15-May-2025 20:28:34 quadrature_weights_vandermonde_2d_test(): MATLAB/Octave version 6.4.0 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: 1.110223024625157e-16 6: 0.6666666666666664 Degree T = 3 Number of points N = 10 Weights: 1: -0.05555555555555486 2: 0.3333333333333333 3: -0.05555555555555551 4: 0.8888888888888887 5: 0.888888888888889 6: 0.2222222222222223 7: 1.333333333333333 8: 0.222222222222222 9: 0.1111111111111108 10: 0.1111111111111111 Degree T = 4 Number of points N = 15 Weights: 1: -0.008888888888889251 2: 0.08104919101111004 3: 0.06117303121111274 4: 0.3874097078666787 5: 0.625923625466654 6: 0.05333333333333305 7: 0.07111111111111068 8: 0.9830822022444256 9: 0.5458066866444652 10: 0.3874097078666777 11: 0.6259236254666551 12: 0.05333333333333296 13: -0.008888888888888542 14: 0.08104919101110955 15: 0.06117303121111251 Degree T = 5 Number of points N = 21 Weights: 1: -0.0103703703703701 2: 0.05037037037036946 3: 0.05037037037036974 4: -0.01037037037037033 5: 0.1876963678740788 6: 0.3460933466518663 7: 0.187696367874079 8: 0.04514390511851746 9: 0.5541130536814715 10: 0.5541130536814705 11: 0.04514390511851736 12: 0.2804517802740689 13: 0.6376103570518394 14: 0.2804517802740697 15: 0.0318931319185196 16: 0.3288499092814917 17: 0.3288499092814909 18: 0.03189313191851931 19: 0.02074074074074051 20: 0.03851851851851897 21: 0.02074074074074081 Degree T = 6 Number of points N = 28 Weights: 1: -0.003023431594860019 2: 0.01957267632451538 3: 0.0263392931329082 4: 0.01425431928029375 5: 0.100638304632974 6: 0.2208900184526947 7: 0.1743144584714003 8: 0.01209372637943873 9: 0.01934996220710418 10: 0.324506482087515 11: 0.4027058473592994 12: 0.1677234226317972 13: 0.1953319357827221 14: 0.4489633053035125 15: 0.3721824611057533 16: 0.02479213907785265 17: 0.01934996220710421 18: 0.324506482087517 19: 0.4027058473592973 20: 0.1677234226317946 21: 0.1006383046329733 22: 0.2208900184526932 23: 0.174314458471403 24: 0.01209372637944074 25: -0.003023431594860976 26: 0.01957267632451696 27: 0.02633929313290793 28: 0.01425431928029169 Degree T = 7 Number of points N = 36 Weights: 1: -0.003287981859408486 2: 0.01337868480725917 3: 0.02063492063492195 4: 0.01337868480725735 5: -0.003287981859411713 6: 0.0594932472188487 7: 0.1306477599993503 8: 0.1306477599993503 9: 0.05949324721885636 10: 0.01263869091685812 11: 0.1979944935601167 12: 0.2832184784823836 13: 0.1979944935601123 14: 0.01263869091685658 15: 0.122181798738979 16: 0.3150266070593478 17: 0.3150266070593444 18: 0.1221817987389793 19: 0.01771365352314962 20: 0.2490926964598249 21: 0.3408041116306964 22: 0.2490926964598297 23: 0.01771365352315087 24: 0.09646986307476847 25: 0.2557725606433922 26: 0.2557725606433934 27: 0.09646986307476378 28: 0.008649923133687119 29: 0.10620079183947 30: 0.1505805844901005 31: 0.1062007918394706 32: 0.008649923133689169 33: 0.006355881462930322 34: 0.01405228180237641 35: 0.01405228180237548 36: 0.00635588146292952 Degree T = 8 Number of points N = 45 Weights: 1: -0.001269841269845166 2: 0.006706089639051655 3: 0.01111455441352904 4: 0.01026455026454835 5: 0.004930678698747072 6: 0.03633146869163778 7: 0.08838322767331673 8: 0.09965911758463922 9: 0.06400185533755531 10: 0.004061629144889623 11: 0.006772486772490949 12: 0.1258344472781266 13: 0.1927501398511169 14: 0.1699470899470927 15: 0.06342599488133434 16: 0.08376332474106575 17: 0.2170841444607147 18: 0.2477307250801701 19: 0.1648098048612228 20: 0.01004771829779497 21: 0.01015873015873471 22: 0.1784328991205248 23: 0.2729409493576674 24: 0.2364021164021138 