Sat Apr 18 23:32:46 2015 TRIANGLE01_INTEGRALS_TEST Python version: Test the TRIANGLES01_INTEGRALS library. I4VEC_PRINT_TEST 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 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 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 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 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 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 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 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 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: TIMESTAMP prints a timestamp of the current date and time. Sat Apr 18 23:32:46 2015 TIMESTAMP_TEST: Normal end of execution. MONOMIAL_VALUE_TEST MONOMIAL_VALUE evaluates a monomial at multiple points X. Spatial dimension M = 2 Number of samples to select is N = 10 Random points. 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 Monomial exponents: 0 1 1 2 Monomial values: J X Y X*Y^2 0: 0.2184 0.9563 0.1998 1: 0.8295 0.5617 0.2617 2: 0.4153 0.06612 0.001816 3: 0.2576 0.11 0.003114 4: 0.04383 0.634 0.01762 5: 0.06173 0.4495 0.01247 6: 0.4013 0.7547 0.2286 7: 0.7973 0.001838 2.695e-06 8: 0.8975 0.3508 0.1104 9: 0.09454 0.01362 1.753e-05 MONOMIAL_VALUE_TEST: Normal end of execution. TRIANGLE01_SAMPLE_TEST 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 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 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. Sat Apr 18 23:32:46 2015