18 May 2007 6:06:00.746 AM NINTLIB_PRB FORTRAN90 version Test routines in 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) = .000000000000 B(1:DIM_NUM) = 1.00000000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.00000000000 25 P5_ND: 1.00000000000 9 ROMBERG_ND: 1.00000000000 500 SAMPLE_ND: 1.00000000000 120 P5_ND+: 1.00000000000 9 P5_ND+: 1.00000000000 36 P5_ND+: 1.00000000000 144 P5_ND+: 1.00000000000 576 P5_ND+: 1.00000000000 2304 P5_ND+: 1.00000000000 9216 MONTE_CARLO_ND: 1.00000000000 80000 MONTE_CARLO_ND: 1.00000000000 640000 MONTE_CARLO_ND: 1.00000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1.00000000000 25 P5_ND: 1.00000000000 9 ROMBERG_ND: 1.00000000000 500 SAMPLE_ND: 1.00000000000 120 P5_ND+: 1.00000000000 9 P5_ND+: 1.00000000000 36 P5_ND+: 1.00000000000 144 P5_ND+: 1.00000000000 576 P5_ND+: 1.00000000000 2304 P5_ND+: 1.00000000000 9216 MONTE_CARLO_ND: .998027405901 80000 MONTE_CARLO_ND: .999766521520 640000 MONTE_CARLO_ND: 1.00015492486 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: .666666666667 25 P5_ND: .666666666667 9 ROMBERG_ND: .666666666667 1400 SAMPLE_ND: .665987531604 120 P5_ND+: .666666666667 9 P5_ND+: .666666666667 36 P5_ND+: .666666666667 144 P5_ND+: .666666666667 576 P5_ND+: .666666666667 2304 P5_ND+: .666666666667 9216 MONTE_CARLO_ND: .664168108442 80000 MONTE_CARLO_ND: .666376318898 640000 MONTE_CARLO_ND: .666799167670 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: .500000000000 25 P5_ND: .500000000000 9 ROMBERG_ND: .500000000000 1400 SAMPLE_ND: .499693384220 120 P5_ND+: .500000000000 9 P5_ND+: .500000000000 36 P5_ND+: .500000000000 144 P5_ND+: .500000000000 576 P5_ND+: .500000000000 2304 P5_ND+: .500000000000 9216 MONTE_CARLO_ND: .497326983052 80000 MONTE_CARLO_ND: .499713738262 640000 MONTE_CARLO_ND: .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: 2.95249213461 500 SAMPLE_ND: 2.94942850067 120 P5_ND+: 2.95248960999 9 P5_ND+: 2.95249239663 36 P5_ND+: 2.95249244130 144 P5_ND+: 2.95249244200 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: 2.95307117170 5120000 F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2)) BOX_ND: .639510304013 25 P5_ND: .639380432842 9 ROMBERG_ND: .639510327294 500 SAMPLE_ND: .639697555310 120 P5_ND+: .639380432842 9 P5_ND+: .639510041677 36 P5_ND+: .639510349723 144 P5_ND+: .639510351837 576 P5_ND+: .639510351870 2304 P5_ND+: .639510351870 9216 MONTE_CARLO_ND: .640366140285 80000 MONTE_CARLO_ND: .639604094414 640000 MONTE_CARLO_ND: .639480970925 5120000 DIM_NUM = 3 A(1:DIM_NUM) = .000000000000 B(1:DIM_NUM) = 1.00000000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.00000000000 125 P5_ND: 1.00000000000 19 ROMBERG_ND: 1.00000000000 9000 SAMPLE_ND: 1.00000000000 400 MONTE_CARLO_ND: 1.00000000000 80000 MONTE_CARLO_ND: 1.00000000000 640000 MONTE_CARLO_ND: 1.00000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1.50000000000 125 P5_ND: 1.50000000000 19 ROMBERG_ND: 1.50000000000 9000 SAMPLE_ND: 1.50000000000 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: 1.00000000000 125 P5_ND: 1.00000000000 19 ROMBERG_ND: 1.00000000000 36000 SAMPLE_ND: 1.00022103832 400 MONTE_CARLO_ND: .995754246374 80000 MONTE_CARLO_ND: .999655853409 640000 MONTE_CARLO_ND: 1.00026702063 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: .750000000000 125 P5_ND: .750000000000 19 ROMBERG_ND: .750000000000 36000 SAMPLE_ND: .750387770055 400 MONTE_CARLO_ND: .745506654189 80000 MONTE_CARLO_ND: .749671836557 640000 MONTE_CARLO_ND: .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: 5.07321411171 36000 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: .535856697388 125 P5_ND: .535741189906 19 ROMBERG_ND: .535856704763 9000 SAMPLE_ND: .535815750597 400 MONTE_CARLO_ND: .537053805496 80000 MONTE_CARLO_ND: .535993984643 640000 MONTE_CARLO_ND: .535829344847 5120000 DIM_NUM = 4 A(1:DIM_NUM) = .000000000000 B(1:DIM_NUM) = 1.00000000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.00000000000 625 P5_ND: 1.00000000000 33 ROMBERG_ND: 1.00000000000 170000 SAMPLE_ND: 1.00000000000 1416 MONTE_CARLO_ND: 1.00000000000 80000 MONTE_CARLO_ND: 1.00000000000 640000 MONTE_CARLO_ND: 1.00000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 2.00000000000 625 P5_ND: 2.00000000000 33 ROMBERG_ND: 2.00000000000 170000 SAMPLE_ND: 2.00000000000 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: 1.33333333333 980000 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: 1.00000000000 625 P5_ND: 1.00000000000 33 ROMBERG_ND: 1.00000000000 980000 SAMPLE_ND: 1.00009382136 1416 MONTE_CARLO_ND: .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: 8.71721161990 980000 SAMPLE_ND: 8.72000061799 1416 MONTE_CARLO_ND: 8.69295681121 80000 MONTE_CARLO_ND: 8.71779095163 640000 MONTE_CARLO_ND: 8.71869139420 5120000 F(X(1:DIM_NUM)) = 1/(1+sum(X(1:DIM_NUM)^2)) BOX_ND: .459360474862 625 P5_ND: .459299029954 33 ROMBERG_ND: .459360450369 170000 SAMPLE_ND: .459211867082 1416 MONTE_CARLO_ND: .460437620766 80000 MONTE_CARLO_ND: .459359350009 640000 MONTE_CARLO_ND: .459346934990 5120000 NINTLIB_PRB Normal end of execution. 18 May 2007 6:07:04.591 AM