29-Jul-2021 09:20:20 quadrature_weights_vandermonde_2d_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) 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: -0.05555555555555508 2: 0.333333333333333 3: -0.05555555555555539 4: 0.8888888888888891 5: 0.8888888888888888 6: 0.2222222222222223 7: 1.333333333333333 8: 0.222222222222222 9: 0.1111111111111109 10: 0.1111111111111111 Degree T = 4 Number of points N = 15 Weights: 1: -0.008888888888888016 2: 0.08104919101111002 3: 0.06117303121111224 4: 0.3874097078666764 5: 0.6259236254666551 6: 0.05333333333333322 7: 0.071111111111111 8: 0.9830822022444256 9: 0.5458066866444646 10: 0.3874097078666781 11: 0.6259236254666551 12: 0.05333333333333341 13: -0.008888888888888861 14: 0.08104919101110998 15: 0.06117303121111202 Degree T = 5 Number of points N = 21 Weights: 1: -0.01037037037037027 2: 0.05037037037037154 3: 0.0503703703703702 4: -0.01037037037037054 5: 0.1876963678740773 6: 0.3460933466518645 7: 0.1876963678740791 8: 0.04514390511851795 9: 0.554113053681472 10: 0.5541130536814711 11: 0.04514390511851756 12: 0.2804517802740691 13: 0.6376103570518394 14: 0.2804517802740696 15: 0.03189313191851932 16: 0.3288499092814918 17: 0.328849909281491 18: 0.03189313191851924 19: 0.0207407407407407 20: 0.03851851851851874 21: 0.02074074074074086 Degree T = 6 Number of points N = 28 Weights: 1: -0.003023431594860248 2: 0.01957267632451802 3: 0.0263392931329091 4: 0.01425431928029055 5: 0.1006383046329711 6: 0.2208900184526883 7: 0.1743144584714054 8: 0.01209372637944192 9: 0.01934996220710542 10: 0.3245064820875216 11: 0.4027058473592959 12: 0.1677234226317923 13: 0.1953319357827189 14: 0.4489633053035127 15: 0.372182461105757 16: 0.02479213907785382 17: 0.01934996220710567 18: 0.3245064820875176 19: 0.4027058473592965 20: 0.1677234226317932 21: 0.1006383046329714 22: 0.2208900184526925 23: 0.1743144584714039 24: 0.01209372637944118 25: -0.003023431594860461 26: 0.01957267632451788 27: 0.02633929313290779 28: 0.01425431928029132 Degree T = 7 Number of points N = 36 Weights: 1: -0.003287981859407903 2: 0.01337868480725643 3: 0.02063492063491914 4: 0.01337868480725687 5: -0.003287981859411675 6: 0.0594932472188473 7: 0.1306477599993569 8: 0.1306477599993561 9: 0.05949324721885504 10: 0.01263869091685862 11: 0.1979944935601199 12: 0.2832184784823764 13: 0.1979944935601089 14: 0.01263869091685898 15: 0.1221817987389753 16: 0.3150266070593395 17: 0.3150266070593492 18: 0.1221817987389768 19: 0.01771365352315201 20: 0.2490926964598321 21: 0.3408041116307018 22: 0.2490926964598327 23: 0.0177136535231512 24: 0.09646986307476277 25: 0.2557725606433925 26: 0.2557725606433867 27: 0.0964698630747611 28: 0.008649923133689818 29: 0.1062007918394705 30: 0.1505805844901016 31: 0.1062007918394752 32: 0.008649923133692058 33: 0.006355881462929059 34: 0.01405228180237605 35: 0.01405228180237532 36: 0.006355881462926076 Degree T = 8 Number of points N = 45 Weights: 1: -0.001269841269836073 2: 0.00670608963905257 3: 0.01111455441353033 4: 0.01026455026455307 5: 0.004930678698743566 6: 0.0363314686916171 7: 0.08838322767331905 8: 0.09965911758462626 9: 0.06400185533755683 10: 0.00406162914489176 11: 0.006772486772490211 12: 0.1258344472781418 13: 0.1927501398511213 14: 0.1699470899470917 15: 0.06342599488133682 16: 0.08376332474107055 17: 0.2170841444607015 18: 0.2477307250801849 19: 0.1648098048612179 20: 0.01004771829779192 21: 0.01015873015873041 22: 0.1784328991205191 23: 0.2729409493576648 24: 0.236402116402111 25: 0.08936689226256524 26: 