R/points_GaussLegendre.R

Defines functions .points_GaussLegendre

.points_GaussLegendre <- function(size){
  size <- as.character(size)
  switch(size,
         "16" = list(
           nodes = c(-0.98940093 ,-0.94457502 ,-0.86563120 ,-0.75540441 ,-0.61787624 ,-0.45801678 ,-0.28160355 ,-0.09501251
                     ,0.09501251  ,0.28160355  ,0.45801678  ,0.61787624  ,0.75540441  ,0.86563120  ,0.94457502  ,0.98940093),
           weights = c(0.02715246 ,0.06225352 ,0.09515851 ,0.12462897 ,0.14959599 ,0.16915652 ,0.18260342 ,0.18945061 ,0.18945061
                     ,0.18260342 ,0.16915652 ,0.14959599 ,0.12462897 ,0.09515851 ,0.06225352 ,0.02715246)),
         "32" = list(
           nodes = c(-0.99726386, -0.98561151, -0.96476226, -0.93490608,
                     -0.89632116, -0.84936761, -0.79448380, -0.73218212,
                     -0.66304427, -0.58771576, -0.50689991, -0.42135128,
                     -0.33186860, -0.23928736, -0.14447196, -0.04830767,
                      0.04830767,  0.14447196,  0.23928736,  0.33186860,
                      0.42135128,  0.50689991,  0.58771576,  0.66304427,
                      0.73218212,  0.79448380,  0.84936761,  0.89632116,
                      0.93490608,  0.96476226,  0.98561151,  0.99726386),
           weights = c(0.00701861, 0.01627439, 0.02539207, 0.03427386,
                       0.04283590, 0.05099806, 0.05868409, 0.06582222,
                       0.07234579, 0.07819390, 0.08331192, 0.08765209,
                       0.09117388, 0.09384440, 0.09563872, 0.09654009,
                       0.09654009, 0.09563872, 0.09384440, 0.09117388,
                       0.08765209, 0.08331192, 0.07819390, 0.07234579,
                       0.06582222, 0.05868409, 0.05099806, 0.04283590,
                       0.03427386, 0.02539207, 0.01627439, 0.00701861)),
         "64" = list(
           nodes = c(-0.99930504, -0.99634012, -0.99101337, -0.98333625,
                     -0.97332683, -0.96100880, -0.94641137, -0.92956917,
                     -0.91052214, -0.88931545, -0.86599940, -0.84062930,
                     -0.81326532, -0.78397236, -0.75281991, -0.71988185,
                     -0.68523631, -0.64896547, -0.61115536, -0.57189565,
                     -0.53127946, -0.48940315, -0.44636602, -0.40227016,
                     -0.35722016, -0.31132287, -0.26468716, -0.21742364,
                     -0.16964442, -0.12146282, -0.07299312, -0.02435029,
                      0.02435029,  0.07299312,  0.12146282,  0.16964442,
                      0.21742364,  0.26468716,  0.31132287,  0.35722016,
                      0.40227016,  0.44636602,  0.48940315,  0.53127946,
                      0.57189565,  0.61115536,  0.64896547,  0.68523631,
                      0.71988185,  0.75281991,  0.78397236,  0.81326532,
                      0.84062930,  0.86599940,  0.88931545,  0.91052214,
                      0.92956917,  0.94641137,  0.96100880,  0.97332683,
                      0.98333625,  0.99101337,  0.99634012,  0.99930504),
           weights = c(0.001783281 ,0.004147033 ,0.006504458 ,0.008846760 ,0.011168139 ,0.013463048
