03-Mar-2019 10:49:58 quadrature_weights_vandermonde_2d_test: MATLAB version 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: 1.850371707708594e-16 2: 0.6666666666666663 3: 2.222222222222223 4: 0.4444444444444444 5: 5.551115123125783e-17 6: 0.6666666666666664 Degree T = 3 Number of points N = 10 Weights: 1: -0.0555555555555558 2: 0.3333333333333335 3: -0.05555555555555547 4: 0.8888888888888888 5: 0.8888888888888888 6: 0.2222222222222222 7: 1.333333333333333 8: 0.222222222222222 9: 0.111111111111111 10: 0.1111111111111112 Degree T = 4 Number of points N = 15 Weights: 1: -0.008888888888889163 2: 0.08104919101111049 3: 0.06117303121111198 4: 0.3874097078666783 5: 0.6259236254666555 6: 0.05333333333333321 7: 0.071111111111111 8: 0.9830822022444236 9: 0.5458066866444652 10: 0.3874097078666785 11: 0.6259236254666555 12: 0.05333333333333308 13: -0.008888888888888981 14: 0.0810491910111098 15: 0.06117303121111221 Degree T = 5 Number of points N = 21 Weights: 1: -0.01037037037036903 2: 0.05037037037037113 3: 0.05037037037036976 4: -0.01037037037037008 5: 0.1876963678740768 6: 0.3460933466518661 7: 0.1876963678740778 8: 0.04514390511851796 9: 0.5541130536814718 10: 0.5541130536814716 11: 0.04514390511851804 12: 0.2804517802740698 13: 0.6376103570518371 14: 0.2804517802740691 15: 0.03189313191851875 16: 0.328849909281492 17: 0.3288499092814927 18: 0.0318931319185194 19: 0.02074074074074106 20: 0.03851851851851838 21: 0.02074074074074043 Degree T = 6 Number of points N = 28 Weights: 1: -0.003023431594860875 2: 0.01957267632451698 3: 0.02633929313290804 4: 0.01425431928029191 5: 0.1006383046329747 6: 0.2208900184526919 7: 0.1743144584714035 8: 0.01209372637944078 9: 0.01934996220710342 10: 0.3245064820875178 11: 0.4027058473592953 12: 0.1677234226317941 13: 0.1953319357827223 14: 0.448963305303514 15: 0.3721824611057575 16: 0.02479213907785312 17: 0.01934996220710475 18: 0.324506482087515 19: 0.4027058473592947 20: 0.1677234226317939 21: 0.1006383046329736 22: 0.2208900184526937 23: 0.1743144584714038 24: 0.01209372637944117 25: -0.003023431594861434 26: 0.0195726763245175 27: 0.02633929313290786 28: 0.01425431928029115 Degree T = 7 Number of points N = 36 Weights: 1: -0.003287981859409192 2: 0.01337868480725621 3: 0.02063492063492007 4: 0.01337868480725568 5: -0.003287981859409287 6: 0.05949324721885026 7: 0.1306477599993569 8: 0.1306477599993548 9: 0.05949324721885216 10: 0.01263869091685684 11: 0.1979944935601154 12: 0.2832184784823782 13: 0.1979944935601146 14: 0.01263869091685669 15: 0.1221817987389796 16: 0.3150266070593436 17: 0.3150266070593443 18: 0.1221817987389799 19: 0.01771365352315095 20: 0.2490926964598305 21: 0.3408041116307007 22: 0.2490926964598292 23: 0.01771365352315046 24: 0.09646986307476163 25: 0.2557725606433905 26: 0.2557725606433905 27: 0.09646986307476382 28: 0.008649923133691133 29: 0.1062007918394729 30: 0.1505805844901025 31: 0.1062007918394718 32: 0.008649923133689803 33: 0.006355881462927652 34: 0.01405228180237517 35: 0.01405228180237534 36: 0.006355881462928576 Degree T = 8 Number of points N = 45 Weights: 1: -0.001269841269845529 2: 0.0067060896390516 3: 0.0111145544135307 4: 0.01026455026455174 5: 0.004930678698744612 6: 0.03633146869163791 7: 0.08838322767331949 8: 0.09965911758462639 9: 0.06400185533755694 10: 0.004061629144890451 11: 0.006772486772487906 12: 0.1258344472781214 13: 0.1927501398511241 14: 0.1699470899470939 15: 0.0634259948813372 16: 0.08376332474107237 17: 0.2170841444607176 18: 0.247730725080175 19: 0.1648098048612169 20: 0.01004771829779256 21: 0.0101587301587312 22: 0.1784328991205201 23: 