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 while 1:
46
47 for r in rules:
48 if r.order == order:
49 return r
50
51 order += 1
52
53 raise RuntimeError("Found no rule for a %s with order %d in family %s" % (polygon, order, family))
54
55
57 """Return list of quadrature rules matching polygon and family."""
58 rules = parse_table_string(polygon, family)
59 rules = scale_table(rules)
60 return rules
61
62
64
65 name = "%s_%s_table" % (family, polygon)
66 tablestring = eval(name)
67
68 nsd = domain2dim[polygon]
69 lines = tablestring.split('\n')
70 rules = []
71 i = 0
72 while i<len(lines):
73 n = int(lines[i])
74 i += 1
75 points = []
76 weights = []
77 for j in range(n):
78 values = lines[i].split()
79 points += [ map(float, values[:nsd]) ]
80 weights += [ float(values[nsd]) ]
81 i += 1
82 comment = lines[i].strip()
83 i += 2
84 order = int(comment.split('=')[-1].split()[-1])
85 rules.append( QuadRule(polygon, nsd, order, points, weights, comment) )
86 return rules
87
88
90 """Scales a set of quadrature rules from [-1,+1]^nsd to [0,1]^nsd."""
91 point_offset = 0.5
92 point_scale = 0.5
93 for rule in rules:
94 ws = point_scale**rule.nsd
95 rule.weights = [ w*ws for w in rule.weights ]
96 rule.points = [ [x*point_scale+point_offset for x in p] for p in rule.points ]
97 return rules
98
99
100
101 gauss_interval_table = """\
102 1
103 0.0000000000000000000000000 2.0000000000000000000000000
104 Gauss quadrature points and weights order 2n-1=1
105
106 2
107 -0.5773502691896257645091488 1.0000000000000000000000000
108 0.5773502691896257645091488 1.0000000000000000000000000
109 Gauss quadrature points and weights order 2n-1=3
110
111 3
112 -0.7745966692414833770358531 0.5555555555555555555555556
113 0.0000000000000000000000000 0.8888888888888888888888889
114 0.7745966692414833770358531 0.5555555555555555555555556
115 Gauss quadrature points and weights order 2n-1=5
116
117 4
118 -0.8611363115940525752239465 0.3478548451374538573730639
119 -0.3399810435848562648026658 0.6521451548625461426269361
120 0.3399810435848562648026658 0.6521451548625461426269361
121 0.8611363115940525752239465 0.3478548451374538573730639
122 Gauss quadrature points and weights order 2n-1=7
123
124 5
125 -0.9061798459386639927976269 0.2369268850561890875142640
126 -0.5384693101056830910363144 0.4786286704993664680412915
127 0.0000000000000000000000000 0.5688888888888888888888889
128 0.5384693101056830910363144 0.4786286704993664680412915
129 0.9061798459386639927976269 0.2369268850561890875142640
130 Gauss quadrature points and weights order 2n-1=9
131
132 6
133 -0.9324695142031520278123016 0.1713244923791703450402961
134 -0.6612093864662645136613996 0.3607615730481386075698335
135 -0.2386191860831969086305017 0.4679139345726910473898703
136 0.2386191860831969086305017 0.4679139345726910473898703
137 0.6612093864662645136613996 0.3607615730481386075698335
138 0.9324695142031520278123016 0.1713244923791703450402961
139 Gauss quadrature points and weights order 2n-1=11
140
141 7
142 -0.9491079123427585245261897 0.1294849661688696932706114
143 -0.7415311855993944398638648 0.2797053914892766679014678
144 -0.4058451513773971669066064 0.3818300505051189449503698
145 0.0000000000000000000000000 0.4179591836734693877551020
146 0.4058451513773971669066064 0.3818300505051189449503698
147 0.7415311855993944398638648 0.2797053914892766679014678
148 0.9491079123427585245261897 0.1294849661688696932706114
149 Gauss quadrature points and weights order 2n-1=13
150
151 8
152 -0.9602898564975362316835609 0.1012285362903762591525314
153 -0.7966664774136267395915539 0.2223810344533744705443560
154 -0.5255324099163289858177390 0.3137066458778872873379622
155 -0.1834346424956498049394761 0.3626837833783619829651504
156 0.1834346424956498049394761 0.3626837833783619829651504
157 0.5255324099163289858177390 0.3137066458778872873379622
158 0.7966664774136267395915539 0.2223810344533744705443560
159 0.9602898564975362316835609 0.1012285362903762591525314
160 Gauss quadrature points and weights order 2n-1=15
161
162 9
163 -0.9681602395076260898355762 0.0812743883615744119718922
164 -0.8360311073266357942994297 0.1806481606948574040584720
165 -0.6133714327005903973087020 0.2606106964029354623187429
166 -0.3242534234038089290385380 0.3123470770400028400686304
167 0.0000000000000000000000000 0.3302393550012597631645251
168 0.3242534234038089290385380 0.3123470770400028400686304
169 0.6133714327005903973087020 0.2606106964029354623187429
170 0.8360311073266357942994298 0.1806481606948574040584720
171 0.9681602395076260898355762 0.0812743883615744119718922
172 Gauss quadrature points and weights order 2n-1=17
173
174 10
175 -0.9739065285171717200779640 0.0666713443086881375935688
176 -0.8650633666889845107320967 0.1494513491505805931457763
177 -0.6794095682990244062343274 0.2190863625159820439955349
178 -0.4333953941292471907992659 0.2692667193099963550912269
179 -0.1488743389816312108848260 0.2955242247147528701738930
180 0.1488743389816312108848260 0.2955242247147528701738930
181 0.4333953941292471907992659 0.2692667193099963550912269
182 0.6794095682990244062343274 0.2190863625159820439955349
183 0.8650633666889845107320967 0.1494513491505805931457763
184 0.9739065285171717200779640 0.0666713443086881375935688
185 Gauss quadrature points and weights order 2n-1=19
186
187 11
188 -0.9782286581460569928039380 0.0556685671161736664827537
189 -0.8870625997680952990751578 0.1255803694649046246346943
190 -0.7301520055740493240934162 0.1862902109277342514260976
191 -0.5190961292068118159257257 0.2331937645919904799185237
192 -0.2695431559523449723315320 0.2628045445102466621806889
193 0.0000000000000000000000000 0.2729250867779006307144835
194 0.2695431559523449723315320 0.2628045445102466621806889
195 0.5190961292068118159257257 0.2331937645919904799185237
196 0.7301520055740493240934163 0.1862902109277342514260980
197 0.8870625997680952990751578 0.1255803694649046246346940
198 0.9782286581460569928039380 0.0556685671161736664827537
199 Gauss quadrature points and weights order 2n-1=21
200
201 12
202 -0.9815606342467192506905491 0.0471753363865118271946160
203 -0.9041172563704748566784659 0.1069393259953184309602547
204 -0.7699026741943046870368938 0.1600783285433462263346525
205 -0.5873179542866174472967024 0.2031674267230659217490645
206 -0.3678314989981801937526915 0.2334925365383548087608499
207 -0.1252334085114689154724414 0.2491470458134027850005624
208 0.1252334085114689154724414 0.2491470458134027850005624
209 0.3678314989981801937526915 0.2334925365383548087608499
210 0.5873179542866174472967024 0.2031674267230659217490645
211 0.7699026741943046870368938 0.1600783285433462263346525
212 0.9041172563704748566784659 0.1069393259953184309602547
213 0.9815606342467192506905491 0.0471753363865118271946160
214 Gauss quadrature points and weights order 2n-1=23
215
216 16
217 -0.9894009349916499325961542 0.0271524594117540948517806
218 -0.9445750230732325760779884 0.0622535239386478928628438
219 -0.8656312023878317438804679 0.0951585116824927848099251
220 -0.7554044083550030338951012 0.1246289712555338720524763
221 -0.6178762444026437484466718 0.1495959888165767320815017
222 -0.4580167776572273863424194 0.1691565193950025381893121
223 -0.2816035507792589132304605 0.1826034150449235888667637
224 -0.0950125098376374401853193 0.1894506104550684962853967
225 0.0950125098376374401853193 0.1894506104550684962853967
226 0.2816035507792589132304605 0.1826034150449235888667637
227 0.4580167776572273863424194 0.1691565193950025381893121
228 0.6178762444026437484466718 0.1495959888165767320815017
229 0.7554044083550030338951012 0.1246289712555338720524763
230 0.8656312023878317438804679 0.0951585116824927848099251
231 0.9445750230732325760779884 0.0622535239386478928628438
232 0.9894009349916499325961542 0.0271524594117540948517806
233 Gauss quadrature points and weights order 2n-1=31
234
235 20
236 -0.9931285991850949247861224 0.0176140071391521183118620
237 -0.9639719272779137912676661 0.0406014298003869413310400
238 -0.9122344282513259058677524 0.0626720483341090635695065
239 -0.8391169718222188233945291 0.0832767415767047487247581
240 -0.7463319064601507926143051 0.1019301198172404350367501
241 -0.6360536807265150254528367 0.1181945319615184173123774
242 -0.5108670019508270980043641 0.1316886384491766268984945
243 -0.3737060887154195606725482 0.1420961093183820513292983
244 -0.2277858511416450780804962 0.1491729864726037467878287
245 -0.0765265211334973337546404 0.1527533871307258506980843
246 0.0765265211334973337546404 0.1527533871307258506980843
247 0.2277858511416450780804962 0.1491729864726037467878287
248 0.3737060887154195606725482 0.1420961093183820513292983
249 0.5108670019508270980043641 0.1316886384491766268984945
250 0.6360536807265150254528367 0.1181945319615184173123774
251 0.7463319064601507926143051 0.1019301198172404350367501
252 0.8391169718222188233945291 0.0832767415767047487247581
253 0.9122344282513259058677524 0.0626720483341090635695065
254 0.9639719272779137912676661 0.0406014298003869413310400
255 0.9931285991850949247861224 0.0176140071391521183118620
256 Gauss quadrature points and weights order 2n-1=39
257
258 24
259 -0.9951872199970213601799974 0.0123412297999871995468057
260 -0.9747285559713094981983919 0.0285313886289336631813078
261 -0.9382745520027327585236490 0.0442774388174198061686027
262 -0.8864155270044010342131543 0.0592985849154367807463678
263 -0.8200019859739029219539499 0.0733464814110803057340336
264 -0.7401241915785543642438281 0.0861901615319532759171852
265 -0.6480936519369755692524958 0.0976186521041138882698807
266 -0.5454214713888395356583756 0.1074442701159656347825773
267 -0.4337935076260451384870842 0.1155056680537256013533445
268 -0.3150426796961633743867933 0.1216704729278033912044632
269 -0.1911188674736163091586398 0.1258374563468282961213754
270 -0.0640568928626056260850431 0.1279381953467521569740562
271 0.0640568928626056260850431 0.1279381953467521569740562
272 0.1911188674736163091586398 0.1258374563468282961213754
273 0.3150426796961633743867933 0.1216704729278033912044632
274 0.4337935076260451384870842 0.1155056680537256013533445
275 0.5454214713888395356583756 0.1074442701159656347825773
276 0.6480936519369755692524958 0.0976186521041138882698807
277 0.7401241915785543642438281 0.0861901615319532759171852
278 0.8200019859739029219539499 0.0733464814110803057340336
279 0.8864155270044010342131543 0.0592985849154367807463678
280 0.9382745520027327585236490 0.0442774388174198061686027
281 0.9747285559130949819839199 0.0285313886289336631813078
282 0.9951872199970213601799974 0.0123412297999871995468057
283 Gauss quadrature points and weights order 2n-1=47
284
285 32
286 -0.9972638618494815635449811 0.0070186100094700966004071
287 -0.9856115115452683354001750 0.0162743947309056706051706
288 -0.9647622555875064307738119 0.0253920653092620594557526
289 -0.9349060759377396891709191 0.0342738629130214331026877
290 -0.8963211557660521239653072 0.0428358980222266806568786
291 -0.8493676137325699701336930 0.0509980592623761761961632
292 -0.7944837959679424069630973 0.0586840934785355471452836
293 -0.7321821187402896803874267 0.0658222227763618468376501
294 -0.6630442669302152009751152 0.0723457941088485062253994
295 -0.5877157572407623290407455 0.0781938957870703064717409
296 -0.5068999089322293900237475 0.0833119242269467552221991
297 -0.4213512761306353453641194 0.0876520930044038111427715
298 -0.3318686022821276497799168 0.0911738786957638847128686
299 -0.2392873622521370745446032 0.0938443990808045656391802
300 -0.1444719615827964934851864 0.0956387200792748594190820
301 -0.0483076656877383162348126 0.0965400885147278005667648
302 0.0483076656877383162348126 0.0965400885147278005667648
303 0.1444719615827964934851864 0.0956387200792748594190820
304 0.2392873622521370745446032 0.0938443990808045656391802
305 0.3318686022821276497799168 0.0911738786957638847128686
306 0.4213512761306353453641194 0.0876520930044038111427715
307 0.5068999089322293900237475 0.0833119242269467552221991
308 0.5877157572407623290407455 0.0781938957870703064717409
309 0.6630442669302152009751152 0.0723457941088485062253994
310 0.7321821187402896803874267 0.0658222227763618468376501
311 0.7944837959679424069630973 0.0586840934785355471452836
312 0.8493676137325699701336930 0.0509980592623761761961632
313 0.8963211557660521239653072 0.0428358980222266806568787
314 0.9349060759377396891709191 0.0342738629130214331026877
315 0.9647622555875064307738119 0.0253920653092620594557526
316 0.9856115115452683354001750 0.0162743947309056706051706
317 0.9972638618494815635449811 0.0070186100094700966004071
318 Gauss quadrature points and weights order 2n-1=63
319
320 40
321 -0.9982377097105592003496227 0.0045212770985331912584717
322 -0.9907262386994570064530544 0.0104982845311528136147422
323 -0.9772599499837742626633703 0.0164210583819078887128635
324 -0.9579168192137916558045410 0.0222458491941669572615043
325 -0.9328128082786765333608522 0.0279370069800234010984892
326 -0.9020988069688742967282533 0.0334601952825478473926782
327 -0.8659595032122595038207818 0.0387821679744720176399720
328 -0.8246122308333116631963202 0.0438709081856732719916747
329 -0.7783056514265193876949715 0.0486958076350722320614342
330 -0.7273182551899271032809965 0.0532278469839368243549965
331 -0.6719566846141795483793545 0.0574397690993915513666177
332 -0.6125538896679802379526125 0.0613062424929289391665380
333 -0.5494671250951282020759313 0.0648040134566010380745545
334 -0.4830758016861787129085666 0.0679120458152339038256901
335 -0.4137792043716050015248797 0.0706116473912867796954836
336 -0.3419940908257584730074925 0.0728865823958040590605107
337 -0.2681521850072536811411843 0.0747231690579682642001893
338 -0.1926975807013710997155169 0.0761103619006262423715581
339 -0.1160840706752552084834513 0.0770398181642479655883075
340 -0.0387724175060508219331934 0.0775059479784248112637240
341 0.0387724175060508219331934 0.0775059479784248112637240
342 0.1160840706752552084834513 0.0770398181642479655883075
343 0.1926975807013710997155169 0.0761103619006262423715581
344 0.2681521850072536811411843 0.0747231690579682642001893
345 0.3419940908257584730074925 0.0728865823958040590605107
346 0.4137792043716050015248797 0.0706116473912867796954836
347 0.4830758016861787129085666 0.0679120458152339038256901
348 0.5494671250951282020759313 0.0648040134566010380745545
349 0.6125538896679802379526125 0.0613062424929289391665380
350 0.6719566846141795483793545 0.0574397690993915513666177
351 0.7273182551899271032809965 0.0532278469839368243549965
352 0.7783056514265193876949715 0.0486958076350722320614342
353 0.8246122308333116631963202 0.0438709081856732719916747
354 0.8659595032122595038207818 0.0387821679744720176399720
355 0.9020988069688742967282533 0.0334601952825478473926782
356 0.9328128082786765333608522 0.0279370069800234010984892
357 0.9579168192137916558045410 0.0222458491941669572615040
358 0.9772599499837742626633703 0.0164210583819078887128635
359 0.9907262386994570064530544 0.0104982845311528136147422
360 0.9982377097105592003496227 0.0045212770985331912584717
361 Gauss quadrature points and weights order 2n-1=79
362
363 48
364 -0.9987710072524261186005415 0.0031533460523058386326773
365 -0.9935301722663507575479288 0.0073275539012762621023840
366 -0.9841245837228268577445836 0.0114772345792345394895927
367 -0.9705915925462472504614120 0.0155793157229438487281770
368 -0.9529877031604308607229607 0.0196161604573555278144607
369 -0.9313866907065543331141744 0.0235707608393243791405193
370 -0.9058791367155696728220748 0.0274265097083569482000738
371 -0.8765720202742478859056936 0.0311672278327980889020658
372 -0.8435882616243935307110898 0.0347772225647704388925486
373 -0.8070662040294426270825530 0.0382413510658307063172173
