1
2
3 """
4 This module contains quadrature rule tables copied from
5 P. Solin, K Segeth, and I Dolezel. Higher–Order Finite Element Methods.
6 Studies in Advanced Mathematics. Chapman and Hall/CRC, 2004.
7
8 Use the function load_table(polygon, family) to get a list of QuadRule objects.
9 The family can be one of {"composite_gauss", "economical_gauss"}, the polygon name one of the UFC polygon names.
10 """
11
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30
31
32 from sfc.quadrature.QuadRule import QuadRule
33
34
35
36
37
38
39 from ufl.geometry import domain2dim
40
42
43 rules = load_table(polygon, family)
44
45 for repeat in range(10):
46
47 for r in rules:
48 if r.order == order:
49 return r
50
51 order += 1
52
53
54 maxr = -1
55 rule = rules[0]
56 for r in rules:
57 if r.order > rule.order:
58 maxr = r.order
59 rule = r
60 return rule
61
62 raise RuntimeError("Found no rule for a %s with order %d in family %s" % (polygon, order, family))
63
64
66 """Return list of quadrature rules matching polygon and family."""
67 rules = parse_table_string(polygon, family)
68 rules = scale_table(rules)
69 return rules
70
71
73
74 name = "%s_%s_table" % (family, polygon)
75 tablestring = eval(name)
76
77 nsd = domain2dim[polygon]
78 lines = tablestring.split('\n')
79 rules = []
80 i = 0
81 while i<len(lines):
82 n = int(lines[i])
83 i += 1
84 points = []
85 weights = []
86 for j in range(n):
87 values = lines[i].split()
88 points += [ map(float, values[:nsd]) ]
89 weights += [ float(values[nsd]) ]
90 i += 1
91 comment = lines[i].strip()
92 i += 2
93 order = int(comment.split('=')[-1].split()[-1])
94 rules.append( QuadRule(polygon, nsd, order, points, weights, comment) )
95 return rules
96
97
99 """Scales a set of quadrature rules from [-1,+1]^nsd to [0,1]^nsd."""
100 point_offset = 0.5
101 point_scale = 0.5
102 for rule in rules:
103 ws = point_scale**rule.nsd
104 rule.weights = [ w*ws for w in rule.weights ]
105 rule.points = [ [x*point_scale+point_offset for x in p] for p in rule.points ]
106 return rules
107
108
109
110 gauss_interval_table = """\
111 1
112 0.0000000000000000000000000 2.0000000000000000000000000
113 Gauss quadrature points and weights order 2n-1=1
114
115 2
116 -0.5773502691896257645091488 1.0000000000000000000000000
117 0.5773502691896257645091488 1.0000000000000000000000000
118 Gauss quadrature points and weights order 2n-1=3
119
120 3
121 -0.7745966692414833770358531 0.5555555555555555555555556
122 0.0000000000000000000000000 0.8888888888888888888888889
123 0.7745966692414833770358531 0.5555555555555555555555556
124 Gauss quadrature points and weights order 2n-1=5
125
126 4
127 -0.8611363115940525752239465 0.3478548451374538573730639
128 -0.3399810435848562648026658 0.6521451548625461426269361
129 0.3399810435848562648026658 0.6521451548625461426269361
130 0.8611363115940525752239465 0.3478548451374538573730639
131 Gauss quadrature points and weights order 2n-1=7
132
133 5
134 -0.9061798459386639927976269 0.2369268850561890875142640
135 -0.5384693101056830910363144 0.4786286704993664680412915
136 0.0000000000000000000000000 0.5688888888888888888888889
137 0.5384693101056830910363144 0.4786286704993664680412915
138 0.9061798459386639927976269 0.2369268850561890875142640
139 Gauss quadrature points and weights order 2n-1=9
140
141 6
142 -0.9324695142031520278123016 0.1713244923791703450402961
143 -0.6612093864662645136613996 0.3607615730481386075698335
144 -0.2386191860831969086305017 0.4679139345726910473898703
145 0.2386191860831969086305017 0.4679139345726910473898703
146 0.6612093864662645136613996 0.3607615730481386075698335
147 0.9324695142031520278123016 0.1713244923791703450402961
148 Gauss quadrature points and weights order 2n-1=11
149
150 7
151 -0.9491079123427585245261897 0.1294849661688696932706114
152 -0.7415311855993944398638648 0.2797053914892766679014678
153 -0.4058451513773971669066064 0.3818300505051189449503698
154 0.0000000000000000000000000 0.4179591836734693877551020
155 0.4058451513773971669066064 0.3818300505051189449503698
156 0.7415311855993944398638648 0.2797053914892766679014678
157 0.9491079123427585245261897 0.1294849661688696932706114
158 Gauss quadrature points and weights order 2n-1=13
159
160 8
161 -0.9602898564975362316835609 0.1012285362903762591525314
162 -0.7966664774136267395915539 0.2223810344533744705443560
163 -0.5255324099163289858177390 0.3137066458778872873379622
164 -0.1834346424956498049394761 0.3626837833783619829651504
165 0.1834346424956498049394761 0.3626837833783619829651504
166 0.5255324099163289858177390 0.3137066458778872873379622
167 0.7966664774136267395915539 0.2223810344533744705443560
168 0.9602898564975362316835609 0.1012285362903762591525314
169 Gauss quadrature points and weights order 2n-1=15
170
171 9
172 -0.9681602395076260898355762 0.0812743883615744119718922
173 -0.8360311073266357942994297 0.1806481606948574040584720
174 -0.6133714327005903973087020 0.2606106964029354623187429
175 -0.3242534234038089290385380 0.3123470770400028400686304
176 0.0000000000000000000000000 0.3302393550012597631645251
177 0.3242534234038089290385380 0.3123470770400028400686304
178 0.6133714327005903973087020 0.2606106964029354623187429
179 0.8360311073266357942994298 0.1806481606948574040584720
180 0.9681602395076260898355762 0.0812743883615744119718922
181 Gauss quadrature points and weights order 2n-1=17
182
183 10
184 -0.9739065285171717200779640 0.0666713443086881375935688
185 -0.8650633666889845107320967 0.1494513491505805931457763
186 -0.6794095682990244062343274 0.2190863625159820439955349
187 -0.4333953941292471907992659 0.2692667193099963550912269
188 -0.1488743389816312108848260 0.2955242247147528701738930
189 0.1488743389816312108848260 0.2955242247147528701738930
190 0.4333953941292471907992659 0.2692667193099963550912269
191 0.6794095682990244062343274 0.2190863625159820439955349
192 0.8650633666889845107320967 0.1494513491505805931457763
193 0.9739065285171717200779640 0.0666713443086881375935688
194 Gauss quadrature points and weights order 2n-1=19
195
196 11
197 -0.9782286581460569928039380 0.0556685671161736664827537
198 -0.8870625997680952990751578 0.1255803694649046246346943
199 -0.7301520055740493240934162 0.1862902109277342514260976
200 -0.5190961292068118159257257 0.2331937645919904799185237
201 -0.2695431559523449723315320 0.2628045445102466621806889
202 0.0000000000000000000000000 0.2729250867779006307144835
203 0.2695431559523449723315320 0.2628045445102466621806889
204 0.5190961292068118159257257 0.2331937645919904799185237
205 0.7301520055740493240934163 0.1862902109277342514260980
206 0.8870625997680952990751578 0.1255803694649046246346940
207 0.9782286581460569928039380 0.0556685671161736664827537
208 Gauss quadrature points and weights order 2n-1=21
209
210 12
211 -0.9815606342467192506905491 0.0471753363865118271946160
212 -0.9041172563704748566784659 0.1069393259953184309602547
213 -0.7699026741943046870368938 0.1600783285433462263346525
214 -0.5873179542866174472967024 0.2031674267230659217490645
215 -0.3678314989981801937526915 0.2334925365383548087608499
216 -0.1252334085114689154724414 0.2491470458134027850005624
217 0.1252334085114689154724414 0.2491470458134027850005624
218 0.3678314989981801937526915 0.2334925365383548087608499
219 0.5873179542866174472967024 0.2031674267230659217490645
220 0.7699026741943046870368938 0.1600783285433462263346525
221 0.9041172563704748566784659 0.1069393259953184309602547
222 0.9815606342467192506905491 0.0471753363865118271946160
223 Gauss quadrature points and weights order 2n-1=23
224
225 16
226 -0.9894009349916499325961542 0.0271524594117540948517806
227 -0.9445750230732325760779884 0.0622535239386478928628438
228 -0.8656312023878317438804679 0.0951585116824927848099251
229 -0.7554044083550030338951012 0.1246289712555338720524763
230 -0.6178762444026437484466718 0.1495959888165767320815017
231 -0.4580167776572273863424194 0.1691565193950025381893121
232 -0.2816035507792589132304605 0.1826034150449235888667637
233 -0.0950125098376374401853193 0.1894506104550684962853967
234 0.0950125098376374401853193 0.1894506104550684962853967
235 0.2816035507792589132304605 0.1826034150449235888667637
236 0.4580167776572273863424194 0.1691565193950025381893121
237 0.6178762444026437484466718 0.1495959888165767320815017
238 0.7554044083550030338951012 0.1246289712555338720524763
239 0.8656312023878317438804679 0.0951585116824927848099251
240 0.9445750230732325760779884 0.0622535239386478928628438
241 0.9894009349916499325961542 0.0271524594117540948517806
242 Gauss quadrature points and weights order 2n-1=31
243
244 20
245 -0.9931285991850949247861224 0.0176140071391521183118620
246 -0.9639719272779137912676661 0.0406014298003869413310400
247 -0.9122344282513259058677524 0.0626720483341090635695065
248 -0.8391169718222188233945291 0.0832767415767047487247581
249 -0.7463319064601507926143051 0.1019301198172404350367501
250 -0.6360536807265150254528367 0.1181945319615184173123774
251 -0.5108670019508270980043641 0.1316886384491766268984945
252 -0.3737060887154195606725482 0.1420961093183820513292983
253 -0.2277858511416450780804962 0.1491729864726037467878287
254 -0.0765265211334973337546404 0.1527533871307258506980843
255 0.0765265211334973337546404 0.1527533871307258506980843
256 0.2277858511416450780804962 0.1491729864726037467878287
257 0.3737060887154195606725482 0.1420961093183820513292983
258 0.5108670019508270980043641 0.1316886384491766268984945
259 0.6360536807265150254528367 0.1181945319615184173123774
260 0.7463319064601507926143051 0.1019301198172404350367501
261 0.8391169718222188233945291 0.0832767415767047487247581
262 0.9122344282513259058677524 0.0626720483341090635695065
263 0.9639719272779137912676661 0.0406014298003869413310400
264 0.9931285991850949247861224 0.0176140071391521183118620
265 Gauss quadrature points and weights order 2n-1=39
266
267 24
268 -0.9951872199970213601799974 0.0123412297999871995468057
269 -0.9747285559713094981983919 0.0285313886289336631813078
270 -0.9382745520027327585236490 0.0442774388174198061686027
271 -0.8864155270044010342131543 0.0592985849154367807463678
272 -0.8200019859739029219539499 0.0733464814110803057340336
273 -0.7401241915785543642438281 0.0861901615319532759171852
274 -0.6480936519369755692524958 0.0976186521041138882698807
275 -0.5454214713888395356583756 0.1074442701159656347825773
276 -0.4337935076260451384870842 0.1155056680537256013533445
277 -0.3150426796961633743867933 0.1216704729278033912044632
278 -0.1911188674736163091586398 0.1258374563468282961213754
279 -0.0640568928626056260850431 0.1279381953467521569740562
280 0.0640568928626056260850431 0.1279381953467521569740562
281 0.1911188674736163091586398 0.1258374563468282961213754
282 0.3150426796961633743867933 0.1216704729278033912044632
283 0.4337935076260451384870842 0.1155056680537256013533445
284 0.5454214713888395356583756 0.1074442701159656347825773
285 0.6480936519369755692524958 0.0976186521041138882698807
286 0.7401241915785543642438281 0.0861901615319532759171852
287 0.8200019859739029219539499 0.0733464814110803057340336
288 0.8864155270044010342131543 0.0592985849154367807463678
289 0.9382745520027327585236490 0.0442774388174198061686027
290 0.9747285559130949819839199 0.0285313886289336631813078
291 0.9951872199970213601799974 0.0123412297999871995468057
292 Gauss quadrature points and weights order 2n-1=47
293
294 32
295 -0.9972638618494815635449811 0.0070186100094700966004071
296 -0.9856115115452683354001750 0.0162743947309056706051706
297 -0.9647622555875064307738119 0.0253920653092620594557526
298 -0.9349060759377396891709191 0.0342738629130214331026877
299 -0.8963211557660521239653072 0.0428358980222266806568786
300 -0.8493676137325699701336930 0.0509980592623761761961632
301 -0.7944837959679424069630973 0.0586840934785355471452836
302 -0.7321821187402896803874267 0.0658222227763618468376501
303 -0.6630442669302152009751152 0.0723457941088485062253994
304 -0.5877157572407623290407455 0.0781938957870703064717409
305 -0.5068999089322293900237475 0.0833119242269467552221991
306 -0.4213512761306353453641194 0.0876520930044038111427715
307 -0.3318686022821276497799168 0.0911738786957638847128686
308 -0.2392873622521370745446032 0.0938443990808045656391802
309 -0.1444719615827964934851864 0.0956387200792748594190820
310 -0.0483076656877383162348126 0.0965400885147278005667648
311 0.0483076656877383162348126 0.0965400885147278005667648
312 0.1444719615827964934851864 0.0956387200792748594190820
313 0.2392873622521370745446032 0.0938443990808045656391802
314 0.3318686022821276497799168 0.0911738786957638847128686
315 0.4213512761306353453641194 0.0876520930044038111427715
316 0.5068999089322293900237475 0.0833119242269467552221991
317 0.5877157572407623290407455 0.0781938957870703064717409
318 0.6630442669302152009751152 0.0723457941088485062253994
319 0.7321821187402896803874267 0.0658222227763618468376501
320 0.7944837959679424069630973 0.0586840934785355471452836
321 0.8493676137325699701336930 0.0509980592623761761961632
322 0.8963211557660521239653072 0.0428358980222266806568787
323 0.9349060759377396891709191 0.0342738629130214331026877
324 0.9647622555875064307738119 0.0253920653092620594557526
325 0.9856115115452683354001750 0.0162743947309056706051706
326 0.9972638618494815635449811 0.0070186100094700966004071
327 Gauss quadrature points and weights order 2n-1=63
328
329 40
330 -0.9982377097105592003496227 0.0045212770985331912584717
331 -0.9907262386994570064530544 0.0104982845311528136147422
332 -0.9772599499837742626633703 0.0164210583819078887128635
333 -0.9579168192137916558045410 0.0222458491941669572615043
334 -0.9328128082786765333608522 0.0279370069800234010984892
335 -0.9020988069688742967282533 0.0334601952825478473926782
336 -0.8659595032122595038207818 0.0387821679744720176399720
337 -0.8246122308333116631963202 0.0438709081856732719916747
338 -0.7783056514265193876949715 0.0486958076350722320614342
339 -0.7273182551899271032809965 0.0532278469839368243549965
340 -0.6719566846141795483793545 0.0574397690993915513666177
341 -0.6125538896679802379526125 0.0613062424929289391665380
