helper variables.
2559
unsigned int rr = 0;
2560
unsigned int ss = 0;
2561
2287
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2562
2288
2563
2289
// Compute basisvalues.
2564
2290
basisvalues[0] = 1.0;
2565
2291
basisvalues[1] = tmp0;
2566
for (unsigned int r = 0; r < 1; r++)
2567
{
2568
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2569
ss = r*(r + 1)/2;
2570
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2571
}// end loop over 'r'
2572
for (unsigned int r = 0; r < 2; r++)
2573
{
2574
for (unsigned int s = 0; s < 2 - r; s++)
2575
{
2576
rr = (r + s)*(r + s + 1)/2 + s;
2577
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2578
}// end loop over 's'
2579
}// end loop over 'r'
2292
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2293
basisvalues[0] *= std::sqrt(0.5);
2294
basisvalues[2] *= std::sqrt(1.0);
2295
basisvalues[1] *= std::sqrt(3.0);
2580
2296
2581
2297
// Table(s) of coefficients.
2582
2298
static const double coefficients0[3] = \
2714
2430
double basisvalues[3] = {0.0, 0.0, 0.0};
2715
2431
2716
2432
// Declare helper variables.
2717
unsigned int rr = 0;
2718
unsigned int ss = 0;
2719
2433
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2720
2434
2721
2435
// Compute basisvalues.
2722
2436
basisvalues[0] = 1.0;
2723
2437
basisvalues[1] = tmp0;
2724
for (unsigned int r = 0; r < 1; r++)
2725
{
2726
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2727
ss = r*(r + 1)/2;
2728
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2729
}// end loop over 'r'
2730
for (unsigned int r = 0; r < 2; r++)
2731
{
2732
for (unsigned int s = 0; s < 2 - r; s++)
2733
{
2734
rr = (r + s)*(r + s + 1)/2 + s;
2735
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2736
}// end loop over 's'
2737
}// end loop over 'r'
2438
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2439
basisvalues[0] *= std::sqrt(0.5);
2440
basisvalues[2] *= std::sqrt(1.0);
2441
basisvalues[1] *= std::sqrt(3.0);
2738
2442
2739
2443
// Table(s) of coefficients.
2740
2444
static const double coefficients0[3] = \
2872
2576
double basisvalues[3] = {0.0, 0.0, 0.0};
2873
2577
2874
2578
// Declare helper variables.
2875
unsigned int rr = 0;
2876
unsigned int ss = 0;
2877
2579
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
2878
2580
2879
2581
// Compute basisvalues.
2880
2582
basisvalues[0] = 1.0;
2881
2583
basisvalues[1] = tmp0;
2882
for (unsigned int r = 0; r < 1; r++)
2883
{
2884
rr = (r + 1)*(r + 1 + 1)/2 + 1;
2885
ss = r*(r + 1)/2;
2886
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
2887
}// end loop over 'r'
2888
for (unsigned int r = 0; r < 2; r++)
2889
{
2890
for (unsigned int s = 0; s < 2 - r; s++)
2891
{
2892
rr = (r + s)*(r + s + 1)/2 + s;
2893
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
2894
}// end loop over 's'
2895
}// end loop over 'r'
2584
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2585
basisvalues[0] *= std::sqrt(0.5);
2586
basisvalues[2] *= std::sqrt(1.0);
2587
basisvalues[1] *= std::sqrt(3.0);
2896
2588
2897
2589
// Table(s) of coefficients.
2898
2590
static const double coefficients0[3] = \
3285
2977
double basisvalues[3] = {0.0, 0.0, 0.0};
3286
2978
3287
2979
// Declare helper variables.
3288
unsigned int rr = 0;
3289
unsigned int ss = 0;
3290
2980
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3291
2981
3292
2982
// Compute basisvalues.
3293
2983
basisvalues[0] = 1.0;
3294
2984
basisvalues[1] = tmp0;
3295
for (unsigned int r = 0; r < 1; r++)
3296
{
3297
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3298
ss = r*(r + 1)/2;
3299
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3300
}// end loop over 'r'
3301
for (unsigned int r = 0; r < 2; r++)
3302
{
3303
for (unsigned int s = 0; s < 2 - r; s++)
3304
{
3305
rr = (r + s)*(r + s + 1)/2 + s;
3306
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3307
}// end loop over 's'
3308
}// end loop over 'r'
2985
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
2986
basisvalues[0] *= std::sqrt(0.5);
2987
basisvalues[2] *= std::sqrt(1.0);
2988
basisvalues[1] *= std::sqrt(3.0);
3309
2989
3310
2990
// Table(s) of coefficients.
