09 May 2025 9:16:33.353 PM hyperball_integrals_test(): Fortran90 version Test hyperball_integrals(). 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 will restrict this test to randomly chosen even exponents. Ex Ey Ez MC-Estimate Exact Error 8 6 8 0.266864E-06 0.262864E-06 0.40E-08 4 4 2 0.855443E-03 0.836921E-03 0.19E-04 0 2 4 0.383166E-01 0.398932E-01 0.16E-02 8 0 2 0.915217E-02 0.976408E-02 0.61E-03 6 4 8 0.440554E-05 0.431848E-05 0.87E-07 2 4 4 0.823340E-03 0.836921E-03 0.14E-04 4 4 6 0.501782E-04 0.492307E-04 0.95E-06 0 0 8 0.125632 0.126933 0.13E-02 0 8 6 0.490904E-03 0.574358E-03 0.83E-04 8 6 0 0.587967E-03 0.574358E-03 0.14E-04 8 4 2 0.116873E-03 0.114872E-03 0.20E-05 0 6 2 0.174280E-01 0.181333E-01 0.71E-03 2 8 6 0.280065E-04 0.302293E-04 0.22E-05 2 0 8 0.946482E-02 0.976408E-02 0.30E-03 0 4 2 0.381546E-01 0.398932E-01 0.17E-02 4 6 4 0.499835E-04 0.492307E-04 0.75E-06 6 6 6 0.316554E-05 0.308463E-05 0.81E-07 2 8 4 0.108897E-03 0.114872E-03 0.60E-05 0 6 0 0.206752 0.199466 0.73E-02 2 4 4 0.823340E-03 0.836921E-03 0.14E-04 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 will restrict this test to randomly chosen even exponents. E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error 6 4 6 6 2 6 0.286300E-13 0.224463E-13 0.62E-14 0 6 4 6 2 0 0.880529E-07 0.853388E-07 0.27E-08 0 0 4 6 0 2 0.607989E-04 0.600785E-04 0.72E-06 6 6 0 4 2 2 0.370898E-08 0.328226E-08 0.43E-09 6 2 4 6 6 0 0.710770E-10 0.586118E-10 0.12E-10 4 6 0 4 0 2 0.392584E-06 0.409626E-06 0.17E-07 4 4 0 6 0 0 0.769688E-05 0.901178E-05 0.13E-05 4 0 2 2 0 6 0.315741E-05 0.300393E-05 0.15E-06 2 2 4 6 6 4 0.117597E-10 0.117224E-10 0.37E-13 6 0 4 6 0 6 0.171554E-08 0.175835E-08 0.43E-10 0 4 0 0 4 6 0.989051E-05 0.901178E-05 0.88E-06 2 6 0 0 6 6 0.195822E-07 0.164113E-07 0.32E-08 0 2 2 2 6 2 0.110692E-05 0.100131E-05 0.11E-06 2 4 6 2 0 6 0.369891E-08 0.328226E-08 0.42E-09 4 6 6 2 4 0 0.316138E-09 0.351671E-09 0.36E-10 6 4 4 6 4 2 0.109686E-11 0.109897E-11 0.21E-14 2 6 0 4 0 6 0.874204E-07 0.853388E-07 0.21E-08 4 6 6 4 6 6 0.164177E-14 0.177208E-14 0.13E-15 4 6 0 6 4 2 0.335988E-09 0.351671E-09 0.16E-10 2 2 2 4 0 4 0.599722E-06 0.600785E-06 0.11E-08 hyperball_integrals_test(): Normal end of execution. 09 May 2025 9:16:33.358 PM