342 -0.5494671250951282020759313 0.0648040134566010380745545
343 -0.4830758016861787129085666 0.0679120458152339038256901
344 -0.4137792043716050015248797 0.0706116473912867796954836
345 -0.3419940908257584730074925 0.0728865823958040590605107
346 -0.2681521850072536811411843 0.0747231690579682642001893
347 -0.1926975807013710997155169 0.0761103619006262423715581
348 -0.1160840706752552084834513 0.0770398181642479655883075
349 -0.0387724175060508219331934 0.0775059479784248112637240
350 0.0387724175060508219331934 0.0775059479784248112637240
351 0.1160840706752552084834513 0.0770398181642479655883075
352 0.1926975807013710997155169 0.0761103619006262423715581
353 0.2681521850072536811411843 0.0747231690579682642001893
354 0.3419940908257584730074925 0.0728865823958040590605107
355 0.4137792043716050015248797 0.0706116473912867796954836
356 0.4830758016861787129085666 0.0679120458152339038256901
357 0.5494671250951282020759313 0.0648040134566010380745545
358 0.6125538896679802379526125 0.0613062424929289391665380
359 0.6719566846141795483793545 0.0574397690993915513666177
360 0.7273182551899271032809965 0.0532278469839368243549965
361 0.7783056514265193876949715 0.0486958076350722320614342
362 0.8246122308333116631963202 0.0438709081856732719916747
363 0.8659595032122595038207818 0.0387821679744720176399720
364 0.9020988069688742967282533 0.0334601952825478473926782
365 0.9328128082786765333608522 0.0279370069800234010984892
366 0.9579168192137916558045410 0.0222458491941669572615040
367 0.9772599499837742626633703 0.0164210583819078887128635
368 0.9907262386994570064530544 0.0104982845311528136147422
369 0.9982377097105592003496227 0.0045212770985331912584717
370 Gauss quadrature points and weights order 2n-1=79
371
372 48
373 -0.9987710072524261186005415 0.0031533460523058386326773
374 -0.9935301722663507575479288 0.0073275539012762621023840
375 -0.9841245837228268577445836 0.0114772345792345394895927
376 -0.9705915925462472504614120 0.0155793157229438487281770
377 -0.9529877031604308607229607 0.0196161604573555278144607
378 -0.9313866907065543331141744 0.0235707608393243791405193
379 -0.9058791367155696728220748 0.0274265097083569482000738
380 -0.8765720202742478859056936 0.0311672278327980889020658
381 -0.8435882616243935307110898 0.0347772225647704388925486
382 -0.8070662040294426270825530 0.0382413510658307063172173
383 -0.7671590325157403392538554 0.0415450829434647492140588
384 -0.7240341309238146546744822 0.0446745608566942804194486
385 -0.6778723796326639052118513 0.0476166584924904748259066
386 -0.6288673967765136239951649 0.0503590355538544749578076
387 -0.5772247260839727038178092 0.0528901894851936670955051
388 -0.5231609747222330336782259 0.0551995036999841628682035
389 -0.4669029047509584045449289 0.0572772921004032157051502
390 -0.4086864819907167299162255 0.0591148396983956357464748
391 -0.3487558862921607381598179 0.0607044391658938800529692
392 -0.2873624873554555767358865 0.0620394231598926639041978
393 -0.2247637903946890612248654 0.0631141922862540256571260
394 -0.1612223560688917180564374 0.0639242385846481866239062
395 -0.0970046992094626989300540 0.0644661644359500822065042
396 -0.0323801709628693620333222 0.0647376968126839225030249
397 0.0323801709628693620333222 0.0647376968126839225030249
398 0.0970046992094626989300540 0.0644661644359500822065042
399 0.1612223560688917180564374 0.0639242385846481866239062
400 0.2247637903946890612248654 0.0631141922862540256571260
401 0.2873624873554555767358865 0.0620394231598926639041978
402 0.3487558862921607381598179 0.0607044391658938800529692
403 0.4086864819907167299162255 0.0591148396983956357464748
404 0.4669029047509584045449289 0.0572772921004032157051502
405 0.5231609747222330336782259 0.0551995036999841628682035
406 0.5772247260839727038178092 0.0528901894851936670955051
407 0.6288673967765136239951649 0.0503590355538544749578076
408 0.6778723796326639052118513 0.0476166584924904748259066
409 0.7240341309238146546744822 0.0446745608566942804194486
410 0.7671590325157403392538554 0.0415450829434647492140588
411 0.8070662040294426270825530 0.0382413510658307063172173
412 0.8435882616243935307110898 0.0347772225647704388925486
413 0.8765720202742478859056936 0.0311672278327980889020658
414 0.9058791367155696728220748 0.0274265097083569482000738
415 0.9313866907065543331141744 0.0235707608393243791405193
416 0.9529877031604308607229607 0.0196161604573555278144607
417 0.9705915925462472504614120 0.0155793157229438487281770
418 0.9841245837228268577445836 0.0114772345792345394895927
419 0.9935301722663507575479288 0.0073275539012762621023840
420 0.9987710072524261186005415 0.0031533460523058386326773
421 Gauss quadrature points and weights order 2n-1=95
422
423 64
424 -0.9993050417357721394569056 0.0017832807216964329472961
425 -0.9963401167719552793469245 0.0041470332605624676352875
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456 0.0243502926634244325089558 0.0486909570091397203833654
457 0.0729931217877990394495429 0.0485754674415034269347991
458 0.1214628192961205544703765 0.0483447622348029571697695
459 0.1696444204239928180373136 0.0479993885964583077281262
460 0.2174236437400070841496487 0.0475401657148303086622822
461 0.2646871622087674163739642 0.0469681828162100173253263
462 0.3113228719902109561575127 0.0462847965813144172959532
463 0.3572201583376681159504426 0.0454916279274181444797710
464 0.4022701579639916036957668 0.0445905581637565630601347
465 0.4463660172534640879849477 0.0435837245293234533768279
466 0.4894031457070529574785263 0.0424735151236535890073398
467 0.5312794640198945456580139 0.0412625632426235286101563
468 0.5718956462026340342838781 0.0399537411327203413866569
469 0.6111553551723932502488530 0.0385501531786156291289625
470 0.6489654712546573398577612 0.0370551285402400460404151
471 0.6852363130542332425635584 0.0354722132568823838106931
472 0.7198818501716108268489402 0.0338051618371416093915655
473 0.7528199072605318966118638 0.0320579283548515535854675
474 0.7839723589433414076102205 0.0302346570724024788679741
475 0.8132653151227975597419233 0.0283396726142594832275113
476 0.8406292962525803627516915 0.0263774697150546586716918
477 0.8659993981540928197607834 0.0243527025687108733381776
478 0.8893154459951141058534040 0.0222701738083832541592983
479 0.9105221370785028057563807 0.0201348231535302093723403
480 0.9295691721319395758214902 0.0179517157756973430850453
481 0.9464113748584028160624815 0.0157260304760247193219660
482 0.9610087996520537189186141 0.0134630478967186425980608
483 0.9733268277899109637418535 0.0111681394601311288185900
484 0.9833362538846259569312993 0.0088467598263639477230309
485 0.9910133714767443207393824 0.0065044579689783628561174
486 0.9963401167719552793469245 0.0041470332605624676352875
487 0.9993050417357721394569056 0.0017832807216964329472961
488 Gauss quadrature points and weights order 2n-1=127
489 """
490
491
492 economical_gauss_quadrilateral_table = """\
493 1
494 0.000000000000000 0.000000000000000 4.000000000000000
495 Gauss quadrature points and weights on the reference quadrilateral order p=0 1
496
497 4
498 0.577350269189626 0.577350269189626 1.000000000000000
499 0.577350269189626 -0.577350269189626 1.000000000000000
500 -0.577350269189626 0.577350269189626 1.000000000000000
501 -0.577350269189626 -0.577350269189626 1.000000000000000
502 Gauss quadrature points and weights on the reference quadrilateral order p=2 3
503
504 8
505 0.683130051063973 0.000000000000000 0.816326530612245
506 -0.683130051063973 0.000000000000000 0.816326530612245
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508 0.000000000000000 -0.683130051063973 0.816326530612245
509 0.881917103688197 0.881917103688197 0.183673469387755
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511 -0.881917103688197 0.881917103688197 0.183673469387755
512 -0.881917103688197 -0.881917103688197 0.183673469387755
513 Gauss quadrature points and weights on the reference quadrilateral order p=4 5
514
515 12
516 0.925820099772551 0.000000000000000 0.241975308641975
517 -0.925820099772551 0.000000000000000 0.241975308641975
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527 -0.380554433208316 -0.380554433208316 0.520592916667394
528 Gauss quadrature points and weights on the reference quadrilateral order p=6 7
529
530 20
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532 -1.121225763866564 0.000000000000000 0.018475842507491
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535 0.451773049920657 0.000000000000000 0.390052939160735
536 -0.451773049920657 0.000000000000000 0.390052939160735
537 0.000000000000000 0.451773049920657 0.390052939160735
538 0.000000000000000 -0.451773049920657 0.390052939160735
539 0.891849420851512 0.891849420851512 0.083095178026482
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550 -0.411623426336542 -0.824396370749276 0.254188020152646
551 Gauss quadrature points and weights on the reference quadrilateral order p=8 9
552
553 25
554 0.000000000000000 0.000000000000000 0.365379525585903
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563 0.935787012440540 0.935787012440540 0.034265103851229
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570 -0.413491953449114 -0.413491953449114 0.308993036133713
571 0.883025508525690 0.575653595840465 0.146684377651312
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578 -0.575653595840465 -0.883025508525690 0.146684377651312
579 Gauss quadrature points and weights on the reference quadrilateral order p=10 11
580
581 36
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583 -1.086056158573971 0.000000000000000 0.005656169693764
584 0.000000000000000 1.086056158573971 0.005656169693764
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618 Gauss quadrature points and weights on the reference quadrilateral order p=12 13
619
620 45
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665 -0.809863684081217 -0.960457474887516 0.028794154400064
666 Gauss quadrature points and weights on the reference quadrilateral order p=14 15
667
668 60
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670 -0.989353074512600 0.000000000000000 0.020614915919991
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721 0.981321179805452 0.706000287798646 0.021922559481864
722 0.981321179805452 -0.706000287798646 0.021922559481864
723 -0.981321179805452 0.706000287798646 0.021922559481864
724 -0.981321179805452 -0.706000287798646 0.021922559481864
725 0.706000287798646 0.981321179805452 0.021922559481864
726 0.706000287798646 -0.981321179805452 0.021922559481864
727 -0.706000287798646 0.981321179805452 0.021922559481864
728 -0.706000287798646 -0.981321179805452 0.021922559481864
729 Gauss quadrature points and weights on the reference quadrilateral order p=16 17
730
731 72
732 0.943962831808239 0.000000000000000 0.038205406871462
733 -0.943962831808239 0.000000000000000 0.038205406871462
734 0.000000000000000 0.943962831808239 0.038205406871462
735 0.000000000000000 -0.943962831808239 0.038205406871462
736 0.536918434376013 0.000000000000000 0.135368502976521
737 -0.536918434376013 0.000000000000000 0.135368502976521
738 0.000000000000000 0.536918434376013 0.135368502976521
739 0.000000000000000 -0.536918434376013 0.135368502976521
740 0.973981076394170 0.973981076394170 0.005773708558664
741 0.973981076394170 -0.973981076394170 0.005773708558664
742 -0.973981076394170 0.973981076394170 0.005773708558664
743 -0.973981076394170 -0.973981076394170 0.005773708558664
744 0.742995535327609 0.742995535327609 0.067460759759473
745 0.742995535327609 -0.742995535327609 0.067460759759473
746 -0.742995535327609 0.742995535327609 0.067460759759473
747 -0.742995535327609 -0.742995535327609 0.067460759759473
748 0.285010052188916 0.285010052188916 0.140899115227892
749 0.285010052188916 -0.285010052188916 0.140899115227892
750 -0.285010052188916 0.285010052188916 0.140899115227892
751 -0.285010052188916 -0.285010052188916 0.140899115227892
752 0.068354569272491 0.068354569272491 0.047466627685662
753 0.068354569272491 -0.068354569272491 0.047466627685662
754 -0.068354569272491 0.068354569272491 0.047466627685662
755 -0.068354569272491 -0.068354569272491 0.047466627685662
756 0.802952004398543 0.203345534163332 0.078619467342982
757 0.802952004398543 -0.203345534163332 0.078619467342982
758 -0.802952004398543 0.203345534163332 0.078619467342982
759 -0.802952004398543 -0.203345534163332 0.078619467342982
760 0.203345534163332 0.802952004398543 0.078619467342982
761 0.203345534163332 -0.802952004398543 0.078619467342982
762 -0.203345534163332 0.802952004398543 0.078619467342982
763 -0.203345534163332 -0.802952004398543 0.078619467342982
764 0.634244672807882 0.426572172992877 0.094979169511394
765 0.634244672807882 -0.426572172992877 0.094979169511394
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767 -0.634244672807882 -0.426572172992877 0.094979169511394
768 0.426572172992877 0.634244672807882 0.094979169511394
769 0.426572172992877 -0.634244672807882 0.094979169511394
770 -0.426572172992877 0.634244672807882 0.094979169511394
771 -0.426572172992877 -0.634244672807882 0.094979169511394
772 0.978350706908227 0.295830776620995 0.022331162356015
773 0.978350706908227 -0.295830776620995 0.022331162356015
774 -0.978350706908227 0.295830776620995 0.022331162356015
775 -0.978350706908227 -0.295830776620995 0.022331162356015
776 0.295830776620995 0.978350706908227 0.022331162356015
777 0.295830776620995 -0.978350706908227 0.022331162356015
778 -0.295830776620995 0.978350706908227 0.022331162356015
779 -0.295830776620995 -0.978350706908227 0.022331162356015
780 0.901672717710389 0.541983037327871 0.055594877793785
781 0.901672717710389 -0.541983037327871 0.055594877793785
782 -0.901672717710389 0.541983037327871 0.055594877793785
783 -0.901672717710389 -0.541983037327871 0.055594877793785
784 0.541983037327871 0.901672717710389 0.055594877793785
785 0.541983037327871 -0.901672717710389 0.055594877793785
786 -0.541983037327871 0.901672717710389 0.055594877793785
787 -0.541983037327871 -0.901672717710389 0.055594877793785
