29 May 2014 04:26:06 PM QWV_2D_PRB: C++ version Test the QWV_2D library. 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: 0: 1 -1 1: 1 1 2: -1 1 Weights: 0: 2 1: 0 2: 2 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: 0: 4 Degree T = 1 Number of points N = 3 Weights: 0: 1 1: 1 2: 2 Degree T = 2 Number of points N = 6 Weights: 0: 6.661338147750939e-16 1: 0.6666666666666663 2: 2.222222222222222 3: 0.4444444444444444 4: 5.551115123125783e-17 5: 0.6666666666666664 Degree T = 3 Number of points N = 10 Weights: 0: -0.0555555555555548 1: 0.3333333333333331 2: -0.0555555555555558 3: 0.8888888888888886 4: 0.8888888888888893 5: 0.2222222222222224 6: 1.333333333333333 7: 0.222222222222222 8: 0.1111111111111109 9: 0.1111111111111112 Degree T = 4 Number of points N = 15 Weights: 0: -0.008888888888888932 1: 0.08104919101110961 2: 0.06117303121111219 3: 0.3874097078666789 4: 0.6259236254666545 5: 0.05333333333333362 6: 0.07111111111111067 7: 0.9830822022444241 8: 0.5458066866444642 9: 0.387409707866678 10: 0.6259236254666568 11: 0.05333333333333383 12: -0.008888888888888703 13: 0.08104919101110968 14: 0.06117303121111135 Degree T = 5 Number of points N = 21 Weights: 0: -0.01037037037037093 1: 0.05037037037036911 2: 0.05037037037037081 3: -0.01037037037036947 4: 0.1876963678740801 5: 0.3460933466518654 6: 0.1876963678740763 7: 0.04514390511851724 8: 0.5541130536814713 9: 0.5541130536814728 10: 0.04514390511851834 11: 0.2804517802740705 12: 0.6376103570518378 13: 0.2804517802740683 14: 0.03189313191851883 15: 0.328849909281491 16: 0.3288499092814925 17: 0.03189313191851956 18: 0.02074074074074123 19: 0.03851851851851849 20: 0.02074074074074051 Degree T = 6 Number of points N = 28 Weights: 0: -0.003023431594858565 1: 0.01957267632451884 2: 0.0263392931329084 3: 0.01425431928029237 4: 0.1006383046329639 5: 0.2208900184526934 6: 0.1743144584714012 7: 0.01209372637943976 8: 0.0193499622071068 9: 0.3245064820875231 10: 0.4027058473592984 11: 0.1677234226317961 12: 0.1953319357827178 13: 0.4489633053035124 14: 0.3721824611057551 15: 0.02479213907785274 16: 0.01934996220710561 17: 0.3245064820875153 18: 0.4027058473592959 19: 0.1677234226317944 20: 0.1006383046329745 21: 0.2208900184526933 22: 0.1743144584714027 23: 0.01209372637944051 24: -0.00302343159486199 25: 0.01957267632451757 26: 0.02633929313290797 27: 0.01425431928029198 Degree T = 7 Number of points N = 36 Weights: 0: -0.003287981859413765 1: 0.01337868480725671 2: 0.02063492063491996 3: 0.01337868480725546 4: -0.003287981859408898 5: 0.05949324721885513 6: 0.1306477599993571 7: 0.1306477599993581 8: 0.05949324721885061 9: 0.01263869091685831 10: 0.1979944935601103 11: 0.283218478482374 12: 0.1979944935601143 13: 0.01263869091685747 14: 0.1221817987389771 15: 0.3150266070593529 16: 0.315026607059344 17: 0.1221817987389802 18: 0.01771365352315134 19: 0.2490926964598258 20: 0.340804111630698 21: 0.2490926964598291 22: 0.01771365352314976 23: 0.09646986307476696 24: 0.2557725606433917 25: 0.2557725606433927 26: 0.09646986307476431 27: 0.008649923133686802 28: 0.1062007918394705 29: 0.1505805844901012 30: 0.1062007918394705 31: 0.008649923133690016 32: 0.006355881462931014 33: 0.01405228180237514 34: 0.01405228180237651 35: 0.006355881462928496 Degree T = 8 Number of points N = 45 Weights: 0: -0.001269841269835311 1: 0.00670608963904127 2: 0.01111455441352989 3: 0.01026455026455282 4: 0.004930678698742625 5: 0.03633146869162523 6: 0.08838322767333079 7: 0.09965911758463214 8: 0.06400185533755555 9: 0.004061629144893127 10: 0.006772486772485166 11: 0.1258344472781388 12: 0.1927501398511116 13: 0.1699470899470907 14: 0.06342599488133535 15: 0.08376332474107638 16: 0.2170841444607031 