lv mc integration - 5

agentperry@warmachine86:~/Documents/CodeFiles2/GeomScale/volesti_fork/test/build$ ./lv_mc_integration
[doctest] doctest version is "1.2.9"
[doctest] run with "--help" for options

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INTEGRATION OF exp(-X.dot(X)) for dimensions 1 to 10  and cube of [-1,1]^n and volume = 2^n
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Volume = 1.95329
Computed integration value = 1.46268
Expected integration value = 1.49364
Exact integration value = 1.49364
Relative error (expected) = 0.0207273
Relative error (exact) = 0.0207273
Volume = 4.00056
Computed integration value = 2.23182
Expected integration value = 2.23096
Exact integration value = 2.23096
Relative error (expected) = 0.000386614
Relative error (exact) = 0.000386614
Volume = 8.02979
Computed integration value = 3.34979
Expected integration value = 3.33225
Exact integration value = 3.33225
Relative error (expected) = 0.00526319
Relative error (exact) = 0.00526319
Volume = 15.9805
Computed integration value = 4.97685
Expected integration value = 4.97718
Exact integration value = 4.97718
Relative error (expected) = 6.65524e-05
Relative error (exact) = 6.65524e-05
Volume = 32.006
Computed integration value = 7.44508
Expected integration value = 7.43412
Exact integration value = 7.43412
Relative error (expected) = 0.00147361
Relative error (exact) = 0.00147361
Volume = 64.1528
Computed integration value = 11.1288
Expected integration value = 11.1039
Exact integration value = 11.1039
Relative error (expected) = 0.00223979
Relative error (exact) = 0.00223979
Volume = 127.786
Computed integration value = 16.562
Expected integration value = 16.5852
Exact integration value = 16.5852
Relative error (expected) = 0.00139981
Relative error (exact) = 0.00139981
Volume = 257.029
Computed integration value = 24.8835
Expected integration value = 24.7724
Exact integration value = 24.7724
Relative error (expected) = 0.00448377
Relative error (exact) = 0.00448377
Volume = 511.314
Computed integration value = 36.9709
Expected integration value = 37.001
Exact integration value = 37.001
Relative error (expected) = 0.000812445
Relative error (exact) = 0.000812445
Volume = 1031.5
Computed integration value = 55.7236
Expected integration value = 55.2662
Exact integration value = 55.2662
Relative error (expected) = 0.00827627
Relative error (exact) = 0.00827627
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INTEGRATION OF exp(-X.dot(X)-X.sum()) for dimensions 1 to 10 and cube of [-1,1]^n and volume = 2^n
=======================================================================================================
Volume = 2.19761
Computed integration value = 1.86413
Expected integration value = 1.69166
Exact integration value = 1.69166
Relative error (expected) = 0.101955
Relative error (exact) = 0.101955
Volume = 3.99323
Computed integration value = 2.85742
Expected integration value = 2.86171
Exact integration value = 2.86171
Relative error (expected) = 0.00149813
Relative error (exact) = 0.00149813
Volume = 8.03054
Computed integration value = 4.85931
Expected integration value = 4.84105
Exact integration value = 4.84105
Relative error (expected) = 0.00377251
Relative error (exact) = 0.00377251
Volume = 15.9182
Computed integration value = 8.15143
Expected integration value = 8.1894
Exact integration value = 8.1894
Relative error (expected) = 0.00463618
Relative error (exact) = 0.00463618
Volume = 31.8702
Computed integration value = 13.7964
Expected integration value = 13.8537
Exact integration value = 13.8537
Relative error (expected) = 0.00413417
Relative error (exact) = 0.00413417
Volume = 63.8002
Computed integration value = 23.3696
Expected integration value = 23.4357
Exact integration value = 23.4357
Relative error (expected) = 0.00281906
Relative error (exact) = 0.00281906
Volume = 127.926
Computed integration value = 39.5835
Expected integration value = 39.6453
Exact integration value = 39.6453
Relative error (expected) = 0.0015576
Relative error (exact) = 0.0015576
Volume = 256.856
Computed integration value = 67.2365
Expected integration value = 67.0663
Exact integration value = 67.0663
Relative error (expected) = 0.00253794
Relative error (exact) = 0.00253794
Volume = 511.118
Computed integration value = 113.552
Expected integration value = 113.453
Exact integration value = 113.453
Relative error (expected) = 0.000869309
Relative error (exact) = 0.000869309
Volume = 1028.14
Computed integration value = 193.451
Expected integration value = 191.925
Exact integration value = 191.925
Relative error (expected) = 0.00794976
Relative error (exact) = 0.00794976
===============================================================================
[doctest] test cases:      2 |      2 passed |      0 failed |      0 skipped
[doctest] assertions:      0 |      0 passed |      0 failed |
[doctest] Status: SUCCESS!