788 1.007018449383116 0.669414798783936 0.006049054506376
789 1.007018449383116 -0.669414798783936 0.006049054506376
790 -1.007018449383116 0.669414798783936 0.006049054506376
791 -1.007018449383116 -0.669414798783936 0.006049054506376
792 0.669414798783936 1.007018449383116 0.006049054506376
793 0.669414798783936 -1.007018449383116 0.006049054506376
794 -0.669414798783936 1.007018449383116 0.006049054506376
795 -0.669414798783936 -1.007018449383116 0.006049054506376
796 0.945161453573471 0.829501421477824 0.024839207949609
797 0.945161453573471 -0.829501421477824 0.024839207949609
798 -0.945161453573471 0.829501421477824 0.024839207949609
799 -0.945161453573471 -0.829501421477824 0.024839207949609
800 0.829501421477824 0.945161453573471 0.024839207949609
801 0.829501421477824 -0.945161453573471 0.024839207949609
802 -0.829501421477824 0.945161453573471 0.024839207949609
803 -0.829501421477824 -0.945161453573471 0.024839207949609
804 Gauss quadrature points and weights on the reference quadrilateral order p=18 19
805
806 88
807 0.980883148832881 0.000000000000000 0.019503841092684
808 -0.980883148832881 0.000000000000000 0.019503841092684
809 0.000000000000000 0.980883148832881 0.019503841092684
810 0.000000000000000 -0.980883148832881 0.019503841092684
811 0.678152700336576 0.000000000000000 0.089012127744268
812 -0.678152700336576 0.000000000000000 0.089012127744268
813 0.000000000000000 0.678152700336576 0.089012127744268
814 0.000000000000000 -0.678152700336576 0.089012127744268
815 0.240599282275864 0.000000000000000 0.114568584702749
816 -0.240599282275864 0.000000000000000 0.114568584702749
817 0.000000000000000 0.240599282275864 0.114568584702749
818 0.000000000000000 -0.240599282275864 0.114568584702749
819 0.965176994929162 0.965176994929162 0.007463627359106
820 0.965176994929162 -0.965176994929162 0.007463627359106
821 -0.965176994929162 0.965176994929162 0.007463627359106
822 -0.965176994929162 -0.965176994929162 0.007463627359106
823 0.749698539312765 0.749698539312765 0.050585943594705
824 0.749698539312765 -0.749698539312765 0.050585943594705
825 -0.749698539312765 0.749698539312765 0.050585943594705
826 -0.749698539312765 -0.749698539312765 0.050585943594705
827 0.568983925500818 0.568983925500818 0.074613865184212
828 0.568983925500818 -0.568983925500818 0.074613865184212
829 -0.568983925500818 0.568983925500818 0.074613865184212
830 -0.568983925500818 -0.568983925500818 0.074613865184212
831 0.971086142843168 0.355832132274584 0.023501091310143
832 0.971086142843168 -0.355832132274584 0.023501091310143
833 -0.971086142843168 0.355832132274584 0.023501091310143
834 -0.971086142843168 -0.355832132274584 0.023501091310143
835 0.355832132274584 0.971086142843168 0.023501091310143
836 0.355832132274584 -0.971086142843168 0.023501091310143
837 -0.355832132274584 0.971086142843168 0.023501091310143
838 -0.355832132274584 -0.971086142843168 0.023501091310143
839 0.983453947854968 0.645588139196562 0.011588562644144
840 0.983453947854968 -0.645588139196562 0.011588562644144
841 -0.983453947854968 0.645588139196562 0.011588562644144
842 -0.983453947854968 -0.645588139196562 0.011588562644144
843 0.645588139196562 0.983453947854968 0.011588562644144
844 0.645588139196562 -0.983453947854968 0.011588562644144
845 -0.645588139196562 0.983453947854968 0.011588562644144
846 -0.645588139196562 -0.983453947854968 0.011588562644144
847 0.933927707027213 0.821920249234369 0.023073245798171
848 0.933927707027213 -0.821920249234369 0.023073245798171
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850 -0.933927707027213 -0.821920249234369 0.023073245798171
851 0.821920249234369 0.933927707027213 0.023073245798171
852 0.821920249234369 -0.933927707027213 0.023073245798171
853 -0.821920249234369 0.933927707027213 0.023073245798171
854 -0.821920249234369 -0.933927707027213 0.023073245798171
855 1.014086498915039 0.862185099566557 0.001570221774472
856 1.014086498915039 -0.862185099566557 0.001570221774472
857 -1.014086498915039 0.862185099566557 0.001570221774472
858 -1.014086498915039 -0.862185099566557 0.001570221774472
859 0.862185099566557 1.014086498915039 0.001570221774472
860 0.862185099566557 -1.014086498915039 0.001570221774472
861 -0.862185099566557 1.014086498915039 0.001570221774472
862 -0.862185099566557 -1.014086498915039 0.001570221774472
863 0.877914842155496 0.168914072450263 0.049102258016227
864 0.877914842155496 -0.168914072450263 0.049102258016227
865 -0.877914842155496 0.168914072450263 0.049102258016227
866 -0.877914842155496 -0.168914072450263 0.049102258016227
867 0.168914072450263 0.877914842155496 0.049102258016227
868 0.168914072450263 -0.877914842155496 0.049102258016227
869 -0.168914072450263 0.877914842155496 0.049102258016227
870 -0.168914072450263 -0.877914842155496 0.049102258016227
871 0.882246882640128 0.568113580166780 0.042512352239126
872 0.882246882640128 -0.568113580166780 0.042512352239126
873 -0.882246882640128 0.568113580166780 0.042512352239126
874 -0.882246882640128 -0.568113580166780 0.042512352239126
875 0.568113580166780 0.882246882640128 0.042512352239126
876 0.568113580166780 -0.882246882640128 0.042512352239126
877 -0.568113580166780 0.882246882640128 0.042512352239126
878 -0.568113580166780 -0.882246882640128 0.042512352239126
879 0.741324453314596 0.371360260002223 0.067270936863160
880 0.741324453314596 -0.371360260002223 0.067270936863160
881 -0.741324453314596 0.371360260002223 0.067270936863160
882 -0.741324453314596 -0.371360260002223 0.067270936863160
883 0.371360260002223 0.741324453314596 0.067270936863160
884 0.371360260002223 -0.741324453314596 0.067270936863160
885 -0.371360260002223 0.741324453314596 0.067270936863160
886 -0.371360260002223 -0.741324453314596 0.067270936863160
887 0.469570217710647 0.237333359193547 0.103507336515645
888 0.469570217710647 -0.237333359193547 0.103507336515645
889 -0.469570217710647 0.237333359193547 0.103507336515645
890 -0.469570217710647 -0.237333359193547 0.103507336515645
891 0.237333359193547 0.469570217710647 0.103507336515645
892 0.237333359193547 -0.469570217710647 0.103507336515645
893 -0.237333359193547 0.469570217710647 0.103507336515645
894 -0.237333359193547 -0.469570217710647 0.103507336515645
895 Gauss quadrature points and weights on the reference quadrilateral order p=20 21
896 """
897
898
899 economical_gauss_hexahedron_table = """\
900 1
901 0.000000000000000 0.000000000000000 0.000000000000000 8.000000000000000
902 Gauss quadrature points and weights on the reference cube order p=0 1
903
904 6
905 1.000000000000000 0.000000000000000 0.000000000000000 1.333333333333333
906 -1.000000000000000 0.000000000000000 0.000000000000000 1.333333333333333
907 0.000000000000000 1.000000000000000 0.000000000000000 1.333333333333333
908 0.000000000000000 -1.000000000000000 0.000000000000000 1.333333333333333
909 0.000000000000000 0.000000000000000 1.000000000000000 1.333333333333333
910 0.000000000000000 0.000000000000000 -1.000000000000000 1.333333333333333
911 Gauss quadrature points and weights on the reference cube order p=2 3
912
913 14
914 0.795822425754221 0.000000000000000 0.000000000000000 0.886426592797784
915 -0.795822425754221 0.000000000000000 0.000000000000000 0.886426592797784
916 0.000000000000000 0.795822425754221 0.000000000000000 0.886426592797784
917 0.000000000000000 -0.795822425754221 0.000000000000000 0.886426592797784
918 0.000000000000000 0.000000000000000 0.795822425754221 0.886426592797784
919 0.000000000000000 0.000000000000000 -0.795822425754221 0.886426592797784
920 0.758786910639328 0.758786910639328 0.758786910639328 0.335180055401662
921 0.758786910639328 -0.758786910639328 0.758786910639328 0.335180055401662
922 0.758786910639328 0.758786910639328 -0.758786910639328 0.335180055401662
923 0.758786910639328 -0.758786910639328 -0.758786910639328 0.335180055401662
924 -0.758786910639328 0.758786910639328 0.758786910639328 0.335180055401662
925 -0.758786910639328 -0.758786910639328 0.758786910639328 0.335180055401662
926 -0.758786910639328 0.758786910639328 -0.758786910639328 0.335180055401662
927 -0.758786910639328 -0.758786910639328 -0.758786910639328 0.335180055401662
928 Gauss quadrature points and weights on the reference cube order p=4 5
929
930 27
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932 0.848418011472252 0.000000000000000 0.000000000000000 0.499369002307720
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934 0.000000000000000 0.848418011472252 0.000000000000000 0.499369002307720
935 0.000000000000000 -0.848418011472252 0.000000000000000 0.499369002307720
936 0.000000000000000 0.000000000000000 0.848418011472252 0.499369002307720
937 0.000000000000000 0.000000000000000 -0.848418011472252 0.499369002307720
938 0.652816472101691 0.652816472101691 0.652816472101691 0.478508449425127
939 0.652816472101691 -0.652816472101691 0.652816472101691 0.478508449425127
940 0.652816472101691 0.652816472101691 -0.652816472101691 0.478508449425127
941 0.652816472101691 -0.652816472101691 -0.652816472101691 0.478508449425127
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944 -0.652816472101691 0.652816472101691 -0.652816472101691 0.478508449425127
945 -0.652816472101691 -0.652816472101691 -0.652816472101691 0.478508449425127
946 0.000000000000000 1.106412898626718 1.106412898626718 0.032303742334037
947 0.000000000000000 -1.106412898626718 1.106412898626718 0.032303742334037
948 0.000000000000000 1.106412898626718 -1.106412898626718 0.032303742334037
949 0.000000000000000 -1.106412898626718 -1.106412898626718 0.032303742334037
950 1.106412898626718 0.000000000000000 1.106412898626718 0.032303742334037
951 -1.106412898626718 0.000000000000000 1.106412898626718 0.032303742334037
952 1.106412898626718 0.000000000000000 -1.106412898626718 0.032303742334037
953 -1.106412898626718 0.000000000000000 -1.106412898626718 0.032303742334037
954 1.106412898626718 1.106412898626718 0.000000000000000 0.032303742334037
955 -1.106412898626718 1.106412898626718 0.000000000000000 0.032303742334037
956 1.106412898626718 -1.106412898626718 0.000000000000000 0.032303742334037
957 -1.106412898626718 -1.106412898626718 0.000000000000000 0.032303742334037
958 Gauss quadrature points and weights on the reference cube order p=6 7
959
960 53
961 0.000000000000000 0.000000000000000 0.000000000000000 0.588405321380412
962 1.064082230328777 0.000000000000000 0.000000000000000 -0.152097068487023
963 -1.064082230328777 0.000000000000000 0.000000000000000 -0.152097068487023
964 0.000000000000000 1.064082230328777 0.000000000000000 -0.152097068487023
965 0.000000000000000 -1.064082230328777 0.000000000000000 -0.152097068487023
966 0.000000000000000 0.000000000000000 1.064082230328777 -0.152097068487023
967 0.000000000000000 0.000000000000000 -1.064082230328777 -0.152097068487023
968 0.905830033000216 0.000000000000000 0.000000000000000 0.369012523996709
969 -0.905830033000216 0.000000000000000 0.000000000000000 0.369012523996709
970 0.000000000000000 0.905830033000216 0.000000000000000 0.369012523996709
971 0.000000000000000 -0.905830033000216 0.000000000000000 0.369012523996709
972 0.000000000000000 0.000000000000000 0.905830033000216 0.369012523996709
973 0.000000000000000 0.000000000000000 -0.905830033000216 0.369012523996709
974 0.817286490798906 0.817286490798906 0.817286490798906 0.104007450974435
975 0.817286490798906 -0.817286490798906 0.817286490798906 0.104007450974435
976 0.817286490798906 0.817286490798906 -0.817286490798906 0.104007450974435
977 0.817286490798906 -0.817286490798906 -0.817286490798906 0.104007450974435
978 -0.817286490798906 0.817286490798906 0.817286490798906 0.104007450974435
979 -0.817286490798906 -0.817286490798906 0.817286490798906 0.104007450974435
980 -0.817286490798906 0.817286490798906 -0.817286490798906 0.104007450974435
981 -0.817286490798906 -0.817286490798906 -0.817286490798906 0.104007450974435
982 0.501292956337400 0.501292956337400 0.501292956337400 0.380660357224238
983 0.501292956337400 -0.501292956337400 0.501292956337400 0.380660357224238
984 0.501292956337400 0.501292956337400 -0.501292956337400 0.380660357224238
985 0.501292956337400 -0.501292956337400 -0.501292956337400 0.380660357224238
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987 -0.501292956337400 -0.501292956337400 0.501292956337400 0.380660357224238
988 -0.501292956337400 0.501292956337400 -0.501292956337400 0.380660357224238
989 -0.501292956337400 -0.501292956337400 -0.501292956337400 0.380660357224238
990 1.017168937265364 0.650007853956632 0.000000000000000 0.0930316449988371
991 1.017168937265364 -0.650007853956632 0.000000000000000 0.0930316449988371
992 0.650007853956632 1.017168937265364 0.000000000000000 0.0930316449988371
993 -0.650007853956632 1.017168937265364 0.000000000000000 0.0930316449988371
994 -1.017168937265364 0.650007853956632 0.000000000000000 0.0930316449988371
995 -1.017168937265364 -0.650007853956632 0.000000000000000 0.0930316449988371
996 0.650007853956632 -1.017168937265364 0.000000000000000 0.0930316449988371
997 -0.650007853956632 -1.017168937265364 0.000000000000000 0.0930316449988371
998 0.000000000000000 0.650007853956632 1.017168937265364 0.0930316449988371
999 0.000000000000000 -0.650007853956632 1.017168937265364 0.0930316449988371
1000 0.000000000000000 1.017168937265364 0.650007853956632 0.0930316449988371
1001 0.000000000000000 1.017168937265364 -0.650007853956632 0.0930316449988371
1002 0.000000000000000 0.650007853956632 -1.017168937265364 0.0930316449988371
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1809
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2008 1.012434400912337 0.978322332670673 1.012434400912337 -0.023175821642762
2009 1.012434400912337 -0.978322332670673 1.012434400912337 -0.023175821642762
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2126 -0.990340675813395 0.853891500333261 0.703401752648627 0.004492075519908
2127 -0.990340675813395 0.853891500333261 -0.703401752648627 0.004492075519908
2128 -0.990340675813395 0.703401752648627 0.853891500333261 0.004492075519908
2129 -0.990340675813395 -0.703401752648627 0.853891500333261 0.004492075519908
