Sun Nov 6 15:24:03 2022 annulus_integrals_test(): Python version: 3.6.9 Test annulus_integrals(). annulus_integrals_test01(): Estimate monomial integrals using Monte Carlo method over the interior of an annulus centered at the origin. Inner radius is 0.0 Outer radius is 1.0 Number of sample points is 4192 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 3.14159 3.14159 4.44e-16 0 2 0.788441 0.785398 3.04e-03 0 4 0.395768 0.392699 3.07e-03 0 6 0.247926 0.245437 2.49e-03 0 8 0.17387 0.171806 2.06e-03 2 0 0.777708 0.785398 7.69e-03 2 2 0.131103 0.1309 2.04e-04 2 4 0.0499065 0.0490874 8.19e-04 2 6 0.0250934 0.0245437 5.50e-04 2 8 0.0146027 0.0143172 2.86e-04 4 0 0.385775 0.392699 6.92e-03 4 2 0.0482868 0.0490874 8.01e-04 4 4 0.0147791 0.0147262 5.29e-05 4 6 0.00625221 0.00613592 1.16e-04 4 8 0.00315013 0.00306796 8.22e-05 6 0 0.239719 0.245437 5.72e-03 6 2 0.0237537 0.0245437 7.90e-04 6 4 0.00604623 0.00613592 8.97e-05 6 6 0.00220078 0.0021914 9.37e-06 6 8 0.000975771 0.000958738 1.70e-05 8 0 0.166921 0.171806 4.88e-03 8 2 0.0136789 0.0143172 6.38e-04 8 4 0.00297016 0.00306796 9.78e-05 8 6 0.000946835 0.000958738 1.19e-05 8 8 0.000374033 0.000372843 1.19e-06 annulus_integrals_test01(): Estimate monomial integrals using Monte Carlo method over the interior of an annulus centered at the origin. Inner radius is 1.0 Outer radius is 2.0 Number of sample points is 4192 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 9.42478 9.42478 1.78e-15 0 2 12.0331 11.781 2.52e-01 0 4 25.4942 24.74 7.54e-01 0 6 65.028 62.5864 2.44e+00 0 8 184.058 175.757 8.30e+00 2 0 11.5556 11.781 2.25e-01 2 2 8.30181 8.24668 5.51e-02 2 4 12.9077 12.5173 3.90e-01 2 6 26.4244 25.1082 1.32e+00 2 8 62.6582 58.6287 4.03e+00 4 0 24.1849 24.74 5.55e-01 4 2 12.3101 12.5173 2.07e-01 4 4 15.1983 15.0649 1.33e-01 4 6 26.0833 25.1266 9.57e-01 4 8 53.5875 50.2624 3.33e+00 6 0 61.4455 62.5864 1.14e+00 6 2 24.2166 25.1082 8.92e-01 6 4 24.61 25.1266 5.17e-01 6 6 36.0221 35.9017 1.20e-01 6 8 64.8613 62.8309 2.03e+00 8 0 173.798 175.757 1.96e+00 8 2 55.901 58.6287 2.73e+00 8 4 48.118 50.2624 2.14e+00 8 6 60.978 62.8309 1.85e+00 8 8 96.918 97.7381 8.20e-01 annulus_integrals_test01(): Estimate monomial integrals using Monte Carlo method over the interior of an annulus centered at the origin. Inner radius is 1.0 Outer radius is 2.0 Number of sample points is 67072 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 0 9.42478 9.42478 1.78e-15 0 2 11.808 11.781 2.70e-02 0 4 24.8403 24.74 1.00e-01 0 6 62.868 62.5864 2.82e-01 0 8 176.512 175.757 7.55e-01 2 0 11.7692 11.781 1.18e-02 2 2 8.22475 8.24668 2.19e-02 2 4 12.5046 12.5173 1.27e-02 2 6 25.1189 25.1082 1.07e-02 2 8 58.6813 58.6287 5.25e-02 4 0 24.7507 24.74 1.07e-02 4 2 12.4631 12.5173 5.41e-02 4 4 14.9887 15.0649 7.62e-02 4 6 25.0125 25.1266 1.14e-01 4 8 50.0714 50.2624 1.91e-01 6 0 62.7425 62.5864 1.56e-01 6 2 24.9995 25.1082 1.09e-01 6 4 24.9575 25.1266 1.69e-01 6 6 35.6229 35.9017 2.79e-01 6 8 62.3597 62.8309 4.71e-01 8 0 176.635 175.757 8.78e-01 8 2 58.4118 58.6287 2.17e-01 8 4 49.9203 50.2624 3.42e-01 8 6 62.2467 62.8309 5.84e-01 8 8 96.759 97.7381 9.79e-01 annulus_integrals_test(): Normal end of execution. Sun Nov 6 15:24:06 2022