07-Jan-2022 23:16:51 nintlib_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test nintlib(). Test routines for estimating the integral of of F(X) in the hypercube [A,B]^DIM_NUM. DIM_NUM = 2 A(1:DIM_NUM) = 0.000000 B(1:DIM_NUM) = 1.000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.000000000000 25 P5_ND: 1.000000000000 9 ROMBERG_ND: 1.000000000000 500 SAMPLE_ND: 1.000000000000 120 P5_ND + : 1.000000000000 9 P5_ND + : 1.000000000000 36 P5_ND + : 1.000000000000 144 P5_ND + : 1.000000000000 576 P5_ND + : 1.000000000000 2304 P5_ND + : 1.000000000000 9216 MONTE_CARLO_ND: 1.000000000000 80000 MONTE_CARLO_ND: 1.000000000000 640000 MONTE_CARLO_ND: 1.000000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1.000000000000 25 P5_ND: 1.000000000000 9 ROMBERG_ND: 1.000000000000 500 SAMPLE_ND: 1.000000000000 120 P5_ND + : 1.000000000000 9 P5_ND + : 1.000000000000 36 P5_ND + : 1.000000000000 144 P5_ND + : 1.000000000000 576 P5_ND + : 1.000000000000 2304 P5_ND + : 1.000000000000 9216 MONTE_CARLO_ND: 1.002552802165 80000 MONTE_CARLO_ND: 0.999623953886 640000 MONTE_CARLO_ND: 1.000130593115 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 0.666666666667 25 P5_ND: 0.666666666667 9 ROMBERG_ND: 0.666666666667 1400 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: 0.664954472813 80000 MONTE_CARLO_ND: 0.667009659047 640000 MONTE_CARLO_ND: 0.667047307565 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 0.500000000000 25 P5_ND: 0.500000000000 9 ROMBERG_ND: 0.500000000000 1400 SAMPLE_ND: 0.499693384220 120 P5_ND + : 0.500000000000 9 P5_ND + : 0.500000000000 36 P5_ND + : 0.500000000000 144 P5_ND + : 0.500000000000 576 P5_ND + : 0.500000000000 2304 P5_ND + : 0.500000000000 9216 MONTE_CARLO_ND: 0.501083407166 80000 MONTE_CARLO_ND: 0.500068481515 640000 MONTE_CARLO_ND: 0.499843489051 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 2.952492442010 25 P5_ND: 2.952489609987 9 ROMBERG_ND: 2.952492134614 500 SAMPLE_ND: 2.949428500673 120 P5_ND + : 2.952489609987 9 P5_ND + : 2.952492396633 36 P5_ND + : 2.952492441299 144 P5_ND + : 2.952492442001 576 P5_ND + : 2.952492442012 2304 P5_ND + : 2.952492442013 9216 MONTE_CARLO_ND: 2.951495432692 80000 MONTE_CARLO_ND: 2.950932949981 640000 MONTE_CARLO_ND: 2.950950652027 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: 0.639510327294 500 SAMPLE_ND: 0.639697555310 120 P5_ND + : 0.639380432842 9 P5_ND + : 0.639510041677 36 P5_ND + : 0.639510349723 144 P5_ND + : 0.639510351837 576 P5_ND + : 0.639510351870 2304 P5_ND + : 0.639510351870 9216 MONTE_CARLO_ND: 0.639910396665 80000 MONTE_CARLO_ND: 0.639503496082 640000 MONTE_CARLO_ND: 0.639488508851 5120000 DIM_NUM = 3 A(1:DIM_NUM) = 0.000000 B(1:DIM_NUM) = 1.000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.000000000000 125 P5_ND: 1.000000000000 19 ROMBERG_ND: 1.000000000000 9000 SAMPLE_ND: 1.000000000000 400 MONTE_CARLO_ND: 1.000000000000 80000 MONTE_CARLO_ND: 1.000000000000 640000 MONTE_CARLO_ND: 