25: 0.08936689226255939 26: 0.08376332474106817 27: 0.2170841444607043 28: 0.247730725080186 29: 0.1648098048612218 30: 0.01004771829779215 31: 0.006772486772488082 32: 0.1258344472781367 33: 0.1927501398511161 34: 0.169947089947086 35: 0.06342599488133741 36: 0.03633146869162684 37: 0.08838322767332223 38: 0.09965911758463228 39: 0.06400185533755741 40: 0.004061629144891246 41: -0.001269841269838464 42: 0.006706089639047645 43: 0.01111455441353001 44: 0.01026455026455188 45: 0.004930678698743795 Degree T = 9 Number of points N = 55 Weights: 1: -0.001368606701938911 2: 0.004837977417136792 3: 0.008876308297142076 4: 0.008876308297144565 5: 0.004837977417147445 6: -0.001368606701935761 7: 0.02425285860991871 8: 0.05727330842923835 9: 0.07008257906578039 10: 0.05727330842922866 11: 0.0242528586098995 12: 0.004659404339100059 13: 0.08354521980499004 14: 0.1370796991940093 15: 0.1370796991940131 16: 0.08354521980499868 17: 0.004659404339110028 18: 0.0556454564023373 19: 0.1524391996823175 20: 0.1877107583774204 21: 0.1524391996823145 22: 0.05564545640232738 23: 0.008186176158689223 24: 0.1295355639606804 25: 0.2061407656847828 26: 0.2061407656847837 27: 0.1295355639606854 28: 0.00818617615868872 29: 0.06234969028097518 30: 0.1730419031522301 31: 0.2169418247418631 32: 0.1730419031522304 33: 0.06234969028097932 34: 0.007506172839507998 35: 0.1142161960569401 36: 0.1802176663769215 37: 0.1802176663769218 38: 0.114216196056934 39: 0.007506172839505869 40: 0.04031900987631074 41: 0.1142976211857212 42: 0.1413353845521545 43: 0.1142976211857221 44: 0.04031900987631522 45: 0.003239075586863931 46: 0.04317587564914797 47: 0.07015250533601773 48: 0.0701525053360184 49: 0.04317587564914723 50: 0.003239075586861552 51: 0.002550690557460687 52: 0.006084230077464609 53: 0.00742151675484864 54: 0.006084230077464071 55: 0.002550690557462172 Degree T = 10 Number of points N = 66 Weights: 1: -0.0006240762604679886 2: 0.002843227149008955 3: 0.00525003194817737 4: 0.005891746241581323 5: 0.0047057364859687 6: 0.002135354637726895 7: 0.01610939653930521 8: 0.04099595211757631 9: 0.05326500934648636 10: 0.04863338516656952 11: 0.0284347474178188 12: 0.001719619179696154 13: 0.002883769745101566 14: 0.05724711668874255 15: 0.09659872841642295 16: 0.1053210323354117 17: 0.08066212502629173 18: 0.02855765663647539 19: 0.03981286043313174 20: 0.1090390674981412 21: 0.1430169021081234 22: 0.1313686303762645 23: 0.07932850918297465 24: 0.004610696968787633 25: 0.005086495679672285 26: 0.09311356395360003 27: 0.156232033411189 28: 0.169605715425473 29: 0.1283581371975507 30: 0.04603059518093614 31: 0.04894888812997302 32: 0.1347281473526386 33: 0.1764193542600293 34: 0.1635037456303039 35: 0.09822749154565456 36: 0.005704840613930054 37: 0.005086495679667309 38: 0.09311356395362895 39: 0.1562320334111966 40: 0.169605715425465 41: 0.1283581371975205 42: 0.04603059518093235 43: 0.03981286043311015 44: 0.1090390674981095 45: 0.1430169021081222 46: 0.1313686303762887 47: 0.07932850918300015 48: 0.00461069696879194 49: 0.002883769745129743 50: 0.05724711668877323 51: 0.09659872841643019 52: 0.1053210323353942 53: 0.08066212502628443 54: 0.02855765663645156 55: 0.01610939653923227 56: 0.0409959521175742 57: 0.05326500934651463 58: 0.04863338516656307 59: 0.02843474741782917 60: 0.001719619179711182 61: -0.0006240762604447642 62: 0.002843227149031487 63: 0.005250031948160803 64: 0.0058917462415779 65: 0.00470573648596952 66: 0.002135354637716051 quadrature_weights_vandermonde_2d_test(): Normal end of execution. 15-May-2025 20:28:35