Thu Sep 13 17:10:12 2018 SQUARE_MONTE_CARLO_TEST Python version: 3.6.5 Test the SQUARE_MONTE_CARLO library. 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. 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. 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. SQUARE01_AREA_TEST Python version: 3.6.5 SQUARE01_AREA returns the area of the unit square. SQUARE01_AREA() = 1 SQUARE01_AREA_TEST Normal end of execution. SQUARE01_MONOMIAL_INTEGRAL_TEST Python version: 3.6.5 SQUARE01_MONOMIAL_INTEGRAL returns the integral of a monomial over the interior of the unit square in 2D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 Ex Ey MC-Estimate Exact Error 5 3 0.0407015 0.0416667 0.00097 0 3 0.24772 0.25 0.0023 3 3 0.0617648 0.0625 0.00074 7 2 0.0409558 0.0416667 0.00071 3 6 0.0347451 0.0357143 0.00097 3 4 0.0490791 0.05 0.00092 5 3 0.0407015 0.0416667 0.00097 4 0 0.205635 0.2 0.0056 2 7 0.0408387 0.0416667 0.00083 6 7 0.0167397 0.0178571 0.0011 1 3 0.124093 0.125 0.00091 2 4 0.065838 0.0666667 0.00083 4 1 0.10114 0.1 0.0011 0 3 0.24772 0.25 0.0023 7 6 0.0166817 0.0178571 0.0012 2 1 0.167784 0.166667 0.0011 7 1 0.0630248 0.0625 0.00052 2 5 0.0546923 0.0555556 0.00086 6 1 0.0721531 0.0714286 0.00072 5 0 0.172018 0.166667 0.0054 SQUARE01_MONOMIAL_INTEGRAL_TEST: Normal end of execution. SQUARE01_MONTE_CARLO_TEST Python version: 3.6.5 Use SQUARE01_SAMPLE to estimate integrals along the interior of the unit square in 2D. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 1 0.0477066 0.914543 0.00227592 0.0436297 0.836389 0.000108576 2 1 0.430283 0.159937 0.251606 0.108923 0.0497802 0.165457 4 1 0.0582811 0.296405 0.00758902 0.0235164 0.131721 0.00111726 8 1 0.370143 0.232241 0.257654 0.0909072 0.153583 0.186543 16 1 0.408361 0.331811 0.268311 0.132152 0.154455 0.192756 32 1 0.288494 0.398708 0.151374 0.133698 0.27324 0.0943414 64 1 0.326911 0.278037 0.182559 0.0849809 0.146277 0.123686 128 1 0.335382 0.373194 0.196099 0.119282 0.235611 0.136597 256 1 0.32321 0.345012 0.189779 0.101983 0.212009 0.135089 512 1 0.341191 0.307699 0.206467 0.106259 0.181644 0.146794 1024 1 0.339862 0.333855 0.210056 0.111993 0.200664 0.15314 2048 1 0.336076 0.331653 0.203245 0.111579 0.197363 0.145473 4096 1 0.327404 0.323945 0.193703 0.108703 0.192395 0.136906 8192 1 0.33204 0.329884 0.198447 0.109315 0.196472 0.141332 16384 1 0.329688 0.336893 0.195917 0.111486 0.202777 0.138902 32768 1 0.333032 0.330336 0.200011 0.10949 0.197202 0.142954 65536 1 0.331851 0.333021 0.19838 0.11126 0.199688 0.141424 Exact %14.6g 1.0 %14.6g 0.3333333333333333 %14.6g 0.3333333333333333 %14.6g 0.2 %14.6g 0.1111111111111111 %14.6g 0.2 %14.6g 0.14285714285714285 SQUARE01_MONTE_CARLO_TEST: Normal end of execution. SQUARE01_SAMPLE_TEST Python version: 3.6.5 SQUARE01_SAMPLE samples the unit square. Sample points in the unit square. Row: 0 1 Col 0 : 0.218418 0.956318 1 : 0.829509 0.561695 2 : 0.415307 0.0661187 3 : 0.257578 0.109957 4 : 0.043829 0.633966 5 : 0.0617272 0.449539 6 : 0.401306 0.754673 7 : 0.797287 0.00183837 8 : 0.897504 0.350752 9 : 0.0945448 0.0136169 SQUARE01_SAMPLE_TEST Normal end of execution. SQUARE_MONTE_CARLO_TEST: Normal end of execution. Thu Sep 13 17:10:13 2018