24 December 2011 09:50:37 AM NINTLIB_PRB C++ version Test the NINTLIB library. TESTND Test routines for estimating the integral of of F(X) in the hypercube [A,B]**DIM_NUM. DIM_NUM = 2 A(1:DIM_NUM) = 0 B(1:DIM_NUM) = 1 F(X(1:DIM_NUM)) = 1 BOX_ND: 1 25 P5_ND: 1 9 ROMBERG_ND: 1 500 SAMPLE_ND: 1 120 P5_ND+: 1 9 P5_ND+: 1 36 P5_ND+: 1 144 P5_ND+: 1 576 P5_ND+: 1 2304 P5_ND+: 1 9216 MONTE_CARLO_ND: 1 80000 MONTE_CARLO_ND: 1 640000 MONTE_CARLO_ND: 1 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1 25 P5_ND: 1 9 ROMBERG_ND: 1 500 SAMPLE_ND: 1 120 P5_ND+: 1 9 P5_ND+: 1 36 P5_ND+: 1 144 P5_ND+: 1 576 P5_ND+: 1 2304 P5_ND+: 1 9216 MONTE_CARLO_ND: 0.998027405901 80000 MONTE_CARLO_ND: 0.99976652152 640000 MONTE_CARLO_ND: 1.00015492486 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 0.666666666667 25 P5_ND: 0.666666666667 9 ROMBERG_ND: 0.665 500 SAMPLE_ND: 0.665987531604 120 P5_ND+: 0.666666666667 9 P5_ND+: 0.666666666667 36 P5_ND+: 0.666666666667 144 P5_ND+: 0.666666666667 576 P5_ND+: 0.666666666667 2304 P5_ND+: 0.666666666667 9216 MONTE_CARLO_ND: 0.664168108442 80000 MONTE_CARLO_ND: 0.666376318898 640000 MONTE_CARLO_ND: 0.66679916767 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 0.5 25 P5_ND: 0.5 9 ROMBERG_ND: 0.4975 500 SAMPLE_ND: 0.49969338422 120 P5_ND+: 0.5 9 P5_ND+: 0.5 36 P5_ND+: 0.5 144 P5_ND+: 0.5 576 P5_ND+: 0.5 2304 P5_ND+: 0.5 9216 MONTE_CARLO_ND: 0.497326983052 80000 MONTE_CARLO_ND: 0.499713738262 640000 MONTE_CARLO_ND: 0.500113843852 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 2.95249244201 25 P5_ND: 2.95248960999 9 ROMBERG_ND: 2.95003326136 500 SAMPLE_ND: 2.94942850067 120 P5_ND+: 2.95248960999 9 P5_ND+: 2.95249239663 36 P5_ND+: 2.9524924413 144 P5_ND+: 2.952492442 576 P5_ND+: 2.95249244201 2304 P5_ND+: 2.95249244201 9216 MONTE_CARLO_ND: 2.94631667255 80000 MONTE_CARLO_ND: 2.95173127592 640000 MONTE_CARLO_ND: 2.9530711717 5120000 F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2)) BOX_ND: 0.639510304013 25 P5_ND: 0.639380432842 9 ROMBERG_ND: 0.639830676649 500 SAMPLE_ND: 0.63969755531 120 P5_ND+: 0.639380432842 9 P5_ND+: 0.639510041677 36 P5_ND+: 0.639510349723 144 P5_ND+: 0.639510351837 576 P5_ND+: 0.63951035187 2304 P5_ND+: 0.63951035187 9216 MONTE_CARLO_ND: 0.640366140285 80000 MONTE_CARLO_ND: 0.639604094414 640000 MONTE_CARLO_ND: 0.639480970925 5120000 DIM_NUM = 3 A(1:DIM_NUM) = 0 B(1:DIM_NUM) = 1 F(X(1:DIM_NUM)) = 1 BOX_ND: 1 125 P5_ND: 1 19 ROMBERG_ND: 1 9000 SAMPLE_ND: 1 400 MONTE_CARLO_ND: 1 80000 MONTE_CARLO_ND: 1 640000 MONTE_CARLO_ND: 1 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1.5 125 P5_ND: 1.5 19 ROMBERG_ND: 1.5 9000 SAMPLE_ND: 1.5 400 