13 September 2010 09:41:45 AM SPHERE_LEBEDEV_RULE_PRB C++ version Test the SPHERE_LEBEDEV_RULE library. TEST01 List Lebedev rule properties. Rule Avail Order Prec 1 1 6 3 2 1 14 5 3 1 26 7 4 1 38 9 5 1 50 11 6 1 74 13 7 1 86 15 8 1 110 17 9 1 146 19 10 1 170 21 11 1 194 23 12 1 230 25 13 1 266 27 14 1 302 29 15 1 350 31 16 0 386 33 17 1 434 35 18 0 482 37 19 0 530 39 20 1 590 41 21 0 650 43 22 0 698 45 23 1 770 47 24 0 830 49 25 0 890 51 26 1 974 53 27 0 1046 55 28 0 1118 57 29 1 1202 59 30 0 1274 61 31 0 1358 63 32 1 1454 65 33 0 1538 67 34 0 1622 69 35 1 1730 71 36 0 1814 73 37 0 1910 75 38 1 2030 77 39 0 2126 79 40 0 2222 81 41 1 2354 83 42 0 2450 85 43 0 2558 87 44 1 2702 89 45 0 2810 91 46 0 2930 93 47 1 3074 95 48 0 3182 97 49 0 3314 99 50 1 3470 101 51 0 3590 103 52 0 3722 105 53 1 3890 107 54 0 4010 109 55 0 4154 111 56 1 4334 113 57 0 4466 115 58 0 4610 117 59 1 4802 119 60 0 4934 121 61 0 5090 123 62 1 5294 125 63 0 5438 127 64 0 5606 129 65 1 5810 131 TEST02 Generate each available rule and test for accuracy. Order = 6 LMAXW = 3 max error = 3.33067e-16 0 90 0.166666666666667 180 90 0.166666666666667 90 90 0.166666666666667 -90 90 0.166666666666667 90 0 0.166666666666667 90 180 0.166666666666667 Order = 14 LMAXW = 5 max error = 2.08166817117217e-16 0 90 0.0666666666666667 180 90 0.0666666666666667 90 90 0.0666666666666667 -90 90 0.0666666666666667 90 0 0.0666666666666667 90 180 0.0666666666666667 45 54.7356103172453 0.075 135 54.7356103172453 0.075 -45 54.7356103172453 0.075 -135 54.7356103172453 0.075 45 125.264389682755 0.075 135 125.264389682755 0.075 -45 125.264389682755 0.075 -135 125.264389682755 0.075 Order = 26 LMAXW = 7 max error = 5.46437894932694e-16 0 90 0.0476190476190476 180 90 0.0476190476190476 90 90 0.0476190476190476 -90 90 0.0476190476190476 90 0 0.0476190476190476 90 180 0.0476190476190476 90 45 0.0380952380952381 -90 45 0.0380952380952381 90 135 0.0380952380952381 -90 135 0.0380952380952381 0 45 0.0380952380952381 180 45 0.0380952380952381 0 135 0.0380952380952381 180 135 0.0380952380952381 45 90 0.0380952380952381 135 90 0.0380952380952381 -45 90 0.0380952380952381 -135 90 0.0380952380952381 45 54.7356103172453 0.0321428571428571 135 54.7356103172453 0.0321428571428571 -45 54.7356103172453 0.0321428571428571 -135 54.7356103172453 0.0321428571428571 45 125.264389682755 0.0321428571428571 135 125.264389682755 0.0321428571428571 -45 125.264389682755 0.0321428571428571 -135 125.264389682755 0.0321428571428571 Order = 38 LMAXW = 9 max error = 4.37150315946155e-16 0 90 0.00952380952380952 180 90 0.00952380952380952 90 90 0.00952380952380952 -90 90 0.00952380952380952 90 0 0.00952380952380952 90 180 0.00952380952380952 45 54.7356103172453 0.0321428571428571 135 54.7356103172453 0.0321428571428571 -45 54.7356103172453 0.0321428571428571 -135 54.7356103172453 0.0321428571428571 45 125.264389682755 0.0321428571428571 135 125.264389682755 0.0321428571428571 -45 125.264389682755 0.0321428571428571 -135 125.264389682755 0.0321428571428571 62.6321948413773 90 0.0285714285714286 117.367805158623 90 0.0285714285714286 -62.6321948413773 90 0.0285714285714286 -117.367805158623 90 0.0285714285714286 27.3678051586227 90 0.0285714285714286 152.632194841377 90 0.0285714285714286 -27.3678051586227 90 0.0285714285714286 -152.632194841377 90 0.0285714285714286 0 27.3678051586227 0.0285714285714286 180 27.3678051586227 0.0285714285714286 0 152.632194841377 0.0285714285714286 180 152.632194841377 0.0285714285714286 0 62.6321948413773 0.0285714285714286 180 62.6321948413773 0.0285714285714286 0 117.367805158623 0.0285714285714286 180 117.367805158623 0.0285714285714286 90 27.3678051586227 0.0285714285714286 -90 27.3678051586227 0.0285714285714286 90 152.632194841377 0.0285714285714286 -90 152.632194841377 0.0285714285714286 90 62.6321948413773 0.0285714285714286 -90 62.6321948413773 0.0285714285714286 90 117.367805158623 0.0285714285714286 -90 117.367805158623 0.0285714285714286 Order = 50 LMAXW = 11 max error = 8.01442245901285e-16 0 90 0.0126984126984127 180 90 0.0126984126984127 90 90 0.0126984126984127 -90 90 0.0126984126984127 90 0 0.0126984126984127 90 180 0.0126984126984127 90 45 0.0225749559082892 -90 45 0.0225749559082892 90 135 0.0225749559082892 -90 135 0.0225749559082892 0 45 0.0225749559082892 180 45 0.0225749559082892 0 135 0.0225749559082892 180 135 0.0225749559082892 45 90 0.0225749559082892 135 90 0.0225749559082892 -45 90 0.0225749559082892 -135 90 0.0225749559082892 45 54.7356103172453 0.02109375 135 54.7356103172453 0.02109375 -45 54.7356103172453 0.02109375 -135 54.7356103172453 0.02109375 45 125.264389682755 0.02109375 135 125.264389682755 0.02109375 -45 125.264389682755 0.02109375 -135 125.264389682755 0.02109375 45 25.2394018206789 0.0201733355379189 135 25.2394018206789 0.0201733355379189 -45 25.2394018206789 0.0201733355379189 -135 25.2394018206789 0.0201733355379189 45 154.760598179321 0.0201733355379189 135 154.760598179321 0.0201733355379189 -45 154.760598179321 0.0201733355379189 -135 154.760598179321 0.0201733355379189 71.565051177078 72.4515993862077 0.0201733355379189 108.434948822922 72.4515993862077 0.0201733355379189 -71.565051177078 72.4515993862077 0.0201733355379189 -108.434948822922 72.4515993862077 0.0201733355379189 71.565051177078 107.548400613792 0.0201733355379189 108.434948822922 107.548400613792 0.0201733355379189 -71.565051177078 107.548400613792 0.0201733355379189 -108.434948822922 107.548400613792 0.0201733355379189 18.434948822922 72.4515993862077 0.0201733355379189 161.565051177078 72.4515993862077 0.0201733355379189 -18.434948822922 72.4515993862077 0.0201733355379189 -161.565051177078 72.4515993862077 0.0201733355379189 18.434948822922 107.548400613792 0.0201733355379189 161.565051177078 107.548400613792 0.0201733355379189 -18.434948822922 107.548400613792 0.0201733355379189 -161.565051177078 107.548400613792 0.0201733355379189 Order = 74 LMAXW = 13 max error = 5.58147278395538e-16 Order = 86 LMAXW = 15 max error = 2.93027321157657e-15 Order = 110 LMAXW = 17 max error = 2.66864167482866e-15 Order = 146 LMAXW = 19 max error = 4.43661678440266e-15 Order = 170 LMAXW = 21 max error = 3.69718065366888e-15 Order = 194 LMAXW = 23 max error = 4.25175775171921e-15 Order = 230 LMAXW = 25 max error = 3.08337780492458e-15 Order = 266 LMAXW = 27 max error = 5.69431841748109e-15 Order = 302 LMAXW = 29 max error = 5.51733882408618e-15 Order = 350 LMAXW = 31 max error = 7.69785754676538e-15 Order = 434 LMAXW = 35 max error = 4.94725739409431e-15 Order = 590 LMAXW = 41 max error = 5.49977970615948e-15 Order = 770 LMAXW = 47 max error = 5.0551429392604e-15 Order = 974 LMAXW = 53 max error = 8.17369216190714e-15 Order = 1202 LMAXW = 59 max error = 7.94037274541572e-15 Order = 1454 LMAXW = 65 max error = 9.98446967163864e-15 Order = 1730 LMAXW = 71 max error = 9.88289025360429e-15 Order = 2030 LMAXW = 77 max error = 1.21540881864346e-14 Order = 2354 LMAXW = 83 max error = 1.50731865112655e-14 Order = 2702 LMAXW = 89 max error = 1.30242403629763e-14 Order = 3074 LMAXW = 95 max error = 1.74414162043395e-14 Order = 3470 LMAXW = 101 max error = 1.16521145831702e-14 Order = 3890 LMAXW = 107 max error = 1.80988735707461e-14 Order = 4334 LMAXW = 113 max error = 1.77958655577358e-14 Order = 4802 LMAXW = 119 max error = 1.57528533604825e-14 Order = 5294 LMAXW = 125 max error = 2.14760759794616e-14 Order = 5810 LMAXW = 131 max error = 2.16476005070369e-14 SPHERE_LEBEDEV_RULE_PRB Normal end of execution. 13 September 2010 09:41:58 AM