2130 -0.990340675813395 -0.853891500333261 0.703401752648627 0.004492075519908
2131 -0.990340675813395 -0.853891500333261 -0.703401752648627 0.004492075519908
2132 -0.990340675813395 0.703401752648627 -0.853891500333261 0.004492075519908
2133 -0.990340675813395 -0.703401752648627 -0.853891500333261 0.004492075519908
2134 0.703401752648627 0.853891500333261 0.990340675813395 0.004492075519908
2135 0.703401752648627 0.853891500333261 -0.990340675813395 0.004492075519908
2136 0.703401752648627 0.990340675813395 0.853891500333261 0.004492075519908
2137 0.703401752648627 -0.990340675813395 0.853891500333261 0.004492075519908
2138 0.703401752648627 -0.853891500333261 0.990340675813395 0.004492075519908
2139 0.703401752648627 -0.853891500333261 -0.990340675813395 0.004492075519908
2140 0.703401752648627 0.990340675813395 -0.853891500333261 0.004492075519908
2141 0.703401752648627 -0.990340675813395 -0.853891500333261 0.004492075519908
2142 -0.703401752648627 0.853891500333261 0.990340675813395 0.004492075519908
2143 -0.703401752648627 0.853891500333261 -0.990340675813395 0.004492075519908
2144 -0.703401752648627 0.990340675813395 0.853891500333261 0.004492075519908
2145 -0.703401752648627 -0.990340675813395 0.853891500333261 0.004492075519908
2146 -0.703401752648627 -0.853891500333261 0.990340675813395 0.004492075519908
2147 -0.703401752648627 -0.853891500333261 -0.990340675813395 0.004492075519908
2148 -0.703401752648627 0.990340675813395 -0.853891500333261 0.004492075519908
2149 -0.703401752648627 -0.990340675813395 -0.853891500333261 0.004492075519908
2150 0.946965100974417 0.623429573213959 0.361644847592954 0.020564739563048
2151 0.946965100974417 0.623429573213959 -0.361644847592954 0.020564739563048
2152 0.946965100974417 0.361644847592954 0.623429573213959 0.020564739563048
2153 0.946965100974417 -0.361644847592954 0.623429573213959 0.020564739563048
2154 0.946965100974417 -0.623429573213959 0.361644847592954 0.020564739563048
2155 0.946965100974417 -0.623429573213959 -0.361644847592954 0.020564739563048
2156 0.946965100974417 0.361644847592954 -0.623429573213959 0.020564739563048
2157 0.946965100974417 -0.361644847592954 -0.623429573213959 0.020564739563048
2158 -0.946965100974417 0.623429573213959 0.361644847592954 0.020564739563048
2159 -0.946965100974417 0.623429573213959 -0.361644847592954 0.020564739563048
2160 -0.946965100974417 0.361644847592954 0.623429573213959 0.020564739563048
2161 -0.946965100974417 -0.361644847592954 0.623429573213959 0.020564739563048
2162 -0.946965100974417 -0.623429573213959 0.361644847592954 0.020564739563048
2163 -0.946965100974417 -0.623429573213959 -0.361644847592954 0.020564739563048
2164 -0.946965100974417 0.361644847592954 -0.623429573213959 0.020564739563048
2165 -0.946965100974417 -0.361644847592954 -0.623429573213959 0.020564739563048
2166 0.623429573213959 0.946965100974417 0.361644847592954 0.020564739563048
2167 0.623429573213959 0.946965100974417 -0.361644847592954 0.020564739563048
2168 0.623429573213959 0.361644847592954 0.946965100974417 0.020564739563048
2169 0.623429573213959 -0.361644847592954 0.946965100974417 0.020564739563048
2170 0.623429573213959 -0.946965100974417 0.361644847592954 0.020564739563048
2171 0.623429573213959 -0.946965100974417 -0.361644847592954 0.020564739563048
2172 0.623429573213959 0.361644847592954 -0.946965100974417 0.020564739563048
2173 0.623429573213959 -0.361644847592954 -0.946965100974417 0.020564739563048
2174 -0.623429573213959 0.946965100974417 0.361644847592954 0.020564739563048
2175 -0.623429573213959 0.946965100974417 -0.361644847592954 0.020564739563048
2176 -0.623429573213959 0.361644847592954 0.946965100974417 0.020564739563048
2177 -0.623429573213959 -0.361644847592954 0.946965100974417 0.020564739563048
2178 -0.623429573213959 -0.946965100974417 0.361644847592954 0.020564739563048
2179 -0.623429573213959 -0.946965100974417 -0.361644847592954 0.020564739563048
2180 -0.623429573213959 0.361644847592954 -0.946965100974417 0.020564739563048
2181 -0.623429573213959 -0.361644847592954 -0.946965100974417 0.020564739563048
2182 0.361644847592954 0.946965100974417 0.623429573213959 0.020564739563048
2183 0.361644847592954 0.946965100974417 -0.623429573213959 0.020564739563048
2184 0.361644847592954 0.623429573213959 0.946965100974417 0.020564739563048
2185 0.361644847592954 -0.623429573213959 0.946965100974417 0.020564739563048
2186 0.361644847592954 -0.946965100974417 0.623429573213959 0.020564739563048
2187 0.361644847592954 -0.946965100974417 -0.623429573213959 0.020564739563048
2188 0.361644847592954 0.623429573213959 -0.946965100974417 0.020564739563048
2189 0.361644847592954 -0.623429573213959 -0.946965100974417 0.020564739563048
2190 -0.361644847592954 0.946965100974417 0.623429573213959 0.020564739563048
2191 -0.361644847592954 0.946965100974417 -0.623429573213959 0.020564739563048
2192 -0.361644847592954 0.623429573213959 0.946965100974417 0.020564739563048
2193 -0.361644847592954 -0.623429573213959 0.946965100974417 0.020564739563048
2194 -0.361644847592954 -0.946965100974417 0.623429573213959 0.020564739563048
2195 -0.361644847592954 -0.946965100974417 -0.623429573213959 0.020564739563048
2196 -0.361644847592954 0.623429573213959 -0.946965100974417 0.020564739563048
2197 -0.361644847592954 -0.623429573213959 -0.946965100974417 0.020564739563048
2198 0.754378926224437 0.538990774213829 0.258107746839302 0.039008180977840
2199 0.754378926224437 0.538990774213829 -0.258107746839302 0.039008180977840
2200 0.754378926224437 0.258107746839302 0.538990774213829 0.039008180977840
2201 0.754378926224437 -0.258107746839302 0.538990774213829 0.039008180977840
2202 0.754378926224437 -0.538990774213829 0.258107746839302 0.039008180977840
2203 0.754378926224437 -0.538990774213829 -0.258107746839302 0.039008180977840
2204 0.754378926224437 0.258107746839302 -0.538990774213829 0.039008180977840
2205 0.754378926224437 -0.258107746839302 -0.538990774213829 0.039008180977840
2206 -0.754378926224437 0.538990774213829 0.258107746839302 0.039008180977840
2207 -0.754378926224437 0.538990774213829 -0.258107746839302 0.039008180977840
2208 -0.754378926224437 0.258107746839302 0.538990774213829 0.039008180977840
2209 -0.754378926224437 -0.258107746839302 0.538990774213829 0.039008180977840
2210 -0.754378926224437 -0.538990774213829 0.258107746839302 0.039008180977840
2211 -0.754378926224437 -0.538990774213829 -0.258107746839302 0.039008180977840
2212 -0.754378926224437 0.258107746839302 -0.538990774213829 0.039008180977840
2213 -0.754378926224437 -0.258107746839302 -0.538990774213829 0.039008180977840
2214 0.538990774213829 0.754378926224437 0.258107746839302 0.039008180977840
2215 0.538990774213829 0.754378926224437 -0.258107746839302 0.039008180977840
2216 0.538990774213829 0.258107746839302 0.754378926224437 0.039008180977840
2217 0.538990774213829 -0.258107746839302 0.754378926224437 0.039008180977840
2218 0.538990774213829 -0.754378926224437 0.258107746839302 0.039008180977840
2219 0.538990774213829 -0.754378926224437 -0.258107746839302 0.039008180977840
2220 0.538990774213829 0.258107746839302 -0.754378926224437 0.039008180977840
2221 0.538990774213829 -0.258107746839302 -0.754378926224437 0.039008180977840
2222 -0.538990774213829 0.754378926224437 0.258107746839302 0.039008180977840
2223 -0.538990774213829 0.754378926224437 -0.258107746839302 0.039008180977840
2224 -0.538990774213829 0.258107746839302 0.754378926224437 0.039008180977840
2225 -0.538990774213829 -0.258107746839302 0.754378926224437 0.039008180977840
2226 -0.538990774213829 -0.754378926224437 0.258107746839302 0.039008180977840
2227 -0.538990774213829 -0.754378926224437 -0.258107746839302 0.039008180977840
2228 -0.538990774213829 0.258107746839302 -0.754378926224437 0.039008180977840
2229 -0.538990774213829 -0.258107746839302 -0.754378926224437 0.039008180977840
2230 0.258107746839302 0.754378926224437 0.538990774213829 0.039008180977840
2231 0.258107746839302 0.754378926224437 -0.538990774213829 0.039008180977840
2232 0.258107746839302 0.538990774213829 0.754378926224437 0.039008180977840
2233 0.258107746839302 -0.538990774213829 0.754378926224437 0.039008180977840
2234 0.258107746839302 -0.754378926224437 0.538990774213829 0.039008180977840
2235 0.258107746839302 -0.754378926224437 -0.538990774213829 0.039008180977840
2236 0.258107746839302 0.538990774213829 -0.754378926224437 0.039008180977840
2237 0.258107746839302 -0.538990774213829 -0.754378926224437 0.039008180977840
2238 -0.258107746839302 0.754378926224437 0.538990774213829 0.039008180977840
2239 -0.258107746839302 0.754378926224437 -0.538990774213829 0.039008180977840
2240 -0.258107746839302 0.538990774213829 0.754378926224437 0.039008180977840
2241 -0.258107746839302 -0.538990774213829 0.754378926224437 0.039008180977840
2242 -0.258107746839302 -0.754378926224437 0.538990774213829 0.039008180977840
2243 -0.258107746839302 -0.754378926224437 -0.538990774213829 0.039008180977840
2244 -0.258107746839302 0.538990774213829 -0.754378926224437 0.039008180977840
2245 -0.258107746839302 -0.538990774213829 -0.754378926224437 0.039008180977840
2246 Gauss quadrature points and weights on the reference cube order p=18 19
2247 """
2248
2249
2250 economical_gauss_triangle_table = """\
2251 1
2252 -0.333333333333333 -0.333333333333333 2.000000000000000
2253 Gauss quadrature points and weights on the reference triangle order p=1
2254
2255 3
2256 -0.666666666666667 -0.666666666666667 0.666666666666667
2257 -0.666666666666667 0.333333333333333 0.666666666666667
2258 0.333333333333333 -0.666666666666667 0.666666666666667
2259 Gauss quadrature points and weights on the reference triangle order p=2
2260
2261 4
2262 -0.333333333333333 -0.333333333333333 -1.125000000000000
2263 -0.600000000000000 -0.600000000000000 1.041666666666667
2264 -0.600000000000000 0.200000000000000 1.041666666666667
2265 0.200000000000000 -0.600000000000000 1.041666666666667
2266 Gauss quadrature points and weights on the reference triangle order p=3
2267
2268 6
2269 -0.108103018168070 -0.108103018168070 0.446763179356022
2270 -0.108103018168070 -0.783793963663860 0.446763179356022
2271 -0.783793963663860 -0.108103018168070 0.446763179356022
2272 -0.816847572980458 -0.816847572980458 0.219903487310644
2273 -0.816847572980458 0.633695145960918 0.219903487310644
2274 0.633695145960918 -0.816847572980458 0.219903487310644
2275 Gauss quadrature points and weights on the reference triangle order p=4
2276
2277 7
2278 -0.333333333333333 -0.333333333333333 0.450000000000000
2279 -0.059715871789770 -0.059715871789770 0.264788305577012
2280 -0.059715871789770 -0.880568256420460 0.264788305577012
2281 -0.880568256420460 -0.059715871789770 0.264788305577012
2282 -0.797426985353088 -0.797426985353088 0.251878361089654
2283 -0.797426985353088 0.594853970706174 0.251878361089654
2284 0.594853970706174 -0.797426985353088 0.251878361089654
2285 Gauss quadrature points and weights on the reference triangle order p=5
2286
2287 12
2288 -0.501426509658180 -0.501426509658180 0.233572551452758
2289 -0.501426509658180 0.002853019316358 0.233572551452758
2290 0.002853019316358 -0.501426509658180 0.233572551452758
2291 -0.873821971016996 -0.873821971016996 0.101689812740414
2292 -0.873821971016996 0.747643942033992 0.101689812740414
2293 0.747643942033992 -0.873821971016996 0.101689812740414
2294 -0.379295097932432 0.273004998242798 0.165702151236748
2295 0.273004998242798 -0.893709900310366 0.165702151236748
2296 -0.893709900310366 -0.379295097932432 0.165702151236748
2297 -0.379295097932432 -0.893709900310366 0.165702151236748
2298 0.273004998242798 -0.379295097932432 0.165702151236748
2299 -0.893709900310366 0.273004998242798 0.165702151236748
2300 Gauss quadrature points and weights on the reference triangle order p=6
2301
2302 13
2303 -0.333333333333333 -0.333333333333333 -0.299140088935364
2304 -0.479308067841920 -0.479308067841920 0.351230514866416
2305 -0.479308067841920 -0.041383864316160 0.351230514866416
2306 -0.041383864316160 -0.479308067841920 0.351230514866416
2307 -0.869739794195568 -0.869739794195568 0.106694471217676
2308 -0.869739794195568 0.739479588391136 0.106694471217676
2309 0.739479588391136 -0.869739794195568 0.106694471217676
2310 -0.374269007990252 0.276888377139620 0.154227521780514
2311 0.276888377139620 -0.902619369149368 0.154227521780514
2312 -0.902619369149368 -0.374269007990252 0.154227521780514
2313 -0.374269007990252 -0.902619369149368 0.154227521780514
2314 0.276888377139620 -0.374269007990252 0.154227521780514
2315 -0.902619369149368 0.276888377139620 0.154227521780514
2316 Gauss quadrature points and weights on the reference triangle order p=7
2317
2318 16
2319 -0.333333333333333 -0.333333333333333 0.288631215355574
2320 -0.081414823414554 -0.081414823414554 0.190183268534570
2321 -0.081414823414554 -0.837170353170892 0.190183268534570
2322 -0.837170353170892 -0.081414823414554 0.190183268534570
2323 -0.658861384496480 -0.658861384496480 0.206434741069436
2324 -0.658861384496480 0.317722768992960 0.206434741069436
2325 0.317722768992960 -0.658861384496480 0.206434741069436
2326 -0.898905543365938 -0.898905543365938 0.064916995246396
2327 -0.898905543365938 0.797811086731876 0.064916995246395
2328 0.797811086731876 -0.898905543365938 0.064916995246396
2329 -0.473774340730724 0.456984785910808 0.054460628348870
2330 0.456984785910808 -0.983210445180084 0.054460628348870
2331 -0.983210445180084 -0.473774340730724 0.054460628348870
2332 -0.473774340730724 -0.983210445180084 0.054460628348870
2333 0.456984785910808 -0.473774340730724 0.054460628348870
2334 -0.983210445180084 0.456984785910808 0.054460628348870
2335 Gauss quadrature points and weights on the reference triangle order p=8
2336
2337 19
2338 -0.333333333333333 -0.333333333333333 0.194271592565598
2339 -0.020634961602524 -0.020634961602524 0.062669400454278
2340 -0.020634961602524 -0.958730076794950 0.062669400454278
2341 -0.958730076794950 -0.020634961602524 0.062669400454278
2342 -0.125820817014126 -0.125820817014126 0.155655082009548
2343 -0.125820817014126 -0.748358365971746 0.155655082009548