3311
2991
static const double coefficients0[3] = \
3325
3005
double basisvalues[3] = {0.0, 0.0, 0.0};
3326
3006
3327
3007
// Declare helper variables.
3328
unsigned int rr = 0;
3329
unsigned int ss = 0;
3330
3008
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3331
3009
3332
3010
// Compute basisvalues.
3333
3011
basisvalues[0] = 1.0;
3334
3012
basisvalues[1] = tmp0;
3335
for (unsigned int r = 0; r < 1; r++)
3336
{
3337
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3338
ss = r*(r + 1)/2;
3339
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3340
}// end loop over 'r'
3341
for (unsigned int r = 0; r < 2; r++)
3342
{
3343
for (unsigned int s = 0; s < 2 - r; s++)
3344
{
3345
rr = (r + s)*(r + s + 1)/2 + s;
3346
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3347
}// end loop over 's'
3348
}// end loop over 'r'
3013
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3014
basisvalues[0] *= std::sqrt(0.5);
3015
basisvalues[2] *= std::sqrt(1.0);
3016
basisvalues[1] *= std::sqrt(3.0);
3349
3017
3350
3018
// Table(s) of coefficients.
3351
3019
static const double coefficients0[3] = \
3365
3033
double basisvalues[3] = {0.0, 0.0, 0.0};
3366
3034
3367
3035
// Declare helper variables.
3368
unsigned int rr = 0;
3369
unsigned int ss = 0;
3370
3036
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3371
3037
3372
3038
// Compute basisvalues.
3373
3039
basisvalues[0] = 1.0;
3374
3040
basisvalues[1] = tmp0;
3375
for (unsigned int r = 0; r < 1; r++)
3376
{
3377
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3378
ss = r*(r + 1)/2;
3379
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3380
}// end loop over 'r'
3381
for (unsigned int r = 0; r < 2; r++)
3382
{
3383
for (unsigned int s = 0; s < 2 - r; s++)
3384
{
3385
rr = (r + s)*(r + s + 1)/2 + s;
3386
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3387
}// end loop over 's'
3388
}// end loop over 'r'
3041
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3042
basisvalues[0] *= std::sqrt(0.5);
3043
basisvalues[2] *= std::sqrt(1.0);
3044
basisvalues[1] *= std::sqrt(3.0);
3389
3045
3390
3046
// Table(s) of coefficients.
3391
3047
static const double coefficients0[3] = \
3405
3061
double basisvalues[3] = {0.0, 0.0, 0.0};
3406
3062
3407
3063
// Declare helper variables.
3408
unsigned int rr = 0;
3409
unsigned int ss = 0;
3410
3064
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3411
3065
3412
3066
// Compute basisvalues.
3413
3067
basisvalues[0] = 1.0;
3414
3068
basisvalues[1] = tmp0;
3415
for (unsigned int r = 0; r < 1; r++)
3416
{
3417
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3418
ss = r*(r + 1)/2;
3419
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3420
}// end loop over 'r'
3421
for (unsigned int r = 0; r < 2; r++)
3422
{
3423
for (unsigned int s = 0; s < 2 - r; s++)
3424
{
3425
rr = (r + s)*(r + s + 1)/2 + s;
3426
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3427
}// end loop over 's'
3428
}// end loop over 'r'
3069
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3070
basisvalues[0] *= std::sqrt(0.5);
3071
basisvalues[2] *= std::sqrt(1.0);
3072
basisvalues[1] *= std::sqrt(3.0);
3429
3073
3430
3074
// Table(s) of coefficients.
3431
3075
static const double coefficients0[3] = \
3445
3089
double basisvalues[3] = {0.0, 0.0, 0.0};
3446
3090
3447
3091
// Declare helper variables.
3448
unsigned int rr = 0;
3449
unsigned int ss = 0;
3450
3092
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3451
3093
3452
3094
// Compute basisvalues.
3453
3095
basisvalues[0] = 1.0;
3454
3096
basisvalues[1] = tmp0;
3455
for (unsigned int r = 0; r < 1; r++)
3456
{
3457
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3458
ss = r*(r + 1)/2;
3459
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3460
}// end loop over 'r'
3461
for (unsigned int r = 0; r < 2; r++)
3462
{
3463
for (unsigned int s = 0; s < 2 - r; s++)
3464
{
3465
rr = (r + s)*(r + s + 1)/2 + s;
3466
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3467
}// end loop over 's'
3468
}// end loop over 'r'
3097
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3098
basisvalues[0] *= std::sqrt(0.5);
3099
basisvalues[2] *= std::sqrt(1.0);
3100
basisvalues[1] *= std::sqrt(3.0);
3469
3101
3470
3102
// Table(s) of coefficients.
