Thu Sep 13 09:51:23 2018 HYPERBALL_MONTE_CARLO_TEST Python version: 3.6.5 Test the HYPERBALL_MONTE_CARLO library. GAMMA_VALUES_TEST: Python version: 3.6.5 GAMMA_VALUES stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322 -0.010000 -100.5871979644108052 0.010000 99.4325851191506018 0.100000 9.5135076986687324 0.200000 4.5908437119988026 0.400000 2.2181595437576882 0.500000 1.7724538509055161 0.600000 1.4891922488128171 0.800000 1.1642297137253030 1.000000 1.0000000000000000 1.100000 0.9513507698668732 1.200000 0.9181687423997607 1.300000 0.8974706963062772 1.400000 0.8872638175030753 1.500000 0.8862269254527581 1.600000 0.8935153492876903 1.700000 0.9086387328532904 1.800000 0.9313837709802427 1.900000 0.9617658319073874 2.000000 1.0000000000000000 3.000000 2.0000000000000000 4.000000 6.0000000000000000 10.000000 362880.0000000000000000 20.000000 121645100408832000.0000000000000000 30.000000 8841761993739701898620088352768.0000000000000000 GAMMA_VALUES_TEST: Normal end of execution. HYPERBALL_MONTE_CARLO_TEST01 Python version: 3.6.5 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 3 N 1 X^2 Y^2 Z^2 X^4 X^2Y^2 Z^4 1 4.18879 1.03683 0.117844 0.541076 0.256639 0.0291693 0.0698921 2 4.18879 1.36177 0.256214 2.0108 0.697316 0.132907 1.42693 4 4.18879 0.704532 0.954586 1.30536 0.223317 0.0771494 0.450174 8 4.18879 0.911916 1.05854 0.430492 0.318723 0.213253 0.178352 16 4.18879 1.30415 0.592706 1.11748 0.664554 0.101514 0.465581 32 4.18879 0.800459 1.04915 1.11545 0.280813 0.172643 0.570938 64 4.18879 0.920802 0.881304 0.8264 0.408491 0.137082 0.32148 128 4.18879 0.883623 0.884691 0.665639 0.402329 0.134449 0.242344 256 4.18879 0.840408 0.888887 0.835941 0.369289 0.119195 0.361917 512 4.18879 0.947095 0.772026 0.835442 0.450666 0.119634 0.364025 1024 4.18879 0.800795 0.862834 0.808179 0.3356 0.119243 0.345652 2048 4.18879 0.83901 0.860449 0.808435 0.356888 0.122752 0.34544 4096 4.18879 0.859803 0.838847 0.859552 0.36865 0.124974 0.37183 8192 4.18879 0.820884 0.849977 0.837145 0.348385 0.121535 0.35992 16384 4.18879 0.844762 0.836117 0.842941 0.361521 0.119839 0.362152 32768 4.18879 0.839744 0.837319 0.836491 0.361111 0.120235 0.357936 65536 4.18879 0.837321 0.840711 0.834304 0.3605 0.119373 0.357186 Exact 4.18879 0.837758 0.837758 0.837758 0.359039 0.11968 0.359039 HYPERBALL_MONTE_CARLO_TEST01 Normal end of execution. HYPERBALL_MONTE_CARLO_TEST02 Python version: 3.6.5 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 6 N 1 U V^2 V^2W^2 X^4 Y^2Z^2 Z^6 1 5.16771 1.98974 0.0870753 0.00673661 0.0371031 0.0295722 0.0955581 2 5.16771 -1.55534 1.53226 0.162179 0.180884 0.000193646 3.76486e-07 4 5.16771 -0.686185 0.314803 0.0269054 0.0713516 0.00392993 0.0619428 8 5.16771 -0.296541 0.521006 0.0693522 0.0470754 0.00345459 0.161042 16 5.16771 0.613805 0.935487 0.0886397 0.435485 0.011341 0.0300525 32 5.16771 -0.458592 0.791475 0.0687205 0.258376 0.0070059 0.063097 64 5.16771 0.18916 0.756214 0.0794278 0.172308 0.00492269 0.0962077 128 5.16771 -0.0305115 0.543142 0.0584992 0.201704 0.00669747 0.135852 256 5.16771 0.0675086 0.729472 0.079016 0.164335 0.00476055 0.0963603 512 5.16771 0.0738884 0.699442 0.0644178 0.18088 0.0050392 0.0786409 1024 5.16771 0.012322 0.635779 0.0613443 0.173965 0.00516896 0.0846845 2048 5.16771 0.0725793 0.617545 0.0609552 0.217276 0.00584118 0.0763982 4096 5.16771 0.0365121 0.648452 0.0613359 0.187645 0.00570912 0.0804734 8192 5.16771 -0.0199676 0.642256 0.0627809 0.186551 0.00522519 0.0780286 16384 5.16771 -0.00121468 0.639601 0.0641863 0.197949 0.00527974 0.0804025 32768 5.16771 -0.00325038 0.644074 0.0635565 0.195108 0.00547604 0.0802482 65536 5.16771 -0.00451174 0.645414 0.0640654 0.192213 0.0054565 0.0808224 Exact 5.16771 0 0.645964 0.0645964 0.193789 0.00538303 0.0807455 HYPERBALL_MONTE_CARLO_TEST02 Use the Monte Carlo method to estimate integrals HYPERBALL01_MONOMIAL_INTEGRAL_TEST Python version: 3.6.5 HYPERBALL01_MONOMIAL_INTEGRAL computes the integral of a monomial over the interior of the