2344 -0.748358365971746 -0.125820817014126 0.155655082009548
2345 -0.623592928761934 -0.623592928761934 0.159295477854420
2346 -0.623592928761934 0.247185857523870 0.159295477854420
2347 0.247185857523870 -0.623592928761934 0.159295477854420
2348 -0.910540973211094 -0.910540973211094 0.051155351317396
2349 -0.910540973211094 0.821081946422190 0.051155351317396
2350 0.821081946422190 -0.910540973211094 0.051155351317396
2351 -0.556074021678468 0.482397197568996 0.086567078754578
2352 0.482397197568996 -0.926323175890528 0.086567078754578
2353 -0.926323175890528 -0.556074021678468 0.086567078754578
2354 -0.556074021678468 -0.926323175890528 0.086567078754578
2355 0.482397197568996 -0.556074021678468 0.086567078754578
2356 -0.926323175890528 0.482397197568996 0.086567078754578
2357 Gauss quadrature points and weights on the reference triangle order p=9
2358
2359 25
2360 -0.333333333333333 -0.333333333333333 0.181635980765508
2361 -0.028844733232686 -0.028844733232686 0.073451915512934
2362 -0.028844733232686 -0.942310533534630 0.073451915512934
2363 -0.942310533534630 -0.028844733232686 0.073451915512934
2364 -0.781036849029926 -0.781036849029926 0.090642118871056
2365 -0.781036849029926 0.562073698059852 0.090642118871056
2366 0.562073698059852 -0.781036849029926 0.090642118871056
2367 -0.384120322471758 0.100705883641998 0.145515833690840
2368 0.100705883641998 -0.716585561170240 0.145515833690840
2369 -0.716585561170240 -0.384120322471758 0.145515833690840
2370 -0.384120322471758 -0.716585561170240 0.145515833690840
2371 0.100705883641998 -0.384120322471758 0.145515833690840
2372 -0.716585561170240 0.100705883641998 0.145515833690840
2373 -0.506654878720194 0.456647809194822 0.056654485062114
2374 0.456647809194822 -0.949992930474628 0.056654485062114
2375 -0.949992930474628 -0.506654878720194 0.056654485062114
2376 -0.506654878720194 -0.949992930474628 0.056654485062114
2377 0.456647809194822 -0.506654878720194 0.056654485062114
2378 -0.949992930474628 0.456647809194822 0.056654485062114
2379 -0.866393497975600 0.847311867175000 0.018843333927466
2380 0.847311867175000 -0.980918369199402 0.018843333927466
2381 -0.980918369199402 -0.866393497975600 0.018843333927466
2382 -0.866393497975600 -0.980918369199402 0.018843333927466
2383 0.847311867175000 -0.866393497975600 0.018843333927466
2384 -0.980918369199402 0.847311867175000 0.018843333927466
2385 Gauss quadrature points and weights on the reference triangle order p=10
2386
2387 27
2388 0.069222096541516 0.069222096541516 0.001854012657922
2389 0.069222096541516 -1.138444193083034 0.001854012657922
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2405 -0.899643723379010 -0.286758703477414 0.104674223924408
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2407 0.186402426856426 -0.286758703477414 0.104674223924408
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2415 Gauss quadrature points and weights on the reference triangle order p=11
2416
2417 33
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2436 -0.448573460628972 -0.769313010930604 0.080743115532762
2437 0.217886471559576 -0.448573460628972 0.080743115532762
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2443 0.391672173575606 -0.437348838020120 0.044713546404606
2444 -0.954323335555486 0.391672173575606 0.044713546404606
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2446 0.716028067088146 -0.948531898903340 0.034632462217318
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2448 -0.767496168184806 -0.948531898903340 0.034632462217318
2449 0.716028067088146 -0.767496168184806 0.034632462217318
2450 -0.948531898903340 0.716028067088146 0.034632462217318
2451 Gauss quadrature points and weights on the reference triangle order p=12
2452
2453 37
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2483 0.380338319973810 -0.416539866531424 0.034802926607644
2484 -0.963798453442386 0.380338319973810 0.034802926607644
2485 -0.747285229016662 0.702819075668482 0.031043573678090
2486 0.702819075668482 -0.955533846651820 0.031043573678090
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2489 0.702819075668482 -0.747285229016662 0.031043573678090
2490 -0.955533846651820 0.702819075668482 0.031043573678090
2491 Gauss quadrature points and weights on the reference triangle order p=13
2492
2493 42
2494 -0.022072179275642 -0.022072179275642 0.043767162738858
2495 -0.022072179275642 -0.955855641448714 0.043767162738858
2496 -0.955855641448714 -0.022072179275642 0.043767162738858
2497 -0.164710561319092 -0.164710561319092 0.065576707088250
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2502 -0.093910113235354 -0.453044943382322 0.103548209014584
2503 -0.645588935174914 -0.645588935174914 0.084325177473986
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2505 0.291177870349826 -0.645588935174914 0.084325177473986
2506 -0.876400233818254 -0.876400233818254 0.028867399339554
2507 -0.876400233818254 0.752800467636510 0.028867399339554
2508 0.752800467636510 -0.876400233818254 0.028867399339554
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2510 -0.961218077502598 0.922436155005196 0.009846807204800
2511 0.9224361550051960 -0.961218077502598 0.009846807204800
2512 -0.655466624357288 0.541217109549992 0.049331506425128
2513 0.541217109549992 -0.885750485192704 0.049331506425128
2514 -0.885750485192704 -0.655466624357288 0.049331506425128
2515 -0.655466624357288 -0.885750485192704 0.049331506425128
2516 0.541217109549992 -0.655466624357288 0.049331506425128
2517 -0.885750485192704 0.541217109549992 0.049331506425128
2518 -0.326277080407310 0.140444581693366 0.077143021574122
2519 0.140444581693366 -0.814167501286056 0.077143021574122
2520 -0.814167501286056 -0.326277080407310 0.077143021574122
2521 -0.326277080407310 -0.814167501286056 0.077143021574122
2522 0.140444581693366 -0.326277080407310 0.077143021574122
2523 -0.814167501286056 0.140444581693366 0.077143021574122
2524 -0.403254235727484 0.373960335616176 0.028872616227068
2525 0.373960335616176 -0.970706099888692 0.028872616227068
2526 -0.970706099888692 -0.403254235727484 0.028872616227068
2527 -0.403254235727484 -0.970706099888692 0.028872616227068
2528 0.373960335616176 -0.403254235727484 0.028872616227068
2529 -0.970706099888692 0.373960335616176 0.028872616227068
2530 -0.762051004606086 0.759514342740342 0.010020457677002
2531 0.759514342740342 -0.997463338134256 0.010020457677002
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2534 0.759514342740342 -0.762051004606086 0.010020457677002
2535 -0.997463338134256 0.759514342740342 0.010020457677002
2536 Gauss quadrature points and weights on the reference triangle order p=14
2537
2538 48
2539 0.013945833716486 0.013945833716486 0.003833751285698
2540 0.013945833716486 -1.027891667432972 0.003833751285698
2541 -1.027891667432972 0.013945833716486 0.003833751285698
2542 -0.137187291433954 -0.137187291433954 0.088498054542290
2543 -0.137187291433954 -0.725625417132090 0.088498054542290
2544 -0.725625417132090 -0.137187291433954 0.088498054542290
2545 -0.444612710305712 -0.444612710305712 0.102373097437704
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2550 0.494140435834984 -0.747070217917492 0.047375471741376
2551 -0.858383228050628 -0.858383228050628 0.026579551380042
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2553 0.716766456101256 -0.858383228050628 0.026579551380042
2554 -0.962069659517854 -0.962069659517854 0.009497833216384
2555 -0.962069659517854 0.924139319035706 0.009497833216384
2556 0.924139319035706 -0.962069659517854 0.009497833216384
2557 -0.477377257719826 0.209908933786582 0.077100145199186
2558 0.209908933786582 -0.732531676066758 0.077100145199186
2559 -0.732531676066758 -0.477377257719826 0.077100145199186
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2563 -0.223906465819462 0.151173111025628 0.054431628641248
2564 0.151173111025628 -0.927266645206166 0.054431628641248
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2566 -0.223906465819462 -0.927266645206166 0.054431628641248
2567 0.151173111025628 -0.223906465819462 0.054431628641248
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2572 -0.428575559900168 -1.020349766253142 0.004364154733594
2573 0.448925326153310 -0.428575559900168 0.004364154733594
2574 -1.020349766253142 0.448925326153310 0.004364154733594
2575 -0.568800671855432 0.495112932103676 0.043010639695462
2576 0.495112932103676 -0.926312260248244 0.043010639695462
2577 -0.926312260248244 -0.568800671855432 0.043010639695462
2578 -0.568800671855432 -0.926312260248244 0.043010639695462
2579 0.495112932103676 -0.568800671855432 0.043010639695462
2580 -0.926312260248244 0.495112932103676 0.043010639695462
2581 -0.792848766847228 0.767929148184832 0.015347885262098
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2584 -0.792848766847228 -0.975080381337602 0.015347885262098
2585 0.767929148184832 -0.792848766847228 0.015347885262098
2586 -0.975080381337602 0.767929148184832 0.015347885262098
2587 Gauss quadrature points and weights on the reference triangle order p=15
2588
2589 52
2590 -0.333333333333333 -0.333333333333333 0.093751394855284
2591 -0.005238916103124 -0.005238916103124 0.012811757157170
2592 -0.005238916103124 -0.989522167793754 0.012811757157170
2593 -0.989522167793754 -0.005238916103124 0.012811757157170
2594 -0.173061122901296 -0.173061122901296 0.083420593478774
2595 -0.173061122901296 -0.653877754197410 0.083420593478774
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2601 -0.518892500060958 0.037785000121916 0.084265045523300
2602 0.037785000121916 -0.518892500060958 0.084265045523300
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2604 -0.704068411554854 0.408136823109708 0.060000533685546
2605 0.408136823109708 -0.704068411554854 0.060000533685546
2606 -0.849069624685052 -0.849069624685052 0.028400197850048
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2608 0.698139249370104 -0.849069624685052 0.028400197850048
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2610 -0.966807194753950 0.933614389507900 0.007164924702546
2611 0.933614389507900 -0.966807194753950 0.007164924702546
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2617 -0.792848615509496 0.199737422349722 0.065546294921254
2618 -0.324553873193842 0.284387049883010 0.030596612496882
2619 0.284387049883010 -0.959833176689168 0.030596612496882
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2628 0.599185441942654 -0.590503436714376 0.004772488385678
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2631 0.537399442802736 -0.916116427063980 0.038169585511798
2632 -0.916116427063980 -0.621283015738754 0.038169585511798
2633 -0.621283015738754 -0.916116427063980 0.038169585511798
2634 0.537399442802736 -0.621283015738754 0.038169585511798
2635 -0.916116427063980 0.537399442802736 0.038169585511798
2636 -0.829432768634686 0.800798128173322 0.013700109093084
2637 0.800798128173322 -0.971365359538638 0.013700109093084
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2639 -0.829432768634686 -0.971365359538638 0.013700109093084
2640 0.800798128173322 -0.829432768634686 0.013700109093084
2641 -0.971365359538638 0.800798128173322 0.013700109093084
2642 Gauss quadrature points and weights on the reference triangle order p=16
2643
2644 61
2645 -0.333333333333333 -0.333333333333333 0.066874398581606
2646 -0.005658918886452 -0.005658918886452 0.010186830881014
2647 -0.005658918886452 -0.988682162227096 0.010186830881014
2648 -0.988682162227096 -0.005658918886452 0.010186830881014
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2657 -0.601064957509588 -0.199467521245206 0.062215101737938
2658 -0.495717464058094 -0.495717464058094 0.062514222437240
2659 -0.495717464058094 -0.008565071883810 0.062514222437240
2660 -0.008565071883810 -0.495717464058094 0.062514222437240
2661 -0.675905990683078 -0.675905990683078 0.049631308679330
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2933 -0.978904561411718 -0.880607781701986 0.007147818771900
2934 -0.880607781701986 -0.978904561411718 0.007147818771900
2935 0.859512343113706 -0.880607781701986 0.007147818771900
2936 -0.978904561411718 0.859512343113706 0.007147818771900
2937 Gauss quadrature points and weights on the reference triangle order p=20
2938 """
2939
2940
2941 economical_gauss_tetrahedron_table = """\
2942 1
2943 -0.500000000000000 -0.500000000000000 -0.500000000000000 1.333333333333333
2944 Gauss quadrature constants for the reference tetrahedron order p=1
2945
2946 4
2947 -0.723606797749979 -0.723606797749979 -0.723606797749979 0.333333333333333
2948 0.170820393249937 -0.723606797749979 -0.723606797749979 0.333333333333333
2949 -0.723606797749979 0.170820393249937 -0.723606797749979 0.333333333333333
2950 -0.723606797749979 -0.723606797749979 0.170820393249937 0.333333333333333
2951 Gauss quadrature constants for the reference tetrahedron order p=2
2952
2953 5
2954 -0.500000000000000 -0.500000000000000 -0.500000000000000 -1.066666666666667
2955 -0.666666666666667 -0.666666666666667 -0.666666666666667 0.600000000000000
2956 -0.666666666666667 -0.666666666666667 0.000000000000000 0.600000000000000
2957 -0.666666666666667 0.000000000000000 -0.666666666666667 0.600000000000000
2958 0.000000000000000 -0.666666666666667 -0.666666666666667 0.600000000000000
2959 Gauss quadrature constants for the reference tetrahedron order p=3
2960
2961 11
2962 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.105244444444444
2963 -0.857142857142857 -0.857142857142857 -0.857142857142857 0.060977777777778
2964 -0.857142857142857 -0.857142857142857 0.571428571428571 0.060977777777778
2965 -0.857142857142857 0.571428571428571 -0.857142857142857 0.060977777777778
2966 0.571428571428571 -0.857142857142857 -0.857142857142857 0.060977777777778
2967 -0.201192847666402 -0.201192847666402 -0.798807152333598 0.199111111111111
2968 -0.201192847666402 -0.798807152333598 -0.201192847666402 0.199111111111111
2969 -0.798807152333598 -0.201192847666402 -0.201192847666402 0.199111111111111
2970 -0.201192847666402 -0.798807152333598 -0.798807152333598 0.199111111111111