3471
3103
static const double coefficients0[3] = \
3485
3117
double basisvalues[3] = {0.0, 0.0, 0.0};
3486
3118
3487
3119
// Declare helper variables.
3488
unsigned int rr = 0;
3489
unsigned int ss = 0;
3490
3120
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3491
3121
3492
3122
// Compute basisvalues.
3493
3123
basisvalues[0] = 1.0;
3494
3124
basisvalues[1] = tmp0;
3495
for (unsigned int r = 0; r < 1; r++)
3496
{
3497
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3498
ss = r*(r + 1)/2;
3499
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3500
}// end loop over 'r'
3501
for (unsigned int r = 0; r < 2; r++)
3502
{
3503
for (unsigned int s = 0; s < 2 - r; s++)
3504
{
3505
rr = (r + s)*(r + s + 1)/2 + s;
3506
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3507
}// end loop over 's'
3508
}// end loop over 'r'
3125
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3126
basisvalues[0] *= std::sqrt(0.5);
3127
basisvalues[2] *= std::sqrt(1.0);
3128
basisvalues[1] *= std::sqrt(3.0);
3509
3129
3510
3130
// Table(s) of coefficients.
3511
3131
static const double coefficients0[3] = \
3525
3145
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3526
3146
3527
3147
// Declare helper variables.
3528
unsigned int rr = 0;
3529
unsigned int ss = 0;
3530
unsigned int tt = 0;
3531
double tmp5 = 0.0;
3532
double tmp6 = 0.0;
3533
double tmp7 = 0.0;
3534
3148
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3535
3149
double tmp1 = (1.0 - Y)/2.0;
3536
3150
double tmp2 = tmp1*tmp1;
3538
3152
// Compute basisvalues.
3539
3153
basisvalues[0] = 1.0;
3540
3154
basisvalues[1] = tmp0;
3541
for (unsigned int r = 1; r < 3; r++)
3542
{
3543
rr = (r + 1)*((r + 1) + 1)/2;
3544
ss = r*(r + 1)/2;
3545
tt = (r - 1)*((r - 1) + 1)/2;
3546
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
3547
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
3548
}// end loop over 'r'
3549
for (unsigned int r = 0; r < 3; r++)
3550
{
3551
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3552
ss = r*(r + 1)/2;
3553
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3554
}// end loop over 'r'
3555
for (unsigned int r = 0; r < 2; r++)
3556
{
3557
for (unsigned int s = 1; s < 3 - r; s++)
3558
{
3559
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3560
ss = (r + s)*(r + s + 1)/2 + s;
3561
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3562
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));
3563
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));
3564
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));
3565
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3566
}// end loop over 's'
3567
}// end loop over 'r'
3568
for (unsigned int r = 0; r < 4; r++)
3569
{
3570
for (unsigned int s = 0; s < 4 - r; s++)
3571
{
3572
rr = (r + s)*(r + s + 1)/2 + s;
3573
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3574
}// end loop over 's'
3575
}// end loop over 'r'
3155
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3156
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
3157
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3158
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
3159
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
3160
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
3161
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
3162
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
3163
basisvalues[0] *= std::sqrt(0.5);
3164
basisvalues[2] *= std::sqrt(1.0);
3165
basisvalues[5] *= std::sqrt(1.5);
3166
basisvalues[9] *= std::sqrt(2.0);
3167
basisvalues[1] *= std::sqrt(3.0);
3168
basisvalues[4] *= std::sqrt(4.5);
3169
basisvalues[8] *= std::sqrt(6.0);
3170
basisvalues[3] *= std::sqrt(7.5);
3171
basisvalues[7] *= std::sqrt(10.0);
3172
basisvalues[6] *= std::sqrt(14.0);
3576
3173
3577
3174
// Table(s) of coefficients.
3578
3175
static const double coefficients0[10] = \
3592
3189
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
3593
3190
3594
3191
// Declare helper variables.
3595
unsigned int rr = 0;
3596
unsigned int ss = 0;
3597
unsigned int tt = 0;
3598
double tmp5 = 0.0;
3599
double tmp6 = 0.0;
3600
double tmp7 = 0.0;
3601
3192
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3602
3193
double tmp1 = (1.0 - Y)/2.0;
3603
3194
double tmp2 = tmp1*tmp1;
3605
3196
// Compute basisvalues.