17: 0.2477307250801775 18: 0.1648098048612226 19: 0.01004771829779292 20: 0.0101587301587291 21: 0.1784328991205164 22: 0.2729409493576765 23: 0.2364021164021134 24: 0.08936689226256009 25: 0.08376332474107701 26: 0.2170841444607054 27: 0.2477307250801761 28: 0.16480980486122 29: 0.0100477182977933 30: 0.006772486772485237 31: 0.1258344472781358 32: 0.1927501398511135 33: 0.1699470899470926 34: 0.06342599488133838 35: 0.03633146869162453 36: 0.08838322767332588 37: 0.09965911758463601 38: 0.06400185533755502 39: 0.004061629144888279 40: -0.001269841269836355 41: 0.006706089639046927 42: 0.01111455441352761 43: 0.01026455026454956 44: 0.004930678698747173 Degree T = 9 Number of points N = 55 Weights: 0: -0.001368606701945113 1: 0.004837977417140975 2: 0.008876308297144902 3: 0.008876308297143068 4: 0.004837977417150492 5: -0.001368606701935084 6: 0.02425285860992349 7: 0.05727330842923516 8: 0.07008257906578071 9: 0.05727330842922034 10: 0.02425285860989794 11: 0.004659404339099723 12: 0.0835452198049855 13: 0.1370796991940044 14: 0.1370796991940248 15: 0.08354521980500107 16: 0.004659404339109654 17: 0.05564545640233619 18: 0.1524391996823315 19: 0.1877107583774149 20: 0.1524391996823176 21: 0.05564545640232402 22: 0.008186176158691754 23: 0.1295355639606716 24: 0.2061407656847711 25: 0.206140765684763 26: 0.1295355639606894 27: 0.008186176158692687 28: 0.06234969028097752 29: 0.1730419031522391 30: 0.2169418247419051 31: 0.1730419031522361 32: 0.06234969028097048 33: 0.007506172839505762 34: 0.114216196056935 35: 0.1802176663769002 36: 0.1802176663769038 37: 0.1142161960569279 38: 0.00750617283951226 39: 0.04031900987631698 40: 0.1142976211857364 41: 0.1413353845521477 42: 0.1142976211857414 43: 0.040319009876317 44: 0.003239075586856897 45: 0.04317587564913915 46: 0.07015250533601934 47: 0.0701525053360193 48: 0.04317587564913908 49: 0.003239075586852207 50: 0.002550690557469151 51: 0.006084230077461027 52: 0.007421516754852508 53: 0.006084230077458821 54: 0.002550690557473353 Degree T = 10 Number of points N = 66 Weights: 0: -0.0006240762604463766 1: 0.002843227149025789 2: 0.005250031948150784 3: 0.00589174624156881 4: 0.004705736485964679 5: 0.002135354637732944 6: 0.01610939653924566 7: 0.04099595211758227 8: 0.05326500934654063 9: 0.04863338516658277 10: 0.02843474741781434 11: 0.001719619179693151 12: 0.002883769745121509 13: 0.05724711668876453 14: 0.09659872841640438 15: 0.1053210323353631 16: 0.08066212502628711 17: 0.02855765663647366 18: 0.03981286043310814 19: 0.1090390674981577 20: 0.1430169021081585 21: 0.1313686303763064 22: 0.07932850918298831 23: 0.004610696968783255 24: 0.005086495679684716 25: 0.09311356395361167 26: 0.1562320334111262 27: 0.1696057154254139 28: 0.1283581371975154 29: 0.04603059518094556 30: 0.0489488881299463 31: 0.1347281473526573 32: 0.1764193542601264 33: 0.1635037456303485 34: 0.0982274915456546 35: 0.005704840613923174 36: 0.005086495679679268 37: 0.09311356395362781 38: 0.1562320334111511 39: 0.1696057154253968 40: 0.1283581371975113 41: 0.04603059518094044 42: 0.03981286043311782 43: 0.1090390674981293 44: 0.1430169021081508 45: 0.1313686303763217 46: 0.07932850918299997 47: 0.004610696968790496 48: 0.00288376974511026 49: 0.05724711668875122 50: 0.09659872841642343 51: 0.1053210323353932 52: 0.08066212502626474 53: 0.02855765663644533 54: 0.0161093965392842 55: 0.04099595211758404 56: 0.05326500934649123 57: 0.04863338516656233 58: 0.0284347474178481 59: 0.001719619179720036 60: -0.000624076260460635 61: 0.002843227149011163 62: 0.005250031948172295 63: 0.005891746241587802 64: 0.004705736485965663 65: 0.002135354637703863 QWV_2D_PRB: Normal end of execution. 29 May 2014 04:26:06 PM