26 August 2021 10:21:50.098 AM annulus_monte_carlo_test(): FORTRAN90 version Test annulus_monte_carlo(). 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 (-0.052982, 0.958178, 0.451987 0.583645 0.428353 (-1.582596, 2.330792, 0.673246 0.699425 0.112898 ( 0.890870, 4.586335, 0.449295 0.468050 0.054051 (-2.941004,-0.987216, 0.323781 0.497456 0.448079 ( 0.842586, 3.540577, 0.520848 0.644356 0.452113 ( 0.216987, 3.262472, 0.735015 0.951419 1.146526 ( 2.298439, 4.626079, 0.928533 1.560294 4.939661 (-3.719032, 4.890077, 0.137662 0.746349 1.690447 ( 0.927534,-4.438628, 0.584161 0.712845 0.524345 (-2.357338, 1.597573, 0.123608 0.639350 1.236186 annulus_sample_test(): annulus_sample() samples an annulus uniformly. Use it to estimate integrals in the annulus centered at ( 0.0000, 0.0000) with R1 = 0.0000 R2 = 1.0000 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 0.178869E-01 0.189276E-01 0.101841E-03 0.107766E-03 0.114036E-03 0.579839E-06 2 3.14159 0.943054 0.510896 0.429478 0.843416E-01 0.115626 0.216809 4 3.14159 1.37587 1.02978 0.814582 0.331351 0.499218 0.582930 8 3.14159 1.10569 0.666675 0.582285 0.179502 0.221162 0.325892 16 3.14159 0.653031 0.998474 0.329674 0.128237 0.519730 0.233948 32 3.14159 0.881239 0.444660 0.426914 0.105812 0.123606 0.239425 64 3.14159 0.746476 0.969876 0.361891 0.139637 0.569257 0.217915 128 3.14159 0.741771 0.780750 0.381551 0.101331 0.431195 0.245067 256 3.14159 0.739760 0.813761 0.349135 0.130286 0.380204 0.209717 512 3.14159 0.804657 0.773803 0.403810 0.133772 0.372969 0.251117 1024 3.14159 0.816074 0.793211 0.413107 0.142697 0.391122 0.260046 2048 3.14159 0.788105 0.763852 0.399137 0.130286 0.377171 0.251562 4096 3.14159 0.785905 0.764709 0.393277 0.129579 0.378354 0.245247 8192 3.14159 0.796788 0.779566 0.399474 0.133109 0.387304 0.250411 16384 3.14159 0.783420 0.786175 0.390257 0.129917 0.393256 0.244182 32768 3.14159 0.789527 0.780494 0.393706 0.131807 0.389052 0.244834 65536 3.14159 0.780699 0.785956 0.389226 0.130621 0.391890 0.242850 Exact 3.14159 0.785398 0.785398 0.392699 0.130900 0.392699 0.245437 annulus_sample_test(): annulus_sample() samples an annulus uniformly. Use it to estimate integrals in the annulus centered at ( 0.0000, 0.0000) with R1 = 0.5000 R2 = 1.0000 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 2.35619 0.756158E-01 0.682565 0.242669E-02 0.219051E-01 0.197732 0.778780E-04 2 2.35619 0.687208 1.45949 0.397310 0.192826 1.17944 0.230723 4 2.35619 0.538211 0.788878 0.210264 0.804489E-01 0.400286 0.900985E-01 8 2.35619 0.723480 0.689176 0.380953 0.112719 0.332801 0.252905 16 2.35619 0.584604 0.924553 0.291658 0.122157 0.534394 0.182703 32 2.35619 0.690933 0.744651 0.344322 0.134406 0.366177 0.210692 64 2.35619 0.759021 0.725752 0.408196 0.114647 0.399597 0.265167 128 2.35619 0.718915 0.681188 0.396818 0.118134 0.319688 0.265718 256 2.35619 0.701932 0.730849 0.351202 0.130783 0.366373 0.215823 512 2.35619 0.755102 0.706447 0.411311 0.123964 0.363966 0.270060 1024 2.35619 0.708033 0.742433 0.362002 0.129585 0.382204 0.224262 2048 2.35619 0.733964 0.753359 0.390503 0.127159 0.407655 0.250145 4096 2.35619 0.726729 0.742977 0.376608 0.131578 0.388424 0.235419 8192 2.35619 0.734803 0.736712 0.383577 0.130063 0.385868 0.241187 16384 2.35619 0.745064 0.722997 0.392451 0.127696 0.377679 0.248755 32768 2.35619 0.740304 0.738523 0.389802 0.130361 0.387413 0.246867 65536 2.35619 0.735393 0.735019 0.385507 0.129188 0.384054 0.243580 annulus_sample_test(): annulus_sample() samples an annulus uniformly. Use it to estimate integrals in the annulus centered at ( 1.0000, 0.0000) with R1 = 0.0000 R2 = 1.0000 N 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 1 3.14159 0.112080 0.796201 0.399858E-02 0.284054E-01 0.201788 0.142654E-03 2 3.14159 3.84894 0.105576 8.65092 0.174356 0.406275E-02 20.2416 4 3.14159 3.87604 0.734551 7.88892 1.00700 0.500112 18.8546 8 3.14159 4.69727 0.668479 11.0531 1.37692 0.312761 27.5702 16 3.14159 3.90723 0.695123 9.25973 0.932974 0.311985 27.6195 32 3.14159 4.20317 0.898819 8.89589 1.15247 0.572983 22.0113 64 3.14159 3.34670 0.795544 5.99305 0.770016 0.398678 13.2134 128 3.14159 3.39830 0.766584 6.98961 0.868970 0.380651 17.6271 256 3.14159 3.94572 0.715485 8.10501 0.843158 0.333541 20.3214 512 3.14159 3.81361 0.762769 7.87359 0.885528 0.384363 19.9469 1024 3.14159 3.90706 0.789483 8.19678 0.931035 0.395104 20.9568 2048 3.14159 3.86349 0.773272 8.04224 0.908885 0.383705 20.3249 4096 3.14159 3.92327 0.784471 8.19658 0.918308 0.387986 20.8604 8192 3.14159 3.84698 0.773758 8.04962 0.888260 0.382086 20.5155 16384 3.14159 3.90931 0.786833 8.21731 0.911306 0.396195 21.0279 32768 3.14159 3.94096 0.786188 8.29711 0.916479 0.393370 21.2209 65536 3.14159 3.91694 0.786115 8.21384 0.913096 0.393981 20.9675 annulus_monte_carlo_test(): Normal end of execution. 26 August 2021 10:21:50.142 AM