Thu Sep 13 19:28:59 2018 TRIANGLE01_INTEGRALS_TEST Python version: 3.6.5 Test the TRIANGLE01_INTEGRALS 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_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. 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. TIMESTAMP_TEST: Python version: 3.6.5 TIMESTAMP prints a timestamp of the current date and time. Thu Sep 13 19:28:59 2018 TIMESTAMP_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. TRIANGLE01_SAMPLE_TEST Python version: 3.6.5 TRIANGLE01_SAMPLE randomly samples the unit triangle. Number of samples to select is N = 10 Random points in unit triangle. Row: 0 1 Col 0 : 0.867886 0.0254803 1 : 0.138259 0.210636 2 : 0.202708 0.329918 3 : 0.112803 0.689309 4 : 0.642508 0.198073 5 : 0.844955 0.014506 6 : 0.346508 0.63118 7 : 0.0242126 0.292589 8 : 0.372621 0.0253558 9 : 0.408253 0.0761431 TRIANGLE01_SAMPLE_TEST: Normal end of execution. TRIANGLE01_MONOMIAL_INTEGRAL_TEST01 Python version: 3.6.5 TRIANGLE01_MONOMIAL_INTEGRAL computes the integral of a monomial X^I Y^J over the unit triangle. I J Integral(X^I Y^J) 0 0 0.5 0 1 0.166667 1 0 0.166667 0 2 0.0833333 1 1 0.0416667 2 0 0.0833333 0 3 0.05 1 2 0.0166667 2 1 0.0166667 3 0 0.05 0 4 0.0333333 1 3 0.00833333 2 2 0.00555556 3 1 0.00833333 4 0 0.0333333 TRIANGLE01_MONOMIAL_INTEGRAL_TEST01: Normal end of execution. TRIANGLE01_MONOMIAL_INTEGRAL_TEST02 Python version: 3.6.5 Estimate monomial integrals using Monte Carlo over the interior of the unit triangle in 2D. Number of sample points used is 4192 We restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 0.5 0.5 0.00e+00 0 1 0.165406 0.166667 1.26e-03 0 2 0.0816578 0.0833333 1.68e-03 0 3 0.048254 0.05 1.75e-03 0 4 0.0316683 0.0333333 1.67e-03 1 0 0.166961 0.166667 2.94e-04 1 1 0.0420597 0.0416667 3.93e-04 1 2 0.0167899 0.0166667 1.23e-04 1 3 0.00832158 0.00833333 1.18e-05 1 4 0.00469451 0.0047619 6.74e-05 2 0 0.083375 0.0833333 4.17e-05 2 1 0.0169313 0.0166667 2.65e-04 2 2 0.00566568 0.00555556 1.10e-04 2 3 0.00241965 0.00238095 3.87e-05 2 4 0.00120037 0.00119048 9.89e-06 3 0 0.0498756 0.05 1.24e-04 3 1 0.00848954 0.00833333 1.56e-04 3 2 0.00244506 0.00238095 6.41e-05 3 3 0.000916488 0.000892857 2.36e-05 3 4 0.000405015 0.000396825 8.19e-06 4 0 0.0331019 0.0333333 2.31e-04 4 1 0.00485231 0.0047619 9.04e-05 4 2 0.0012276 0.00119048 3.71e-05 4 3 0.00041029 0.000396825 1.35e-05 4 4 0.000163516 0.00015873 4.79e-06 TRIANGLE01_MONOMIAL_INTEGRAL_TEST02: Normal end of execution. TRIANGLE01_INTEGRALS_TEST: Normal end of execution. Thu Sep 13 19:28:59 2018