3606
3197
basisvalues[0] = 1.0;
3607
3198
basisvalues[1] = tmp0;
3608
for (unsigned int r = 1; r < 3; r++)
3609
{
3610
rr = (r + 1)*((r + 1) + 1)/2;
3611
ss = r*(r + 1)/2;
3612
tt = (r - 1)*((r - 1) + 1)/2;
3613
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
3614
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
3615
}// end loop over 'r'
3616
for (unsigned int r = 0; r < 3; r++)
3617
{
3618
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3619
ss = r*(r + 1)/2;
3620
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3621
}// end loop over 'r'
3622
for (unsigned int r = 0; r < 2; r++)
3623
{
3624
for (unsigned int s = 1; s < 3 - r; s++)
3625
{
3626
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
3627
ss = (r + s)*(r + s + 1)/2 + s;
3628
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
3629
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));
3630
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));
3631
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));
3632
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
3633
}// end loop over 's'
3634
}// end loop over 'r'
3635
for (unsigned int r = 0; r < 4; r++)
3636
{
3637
for (unsigned int s = 0; s < 4 - r; s++)
3638
{
3639
rr = (r + s)*(r + s + 1)/2 + s;
3640
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3641
}// end loop over 's'
3642
}// end loop over 'r'
3199
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
3200
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
3201
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3202
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
3203
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
3204
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
3205
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
3206
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
3207
basisvalues[0] *= std::sqrt(0.5);
3208
basisvalues[2] *= std::sqrt(1.0);
3209
basisvalues[5] *= std::sqrt(1.5);
3210
basisvalues[9] *= std::sqrt(2.0);
3211
basisvalues[1] *= std::sqrt(3.0);
3212
basisvalues[4] *= std::sqrt(4.5);
3213
basisvalues[8] *= std::sqrt(6.0);
3214
basisvalues[3] *= std::sqrt(7.5);
3215
basisvalues[7] *= std::sqrt(10.0);
3216
basisvalues[6] *= std::sqrt(14.0);
3643
3217
3644
3218
// Table(s) of coefficients.
3645
3219
static const double coefficients0[10] = \
3659
3233
double basisvalues[3] = {0.0, 0.0, 0.0};
3660
3234
3661
3235
// Declare helper variables.
3662
unsigned int rr = 0;
3663
unsigned int ss = 0;
3664
3236
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3665
3237
3666
3238
// Compute basisvalues.
3667
3239
basisvalues[0] = 1.0;
3668
3240
basisvalues[1] = tmp0;
3669
for (unsigned int r = 0; r < 1; r++)
3670
{
3671
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3672
ss = r*(r + 1)/2;
3673
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3674
}// end loop over 'r'
3675
for (unsigned int r = 0; r < 2; r++)
3676
{
3677
for (unsigned int s = 0; s < 2 - r; s++)
3678
{
3679
rr = (r + s)*(r + s + 1)/2 + s;
3680
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3681
}// end loop over 's'
3682
}// end loop over 'r'
3241
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3242
basisvalues[0] *= std::sqrt(0.5);
3243
basisvalues[2] *= std::sqrt(1.0);
3244
basisvalues[1] *= std::sqrt(3.0);
3683
3245
3684
3246
// Table(s) of coefficients.
3685
3247
static const double coefficients0[3] = \
3699
3261
double basisvalues[3] = {0.0, 0.0, 0.0};
3700
3262
3701
3263
// Declare helper variables.
3702
unsigned int rr = 0;
3703
unsigned int ss = 0;
3704
3264
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3705
3265
3706
3266
// Compute basisvalues.
3707
3267
basisvalues[0] = 1.0;
3708
3268
basisvalues[1] = tmp0;
3709
for (unsigned int r = 0; r < 1; r++)
3710
{
3711
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3712
ss = r*(r + 1)/2;
3713
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3714
}// end loop over 'r'
3715
for (unsigned int r = 0; r < 2; r++)
3716
{
3717
for (unsigned int s = 0; s < 2 - r; s++)
3718
{
3719
rr = (r + s)*(r + s + 1)/2 + s;
3720
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3721
}// end loop over 's'
3722
}// end loop over 'r'
3269
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3270
basisvalues[0] *= std::sqrt(0.5);
3271
basisvalues[2] *= std::sqrt(1.0);
3272
basisvalues[1] *= std::sqrt(3.0);
3723
3273
3724
3274
// Table(s) of coefficients.
3725
3275
static const double coefficients0[3] = \
3739
3289
double basisvalues[3] = {0.0, 0.0, 0.0};
3740
3290
3741
3291
// Declare helper variables.
3742
unsigned int rr = 0;
3743
unsigned int ss = 0;
3744
3292
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3745
3293
3746
3294
// Compute basisvalues.
