Thu Sep 13 13:02:02 2018 PYRAMID_MONTE_CARLO_TEST Python version: 3.6.5 Test the PYRAMID_MONTE_CARLO library. GAMMA_LOG_VALUES: GAMMA_LOG_VALUES stores values of the logarithm of the Gamma function. X GAMMA_LOG(X) 0.200000 1.5240638224307841 0.400000 0.7966778177017837 0.600000 0.3982338580692348 0.800000 0.1520596783998375 1.000000 0.0000000000000000 1.100000 -0.0498724412598397 1.200000 -0.0853740900033158 1.300000 -0.1081748095078604 1.400000 -0.1196129141723712 1.500000 -0.1207822376352452 1.600000 -0.1125917656967557 1.700000 -0.0958076974070659 1.800000 -0.0710838729143722 1.900000 -0.0389842759230833 2.000000 0.0000000000000000 3.000000 0.6931471805599453 4.000000 1.7917594692280550 10.000000 12.8018274800814691 20.000000 39.3398841871994946 30.000000 71.2570389671680147 GAMMA_LOG_VALUES_TEST: Normal end of execution. I4_UNIFORM_AB_TEST Python version: 3.6.5 I4_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 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 I4_UNIFORM_AB_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. PYRAMID01_INTEGRAL_TEST Python version: 3.6.5 PYRAMID01_INTEGRAL returns the integral of a monomial over the unit pyramid in 3D. Compare to a Monte Carlo estimate. Number of sample points used is 500000 E1 E2 E3 MC-Estimate Exact Error 0 0 0 1.33333 1.33333 0 2 0 0 0.265432 0.266667 0.0012 4 0 0 0.113616 0.114286 0.00067 6 0 0 0.0630826 0.0634921 0.00041 0 2 0 0.266404 0.266667 0.00026 2 2 0 0.0631172 0.0634921 0.00037 4 2 0 0.0294246 0.0296296 0.0002 0 4 0 0.114151 0.114286 0.00013 2 4 0 0.0294431 0.0296296 0.00019 0 6 0 0.0633977 0.0634921 9.4e-05 0 0 1 0.333908 0.333333 0.00058 2 0 1 0.0443021 0.0444444 0.00014 4 0 1 0.0142281 0.0142857 5.8e-05 0 2 1 0.0445419 0.0444444 9.7e-05 2 2 1 0.00791511 0.00793651 2.1e-05 0 4 1 0.0143255 0.0142857 4e-05 0 0 2 0.133741 0.133333 0.00041 2 0 2 0.0126683 0.0126984 3e-05 4 0 2 0.00316495 0.0031746 9.7e-06 0 2 2 0.0127463 0.0126984 4.8e-05 2 2 2 0.00176164 0.00176367 2e-06 0 4 2 0.00318874 0.0031746 1.4e-05 0 0 3 0.066929 0.0666667 0.00026 2 0 3 0.00475339 0.0047619 8.5e-06 0 2 3 0.0047852 0.0047619 2.3e-05 0 0 4 0.0382648 0.0380952 0.00017 2 0 4 0.00211345 0.0021164 2.9e-06 0 2 4 0.00212875 0.0021164 1.2e-05 0 0 5 0.0239229 0.0238095 0.00011 0 0 6 0.0159526 0.015873 8e-05 PYRAMID01_INTEGRAL_TEST: Normal end of execution. PYRAMID01_MONTE_CARLO_TEST Python version: 3.6.5 Use PYRAMID01_SAMPLE to estimate integrals over the interior of the unit pyramid in 3D. N 1 Z X^2 Y^2 Z^2 X^2Z Y^2Z Z^3 X^2Y^2 X^2Z^2 1 1.33333 0.0805408 0.373326 0.980424 0.00486512 0.022551 0.0592231 0.000293881 0.274513 0.00136221 2 1.33333 0.828705 0.0211411 0.0535591 0.515958 0.0136013 0.0345134 0.321794 0.0014815 0.0087546 4 1.33333 0.216938 0.387863 0.614484 0.0497824 0.0623849 0.0855273 0.0129738 0.229948 0.0156092 8 1.33333 0.472294 0.113265 0.172749 0.229933 0.0305924 0.0485688 0.135519 0.00896647 0.0108669 16 1.33333 0.411529 0.229055 0.233929 0.19321 0.0548249 0.0534605 0.108439 0.0386064 0.0195821 32 1.33333 0.281716 0.30371 0.213996 0.0920697 0.0523294 0.031091 0.0382608 0.0592789 0.0149762 64 1.33333 0.33859 0.309114 0.249012 0.132766 0.0581633 0.0388547 0.0633169 0.071995 0.0176222 128 1.33333 0.329631 0.226658 0.263372 0.128703 0.0366629 0.0453023 0.0627059 0.0485369 0.00981415 256 1.33333 0.349132 0.264589 0.268959 0.14403 0.0459386 0.0472589 0.0728824 0.0629474 0.0138414 