                       ,0.015726030 ,0.017951716 ,0.020134823 ,0.022270174 ,0.024352703 ,0.026377470
                       ,0.028339673 ,0.030234657 ,0.032057928 ,0.033805162 ,0.035472213 ,0.037055129
                       ,0.038550153 ,0.039953741 ,0.041262563 ,0.042473515 ,0.043583725 ,0.044590558
                       ,0.045491628 ,0.046284797 ,0.046968183 ,0.047540166 ,0.047999389 ,0.048344762
                       ,0.048575467 ,0.048690957 ,0.048690957 ,0.048575467 ,0.048344762 ,0.047999389
                       ,0.047540166 ,0.046968183 ,0.046284797 ,0.045491628 ,0.044590558 ,0.043583725
                       ,0.042473515 ,0.041262563 ,0.039953741 ,0.038550153 ,0.037055129 ,0.035472213
                       ,0.033805162 ,0.032057928 ,0.030234657 ,0.028339673 ,0.026377470 ,0.024352703
                       ,0.022270174 ,0.020134823 ,0.017951716 ,0.015726030 ,0.013463048 ,0.011168139
                       ,0.008846760 ,0.006504458 ,0.004147033 ,0.001783281)),
         "100" = list(
           nodes = c(-0.99971373 ,-0.99849195 ,-0.99629513 ,-0.99312494 ,-0.98898440 ,-0.98387754 ,-0.97780936 ,-0.97078578 ,-0.96281365
                     ,-0.95390078 ,-0.94405587 ,-0.93328854 ,-0.92160930 ,-0.90902957 ,-0.89556164 ,-0.88121868 ,-0.86601469 ,-0.84996453
                     ,-0.83308388 ,-0.81538924 ,-0.79689789 ,-0.77762791 ,-0.75759812 ,-0.73682809 ,-0.71533812 ,-0.69314920 ,-0.67028302
                     ,-0.64676191 ,-0.62260886 ,-0.59784747 ,-0.57250193 ,-0.54659701 ,-0.52015802 ,-0.49321079 ,-0.46578165 ,-0.43789740
                     ,-0.40958529 ,-0.38087298 ,-0.35178853 ,-0.32236034 ,-0.29261719 ,-0.26258812 ,-0.23230248 ,-0.20178986 ,-0.17108008
                     ,-0.14020314 ,-0.10918920 ,-0.07806858 ,-0.04687168 ,-0.01562898  ,0.01562898  ,0.04687168  ,0.07806858  ,0.10918920
                     ,0.14020314  ,0.17108008  ,0.20178986  ,0.23230248  ,0.26258812  ,0.29261719  ,0.32236034  ,0.35178853  ,0.38087298
                     ,0.40958529  ,0.43789740  ,0.46578165  ,0.49321079  ,0.52015802  ,0.54659701  ,0.57250193  ,0.59784747  ,0.62260886
                     ,0.64676191  ,0.67028302  ,0.69314920  ,0.71533812  ,0.73682809  ,0.75759812  ,0.77762791  ,0.79689789  ,0.81538924
                     ,0.83308388  ,0.84996453  ,0.86601469  ,0.88121868  ,0.89556164  ,0.90902957  ,0.92160930  ,0.93328854  ,0.94405587
                     ,0.95390078  ,0.96281365  ,0.97078578  ,0.97780936  ,0.98387754  ,0.98898440  ,0.99312494  ,0.99629513  ,0.99849195
                     ,0.99971373),
           weights = c(0.0007346345 ,0.0017093927 ,0.0026839254 ,0.0036559612 ,0.0046244501 ,0.0055884280 ,0.0065469485 ,0.0074990733
                       ,0.0084438715 ,0.0093804197 ,0.0103078026 ,0.0112251140 ,0.0121314577 ,0.0130259479 ,0.0139077107 ,0.0147758845
                       ,0.0156296211 ,0.0164680862 ,0.0172904606 ,0.0180959407 ,0.0188837396 ,0.0196530875 ,0.0204032326 ,0.0211334421
                       ,0.0218430024 ,0.0225312203 ,0.0231974232 ,0.0238409603 ,0.0244612027 ,0.0250575445 ,0.0256294029 ,0.0261762192
                       ,0.0266974592 ,0.0271926134 ,0.0276611982 ,0.0281027557 ,0.0285168543 ,0.0289030896 ,0.0292610841 ,0.0295904881