0.08376332474107484 27: 0.2170841444607161 28: 0.2477307250801763 29: 0.1648098048612224 30: 0.0100477182977901 31: 0.006772486772486352 32: 0.125834447278128 33: 0.1927501398511151 34: 0.1699470899470919 35: 0.06342599488133731 36: 0.03633146869163195 37: 0.08838322767332349 38: 0.0996591175846331 39: 0.06400185533755548 40: 0.004061629144891383 41: -0.001269841269840403 42: 0.006706089639047601 43: 0.01111455441352944 44: 0.01026455026455123 45: 0.00493067869874442 Degree T = 9 Number of points N = 55 Weights: 1: -0.001368606701926732 2: 0.004837977417139813 3: 0.008876308297147299 4: 0.008876308297144942 5: 0.004837977417140906 6: -0.001368606701929034 7: 0.02425285860989253 8: 0.05727330842923066 9: 0.07008257906577378 10: 0.05727330842923428 11: 0.02425285860989275 12: 0.004659404339098576 13: 0.08354521980501504 14: 0.1370796991940141 15: 0.1370796991940116 16: 0.08354521980501152 17: 0.004659404339104106 18: 0.05564545640234211 19: 0.1524391996823042 20: 0.1877107583774254 21: 0.1524391996823028 22: 0.05564545640233191 23: 0.008186176158685429 24: 0.1295355639606666 25: 0.2061407656847845 26: 0.2061407656847905 27: 0.1295355639606822 28: 0.008186176158689752 29: 0.06234969028098721 30: 0.1730419031522427 31: 0.2169418247418597 32: 0.1730419031522303 33: 0.06234969028097659 34: 0.007506172839503082 35: 0.1142161960569305 36: 0.1802176663769167 37: 0.1802176663769164 38: 0.1142161960569382 39: 0.007506172839507766 40: 0.04031900987631599 41: 0.1142976211857288 42: 0.141335384552158 43: 0.1142976211857274 44: 0.04031900987631019 45: 0.003239075586863022 46: 0.04317587564914498 47: 0.07015250533600864 48: 0.07015250533601376 49: 0.04317587564914746 50: 0.00323907558686322 51: 0.002550690557461175 52: 0.006084230077466998 53: 0.00742151675485498 54: 0.006084230077462907 55: 0.002550690557461984 Degree T = 10 Number of points N = 66 Weights: 1: -0.000624076260435463 2: 0.002843227149046068 3: 0.005250031948175669 4: 0.005891746241575015 5: 0.00470573648594401 6: 0.002135354637723732 7: 0.01610939653919491 8: 0.04099595211754727 9: 0.05326500934649504 10: 0.04863338516660557 11: 0.02843474741784021 12: 0.001719619179702493 13: 0.002883769745147491 14: 0.05724711668880809 15: 0.09659872841644551 16: 0.1053210323353731 17: 0.0806621250262796 18: 0.0285576566364501 19: 0.03981286043307519 20: 0.1090390674980934 21: 0.1430169021081421 22: 0.1313686303762712 23: 0.07932850918300019 24: 0.004610696968795885 25: 0.005086495679686678 26: 0.09311356395365469 27: 0.1562320334111802 28: 0.1696057154254728 29: 0.1283581371975286 30: 0.04603059518092913 31: 0.04894888812993784 32: 0.1347281473526218 33: 0.1764193542600415 34: 0.1635037456303211 35: 0.09822749154565348 36: 0.005704840613932251 37: 0.005086495679686912 38: 0.09311356395363804 39: 0.1562320334112064 40: 0.1696057154254392 41: 0.1283581371975291 42: 0.04603059518092788 43: 0.03981286043309525 44: 0.1090390674981051 45: 0.1430169021081239 46: 0.1313686303762947 47: 0.07932850918300019 48: 0.004610696968796337 49: 0.002883769745125746 50: 0.05724711668878235 51: 0.09659872841643632 52: 0.1053210323354014 53: 0.0806621250262692 54: 0.02855765663644614 55: 0.01610939653924784 56: 0.04099595211755649 57: 0.05326500934649345 58: 0.04863338516657508 59: 0.02843474741784554 60: 0.001719619179712371 61: -0.0006240762604514234 62: 0.002843227149029606 63: 0.005250031948179347 64: 0.005891746241578371 65: 0.004705736485959514 66: 0.002135354637712001 quadrature_weights_vandermonde_2d_test(): Normal end of execution. 29-Jul-2021 09:20:20