2971 -0.798807152333598 -0.201192847666402 -0.798807152333598 0.199111111111111
2972 -0.798807152333598 -0.798807152333598 -0.201192847666402 0.199111111111111
2973 Gauss quadrature constants for the reference tetrahedron order p=4
2974
2975 14
2976 -0.814529499378218 -0.814529499378218 -0.814529499378218 0.097990724155149
2977 0.443588498134653 -0.814529499378218 -0.814529499378218 0.097990724155149
2978 -0.814529499378218 0.443588498134653 -0.814529499378218 0.097990724155149
2979 -0.814529499378218 -0.814529499378218 0.443588498134653 0.097990724155149
2980 -0.378228161473399 -0.378228161473399 -0.378228161473399 0.150250567624021
2981 -0.865315515579804 -0.378228161473399 -0.378228161473399 0.150250567624021
2982 -0.378228161473399 -0.865315515579804 -0.378228161473399 0.150250567624021
2983 -0.378228161473399 -0.378228161473399 -0.865315515579804 0.150250567624021
2984 -0.091007408251299 -0.091007408251299 -0.908992591748701 0.056728027702775
2985 -0.091007408251299 -0.908992591748701 -0.091007408251299 0.056728027702775
2986 -0.908992591748701 -0.091007408251299 -0.091007408251299 0.056728027702775
2987 -0.091007408251299 -0.908992591748701 -0.908992591748701 0.056728027702775
2988 -0.908992591748701 -0.091007408251299 -0.908992591748701 0.056728027702775
2989 -0.908992591748701 -0.908992591748701 -0.091007408251299 0.056728027702775
2990 Gauss quadrature constants for the reference tetrahedron order p=5
2991
2992 24
2993 -0.570794257481696 -0.570794257481696 -0.570794257481696 0.053230333677557
2994 -0.287617227554912 -0.570794257481696 -0.570794257481696 0.053230333677557
2995 -0.570794257481696 -0.287617227554912 -0.570794257481696 0.053230333677557
2996 -0.570794257481696 -0.570794257481696 -0.287617227554912 0.053230333677557
2997 -0.918652082930777 -0.918652082930777 -0.918652082930777 0.013436281407094
2998 0.755956248792332 -0.918652082930777 -0.918652082930777 0.013436281407094
2999 -0.918652082930777 0.755956248792332 -0.918652082930777 0.013436281407094
3000 -0.918652082930777 -0.918652082930777 0.755956248792332 0.013436281407094
3001 -0.355324219715449 -0.355324219715449 -0.355324219715449 0.073809575391540
3002 -0.934027340853653 -0.355324219715449 -0.355324219715449 0.073809575391540
3003 -0.355324219715449 -0.934027340853653 -0.355324219715449 0.073809575391540
3004 -0.355324219715449 -0.355324219715449 -0.934027340853653 0.073809575391540
3005 -0.872677996249965 -0.872677996249965 -0.460655337083368 0.064285714285714
3006 -0.872677996249965 -0.460655337083368 -0.872677996249965 0.064285714285714
3007 -0.872677996249965 -0.872677996249965 0.206011329583298 0.064285714285714
3008 -0.872677996249965 0.206011329583298 -0.872677996249965 0.064285714285714
3009 -0.872677996249965 -0.460655337083368 0.206011329583298 0.064285714285714
3010 -0.872677996249965 0.206011329583298 -0.460655337083368 0.064285714285714
3011 -0.460655337083368 -0.872677996249965 -0.872677996249965 0.064285714285714
3012 -0.460655337083368 -0.872677996249965 0.206011329583298 0.064285714285714
3013 -0.460655337083368 0.206011329583298 -0.872677996249965 0.064285714285714
3014 0.206011329583298 -0.872677996249965 -0.460655337083368 0.064285714285714
3015 0.206011329583298 -0.872677996249965 -0.872677996249965 0.064285714285714
3016 0.206011329583298 -0.460655337083368 -0.872677996249965 0.064285714285714
3017 Gauss quadrature constants for the reference tetrahedron order p=6
3018
3019 31
3020 0.000000000000000 0.000000000000000 -1.000000000000000 0.007760141093474
3021 0.000000000000000 -1.000000000000000 0.000000000000000 0.007760141093474
3022 -1.000000000000000 0.000000000000000 0.000000000000000 0.007760141093474
3023 -1.000000000000000 -1.000000000000000 0.000000000000000 0.007760141093474
3024 -1.000000000000000 0.000000000000000 -1.000000000000000 0.007760141093474
3025 0.000000000000000 -1.000000000000000 -1.000000000000000 0.007760141093474
3026 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.146113787728871
3027 -0.843573615339364 -0.843573615339364 -0.843573615339364 0.084799532195309
3028 -0.843573615339364 -0.843573615339364 0.530720846018092 0.084799532195309
3029 -0.843573615339364 0.530720846018092 -0.843573615339364 0.084799532195309
3030 0.530720846018092 -0.843573615339364 -0.843573615339364 0.084799532195309
3031 -0.756313566672190 -0.756313566672190 -0.756313566672190 -0.500141920914655
3032 -0.756313566672190 -0.756313566672190 0.268940700016569 -0.500141920914655
3033 -0.756313566672190 0.268940700016569 -0.756313566672190 -0.500141920914655
3034 0.268940700016569 -0.756313566672190 -0.756313566672190 -0.500141920914655
3035 -0.334921671107159 -0.334921671107159 -0.334921671107159 0.039131402104588
3036 -0.334921671107159 -0.334921671107159 -0.995234986678524 0.039131402104588
3037 -0.334921671107159 -0.995234986678524 -0.334921671107159 0.039131402104588
3038 -0.995234986678524 -0.334921671107159 -0.334921671107159 0.039131402104588
3039 -0.800000000000000 -0.800000000000000 -0.600000000000000 0.220458553791887
3040 -0.800000000000000 -0.600000000000000 -0.800000000000000 0.220458553791887
3041 -0.800000000000000 -0.800000000000000 0.200000000000000 0.220458553791887
3042 -0.800000000000000 0.200000000000000 -0.800000000000000 0.220458553791887
3043 -0.800000000000000 -0.600000000000000 0.200000000000000 0.220458553791887
3044 -0.800000000000000 0.200000000000000 -0.600000000000000 0.220458553791887
3045 -0.600000000000000 -0.800000000000000 -0.800000000000000 0.220458553791887
3046 -0.600000000000000 -0.800000000000000 0.200000000000000 0.220458553791887
3047 -0.600000000000000 0.200000000000000 -0.800000000000000 0.220458553791887
3048 0.200000000000000 -0.800000000000000 -0.600000000000000 0.220458553791887
3049 0.200000000000000 -0.800000000000000 -0.800000000000000 0.220458553791887
3050 0.200000000000000 -0.600000000000000 -0.800000000000000 0.220458553791887
3051 Gauss quadrature constants for the reference tetrahedron order p=7
3052
3053 43
3054 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.164001509269119
3055 -0.586340136778654 -0.586340136778654 -0.586340136778654 0.114002446582935
3056 -0.586340136778654 -0.586340136778654 -0.240979589664039 0.114002446582935
3057 -0.586340136778654 -0.240979589664039 -0.586340136778654 0.114002446582935
3058 -0.240979589664039 -0.586340136778654 -0.586340136778654 0.114002446582935
3059 -0.835792823378907 -0.835792823378907 -0.835792823378907 0.015736266505071
3060 -0.835792823378907 -0.835792823378907 0.507378470136720 0.015736266505071
3061 -0.835792823378907 0.507378470136720 -0.835792823378907 0.015736266505071
3062 0.507378470136720 -0.835792823378907 -0.835792823378907 0.015736266505071
3063 -0.988436098989604 -0.988436098989604 -0.988436098989604 0.001358672872743
3064 -0.988436098989604 -0.988436098989604 0.965308296968812 0.001358672872743
3065 -0.988436098989604 0.965308296968812 -0.988436098989604 0.001358672872743
3066 0.965308296968812 -0.988436098989604 -0.988436098989604 0.001358672872743
3067 -0.898934519962212 -0.898934519962212 -0.101065480037788 0.036637470595738
3068 -0.898934519962212 -0.101065480037788 -0.898934519962212 0.036637470595738
3069 -0.101065480037788 -0.898934519962212 -0.898934519962212 0.036637470595738
3070 -0.898934519962212 -0.101065480037788 -0.101065480037788 0.036637470595738
3071 -0.101065480037788 -0.898934519962212 -0.101065480037788 0.036637470595738
3072 -0.101065480037788 -0.101065480037788 -0.898934519962212 0.036637470595738
3073 -0.541866927766378 -0.541866927766378 -0.928720834422932 0.045635886469455
3074 -0.541866927766378 -0.928720834422932 -0.541866927766378 0.045635886469455
3075 -0.541866927766378 -0.541866927766378 0.012454689955687 0.045635886469455
3076 -0.541866927766378 0.012454689955687 -0.541866927766378 0.045635886469455
3077 -0.541866927766378 -0.928720834422932 0.012454689955687 0.045635886469455
3078 -0.541866927766378 0.012454689955687 -0.928720834422932 0.045635886469455
3079 -0.928720834422932 -0.541866927766378 -0.541866927766378 0.045635886469455
3080 -0.928720834422932 -0.541866927766378 0.012454689955687 0.045635886469455
3081 -0.928720834422932 0.012454689955687 -0.541866927766378 0.045635886469455
3082 0.012454689955687 -0.541866927766378 -0.928720834422932 0.045635886469455
3083 0.012454689955687 -0.541866927766378 -0.541866927766378 0.045635886469455
3084 0.012454689955687 -0.928720834422932 -0.541866927766378 0.045635886469455
3085 -0.926784500893605 -0.926784500893605 -0.619027916130733 0.017124153129297
3086 -0.926784500893605 -0.619027916130733 -0.926784500893605 0.017124153129297
3087 -0.926784500893605 -0.926784500893605 0.472596917917943 0.017124153129297
3088 -0.926784500893605 0.472596917917943 -0.926784500893605 0.017124153129297
3089 -0.926784500893605 -0.619027916130733 0.472596917917943 0.017124153129297
3090 -0.926784500893605 0.472596917917943 -0.619027916130733 0.017124153129297
3091 -0.619027916130733 -0.926784500893605 -0.926784500893605 0.017124153129297
3092 -0.619027916130733 -0.926784500893605 0.472596917917943 0.017124153129297
3093 -0.619027916130733 0.472596917917943 -0.926784500893605 0.017124153129297
3094 0.472596917917943 -0.926784500893605 -0.619027916130733 0.017124153129297
3095 0.472596917917943 -0.926784500893605 -0.926784500893605 0.017124153129297
3096 0.472596917917943 -0.619027916130733 -0.926784500893605 0.017124153129297
3097 Gauss quadrature constants for the reference tetrahedron order p=8
3098
3099 53
3100 -0.500000000000000 -0.500000000000000 -0.500000000000000 -1.102392306608869
3101 -0.903297922900526 -0.903297922900526 -0.903297922900526 0.014922692552682
3102 -0.903297922900526 -0.903297922900526 0.709893768701580 0.014922692552682
3103 -0.903297922900526 0.709893768701580 -0.903297922900526 0.014922692552682
3104 0.709893768701580 -0.903297922900526 -0.903297922900526 0.014922692552682
3105 -0.350841439764235 -0.350841439764235 -0.350841439764235 0.034475391755947
3106 -0.350841439764235 -0.350841439764235 -0.947475680707294 0.034475391755947
3107 -0.350841439764235 -0.947475680707294 -0.350841439764235 0.034475391755947
3108 -0.947475680707294 -0.350841439764235 -0.350841439764235 0.034475391755947
3109 -0.770766919552010 -0.770766919552010 -0.770766919552010 -0.721478131849612
3110 -0.770766919552010 -0.770766919552010 0.312300758656029 -0.721478131849612
3111 -0.770766919552010 0.312300758656029 -0.770766919552010 -0.721478131849612
3112 0.312300758656029 -0.770766919552010 -0.770766919552010 -0.721478131849612
3113 -0.549020096176972 -0.549020096176972 -0.549020096176972 0.357380609620092
3114 -0.549020096176972 -0.549020096176972 -0.352939711469084 0.357380609620092
3115 -0.549020096176972 -0.352939711469084 -0.549020096176972 0.357380609620092
3116 -0.352939711469084 -0.549020096176972 -0.549020096176972 0.357380609620092
3117 -0.736744381506260 -0.736744381506260 -0.832670596765630 0.277603247076406
3118 -0.736744381506260 -0.832670596765630 -0.736744381506260 0.277603247076406
3119 -0.736744381506260 -0.736744381506260 0.306159359778151 0.277603247076406
3120 -0.736744381506260 0.306159359778151 -0.736744381506260 0.277603247076406
3121 -0.736744381506260 -0.832670596765630 0.306159359778151 0.277603247076406
3122 -0.736744381506260 0.306159359778151 -0.832670596765630 0.277603247076406
3123 -0.832670596765630 -0.736744381506260 -0.736744381506260 0.277603247076406
3124 -0.832670596765630 -0.736744381506260 0.306159359778151 0.277603247076406
3125 -0.832670596765630 0.306159359778151 -0.736744381506260 0.277603247076406
3126 0.306159359778151 -0.736744381506260 -0.832670596765630 0.277603247076406
3127 0.306159359778151 -0.736744381506260 -0.736744381506260 0.277603247076406
3128 0.306159359778151 -0.832670596765630 -0.736744381506260 0.277603247076406
3129 -0.132097077177186 -0.132097077177186 -0.784460280901143 0.026820671221285
3130 -0.132097077177186 -0.784460280901143 -0.132097077177186 0.026820671221285
3131 -0.132097077177186 -0.132097077177186 -0.951345564744484 0.026820671221285
3132 -0.132097077177186 -0.951345564744484 -0.132097077177186 0.026820671221285
3133 -0.132097077177186 -0.784460280901143 -0.951345564744484 0.026820671221285
3134 -0.132097077177186 -0.951345564744484 -0.784460280901143 0.026820671221285
3135 -0.784460280901143 -0.132097077177186 -0.132097077177186 0.026820671221285
3136 -0.784460280901143 -0.132097077177186 -0.951345564744484 0.026820671221285
3137 -0.784460280901143 -0.951345564744484 -0.132097077177186 0.026820671221285
3138 -0.951345564744484 -0.132097077177186 -0.784460280901143 0.026820671221285
3139 -0.951345564744484 -0.132097077177186 -0.132097077177186 0.026820671221285
3140 -0.951345564744484 -0.784460280901143 -0.132097077177186 0.026820671221285
3141 -1.002752554636276 -1.002752554636276 -0.446893054726385 0.003453031004456
3142 -1.002752554636276 -0.446893054726385 -1.002752554636276 0.003453031004456
3143 -1.002752554636276 -1.002752554636276 0.452398163998938 0.003453031004456
3144 -1.002752554636276 0.452398163998938 -1.002752554636276 0.003453031004456
3145 -1.002752554636276 -0.446893054726385 0.452398163998938 0.003453031004456
3146 -1.002752554636276 0.452398163998938 -0.446893054726385 0.003453031004456
3147 -0.446893054726385 -1.002752554636276 -1.002752554636276 0.003453031004456
3148 -0.446893054726385 -1.002752554636276 0.452398163998938 0.003453031004456
3149 -0.446893054726385 0.452398163998938 -1.002752554636276 0.003453031004456
3150 0.452398163998938 -1.002752554636276 -0.446893054726385 0.003453031004456
3151 0.452398163998938 -1.002752554636276 -1.002752554636276 0.003453031004456
3152 0.452398163998938 -0.446893054726385 -1.002752554636276 0.003453031004456
3153 Gauss quadrature constants for the reference tetrahedron order p=9
3154
3155 126
3156 -0.857142857142857 -0.857142857142857 0.571428571428571 0.362902592520648
3157 -0.857142857142857 -0.571428571428571 0.285714285714286 0.362902592520648
3158 -0.857142857142857 -0.285714285714286 0.000000000000000 0.362902592520648
3159 -0.857142857142857 0.000000000000000 -0.285714285714286 0.362902592520648