374 -0.7671590325157403392538554 0.0415450829434647492140588
375 -0.7240341309238146546744822 0.0446745608566942804194486
376 -0.6778723796326639052118513 0.0476166584924904748259066
377 -0.6288673967765136239951649 0.0503590355538544749578076
378 -0.5772247260839727038178092 0.0528901894851936670955051
379 -0.5231609747222330336782259 0.0551995036999841628682035
380 -0.4669029047509584045449289 0.0572772921004032157051502
381 -0.4086864819907167299162255 0.0591148396983956357464748
382 -0.3487558862921607381598179 0.0607044391658938800529692
383 -0.2873624873554555767358865 0.0620394231598926639041978
384 -0.2247637903946890612248654 0.0631141922862540256571260
385 -0.1612223560688917180564374 0.0639242385846481866239062
386 -0.0970046992094626989300540 0.0644661644359500822065042
387 -0.0323801709628693620333222 0.0647376968126839225030249
388 0.0323801709628693620333222 0.0647376968126839225030249
389 0.0970046992094626989300540 0.0644661644359500822065042
390 0.1612223560688917180564374 0.0639242385846481866239062
391 0.2247637903946890612248654 0.0631141922862540256571260
392 0.2873624873554555767358865 0.0620394231598926639041978
393 0.3487558862921607381598179 0.0607044391658938800529692
394 0.4086864819907167299162255 0.0591148396983956357464748
395 0.4669029047509584045449289 0.0572772921004032157051502
396 0.5231609747222330336782259 0.0551995036999841628682035
397 0.5772247260839727038178092 0.0528901894851936670955051
398 0.6288673967765136239951649 0.0503590355538544749578076
399 0.6778723796326639052118513 0.0476166584924904748259066
400 0.7240341309238146546744822 0.0446745608566942804194486
401 0.7671590325157403392538554 0.0415450829434647492140588
402 0.8070662040294426270825530 0.0382413510658307063172173
403 0.8435882616243935307110898 0.0347772225647704388925486
404 0.8765720202742478859056936 0.0311672278327980889020658
405 0.9058791367155696728220748 0.0274265097083569482000738
406 0.9313866907065543331141744 0.0235707608393243791405193
407 0.9529877031604308607229607 0.0196161604573555278144607
408 0.9705915925462472504614120 0.0155793157229438487281770
409 0.9841245837228268577445836 0.0114772345792345394895927
410 0.9935301722663507575479288 0.0073275539012762621023840
411 0.9987710072524261186005415 0.0031533460523058386326773
412 Gauss quadrature points and weights order 2n-1=95
413
414 64
415 -0.9993050417357721394569056 0.0017832807216964329472961
416 -0.9963401167719552793469245 0.0041470332605624676352875
417 -0.9910133714767443207393824 0.0065044579689783628561174
418 -0.9833362538846259569312993 0.0088467598263639477230309
419 -0.9733268277899109637418535 0.0111681394601311288185905
420 -0.9610087996520537189186141 0.0134630478967186425980608
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426 -0.8406292962525803627516915 0.0263774697150546586716918
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428 -0.7839723589433414076102205 0.0302346570724024788679741
429 -0.7528199072605318966118638 0.0320579283548515535854675
430 -0.7198818501716108268489402 0.0338051618371416093915655
431 -0.6852363130542332425635584 0.0354722132568823838106931
432 -0.6489654712546573398577612 0.0370551285402400460404151
433 -0.6111553551723932502488530 0.0385501531786156291289625
434 -0.5718956462026340342838781 0.0399537411327203413866569
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437 -0.4463660172534640879849477 0.0435837245293234533768279
438 -0.4022701579639916036957668 0.0445905581637565630601347
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440 -0.3113228719902109561575127 0.0462847965813144172959532
441 -0.2646871622087674163739642 0.0469681828162100173253263
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443 -0.1696444204239928180373136 0.0479993885964583077281262
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445 -0.0729931217877990394495429 0.0485754674415034269347991
446 -0.0243502926634244325089558 0.0486909570091397203833654
447 0.0243502926634244325089558 0.0486909570091397203833654
448 0.0729931217877990394495429 0.0485754674415034269347991
449 0.1214628192961205544703765 0.0483447622348029571697695
450 0.1696444204239928180373136 0.0479993885964583077281262
451 0.2174236437400070841496487 0.0475401657148303086622822
452 0.2646871622087674163739642 0.0469681828162100173253263
453 0.3113228719902109561575127 0.0462847965813144172959532
454 0.3572201583376681159504426 0.0454916279274181444797710
455 0.4022701579639916036957668 0.0445905581637565630601347
456 0.4463660172534640879849477 0.0435837245293234533768279
457 0.4894031457070529574785263 0.0424735151236535890073398
458 0.5312794640198945456580139 0.0412625632426235286101563
459 0.5718956462026340342838781 0.0399537411327203413866569
460 0.6111553551723932502488530 0.0385501531786156291289625
461 0.6489654712546573398577612 0.0370551285402400460404151
462 0.6852363130542332425635584 0.0354722132568823838106931
463 0.7198818501716108268489402 0.0338051618371416093915655
464 0.7528199072605318966118638 0.0320579283548515535854675
465 0.7839723589433414076102205 0.0302346570724024788679741
466 0.8132653151227975597419233 0.0283396726142594832275113
467 0.8406292962525803627516915 0.0263774697150546586716918
468 0.8659993981540928197607834 0.0243527025687108733381776
469 0.8893154459951141058534040 0.0222701738083832541592983
470 0.9105221370785028057563807 0.0201348231535302093723403
471 0.9295691721319395758214902 0.0179517157756973430850453
472 0.9464113748584028160624815 0.0157260304760247193219660
473 0.9610087996520537189186141 0.0134630478967186425980608
474 0.9733268277899109637418535 0.0111681394601311288185900
475 0.9833362538846259569312993 0.0088467598263639477230309
476 0.9910133714767443207393824 0.0065044579689783628561174
477 0.9963401167719552793469245 0.0041470332605624676352875
478 0.9993050417357721394569056 0.0017832807216964329472961
479 Gauss quadrature points and weights order 2n-1=127
480 """
481
482
483 economical_gauss_quadrilateral_table = """\
484 1
485 0.000000000000000 0.000000000000000 4.000000000000000
486 Gauss quadrature points and weights on the reference quadrilateral order p=0 1
487
488 4
489 0.577350269189626 0.577350269189626 1.000000000000000
490 0.577350269189626 -0.577350269189626 1.000000000000000
491 -0.577350269189626 0.577350269189626 1.000000000000000
492 -0.577350269189626 -0.577350269189626 1.000000000000000
493 Gauss quadrature points and weights on the reference quadrilateral order p=2 3
494
495 8
496 0.683130051063973 0.000000000000000 0.816326530612245
497 -0.683130051063973 0.000000000000000 0.816326530612245
498 0.000000000000000 0.683130051063973 0.816326530612245
499 0.000000000000000 -0.683130051063973 0.816326530612245
500 0.881917103688197 0.881917103688197 0.183673469387755
501 0.881917103688197 -0.881917103688197 0.183673469387755
502 -0.881917103688197 0.881917103688197 0.183673469387755
503 -0.881917103688197 -0.881917103688197 0.183673469387755
504 Gauss quadrature points and weights on the reference quadrilateral order p=4 5
505
506 12
507 0.925820099772551 0.000000000000000 0.241975308641975
508 -0.925820099772551 0.000000000000000 0.241975308641975
509 0.000000000000000 0.925820099772551 0.241975308641975
510 0.000000000000000 -0.925820099772551 0.241975308641975
511 0.805979782918599 0.805979782918599 0.237431774690630
512 0.805979782918599 -0.805979782918599 0.237431774690630
513 -0.805979782918599 0.805979782918599 0.237431774690630
514 -0.805979782918599 -0.805979782918599 0.237431774690630
515 0.380554433208316 0.380554433208316 0.520592916667394
516 0.380554433208316 -0.380554433208316 0.520592916667394
517 -0.380554433208316 0.380554433208316 0.520592916667394
518 -0.380554433208316 -0.380554433208316 0.520592916667394
519 Gauss quadrature points and weights on the reference quadrilateral order p=6 7
520
521 20
522 1.121225763866564 0.000000000000000 0.018475842507491
523 -1.121225763866564 0.000000000000000 0.018475842507491
524 0.000000000000000 1.121225763866564 0.018475842507491
525 0.000000000000000 -1.121225763866564 0.018475842507491
526 0.451773049920657 0.000000000000000 0.390052939160735
527 -0.451773049920657 0.000000000000000 0.390052939160735
528 0.000000000000000 0.451773049920657 0.390052939160735
529 0.000000000000000 -0.451773049920657 0.390052939160735
530 0.891849420851512 0.891849420851512 0.083095178026482
531 0.891849420851512 -0.891849420851512 0.083095178026482
532 -0.891849420851512 0.891849420851512 0.083095178026482
533 -0.891849420851512 -0.891849420851512 0.083095178026482
534 0.824396370749276 0.411623426336542 0.254188020152646
535 0.824396370749276 -0.411623426336542 0.254188020152646
536 -0.824396370749276 0.411623426336542 0.254188020152646
537 -0.824396370749276 -0.411623426336542 0.254188020152646
538 0.411623426336542 0.824396370749276 0.254188020152646
539 0.411623426336542 -0.824396370749276 0.254188020152646
540 -0.411623426336542 0.824396370749276 0.254188020152646
541 -0.411623426336542 -0.824396370749276 0.254188020152646
542 Gauss quadrature points and weights on the reference quadrilateral order p=8 9
543
544 25
545 0.000000000000000 0.000000000000000 0.365379525585903
546 1.044402915409813 0.000000000000000 0.027756165564204
547 -1.044402915409813 0.000000000000000 0.027756165564204
548 0.000000000000000 1.044402915409813 0.027756165564204
549 0.000000000000000 -1.044402915409813 0.027756165564204
550 0.769799068396649 0.000000000000000 0.244272057751754
551 -0.769799068396649 0.000000000000000 0.244272057751754
552 0.000000000000000 0.769799068396649 0.244272057751754
553 0.000000000000000 -0.769799068396649 0.244272057751754
554 0.935787012440540 0.935787012440540 0.034265103851229
555 0.935787012440540 -0.935787012440540 0.034265103851229
556 -0.935787012440540 0.935787012440540 0.034265103851229
557 -0.935787012440540 -0.935787012440540 0.034265103851229
558 0.413491953449114 0.413491953449114 0.308993036133713
559 0.413491953449114 -0.413491953449114 0.308993036133713
560 -0.413491953449114 0.413491953449114 0.308993036133713
561 -0.413491953449114 -0.413491953449114 0.308993036133713
562 0.883025508525690 0.575653595840465 0.146684377651312
563 0.883025508525690 -0.575653595840465 0.146684377651312
564 -0.883025508525690 0.575653595840465 0.146684377651312
565 -0.883025508525690 -0.575653595840465 0.146684377651312
566 0.575653595840465 0.883025508525690 0.146684377651312
567 0.575653595840465 -0.883025508525690 0.146684377651312
568 -0.575653595840465 0.883025508525690 0.146684377651312
569 -0.575653595840465 -0.883025508525690 0.146684377651312
570 Gauss quadrature points and weights on the reference quadrilateral order p=10 11
571
572 36
573 1.086056158573971 0.000000000000000 0.005656169693764
574 -1.086056158573971 0.000000000000000 0.005656169693764
575 0.000000000000000 1.086056158573971 0.005656169693764
576 0.000000000000000 -1.086056158573971 0.005656169693764
577 0.658208197042585 0.000000000000000 0.192443967470396
578 -0.658208197042585 0.000000000000000 0.192443967470396
579 0.000000000000000 0.658208197042585 0.192443967470396
580 0.000000000000000 -0.658208197042585 0.192443967470396
581 1.001300602991729 1.001300602991729 0.005166832979773
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585 0.584636168775946 0.584636168775946 0.200302559622138
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588 -0.584636168775946 -0.584636168775946 0.200302559622138
589 0.246795612720261 0.246795612720261 0.228125175912536
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591 -0.246795612720261 0.246795612720261 0.228125175912536
592 -0.246795612720261 -0.246795612720261 0.228125175912536
593 0.900258815287201 0.304720678579870 0.117496926974491
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596 -0.900258815287201 -0.304720678579870 0.117496926974491
597 0.304720678579870 0.900258815287201 0.117496926974491
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599 -0.304720678579870 0.900258815287201 0.117496926974491
600 -0.304720678579870 -0.900258815287201 0.117496926974491
601 0.929866705560780 0.745052720131169 0.066655770186205
602 0.929866705560780 -0.745052720131169 0.066655770186205
603 -0.929866705560780 0.745052720131169 0.066655770186205
604 -0.929866705560780 -0.745052720131169 0.066655770186205
605 0.745052720131169 0.929866705560780 0.066655770186205
606 0.745052720131169 -0.929866705560780 0.066655770186205
607 -0.745052720131169 0.929866705560780 0.066655770186205
608 -0.745052720131169 -0.929866705560780 0.066655770186205
609 Gauss quadrature points and weights on the reference quadrilateral order p=12 13
610
611 45
612 0.000000000000000 0.000000000000000 -0.001768979827207
613 1.027314357719367 0.000000000000000 0.012816726617512
614 -1.027314357719367 0.000000000000000 0.012816726617512
615 0.000000000000000 1.027314357719367 0.012816726617512
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633 0.621974427996805 0.321696694921009 0.168053047203816
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648 -0.455124178121179 -0.928618480068352 0.076169694452294
649 0.960457474887516 0.809863684081217 0.028794154400064
650 0.960457474887516 -0.809863684081217 0.028794154400064
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655 -0.809863684081217 0.960457474887516 0.028794154400064
656 -0.809863684081217 -0.960457474887516 0.028794154400064
657 Gauss quadrature points and weights on the reference quadrilateral order p=14 15
658
659 60
660 0.989353074512600 0.000000000000000 0.020614915919991
661 -0.989353074512600 0.000000000000000 0.020614915919991
662 0.000000000000000 0.989353074512600 0.020614915919991
663 0.000000000000000 -0.989353074512600 0.020614915919991
664 0.376285207157973 0.000000000000000 0.128025716179910
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711 -0.347386316166203 -0.936506276127495 0.057387752969213
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718 -0.706000287798646 0.981321179805452 0.021922559481864
719 -0.706000287798646 -0.981321179805452 0.021922559481864
720 Gauss quadrature points and weights on the reference quadrilateral order p=16 17
721
722 72
723 0.943962831808239 0.000000000000000 0.038205406871462
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731 0.973981076394170 0.973981076394170 0.005773708558664
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743 0.068354569272491 0.068354569272491 0.047466627685662
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747 0.802952004398543 0.203345534163332 0.078619467342982
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755 0.634244672807882 0.426572172992877 0.094979169511394
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763 0.978350706908227 0.295830776620995 0.022331162356015
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775 0.541983037327871 0.901672717710389 0.055594877793785
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777 -0.541983037327871 0.901672717710389 0.055594877793785
778 -0.541983037327871 -0.901672717710389 0.055594877793785
779 1.007018449383116 0.669414798783936 0.006049054506376
780 1.007018449383116 -0.669414798783936 0.006049054506376
781 -1.007018449383116 0.669414798783936 0.006049054506376
782 -1.007018449383116 -0.669414798783936 0.006049054506376
783 0.669414798783936 1.007018449383116 0.006049054506376
784 0.669414798783936 -1.007018449383116 0.006049054506376
785 -0.669414798783936 1.007018449383116 0.006049054506376
786 -0.669414798783936 -1.007018449383116 0.006049054506376
787 0.945161453573471 0.829501421477824 0.024839207949609
788 0.945161453573471 -0.829501421477824 0.024839207949609
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793 -0.829501421477824 0.945161453573471 0.024839207949609
