Thu Sep 13 09:51:34 2018 HYPERCUBE_MONTE_CARLO_TEST Python version: 3.6.5 Test the HYPERCUBE_MONTE_CARLO library. HYPERCUBE01_MONOMIAL_INTEGRAL_TEST Python version: 3.6.5 HYPERCUBE01_MONOMIAL_INTEGRAL returns the integral of a monomial over the interior of the unit hypercube in 3D. Compare with a Monte Carlo estimate. Using M = 3 Number of sample points used is 4192 Ex Ey Ez MC-Estimate Exact Error 4 3 0 0.0479881 0.05 0.002 0 2 3 0.0817332 0.0833333 0.0016 4 4 2 0.0118586 0.0133333 0.0015 0 3 0 0.246879 0.25 0.0031 4 3 0 0.0479881 0.05 0.002 4 0 4 0.0375109 0.04 0.0025 3 4 0 0.0481349 0.05 0.0019 1 0 4 0.0964596 0.1 0.0035 1 3 0 0.121836 0.125 0.0032 0 4 2 0.0645985 0.0666667 0.0021 1 2 2 0.0532703 0.0555556 0.0023 3 0 4 0.0470921 0.05 0.0029 1 0 1 0.243841 0.25 0.0062 4 1 4 0.0183829 0.02 0.0016 3 3 0 0.0602641 0.0625 0.0022 4 4 2 0.0118586 0.0133333 0.0015 0 4 4 0.03867 0.04 0.0013 1 3 2 0.0395885 0.0416667 0.0021 0 4 0 0.197368 0.2 0.0026 0 4 3 0.0484177 0.05 0.0016 HYPERCUBE01_MONOMIAL_INTEGRAL_TEST: Normal end of execution. HYPERCUBE01_MONTE_CARLO_TEST01 Python version: 3.6.5 Use HYPERCUBE01_SAMPLE to estimate integrals along the interior of the unit hypercube in 3D. N 1 X Y Z X^2 XY XZ Y^2 YZ Z^2 1 1 0.218418 0.956318 0.829509 0.0477066 0.208877 0.18118 0.914543 0.793274 0.688086 2 1 0.409637 0.262632 0.0549739 0.190924 0.130799 0.024214 0.0922852 0.0161394 0.00314633 4 1 0.282914 0.43188 0.614169 0.142975 0.0862314 0.171704 0.34476 0.238985 0.424707 8 1 0.448764 0.628688 0.353048 0.254287 0.238301 0.158954 0.46407 0.242944 0.190148 16 1 0.577699 0.448109 0.427455 0.424276 0.2827 0.262341 0.287263 0.173018 0.273017 32 1 0.515482 0.515035 0.544601 0.361026 0.247016 0.257241 0.325622 0.293727 0.36065 64 1 0.480189 0.485151 0.489409 0.333062 0.239247 0.225187 0.311633 0.222457 0.32229 128 1 0.522288 0.527152 0.500881 0.340195 0.277869 0.255059 0.35926 0.269568 0.332462 256 1 0.518508 0.474727 0.483861 0.354571 0.248632 0.243592 0.312454 0.216697 0.319905 512 1 0.50878 0.497615 0.486234 0.34348 0.252898 0.252131 0.334466 0.242949 0.31835 1024 1 0.490345 0.513345 0.517057 0.323702 0.250676 0.250157 0.344286 0.266699 0.355972 2048 1 0.491744 0.489847 0.488673 0.324386 0.241942 0.239161 0.322013 0.239861 0.322957 4096 1 0.504534 0.498569 0.500109 0.338882 0.251314 0.252754 0.328975 0.252365 0.333069 8192 1 0.501019 0.497158 0.500549 0.333224 0.248799 0.251007 0.330668 0.248406 0.332779 16384 1 0.497685 0.500676 0.499293 0.330493 0.250014 0.249553 0.333813 0.249133 0.332566 32768 1 0.49489 0.499854 0.49986 0.328029 0.247185 0.247649 0.332854 0.250109 0.332957 65536 1 0.499523 0.500937 0.498091 0.332645 0.250628 0.248412 0.334921 0.249898 0.331342 Exact 1 0.5 0.5 0.5 0.333333 0.25 0.25 0.333333 0.25 0.333333 HYPERCUBE01_MONTE_CARLO_TEST01 Normal end of execution. HYPERCUBE01_MONTE_CARLO_TEST02 Python version: 3.6.5 Use HYPERCUBE01_SAMPLE to estimate integrals along the interior of the unit hypercube in 6D. N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 1 0.218418 0.914543 0.629284 0.0995414 3.59721e-05 8.35501e-08 2 1 0.329442 0.290811 0.181028 0.0807668 0.00800541 0.00505748 4 1 0.308967 0.432037 0.0840648 0.139689 0.0368181 0.0121251 8 1 0.6605 0.355774 0.0421925 0.149312 0.0195489 0.11284 16 1 0.493475 0.405808 0.149726 0.293121 0.0563945 0.163816 32 1 0.473714 0.286581 0.0980965 0.201767 0.0254793 0.143554 64 1 0.511575 0.405931 0.154639 0.215411 0.0338462 0.149255 128 1 0.527234 0.299406 0.0852711 0.208662 0.0359612 0.138457 256 1 0.51127 0.320302 0.107357 0.207969 0.0394189 0.118593 512 1 0.468988 0.341574 0.122401 0.206524 0.0414207 0.155458 1024 1 0.495952 0.308343 0.0970281 0.188538 0.0410239 0.133455 2048 1 0.499629 0.324461 0.109222 0.211872 0.0390518 0.143671 4096 1 0.50066 0.332315 0.107506 