23 October 2023 10:11:13.160 AM hypersphere_integrals_test(): FORTRAN77 version Test hypersphere_integrals(). TEST01 Estimate monomial integrals using Monte Carlo over the surface of the unit hypersphere in 3D. Number of sample points used is 4192 If any exponent is odd, the integral is zero. We restrict this test to randomly chosen even exponents. Ex Ey Ez MC-Estimate Exact Error 8 0 2 0.121941 0.126933 0.50E-02 4 2 8 0.190447E-02 0.195282E-02 0.48E-04 8 2 4 0.191300E-02 0.195282E-02 0.40E-04 0 8 4 0.290258E-01 0.292922E-01 0.27E-03 0 0 6 1.82320 1.79520 0.28E-01 2 6 8 0.580181E-03 0.574358E-03 0.58E-05 0 2 0 4.24472 4.18879 0.56E-01 4 6 4 0.835833E-03 0.836921E-03 0.11E-05 6 2 0 0.200113 0.199466 0.65E-03 8 8 2 0.214468E-03 0.211605E-03 0.29E-05 8 4 8 0.292818E-04 0.302293E-04 0.95E-06 2 2 8 0.968920E-02 0.976408E-02 0.75E-04 6 0 4 0.521780E-01 0.543999E-01 0.22E-02 8 4 0 0.297251E-01 0.292922E-01 0.43E-03 6 0 0 1.77314 1.79520 0.22E-01 8 2 0 0.127238 0.126933 0.30E-03 8 4 2 0.195897E-02 0.195282E-02 0.62E-05 2 6 0 0.200470 0.199466 0.10E-02 2 8 8 0.214805E-03 0.211605E-03 0.32E-05 0 2 2 0.828215 0.837758 0.95E-02 TEST02 Estimate monomial integrals using Monte Carlo over the surface of the unit hypersphere in 6D. Number of sample points used is 4192 If any exponent is odd, the integral is zero. We restrict this test to randomly chosen even exponents. Ex Ey Ez MC-Estimate Exact Error 6 6 6 6 6 6 0.972609E-15 0.110755E-14 0.13E-15 2 0 6 4 0 4 0.942120E-05 0.901178E-05 0.41E-06 4 4 2 4 0 6 0.492505E-07 0.512033E-07 0.20E-08 4 4 0 6 4 6 0.951410E-09 0.105501E-08 0.10E-09 0 2 4 2 6 6 0.694566E-07 0.853388E-07 0.16E-07 4 6 2 2 6 2 0.310547E-08 0.328226E-08 0.18E-09 0 6 6 2 0 0 0.294144E-03 0.300393E-03 0.62E-05 0 2 4 0 4 0 0.347433E-02 0.346052E-02 0.14E-04 6 2 2 6 6 0 0.157771E-07 0.164113E-07 0.63E-09 2 0 0 0 4 0 0.191455 0.193789 0.23E-02 0 6 6 0 0 2 0.303096E-03 0.300393E-03 0.27E-05 2 6 4 4 2 4 0.184291E-08 0.196936E-08 0.13E-09 6 0 2 4 2 6 0.878755E-07 0.853388E-07 0.25E-08 2 4 0 4 6 0 0.947199E-05 0.901178E-05 0.46E-06 4 6 2 0 6 0 0.198882E-05 0.204813E-05 0.59E-07 0 2 2 2 0 6 0.369649E-03 0.360471E-03 0.92E-05 2 0 6 0 6 6 0.402629E-06 0.426694E-06 0.24E-07 0 0 4 6 4 4 0.105238E-05 0.122888E-05 0.18E-06 0 0 2 4 6 2 0.515405E-04 0.600785E-04 0.85E-05 6 2 6 6 6 2 0.839922E-11 0.915809E-11 0.76E-12 hypersphere_integrals_test(): Normal end of execution. 23 October 2023 10:11:13.168 AM