794 -0.829501421477824 -0.945161453573471 0.024839207949609
795 Gauss quadrature points and weights on the reference quadrilateral order p=18 19
796
797 88
798 0.980883148832881 0.000000000000000 0.019503841092684
799 -0.980883148832881 0.000000000000000 0.019503841092684
800 0.000000000000000 0.980883148832881 0.019503841092684
801 0.000000000000000 -0.980883148832881 0.019503841092684
802 0.678152700336576 0.000000000000000 0.089012127744268
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804 0.000000000000000 0.678152700336576 0.089012127744268
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806 0.240599282275864 0.000000000000000 0.114568584702749
807 -0.240599282275864 0.000000000000000 0.114568584702749
808 0.000000000000000 0.240599282275864 0.114568584702749
809 0.000000000000000 -0.240599282275864 0.114568584702749
810 0.965176994929162 0.965176994929162 0.007463627359106
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814 0.749698539312765 0.749698539312765 0.050585943594705
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816 -0.749698539312765 0.749698539312765 0.050585943594705
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818 0.568983925500818 0.568983925500818 0.074613865184212
819 0.568983925500818 -0.568983925500818 0.074613865184212
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821 -0.568983925500818 -0.568983925500818 0.074613865184212
822 0.971086142843168 0.355832132274584 0.023501091310143
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826 0.355832132274584 0.971086142843168 0.023501091310143
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828 -0.355832132274584 0.971086142843168 0.023501091310143
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834 0.645588139196562 0.983453947854968 0.011588562644144
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838 0.933927707027213 0.821920249234369 0.023073245798171
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842 0.821920249234369 0.933927707027213 0.023073245798171
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845 -0.821920249234369 -0.933927707027213 0.023073245798171
846 1.014086498915039 0.862185099566557 0.001570221774472
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850 0.862185099566557 1.014086498915039 0.001570221774472
851 0.862185099566557 -1.014086498915039 0.001570221774472
852 -0.862185099566557 1.014086498915039 0.001570221774472
853 -0.862185099566557 -1.014086498915039 0.001570221774472
854 0.877914842155496 0.168914072450263 0.049102258016227
855 0.877914842155496 -0.168914072450263 0.049102258016227
856 -0.877914842155496 0.168914072450263 0.049102258016227
857 -0.877914842155496 -0.168914072450263 0.049102258016227
858 0.168914072450263 0.877914842155496 0.049102258016227
859 0.168914072450263 -0.877914842155496 0.049102258016227
860 -0.168914072450263 0.877914842155496 0.049102258016227
861 -0.168914072450263 -0.877914842155496 0.049102258016227
862 0.882246882640128 0.568113580166780 0.042512352239126
863 0.882246882640128 -0.568113580166780 0.042512352239126
864 -0.882246882640128 0.568113580166780 0.042512352239126
865 -0.882246882640128 -0.568113580166780 0.042512352239126
866 0.568113580166780 0.882246882640128 0.042512352239126
867 0.568113580166780 -0.882246882640128 0.042512352239126
868 -0.568113580166780 0.882246882640128 0.042512352239126
869 -0.568113580166780 -0.882246882640128 0.042512352239126
870 0.741324453314596 0.371360260002223 0.067270936863160
871 0.741324453314596 -0.371360260002223 0.067270936863160
872 -0.741324453314596 0.371360260002223 0.067270936863160
873 -0.741324453314596 -0.371360260002223 0.067270936863160
874 0.371360260002223 0.741324453314596 0.067270936863160
875 0.371360260002223 -0.741324453314596 0.067270936863160
876 -0.371360260002223 0.741324453314596 0.067270936863160
877 -0.371360260002223 -0.741324453314596 0.067270936863160
878 0.469570217710647 0.237333359193547 0.103507336515645
879 0.469570217710647 -0.237333359193547 0.103507336515645
880 -0.469570217710647 0.237333359193547 0.103507336515645
881 -0.469570217710647 -0.237333359193547 0.103507336515645
882 0.237333359193547 0.469570217710647 0.103507336515645
883 0.237333359193547 -0.469570217710647 0.103507336515645
884 -0.237333359193547 0.469570217710647 0.103507336515645
885 -0.237333359193547 -0.469570217710647 0.103507336515645
886 Gauss quadrature points and weights on the reference quadrilateral order p=20 21
887 """
888
889
890 economical_gauss_hexahedron_table = """\
891 1
892 0.000000000000000 0.000000000000000 0.000000000000000 8.000000000000000
893 Gauss quadrature points and weights on the reference cube order p=0 1
894
895 6
896 1.000000000000000 0.000000000000000 0.000000000000000 1.333333333333333
897 -1.000000000000000 0.000000000000000 0.000000000000000 1.333333333333333
898 0.000000000000000 1.000000000000000 0.000000000000000 1.333333333333333
899 0.000000000000000 -1.000000000000000 0.000000000000000 1.333333333333333
900 0.000000000000000 0.000000000000000 1.000000000000000 1.333333333333333
901 0.000000000000000 0.000000000000000 -1.000000000000000 1.333333333333333
902 Gauss quadrature points and weights on the reference cube order p=2 3
903
904 14
905 0.795822425754221 0.000000000000000 0.000000000000000 0.886426592797784
906 -0.795822425754221 0.000000000000000 0.000000000000000 0.886426592797784
907 0.000000000000000 0.795822425754221 0.000000000000000 0.886426592797784
908 0.000000000000000 -0.795822425754221 0.000000000000000 0.886426592797784
909 0.000000000000000 0.000000000000000 0.795822425754221 0.886426592797784
910 0.000000000000000 0.000000000000000 -0.795822425754221 0.886426592797784
911 0.758786910639328 0.758786910639328 0.758786910639328 0.335180055401662
912 0.758786910639328 -0.758786910639328 0.758786910639328 0.335180055401662
913 0.758786910639328 0.758786910639328 -0.758786910639328 0.335180055401662
914 0.758786910639328 -0.758786910639328 -0.758786910639328 0.335180055401662
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917 -0.758786910639328 0.758786910639328 -0.758786910639328 0.335180055401662
918 -0.758786910639328 -0.758786910639328 -0.758786910639328 0.335180055401662
919 Gauss quadrature points and weights on the reference cube order p=4 5
920
921 27
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923 0.848418011472252 0.000000000000000 0.000000000000000 0.499369002307720
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926 0.000000000000000 -0.848418011472252 0.000000000000000 0.499369002307720
927 0.000000000000000 0.000000000000000 0.848418011472252 0.499369002307720
928 0.000000000000000 0.000000000000000 -0.848418011472252 0.499369002307720
929 0.652816472101691 0.652816472101691 0.652816472101691 0.478508449425127
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937 0.000000000000000 1.106412898626718 1.106412898626718 0.032303742334037
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940 0.000000000000000 -1.106412898626718 -1.106412898626718 0.032303742334037
941 1.106412898626718 0.000000000000000 1.106412898626718 0.032303742334037
942 -1.106412898626718 0.000000000000000 1.106412898626718 0.032303742334037
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945 1.106412898626718 1.106412898626718 0.000000000000000 0.032303742334037
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947 1.106412898626718 -1.106412898626718 0.000000000000000 0.032303742334037
948 -1.106412898626718 -1.106412898626718 0.000000000000000 0.032303742334037
949 Gauss quadrature points and weights on the reference cube order p=6 7
950
951 53
952 0.000000000000000 0.000000000000000 0.000000000000000 0.588405321380412
953 1.064082230328777 0.000000000000000 0.000000000000000 -0.152097068487023
954 -1.064082230328777 0.000000000000000 0.000000000000000 -0.152097068487023
955 0.000000000000000 1.064082230328777 0.000000000000000 -0.152097068487023
956 0.000000000000000 -1.064082230328777 0.000000000000000 -0.152097068487023
957 0.000000000000000 0.000000000000000 1.064082230328777 -0.152097068487023
958 0.000000000000000 0.000000000000000 -1.064082230328777 -0.152097068487023
959 0.905830033000216 0.000000000000000 0.000000000000000 0.369012523996709
960 -0.905830033000216 0.000000000000000 0.000000000000000 0.369012523996709
961 0.000000000000000 0.905830033000216 0.000000000000000 0.369012523996709
962 0.000000000000000 -0.905830033000216 0.000000000000000 0.369012523996709
963 0.000000000000000 0.000000000000000 0.905830033000216 0.369012523996709
964 0.000000000000000 0.000000000000000 -0.905830033000216 0.369012523996709
965 0.817286490798906 0.817286490798906 0.817286490798906 0.104007450974435
966 0.817286490798906 -0.817286490798906 0.817286490798906 0.104007450974435
967 0.817286490798906 0.817286490798906 -0.817286490798906 0.104007450974435
968 0.817286490798906 -0.817286490798906 -0.817286490798906 0.104007450974435
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980 -0.501292956337400 -0.501292956337400 -0.501292956337400 0.380660357224238
981 1.017168937265364 0.650007853956632 0.000000000000000 0.0930316449988371
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986 -1.017168937265364 -0.650007853956632 0.000000000000000 0.0930316449988371
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989 0.000000000000000 0.650007853956632 1.017168937265364 0.0930316449988371
990 0.000000000000000 -0.650007853956632 1.017168937265364 0.0930316449988371
991 0.000000000000000 1.017168937265364 0.650007853956632 0.0930316449988371
992 0.000000000000000 1.017168937265364 -0.650007853956632 0.0930316449988371
993 0.000000000000000 0.650007853956632 -1.017168937265364 0.0930316449988371
994 0.000000000000000 -0.650007853956632 -1.017168937265364 0.0930316449988371
995 0.000000000000000 -1.017168937265364 0.650007853956632 0.0930316449988371
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2014 0.978322332670673 1.012434400912337 -1.012434400912337 -0.023175821642762
2015 0.978322332670673 -1.012434400912337 1.012434400912337 -0.023175821642762
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2119 -0.990340675813395 0.703401752648627 0.853891500333261 0.004492075519908
2120 -0.990340675813395 -0.703401752648627 0.853891500333261 0.004492075519908
2121 -0.990340675813395 -0.853891500333261 0.703401752648627 0.004492075519908
2122 -0.990340675813395 -0.853891500333261 -0.703401752648627 0.004492075519908
2123 -0.990340675813395 0.703401752648627 -0.853891500333261 0.004492075519908
2124 -0.990340675813395 -0.703401752648627 -0.853891500333261 0.004492075519908
2125 0.703401752648627 0.853891500333261 0.990340675813395 0.004492075519908
2126 0.703401752648627 0.853891500333261 -0.990340675813395 0.004492075519908
2127 0.703401752648627 0.990340675813395 0.853891500333261 0.004492075519908
2128 0.703401752648627 -0.990340675813395 0.853891500333261 0.004492075519908
2129 0.703401752648627 -0.853891500333261 0.990340675813395 0.004492075519908
2130 0.703401752648627 -0.853891500333261 -0.990340675813395 0.004492075519908
2131 0.703401752648627 0.990340675813395 -0.853891500333261 0.004492075519908
2132 0.703401752648627 -0.990340675813395 -0.853891500333261 0.004492075519908
2133 -0.703401752648627 0.853891500333261 0.990340675813395 0.004492075519908
2134 -0.703401752648627 0.853891500333261 -0.990340675813395 0.004492075519908
2135 -0.703401752648627 0.990340675813395 0.853891500333261 0.004492075519908
2136 -0.703401752648627 -0.990340675813395 0.853891500333261 0.004492075519908
2137 -0.703401752648627 -0.853891500333261 0.990340675813395 0.004492075519908
2138 -0.703401752648627 -0.853891500333261 -0.990340675813395 0.004492075519908
2139 -0.703401752648627 0.990340675813395 -0.853891500333261 0.004492075519908
2140 -0.703401752648627 -0.990340675813395 -0.853891500333261 0.004492075519908
2141 0.946965100974417 0.623429573213959 0.361644847592954 0.020564739563048
2142 0.946965100974417 0.623429573213959 -0.361644847592954 0.020564739563048
2143 0.946965100974417 0.361644847592954 0.623429573213959 0.020564739563048
2144 0.946965100974417 -0.361644847592954 0.623429573213959 0.020564739563048
2145 0.946965100974417 -0.623429573213959 0.361644847592954 0.020564739563048
2146 0.946965100974417 -0.623429573213959 -0.361644847592954 0.020564739563048
2147 0.946965100974417 0.361644847592954 -0.623429573213959 0.020564739563048
2148 0.946965100974417 -0.361644847592954 -0.623429573213959 0.020564739563048
2149 -0.946965100974417 0.623429573213959 0.361644847592954 0.020564739563048
2150 -0.946965100974417 0.623429573213959 -0.361644847592954 0.020564739563048
2151 -0.946965100974417 0.361644847592954 0.623429573213959 0.020564739563048
2152 -0.946965100974417 -0.361644847592954 0.623429573213959 0.020564739563048
2153 -0.946965100974417 -0.623429573213959 0.361644847592954 0.020564739563048
2154 -0.946965100974417 -0.623429573213959 -0.361644847592954 0.020564739563048
2155 -0.946965100974417 0.361644847592954 -0.623429573213959 0.020564739563048
2156 -0.946965100974417 -0.361644847592954 -0.623429573213959 0.020564739563048
2157 0.623429573213959 0.946965100974417 0.361644847592954 0.020564739563048
2158 0.623429573213959 0.946965100974417 -0.361644847592954 0.020564739563048
2159 0.623429573213959 0.361644847592954 0.946965100974417 0.020564739563048
2160 0.623429573213959 -0.361644847592954 0.946965100974417 0.020564739563048
2161 0.623429573213959 -0.946965100974417 0.361644847592954 0.020564739563048
2162 0.623429573213959 -0.946965100974417 -0.361644847592954 0.020564739563048
2163 0.623429573213959 0.361644847592954 -0.946965100974417 0.020564739563048
2164 0.623429573213959 -0.361644847592954 -0.946965100974417 0.020564739563048
2165 -0.623429573213959 0.946965100974417 0.361644847592954 0.020564739563048
2166 -0.623429573213959 0.946965100974417 -0.361644847592954 0.020564739563048
2167 -0.623429573213959 0.361644847592954 0.946965100974417 0.020564739563048
2168 -0.623429573213959 -0.361644847592954 0.946965100974417 0.020564739563048
2169 -0.623429573213959 -0.946965100974417 0.361644847592954 0.020564739563048
2170 -0.623429573213959 -0.946965100974417 -0.361644847592954 0.020564739563048
2171 -0.623429573213959 0.361644847592954 -0.946965100974417 0.020564739563048
2172 -0.623429573213959 -0.361644847592954 -0.946965100974417 0.020564739563048
2173 0.361644847592954 0.946965100974417 0.623429573213959 0.020564739563048
2174 0.361644847592954 0.946965100974417 -0.623429573213959 0.020564739563048
2175 0.361644847592954 0.623429573213959 0.946965100974417 0.020564739563048
2176 0.361644847592954 -0.623429573213959 0.946965100974417 0.020564739563048
2177 0.361644847592954 -0.946965100974417 0.623429573213959 0.020564739563048
2178 0.361644847592954 -0.946965100974417 -0.623429573213959 0.020564739563048
2179 0.361644847592954 0.623429573213959 -0.946965100974417 0.020564739563048
2180 0.361644847592954 -0.623429573213959 -0.946965100974417 0.020564739563048
2181 -0.361644847592954 0.946965100974417 0.623429573213959 0.020564739563048
2182 -0.361644847592954 0.946965100974417 -0.623429573213959 0.020564739563048
2183 -0.361644847592954 0.623429573213959 0.946965100974417 0.020564739563048
2184 -0.361644847592954 -0.623429573213959 0.946965100974417 0.020564739563048
2185 -0.361644847592954 -0.946965100974417 0.623429573213959 0.020564739563048
2186 -0.361644847592954 -0.946965100974417 -0.623429573213959 0.020564739563048
2187 -0.361644847592954 0.623429573213959 -0.946965100974417 0.020564739563048
2188 -0.361644847592954 -0.623429573213959 -0.946965100974417 0.020564739563048
2189 0.754378926224437 0.538990774213829 0.258107746839302 0.039008180977840
