Thu Sep 13 19:29:10 2018

TRIANGLE_MONTE_CARLO_TEST@
  Python version: 3.6.5
  Test the TRIANGLE_MONTE_CARLO library.

REFERENCE_TO_PHYSICAL_T3_TEST:
  Python version: 3.6.5
  REFERENCE_TO_PHYSICAL_T3 maps points in a reference triangle
  to points in a physical triangle.

  XY triangle vertices:

  Row: 
      0       
      1       

  Col
      0 :
           2  
           0  

      1 :
           3  
           4  

      2 :
           0  
           3  


  Apply map to RS triangle vertices.
  Recover XY vertices (2,0), (3,4) and (0,3).

  V(0) = ( 2, 0 )
  V(1) = ( 3, 4 )
  V(2) = ( 0, 3 )

REFERENCE_TO_PHYSICAL_T3_TEST:
  Normal end of execution.

TRIANGLE01_SAMPLE_TEST
  Python version: 3.6.5
  TRIANGLE01_SAMPLE samples the unit triangle.

  Triangle vertices:

  Row: 
      0       
      1       

  Col
      0 :
           0  
           1  

      1 :
           0  
           0  

      2 :
           1  
           0  


  Sample points:

  Row: 
      0       
      1       

  Col
      0 :
    0.867886  
   0.0254803  

      1 :
    0.138259  
    0.210636  

      2 :
    0.202708  
    0.329918  

      3 :
    0.112803  
    0.689309  

      4 :
    0.642508  
    0.198073  

      5 :
    0.844955  
    0.014506  

      6 :
    0.346508  
     0.63118  

      7 :
   0.0242126  
    0.292589  

      8 :
    0.372621  
   0.0253558  

      9 :
    0.408253  
   0.0761431  


TRIANGLE01_SAMPLE_TEST
  Normal end of execution.

TRIANGLE_MONTE_CARLO_TEST
  TRIANGLE_MONTE_CARLO estimates an integral over
  a general triangle using the Monte Carlo method.

  Triangle vertices:

  Row: 
      0       
      1       

  Col
      0 :
           2  
           0  

      1 :
           3  
           4  

      2 :
           0  
           3  


         N        1               X               Y 
             X^2               XY             Y^2             X^3

         1
             5.5
         9.44344
         9.90323
         2.96466
         39.0943
         64.4558
         7.00855

         2
             5.5
         9.72966
         13.9558
          19.153
         7.65614
         47.0485
         31.4558

         4
             5.5
         8.24879
         14.1972
         27.4564
         16.8574
         19.3974
         34.1304

         8
             5.5
         9.99705
         11.1345
         18.3189
         14.1345
         40.0374
         37.1143

        16
             5.5
         7.85305
         11.6748
         18.5523
         22.8441
         23.2121
         37.3311

        32
             5.5
         8.14412
         12.3194
         14.1822
         17.9337
         27.6778
         33.1654

        64
             5.5
         8.73675
         12.1149
         18.5207
         20.4762
         36.5059
         35.6773

       128
             5.5
         9.83794
         13.1677
         17.1602
         23.3831
         31.5107
         39.6859

       256
             5.5
         9.21282
         12.8666
         16.6081
         22.1204
         34.2558
         33.0773

       512
             5.5
         9.32616
         13.0496
         17.4322
         20.5341
         32.2344
         35.9924

      1024
             5.5
         9.21427
          12.962
         17.1719
         20.8233
         32.7057
         35.8995

      2048
             5.5
         9.24195
         12.8806
         17.5884
         21.6496
         33.9564
         35.8498

      4096
             5.5
         9.26493
         12.9449
         17.9556
         21.3639
         33.7671
            35.4

      8192
             5.5
         9.16205
         12.8594
         17.4342
         21.4227
          33.849
         36.1119

     16384
             5.5
         9.13616
         12.8142
         17.4157
         21.4174
         33.7417
         36.1265

     32768
             5.5
          9.1728
         12.8189
         17.3805
         21.5125
         33.8151
         35.5182

     65536
             5.5
         9.16593
          12.813
         17.3987
         21.5145
         33.8392
          35.606


TRIANGLE_MONTE_CARLO_TEST:
  Normal end of execution.

TRIANGLE_MONTE_CARLO_TEST01
  Integrate xy^3
  Integration region is the unit triangle.
  Use an increasing number of points N.

     N          XY^3

         1        0.034854
         2        0.001403
         4        0.016035
         8        0.015451
        16        0.004655
        32        0.009818
        64        0.008298
       128        0.007687
       256        0.006712
       512        0.008354
      1024        0.008811
      2048        0.008127
      4096        0.008282
      8192        0.008287
     16384        0.008374
     32768        0.008486
     65536        0.008360

  Triangle vertices:

  Row: 
      0       
      1       

  Col
      0 :
           2  
           0  

      1 :
           3  
           4  

      2 :
           0  
           3  


TRIANGLE_MONTE_CARLO_TEST02
  Integrate xy^3
  Integration region is a general triangle.
  Use an increasing number of points N.

     N          XY^3

         1      691.964152
         2       32.624653
         4      321.916444
         8      124.029652
        16      108.055033
        32      204.353691
        64      176.548690
       128      162.920038
       256      154.270024
       512      156.512585
      1024      185.732881
      2048      166.774536
      4096      168.752864
      8192      168.471772
     16384      168.680305
     32768      171.491438
     65536      169.037903

TRIANGLE_MONTE_CARLO_TESTS:
  Normal end of execution.
Thu Sep 13 19:29:24 2018