Wed Sep 12 14:15:56 2018 ANNULUS_MONTE_CARLO_TEST Python version Test the ANNULUS_MONTE_CARLO library. ANNULUS_AREA_TEST ANNULUS_AREA computes the area of an annulus with center = (CX,CY), inner radius R1 and outer radius R2. ( CX CY ) R1 R2 Area (-2.815817, 4.563176) 0.829509 1.391205 3.918712 (-0.846929,-4.338813) 0.257578 0.367535 0.215938 (-4.561710, 1.339657) 0.061727 0.511266 0.809220 (-0.986937, 2.546735) 0.797287 0.799125 0.009220 ( 3.975041,-1.492477) 0.094545 0.108162 0.008672 ( 3.590969, 3.408475) 0.123104 0.130616 0.005988 (-2.396970, 4.124837) 0.113664 0.465293 0.639558 ( 3.228873,-2.328677) 0.692066 1.253729 3.433385 ( 3.612158,-0.462062) 0.911977 1.509894 4.549270 (-3.110453, 2.614921) 0.396988 0.582303 0.570125 ANNULUS_AREA_TEST Normal end of execution. ANNULUS_SAMPLE_TEST ANNULUS_SAMPLE can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (0,0) with R1 = 0, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 0.116755 2.88761 0.00433911 0.107316 2.65415 0.00016126 2 3.14159 0.238728 0.517494 0.0193133 0.0487479 0.160989 0.0016458 4 3.14159 0.764738 0.544714 0.252562 0.15736 0.168224 0.0847672 8 3.14159 0.525731 0.596884 0.146334 0.152081 0.256623 0.0457607 16 3.14159 0.815469 0.96975 0.402256 0.197352 0.493433 0.23388 32 3.14159 1.04885 0.765539 0.635825 0.143291 0.382857 0.461052 64 3.14159 0.818634 0.60318 0.400714 0.131123 0.245562 0.239485 128 3.14159 0.875286 0.829331 0.451678 0.158221 0.391268 0.284837 256 3.14159 0.799161 0.758949 0.397981 0.137733 0.373594 0.242345 512 3.14159 0.764972 0.774272 0.377314 0.128265 0.380235 0.234248 1024 3.14159 0.785671 0.79404 0.402767 0.127299 0.402444 0.257212 2048 3.14159 0.762183 0.780486 0.373013 0.129276 0.387494 0.227042 4096 3.14159 0.76976 0.789162 0.381274 0.128883 0.3943 0.237809 8192 3.14159 0.766972 0.782296 0.378725 0.126612 0.391855 0.234046 16384 3.14159 0.778852 0.78596 0.386838 0.13099 0.391657 0.240662 32768 3.14159 0.776924 0.784172 0.385715 0.129529 0.393607 0.240038 65536 3.14159 0.791979 0.779118 0.397518 0.130846 0.38761 0.249153 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 ANNULUS_SAMPLE_TEST ANNULUS_SAMPLE can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (0,0) with R1 = 0.5, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 2.35619 0.0885661 2.19044 0.00332908 0.0823355 2.03634 0.000125136 2 2.35619 0.454314 0.560109 0.0972395 0.0786235 0.222659 0.022467 4 2.35619 0.719692 0.605923 0.302245 0.158154 0.207283 0.131207 8 2.35619 0.623175 0.597345 0.207736 0.147882 0.257812 0.07771 16 2.35619 0.714895 0.87834 0.362866 0.183493 0.463888 0.215749 32 2.35619 0.903296 0.706346 0.564568 0.13744 0.368769 0.416115 64 2.35619 0.781418 0.607401 0.403107 0.131737 0.26385 0.245899 128 2.35619 0.789071 0.758825 0.428412 0.149243 0.388903 0.274644 256 2.35619 0.742375 0.723111 0.391338 0.132642 0.370579 0.244513 512 2.35619 0.725791 0.729082 0.375619 0.126694 0.378982 0.235219 1024 2.35619 0.726703 0.750933 0.391357 0.124425 0.398455 0.253272 2048 2.35619 0.722388 0.734412 0.372114 0.127568 0.383803 0.230233 4096 2.35619 0.724745 0.741198 0.376746 0.127911 0.389083 0.2371 8192 2.35619 0.724918 0.735594 0.376741 0.125533 0.387104 0.235902 16384 2.35619 0.731639 0.737616 0.381732 0.129162 0.386259 0.240481 32768 2.35619 0.731222 0.735943 0.38143 0.127999 0.386959 0.240151 65536 2.35619 0.741739 0.731052 0.390752 0.128958 0.382092 0.247811 ANNULUS_SAMPLE_TEST ANNULUS_SAMPLE can sample an annulus uniformly. Use it to estimate integrals in the annulus centered at (1,0) with R1 = 0, R2 = 1 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 4.46962 2.88761 6.35904 4.10827 2.65415 9.04717 2 3.14159 3.60232 0.517494 5.13737 0.869534 0.160989 8.19961 4 3.14159 4.74797 0.544714 10.2021 0.495919 0.168224 23.9566 8 3.14159 5.04647 0.596884 9.71639 0.797756 0.256623 20.2003 16 3.14159 2.33963 0.96975 3.34503 0.910989 0.493433 5.85419 32 3.14159 4.78455 0.765539 11.8033 1.03597 0.382857 33.916 64 3.14159 3.38993 0.60318 6.87786 0.690068 0.245562 17.4625 128 3.14159 4.15228 0.829331 9.51063 0.897973 0.391268 26.3169 256 3.14159 3.76998 0.758949 7.90009 0.862236 0.373594 20.3557 512 3.14159 3.96071 0.774272 8.15967 0.901526 0.380235 20.2621 1024 3.14159 4.05895 0.79404 8.5878 0.96757 0.402444 21.9773 2048 3.14159 3.97184 0.780486 8.32042 0.923644 0.387494 21.1969 4096 3.14159 3.90401 0.789162 8.16316 0.912494 0.3943 20.8757 8192 3.14159 3.87961 0.782296 8.04042 0.904058 0.391855 20.3227 16384 3.14159 3.89976 0.78596 8.14393 0.910112 0.391657 20.7042 32768 3.14159 3.92244 0.784172 8.21072 0.914833 0.393607 20.9199 65536 3.14159 3.89878 0.779118 8.18676 0.90226 0.38761 20.9222 ANNULUS_MONTE_CARLO_TEST Normal end of execution. Wed Sep 12 14:15:58 2018