0.2729409493576554 24: 0.2364021164021176 25: 0.08936689226256467 26: 0.08376332474107238 27: 0.2170841444607155 28: 0.247730725080184 29: 0.1648098048612177 30: 0.01004771829779053 31: 0.006772486772488131 32: 0.1258344472781267 33: 0.1927501398511155 34: 0.169947089947088 35: 0.06342599488134021 36: 0.03633146869163258 37: 0.08838322767332311 38: 0.09965911758463414 39: 0.06400185533755633 40: 0.004061629144889334 41: -0.001269841269841718 42: 0.006706089639049015 43: 0.01111455441352852 44: 0.01026455026455104 45: 0.004930678698745426 Degree T = 9 Number of points N = 55 Weights: 1: -0.001368606701932932 2: 0.004837977417139464 3: 0.008876308297148972 4: 0.008876308297148453 5: 0.004837977417143963 6: -0.001368606701942247 7: 0.02425285860989651 8: 0.05727330842923434 9: 0.07008257906577112 10: 0.05727330842922536 11: 0.0242528586099178 12: 0.004659404339103787 13: 0.08354521980501227 14: 0.1370796991940089 15: 0.1370796991940121 16: 0.08354521980499 17: 0.004659404339103149 18: 0.05564545640233226 19: 0.1524391996823048 20: 0.1877107583774372 21: 0.1524391996823277 22: 0.05564545640233312 23: 0.008186176158688222 24: 0.1295355639606772 25: 0.2061407656847799 26: 0.2061407656847598 27: 0.1295355639606767 28: 0.008186176158689383 29: 0.06234969028098417 30: 0.173041903152243 31: 0.2169418247418667 32: 0.1730419031522442 33: 0.06234969028097959 34: 0.007506172839503699 35: 0.1142161960569234 36: 0.1802176663769147 37: 0.1802176663769254 38: 0.1142161960569271 39: 0.00750617283950696 40: 0.0403190098763223 41: 0.1142976211857312 42: 0.1413353845521487 43: 0.1142976211857232 44: 0.04031900987631756 45: 0.003239075586855884 46: 0.04317587564914297 47: 0.07015250533601769 48: 0.07015250533601902 49: 0.04317587564914905 50: 0.003239075586858144 51: 0.002550690557467416 52: 0.006084230077461787 53: 0.007421516754852347 54: 0.006084230077460394 55: 0.002550690557464578 Degree T = 10 Number of points N = 66 Weights: 1: -0.0006240762604456411 2: 0.002843227149045671 3: 0.005250031948150504 4: 0.005891746241561887 5: 0.004705736485967151 6: 0.00213535463774861 7: 0.01610939653921673 8: 0.04099595211756905 9: 0.05326500934654649 10: 0.04863338516658233 11: 0.02843474741780102 12: 0.001719619179675556 13: 0.002883769745154251 14: 0.05724711668877426 15: 0.09659872841641358 16: 0.105321032335371 17: 0.08066212502629806 18: 0.02855765663648888 19: 0.03981286043306777 20: 0.1090390674981264 21: 0.1430169021081336 22: 0.1313686303762902 23: 0.07932850918297153 24: 0.004610696968791256 25: 0.005086495679686279 26: 0.09311356395365591 27: 0.1562320334111943 28: 0.1696057154254513 29: 0.1283581371975304 30: 0.04603059518093 31: 0.04894888812994926 32: 0.1347281473525934 33: 0.1764193542600357 34: 0.1635037456303302 35: 0.09822749154566743 36: 0.005704840613930402 37: 0.005086495679677092 38: 0.09311356395364541 39: 0.1562320334112259 40: 0.1696057154254504 41: 0.1283581371975124 42: 0.0460305951809295 43: 0.03981286043309987 44: 0.1090390674981015 45: 0.1430169021081183 46: 0.131368630376284 47: 0.07932850918299816 48: 0.004610696968791403 49: 0.002883769745126406 50: 0.05724711668878487 51: 0.09659872841641635 52: 0.1053210323354087 53: 0.08066212502628883 54: 0.02855765663646052 55: 0.01610939653923553 56: 0.04099595211757937 57: 0.05326500934651333 58: 0.04863338516655986 59: 0.02843474741781865 60: 0.00171961917970239 61: -0.0006240762604431324 62: 0.002843227149022229 63: 0.00525003194816539 64: 0.005891746241575469 65: 0.004705736485972565 66: 0.002135354637725104 quadrature_weights_vandermonde_2d_test: Normal end of execution. 03-Mar-2019 10:49:58