1.000000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 1.500000000000 125 P5_ND: 1.500000000000 19 ROMBERG_ND: 1.500000000000 9000 SAMPLE_ND: 1.500000000000 400 MONTE_CARLO_ND: 1.499167256546 80000 MONTE_CARLO_ND: 1.499237034334 640000 MONTE_CARLO_ND: 1.499758732254 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 1.000000000000 125 P5_ND: 1.000000000000 19 ROMBERG_ND: 1.000000000000 36000 SAMPLE_ND: 1.000221038315 400 MONTE_CARLO_ND: 1.000088791648 80000 MONTE_CARLO_ND: 1.000264739716 640000 MONTE_CARLO_ND: 0.999609078023 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 0.750000000000 125 P5_ND: 0.750000000000 19 ROMBERG_ND: 0.750000000000 36000 SAMPLE_ND: 0.750387770055 400 MONTE_CARLO_ND: 0.750600786920 80000 MONTE_CARLO_ND: 0.749208562738 640000 MONTE_CARLO_ND: 0.750096506072 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 5.073214111767 125 P5_ND: 5.072870243744 19 ROMBERG_ND: 5.073214111706 36000 SAMPLE_ND: 5.072253233876 400 MONTE_CARLO_ND: 5.067218840991 80000 MONTE_CARLO_ND: 5.071671886734 640000 MONTE_CARLO_ND: 5.074069476495 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: 0.535856704763 9000 SAMPLE_ND: 0.535815750597 400 MONTE_CARLO_ND: 0.536072392321 80000 MONTE_CARLO_ND: 0.536207435103 640000 MONTE_CARLO_ND: 0.535971116537 5120000 DIM_NUM = 4 A(1:DIM_NUM) = 0.000000 B(1:DIM_NUM) = 1.000000 F(X(1:DIM_NUM)) = 1 BOX_ND: 1.000000000000 625 P5_ND: 1.000000000000 33 ROMBERG_ND: 1.000000000000 170000 SAMPLE_ND: 1.000000000000 1416 MONTE_CARLO_ND: 1.000000000000 80000 MONTE_CARLO_ND: 1.000000000000 640000 MONTE_CARLO_ND: 1.000000000000 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM) ) BOX_ND: 2.000000000000 625 P5_ND: 2.000000000000 33 ROMBERG_ND: 2.000000000000 170000 SAMPLE_ND: 2.000000000000 1416 MONTE_CARLO_ND: 1.999977726089 80000 MONTE_CARLO_ND: 1.999534876919 640000 MONTE_CARLO_ND: 1.999878963785 5120000 F(X(1:DIM_NUM)) = sum( X(1:DIM_NUM)^2 ) BOX_ND: 1.333333333333 625 P5_ND: 1.333333333333 33 ROMBERG_ND: 1.333333333333 980000 SAMPLE_ND: 1.334074780064 1416 MONTE_CARLO_ND: 1.333618644029 80000 MONTE_CARLO_ND: 1.332783350390 640000 MONTE_CARLO_ND: 1.333241676840 5120000 F(X(1:DIM_NUM)) = sum ( X(1:DIM_NUM)^3 ) BOX_ND: 1.000000000000 625 P5_ND: 1.000000000000 33 ROMBERG_ND: 1.000000000000 980000 SAMPLE_ND: 1.000093821362 1416 MONTE_CARLO_ND: 0.998377219577 80000 MONTE_CARLO_ND: 1.000502840688 640000 MONTE_CARLO_ND: 0.999823799545 5120000 F(X(1:DIM_NUM)) = exp(sum(X(1:DIM_NUM))) BOX_ND: 8.717211620128 625 P5_ND: 8.714951853523 33 ROMBERG_ND: 8.717211619899 980000 SAMPLE_ND: 8.720000617987 1416 MONTE_CARLO_ND: 8.721030318637 80000 MONTE_CARLO_ND: 8.715650925420 640000 MONTE_CARLO_ND: 8.715104447268 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: 0.459360450369 170000 SAMPLE_ND: 0.459211867082 1416 MONTE_CARLO_ND: 0.458687945448 80000 MONTE_CARLO_ND: 0.459221259533 640000 MONTE_CARLO_ND: 0.459307491830 5120000 nintlib_test(): Normal end of execution. 07-Jan-2022 23:19:10