23 January 2020 02:31:40 PM ANNULUS_MONTE_CARLO_TEST C++ version Test ANNULUS_MONTE_CARLO. ANNULUS_AREA_TEST ANNULUS_AREA computes the area of an annulus with center = (CX,CY) and inner radius R1, outer radius R2. ( CX CY ) R1 R2 Area ( -2.81582, 4.56318) 0.829509 1.3912 3.91871 (-0.846929, -4.33881) 0.257578 0.367535 0.215938 ( -4.56171, 1.33966) 0.0617272 0.511266 0.80922 (-0.986937, 2.54673) 0.797287 0.799125 0.00921994 ( 3.97504, -1.49248) 0.0945448 0.108162 0.00867152 ( 3.59097, 3.40847) 0.123104 0.130616 0.005988 ( -2.39697, 4.12484) 0.113664 0.465293 0.639558 ( 3.22887, -2.32868) 0.692066 1.25373 3.43338 ( 3.61216,-0.462062) 0.911977 1.50989 4.54927 ( -3.11045, 2.61492) 0.396988 0.582303 0.570125 ANNULUS_SAMPLE_TEST Use ANNULUS_SAMPLE to estimate integrals in the annulus with center (0,0), inner radius 0, outer radius 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 Use ANNULUS_SAMPLE to estimate integrals in the annulus with center (1,0), inner radius 0.5, outer radius 1. N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 2.35619 3.35839 2.19044 4.78686 3.12212 2.03634 6.82292 2 2.35619 2.46232 0.560109 4.08774 0.95353 0.222659 7.4373 4 2.35619 3.87367 0.605923 9.40267 0.633431 0.207283 24.9946 8 2.35619 4.61965 0.597345 10.5571 0.902496 0.257812 25.223 16 2.35619 1.85199 0.87834 3.01053 0.839724 0.463888 5.80583 32 2.35619 3.73755 0.706346 9.76686 0.965716 0.368769 29.0577 64 2.35619 2.57622 0.607401 5.80673 0.692015 0.26385 15.705 128 2.35619 3.24365 0.758825 8.04472 0.830821 0.388903 23.3415 256 2.35619 2.9321 0.723111 6.75019 0.822466 0.370579 18.4622 512 2.35619 3.15369 0.729082 7.22047 0.866806 0.378982 19.2106 1024 2.35619 3.19604 0.750933 7.39976 0.918689 0.398455 20.0757 2048 2.35619 3.13174 0.734412 7.24335 0.873564 0.383803 19.6283 4096 2.35619 3.07412 0.741198 7.08953 0.86234 0.389083 19.2545 8192 2.35619 3.05368 0.735594 7.00492 0.855427 0.387104 18.8946 16384 2.35619 3.06739 0.737616 7.07108 0.860881 0.386259 19.1417 32768 2.35619 3.08582 0.735943 7.12831 0.864697 0.386959 19.3262 65536 2.35619 3.07019 0.731052 7.11238 0.853102 0.382092 19.331 ANNULUS_SAMPLE_TEST Use ANNULUS_SAMPLE to estimate integrals in the annulus with center (1,0), inner radius 0, outer radius 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. 23 January 2020 02:31:40 PM