3747
3295
basisvalues[0] = 1.0;
3748
3296
basisvalues[1] = tmp0;
3749
for (unsigned int r = 0; r < 1; r++)
3750
{
3751
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3752
ss = r*(r + 1)/2;
3753
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3754
}// end loop over 'r'
3755
for (unsigned int r = 0; r < 2; r++)
3756
{
3757
for (unsigned int s = 0; s < 2 - r; s++)
3758
{
3759
rr = (r + s)*(r + s + 1)/2 + s;
3760
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3761
}// end loop over 's'
3762
}// end loop over 'r'
3297
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3298
basisvalues[0] *= std::sqrt(0.5);
3299
basisvalues[2] *= std::sqrt(1.0);
3300
basisvalues[1] *= std::sqrt(3.0);
3763
3301
3764
3302
// Table(s) of coefficients.
3765
3303
static const double coefficients0[3] = \
3901
3439
double basisvalues[3] = {0.0, 0.0, 0.0};
3902
3440
3903
3441
// Declare helper variables.
3904
unsigned int rr = 0;
3905
unsigned int ss = 0;
3906
3442
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
3907
3443
3908
3444
// Compute basisvalues.
3909
3445
basisvalues[0] = 1.0;
3910
3446
basisvalues[1] = tmp0;
3911
for (unsigned int r = 0; r < 1; r++)
3912
{
3913
rr = (r + 1)*(r + 1 + 1)/2 + 1;
3914
ss = r*(r + 1)/2;
3915
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
3916
}// end loop over 'r'
3917
for (unsigned int r = 0; r < 2; r++)
3918
{
3919
for (unsigned int s = 0; s < 2 - r; s++)
3920
{
3921
rr = (r + s)*(r + s + 1)/2 + s;
3922
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
3923
}// end loop over 's'
3924
}// end loop over 'r'
3447
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3448
basisvalues[0] *= std::sqrt(0.5);
3449
basisvalues[2] *= std::sqrt(1.0);
3450
basisvalues[1] *= std::sqrt(3.0);
3925
3451
3926
3452
// Table(s) of coefficients.
3927
3453
static const double coefficients0[3] = \
4059
3585
double basisvalues[3] = {0.0, 0.0, 0.0};
4060
3586
4061
3587
// Declare helper variables.
4062
unsigned int rr = 0;
4063
unsigned int ss = 0;
4064
3588
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4065
3589
4066
3590
// Compute basisvalues.
4067
3591
basisvalues[0] = 1.0;
4068
3592
basisvalues[1] = tmp0;
4069
for (unsigned int r = 0; r < 1; r++)
4070
{
4071
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4072
ss = r*(r + 1)/2;
4073
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4074
}// end loop over 'r'
4075
for (unsigned int r = 0; r < 2; r++)
4076
{
4077
for (unsigned int s = 0; s < 2 - r; s++)
4078
{
4079
rr = (r + s)*(r + s + 1)/2 + s;
4080
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4081
}// end loop over 's'
4082
}// end loop over 'r'
3593
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3594
basisvalues[0] *= std::sqrt(0.5);
3595
basisvalues[2] *= std::sqrt(1.0);
3596
basisvalues[1] *= std::sqrt(3.0);
4083
3597
4084
3598
// Table(s) of coefficients.
4085
3599
static const double coefficients0[3] = \
4217
3731
double basisvalues[3] = {0.0, 0.0, 0.0};
4218
3732
4219
3733
// Declare helper variables.
4220
unsigned int rr = 0;
4221
unsigned int ss = 0;
4222
3734
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4223
3735
4224
3736
// Compute basisvalues.
4225
3737
basisvalues[0] = 1.0;
4226
3738
basisvalues[1] = tmp0;
4227
for (unsigned int r = 0; r < 1; r++)
4228
{
4229
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4230
ss = r*(r + 1)/2;
4231
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4232
}// end loop over 'r'
4233
for (unsigned int r = 0; r < 2; r++)
4234
{
4235
for (unsigned int s = 0; s < 2 - r; s++)
4236
{
4237
rr = (r + s)*(r + s + 1)/2 + s;
4238
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4239
}// end loop over 's'
4240
}// end loop over 'r'
3739
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3740
basisvalues[0] *= std::sqrt(0.5);
3741
basisvalues[2] *= std::sqrt(1.0);
3742
basisvalues[1] *= std::sqrt(3.0);
4241
3743
4242
3744
// Table(s) of coefficients.
4243
3745
static const double coefficients0[3] = \
4375
3877
double basisvalues[3] = {0.0, 0.0, 0.0};
4376
3878
4377
3879
// Declare helper variables.
