04-Nov-2022 18:58:39 annulus_integrals_test(): MATLAB/Octave version 4.2.2 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 Outer radius is 1 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 0.783953 0.785398 1.45e-03 0 4 0.396902 0.392699 4.20e-03 0 6 0.25125 0.245437 5.81e-03 0 8 0.177776 0.171806 5.97e-03 2 0 0.788007 0.785398 2.61e-03 2 2 0.131059 0.1309 1.60e-04 2 4 0.0494242 0.0490874 3.37e-04 2 6 0.0248817 0.0245437 3.38e-04 2 8 0.0146111 0.0143172 2.94e-04 4 0 0.394354 0.392699 1.65e-03 4 2 0.0489703 0.0490874 1.17e-04 4 4 0.0148118 0.0147262 8.56e-05 4 6 0.00624502 0.00613592 1.09e-04 4 8 0.00316344 0.00306796 9.55e-05 6 0 0.246598 0.245437 1.16e-03 6 2 0.0242352 0.0245437 3.09e-04 6 4 0.00608625 0.00613592 4.97e-05 6 6 0.0022023 0.0021914 1.09e-05 6 8 0.000980847 0.000958738 2.21e-05 8 0 0.172822 0.171806 1.02e-03 8 2 0.0140038 0.0143172 3.13e-04 8 4 0.00299221 0.00306796 7.58e-05 8 6 0.000943927 0.000958738 1.48e-05 8 8 0.000373934 0.000372843 1.09e-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 Outer radius is 2 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 11.8899 11.781 1.09e-01 0 4 25.2294 24.74 4.89e-01 0 6 64.3398 62.5864 1.75e+00 0 8 181.481 175.757 5.72e+00 2 0 11.7816 11.781 6.26e-04 2 2 8.20442 8.24668 4.23e-02 2 4 12.415 12.5173 1.02e-01 2 6 25.0344 25.1082 7.38e-02 2 8 59.0106 58.6287 3.82e-01 4 0 24.7017 24.74 3.83e-02 4 2 12.4738 12.5173 4.35e-02 4 4 14.8281 15.0649 2.37e-01 4 6 24.5601 25.1266 5.67e-01 4 8 49.1988 50.2624 1.06e+00 6 0 62.0562 62.5864 5.30e-01 6 2 25.0724 25.1082 3.58e-02 6 4 24.8447 25.1266 2.82e-01 6 6 35.0555 35.9017 8.46e-01 6 8 60.9615 62.8309 1.87e+00 8 0 172.583 175.757 3.17e+00 8 2 58.4634 58.6287 1.65e-01 8 4 49.992 50.2624 2.70e-01 8 6 61.7297 62.8309 1.10e+00 8 8 95.02 97.7381 2.72e+00 annulus_integrals_test01(): Estimate monomial integrals using Monte Carlo method over the interior of an annulus centered at the origin. Inner radius is 1 Outer radius is 2 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 11.7718 11.781 9.14e-03 0 4 24.7011 24.74 3.90e-02 0 6 62.4183 62.5864 1.68e-01 0 8 175.106 175.757 6.51e-01 2 0 11.7226 11.781 5.84e-02 2 2 8.18629 8.24668 6.04e-02 2 4 12.4144 12.5173 1.03e-01 2 6 24.8799 25.1082 2.28e-01 2 8 58.0425 58.6287 5.86e-01 4 0 24.5388 24.74 2.01e-01 4 2 12.3859 12.5173 1.31e-01 4 4 14.8911 15.0649 1.74e-01 4 6 24.8266 25.1266 3.00e-01 4 8 49.6485 50.2624 6.14e-01 6 0 61.9176 62.5864 6.69e-01 6 2 24.776 25.1082 3.32e-01 6 4 24.7469 25.1266 3.80e-01 6 6 35.3428 35.9017 5.59e-01 6 8 61.8645 62.8309 9.66e-01 8 0 173.563 175.757 2.19e+00 8 2 57.7411 58.6287 8.88e-01 8 4 49.3436 50.2624 9.19e-01 8 6 61.6085 62.8309 1.22e+00 8 8 95.8433 97.7381 1.89e+00 annulus_integrals_test(): Normal end of execution. 04-Nov-2022 18:58:39