2190 0.754378926224437 0.538990774213829 -0.258107746839302 0.039008180977840
2191 0.754378926224437 0.258107746839302 0.538990774213829 0.039008180977840
2192 0.754378926224437 -0.258107746839302 0.538990774213829 0.039008180977840
2193 0.754378926224437 -0.538990774213829 0.258107746839302 0.039008180977840
2194 0.754378926224437 -0.538990774213829 -0.258107746839302 0.039008180977840
2195 0.754378926224437 0.258107746839302 -0.538990774213829 0.039008180977840
2196 0.754378926224437 -0.258107746839302 -0.538990774213829 0.039008180977840
2197 -0.754378926224437 0.538990774213829 0.258107746839302 0.039008180977840
2198 -0.754378926224437 0.538990774213829 -0.258107746839302 0.039008180977840
2199 -0.754378926224437 0.258107746839302 0.538990774213829 0.039008180977840
2200 -0.754378926224437 -0.258107746839302 0.538990774213829 0.039008180977840
2201 -0.754378926224437 -0.538990774213829 0.258107746839302 0.039008180977840
2202 -0.754378926224437 -0.538990774213829 -0.258107746839302 0.039008180977840
2203 -0.754378926224437 0.258107746839302 -0.538990774213829 0.039008180977840
2204 -0.754378926224437 -0.258107746839302 -0.538990774213829 0.039008180977840
2205 0.538990774213829 0.754378926224437 0.258107746839302 0.039008180977840
2206 0.538990774213829 0.754378926224437 -0.258107746839302 0.039008180977840
2207 0.538990774213829 0.258107746839302 0.754378926224437 0.039008180977840
2208 0.538990774213829 -0.258107746839302 0.754378926224437 0.039008180977840
2209 0.538990774213829 -0.754378926224437 0.258107746839302 0.039008180977840
2210 0.538990774213829 -0.754378926224437 -0.258107746839302 0.039008180977840
2211 0.538990774213829 0.258107746839302 -0.754378926224437 0.039008180977840
2212 0.538990774213829 -0.258107746839302 -0.754378926224437 0.039008180977840
2213 -0.538990774213829 0.754378926224437 0.258107746839302 0.039008180977840
2214 -0.538990774213829 0.754378926224437 -0.258107746839302 0.039008180977840
2215 -0.538990774213829 0.258107746839302 0.754378926224437 0.039008180977840
2216 -0.538990774213829 -0.258107746839302 0.754378926224437 0.039008180977840
2217 -0.538990774213829 -0.754378926224437 0.258107746839302 0.039008180977840
2218 -0.538990774213829 -0.754378926224437 -0.258107746839302 0.039008180977840
2219 -0.538990774213829 0.258107746839302 -0.754378926224437 0.039008180977840
2220 -0.538990774213829 -0.258107746839302 -0.754378926224437 0.039008180977840
2221 0.258107746839302 0.754378926224437 0.538990774213829 0.039008180977840
2222 0.258107746839302 0.754378926224437 -0.538990774213829 0.039008180977840
2223 0.258107746839302 0.538990774213829 0.754378926224437 0.039008180977840
2224 0.258107746839302 -0.538990774213829 0.754378926224437 0.039008180977840
2225 0.258107746839302 -0.754378926224437 0.538990774213829 0.039008180977840
2226 0.258107746839302 -0.754378926224437 -0.538990774213829 0.039008180977840
2227 0.258107746839302 0.538990774213829 -0.754378926224437 0.039008180977840
2228 0.258107746839302 -0.538990774213829 -0.754378926224437 0.039008180977840
2229 -0.258107746839302 0.754378926224437 0.538990774213829 0.039008180977840
2230 -0.258107746839302 0.754378926224437 -0.538990774213829 0.039008180977840
2231 -0.258107746839302 0.538990774213829 0.754378926224437 0.039008180977840
2232 -0.258107746839302 -0.538990774213829 0.754378926224437 0.039008180977840
2233 -0.258107746839302 -0.754378926224437 0.538990774213829 0.039008180977840
2234 -0.258107746839302 -0.754378926224437 -0.538990774213829 0.039008180977840
2235 -0.258107746839302 0.538990774213829 -0.754378926224437 0.039008180977840
2236 -0.258107746839302 -0.538990774213829 -0.754378926224437 0.039008180977840
2237 Gauss quadrature points and weights on the reference cube order p=18 19
2238 """
2239
2240
2241 economical_gauss_triangle_table = """\
2242 1
2243 -0.333333333333333 -0.333333333333333 2.000000000000000
2244 Gauss quadrature points and weights on the reference triangle order p=1
2245
2246 3
2247 -0.666666666666667 -0.666666666666667 0.666666666666667
2248 -0.666666666666667 0.333333333333333 0.666666666666667
2249 0.333333333333333 -0.666666666666667 0.666666666666667
2250 Gauss quadrature points and weights on the reference triangle order p=2
2251
2252 4
2253 -0.333333333333333 -0.333333333333333 -1.125000000000000
2254 -0.600000000000000 -0.600000000000000 1.041666666666667
2255 -0.600000000000000 0.200000000000000 1.041666666666667
2256 0.200000000000000 -0.600000000000000 1.041666666666667
2257 Gauss quadrature points and weights on the reference triangle order p=3
2258
2259 6
2260 -0.108103018168070 -0.108103018168070 0.446763179356022
2261 -0.108103018168070 -0.783793963663860 0.446763179356022
2262 -0.783793963663860 -0.108103018168070 0.446763179356022
2263 -0.816847572980458 -0.816847572980458 0.219903487310644
2264 -0.816847572980458 0.633695145960918 0.219903487310644
2265 0.633695145960918 -0.816847572980458 0.219903487310644
2266 Gauss quadrature points and weights on the reference triangle order p=4
2267
2268 7
2269 -0.333333333333333 -0.333333333333333 0.450000000000000
2270 -0.059715871789770 -0.059715871789770 0.264788305577012
2271 -0.059715871789770 -0.880568256420460 0.264788305577012
2272 -0.880568256420460 -0.059715871789770 0.264788305577012
2273 -0.797426985353088 -0.797426985353088 0.251878361089654
2274 -0.797426985353088 0.594853970706174 0.251878361089654
2275 0.594853970706174 -0.797426985353088 0.251878361089654
2276 Gauss quadrature points and weights on the reference triangle order p=5
2277
2278 12
2279 -0.501426509658180 -0.501426509658180 0.233572551452758
2280 -0.501426509658180 0.002853019316358 0.233572551452758
2281 0.002853019316358 -0.501426509658180 0.233572551452758
2282 -0.873821971016996 -0.873821971016996 0.101689812740414
2283 -0.873821971016996 0.747643942033992 0.101689812740414
2284 0.747643942033992 -0.873821971016996 0.101689812740414
2285 -0.379295097932432 0.273004998242798 0.165702151236748
2286 0.273004998242798 -0.893709900310366 0.165702151236748
2287 -0.893709900310366 -0.379295097932432 0.165702151236748
2288 -0.379295097932432 -0.893709900310366 0.165702151236748
2289 0.273004998242798 -0.379295097932432 0.165702151236748
2290 -0.893709900310366 0.273004998242798 0.165702151236748
2291 Gauss quadrature points and weights on the reference triangle order p=6
2292
2293 13
2294 -0.333333333333333 -0.333333333333333 -0.299140088935364
2295 -0.479308067841920 -0.479308067841920 0.351230514866416
2296 -0.479308067841920 -0.041383864316160 0.351230514866416
2297 -0.041383864316160 -0.479308067841920 0.351230514866416
2298 -0.869739794195568 -0.869739794195568 0.106694471217676
2299 -0.869739794195568 0.739479588391136 0.106694471217676
2300 0.739479588391136 -0.869739794195568 0.106694471217676
2301 -0.374269007990252 0.276888377139620 0.154227521780514
2302 0.276888377139620 -0.902619369149368 0.154227521780514
2303 -0.902619369149368 -0.374269007990252 0.154227521780514
2304 -0.374269007990252 -0.902619369149368 0.154227521780514
2305 0.276888377139620 -0.374269007990252 0.154227521780514
2306 -0.902619369149368 0.276888377139620 0.154227521780514
2307 Gauss quadrature points and weights on the reference triangle order p=7
2308
2309 16
2310 -0.333333333333333 -0.333333333333333 0.288631215355574
2311 -0.081414823414554 -0.081414823414554 0.190183268534570
2312 -0.081414823414554 -0.837170353170892 0.190183268534570
2313 -0.837170353170892 -0.081414823414554 0.190183268534570
2314 -0.658861384496480 -0.658861384496480 0.206434741069436
2315 -0.658861384496480 0.317722768992960 0.206434741069436
2316 0.317722768992960 -0.658861384496480 0.206434741069436
2317 -0.898905543365938 -0.898905543365938 0.064916995246396
2318 -0.898905543365938 0.797811086731876 0.064916995246395
2319 0.797811086731876 -0.898905543365938 0.064916995246396
2320 -0.473774340730724 0.456984785910808 0.054460628348870
2321 0.456984785910808 -0.983210445180084 0.054460628348870
2322 -0.983210445180084 -0.473774340730724 0.054460628348870
2323 -0.473774340730724 -0.983210445180084 0.054460628348870
2324 0.456984785910808 -0.473774340730724 0.054460628348870
2325 -0.983210445180084 0.456984785910808 0.054460628348870
2326 Gauss quadrature points and weights on the reference triangle order p=8
2327
2328 19
2329 -0.333333333333333 -0.333333333333333 0.194271592565598
2330 -0.020634961602524 -0.020634961602524 0.062669400454278
2331 -0.020634961602524 -0.958730076794950 0.062669400454278
2332 -0.958730076794950 -0.020634961602524 0.062669400454278
2333 -0.125820817014126 -0.125820817014126 0.155655082009548
2334 -0.125820817014126 -0.748358365971746 0.155655082009548
2335 -0.748358365971746 -0.125820817014126 0.155655082009548
2336 -0.623592928761934 -0.623592928761934 0.159295477854420
2337 -0.623592928761934 0.247185857523870 0.159295477854420
2338 0.247185857523870 -0.623592928761934 0.159295477854420
2339 -0.910540973211094 -0.910540973211094 0.051155351317396
2340 -0.910540973211094 0.821081946422190 0.051155351317396
2341 0.821081946422190 -0.910540973211094 0.051155351317396
2342 -0.556074021678468 0.482397197568996 0.086567078754578
2343 0.482397197568996 -0.926323175890528 0.086567078754578
2344 -0.926323175890528 -0.556074021678468 0.086567078754578
2345 -0.556074021678468 -0.926323175890528 0.086567078754578
2346 0.482397197568996 -0.556074021678468 0.086567078754578
2347 -0.926323175890528 0.482397197568996 0.086567078754578
2348 Gauss quadrature points and weights on the reference triangle order p=9
2349
2350 25
2351 -0.333333333333333 -0.333333333333333 0.181635980765508
2352 -0.028844733232686 -0.028844733232686 0.073451915512934
2353 -0.028844733232686 -0.942310533534630 0.073451915512934
2354 -0.942310533534630 -0.028844733232686 0.073451915512934
2355 -0.781036849029926 -0.781036849029926 0.090642118871056
2356 -0.781036849029926 0.562073698059852 0.090642118871056
2357 0.562073698059852 -0.781036849029926 0.090642118871056
2358 -0.384120322471758 0.100705883641998 0.145515833690840
2359 0.100705883641998 -0.716585561170240 0.145515833690840
2360 -0.716585561170240 -0.384120322471758 0.145515833690840
2361 -0.384120322471758 -0.716585561170240 0.145515833690840
2362 0.100705883641998 -0.384120322471758 0.145515833690840
2363 -0.716585561170240 0.100705883641998 0.145515833690840
2364 -0.506654878720194 0.456647809194822 0.056654485062114
2365 0.456647809194822 -0.949992930474628 0.056654485062114
2366 -0.949992930474628 -0.506654878720194 0.056654485062114
2367 -0.506654878720194 -0.949992930474628 0.056654485062114
2368 0.456647809194822 -0.506654878720194 0.056654485062114
2369 -0.949992930474628 0.456647809194822 0.056654485062114
2370 -0.866393497975600 0.847311867175000 0.018843333927466
2371 0.847311867175000 -0.980918369199402 0.018843333927466
2372 -0.980918369199402 -0.866393497975600 0.018843333927466
2373 -0.866393497975600 -0.980918369199402 0.018843333927466
2374 0.847311867175000 -0.866393497975600 0.018843333927466
2375 -0.980918369199402 0.847311867175000 0.018843333927466
2376 Gauss quadrature points and weights on the reference triangle order p=10
2377
2378 27
2379 0.069222096541516 0.069222096541516 0.001854012657922
2380 0.069222096541516 -1.138444193083034 0.001854012657922
2381 -1.138444193083034 0.069222096541516 0.001854012657922
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2397 -0.286758703477414 -0.899643723379010 0.104674223924408
2398 0.186402426856426 -0.286758703477414 0.104674223924408
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2406 Gauss quadrature points and weights on the reference triangle order p=11
2407
2408 33
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2420 0.489695417833656 -0.744847708916828 0.069592225861418
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2427 -0.448573460628972 -0.769313010930604 0.080743115532762
2428 0.217886471559576 -0.448573460628972 0.080743115532762
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2435 -0.954323335555486 0.391672173575606 0.044713546404606
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2437 0.716028067088146 -0.948531898903340 0.034632462217318
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2439 -0.767496168184806 -0.948531898903340 0.034632462217318
2440 0.716028067088146 -0.767496168184806 0.034632462217318
2441 -0.948531898903340 0.716028067088146 0.034632462217318
2442 Gauss quadrature points and weights on the reference triangle order p=12
2443
2444 37
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2457 0.082401711828674 -0.541200855914338 0.094727173072710
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2468 0.272702349123320 -0.462410005882478 0.073696805457464
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2474 0.380338319973810 -0.416539866531424 0.034802926607644
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2480 0.702819075668482 -0.747285229016662 0.031043573678090
2481 -0.955533846651820 0.702819075668482 0.031043573678090
2482 Gauss quadrature points and weights on the reference triangle order p=13
2483
2484 42
2485 -0.022072179275642 -0.022072179275642 0.043767162738858
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2499 0.752800467636510 -0.876400233818254 0.028867399339554
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2502 0.9224361550051960 -0.961218077502598 0.009846807204800
2503 -0.655466624357288 0.541217109549992 0.049331506425128
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2505 -0.885750485192704 -0.655466624357288 0.049331506425128
2506 -0.655466624357288 -0.885750485192704 0.049331506425128
2507 0.541217109549992 -0.655466624357288 0.049331506425128
2508 -0.885750485192704 0.541217109549992 0.049331506425128
2509 -0.326277080407310 0.140444581693366 0.077143021574122
2510 0.140444581693366 -0.814167501286056 0.077143021574122
2511 -0.814167501286056 -0.326277080407310 0.077143021574122
2512 -0.326277080407310 -0.814167501286056 0.077143021574122
2513 0.140444581693366 -0.326277080407310 0.077143021574122
2514 -0.814167501286056 0.140444581693366 0.077143021574122
2515 -0.403254235727484 0.373960335616176 0.028872616227068
2516 0.373960335616176 -0.970706099888692 0.028872616227068
2517 -0.970706099888692 -0.403254235727484 0.028872616227068
2518 -0.403254235727484 -0.970706099888692 0.028872616227068
2519 0.373960335616176 -0.403254235727484 0.028872616227068
2520 -0.970706099888692 0.373960335616176 0.028872616227068
2521 -0.762051004606086 0.759514342740342 0.010020457677002
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2525 0.759514342740342 -0.762051004606086 0.010020457677002
2526 -0.997463338134256 0.759514342740342 0.010020457677002
2527 Gauss quadrature points and weights on the reference triangle order p=14
2528
2529 48
2530 0.013945833716486 0.013945833716486 0.003833751285698
2531 0.013945833716486 -1.027891667432972 0.003833751285698
2532 -1.027891667432972 0.013945833716486 0.003833751285698
2533 -0.137187291433954 -0.137187291433954 0.088498054542290
2534 -0.137187291433954 -0.725625417132090 0.088498054542290
2535 -0.725625417132090 -0.137187291433954 0.088498054542290
2536 -0.444612710305712 -0.444612710305712 0.102373097437704
2537 -0.444612710305712 -0.110774579388578 0.102373097437704
2538 -0.110774579388578 -0.444612710305712 0.102373097437704
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2540 -0.747070217917492 0.494140435834984 0.047375471741376
2541 0.494140435834984 -0.747070217917492 0.047375471741376
2542 -0.858383228050628 -0.858383228050628 0.026579551380042
2543 -0.858383228050628 0.716766456101256 0.026579551380042
2544 0.716766456101256 -0.858383228050628 0.026579551380042
2545 -0.962069659517854 -0.962069659517854 0.009497833216384