                       ,0.0298909796 ,0.0301622651 ,0.0304040795 ,0.0306161866 ,0.0307983790 ,0.0309504789 ,0.0310723374 ,0.0311638357
                       ,0.0312248843 ,0.0312554235 ,0.0312554235 ,0.0312248843 ,0.0311638357 ,0.0310723374 ,0.0309504789 ,0.0307983790
                       ,0.0306161866 ,0.0304040795 ,0.0301622651 ,0.0298909796 ,0.0295904881 ,0.0292610841 ,0.0289030896 ,0.0285168543
                       ,0.0281027557 ,0.0276611982 ,0.0271926134 ,0.0266974592 ,0.0261762192 ,0.0256294029 ,0.0250575445 ,0.0244612027
                       ,0.0238409603 ,0.0231974232 ,0.0225312203 ,0.0218430024 ,0.0211334421 ,0.0204032326 ,0.0196530875 ,0.0188837396
                       ,0.0180959407 ,0.0172904606 ,0.0164680862 ,0.0156296211 ,0.0147758845 ,0.0139077107 ,0.0130259479 ,0.0121314577
                       ,0.0112251140 ,0.0103078026 ,0.0093804197 ,0.0084438715 ,0.0074990733 ,0.0065469485 ,0.0055884280 ,0.0046244501
                       ,0.0036559612 ,0.0026839254 ,0.0017093927 ,0.0007346345)),
         "150" = list(
           nodes = c(-0.99987234 ,-0.99932743 ,-0.99834734 ,-0.99693229 ,-0.99508286 ,-0.99279986 ,-0.99008427 ,-0.98693728 ,-0.98336025
                     ,-0.97935476 ,-0.97492253 ,-0.97006551 ,-0.96478581 ,-0.95908573 ,-0.95296776 ,-0.94643455 ,-0.93948896 ,-0.93213401
                     ,-0.92437291 ,-0.91620904 ,-0.90764596 ,-0.89868739 ,-0.88933724 ,-0.87959959 ,-0.86947868 ,-0.85897891 ,-0.84810486
                     ,-0.83686128 ,-0.82525306 ,-0.81328525 ,-0.80096308 ,-0.78829191 ,-0.77527726 ,-0.76192480 ,-0.74824036 ,-0.73422989
                     ,-0.71989950 ,-0.70525543 ,-0.69030407 ,-0.67505192 ,-0.65950564 ,-0.64367200 ,-0.62755789 ,-0.61117034 ,-0.59451649
                     ,-0.57760360 ,-0.56043903 ,-0.54303026 ,-0.52538488 ,-0.50751058 ,-0.48941515 ,-0.47110646 ,-0.45259251 ,-0.43388134
                     ,-0.41498113 ,-0.39590010 ,-0.37664657 ,-0.35722892 ,-0.33765562 ,-0.31793519 ,-0.29807624 ,-0.27808740 ,-0.25797739
                     ,-0.23775498 ,-0.21742898 ,-0.19700823 ,-0.17650164 ,-0.15591815 ,-0.13526672 ,-0.11455635 ,-0.09379607 ,-0.07299491
                     ,-0.05216195 ,-0.03130627 ,-0.01043694  ,0.01043694  ,0.03130627  ,0.05216195  ,0.07299491  ,0.09379607  ,0.11455635
                     ,0.13526672  ,0.15591815  ,0.17650164  ,0.19700823  ,0.21742898  ,0.23775498  ,0.25797739  ,0.27808740  ,0.29807624
                     ,0.31793519  ,0.33765562  ,0.35722892  ,0.37664657  ,0.39590010  ,0.41498113  ,0.43388134  ,0.45259251  ,0.47110646
                     ,0.48941515  ,0.50751058  ,0.52538488  ,0.54303026  ,0.56043903  ,0.57760360  ,0.59451649  ,0.61117034  ,0.62755789
                     ,0.64367200  ,0.65950564  ,0.67505192  ,0.69030407  ,0.70525543  ,0.71989950  ,0.73422989  ,0.74824036  ,0.76192480
                     ,0.77527726  ,0.78829191  ,0.80096308  ,0.81328525  ,0.82525306  ,0.83686128  ,0.84810486  ,0.85897891  ,0.86947868
                     ,0.87959959  ,0.88933724  ,0.89868739  ,0.90764596  ,0.91620904  ,0.92437291  ,0.93213401  ,0.93948896  ,0.94643455