0.19954 0.0373718 0.143336 8192 1 0.498742 0.331866 0.111009 0.197399 0.0370256 0.141139 16384 1 0.493463 0.332789 0.111119 0.195224 0.0364105 0.142021 32768 1 0.499804 0.332445 0.109761 0.19986 0.0378825 0.141774 65536 1 0.502609 0.331401 0.110264 0.198122 0.0370926 0.142865 Exact 1 0.5 0.333333 0.111111 0.2 0.037037 0.142857 HYPERCUBE01_MONTE_CARLO_TEST02 Normal end of execution. HYPERCUBE01_SAMPLE_TEST Python version: 3.6.5 HYPERUBE01_SAMPLE samples the unit hypercube in M dimensions. Sample points in the unit hypercube. Row: 0 1 2 Col 0 : 0.218418 0.956318 0.829509 1 : 0.561695 0.415307 0.0661187 2 : 0.257578 0.109957 0.043829 3 : 0.633966 0.0617272 0.449539 4 : 0.401306 0.754673 0.797287 5 : 0.00183837 0.897504 0.350752 6 : 0.0945448 0.0136169 0.859097 7 : 0.840847 0.123104 0.00751236 8 : 0.260303 0.912484 0.113664 9 : 0.351629 0.822887 0.267132 HYPERCUBE01_SAMPLE_TEST Normal end of execution. HYPERCUBE01_VOLUME_TEST Python version: 3.6.5 HYPERCUBE01_VOLUME returns the volume of the unit hypercube in M dimensions. HYPERCUBE01_VOLUME(3) = 1 HYPERCUBE01_VOLUME_TEST Normal end of execution. I4VEC_PRINT_TEST Python version: 3.6.5 I4VEC_PRINT prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 I4VEC_PRINT_TEST: Normal end of execution. I4VEC_TRANSPOSE_PRINT_TEST Python version: 3.6.5 I4VEC_TRANSPOSE_PRINT prints an I4VEC with 5 entries to a row, and an optional title. My array: 1 2 3 4 5 6 7 8 9 10 11 12 I4VEC_TRANSPOSE_PRINT_TEST: Normal end of execution. I4VEC_UNIFORM_AB_TEST Python version: 3.6.5 I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 The random vector: 0 -35 1 187 2 149 3 69 4 25 5 -81 6 -23 7 -67 8 -87 9 90 10 -82 11 35 12 20 13 127 14 139 15 -100 16 170 17 5 18 -72 19 -96 I4VEC_UNIFORM_AB_TEST: Normal end of execution. MONOMIAL_VALUE_TEST Python version: 3.6.5 Use monomial_value() to evaluate some monomials in dimensions 1 through 3. Spatial dimension M = 1 Exponents: -1 V(X) X(0) 0.111111 9.0000 0.125 8.0000 0.2 5.0000 0.333333 3.0000 -1 -1.0000 Spatial dimension M = 2 Exponents: -1 -2 V(X) X(0) X(1) -0.0277778 -1.0000 6.0000 -0.111111 -1.0000 3.0000 0.00680272 3.0000 7.0000 0.03125 8.0000 -2.0000 0.0277778 9.0000 2.0000 Spatial dimension M = 3 Exponents: -3 -3 5 V(X) X(0) X(1) X(2) 0.0625 8.0000 -1.0000 -2.0000 -0.00137174 1.0000 9.0000 -1.0000 0.000244141 2.0000 8.0000 1.0000 1.21363 6.0000 5.0000 8.0000 0.158766 3.0000 9.0000 5.0000 MONOMIAL_VALUE_TEST Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8MAT_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT prints an R8MAT. Here is an R8MAT, transposed: Row: 0 1 2 3 Col 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 R8MAT_TRANSPOSE_PRINT_TEST: Normal end of execution. R8MAT_TRANSPOSE_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed. R8MAT, rows 0:2, cols 3:5: Row: 0 1 2 Col 3 : 14 24 34 4 : 15 25 35 5 : 16 26 36 R8MAT_TRANSPOSE_PRINT_SOME_TEST: Normal end of execution. R8MAT_UNIFORM_01_TEST Python version: 3.6.5 R8MAT_UNIFORM_01 computes a random R8MAT. 0 <= X <= 1 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.218418 0.0661187 0.0617272 0.00183837 1 : 0.956318 0.257578 0.449539 0.897504 2 : 0.829509 0.109957 0.401306 0.350752 3 : 0.561695 0.043829 0.754673 0.0945448 4 : 0.415307 0.633966 0.797287 0.0136169 R8MAT_UNIFORM_01_TEST: Normal end of execution. R8MAT_UNIFORM_AB_TEST Python version: 3.6.5 R8MAT_UNIFORM_AB computes a random R8MAT. -1 <= X <= 5 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.31051 -0.603288 -0.629637 -0.98897 1 : 4.73791 0.545467 1.69723 4.38502 2 : 3.97706 -0.340259 1.40784 1.10451 3 : 2.37017 -0.737026 3.52804 -0.432731 4 : 1.49184 2.80379 3.78372 -0.918299 R8MAT_UNIFORM_AB_TEST: Normal end of execution. HYPERCUBE_MONTE_CARLO_TEST: Normal end of execution. Thu Sep 13 09:51:36 2018