MONTE_CARLO_ND: 1.49674872143 80000 MONTE_CARLO_ND: 1.49969111716 640000 MONTE_CARLO_ND: 1.50032137192 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 1 125 P5_ND: 1 19 ROMBERG_ND: 0.9975 9000 SAMPLE_ND: 1.00022103832 400 MONTE_CARLO_ND: 0.995754246374 80000 MONTE_CARLO_ND: 0.999655853409 640000 MONTE_CARLO_ND: 1.00026702063 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 0.75 125 P5_ND: 0.75 19 ROMBERG_ND: 0.74625 9000 SAMPLE_ND: 0.750387770055 400 MONTE_CARLO_ND: 0.745506654189 80000 MONTE_CARLO_ND: 0.749671836557 640000 MONTE_CARLO_ND: 0.750206851687 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 5.07321411177 125 P5_ND: 5.07287024374 19 ROMBERG_ND: 5.06687708365 9000 SAMPLE_ND: 5.07225323388 400 MONTE_CARLO_ND: 5.05762616455 80000 MONTE_CARLO_ND: 5.07224119444 640000 MONTE_CARLO_ND: 5.07549508414 5120000 F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2)) BOX_ND: 0.535856697388 125 P5_ND: 0.535741189906 19 ROMBERG_ND: 0.536234844855 9000 SAMPLE_ND: 0.535815750597 400 MONTE_CARLO_ND: 0.537053805496 80000 MONTE_CARLO_ND: 0.535993984643 640000 MONTE_CARLO_ND: 0.535829344847 5120000 DIM_NUM = 4 A(1:DIM_NUM) = 0 B(1:DIM_NUM) = 1 F(X(1:DIM_NUM)) = 1 BOX_ND: 1 625 P5_ND: 1 33 ROMBERG_ND: 1 170000 SAMPLE_ND: 1 1416 MONTE_CARLO_ND: 1 80000 MONTE_CARLO_ND: 1 640000 MONTE_CARLO_ND: 1 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 2 625 P5_ND: 2 33 ROMBERG_ND: 2 170000 SAMPLE_ND: 2 1416 MONTE_CARLO_ND: 1.99613010771 80000 MONTE_CARLO_ND: 2.00019340401 640000 MONTE_CARLO_ND: 2.00018639408 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 1.33333333333 625 P5_ND: 1.33333333333 33 ROMBERG_ND: 1.33 170000 SAMPLE_ND: 1.33407478006 1416 MONTE_CARLO_ND: 1.32892112048 80000 MONTE_CARLO_ND: 1.33343780552 640000 MONTE_CARLO_ND: 1.33346221145 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 1 625 P5_ND: 1 33 ROMBERG_ND: 0.995 170000 SAMPLE_ND: 1.00009382136 1416 MONTE_CARLO_ND: 0.995656993813 80000 MONTE_CARLO_ND: 1.00004230277 640000 MONTE_CARLO_ND: 1.00008654224 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 8.71721162013 625 P5_ND: 8.71495185352 33 ROMBERG_ND: 8.70269624314 170000 SAMPLE_ND: 8.72000061799 1416 MONTE_CARLO_ND: 8.69295681121 80000 MONTE_CARLO_ND: 8.71779095163 640000 MONTE_CARLO_ND: 8.7186913942 5120000 F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2)) BOX_ND: 0.459360474862 625 P5_ND: 0.459299029954 33 ROMBERG_ND: 0.459765390279 170000 SAMPLE_ND: 0.459211867082 1416 MONTE_CARLO_ND: 0.460437620766 80000 MONTE_CARLO_ND: 0.459359350009 640000 MONTE_CARLO_ND: 0.45934693499 5120000 NINTLIB_PRB Normal end of execution. 24 December 2011 09:50:48 AM