2546 -0.962069659517854 0.924139319035706 0.009497833216384
2547 0.924139319035706 -0.962069659517854 0.009497833216384
2548 -0.477377257719826 0.209908933786582 0.077100145199186
2549 0.209908933786582 -0.732531676066758 0.077100145199186
2550 -0.732531676066758 -0.477377257719826 0.077100145199186
2551 -0.477377257719826 -0.732531676066758 0.077100145199186
2552 0.209908933786582 -0.477377257719826 0.077100145199186
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2554 -0.223906465819462 0.151173111025628 0.054431628641248
2555 0.151173111025628 -0.927266645206166 0.054431628641248
2556 -0.927266645206166 -0.223906465819462 0.054431628641248
2557 -0.223906465819462 -0.927266645206166 0.054431628641248
2558 0.151173111025628 -0.223906465819462 0.054431628641248
2559 -0.927266645206166 0.151173111025628 0.054431628641248
2560 -0.428575559900168 0.448925326153310 0.004364154733594
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2563 -0.428575559900168 -1.020349766253142 0.004364154733594
2564 0.448925326153310 -0.428575559900168 0.004364154733594
2565 -1.020349766253142 0.448925326153310 0.004364154733594
2566 -0.568800671855432 0.495112932103676 0.043010639695462
2567 0.495112932103676 -0.926312260248244 0.043010639695462
2568 -0.926312260248244 -0.568800671855432 0.043010639695462
2569 -0.568800671855432 -0.926312260248244 0.043010639695462
2570 0.495112932103676 -0.568800671855432 0.043010639695462
2571 -0.926312260248244 0.495112932103676 0.043010639695462
2572 -0.792848766847228 0.767929148184832 0.015347885262098
2573 0.767929148184832 -0.975080381337602 0.015347885262098
2574 -0.975080381337602 -0.792848766847228 0.015347885262098
2575 -0.792848766847228 -0.975080381337602 0.015347885262098
2576 0.767929148184832 -0.792848766847228 0.015347885262098
2577 -0.975080381337602 0.767929148184832 0.015347885262098
2578 Gauss quadrature points and weights on the reference triangle order p=15
2579
2580 52
2581 -0.333333333333333 -0.333333333333333 0.093751394855284
2582 -0.005238916103124 -0.005238916103124 0.012811757157170
2583 -0.005238916103124 -0.989522167793754 0.012811757157170
2584 -0.989522167793754 -0.005238916103124 0.012811757157170
2585 -0.173061122901296 -0.173061122901296 0.083420593478774
2586 -0.173061122901296 -0.653877754197410 0.083420593478774
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2593 0.037785000121916 -0.518892500060958 0.084265045523300
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2599 0.698139249370104 -0.849069624685052 0.028400197850048
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2606 -0.406888806840226 -0.792848615509496 0.065546294921254
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2608 -0.792848615509496 0.199737422349722 0.065546294921254
2609 -0.324553873193842 0.284387049883010 0.030596612496882
2610 0.284387049883010 -0.959833176689168 0.030596612496882
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2619 0.599185441942654 -0.590503436714376 0.004772488385678
2620 -1.008682005228278 0.599185441942654 0.004772488385678
2621 -0.621283015738754 0.537399442802736 0.038169585511798
2622 0.537399442802736 -0.916116427063980 0.038169585511798
2623 -0.916116427063980 -0.621283015738754 0.038169585511798
2624 -0.621283015738754 -0.916116427063980 0.038169585511798
2625 0.537399442802736 -0.621283015738754 0.038169585511798
2626 -0.916116427063980 0.537399442802736 0.038169585511798
2627 -0.829432768634686 0.800798128173322 0.013700109093084
2628 0.800798128173322 -0.971365359538638 0.013700109093084
2629 -0.971365359538638 -0.829432768634686 0.013700109093084
2630 -0.829432768634686 -0.971365359538638 0.013700109093084
2631 0.800798128173322 -0.829432768634686 0.013700109093084
2632 -0.971365359538638 0.800798128173322 0.013700109093084
2633 Gauss quadrature points and weights on the reference triangle order p=16
2634
2635 61
2636 -0.333333333333333 -0.333333333333333 0.066874398581606
2637 -0.005658918886452 -0.005658918886452 0.010186830881014
2638 -0.005658918886452 -0.988682162227096 0.010186830881014
2639 -0.988682162227096 -0.005658918886452 0.010186830881014
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2645 -0.800959876083126 -0.099520061958436 0.048701756707344
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2648 -0.601064957509588 -0.199467521245206 0.062215101737938
2649 -0.495717464058094 -0.495717464058094 0.062514222437240
2650 -0.495717464058094 -0.008565071883810 0.062514222437240
2651 -0.008565071883810 -0.495717464058094 0.062514222437240
2652 -0.675905990683078 -0.675905990683078 0.049631308679330
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2654 0.351811981366154 -0.675905990683078 0.049631308679330
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2657 0.696496470957016 -0.848248235478508 0.028112146141114
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2659 -0.968690546064356 0.937381092128712 0.006389352347558
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2665 0.310986407618846 -0.331360265272684 0.016239310637986
2666 -0.979626142346162 0.310986407618846 0.016239310637986
2667 -0.415556924406112 0.144675181064040 0.053611484566326
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2670 -0.415556924406112 -0.729118256657928 0.053611484566326
2671 0.144675181064040 -0.415556924406112 0.053611484566326
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2673 -0.360850229153620 0.252002380572456 0.036919986421644
2674 0.252002380572456 -0.891152151418834 0.036919986421644
2675 -0.891152151418834 -0.360850229153620 0.036919986421644
2676 -0.360850229153620 -0.891152151418834 0.036919986421644
2677 0.252002380572456 -0.360850229153620 0.036919986421644
2678 -0.891152151418834 0.252002380572456 0.036919986421644
2679 -0.618591551615416 0.592854429948142 0.016953737068656
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2683 0.592854429948142 -0.618591551615416 0.016953737068656
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2695 0.809251008191216 -0.838577372640872 0.013331264008330
2696 -0.970673635550344 0.809251008191216 0.013331264008330
2697 Gauss quadrature points and weights on the reference triangle order p=17
2698
2699 70
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2719 -0.846803545029258 -0.846803545029258 0.030543855943664
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2723 -0.951495121293100 0.902990242586200 0.013587844045926
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2726 -0.913707265566070 0.827414531132142 -0.004446197459840
2727 0.827414531132142 -0.913707265566070 -0.004446197459840
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2729 0.265315937713272 -0.983138927595160 0.012663828152812
2730 -0.983138927595160 -0.282177010118112 0.012663828152812
2731 -0.282177010118112 -0.983138927595160 0.012663828152812
2732 0.265315937713272 -0.282177010118112 0.012663828152812
2733 -0.983138927595160 0.265315937713272 0.012663828152812
2734 -0.411195046496086 0.148821943021710 0.054515076098276
2735 0.148821943021710 -0.737626896525624 0.054515076098276
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2737 -0.411195046496086 -0.737626896525624 0.054515076098276
2738 0.148821943021710 -0.411195046496086 0.054515076098276
2739 -0.737626896525624 0.148821943021710 0.054515076098276
2740 -0.349964396716372 0.249558093585024 0.035353571298930
2741 0.249558093585024 -0.899593696868650 0.035353571298930
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2743 -0.349964396716372 -0.899593696868650 0.035353571298930
2744 0.249558093585024 -0.349964396716372 0.035353571298930
2745 -0.899593696868650 0.249558093585024 0.035353571298930
2746 -0.630524880667908 0.497866353046074 0.036758969276140
2747 0.497866353046074 -0.867341472378168 0.036758969276140
2748 -0.867341472378168 -0.630524880667908 0.036758969276140
2749 -0.630524880667908 -0.867341472378168 0.036758969276140
2750 0.497866353046074 -0.630524880667908 0.036758969276140
2751 -0.867341472378168 0.497866353046074 0.036758969276140
2752 -0.562406399973358 0.538414010840886 0.016209465616384
2753 0.538414010840886 -0.976007610867528 0.016209465616384
2754 -0.976007610867528 -0.562406399973358 0.016209465616384
2755 -0.562406399973358 -0.976007610867528 0.016209465616384
2756 0.538414010840886 -0.562406399973358 0.016209465616384
2757 -0.976007610867528 0.538414010840886 0.016209465616384
2758 -0.797640805727184 0.767924604546934 0.015268258141450
2759 0.767924604546934 -0.970283798819750 0.015268258141450
2760 -0.970283798819750 -0.797640805727184 0.015268258141450
2761 -0.797640805727184 -0.970283798819750 0.015268258141450
2762 0.767924604546934 -0.797640805727184 0.015268258141450
2763 -0.970283798819750 0.767924604546934 0.015268258141450
2764 -0.958250489434828 1.028694520010726 0.000092375321588
2765 1.028694520010726 -1.070444030575898 0.000092375321588
2766 -1.070444030575898 -0.9582504894348281 0.000092375321588
2767 -0.958250489434828 -1.070444030575898 0.000092375321588
2768 1.028694520010726 -0.958250489434828 0.000092375321588
2769 -1.070444030575898 1.028694520010726 0.000092375321588
2770 Gauss quadrature points and weights on the reference triangle order p=18
2771
2772 73
2773 -0.333333333333333 -0.333333333333333 0.065812662777838
2774 -0.020780025853988 -0.020780025853988 0.020661463782544
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2780 -0.197166638701138 -0.197166638701138 0.060532251738936
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2787 -0.645844115695740 0.291688231391482 0.048318425483282
2788 0.291688231391482 -0.645844115695740 0.048318425483282
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2790 -0.779877893544096 0.559755787088192 0.032101607173602
2791 0.559755787088192 -0.779877893544096 0.032101607173602
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2794 0.777885502992642 -0.888942751496320 0.016169160523568
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2797 0.949512544891086 -0.974756272445542 0.004158724054970
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2799 0.201267589589290 -0.992777164303176 0.007769753809962
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2802 0.201267589589290 -0.208490425286114 0.007769753809962
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2805 0.115206523177568 -0.731066490938440 0.051148321224044
2806 -0.731066490938440 -0.384140032239128 0.051148321224044
2807 -0.384140032239128 -0.731066490938440 0.051148321224044
2808 0.115206523177568 -0.384140032239128 0.051148321224044
2809 -0.731066490938440 0.115206523177568 0.051148321224044
2810 -0.470866103186960 0.441974051634730 0.017761807146676
2811 0.441974051634730 -0.971107948447770 0.017761807146676
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2813 -0.470866103186960 -0.971107948447770 0.017761807146676
2814 0.441974051634730 -0.470866103186960 0.017761807146676
2815 -0.971107948447770 0.441974051634730 0.017761807146676
2816 -0.282921295588098 0.189054137911742 0.032249093523462
2817 0.189054137911742 -0.906132842323644 0.032249093523462
2818 -0.906132842323644 -0.282921295588098 0.032249093523462
2819 -0.282921295588098 -0.906132842323644 0.032249093523462
2820 0.189054137911742 -0.282921295588098 0.032249093523462
2821 -0.906132842323644 0.189054137911742 0.032249093523462
2822 -0.684385188062810 0.678662947361678 0.004983883634982
2823 0.678662947361678 -0.994277759298866 0.004983883634982
2824 -0.994277759298866 -0.684385188062810 0.004983883634982
2825 -0.684385188062810 -0.994277759298866 0.004983883634982
2826 0.678662947361678 -0.684385188062810 0.004983883634982
2827 -0.994277759298866 0.678662947361678 0.004983883634982
2828 -0.849898806048178 0.402175957852346 0.036485680237902
2829 0.402175957852346 -0.552277151804168 0.036485680237902
2830 -0.552277151804168 -0.849898806048178 0.036485680237902
2831 -0.849898806048178 -0.552277151804168 0.036485680237902
2832 0.402175957852346 -0.849898806048178 0.036485680237902
2833 -0.552277151804168 0.402175957852346 0.036485680237902
2834 -0.715156797773234 0.645862648139714 0.020517127472398
2835 0.645862648139714 -0.930705850366480 0.020517127472398
2836 -0.930705850366480 -0.715156797773234 0.020517127472398
2837 -0.715156797773234 -0.930705850366480 0.020517127472398
2838 0.645862648139714 -0.715156797773234 0.020517127472398
2839 -0.930705850366480 0.645862648139714 0.020517127472398
2840 -0.869010743834124 0.848688505241568 0.007599857710604
2841 0.848688505241568 -0.979677761407444 0.007599857710604
2842 -0.979677761407444 -0.869010743834124 0.007599857710604
2843 -0.869010743834124 -0.979677761407444 0.007599857710604
2844 0.848688505241568 -0.869010743834124 0.007599857710604
2845 -0.979677761407444 0.848688505241568 0.007599857710604
2846 Gauss quadrature points and weights on the reference triangle order p=19
2847
2848 79
2849 -0.333333333333333 -0.333333333333333 0.066114111083248
2850 0.001900928704400 0.001900928704400 0.001734038371326
2851 0.001900928704400 -1.003801857408800 0.001734038371326
2852 -1.003801857408800 0.001900928704400 0.001734038371326
2853 -0.023574084130543 -0.023574084130543 0.023320105432896
2854 -0.023574084130543 -0.952851831738914 0.023320105432896
2855 -0.952851831738914 -0.023574084130543 0.023320105432896
2856 -0.089726626099435 -0.089726626099435 0.045753872712842
2857 -0.089726626099435 -0.820546727801130 0.045753872712842
2858 -0.820546727801130 -0.089726626099435 0.045753872712842
2859 -0.196007481363421 -0.196007481363421 0.060897965347876
2860 -0.196007481363421 -0.607985037273158 0.060897965347876
2861 -0.607985037273158 -0.196007481363421 0.060897965347876
2862 -0.488214180481157 -0.488214180481157 0.061249783450710
2863 -0.488214180481157 -0.023571639037686 0.061249783450710
2864 -0.023571639037686 -0.488214180481157 0.061249783450710
2865 -0.647023488009788 -0.647023488009788 0.048736115353600
2866 -0.647023488009788 0.294046976019576 0.048736115353600
2867 0.294046976019576 -0.647023488009788 0.048736115353600
2868 -0.791658289326483 -0.791658289326483 0.031994864064048
2869 -0.791658289326483 0.583316578652966 0.031994864064048
2870 0.583316578652966 -0.791658289326483 0.031994864064048
2871 -0.893862072318140 -0.893862072318140 0.015396603631204
2872 -0.893862072318140 0.787724144636280 0.015396603631204
2873 0.787724144636280 -0.893862072318140 0.015396603631204
2874 -0.916762569607942 -0.916762569607942 -0.001264120994976
2875 -0.916762569607942 0.833525139215884 -0.001264120994976
2876 0.833525139215884 -0.916762569607942 -0.001264120994976
2877 -0.976836157186356 -0.976836157186356 0.003502268602386
2878 -0.976836157186356 0.953672314372712 0.003502268602386
2879 0.953672314372712 -0.976836157186356 0.003502268602386
2880 -0.310288459541998 0.212805292212320 0.032931678379152
2881 0.212805292212320 -0.902516832670322 0.032931678379152
2882 -0.902516832670322 -0.310288459541998 0.032931678379152
2883 -0.310288459541998 -0.902516832670322 0.032931678379152
2884 0.212805292212320 -0.310288459541998 0.032931678379152
2885 -0.902516832670322 0.212805292212320 0.032931678379152
2886 -0.244313460810292 0.231685228913082 0.009678067080970
2887 0.231685228913082 -0.987371768102790 0.009678067080970
2888 -0.987371768102790 -0.244313460810292 0.009678067080970
2889 -0.244313460810292 -0.987371768102790 0.009678067080970
2890 0.231685228913082 -0.244313460810292 0.009678067080970
2891 -0.987371768102790 0.231685228913082 0.009678067080970
2892 -0.386729041875286 0.118096000780590 0.051609813069300
2893 0.118096000780590 -0.731366958905304 0.051609813069300
2894 -0.731366958905304 -0.386729041875286 0.051609813069300
2895 -0.386729041875286 -0.731366958905304 0.051609813069300
2896 0.118096000780590 -0.386729041875286 0.051609813069300