                     ,0.95296776  ,0.95908573  ,0.96478581  ,0.97006551  ,0.97492253  ,0.97935476  ,0.98336025  ,0.98693728  ,0.99008427
                     ,0.99279986  ,0.99508286  ,0.99693229  ,0.99834734  ,0.99932743  ,0.99987234),
           weights = c(0.0003276087 ,0.0007624721 ,0.0011976475 ,0.0016323570 ,0.0020663665 ,0.0024994790 ,0.0029315037 ,0.0033622516
                       ,0.0037915348 ,0.0042191661 ,0.0046449591 ,0.0050687283 ,0.0054902889 ,0.0059094573 ,0.0063260508 ,0.0067398879
                       ,0.0071507883 ,0.0075585730 ,0.0079630642 ,0.0083640857 ,0.0087614628 ,0.0091550223 ,0.0095445927 ,0.0099300044
                       ,0.0103110893 ,0.0106876814 ,0.0110596167 ,0.0114267330 ,0.0117888704 ,0.0121458712 ,0.0124975797 ,0.0128438427
                       ,0.0131845093 ,0.0135194312 ,0.0138484623 ,0.0141714593 ,0.0144882815 ,0.0147987908 ,0.0151028519 ,0.0154003323
                       ,0.0156911025 ,0.0159750356 ,0.0162520081 ,0.0165218992 ,0.0167845913 ,0.0170399700 ,0.0172879240 ,0.0175283452
                       ,0.0177611289 ,0.0179861736 ,0.0182033814 ,0.0184126575 ,0.0186139108 ,0.0188070535 ,0.0189920016 ,0.0191686745
                       ,0.0193369950 ,0.0194968901 ,0.0196482898 ,0.0197911283 ,0.0199253434 ,0.0200508765 ,0.0201676730 ,0.0202756820
                       ,0.0203748564 ,0.0204651529 ,0.0205465324 ,0.0206189592 ,0.0206824018 ,0.0207368327 ,0.0207822280 ,0.0208185680
                       ,0.0208458369 ,0.0208640227 ,0.0208731176 ,0.0208731176 ,0.0208640227 ,0.0208458369 ,0.0208185680 ,0.0207822280
                       ,0.0207368327 ,0.0206824018 ,0.0206189592 ,0.0205465324 ,0.0204651529 ,0.0203748564 ,0.0202756820 ,0.0201676730
                       ,0.0200508765 ,0.0199253434 ,0.0197911283 ,0.0196482898 ,0.0194968901 ,0.0193369950 ,0.0191686745 ,0.0189920016
                       ,0.0188070535 ,0.0186139108 ,0.0184126575 ,0.0182033814 ,0.0179861736 ,0.0177611289 ,0.0175283452 ,0.0172879240
                       ,0.0170399700 ,0.0167845913 ,0.0165218992 ,0.0162520081 ,0.0159750356 ,0.0156911025 ,0.0154003323 ,0.0151028519
                       ,0.0147987908 ,0.0144882815 ,0.0141714593 ,0.0138484623 ,0.0135194312 ,0.0131845093 ,0.0128438427 ,0.0124975797
                       ,0.0121458712 ,0.0117888704 ,0.0114267330 ,0.0110596167 ,0.0106876814 ,0.0103110893 ,0.0099300044 ,0.0095445927
                       ,0.0091550223 ,0.0087614628 ,0.0083640857 ,0.0079630642 ,0.0075585730 ,0.0071507883 ,0.0067398879 ,0.0063260508
                       ,0.0059094573 ,0.0054902889 ,0.0050687283 ,0.0046449591 ,0.0042191661 ,0.0037915348 ,0.0033622516 ,0.0029315037
                       ,0.0024994790 ,0.0020663665 ,0.0016323570 ,0.0011976475 ,0.0007624721 ,0.0003276087)),
         "200" = list(
           nodes = c(-0.999928071 ,-0.999621031 ,-0.999068722 ,-0.998271156 ,-0.997228514 ,-0.995941049 ,-0.994409076 ,-0.992632969
                     ,-0.990613166 ,-0.988350161 ,-0.985844511 ,-0.983096830 ,-0.980107793 ,-0.976878133 ,-0.973408644 ,-0.969700178
                     ,-0.965753644 ,-0.961570012 ,-0.957150309 ,-0.952495619 ,-0.947607087 ,-0.942485911 ,-0.937133349 ,-0.931550715