4378
unsigned int rr = 0;
4379
unsigned int ss = 0;
4380
3880
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4381
3881
4382
3882
// Compute basisvalues.
4383
3883
basisvalues[0] = 1.0;
4384
3884
basisvalues[1] = tmp0;
4385
for (unsigned int r = 0; r < 1; r++)
4386
{
4387
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4388
ss = r*(r + 1)/2;
4389
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4390
}// end loop over 'r'
4391
for (unsigned int r = 0; r < 2; r++)
4392
{
4393
for (unsigned int s = 0; s < 2 - r; s++)
4394
{
4395
rr = (r + s)*(r + s + 1)/2 + s;
4396
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4397
}// end loop over 's'
4398
}// end loop over 'r'
3885
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
3886
basisvalues[0] *= std::sqrt(0.5);
3887
basisvalues[2] *= std::sqrt(1.0);
3888
basisvalues[1] *= std::sqrt(3.0);
4399
3889
4400
3890
// Table(s) of coefficients.
4401
3891
static const double coefficients0[3] = \
4533
4023
double basisvalues[3] = {0.0, 0.0, 0.0};
4534
4024
4535
4025
// Declare helper variables.
4536
unsigned int rr = 0;
4537
unsigned int ss = 0;
4538
4026
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4539
4027
4540
4028
// Compute basisvalues.
4541
4029
basisvalues[0] = 1.0;
4542
4030
basisvalues[1] = tmp0;
4543
for (unsigned int r = 0; r < 1; r++)
4544
{
4545
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4546
ss = r*(r + 1)/2;
4547
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4548
}// end loop over 'r'
4549
for (unsigned int r = 0; r < 2; r++)
4550
{
4551
for (unsigned int s = 0; s < 2 - r; s++)
4552
{
4553
rr = (r + s)*(r + s + 1)/2 + s;
4554
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4555
}// end loop over 's'
4556
}// end loop over 'r'
4031
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4032
basisvalues[0] *= std::sqrt(0.5);
4033
basisvalues[2] *= std::sqrt(1.0);
4034
basisvalues[1] *= std::sqrt(3.0);
4557
4035
4558
4036
// Table(s) of coefficients.
4559
4037
static const double coefficients0[3] = \
4691
4169
double basisvalues[3] = {0.0, 0.0, 0.0};
4692
4170
4693
4171
// Declare helper variables.
4694
unsigned int rr = 0;
4695
unsigned int ss = 0;
4696
4172
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4697
4173
4698
4174
// Compute basisvalues.
4699
4175
basisvalues[0] = 1.0;
4700
4176
basisvalues[1] = tmp0;
4701
for (unsigned int r = 0; r < 1; r++)
4702
{
4703
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4704
ss = r*(r + 1)/2;
4705
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4706
}// end loop over 'r'
4707
for (unsigned int r = 0; r < 2; r++)
4708
{
4709
for (unsigned int s = 0; s < 2 - r; s++)
4710
{
4711
rr = (r + s)*(r + s + 1)/2 + s;
4712
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4713
}// end loop over 's'
4714
}// end loop over 'r'
4177
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4178
basisvalues[0] *= std::sqrt(0.5);
4179
basisvalues[2] *= std::sqrt(1.0);
4180
basisvalues[1] *= std::sqrt(3.0);
4715
4181
4716
4182
// Table(s) of coefficients.
4717
4183
static const double coefficients0[3] = \
4849
4315
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
4850
4316
4851
4317
// Declare helper variables.
4852
unsigned int rr = 0;
4853
unsigned int ss = 0;
4854
unsigned int tt = 0;
4855
double tmp5 = 0.0;
4856
double tmp6 = 0.0;
4857
double tmp7 = 0.0;
4858
4318
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
4859
4319
double tmp1 = (1.0 - Y)/2.0;
4860
4320
double tmp2 = tmp1*tmp1;
4862
4322
// Compute basisvalues.