2897 -0.731366958905304 0.118096000780590 0.051609813069300
2898 -0.501161274450516 0.473213486525732 0.016942182108882
2899 0.473213486525732 -0.972052212075216 0.016942182108882
2900 -0.972052212075216 -0.501161274450516 0.016942182108882
2901 -0.501161274450516 -0.972052212075216 0.016942182108882
2902 0.473213486525732 -0.501161274450516 0.016942182108882
2903 -0.972052212075216 0.473213486525732 0.016942182108882
2904 -0.574448550394396 0.423350284574868 0.036709828212560
2905 0.423350284574868 -0.848901734180472 0.036709828212560
2906 -0.848901734180472 -0.574448550394396 0.036709828212560
2907 -0.574448550394396 -0.848901734180472 0.036709828212560
2908 0.423350284574868 -0.574448550394396 0.036709828212560
2909 -0.848901734180472 0.423350284574868 0.036709828212560
2910 -0.706069127893522 0.722805434309974 0.001408809355816
2911 0.722805434309974 -1.016736306416454 0.001408809355816
2912 -1.016736306416454 -0.706069127893522 0.001408809355816
2913 -0.706069127893522 -1.016736306416454 0.001408809355816
2914 0.722805434309974 -0.706069127893522 0.001408809355816
2915 -1.016736306416454 0.722805434309974 0.001408809355816
2916 -0.724546042342154 0.671173915824726 0.020225369854924
2917 0.671173915824726 -0.946627873482572 0.020225369854924
2918 -0.946627873482572 -0.724546042342154 0.020225369854924
2919 -0.724546042342154 -0.946627873482572 0.020225369854924
2920 0.671173915824726 -0.724546042342154 0.020225369854924
2921 -0.946627873482572 0.671173915824726 0.020225369854924
2922 -0.880607781701986 0.859512343113706 0.007147818771900
2923 0.859512343113706 -0.978904561411718 0.007147818771900
2924 -0.978904561411718 -0.880607781701986 0.007147818771900
2925 -0.880607781701986 -0.978904561411718 0.007147818771900
2926 0.859512343113706 -0.880607781701986 0.007147818771900
2927 -0.978904561411718 0.859512343113706 0.007147818771900
2928 Gauss quadrature points and weights on the reference triangle order p=20
2929 """
2930
2931
2932 economical_gauss_tetrahedron_table = """\
2933 1
2934 -0.500000000000000 -0.500000000000000 -0.500000000000000 1.333333333333333
2935 Gauss quadrature constants for the reference tetrahedron order p=1
2936
2937 4
2938 -0.723606797749979 -0.723606797749979 -0.723606797749979 0.333333333333333
2939 0.170820393249937 -0.723606797749979 -0.723606797749979 0.333333333333333
2940 -0.723606797749979 0.170820393249937 -0.723606797749979 0.333333333333333
2941 -0.723606797749979 -0.723606797749979 0.170820393249937 0.333333333333333
2942 Gauss quadrature constants for the reference tetrahedron order p=2
2943
2944 5
2945 -0.500000000000000 -0.500000000000000 -0.500000000000000 -1.066666666666667
2946 -0.666666666666667 -0.666666666666667 -0.666666666666667 0.600000000000000
2947 -0.666666666666667 -0.666666666666667 0.000000000000000 0.600000000000000
2948 -0.666666666666667 0.000000000000000 -0.666666666666667 0.600000000000000
2949 0.000000000000000 -0.666666666666667 -0.666666666666667 0.600000000000000
2950 Gauss quadrature constants for the reference tetrahedron order p=3
2951
2952 11
2953 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.105244444444444
2954 -0.857142857142857 -0.857142857142857 -0.857142857142857 0.060977777777778
2955 -0.857142857142857 -0.857142857142857 0.571428571428571 0.060977777777778
2956 -0.857142857142857 0.571428571428571 -0.857142857142857 0.060977777777778
2957 0.571428571428571 -0.857142857142857 -0.857142857142857 0.060977777777778
2958 -0.201192847666402 -0.201192847666402 -0.798807152333598 0.199111111111111
2959 -0.201192847666402 -0.798807152333598 -0.201192847666402 0.199111111111111
2960 -0.798807152333598 -0.201192847666402 -0.201192847666402 0.199111111111111
2961 -0.201192847666402 -0.798807152333598 -0.798807152333598 0.199111111111111
2962 -0.798807152333598 -0.201192847666402 -0.798807152333598 0.199111111111111
2963 -0.798807152333598 -0.798807152333598 -0.201192847666402 0.199111111111111
2964 Gauss quadrature constants for the reference tetrahedron order p=4
2965
2966 14
2967 -0.814529499378218 -0.814529499378218 -0.814529499378218 0.097990724155149
2968 0.443588498134653 -0.814529499378218 -0.814529499378218 0.097990724155149
2969 -0.814529499378218 0.443588498134653 -0.814529499378218 0.097990724155149
2970 -0.814529499378218 -0.814529499378218 0.443588498134653 0.097990724155149
2971 -0.378228161473399 -0.378228161473399 -0.378228161473399 0.150250567624021
2972 -0.865315515579804 -0.378228161473399 -0.378228161473399 0.150250567624021
2973 -0.378228161473399 -0.865315515579804 -0.378228161473399 0.150250567624021
2974 -0.378228161473399 -0.378228161473399 -0.865315515579804 0.150250567624021
2975 -0.091007408251299 -0.091007408251299 -0.908992591748701 0.056728027702775
2976 -0.091007408251299 -0.908992591748701 -0.091007408251299 0.056728027702775
2977 -0.908992591748701 -0.091007408251299 -0.091007408251299 0.056728027702775
2978 -0.091007408251299 -0.908992591748701 -0.908992591748701 0.056728027702775
2979 -0.908992591748701 -0.091007408251299 -0.908992591748701 0.056728027702775
2980 -0.908992591748701 -0.908992591748701 -0.091007408251299 0.056728027702775
2981 Gauss quadrature constants for the reference tetrahedron order p=5
2982
2983 24
2984 -0.570794257481696 -0.570794257481696 -0.570794257481696 0.053230333677557
2985 -0.287617227554912 -0.570794257481696 -0.570794257481696 0.053230333677557
2986 -0.570794257481696 -0.287617227554912 -0.570794257481696 0.053230333677557
2987 -0.570794257481696 -0.570794257481696 -0.287617227554912 0.053230333677557
2988 -0.918652082930777 -0.918652082930777 -0.918652082930777 0.013436281407094
2989 0.755956248792332 -0.918652082930777 -0.918652082930777 0.013436281407094
2990 -0.918652082930777 0.755956248792332 -0.918652082930777 0.013436281407094
2991 -0.918652082930777 -0.918652082930777 0.755956248792332 0.013436281407094
2992 -0.355324219715449 -0.355324219715449 -0.355324219715449 0.073809575391540
2993 -0.934027340853653 -0.355324219715449 -0.355324219715449 0.073809575391540
2994 -0.355324219715449 -0.934027340853653 -0.355324219715449 0.073809575391540
2995 -0.355324219715449 -0.355324219715449 -0.934027340853653 0.073809575391540
2996 -0.872677996249965 -0.872677996249965 -0.460655337083368 0.064285714285714
2997 -0.872677996249965 -0.460655337083368 -0.872677996249965 0.064285714285714
2998 -0.872677996249965 -0.872677996249965 0.206011329583298 0.064285714285714
2999 -0.872677996249965 0.206011329583298 -0.872677996249965 0.064285714285714
3000 -0.872677996249965 -0.460655337083368 0.206011329583298 0.064285714285714
3001 -0.872677996249965 0.206011329583298 -0.460655337083368 0.064285714285714
3002 -0.460655337083368 -0.872677996249965 -0.872677996249965 0.064285714285714
3003 -0.460655337083368 -0.872677996249965 0.206011329583298 0.064285714285714
3004 -0.460655337083368 0.206011329583298 -0.872677996249965 0.064285714285714
3005 0.206011329583298 -0.872677996249965 -0.460655337083368 0.064285714285714
3006 0.206011329583298 -0.872677996249965 -0.872677996249965 0.064285714285714
3007 0.206011329583298 -0.460655337083368 -0.872677996249965 0.064285714285714
3008 Gauss quadrature constants for the reference tetrahedron order p=6
3009
3010 31
3011 0.000000000000000 0.000000000000000 -1.000000000000000 0.007760141093474
3012 0.000000000000000 -1.000000000000000 0.000000000000000 0.007760141093474
3013 -1.000000000000000 0.000000000000000 0.000000000000000 0.007760141093474
3014 -1.000000000000000 -1.000000000000000 0.000000000000000 0.007760141093474
3015 -1.000000000000000 0.000000000000000 -1.000000000000000 0.007760141093474
3016 0.000000000000000 -1.000000000000000 -1.000000000000000 0.007760141093474
3017 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.146113787728871
3018 -0.843573615339364 -0.843573615339364 -0.843573615339364 0.084799532195309
3019 -0.843573615339364 -0.843573615339364 0.530720846018092 0.084799532195309
3020 -0.843573615339364 0.530720846018092 -0.843573615339364 0.084799532195309
3021 0.530720846018092 -0.843573615339364 -0.843573615339364 0.084799532195309
3022 -0.756313566672190 -0.756313566672190 -0.756313566672190 -0.500141920914655
3023 -0.756313566672190 -0.756313566672190 0.268940700016569 -0.500141920914655
3024 -0.756313566672190 0.268940700016569 -0.756313566672190 -0.500141920914655
3025 0.268940700016569 -0.756313566672190 -0.756313566672190 -0.500141920914655
3026 -0.334921671107159 -0.334921671107159 -0.334921671107159 0.039131402104588
3027 -0.334921671107159 -0.334921671107159 -0.995234986678524 0.039131402104588
3028 -0.334921671107159 -0.995234986678524 -0.334921671107159 0.039131402104588
3029 -0.995234986678524 -0.334921671107159 -0.334921671107159 0.039131402104588
3030 -0.800000000000000 -0.800000000000000 -0.600000000000000 0.220458553791887
3031 -0.800000000000000 -0.600000000000000 -0.800000000000000 0.220458553791887
3032 -0.800000000000000 -0.800000000000000 0.200000000000000 0.220458553791887
3033 -0.800000000000000 0.200000000000000 -0.800000000000000 0.220458553791887
3034 -0.800000000000000 -0.600000000000000 0.200000000000000 0.220458553791887
3035 -0.800000000000000 0.200000000000000 -0.600000000000000 0.220458553791887
3036 -0.600000000000000 -0.800000000000000 -0.800000000000000 0.220458553791887
3037 -0.600000000000000 -0.800000000000000 0.200000000000000 0.220458553791887
3038 -0.600000000000000 0.200000000000000 -0.800000000000000 0.220458553791887
3039 0.200000000000000 -0.800000000000000 -0.600000000000000 0.220458553791887
3040 0.200000000000000 -0.800000000000000 -0.800000000000000 0.220458553791887
3041 0.200000000000000 -0.600000000000000 -0.800000000000000 0.220458553791887
3042 Gauss quadrature constants for the reference tetrahedron order p=7
3043
3044 43
3045 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.164001509269119
3046 -0.586340136778654 -0.586340136778654 -0.586340136778654 0.114002446582935
3047 -0.586340136778654 -0.586340136778654 -0.240979589664039 0.114002446582935
3048 -0.586340136778654 -0.240979589664039 -0.586340136778654 0.114002446582935
3049 -0.240979589664039 -0.586340136778654 -0.586340136778654 0.114002446582935
3050 -0.835792823378907 -0.835792823378907 -0.835792823378907 0.015736266505071
3051 -0.835792823378907 -0.835792823378907 0.507378470136720 0.015736266505071
3052 -0.835792823378907 0.507378470136720 -0.835792823378907 0.015736266505071
3053 0.507378470136720 -0.835792823378907 -0.835792823378907 0.015736266505071
3054 -0.988436098989604 -0.988436098989604 -0.988436098989604 0.001358672872743
3055 -0.988436098989604 -0.988436098989604 0.965308296968812 0.001358672872743
3056 -0.988436098989604 0.965308296968812 -0.988436098989604 0.001358672872743
3057 0.965308296968812 -0.988436098989604 -0.988436098989604 0.001358672872743
3058 -0.898934519962212 -0.898934519962212 -0.101065480037788 0.036637470595738
3059 -0.898934519962212 -0.101065480037788 -0.898934519962212 0.036637470595738
3060 -0.101065480037788 -0.898934519962212 -0.898934519962212 0.036637470595738
3061 -0.898934519962212 -0.101065480037788 -0.101065480037788 0.036637470595738
3062 -0.101065480037788 -0.898934519962212 -0.101065480037788 0.036637470595738
3063 -0.101065480037788 -0.101065480037788 -0.898934519962212 0.036637470595738
3064 -0.541866927766378 -0.541866927766378 -0.928720834422932 0.045635886469455
3065 -0.541866927766378 -0.928720834422932 -0.541866927766378 0.045635886469455
3066 -0.541866927766378 -0.541866927766378 0.012454689955687 0.045635886469455
3067 -0.541866927766378 0.012454689955687 -0.541866927766378 0.045635886469455
3068 -0.541866927766378 -0.928720834422932 0.012454689955687 0.045635886469455
3069 -0.541866927766378 0.012454689955687 -0.928720834422932 0.045635886469455
3070 -0.928720834422932 -0.541866927766378 -0.541866927766378 0.045635886469455
3071 -0.928720834422932 -0.541866927766378 0.012454689955687 0.045635886469455
3072 -0.928720834422932 0.012454689955687 -0.541866927766378 0.045635886469455
3073 0.012454689955687 -0.541866927766378 -0.928720834422932 0.045635886469455
3074 0.012454689955687 -0.541866927766378 -0.541866927766378 0.045635886469455
3075 0.012454689955687 -0.928720834422932 -0.541866927766378 0.045635886469455
3076 -0.926784500893605 -0.926784500893605 -0.619027916130733 0.017124153129297
3077 -0.926784500893605 -0.619027916130733 -0.926784500893605 0.017124153129297
3078 -0.926784500893605 -0.926784500893605 0.472596917917943 0.017124153129297
3079 -0.926784500893605 0.472596917917943 -0.926784500893605 0.017124153129297
3080 -0.926784500893605 -0.619027916130733 0.472596917917943 0.017124153129297
3081 -0.926784500893605 0.472596917917943 -0.619027916130733 0.017124153129297
3082 -0.619027916130733 -0.926784500893605 -0.926784500893605 0.017124153129297
3083 -0.619027916130733 -0.926784500893605 0.472596917917943 0.017124153129297
3084 -0.619027916130733 0.472596917917943 -0.926784500893605 0.017124153129297
3085 0.472596917917943 -0.926784500893605 -0.619027916130733 0.017124153129297
3086 0.472596917917943 -0.926784500893605 -0.926784500893605 0.017124153129297
3087 0.472596917917943 -0.619027916130733 -0.926784500893605 0.017124153129297
3088 Gauss quadrature constants for the reference tetrahedron order p=8
3089
3090 53
3091 -0.500000000000000 -0.500000000000000 -0.500000000000000 -1.102392306608869
3092 -0.903297922900526 -0.903297922900526 -0.903297922900526 0.014922692552682
3093 -0.903297922900526 -0.903297922900526 0.709893768701580 0.014922692552682
3094 -0.903297922900526 0.709893768701580 -0.903297922900526 0.014922692552682
3095 0.709893768701580 -0.903297922900526 -0.903297922900526 0.014922692552682
3096 -0.350841439764235 -0.350841439764235 -0.350841439764235 0.034475391755947
3097 -0.350841439764235 -0.350841439764235 -0.947475680707294 0.034475391755947
3098 -0.350841439764235 -0.947475680707294 -0.350841439764235 0.034475391755947
3099 -0.947475680707294 -0.350841439764235 -0.350841439764235 0.034475391755947
3100 -0.770766919552010 -0.770766919552010 -0.770766919552010 -0.721478131849612
3101 -0.770766919552010 -0.770766919552010 0.312300758656029 -0.721478131849612
3102 -0.770766919552010 0.312300758656029 -0.770766919552010 -0.721478131849612
3103 0.312300758656029 -0.770766919552010 -0.770766919552010 -0.721478131849612
3104 -0.549020096176972 -0.549020096176972 -0.549020096176972 0.357380609620092
3105 -0.549020096176972 -0.549020096176972 -0.352939711469084 0.357380609620092
3106 -0.549020096176972 -0.352939711469084 -0.549020096176972 0.357380609620092
3107 -0.352939711469084 -0.549020096176972 -0.549020096176972 0.357380609620092
3108 -0.736744381506260 -0.736744381506260 -0.832670596765630 0.277603247076406
3109 -0.736744381506260 -0.832670596765630 -0.736744381506260 0.277603247076406
3110 -0.736744381506260 -0.736744381506260 0.306159359778151 0.277603247076406
3111 -0.736744381506260 0.306159359778151 -0.736744381506260 0.277603247076406
3112 -0.736744381506260 -0.832670596765630 0.306159359778151 0.277603247076406
3113 -0.736744381506260 0.306159359778151 -0.832670596765630 0.277603247076406
3114 -0.832670596765630 -0.736744381506260 -0.736744381506260 0.277603247076406
3115 -0.832670596765630 -0.736744381506260 0.306159359778151 0.277603247076406
3116 -0.832670596765630 0.306159359778151 -0.736744381506260 0.277603247076406
3117 0.306159359778151 -0.736744381506260 -0.832670596765630 0.277603247076406
3118 0.306159359778151 -0.736744381506260 -0.736744381506260 0.277603247076406
3119 0.306159359778151 -0.832670596765630 -0.736744381506260 0.277603247076406
3120 -0.132097077177186 -0.132097077177186 -0.784460280901143 0.026820671221285
3121 -0.132097077177186 -0.784460280901143 -0.132097077177186 0.026820671221285