unit hyperball in M dimensions. Compare with a Monte Carlo estimate. Spatial dimension M = 3 Number of sample points used is 4192 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey Ez MC-Estimate Exact Error 0 2 6 0.0170667 0.0181333 0.0011 4 0 6 0.00414237 0.00418461 4.2e-05 8 0 4 0.00197222 0.00195282 1.9e-05 4 8 8 1.214e-06 1.31432e-06 1e-07 0 0 6 0.196024 0.199466 0.0034 8 8 8 6.61499e-08 6.81499e-08 2e-09 2 4 8 0.000106993 0.000114872 7.9e-06 2 6 8 2.76309e-05 3.02293e-05 2.6e-06 8 2 0 0.0095903 0.00976408 0.00017 0 8 0 0.128169 0.126933 0.0012 2 0 4 0.0391635 0.0398932 0.00073 6 4 4 4.74864e-05 4.92307e-05 1.7e-06 4 8 6 4.02668e-06 4.31848e-06 2.9e-07 0 0 2 0.814873 0.837758 0.023 4 6 4 4.68185e-05 4.92307e-05 2.4e-06 0 6 2 0.0174937 0.0181333 0.00064 8 0 4 0.00197222 0.00195282 1.9e-05 0 6 6 0.00130801 0.00139487 8.7e-05 6 2 4 0.000272561 0.000278974 6.4e-06 4 2 0 0.0400729 0.0398932 0.00018 HYPERBALL01_MONOMIAL_INTEGRAL_TEST Normal end of execution. HYPERBALL01_SAMPLE_TEST Python version: 3.6.5 HYPERBALL01_SAMPLE samples the unit hyperball. Sample points in the unit hyperball. Row: 0 1 2 Col 0 : 0.497518 -0.16773 0.359406 1 : 0.756069 0.330465 -0.384785 2 : 0.280276 -0.114567 0.901126 3 : 0.523193 -0.251279 0.401636 4 : -0.0681996 -0.80761 -0.532481 5 : 0.152427 -0.236512 -0.65837 6 : -0.609231 -0.374499 -0.606816 7 : 0.42781 0.522948 -0.0155662 8 : 0.0146253 -0.230002 -0.122921 9 : 0.231257 -0.039156 0.11065 HYPERBALL01_SAMPLE_TEST Normal end of execution. HYPERBALL01_VOLUME_TEST Python version: 3.6.5 HYPERBALL01_VOLUME returns the volume of the unit hyperball in M dimensions. M Volume 1 2 2 3.14159 3 4.18879 4 4.9348 5 5.26379 6 5.16771 7 4.72477 8 4.05871 9 3.29851 10 2.55016 HYPERBALL01_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. R8_GAMMA_TEST: Python version: 3.6.5 R8_GAMMA evaluates the Gamma function. X GAMMA(X) R8_GAMMA(X) -0.5 -3.544907701811032 -3.544907701811032 -0.01 -100.5871979644108 -100.5871979644108 0.01 99.4325851191506 99.4325851191506 0.1 9.513507698668732 9.513507698668731 0.2 4.590843711998803 4.590843711998803 0.4 2.218159543757688 2.218159543757688 0.5 1.772453850905516 1.772453850905516 0.6 1.489192248812817 1.489192248812817 0.8 1.164229713725303 1.164229713725303 1 1 1 1.1 0.9513507698668732 0.9513507698668732 1.2 0.9181687423997607 0.9181687423997607 1.3 0.8974706963062772 0.8974706963062772 1.4 0.8872638175030753 0.8872638175030754 1.5 0.8862269254527581 0.8862269254527581 1.6 0.8935153492876903 0.8935153492876903 1.7 0.9086387328532904 0.9086387328532904 1.8 0.9313837709802427 0.9313837709802427 1.9 0.9617658319073874 0.9617658319073874 2 1 1 3 2 2 4 6 6 10 362880 362880 20 1.21645100408832e+17 1.216451004088321e+17 30 8.841761993739702e+30 8.841761993739751e+30 R8_GAMMA_TEST Normal end of execution. R8_NORMAL_01_TEST Python version: 3.6.5 R8_NORMAL_01 generates normally distributed random values. Using initial random number seed = 123456789 1.679040 -0.566060 1.212934 1.269381 -1.666087 -2.242464 0.039675 0.673068 -0.275127 2.164005 0.297785 2.044536 1.398819 -1.242985 -0.067084 -0.794396 -0.523768 -0.350567 0.131700 0.537380 R8_NORMAL_01_TEST Normal end of execution. R8_UNIFORM_01_TEST Python version: 3.6.5 R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 R8_UNIFORM_01_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 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. R8VEC_NORM_TEST Python version: 3.6.5 R8VEC_NORM computes the L2 norm of an R8VEC. Input vector: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 L2 norm = 1.62017 R8VEC_NORM_TEST: Normal end of execution. R8VEC_NORMAL_01_TEST Python version: 3.6.5 R8VEC_NORMAL_01 returns a vector of Normal 01 values SEED = 123456789 Vector: 0: 1.67904 1: -0.56606 2: 1.21293 3: 1.26938 4: -1.66609 5: -2.24246 6: 0.0396749 7: 0.673068 8: -0.275127 9: 2.164 R8VEC_NORMAL_01_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. HYPERBALL_MONTE_CARLO_TEST Normal end of execution. Thu Sep 13 09:51:34 2018