                     ,-0.925739380 ,-0.919700770 ,-0.913436369 ,-0.906947713 ,-0.900236396 ,-0.893304066 ,-0.886152424 ,-0.878783226
                     ,-0.871198282 ,-0.863399454 ,-0.855388656 ,-0.847167854 ,-0.838739068 ,-0.830104367 ,-0.821265870 ,-0.812225747
                     ,-0.802986218 ,-0.793549551 ,-0.783918062 ,-0.774094117 ,-0.764080128 ,-0.753878552 ,-0.743491895 ,-0.732922705
                     ,-0.722173579 ,-0.711247155 ,-0.700146116 ,-0.688873186 ,-0.677431134 ,-0.665822768 ,-0.654050939 ,-0.642118537
                     ,-0.630028490 ,-0.617783768 ,-0.605387377 ,-0.592842359 ,-0.580151794 ,-0.567318799 ,-0.554346524 ,-0.541238153
                     ,-0.527996905 ,-0.514626031 ,-0.501128813 ,-0.487508565 ,-0.473768630 ,-0.459912383 ,-0.445943224 ,-0.431864583
                     ,-0.417679918 ,-0.403392709 ,-0.389006465 ,-0.374524717 ,-0.359951022 ,-0.345288956 ,-0.330542120 ,-0.315714133
                     ,-0.300808637 ,-0.285829291 ,-0.270779772 ,-0.255663775 ,-0.240485010 ,-0.225247206 ,-0.209954102 ,-0.194609452
                     ,-0.179217025 ,-0.163780599 ,-0.148303964 ,-0.132790920 ,-0.117245274 ,-0.101670845 ,-0.086071454 ,-0.070450932
                     ,-0.054813114 ,-0.039161839 ,-0.023500950 ,-0.007834291  ,0.007834291  ,0.023500950  ,0.039161839  ,0.054813114
                     ,0.070450932  ,0.086071454  ,0.101670845  ,0.117245274  ,0.132790920  ,0.148303964  ,0.163780599  ,0.179217025
                     ,0.194609452  ,0.209954102  ,0.225247206  ,0.240485010  ,0.255663775  ,0.270779772  ,0.285829291  ,0.300808637
                     ,0.315714133  ,0.330542120  ,0.345288956  ,0.359951022  ,0.374524717  ,0.389006465  ,0.403392709  ,0.417679918
                     ,0.431864583  ,0.445943224  ,0.459912383  ,0.473768630  ,0.487508565  ,0.501128813  ,0.514626031  ,0.527996905
                     ,0.541238153  ,0.554346524  ,0.567318799  ,0.580151794  ,0.592842359  ,0.605387377  ,0.617783768  ,0.630028490
                     ,0.642118537  ,0.654050939  ,0.665822768  ,0.677431134  ,0.688873186  ,0.700146116  ,0.711247155  ,0.722173579
                     ,0.732922705  ,0.743491895  ,0.753878552  ,0.764080128  ,0.774094117  ,0.783918062  ,0.793549551  ,0.802986218
                     ,0.812225747  ,0.821265870  ,0.830104367  ,0.838739068  ,0.847167854  ,0.855388656  ,0.863399454  ,0.871198282
                     ,0.878783226  ,0.886152424  ,0.893304066  ,0.900236396  ,0.906947713  ,0.913436369  ,0.919700770  ,0.925739380
                     ,0.931550715  ,0.937133349  ,0.942485911  ,0.947607087  ,0.952495619  ,0.957150309  ,0.961570012  ,0.965753644
                     ,0.969700178  ,0.973408644  ,0.976878133  ,0.980107793  ,0.983096830  ,0.985844511  ,0.988350161  ,0.990613166
                     ,0.992632969  ,0.994409076  ,0.995941049  ,0.997228514  ,0.998271156  ,0.999068722  ,0.999621031  ,0.999928071),
           weights = c(0.0001845901 ,0.0004296466 ,0.0006749606 ,0.0009201405 ,0.0011651007 ,0.0014097768 ,0.0016541076 ,0.0018980325
                       ,0.0021414916 ,0.0023844251 ,0.0026267732 ,0.0028684765 ,0.0031094756 ,0.0033497113 ,0.0035891246 ,0.0038276568