3122 -0.132097077177186 -0.132097077177186 -0.951345564744484 0.026820671221285
3123 -0.132097077177186 -0.951345564744484 -0.132097077177186 0.026820671221285
3124 -0.132097077177186 -0.784460280901143 -0.951345564744484 0.026820671221285
3125 -0.132097077177186 -0.951345564744484 -0.784460280901143 0.026820671221285
3126 -0.784460280901143 -0.132097077177186 -0.132097077177186 0.026820671221285
3127 -0.784460280901143 -0.132097077177186 -0.951345564744484 0.026820671221285
3128 -0.784460280901143 -0.951345564744484 -0.132097077177186 0.026820671221285
3129 -0.951345564744484 -0.132097077177186 -0.784460280901143 0.026820671221285
3130 -0.951345564744484 -0.132097077177186 -0.132097077177186 0.026820671221285
3131 -0.951345564744484 -0.784460280901143 -0.132097077177186 0.026820671221285
3132 -1.002752554636276 -1.002752554636276 -0.446893054726385 0.003453031004456
3133 -1.002752554636276 -0.446893054726385 -1.002752554636276 0.003453031004456
3134 -1.002752554636276 -1.002752554636276 0.452398163998938 0.003453031004456
3135 -1.002752554636276 0.452398163998938 -1.002752554636276 0.003453031004456
3136 -1.002752554636276 -0.446893054726385 0.452398163998938 0.003453031004456
3137 -1.002752554636276 0.452398163998938 -0.446893054726385 0.003453031004456
3138 -0.446893054726385 -1.002752554636276 -1.002752554636276 0.003453031004456
3139 -0.446893054726385 -1.002752554636276 0.452398163998938 0.003453031004456
3140 -0.446893054726385 0.452398163998938 -1.002752554636276 0.003453031004456
3141 0.452398163998938 -1.002752554636276 -0.446893054726385 0.003453031004456
3142 0.452398163998938 -1.002752554636276 -1.002752554636276 0.003453031004456
3143 0.452398163998938 -0.446893054726385 -1.002752554636276 0.003453031004456
3144 Gauss quadrature constants for the reference tetrahedron order p=9
3145
3146 126
3147 -0.857142857142857 -0.857142857142857 0.571428571428571 0.362902592520648
3148 -0.857142857142857 -0.571428571428571 0.285714285714286 0.362902592520648
3149 -0.857142857142857 -0.285714285714286 0.000000000000000 0.362902592520648
3150 -0.857142857142857 0.000000000000000 -0.285714285714286 0.362902592520648
3151 -0.857142857142857 0.285714285714286 -0.571428571428571 0.362902592520648
3152 -0.857142857142857 0.571428571428571 -0.857142857142857 0.362902592520648
3153 -0.571428571428571 -0.857142857142857 0.285714285714286 0.362902592520648
3154 -0.571428571428571 -0.571428571428571 0.000000000000000 0.362902592520648
3155 -0.571428571428571 -0.285714285714286 -0.285714285714286 0.362902592520648
3156 -0.571428571428571 0.000000000000000 -0.571428571428571 0.362902592520648
3157 -0.571428571428571 0.285714285714286 -0.857142857142857 0.362902592520648
3158 -0.285714285714286 -0.857142857142857 0.000000000000000 0.362902592520648
3159 -0.285714285714286 -0.571428571428571 -0.285714285714286 0.362902592520648
3160 -0.285714285714286 -0.285714285714286 -0.571428571428571 0.362902592520648
3161 -0.285714285714286 0.000000000000000 -0.857142857142857 0.362902592520648
3162 0.000000000000000 -0.857142857142857 -0.285714285714286 0.362902592520648
3163 0.000000000000000 -0.571428571428571 -0.571428571428571 0.362902592520648
3164 0.000000000000000 -0.285714285714286 -0.857142857142857 0.362902592520648
3165 0.285714285714286 -0.857142857142857 -0.571428571428571 0.362902592520648
3166 0.285714285714286 -0.571428571428571 -0.857142857142857 0.362902592520648
3167 0.571428571428571 -0.857142857142857 -0.857142857142857 0.362902592520648
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3721 -0.571428571428571 -0.285714285714286 -0.571428571428571 1.815269009670992
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3723 -0.285714285714286 -0.857142857142857 -0.285714285714286 1.815269009670992
3724 -0.285714285714286 -0.571428571428571 -0.571428571428571 1.815269009670992
3725 -0.285714285714286 -0.285714285714286 -0.857142857142857 1.815269009670992
3726 0.000000000000000 -0.857142857142857 -0.571428571428571 1.815269009670992
3727 0.000000000000000 -0.571428571428571 -0.857142857142857 1.815269009670992
3728 0.285714285714286 -0.857142857142857 -0.857142857142857 1.815269009670992
3729 -0.857142857142857 -0.857142857142857 0.000000000000000 1.815269009670992
3730 -0.857142857142857 -0.571428571428571 -0.285714285714286 1.815269009670992
3731 -0.857142857142857 -0.285714285714286 -0.571428571428571 1.815269009670992
3732 -0.857142857142857 0.000000000000000 -0.857142857142857 1.815269009670992
3733 -0.571428571428571 -0.857142857142857 -0.285714285714286 1.815269009670992
3734 -0.571428571428571 -0.571428571428571 -0.571428571428571 1.815269009670992
3735 -0.571428571428571 -0.285714285714286 -0.857142857142857 1.815269009670992
3736 -0.285714285714286 -0.857142857142857 -0.571428571428571 1.815269009670992
3737 -0.285714285714286 -0.571428571428571 -0.857142857142857 1.815269009670992
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3739 -0.857142857142857 -0.857142857142857 -0.285714285714286 1.815269009670992
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3745 -0.857142857142857 -0.857142857142857 -0.571428571428571 1.815269009670992
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3760 -0.166666666666667 -0.166666666666667 -0.833333333333333 -0.958821749678893
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3762 0.166666666666667 -0.500000000000000 -0.833333333333333 -0.958821749678893
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3764 -0.833333333333333 -0.833333333333333 0.166666666666667 -0.958821749678893
3765 -0.833333333333333 -0.500000000000000 -0.166666666666667 -0.958821749678893
3766 -0.833333333333333 -0.166666666666667 -0.500000000000000 -0.958821749678893
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3772 -0.166666666666667 -0.500000000000000 -0.833333333333333 -0.958821749678893
3773 0.166666666666667 -0.833333333333333 -0.833333333333333 -0.958821749678893
3774 -0.833333333333333 -0.833333333333333 -0.166666666666667 -0.958821749678893
3775 -0.833333333333333 -0.500000000000000 -0.500000000000000 -0.958821749678893
3776 -0.833333333333333 -0.166666666666667 -0.833333333333333 -0.958821749678893
3777 -0.500000000000000 -0.833333333333333 -0.500000000000000 -0.958821749678893
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3779 -0.166666666666667 -0.833333333333333 -0.833333333333333 -0.958821749678893
3780 -0.833333333333333 -0.833333333333333 -0.500000000000000 -0.958821749678893
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3783 -0.833333333333333 -0.833333333333333 -0.833333333333333 -0.958821749678893
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3785 -0.800000000000000 -0.400000000000000 0.000000000000000 0.233372916620478
3786 -0.800000000000000 0.000000000000000 -0.400000000000000 0.233372916620478
3787 -0.800000000000000 0.400000000000000 -0.800000000000000 0.233372916620478
3788 -0.400000000000000 -0.800000000000000 0.000000000000000 0.233372916620478
3789 -0.400000000000000 -0.400000000000000 -0.400000000000000 0.233372916620478
3790 -0.400000000000000 0.000000000000000 -0.800000000000000 0.233372916620478
3791 0.000000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3792 0.000000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
3793 0.400000000000000 -0.800000000000000 -0.800000000000000 0.233372916620478
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3795 -0.800000000000000 -0.400000000000000 -0.400000000000000 0.233372916620478
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3797 -0.400000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3798 -0.400000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
3799 0.000000000000000 -0.800000000000000 -0.800000000000000 0.233372916620478
3800 -0.800000000000000 -0.800000000000000 -0.400000000000000 0.233372916620478
3801 -0.800000000000000 -0.400000000000000 -0.800000000000000 0.233372916620478
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3803 -0.800000000000000 -0.800000000000000 -0.800000000000000 0.233372916620478
3804 -0.750000000000000 -0.750000000000000 0.250000000000000 -0.022991022694726
3805 -0.750000000000000 -0.250000000000000 -0.250000000000000 -0.022991022694726
3806 -0.750000000000000 0.250000000000000 -0.750000000000000 -0.022991022694726
3807 -0.250000000000000 -0.750000000000000 -0.250000000000000 -0.022991022694726
3808 -0.250000000000000 -0.250000000000000 -0.750000000000000 -0.022991022694726
3809 0.250000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3810 -0.750000000000000 -0.750000000000000 -0.250000000000000 -0.022991022694726
3811 -0.750000000000000 -0.250000000000000 -0.750000000000000 -0.022991022694726
3812 -0.250000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3813 -0.750000000000000 -0.750000000000000 -0.750000000000000 -0.022991022694726
3814 -0.666666666666667 -0.666666666666667 0.000000000000000 0.000665685876623
3815 -0.666666666666667 0.000000000000000 -0.666666666666667 0.000665685876623
3816 0.000000000000000 -0.666666666666667 -0.666666666666667 0.000665685876623
3817 -0.666666666666667 -0.666666666666667 -0.666666666666667 0.000665685876623
3818 -0.500000000000000 -0.500000000000000 -0.500000000000000 -0.000002606055516
3819 Gauss quadrature constants for the reference tetrahedron order p=15
3820
3821 495
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3824 -0.900000000000000 -0.500000000000000 0.300000000000000 0.657650819729946
3825 -0.900000000000000 -0.300000000000000 0.100000000000000 0.657650819729946
3826 -0.900000000000000 -0.100000000000000 -0.100000000000000 0.657650819729946
3827 -0.900000000000000 0.100000000000000 -0.300000000000000 0.657650819729946
3828 -0.900000000000000 0.300000000000000 -0.500000000000000 0.657650819729946
3829 -0.900000000000000 0.500000000000000 -0.700000000000000 0.657650819729946
3830 -0.900000000000000 0.700000000000000 -0.900000000000000 0.657650819729946
3831 -0.700000000000000 -0.900000000000000 0.500000000000000 0.657650819729946
3832 -0.700000000000000 -0.700000000000000 0.300000000000000 0.657650819729946
3833 -0.700000000000000 -0.500000000000000 0.100000000000000 0.657650819729946
3834 -0.700000000000000 -0.300000000000000 -0.100000000000000 0.657650819729946
3835 -0.700000000000000 -0.100000000000000 -0.300000000000000 0.657650819729946
3836 -0.700000000000000 0.100000000000000 -0.500000000000000 0.657650819729946
3837 -0.700000000000000 0.300000000000000 -0.700000000000000 0.657650819729946
3838 -0.700000000000000 0.500000000000000 -0.900000000000000 0.657650819729946
3839 -0.500000000000000 -0.900000000000000 0.300000000000000 0.657650819729946
3840 -0.500000000000000 -0.700000000000000 0.100000000000000 0.657650819729946
3841 -0.500000000000000 -0.500000000000000 -0.100000000000000 0.657650819729946
3842 -0.500000000000000 -0.300000000000000 -0.300000000000000 0.657650819729946
3843 -0.500000000000000 -0.100000000000000 -0.500000000000000 0.657650819729946
3844 -0.500000000000000 0.100000000000000 -0.700000000000000 0.657650819729946
3845 -0.500000000000000 0.300000000000000 -0.900000000000000 0.657650819729946
3846 -0.300000000000000 -0.900000000000000 0.100000000000000 0.657650819729946
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3849 -0.300000000000000 -0.300000000000000 -0.500000000000000 0.657650819729946
3850 -0.300000000000000 -0.100000000000000 -0.700000000000000 0.657650819729946
3851 -0.300000000000000 0.100000000000000 -0.900000000000000 0.657650819729946
3852 -0.100000000000000 -0.900000000000000 -0.100000000000000 0.657650819729946
3853 -0.100000000000000 -0.700000000000000 -0.300000000000000 0.657650819729946
3854 -0.100000000000000 -0.500000000000000 -0.500000000000000 0.657650819729946
3855 -0.100000000000000 -0.300000000000000 -0.700000000000000 0.657650819729946
3856 -0.100000000000000 -0.100000000000000 -0.900000000000000 0.657650819729946
3857 0.100000000000000 -0.900000000000000 -0.300000000000000 0.657650819729946
3858 0.100000000000000 -0.700000000000000 -0.500000000000000 0.657650819729946
3859 0.100000000000000 -0.500000000000000 -0.700000000000000 0.657650819729946
3860 0.100000000000000 -0.300000000000000 -0.900000000000000 0.657650819729946
3861 0.300000000000000 -0.900000000000000 -0.500000000000000 0.657650819729946
3862 0.300000000000000 -0.700000000000000 -0.700000000000000 0.657650819729946
3863 0.300000000000000 -0.500000000000000 -0.900000000000000 0.657650819729946
3864 0.500000000000000 -0.900000000000000 -0.700000000000000 0.657650819729946
3865 0.500000000000000 -0.700000000000000 -0.900000000000000 0.657650819729946
3866 0.700000000000000 -0.900000000000000 -0.900000000000000 0.657650819729946
3867 -0.900000000000000 -0.900000000000000 0.500000000000000 0.657650819729946
3868 -0.900000000000000 -0.700000000000000 0.300000000000000 0.657650819729946
3869 -0.900000000000000 -0.500000000000000 0.100000000000000 0.657650819729946
3870 -0.900000000000000 -0.300000000000000 -0.100000000000000 0.657650819729946
3871 -0.900000000000000 -0.100000000000000 -0.300000000000000 0.657650819729946
3872 -0.900000000000000 0.100000000000000 -0.500000000000000 0.657650819729946
3873 -0.900000000000000 0.300000000000000 -0.700000000000000 0.657650819729946
3874 -0.900000000000000 0.500000000000000 -0.900000000000000 0.657650819729946
3875 -0.700000000000000 -0.900000000000000 0.300000000000000 0.657650819729946
3876 -0.700000000000000 -0.700000000000000 0.100000000000000 0.657650819729946
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4289 0.000000000000000 -0.800000000000000 -0.400000000000000 -0.077790972206826
4290 0.000000000000000 -0.400000000000000 -0.800000000000000 -0.077790972206826
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4299 -0.800000000000000 -0.400000000000000 -0.800000000000000 -0.077790972206826
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4301 -0.800000000000000 -0.800000000000000 -0.800000000000000 -0.077790972206826
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4317 Gauss quadrature constants for the reference tetrahedron order p=17
4318
4319 715
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4350 -0.363636363636364 -0.363636363636364 -0.363636363636364 0.870591471154497
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5015 0.000000000000000 -0.800000000000000 -0.800000000000000 0.020258065678861
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5021 -0.750000000000000 -0.250000000000000 -0.250000000000000 -0.000667313130368
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5024 -0.250000000000000 -0.250000000000000 -0.750000000000000 -0.000667313130368
5025 0.250000000000000 -0.750000000000000 -0.750000000000000 -0.000667313130368
5026 -0.750000000000000 -0.750000000000000 -0.250000000000000 -0.000667313130368
5027 -0.750000000000000 -0.250000000000000 -0.750000000000000 -0.000667313130368
5028 -0.250000000000000 -0.750000000000000 -0.750000000000000 -0.000667313130368
5029 -0.750000000000000 -0.750000000000000 -0.750000000000000 -0.000667313130368
5030 -0.666666666666667 -0.666666666666667 0.000000000000000 0.000005290478415
5031 -0.666666666666667 0.000000000000000 -0.666666666666667 0.000005290478415
5032 0.000000000000000 -0.666666666666667 -0.666666666666667 0.000005290478415
5033 -0.666666666666667 -0.666666666666667 -0.666666666666667 0.000005290478415
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5035 Gauss quadrature constants for the reference tetrahedron order p=19
5036
5037 1001
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5941 -0.571428571428571 -0.285714285714286 -0.571428571428571 -0.612213575618572
5942 -0.571428571428571 0.000000000000000 -0.857142857142857 -0.612213575618572
5943 -0.285714285714286 -0.857142857142857 -0.285714285714286 -0.612213575618572
