14-Jun-2023 12:43:22 quadrature_weights_vandermonde_2d_test(): MATLAB/Octave version 5.2.0 Test quadrature_weights_vandermonde_2d(). quadrature_weights_vandermonde_2d_test01(): Compute the weights associated with an interpolatory quadrature rule defined by N=(T+1)*(T+2)/2 points, exact for polynomials of total degree T or less. Degree T = 1 Number of points N = 3 X Interval = [-1,1] Y Interval = [-1,1] Abscissas: 1: 1 -1 2: 1 1 3: -1 1 Weights: 1: 2 2: 0 3: 2 quadrature_weights_vandermonde_2d_test02(): Compute the weights associated with an interpolatory quadrature rule defined by N=(T+1)*(T+2)/2 points, exact for polynomials of total degree T or less. X Interval = [-1,1] Y Interval = [-1,1] Degree T = 0 Number of points N = 1 Weights: 1: 4 Degree T = 1 Number of points N = 3 Weights: 1: 1 2: 1 3: 2 Degree T = 2 Number of points N = 6 Weights: 1: 1.110223024625157e-16 2: 0.6666666666666664 3: 2.222222222222222 4: 0.4444444444444446 5: 1.665334536937735e-16 6: 0.6666666666666664 Degree T = 3 Number of points N = 10 Weights: 1: -0.05555555555555608 2: 0.3333333333333336 3: -0.05555555555555576 4: 0.8888888888888885 5: 0.8888888888888893 6: 0.2222222222222222 7: 1.333333333333333 8: 0.2222222222222221 9: 0.1111111111111109 10: 0.111111111111111 Degree T = 4 Number of points N = 15 Weights: 1: -0.008888888888889598 2: 0.08104919101111037 3: 0.06117303121111237 4: 0.3874097078666789 5: 0.6259236254666545 6: 0.05333333333333334 7: 0.07111111111111049 8: 0.9830822022444247 9: 0.5458066866444651 10: 0.3874097078666779 11: 0.6259236254666551 12: 0.05333333333333316 13: -0.008888888888888696 14: 0.08104919101110994 15: 0.06117303121111222 Degree T = 5 Number of points N = 21 Weights: 1: -0.01037037037036929 2: 0.05037037037037107 3: 0.05037037037036952 4: -0.01037037037037103 5: 0.1876963678740756 6: 0.3460933466518658 7: 0.1876963678740804 8: 0.04514390511851816 9: 0.5541130536814732 10: 0.5541130536814687 11: 0.04514390511851758 12: 0.2804517802740689 13: 0.6376103570518399 14: 0.2804517802740705 15: 0.03189313191851924 16: 0.328849909281492 17: 0.3288499092814908 18: 0.03189313191851832 19: 0.0207407407407407 20: 0.03851851851851823 21: 0.02074074074074174 Degree T = 6 Number of points N = 28 Weights: 1: -0.003023431594862267 2: 0.01957267632451963 3: 0.02633929313290665 4: 0.01425431928029201 5: 0.1006383046329705 6: 0.220890018452691 7: 0.1743144584714059 8: 0.01209372637944003 9: 0.01934996220710765 10: 0.3245064820875185 11: 0.4027058473592957 12: 0.1677234226317942 13: 0.1953319357827173 14: 0.448963305303514 15: 0.3721824611057553 16: 0.02479213907785328 17: 0.01934996220710566 18: 0.3245064820875188 19: 0.4027058473592967 20: 0.1677234226317945 21: 0.100638304632972 22: 0.2208900184526915 23: 0.1743144584714031 24: 0.01209372637944078 25: -0.003023431594860949 26: 0.01957267632451813 27: 0.02633929313290831 28: 0.01425431928029161 Degree T = 7 Number of points N = 36 Weights: 1: -0.003287981859412393 2: 0.01337868480726067 3: 0.02063492063492018 4: 0.01337868480725627 5: -0.003287981859410023 6: 0.05949324721885149 7: 0.1306477599993515 8: 0.1306477599993547 9: 0.05949324721885231 10: 0.01263869091686278 11: 0.1979944935601121 12: 0.2832184784823852 13: 0.1979944935601139 14: 0.01263869091685783 15: 0.1221817987389728 16: 0.3150266070593429 17: 0.3150266070593393 18: 0.122181798738978 19: 0.01771365352315135 20: 0.2490926964598361 21: 0.3408041116307026 22: 0.2490926964598325 23: 0.01771365352315133 24: 0.09646986307476131 25: 0.2557725606433862 26: 0.2557725606433905 27: 0.09646986307476239 28: 0.008649923133691437 29: 0.1062007918394747 30: 0.150580584490102 31: 0.1062007918394723 32: 0.008649923133689914 33: 0.006355881462926732 34: 0.01405228180237519 35: 0.01405228180237548 36: 0.00635588146292855 Degree T = 8 Number of points N = 45 Weights: 1: -0.001269841269838309 2: 0.006706089639054568 3: 0.01111455441353405 4: 0.01026455026454613 5: 0.004930678698744659 6: 0.0363314686916219 7: 0.08838322767331031 