21 October 2023 7:32:00.465 PM HYPERBALL_INTEGRALS_PRB FORTRAN77 version Test the BALL_INTEGRALS library. TEST01 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 3 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 0 4 0.394126E-02 0.418461E-02 0.24E-03 6 6 0 0.142603E-02 0.139487E-02 0.31E-04 8 0 2 0.965872E-02 0.976408E-02 0.11E-03 0 4 0 0.364398 0.359039 0.54E-02 0 8 4 0.187776E-02 0.195282E-02 0.75E-04 8 4 6 0.387801E-05 0.431848E-05 0.44E-06 8 8 4 0.129103E-05 0.131432E-05 0.23E-07 8 0 4 0.184647E-02 0.195282E-02 0.11E-03 2 2 4 0.351040E-02 0.362666E-02 0.12E-03 8 8 8 0.667825E-07 0.681499E-07 0.14E-08 2 4 2 0.352597E-02 0.362666E-02 0.10E-03 2 0 8 0.968985E-02 0.976408E-02 0.74E-04 4 4 2 0.804125E-03 0.836921E-03 0.33E-04 0 2 2 0.117002 0.119680 0.27E-02 6 6 8 0.890667E-06 0.938800E-06 0.48E-07 4 6 8 0.416897E-05 0.431848E-05 0.15E-06 0 4 4 0.106290E-01 0.108800E-01 0.25E-03 4 2 8 0.106263E-03 0.114872E-03 0.86E-05 4 0 4 0.103571E-01 0.108800E-01 0.52E-03 6 4 4 0.463140E-04 0.492307E-04 0.29E-05 TEST02 Use the Monte Carlo method to estimate integrals over the interior of the unit hyperball in M dimensions. Spatial dimension M = 6 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. E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error 0 2 4 4 0 6 0.389385E-06 0.409626E-06 0.20E-07 6 0 2 2 6 6 0.625469E-09 0.586118E-09 0.39E-10 0 0 4 6 6 6 0.172458E-08 0.175835E-08 0.34E-10 2 4 6 2 6 6 0.166042E-11 0.183162E-11 0.17E-12 6 2 0 0 6 0 0.136101E-04 0.150196E-04 0.14E-05 2 0 2 6 4 4 0.167944E-07 0.170678E-07 0.27E-09 2 6 4 0 0 0 0.677166E-04 0.600785E-04 0.76E-05 4 6 4 0 4 2 0.184996E-08 0.196936E-08 0.12E-09 6 0 4 0 6 4 0.101762E-07 0.984678E-08 0.33E-09 4 2 4 4 0 0 0.172886E-05 0.180236E-05 0.73E-07 2 0 2 6 0 6 0.737487E-06 0.682710E-06 0.55E-07 0 4 4 2 2 6 0.156602E-07 0.170678E-07 0.14E-08 6 2 0 2 6 4 0.316559E-08 0.328226E-08 0.12E-09 0 6 2 4 2 2 0.127207E-06 0.136542E-06 0.93E-08 0 6 4 0 6 0 0.173984E-05 0.204813E-05 0.31E-06 2 0 6 0 4 0 0.671999E-04 0.600785E-04 0.71E-05 6 0 2 4 0 4 0.415704E-06 0.409626E-06 0.61E-08 0 2 2 4 2 4 0.573932E-06 0.600785E-06 0.27E-07 2 4 6 6 2 0 0.308302E-08 0.328226E-08 0.20E-09 4 6 0 2 4 2 0.184982E-07 0.170678E-07 0.14E-08 HYPERBALL_INTEGRALS_PRB Normal end of execution. 21 October 2023 7:32:00.472 PM