5944 -0.285714285714286 -0.571428571428571 -0.571428571428571 -0.612213575618572
5945 -0.285714285714286 -0.285714285714286 -0.857142857142857 -0.612213575618572
5946 0.000000000000000 -0.857142857142857 -0.571428571428571 -0.612213575618572
5947 0.000000000000000 -0.571428571428571 -0.857142857142857 -0.612213575618572
5948 0.285714285714286 -0.857142857142857 -0.857142857142857 -0.612213575618572
5949 -0.857142857142857 -0.857142857142857 0.000000000000000 -0.612213575618572
5950 -0.857142857142857 -0.571428571428571 -0.285714285714286 -0.612213575618572
5951 -0.857142857142857 -0.285714285714286 -0.571428571428571 -0.612213575618572
5952 -0.857142857142857 0.000000000000000 -0.857142857142857 -0.612213575618572
5953 -0.571428571428571 -0.857142857142857 -0.285714285714286 -0.612213575618572
5954 -0.571428571428571 -0.571428571428571 -0.571428571428571 -0.612213575618572
5955 -0.571428571428571 -0.285714285714286 -0.857142857142857 -0.612213575618572
5956 -0.285714285714286 -0.857142857142857 -0.571428571428571 -0.612213575618572
5957 -0.285714285714286 -0.571428571428571 -0.857142857142857 -0.612213575618572
5958 0.000000000000000 -0.857142857142857 -0.857142857142857 -0.612213575618572
5959 -0.857142857142857 -0.857142857142857 -0.285714285714286 -0.612213575618572
5960 -0.857142857142857 -0.571428571428571 -0.571428571428571 -0.612213575618572
5961 -0.857142857142857 -0.285714285714286 -0.857142857142857 -0.612213575618572
5962 -0.571428571428571 -0.857142857142857 -0.571428571428571 -0.612213575618572
5963 -0.571428571428571 -0.571428571428571 -0.857142857142857 -0.612213575618572
5964 -0.285714285714286 -0.857142857142857 -0.857142857142857 -0.612213575618572
5965 -0.857142857142857 -0.857142857142857 -0.571428571428571 -0.612213575618572
5966 -0.857142857142857 -0.571428571428571 -0.857142857142857 -0.612213575618572
5967 -0.571428571428571 -0.857142857142857 -0.857142857142857 -0.612213575618572
5968 -0.857142857142857 -0.857142857142857 -0.857142857142857 -0.612213575618572
5969 -0.833333333333333 -0.833333333333333 0.500000000000000 0.076141727180383
5970 -0.833333333333333 -0.500000000000000 0.166666666666667 0.076141727180383
5971 -0.833333333333333 -0.166666666666667 -0.166666666666667 0.076141727180383
5972 -0.833333333333333 0.166666666666667 -0.500000000000000 0.076141727180383
5973 -0.833333333333333 0.500000000000000 -0.833333333333333 0.076141727180383
5974 -0.500000000000000 -0.833333333333333 0.166666666666667 0.076141727180383
5975 -0.500000000000000 -0.500000000000000 -0.166666666666667 0.076141727180383
5976 -0.500000000000000 -0.166666666666667 -0.500000000000000 0.076141727180383
5977 -0.500000000000000 0.166666666666667 -0.833333333333333 0.076141727180383
5978 -0.166666666666667 -0.833333333333333 -0.166666666666667 0.076141727180383
5979 -0.166666666666667 -0.500000000000000 -0.500000000000000 0.076141727180383
5980 -0.166666666666667 -0.166666666666667 -0.833333333333333 0.076141727180383
5981 0.166666666666667 -0.833333333333333 -0.500000000000000 0.076141727180383
5982 0.166666666666667 -0.500000000000000 -0.833333333333333 0.076141727180383
5983 0.500000000000000 -0.833333333333333 -0.833333333333333 0.076141727180383
5984 -0.833333333333333 -0.833333333333333 0.166666666666667 0.076141727180383
5985 -0.833333333333333 -0.500000000000000 -0.166666666666667 0.076141727180383
5986 -0.833333333333333 -0.166666666666667 -0.500000000000000 0.076141727180383
5987 -0.833333333333333 0.166666666666667 -0.833333333333333 0.076141727180383
5988 -0.500000000000000 -0.833333333333333 -0.166666666666667 0.076141727180383
5989 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.076141727180383
5990 -0.500000000000000 -0.166666666666667 -0.833333333333333 0.076141727180383
5991 -0.166666666666667 -0.833333333333333 -0.500000000000000 0.076141727180383
5992 -0.166666666666667 -0.500000000000000 -0.833333333333333 0.076141727180383
5993 0.166666666666667 -0.833333333333333 -0.833333333333333 0.076141727180383
5994 -0.833333333333333 -0.833333333333333 -0.166666666666667 0.076141727180383
5995 -0.833333333333333 -0.500000000000000 -0.500000000000000 0.076141727180383
5996 -0.833333333333333 -0.166666666666667 -0.833333333333333 0.076141727180383
5997 -0.500000000000000 -0.833333333333333 -0.500000000000000 0.076141727180383
5998 -0.500000000000000 -0.500000000000000 -0.833333333333333 0.076141727180383
5999 -0.166666666666667 -0.833333333333333 -0.833333333333333 0.076141727180383
6000 -0.833333333333333 -0.833333333333333 -0.500000000000000 0.076141727180383
6001 -0.833333333333333 -0.500000000000000 -0.833333333333333 0.076141727180383
6002 -0.500000000000000 -0.833333333333333 -0.833333333333333 0.076141727180383
6003 -0.833333333333333 -0.833333333333333 -0.833333333333333 0.076141727180383
6004 -0.800000000000000 -0.800000000000000 0.400000000000000 -0.004255896151021
6005 -0.800000000000000 -0.400000000000000 0.000000000000000 -0.004255896151021
6006 -0.800000000000000 0.000000000000000 -0.400000000000000 -0.004255896151021
6007 -0.800000000000000 0.400000000000000 -0.800000000000000 -0.004255896151021
6008 -0.400000000000000 -0.800000000000000 0.000000000000000 -0.004255896151021
6009 -0.400000000000000 -0.400000000000000 -0.400000000000000 -0.004255896151021
6010 -0.400000000000000 0.000000000000000 -0.800000000000000 -0.004255896151021
6011 0.000000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6012 0.000000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6013 0.400000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6014 -0.800000000000000 -0.800000000000000 0.000000000000000 -0.004255896151021
6015 -0.800000000000000 -0.400000000000000 -0.400000000000000 -0.004255896151021
6016 -0.800000000000000 0.000000000000000 -0.800000000000000 -0.004255896151021
6017 -0.400000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6018 -0.400000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6019 0.000000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6020 -0.800000000000000 -0.800000000000000 -0.400000000000000 -0.004255896151021
6021 -0.800000000000000 -0.400000000000000 -0.800000000000000 -0.004255896151021
6022 -0.400000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6023 -0.800000000000000 -0.800000000000000 -0.800000000000000 -0.004255896151021
6024 -0.750000000000000 -0.750000000000000 0.250000000000000 0.000083414141296
6025 -0.750000000000000 -0.250000000000000 -0.250000000000000 0.000083414141296
6026 -0.750000000000000 0.250000000000000 -0.750000000000000 0.000083414141296
6027 -0.250000000000000 -0.750000000000000 -0.250000000000000 0.000083414141296
6028 -0.250000000000000 -0.250000000000000 -0.750000000000000 0.000083414141296
6029 0.250000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6030 -0.750000000000000 -0.750000000000000 -0.250000000000000 0.000083414141296
6031 -0.750000000000000 -0.250000000000000 -0.750000000000000 0.000083414141296
6032 -0.250000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6033 -0.750000000000000 -0.750000000000000 -0.750000000000000 0.000083414141296
6034 -0.666666666666667 -0.666666666666667 0.000000000000000 -0.000000352698561
6035 -0.666666666666667 0.000000000000000 -0.666666666666667 -0.000000352698561
6036 0.000000000000000 -0.666666666666667 -0.666666666666667 -0.000000352698561
6037 -0.666666666666667 -0.666666666666667 -0.666666666666667 -0.000000352698561
6038 -0.500000000000000 -0.500000000000000 -0.500000000000000 0.000000000106067
6039 Gauss quadrature constants for the reference tetrahedron order p=21
6040 """
6041
6042
6043
6044
6045 newton_cotes_table = """\
6046 2
6047 1 1
6048 -1 1
6049 Closed Newton-Cotes quadrature constants order n=1
6050
6051 3
6052 1 1/3
6053 0 4/3
6054 -1 1/3
6055 Closed Newton-Cotes quadrature constants order n=2
6056
6057 4
6058 1 1/4
6059 1/3 3/4
6060 -1/3 3/4
6061 -1 1/4
6062 Closed Newton-Cotes quadrature constants order n=3
6063
6064 5
6065 1 7/45
6066 1/2 32/45
6067 0 12/45
6068 -1/2 32/45
6069 -1 7/45
6070 Closed Newton-Cotes quadrature constants order n=4
6071
6072 6
6073 1 19/144
6074 3/5 75/144
6075 1/5 50/144
6076 -1/5 50/144
6077 -3/5 75/144
6078 -1 19/144
6079 Closed Newton-Cotes quadrature constants order n=5
6080
6081 7
6082 1 41/420
6083 2/3 216/420
6084 1/3 27/420
6085 0 272/420
6086 -1/3 27/420
6087 -2/3 216/420
6088 -1 41/420
6089 Closed Newton-Cotes quadrature constants order n=6
6090
6091 8
6092 1 751/8640
6093 5/7 3577/8640
6094 3/7 1323/8640
6095 1/7 2989/8640
6096 -1/7 2989/8640
6097 -3/7 1323/8640
6098 -5/7 3577/8640
6099 -1 751/8640
6100 Closed Newton-Cotes quadrature constants order n=7
6101 """
6102
6103
6104 chebyshev_table = """\
6105 2
6106 0.5773502691896257645091488 1
6107 -0.5773502691896257645091488 1
6108 Chebyshev quadrature constants order n+1=3
6109
6110 3
6111 0.7071067811865475244008444 2/3
6112 0.0000000000000000000000000 2/3
6113 -0.7071067811865475244008444 2/3
6114 Chebyshev quadrature constants order n+1=4
6115
6116 4
6117 0.7946544722917661229555309 1/2
6118 0.1875924740850798998601393 1/2
6119 -0.1875924740850798998601393 1/2
6120 -0.7946544722917661229555309 1/2
6121 Chebyshev quadrature constants order n+1=5
6122
6123 5
6124 0.8324974870009818758925836 2/5
6125 0.3745414095535810655860444 2/5
6126 0.0000000000000000000000000 2/5
6127 -0.3745414095535810655860444 2/5
6128 -0.8324974870009818758925836 2/5
6129 Chebyshev quadrature constants order n+1=6
6130
6131 6
6132 0.8662468181078205913835981 1/3
6133 0.4225186537611115291185464 1/3
6134 0.2666354015167047203315346 1/3
6135 -0.2666354015167047203315346 1/3
6136 -0.4225186537611115291185464 1/3
6137 -0.8662468181078205913835981 1/3
6138 Chebyshev quadrature constants order n+1=7
6139
6140 7
6141 0.8838617007580490357042241 2/7
6142 0.5296567752851568113850475 2/7
6143 0.3239118105199076375196731 2/7
6144 0.0000000000000000000000000 2/7
6145 -0.3239118105199076375196731 2/7
6146 -0.5296567752851568113850475 2/7
6147 -0.8838617007580490357042241 2/7
6148 Chebyshev quadrature constants order n+1=8
6149
6150 9
6151 0.9115893077284344736649486 2/9
6152 0.6010186553802380714281279 2/9
6153 0.5287617830578799932601816 2/9
6154 0.1679061842148039430680319 2/9
6155 0.0000000000000000000000000 2/9
6156 -0.1679061842148039430680319 2/9
6157 -0.5287617830578799932601816 2/9
6158 -0.6010186553802380714281279 2/9
6159 -0.9115893077284344736649486 2/9
6160 Chebyshev quadrature constants order n+1=10
6161 """
6162
6163
6164 lobatto_table = """\
6165 3
6166 1.0000000000000000000000000 0.3333333333333333333333333
6167 0.0000000000000000000000000 1.3333333333333333333333333
6168 -1.0000000000000000000000000 0.3333333333333333333333333
6169 Lobatto (Radau) quadrature constants order 2n-3=3
6170
6171 4
6172 1.0000000000000000000000000 0.1666666666666666666666667
6173 0.4472135954999579392818347 0.8333333333333333333333333
6174 -0.4472135954999579392818347 0.8333333333333333333333333
6175 -1.0000000000000000000000000 0.1666666666666666666666667
6176 Lobatto (Radau) quadrature constants order 2n-3=5
6177
6178 5
6179 1.0000000000000000000000000 0.1000000000000000000000000
6180 0.6546536707079771437982925 0.5444444444444444444444444
6181 0.0000000000000000000000000 0.7111111111111111111111111
6182 -0.6546536707079771437982925 0.5444444444444444444444444
6183 -1.0000000000000000000000000 0.1000000000000000000000000
6184 Lobatto (Radau) quadrature constants order 2n-3=7
6185
6186 6
6187 1.0000000000000000000000000 0.0666666666666666666666667
6188 0.7650553239294646928510030 0.3784749562978469803166128
6189 0.2852315164806450963141510 0.5548583770354863530167205
6190 -0.2852315164806450963141510 0.5548583770354863530167205
6191 -0.7650553239294646928510030 0.3784749562978469803166128
6192 -1.0000000000000000000000000 0.0666666666666666666666667
6193 Lobatto (Radau) quadrature constants order 2n-3=9
6194
6195 7
6196 1.0000000000000000000000000 0.0476190476190476190476190
6197 0.8302238962785669298720322 0.2768260473615659480107004
6198 0.4688487934707142138037719 0.4317453812098626234178710
6199 0.0000000000000000000000000 0.4876190476190476190476190
6200 -0.4688487934707142138037719 0.4317453812098626234178710
6201 -0.8302238962785669298720322 0.2768260473615659480107004
6202 -1.0000000000000000000000000 0.0476190476190476190476190
6203 Lobatto (Radau) quadrature constants order 2n-3=11
6204
6205 8
6206 1.0000000000000000000000000 0.0357142857142857142857143
6207 0.8717401485096066153374457 0.2107042271435060393829921
6208 0.5917001814331423021445107 0.3411226924835043647642407
6209 0.2092992179024788687686573 0.4124587946587038815670530
6210 -0.2092992179024788687686573 0.4124587946587038815670530
6211 -0.5917001814331423021445107 0.3411226924835043647642407
6212 -0.8717401485096066153374457 0.2107042271435060393829921
6213 -1.0000000000000000000000000 0.0357142857142857142857143
6214 Lobatto (Radau) quadrature constants order 2n-3=13
6215
6216 9
6217 1.0000000000000000000000000 0.0277777777777777777777778
6218 0.8997579954114601573123452 0.1654953615608055250463397
6219 0.6771862795107377534458854 0.2745387125001617352807056
6220 0.3631174638261781587107521 0.3464285109730463451151315
6221 0.0000000000000000000000000 0.3715192743764172335600907
6222 -0.3631174638261781587107521 0.3464285109730463451151315
6223 -0.6771862795107377534458854 0.2745387125001617352807056
6224 -0.8997579954114601573123452 0.1654953615608055250463397
6225 -1.0000000000000000000000000 0.0277777777777777777777778
6226 Lobatto (Radau) quadrature constants order 2n-3=15
6227
6228 10
6229 1.0000000000000000000000000 0.0222222222222222222222222
6230 0.9195339081664588138289327 0.1333059908510701111262272
6231 0.7387738651055050750031062 0.2248893420631264521194578
6232 0.4779249498104444956611751 0.2920426836796837578755823
6233 0.1652789576663870246262198 0.3275397611838974566565105
6234 -0.1652789576663870246262198 0.3275397611838974566565105
6235 -0.4779249498104444956611751 0.2920426836796837578755823
6236 -0.7387738651055050750031062 0.2248893420631264521194578
6237 -0.9195339081664588138289327 0.1333059908510701111262272
6238 -1.0000000000000000000000000 0.0222222222222222222222222
6239 Lobatto (Radau) quadrature constants order 2n-3=17
6240
6241 11
6242 1.0000000000000000000000000 0.0181818181818181818181818
6243 0.9340014304080591343322741 0.1096122732669948644614034
6244 0.7844834736631444186224178 0.1871698817803052041081415
6245 0.5652353269962050064709640 0.2480481042640283140400849
6246 0.2957581355869393914319115 0.2868791247790080886792224
6247 0.0000000000000000000000000 0.3002175954556906937859319
6248 -0.2957581355869393914319115 0.2868791247790080886792224
6249 -0.5652353269962050064709640 0.2480481042640283140400849
6250 -0.7844834736631444186224178 0.1871698817803052041081415
6251 -0.9340014304080591343322741 0.1096122732669948644614034
6252 -1.0000000000000000000000000 0.0181818181818181818181818
6253 Lobatto (Radau) quadrature constants order 2n-3=19
6254
6255 12
6256 1.0000000000000000000000000 0.0151515151515151515151515
6257 0.9448992722228822234075801 0.0916845174131961306683426
6258 0.8192793216440066783486416 0.1579747055643701151646710
6259 0.6328761530318606776624049 0.2125084177610211453583021
6260 0.3995309409653489322643498 0.2512756031992012802932444
6261 0.1365529328549275548640619 0.2714052409106961770002883
6262 -0.1365529328549275548640619 0.2714052409106961770002883
6263 -0.3995309409653489322643498 0.2512756031992012802932444
6264 -0.6328761530318606776624049 0.2125084177610211453583021
6265 -0.8192793216440066783486416 0.1579747055643701151646710
6266 -0.9448992722228822234075801 0.0916845174131961306683426
6267 -1.0000000000000000000000000 0.0151515151515151515151515
6268 Lobatto (Radau) quadrature constants order 2n-3=21
6269 """
6270