8: 0.09965911758463455 9: 0.06400185533756222 10: 0.004061629144891075 11: 0.006772486772492202 12: 0.1258344472781392 13: 0.1927501398511237 14: 0.1699470899470884 15: 0.06342599488133005 16: 0.08376332474106389 17: 0.2170841444607008 18: 0.2477307250801775 19: 0.1648098048612264 20: 0.01004771829779853 21: 0.01015873015873574 22: 0.1784328991205269 23: 0.2729409493576727 24: 0.236402116402108 25: 0.08936689226255194 26: 0.08376332474106538 27: 0.2170841444607087 28: 0.2477307250801805 29: 0.164809804861228 30: 0.01004771829779579 31: 0.006772486772489562 32: 0.1258344472781367 33: 0.1927501398511089 34: 0.1699470899470876 35: 0.06342599488133314 36: 0.03633146869162644 37: 0.08838322767332378 38: 0.09965911758463855 39: 0.06400185533755953 40: 0.004061629144890821 41: -0.001269841269838733 42: 0.006706089639047598 43: 0.01111455441352922 44: 0.0102645502645475 45: 0.004930678698744777 Degree T = 9 Number of points N = 55 Weights: 1: -0.001368606701928076 2: 0.004837977417147541 3: 0.008876308297144087 4: 0.008876308297142083 5: 0.004837977417149418 6: -0.001368606701933467 7: 0.02425285860988661 8: 0.05727330842922638 9: 0.07008257906578365 10: 0.05727330842922601 11: 0.02425285860989356 12: 0.004659404339106939 13: 0.08354521980501411 14: 0.1370796991940131 15: 0.1370796991940127 16: 0.08354521980500548 17: 0.004659404339111468 18: 0.05564545640233233 19: 0.1524391996823045 20: 0.1877107583774186 21: 0.152439199682313 22: 0.05564545640232336 23: 0.008186176158688102 24: 0.1295355639606756 25: 0.2061407656847928 26: 0.2061407656847876 27: 0.1295355639606875 28: 0.008186176158690356 29: 0.06234969028098169 30: 0.1730419031522366 31: 0.216941824741853 32: 0.1730419031522199 33: 0.06234969028097538 34: 0.007506172839505442 35: 0.1142161960569384 36: 0.1802176663769141 37: 0.1802176663769346 38: 0.1142161960569467 39: 0.007506172839510119 40: 0.04031900987630967 41: 0.1142976211857209 42: 0.1413353845521616 43: 0.1142976211857124 44: 0.04031900987629731 45: 0.003239075586865803 46: 0.04317587564915148 47: 0.07015250533601401 48: 0.07015250533600842 49: 0.04317587564916202 50: 0.003239075586875191 51: 0.002550690557458576 52: 0.006084230077463266 53: 0.007421516754854941 54: 0.006084230077464776 55: 0.002550690557449139 Degree T = 10 Number of points N = 66 Weights: 1: -0.0006240762604485385 2: 0.002843227149029473 3: 0.005250031948170099 4: 0.005891746241580334 5: 0.004705736485982276 6: 0.00213535463775728 7: 0.01610939653924503 8: 0.04099595211756455 9: 0.05326500934651114 10: 0.04863338516654146 11: 0.02843474741777358 12: 0.001719619179668798 13: 0.00288376974512999 14: 0.05724711668877085 15: 0.09659872841641835 16: 0.1053210323354191 17: 0.08066212502634017 18: 0.02855765663651391 19: 0.03981286043309895 20: 0.1090390674981266 21: 0.1430169021081182 22: 0.1313686303762309 23: 0.07932850918293012 24: 0.00461069696877172 25: 0.005086495679678558 26: 0.0931135639536379 27: 0.1562320334111958 28: 0.1696057154254737 29: 0.1283581371975964 30: 0.04603059518098125 31: 0.04894888812995488 32: 0.1347281473526085 33: 0.1764193542600553 34: 0.1635037456302797 35: 0.09822749154560256 36: 0.005704840613902773 37: 0.005086495679678713 38: 0.09311356395363346 39: 0.1562320334111808 40: 0.1696057154254774 41: 0.1283581371975583 42: 0.04603059518098872 43: 0.03981286043310196 44: 0.1090390674981535 45: 0.1430169021080935 46: 0.1313686303762708 47: 0.07932850918295671 48: 0.004610696968763288 49: 0.002883769745125264 50: 0.05724711668873503 51: 0.09659872841643503 52: 0.1053210323354192 53: 0.08066212502630565 54: 0.0285576566364993 55: 0.01610939653928591 56: 0.04099595211756667 57: 0.05326500934650459 58: 0.04863338516654175 59: 0.02843474741779626 60: 0.001719619179690429 61: -0.0006240762604690484 62: 0.002843227149027327 63: 0.005250031948169366 64: 0.005891746241580984 65: 0.004705736485985881 66: 0.002135354637733299 quadrature_weights_vandermonde_2d_test(): Normal end of execution. 14-Jun-2023 12:43:23