4863
4323
basisvalues[0] = 1.0;
4864
4324
basisvalues[1] = tmp0;
4865
for (unsigned int r = 1; r < 3; r++)
4866
{
4867
rr = (r + 1)*((r + 1) + 1)/2;
4868
ss = r*(r + 1)/2;
4869
tt = (r - 1)*((r - 1) + 1)/2;
4870
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
4871
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
4872
}// end loop over 'r'
4873
for (unsigned int r = 0; r < 3; r++)
4874
{
4875
rr = (r + 1)*(r + 1 + 1)/2 + 1;
4876
ss = r*(r + 1)/2;
4877
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
4878
}// end loop over 'r'
4879
for (unsigned int r = 0; r < 2; r++)
4880
{
4881
for (unsigned int s = 1; s < 3 - r; s++)
4882
{
4883
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
4884
ss = (r + s)*(r + s + 1)/2 + s;
4885
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
4886
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));
4887
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));
4888
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));
4889
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
4890
}// end loop over 's'
4891
}// end loop over 'r'
4892
for (unsigned int r = 0; r < 4; r++)
4893
{
4894
for (unsigned int s = 0; s < 4 - r; s++)
4895
{
4896
rr = (r + s)*(r + s + 1)/2 + s;
4897
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
4898
}// end loop over 's'
4899
}// end loop over 'r'
4325
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4326
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
4327
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4328
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
4329
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
4330
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
4331
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
4332
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
4333
basisvalues[0] *= std::sqrt(0.5);
4334
basisvalues[2] *= std::sqrt(1.0);
4335
basisvalues[5] *= std::sqrt(1.5);
4336
basisvalues[9] *= std::sqrt(2.0);
4337
basisvalues[1] *= std::sqrt(3.0);
4338
basisvalues[4] *= std::sqrt(4.5);
4339
basisvalues[8] *= std::sqrt(6.0);
4340
basisvalues[3] *= std::sqrt(7.5);
4341
basisvalues[7] *= std::sqrt(10.0);
4342
basisvalues[6] *= std::sqrt(14.0);
4900
4343
4901
4344
// Table(s) of coefficients.
4902
4345
static const double coefficients0[10] = \
5062
4505
double basisvalues[10] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
5063
4506
5064
4507
// Declare helper variables.
5065
unsigned int rr = 0;
5066
unsigned int ss = 0;
5067
unsigned int tt = 0;
5068
double tmp5 = 0.0;
5069
double tmp6 = 0.0;
5070
double tmp7 = 0.0;
5071
4508
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5072
4509
double tmp1 = (1.0 - Y)/2.0;
5073
4510
double tmp2 = tmp1*tmp1;
5075
4512
// Compute basisvalues.
5076
4513
basisvalues[0] = 1.0;
5077
4514
basisvalues[1] = tmp0;
5078
for (unsigned int r = 1; r < 3; r++)
5079
{
5080
rr = (r + 1)*((r + 1) + 1)/2;
5081
ss = r*(r + 1)/2;
5082
tt = (r - 1)*((r - 1) + 1)/2;
5083
tmp5 = (1.0 + 2.0*r)/(1.0 + r);
5084
basisvalues[rr] = (basisvalues[ss]*tmp0*tmp5 - basisvalues[tt]*tmp2*r/(1.0 + r));
5085
}// end loop over 'r'
5086
for (unsigned int r = 0; r < 3; r++)
5087
{
5088
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5089
ss = r*(r + 1)/2;
5090
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
5091
}// end loop over 'r'
5092
for (unsigned int r = 0; r < 2; r++)
5093
{
5094
for (unsigned int s = 1; s < 3 - r; s++)
5095
{
5096
rr = (r + s + 1)*(r + s + 1 + 1)/2 + s + 1;
5097
ss = (r + s)*(r + s + 1)/2 + s;
5098
tt = (r + s - 1)*(r + s - 1 + 1)/2 + s - 1;
5099
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));
5100
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));
5101
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));
5102
basisvalues[rr] = (basisvalues[ss]*(tmp6 + Y*tmp5) - basisvalues[tt]*tmp7);
5103
}// end loop over 's'
5104
}// end loop over 'r'
5105
for (unsigned int r = 0; r < 4; r++)
5106
{
5107
for (unsigned int s = 0; s < 4 - r; s++)
5108
{
5109
rr = (r + s)*(r + s + 1)/2 + s;
5110
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
5111
}// end loop over 's'
5112
}// end loop over 'r'
4515
basisvalues[3] = basisvalues[1]*1.5*tmp0 - basisvalues[0]*0.5*tmp2;
4516
basisvalues[6] = basisvalues[3]*1.6666667*tmp0 - basisvalues[1]*0.66666667*tmp2;
4517
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4518
basisvalues[4] = basisvalues[1]*(1.5 + 2.5*Y);
4519
basisvalues[7] = basisvalues[3]*(2.5 + 3.5*Y);
4520
basisvalues[5] = basisvalues[2]*(0.11111111 + Y*1.6666667) - basisvalues[0]*0.55555556;
4521
basisvalues[9] = basisvalues[5]*(0.05 + Y*1.75) - basisvalues[2]*0.7;
4522
basisvalues[8] = basisvalues[4]*(0.54 + Y*2.1) - basisvalues[1]*0.56;
4523
basisvalues[0] *= std::sqrt(0.5);
4524
basisvalues[2] *= std::sqrt(1.0);
4525
basisvalues[5] *= std::sqrt(1.5);
4526
basisvalues[9] *= std::sqrt(2.0);
4527
basisvalues[1] *= std::sqrt(3.0);
4528
basisvalues[4] *= std::sqrt(4.5);
4529
basisvalues[8] *= std::sqrt(6.0);
4530
basisvalues[3] *= std::sqrt(7.5);
4531
basisvalues[7] *= std::sqrt(10.0);
4532
basisvalues[6] *= std::sqrt(14.0);
5113
4533
5114
4534
// Table(s) of coefficients.