3160 -0.857142857142857 0.285714285714286 -0.571428571428571 0.362902592520648
3161 -0.857142857142857 0.571428571428571 -0.857142857142857 0.362902592520648
3162 -0.571428571428571 -0.857142857142857 0.285714285714286 0.362902592520648
3163 -0.571428571428571 -0.571428571428571 0.000000000000000 0.362902592520648
3164 -0.571428571428571 -0.285714285714286 -0.285714285714286 0.362902592520648
3165 -0.571428571428571 0.000000000000000 -0.571428571428571 0.362902592520648
3166 -0.571428571428571 0.285714285714286 -0.857142857142857 0.362902592520648
3167 -0.285714285714286 -0.857142857142857 0.000000000000000 0.362902592520648
3168 -0.285714285714286 -0.571428571428571 -0.285714285714286 0.362902592520648
3169 -0.285714285714286 -0.285714285714286 -0.571428571428571 0.362902592520648
3170 -0.285714285714286 0.000000000000000 -0.857142857142857 0.362902592520648
3171 0.000000000000000 -0.857142857142857 -0.285714285714286 0.362902592520648
3172 0.000000000000000 -0.571428571428571 -0.571428571428571 0.362902592520648
3173 0.000000000000000 -0.285714285714286 -0.857142857142857 0.362902592520648
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3746 -0.285714285714286 -0.571428571428571 -0.857142857142857 1.815269009670992
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3781 -0.166666666666667 -0.500000000000000 -0.833333333333333 -0.958821749678893
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3783 -0.833333333333333 -0.833333333333333 -0.166666666666667 -0.958821749678893
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3795 -0.800000000000000 0.000000000000000 -0.400000000000000 0.233372916620478
3796 -0.800000000000000 0.400000000000000 -0.800000000000000 0.233372916620478
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3798 -0.400000000000000 -0.400000000000000 -0.400000000000000 0.233372916620478
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3800 0.000000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3801 0.000000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
3802 0.400000000000000 -0.800000000000000 -0.800000000000000 0.233372916620478
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3806 -0.400000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3807 -0.400000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
3808 0.000000000000000 -0.800000000000000 -0.800000000000000 0.233372916620478
3809 -0.800000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3810 -0.800000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
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3813 -0.750000000000000 -0.750000000000000 0.250000000000000 -0.022991022694726
3814 -0.750000000000000 -0.250000000000000 -0.250000000000000 -0.022991022694726
3815 -0.750000000000000 0.250000000000000 -0.750000000000000 -0.022991022694726
3816 -0.250000000000000 -0.750000000000000 -0.250000000000000 -0.022991022694726
3817 -0.250000000000000 -0.250000000000000 -0.750000000000000 -0.022991022694726
3818 0.250000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3819 -0.750000000000000 -0.750000000000000 -0.250000000000000 -0.022991022694726
3820 -0.750000000000000 -0.250000000000000 -0.750000000000000 -0.022991022694726
3821 -0.250000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3822 -0.750000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3823 -0.666666666666667 -0.666666666666667 0.000000000000000 0.000665685876623
3824 -0.666666666666667 0.000000000000000 -0.666666666666667 0.000665685876623
3825 0.000000000000000 -0.666666666666667 -0.666666666666667 0.000665685876623
3826 -0.666666666666667 -0.666666666666667 -0.666666666666667 0.000665685876623
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3828 Gauss quadrature constants for the reference tetrahedron order p=15
3829
3830 495
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3849 -0.500000000000000 -0.700000000000000 0.100000000000000 0.657650819729946
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3864 -0.100000000000000 -0.300000000000000 -0.700000000000000 0.657650819729946
3865 -0.100000000000000 -0.100000000000000 -0.900000000000000 0.657650819729946
3866 0.100000000000000 -0.900000000000000 -0.300000000000000 0.657650819729946
3867 0.100000000000000 -0.700000000000000 -0.500000000000000 0.657650819729946
3868 0.100000000000000 -0.500000000000000 -0.700000000000000 0.657650819729946
3869 0.100000000000000 -0.300000000000000 -0.900000000000000 0.657650819729946
3870 0.300000000000000 -0.900000000000000 -0.500000000000000 0.657650819729946
3871 0.300000000000000 -0.700000000000000 -0.700000000000000 0.657650819729946
3872 0.300000000000000 -0.500000000000000 -0.900000000000000 0.657650819729946
3873 0.500000000000000 -0.900000000000000 -0.700000000000000 0.657650819729946
3874 0.500000000000000 -0.700000000000000 -0.900000000000000 0.657650819729946
3875 0.700000000000000 -0.900000000000000 -0.900000000000000 0.657650819729946
3876 -0.900000000000000 -0.900000000000000 0.500000000000000 0.657650819729946
3877 -0.900000000000000 -0.700000000000000 0.300000000000000 0.657650819729946
3878 -0.900000000000000 -0.500000000000000 0.100000000000000 0.657650819729946
3879 -0.900000000000000 -0.300000000000000 -0.100000000000000 0.657650819729946
3880 -0.900000000000000 -0.100000000000000 -0.300000000000000 0.657650819729946
3881 -0.900000000000000 0.100000000000000 -0.500000000000000 0.657650819729946
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4232 -0.285714285714286 -0.285714285714286 -0.857142857142857 -1.744081989683894
4233 0.000000000000000 -0.857142857142857 -0.571428571428571 -1.744081989683894
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4239 -0.857142857142857 0.000000000000000 -0.857142857142857 -1.744081989683894
4240 -0.571428571428571 -0.857142857142857 -0.285714285714286 -1.744081989683894
4241 -0.571428571428571 -0.571428571428571 -0.571428571428571 -1.744081989683894
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4246 -0.857142857142857 -0.857142857142857 -0.285714285714286 -1.744081989683894
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4256 -0.833333333333333 -0.833333333333333 0.500000000000000 0.539337234194377
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4280 0.166666666666667 -0.833333333333333 -0.833333333333333 0.539337234194377
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4286 -0.166666666666667 -0.833333333333333 -0.833333333333333 0.539337234194377
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4291 -0.800000000000000 -0.800000000000000 0.400000000000000 -0.077790972206826
4292 -0.800000000000000 -0.400000000000000 0.000000000000000 -0.077790972206826
4293 -0.800000000000000 0.000000000000000 -0.400000000000000 -0.077790972206826
4294 -0.800000000000000 0.400000000000000 -0.800000000000000 -0.077790972206826
4295 -0.400000000000000 -0.800000000000000 0.000000000000000 -0.077790972206826
4296 -0.400000000000000 -0.400000000000000 -0.400000000000000 -0.077790972206826
4297 -0.400000000000000 0.000000000000000 -0.800000000000000 -0.077790972206826
4298 0.000000000000000 -0.800000000000000 -0.400000000000000 -0.077790972206826
4299 0.000000000000000 -0.400000000000000 -0.800000000000000 -0.077790972206826
4300 0.400000000000000 -0.800000000000000 -0.800000000000000 -0.077790972206826
4301 -0.800000000000000 -0.800000000000000 0.000000000000000 -0.077790972206826
4302 -0.800000000000000 -0.400000000000000 -0.400000000000000 -0.077790972206826
4303 -0.800000000000000 0.000000000000000 -0.800000000000000 -0.077790972206826
4304 -0.400000000000000 -0.800000000000000 -0.400000000000000 -0.077790972206826
4305 -0.400000000000000 -0.400000000000000 -0.800000000000000 -0.077790972206826
4306 0.000000000000000 -0.800000000000000 -0.800000000000000 -0.077790972206826
4307 -0.800000000000000 -0.800000000000000 -0.400000000000000 -0.077790972206826
4308 -0.800000000000000 -0.400000000000000 -0.800000000000000 -0.077790972206826
4309 -0.400000000000000 -0.800000000000000 -0.800000000000000 -0.077790972206826
4310 -0.800000000000000 -0.800000000000000 -0.800000000000000 -0.077790972206826
4311 -0.750000000000000 -0.750000000000000 0.250000000000000 0.004379242418043
4312 -0.750000000000000 -0.250000000000000 -0.250000000000000 0.004379242418043
4313 -0.750000000000000 0.250000000000000 -0.750000000000000 0.004379242418043
4314 -0.250000000000000 -0.750000000000000 -0.250000000000000 0.004379242418043
4315 -0.250000000000000 -0.250000000000000 -0.750000000000000 0.004379242418043
4316 0.250000000000000 -0.750000000000000 -0.750000000000000 0.004379242418043
4317 -0.750000000000000 -0.750000000000000 -0.250000000000000 0.004379242418043
4318 -0.750000000000000 -0.250000000000000 -0.750000000000000 0.004379242418043
4319 -0.250000000000000 -0.750000000000000 -0.750000000000000 0.004379242418043
4320 -0.750000000000000 -0.750000000000000 -0.750000000000000 0.004379242418043
4321 -0.666666666666667 -0.666666666666667 0.000000000000000 -0.000065837064721
4322 -0.666666666666667 0.000000000000000 -0.666666666666667 -0.000065837064721
4323 0.000000000000000 -0.666666666666667 -0.666666666666667 -0.000065837064721
4324 -0.666666666666667 -0.666666666666667 -0.666666666666667 -0.000065837064721
4325 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.000000108585647
4326 Gauss quadrature constants for the reference tetrahedron order p=17
4327
4328 715
4329 -0.909090909090909 -0.909090909090909 0.727272727272727 0.870591471154497
4330 -0.909090909090909 -0.727272727272727 0.545454545454545 0.870591471154497
4331 -0.909090909090909 -0.545454545454545 0.363636363636364 0.870591471154497
4332 -0.909090909090909 -0.363636363636364 0.181818181818182 0.870591471154497
4333 -0.909090909090909 -0.181818181818182 0.000000000000000 0.870591471154497
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4335 -0.909090909090909 0.181818181818182 -0.363636363636364 0.870591471154497
4336 -0.909090909090909 0.363636363636364 -0.545454545454545 0.870591471154497
4337 -0.909090909090909 0.545454545454545 -0.727272727272727 0.870591471154497
4338 -0.909090909090909 0.727272727272727 -0.909090909090909 0.870591471154497
4339 -0.727272727272727 -0.909090909090909 0.545454545454545 0.870591471154497
4340 -0.727272727272727 -0.727272727272727 0.363636363636364 0.870591471154497
4341 -0.727272727272727 -0.545454545454545 0.181818181818182 0.870591471154497
4342 -0.727272727272727 -0.363636363636364 0.000000000000000 0.870591471154497
4343 -0.727272727272727 -0.181818181818182 -0.181818181818182 0.870591471154497
4344 -0.727272727272727 0.000000000000000 -0.363636363636364 0.870591471154497
4345 -0.727272727272727 0.181818181818182 -0.545454545454545 0.870591471154497
4346 -0.727272727272727 0.363636363636364 -0.727272727272727 0.870591471154497
4347 -0.727272727272727 0.545454545454545 -0.909090909090909 0.870591471154497
4348 -0.545454545454545 -0.909090909090909 0.363636363636364 0.870591471154497
4349 -0.545454545454545 -0.727272727272727 0.181818181818182 0.870591471154497
4350 -0.545454545454545 -0.545454545454545 0.000000000000000 0.870591471154497
4351 -0.545454545454545 -0.363636363636364 -0.181818181818182 0.870591471154497
4352 -0.545454545454545 -0.181818181818182 -0.363636363636364 0.870591471154497
4353 -0.545454545454545 0.000000000000000 -0.545454545454545 0.870591471154497
4354 -0.545454545454545 0.181818181818182 -0.727272727272727 0.870591471154497
4355 -0.545454545454545 0.363636363636364 -0.909090909090909 0.870591471154497
4356 -0.363636363636364 -0.909090909090909 0.181818181818182 0.870591471154497
4357 -0.363636363636364 -0.727272727272727 0.000000000000000 0.870591471154497
4358 -0.363636363636364 -0.545454545454545 -0.181818181818182 0.870591471154497
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5043 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.000000003712330
5044 Gauss quadrature constants for the reference tetrahedron order p=19
5045
5046 1001
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5105 0.250000000000000 -0.583333333333333 -0.750000000000000 1.186370883531411
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5948 -0.571428571428571 -0.857142857142857 0.000000000000000 -0.612213575618572
5949 -0.571428571428571 -0.571428571428571 -0.285714285714286 -0.612213575618572
5950 -0.571428571428571 -0.285714285714286 -0.571428571428571 -0.612213575618572
5951 -0.571428571428571 0.000000000000000 -0.857142857142857 -0.612213575618572
5952 -0.285714285714286 -0.857142857142857 -0.285714285714286 -0.612213575618572
5953 -0.285714285714286 -0.571428571428571 -0.571428571428571 -0.612213575618572
5954 -0.285714285714286 -0.285714285714286 -0.857142857142857 -0.612213575618572
5955 0.000000000000000 -0.857142857142857 -0.571428571428571 -0.612213575618572
5956 0.000000000000000 -0.571428571428571 -0.857142857142857 -0.612213575618572
5957 0.285714285714286 -0.857142857142857 -0.857142857142857 -0.612213575618572
5958 -0.857142857142857 -0.857142857142857 0.000000000000000 -0.612213575618572
5959 -0.857142857142857 -0.571428571428571 -0.285714285714286 -0.612213575618572
5960 -0.857142857142857 -0.285714285714286 -0.571428571428571 -0.612213575618572
5961 -0.857142857142857 0.000000000000000 -0.857142857142857 -0.612213575618572
5962 -0.571428571428571 -0.857142857142857 -0.285714285714286 -0.612213575618572
5963 -0.571428571428571 -0.571428571428571 -0.571428571428571 -0.612213575618572
5964 -0.571428571428571 -0.285714285714286 -0.857142857142857 -0.612213575618572
5965 -0.285714285714286 -0.857142857142857 -0.571428571428571 -0.612213575618572
5966 -0.285714285714286 -0.571428571428571 -0.857142857142857 -0.612213575618572
5967 0.000000000000000 -0.857142857142857 -0.857142857142857 -0.612213575618572
5968 -0.857142857142857 -0.857142857142857 -0.285714285714286 -0.612213575618572
5969 -0.857142857142857 -0.571428571428571 -0.571428571428571 -0.612213575618572
5970 -0.857142857142857 -0.285714285714286 -0.857142857142857 -0.612213575618572
5971 -0.571428571428571 -0.857142857142857 -0.571428571428571 -0.612213575618572
5972 -0.571428571428571 -0.571428571428571 -0.857142857142857 -0.612213575618572