512 1.33333 0.344229 0.266463 0.268343 0.139162 0.0458422 0.0477898 0.0698209 0.0614337 0.0133076 1024 1.33333 0.323395 0.264595 0.259571 0.130926 0.0437822 0.0424851 0.0665184 0.0596971 0.0128269 2048 1.33333 0.346192 0.25989 0.25794 0.143914 0.0431756 0.0438319 0.0749375 0.062771 0.0125251 4096 1.33333 0.333751 0.272191 0.258348 0.134109 0.0450484 0.0425979 0.0675956 0.0623705 0.0126667 8192 1.33333 0.332181 0.264563 0.267983 0.132169 0.0440421 0.0447832 0.0658987 0.0617065 0.0124026 16384 1.33333 0.334308 0.265773 0.26661 0.134262 0.0440533 0.044185 0.0674713 0.064037 0.0125161 32768 1.33333 0.33348 0.26574 0.265681 0.133488 0.0443534 0.0442792 0.0668804 0.0630149 0.0126593 65536 1.33333 0.334955 0.265387 0.267659 0.134301 0.0443835 0.0449525 0.0672506 0.0633764 0.0126845 Exact 1.33333 0.333333 0.266667 0.266667 0.133333 0.0444444 0.0444444 0.0666667 0.0634921 0.0126984 PYRAMID01_MONTE_CARLO_TEST Normal end of execution. PYRAMID01_SAMPLE_TEST Python version: 3.6.5 PYRAMID01_SAMPLE samples points from the unit pyramid. Unit pyramid points Row: 0 1 2 Col 0 : -0.529145 0.857507 0.0604056 1 : 0.0498951 -0.0684939 0.595634 2 : -0.170945 -0.27504 0.647423 3 : 0.205248 -0.671476 0.233952 4 : -0.183031 0.472301 0.0727328 5 : -0.702641 0.560667 0.294766 6 : -0.77088 -0.924746 0.0493645 7 : 0.133511 -0.147631 0.804149 8 : -0.23222 0.399618 0.515596 9 : -0.191112 0.415901 0.355966 10 : 0.36547 0.117333 0.0485835 11 : -0.0778534 0.694145 0.157545 12 : -0.457207 0.384369 0.265047 13 : -0.450616 0.106489 0.284023 14 : 0.139976 -0.165375 0.402856 15 : 0.286934 -0.511457 0.331066 16 : 0.257074 0.256803 0.604505 17 : 0.387721 -0.757334 0.0802734 18 : 0.473565 -0.369359 0.0347348 19 : 0.390594 0.387917 0.258939 PYRAMID01_SAMPLE_TEST Normal end of execution. PYRAMID01_VOLUME_TEST Python version: 3.6.5 PYRAMID01_VOLUME returns the volume of the unit pyramid. PYRAMID01_VOLUME() = 1.33333 PYRAMID01_VOLUME_TEST Normal end of execution. R8_CHOOSE_TEST Python version: 3.6.5 R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 5 0 1 5 1 5 5 2 10 5 3 10 5 4 5 5 5 1 R8_CHOOSE_TEST Normal end of execution. R8_GAMMA_LOG_TEST: Python version: 3.6.5 R8_GAMMA_LOG evaluates the logarithm of the Gamma function. X GAMMA_LOG(X) R8_GAMMA_LOG(X) 0.2 1.524063822430784 1.524063822430784 0.4 0.7966778177017837 0.7966778177017837 0.6 0.3982338580692348 0.3982338580692349 0.8 0.1520596783998375 0.1520596783998376 1 0 0 1.1 -0.04987244125983972 -0.04987244125983976 1.2 -0.08537409000331583 -0.08537409000331585 1.3 -0.1081748095078604 -0.1081748095078605 1.4 -0.1196129141723712 -0.1196129141723713 1.5 -0.1207822376352452 -0.1207822376352453 1.6 -0.1125917656967557 -0.1125917656967558 1.7 -0.09580769740706586 -0.09580769740706586 1.8 -0.07108387291437215 -0.07108387291437215 1.9 -0.03898427592308333 -0.03898427592308337 2 0 0 3 0.6931471805599453 0.6931471805599454 4 1.791759469228055 1.791759469228055 10 12.80182748008147 12.80182748008147 20 39.33988418719949 39.33988418719949 30 71.25703896716801 71.257038967168 R8_GAMMA_LOG_TEST Normal end of execution. R8_MOP_TEST Python version: 3.6.5 R8_MOP evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) -57 -1.0 92 1.0 66 1.0 12 1.0 -17 -1.0 -87 -1.0 -49 -1.0 -78 1.0 -92 1.0 27 -1.0 R8_MOP_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. PYRAMID_MONTE_CARLO_TEST: Normal end of execution. Thu Sep 13 13:02:16 2018