12 October 2018 07:03:17 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

  (-2.815817, 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_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.

12 October 2018 07:03:17 PM