5115
4535
static const double coefficients0[10] = \
5275
4695
double basisvalues[3] = {0.0, 0.0, 0.0};
5276
4696
5277
4697
// Declare helper variables.
5278
unsigned int rr = 0;
5279
unsigned int ss = 0;
5280
4698
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5281
4699
5282
4700
// Compute basisvalues.
5283
4701
basisvalues[0] = 1.0;
5284
4702
basisvalues[1] = tmp0;
5285
for (unsigned int r = 0; r < 1; r++)
5286
{
5287
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5288
ss = r*(r + 1)/2;
5289
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
5290
}// end loop over 'r'
5291
for (unsigned int r = 0; r < 2; r++)
5292
{
5293
for (unsigned int s = 0; s < 2 - r; s++)
5294
{
5295
rr = (r + s)*(r + s + 1)/2 + s;
5296
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
5297
}// end loop over 's'
5298
}// end loop over 'r'
4703
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4704
basisvalues[0] *= std::sqrt(0.5);
4705
basisvalues[2] *= std::sqrt(1.0);
4706
basisvalues[1] *= std::sqrt(3.0);
5299
4707
5300
4708
// Table(s) of coefficients.
5301
4709
static const double coefficients0[3] = \
5433
4841
double basisvalues[3] = {0.0, 0.0, 0.0};
5434
4842
5435
4843
// Declare helper variables.
5436
unsigned int rr = 0;
5437
unsigned int ss = 0;
5438
4844
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5439
4845
5440
4846
// Compute basisvalues.
5441
4847
basisvalues[0] = 1.0;
5442
4848
basisvalues[1] = tmp0;
5443
for (unsigned int r = 0; r < 1; r++)
5444
{
5445
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5446
ss = r*(r + 1)/2;
5447
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
5448
}// end loop over 'r'
5449
for (unsigned int r = 0; r < 2; r++)
5450
{
5451
for (unsigned int s = 0; s < 2 - r; s++)
5452
{
5453
rr = (r + s)*(r + s + 1)/2 + s;
5454
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
5455
}// end loop over 's'
5456
}// end loop over 'r'
4849
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4850
basisvalues[0] *= std::sqrt(0.5);
4851
basisvalues[2] *= std::sqrt(1.0);
4852
basisvalues[1] *= std::sqrt(3.0);
5457
4853
5458
4854
// Table(s) of coefficients.
5459
4855
static const double coefficients0[3] = \
5591
4987
double basisvalues[3] = {0.0, 0.0, 0.0};
5592
4988
5593
4989
// Declare helper variables.
5594
unsigned int rr = 0;
5595
unsigned int ss = 0;
5596
4990
double tmp0 = (1.0 + Y + 2.0*X)/2.0;
5597
4991
5598
4992
// Compute basisvalues.
5599
4993
basisvalues[0] = 1.0;
5600
4994
basisvalues[1] = tmp0;
5601
for (unsigned int r = 0; r < 1; r++)
5602
{
5603
rr = (r + 1)*(r + 1 + 1)/2 + 1;
5604
ss = r*(r + 1)/2;
5605
basisvalues[rr] = basisvalues[ss]*(0.5 + r + Y*(1.5 + r));
5606
}// end loop over 'r'
5607
for (unsigned int r = 0; r < 2; r++)
5608
{
5609
for (unsigned int s = 0; s < 2 - r; s++)
5610
{
5611
rr = (r + s)*(r + s + 1)/2 + s;
5612
basisvalues[rr] *= std::sqrt((0.5 + r)*(1.0 + r + s));
5613
}// end loop over 's'
5614
}// end loop over 'r'
4995
basisvalues[2] = basisvalues[0]*(0.5 + 1.5*Y);
4996
basisvalues[0] *= std::sqrt(0.5);
4997
basisvalues[2] *= std::sqrt(1.0);
4998
basisvalues[1] *= std::sqrt(3.0);
5615
4999
5616
5000
// Table(s) of coefficients.
5617
5001
static const double coefficients0[3] = \
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