                       ,0.0040652492 ,0.0043018437 ,0.0045373820 ,0.0047718063 ,0.0050050592 ,0.0052370832 ,0.0054678216 ,0.0056972175
                       ,0.0059252148 ,0.0061517573 ,0.0063767896 ,0.0066002564 ,0.0068221027 ,0.0070422742 ,0.0072607168 ,0.0074773768
                       ,0.0076922010 ,0.0079051368 ,0.0081161318 ,0.0083251343 ,0.0085320929 ,0.0087369568 ,0.0089396758 ,0.0091402000
                       ,0.0093384802 ,0.0095344678 ,0.0097281146 ,0.0099193731 ,0.0101081963 ,0.0102945379 ,0.0104783521 ,0.0106595939
                       ,0.0108382186 ,0.0110141825 ,0.0111874423 ,0.0113579556 ,0.0115256804 ,0.0116905756 ,0.0118526007 ,0.0120117159
                       ,0.0121678822 ,0.0123210611 ,0.0124712152 ,0.0126183075 ,0.0127623019 ,0.0129031632 ,0.0130408566 ,0.0131753484
                       ,0.0133066056 ,0.0134345959 ,0.0135592880 ,0.0136806511 ,0.0137986556 ,0.0139132724 ,0.0140244735 ,0.0141322314
                       ,0.0142365198 ,0.0143373131 ,0.0144345864 ,0.0145283160 ,0.0146184788 ,0.0147050527 ,0.0147880164 ,0.0148673495
                       ,0.0149430326 ,0.0150150471 ,0.0150833754 ,0.0151480005 ,0.0152089068 ,0.0152660791 ,0.0153195036 ,0.0153691670
                       ,0.0154150572 ,0.0154571629 ,0.0154954738 ,0.0155299804 ,0.0155606744 ,0.0155875481 ,0.0156105950 ,0.0156298094
                       ,0.0156451865 ,0.0156567227 ,0.0156644151 ,0.0156682617 ,0.0156682617 ,0.0156644151 ,0.0156567227 ,0.0156451865
                       ,0.0156298094 ,0.0156105950 ,0.0155875481 ,0.0155606744 ,0.0155299804 ,0.0154954738 ,0.0154571629 ,0.0154150572
                       ,0.0153691670 ,0.0153195036 ,0.0152660791 ,0.0152089068 ,0.0151480005 ,0.0150833754 ,0.0150150471 ,0.0149430326
                       ,0.0148673495 ,0.0147880164 ,0.0147050527 ,0.0146184788 ,0.0145283160 ,0.0144345864 ,0.0143373131 ,0.0142365198
                       ,0.0141322314 ,0.0140244735 ,0.0139132724 ,0.0137986556 ,0.0136806511 ,0.0135592880 ,0.0134345959 ,0.0133066056
                       ,0.0131753484 ,0.0130408566 ,0.0129031632 ,0.0127623019 ,0.0126183075 ,0.0124712152 ,0.0123210611 ,0.0121678822
                       ,0.0120117159 ,0.0118526007 ,0.0116905756 ,0.0115256804 ,0.0113579556 ,0.0111874423 ,0.0110141825 ,0.0108382186
                       ,0.0106595939 ,0.0104783521 ,0.0102945379 ,0.0101081963 ,0.0099193731 ,0.0097281146 ,0.0095344678 ,0.0093384802
                       ,0.0091402000 ,0.0089396758 ,0.0087369568 ,0.0085320929 ,0.0083251343 ,0.0081161318 ,0.0079051368 ,0.0076922010
                       ,0.0074773768 ,0.0072607168 ,0.0070422742 ,0.0068221027 ,0.0066002564 ,0.0063767896 ,0.0061517573 ,0.0059252148
                       ,0.0056972175 ,0.0054678216 ,0.0052370832 ,0.0050050592 ,0.0047718063 ,0.0045373820 ,0.0043018437 ,0.0040652492
                       ,0.0038276568 ,0.0035891246 ,0.0033497113 ,0.0031094756 ,0.0028684765 ,0.0026267732 ,0.0023844251 ,0.0021414916
                       ,0.0018980325 ,0.0016541076 ,0.0014097768 ,0.0011651007 ,0.0009201405 ,0.0006749606 ,0.0004296466 ,0.0001845901))
         )
}

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SMR documentation built on Oct. 8, 2023, 1:07 a.m.