5973 -0.285714285714286 -0.857142857142857 -0.857142857142857 -0.612213575618572
5974 -0.857142857142857 -0.857142857142857 -0.571428571428571 -0.612213575618572
5975 -0.857142857142857 -0.571428571428571 -0.857142857142857 -0.612213575618572
5976 -0.571428571428571 -0.857142857142857 -0.857142857142857 -0.612213575618572
5977 -0.857142857142857 -0.857142857142857 -0.857142857142857 -0.612213575618572
5978 -0.833333333333333 -0.833333333333333 0.500000000000000 0.076141727180383
5979 -0.833333333333333 -0.500000000000000 0.166666666666667 0.076141727180383
5980 -0.833333333333333 -0.166666666666667 -0.166666666666667 0.076141727180383
5981 -0.833333333333333 0.166666666666667 -0.500000000000000 0.076141727180383
5982 -0.833333333333333 0.500000000000000 -0.833333333333333 0.076141727180383
5983 -0.500000000000000 -0.833333333333333 0.166666666666667 0.076141727180383
5984 -0.500000000000000 -0.500000000000000 -0.166666666666667 0.076141727180383
5985 -0.500000000000000 -0.166666666666667 -0.500000000000000 0.076141727180383
5986 -0.500000000000000 0.166666666666667 -0.833333333333333 0.076141727180383
5987 -0.166666666666667 -0.833333333333333 -0.166666666666667 0.076141727180383
5988 -0.166666666666667 -0.500000000000000 -0.500000000000000 0.076141727180383
5989 -0.166666666666667 -0.166666666666667 -0.833333333333333 0.076141727180383
5990 0.166666666666667 -0.833333333333333 -0.500000000000000 0.076141727180383
5991 0.166666666666667 -0.500000000000000 -0.833333333333333 0.076141727180383
5992 0.500000000000000 -0.833333333333333 -0.833333333333333 0.076141727180383
5993 -0.833333333333333 -0.833333333333333 0.166666666666667 0.076141727180383
5994 -0.833333333333333 -0.500000000000000 -0.166666666666667 0.076141727180383
5995 -0.833333333333333 -0.166666666666667 -0.500000000000000 0.076141727180383
5996 -0.833333333333333 0.166666666666667 -0.833333333333333 0.076141727180383
5997 -0.500000000000000 -0.833333333333333 -0.166666666666667 0.076141727180383
5998 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.076141727180383
5999 -0.500000000000000 -0.166666666666667 -0.833333333333333 0.076141727180383
6000 -0.166666666666667 -0.833333333333333 -0.500000000000000 0.076141727180383
6001 -0.166666666666667 -0.500000000000000 -0.833333333333333 0.076141727180383
6002 0.166666666666667 -0.833333333333333 -0.833333333333333 0.076141727180383
6003 -0.833333333333333 -0.833333333333333 -0.166666666666667 0.076141727180383
6004 -0.833333333333333 -0.500000000000000 -0.500000000000000 0.076141727180383
6005 -0.833333333333333 -0.166666666666667 -0.833333333333333 0.076141727180383
6006 -0.500000000000000 -0.833333333333333 -0.500000000000000 0.076141727180383
6007 -0.500000000000000 -0.500000000000000 -0.833333333333333 0.076141727180383
6008 -0.166666666666667 -0.833333333333333 -0.833333333333333 0.076141727180383
6009 -0.833333333333333 -0.833333333333333 -0.500000000000000 0.076141727180383
6010 -0.833333333333333 -0.500000000000000 -0.833333333333333 0.076141727180383
6011 -0.500000000000000 -0.833333333333333 -0.833333333333333 0.076141727180383
6012 -0.833333333333333 -0.833333333333333 -0.833333333333333 0.076141727180383
6013 -0.800000000000000 -0.800000000000000 0.400000000000000 -0.004255896151021
6014 -0.800000000000000 -0.400000000000000 0.000000000000000 -0.004255896151021
6015 -0.800000000000000 0.000000000000000 -0.400000000000000 -0.004255896151021
6016 -0.800000000000000 0.400000000000000 -0.800000000000000 -0.004255896151021
6017 -0.400000000000000 -0.800000000000000 0.000000000000000 -0.004255896151021
6018 -0.400000000000000 -0.400000000000000 -0.400000000000000 -0.004255896151021
6019 -0.400000000000000 0.000000000000000 -0.800000000000000 -0.004255896151021
6020 0.000000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6021 0.000000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6022 0.400000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6023 -0.800000000000000 -0.800000000000000 0.000000000000000 -0.004255896151021
6024 -0.800000000000000 -0.400000000000000 -0.400000000000000 -0.004255896151021
6025 -0.800000000000000 0.000000000000000 -0.800000000000000 -0.004255896151021
6026 -0.400000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6027 -0.400000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6028 0.000000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6029 -0.800000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6030 -0.800000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6031 -0.400000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6032 -0.800000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6033 -0.750000000000000 -0.750000000000000 0.250000000000000 0.000083414141296
6034 -0.750000000000000 -0.250000000000000 -0.250000000000000 0.000083414141296
6035 -0.750000000000000 0.250000000000000 -0.750000000000000 0.000083414141296
6036 -0.250000000000000 -0.750000000000000 -0.250000000000000 0.000083414141296
6037 -0.250000000000000 -0.250000000000000 -0.750000000000000 0.000083414141296
6038 0.250000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6039 -0.750000000000000 -0.750000000000000 -0.250000000000000 0.000083414141296
6040 -0.750000000000000 -0.250000000000000 -0.750000000000000 0.000083414141296
6041 -0.250000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6042 -0.750000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6043 -0.666666666666667 -0.666666666666667 0.000000000000000 -0.000000352698561
6044 -0.666666666666667 0.000000000000000 -0.666666666666667 -0.000000352698561
6045 0.000000000000000 -0.666666666666667 -0.666666666666667 -0.000000352698561
6046 -0.666666666666667 -0.666666666666667 -0.666666666666667 -0.000000352698561
6047 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.000000000106067
6048 Gauss quadrature constants for the reference tetrahedron order p=21
6049 """
6050
6051
6052
6053
6054 newton_cotes_table = """\
6055 2
6056 1 1
6057 -1 1
6058 Closed Newton-Cotes quadrature constants order n=1
6059
6060 3
6061 1 1/3
6062 0 4/3
6063 -1 1/3
6064 Closed Newton-Cotes quadrature constants order n=2
6065
6066 4
6067 1 1/4
6068 1/3 3/4
6069 -1/3 3/4
6070 -1 1/4
6071 Closed Newton-Cotes quadrature constants order n=3
6072
6073 5
6074 1 7/45
6075 1/2 32/45
6076 0 12/45
6077 -1/2 32/45
6078 -1 7/45
6079 Closed Newton-Cotes quadrature constants order n=4
6080
6081 6
6082 1 19/144
6083 3/5 75/144
6084 1/5 50/144
6085 -1/5 50/144
6086 -3/5 75/144
6087 -1 19/144
6088 Closed Newton-Cotes quadrature constants order n=5
6089
6090 7
6091 1 41/420
6092 2/3 216/420
6093 1/3 27/420
6094 0 272/420
6095 -1/3 27/420
6096 -2/3 216/420
6097 -1 41/420
6098 Closed Newton-Cotes quadrature constants order n=6
6099
6100 8
6101 1 751/8640
6102 5/7 3577/8640
6103 3/7 1323/8640
6104 1/7 2989/8640
6105 -1/7 2989/8640
6106 -3/7 1323/8640
6107 -5/7 3577/8640
6108 -1 751/8640
6109 Closed Newton-Cotes quadrature constants order n=7
6110 """
6111
6112
6113 chebyshev_table = """\
6114 2
6115 0.5773502691896257645091488 1
6116 -0.5773502691896257645091488 1
6117 Chebyshev quadrature constants order n+1=3
6118
6119 3
6120 0.7071067811865475244008444 2/3
6121 0.0000000000000000000000000 2/3
6122 -0.7071067811865475244008444 2/3
6123 Chebyshev quadrature constants order n+1=4
6124
6125 4
6126 0.7946544722917661229555309 1/2
6127 0.1875924740850798998601393 1/2
6128 -0.1875924740850798998601393 1/2
6129 -0.7946544722917661229555309 1/2
6130 Chebyshev quadrature constants order n+1=5
6131
6132 5
6133 0.8324974870009818758925836 2/5
6134 0.3745414095535810655860444 2/5
6135 0.0000000000000000000000000 2/5
6136 -0.3745414095535810655860444 2/5
6137 -0.8324974870009818758925836 2/5
6138 Chebyshev quadrature constants order n+1=6
6139
6140 6
6141 0.8662468181078205913835981 1/3
6142 0.4225186537611115291185464 1/3
6143 0.2666354015167047203315346 1/3
6144 -0.2666354015167047203315346 1/3
6145 -0.4225186537611115291185464 1/3
6146 -0.8662468181078205913835981 1/3
6147 Chebyshev quadrature constants order n+1=7
6148
6149 7
6150 0.8838617007580490357042241 2/7
6151 0.5296567752851568113850475 2/7
6152 0.3239118105199076375196731 2/7
6153 0.0000000000000000000000000 2/7
6154 -0.3239118105199076375196731 2/7
6155 -0.5296567752851568113850475 2/7
6156 -0.8838617007580490357042241 2/7
6157 Chebyshev quadrature constants order n+1=8
6158
6159 9
6160 0.9115893077284344736649486 2/9
6161 0.6010186553802380714281279 2/9
6162 0.5287617830578799932601816 2/9
6163 0.1679061842148039430680319 2/9
6164 0.0000000000000000000000000 2/9
6165 -0.1679061842148039430680319 2/9
6166 -0.5287617830578799932601816 2/9
6167 -0.6010186553802380714281279 2/9
6168 -0.9115893077284344736649486 2/9
6169 Chebyshev quadrature constants order n+1=10
6170 """
6171
6172
6173 lobatto_table = """\
6174 3
6175 1.0000000000000000000000000 0.3333333333333333333333333
6176 0.0000000000000000000000000 1.3333333333333333333333333
6177 -1.0000000000000000000000000 0.3333333333333333333333333
6178 Lobatto (Radau) quadrature constants order 2n-3=3
6179
6180 4
6181 1.0000000000000000000000000 0.1666666666666666666666667
6182 0.4472135954999579392818347 0.8333333333333333333333333
6183 -0.4472135954999579392818347 0.8333333333333333333333333
6184 -1.0000000000000000000000000 0.1666666666666666666666667
6185 Lobatto (Radau) quadrature constants order 2n-3=5
6186
6187 5
6188 1.0000000000000000000000000 0.1000000000000000000000000
6189 0.6546536707079771437982925 0.5444444444444444444444444
6190 0.0000000000000000000000000 0.7111111111111111111111111
6191 -0.6546536707079771437982925 0.5444444444444444444444444
6192 -1.0000000000000000000000000 0.1000000000000000000000000
6193 Lobatto (Radau) quadrature constants order 2n-3=7
6194
6195 6
6196 1.0000000000000000000000000 0.0666666666666666666666667
6197 0.7650553239294646928510030 0.3784749562978469803166128
6198 0.2852315164806450963141510 0.5548583770354863530167205
6199 -0.2852315164806450963141510 0.5548583770354863530167205
6200 -0.7650553239294646928510030 0.3784749562978469803166128
6201 -1.0000000000000000000000000 0.0666666666666666666666667
6202 Lobatto (Radau) quadrature constants order 2n-3=9
6203
6204 7
6205 1.0000000000000000000000000 0.0476190476190476190476190
6206 0.8302238962785669298720322 0.2768260473615659480107004
6207 0.4688487934707142138037719 0.4317453812098626234178710
6208 0.0000000000000000000000000 0.4876190476190476190476190
6209 -0.4688487934707142138037719 0.4317453812098626234178710
6210 -0.8302238962785669298720322 0.2768260473615659480107004
6211 -1.0000000000000000000000000 0.0476190476190476190476190
6212 Lobatto (Radau) quadrature constants order 2n-3=11
6213
6214 8
6215 1.0000000000000000000000000 0.0357142857142857142857143
6216 0.8717401485096066153374457 0.2107042271435060393829921
6217 0.5917001814331423021445107 0.3411226924835043647642407
6218 0.2092992179024788687686573 0.4124587946587038815670530
6219 -0.2092992179024788687686573 0.4124587946587038815670530
6220 -0.5917001814331423021445107 0.3411226924835043647642407
6221 -0.8717401485096066153374457 0.2107042271435060393829921
6222 -1.0000000000000000000000000 0.0357142857142857142857143
6223 Lobatto (Radau) quadrature constants order 2n-3=13
6224
6225 9
6226 1.0000000000000000000000000 0.0277777777777777777777778
6227 0.8997579954114601573123452 0.1654953615608055250463397
6228 0.6771862795107377534458854 0.2745387125001617352807056
6229 0.3631174638261781587107521 0.3464285109730463451151315
6230 0.0000000000000000000000000 0.3715192743764172335600907
6231 -0.3631174638261781587107521 0.3464285109730463451151315
6232 -0.6771862795107377534458854 0.2745387125001617352807056
6233 -0.8997579954114601573123452 0.1654953615608055250463397
6234 -1.0000000000000000000000000 0.0277777777777777777777778
6235 Lobatto (Radau) quadrature constants order 2n-3=15
6236
6237 10
6238 1.0000000000000000000000000 0.0222222222222222222222222
6239 0.9195339081664588138289327 0.1333059908510701111262272
6240 0.7387738651055050750031062 0.2248893420631264521194578
6241 0.4779249498104444956611751 0.2920426836796837578755823
6242 0.1652789576663870246262198 0.3275397611838974566565105
6243 -0.1652789576663870246262198 0.3275397611838974566565105
6244 -0.4779249498104444956611751 0.2920426836796837578755823
6245 -0.7387738651055050750031062 0.2248893420631264521194578
6246 -0.9195339081664588138289327 0.1333059908510701111262272
6247 -1.0000000000000000000000000 0.0222222222222222222222222
6248 Lobatto (Radau) quadrature constants order 2n-3=17
6249
6250 11
6251 1.0000000000000000000000000 0.0181818181818181818181818
6252 0.9340014304080591343322741 0.1096122732669948644614034
6253 0.7844834736631444186224178 0.1871698817803052041081415
6254 0.5652353269962050064709640 0.2480481042640283140400849
6255 0.2957581355869393914319115 0.2868791247790080886792224
6256 0.0000000000000000000000000 0.3002175954556906937859319
6257 -0.2957581355869393914319115 0.2868791247790080886792224
6258 -0.5652353269962050064709640 0.2480481042640283140400849
6259 -0.7844834736631444186224178 0.1871698817803052041081415
6260 -0.9340014304080591343322741 0.1096122732669948644614034
6261 -1.0000000000000000000000000 0.0181818181818181818181818
6262 Lobatto (Radau) quadrature constants order 2n-3=19
6263
6264 12
6265 1.0000000000000000000000000 0.0151515151515151515151515
6266 0.9448992722228822234075801 0.0916845174131961306683426
6267 0.8192793216440066783486416 0.1579747055643701151646710
6268 0.6328761530318606776624049 0.2125084177610211453583021
6269 0.3995309409653489322643498 0.2512756031992012802932444
6270 0.1365529328549275548640619 0.2714052409106961770002883
6271 -0.1365529328549275548640619 0.2714052409106961770002883
6272 -0.3995309409653489322643498 0.2512756031992012802932444
6273 -0.6328761530318606776624049 0.2125084177610211453583021
6274 -0.8192793216440066783486416 0.1579747055643701151646710
6275 -0.9448992722228822234075801 0.0916845174131961306683426
6276 -1.0000000000000000000000000 0.0151515151515151515151515
6277 Lobatto (Radau) quadrature constants order 2n-3=21
6278 """
6279