C 代码 返回任何单项式积分的精确值 在 M 维单位超球体的表面上.rar

26 February 2022 07:22:22 PM HYPERSPHERE_INTEGRALS_PRB C version Test the HYPERSPHERE_INTEGRALS library. 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 will restrict this test to randomly chosen even exponents. Ex Ey Ez MC-Estimate Exact Error 8 6 0 0.0101008 0.00976408 3.37e-04 0 4 6 0.0523806 0.0543999 2.02e-03 8 8 4 3.0704e-05 3.02293e-05 4.75e-07 0 6 0 1.77434 1.7952 2.09e-02 8 6 0 0.0101008 0.00976408 3.37e-04 8 0 8 0.00390143 0.0040205 1.19e-04 6 8 0 0.0097385 0.00976408 2.56e-05 2 0 8 0.129394 0.126933 2.46e-03 2 6 0 0.19463 0.199466 4.84e-03 0 8 4 0.0277834 0.0292922 1.51e-03 2 4 4 0.0106938 0.01088 1.86e-04 6 0 8 0.00950729 0.00976408 2.57e-04 2 0 2 0.833768 0.837758 3.99e-03 8 2 8 0.000206441 0.000211605 5.16e-06 6 6 0 0.0212456 0.020923 3.23e-04 8 8 4 3.0704e-05 3.02293e-05 4.75e-07 0 8 8 0.00373499 0.0040205 2.86e-04 2 6 4 0.00406454 0.00418461 1.20e-04 0 8 0 1.38603 1.39626 1.02e-02 0 8 6 0.00910394 0.00976408 6.60e-04 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 will restrict this test to randomly chosen even exponents. E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error 6 6 6 6 6 6 9.72609e-16 1.10755e-15 1.35e-16 2 0 6 4 0 4 9.4212e-06 9.01178e-06 4.09e-07 4 4 2 4 0 6 4.92505e-08 5.12033e-08 1.95e-09 4 4 0 6 4 6 9.5141e-10 1.05501e-09 1.04e-10 0 2 4 2 6 6 6.94566e-08 8.53388e-08 1.59e-08 4 6 2 2 6 2 3.10547e-09 3.28226e-09 1.77e-10 0 6 6 2 0 0 0.000294144 0.000300393 6.25e-06 0 2 4 0 4 0 0.00347433 0.00346052 1.38e-05 6 2 2 6 6 0 1.57771e-08 1.64113e-08 6.34e-10 2 0 0 0 4 0 0.191455 0.193789 2.33e-03 0 6 6 0 0 2 0.000303096 0.000300393 2.70e-06 2 6 4 4 2 4 1.84291e-09 1.96936e-09 1.26e-10 6 0 2 4 2 6 8.78755e-08 8.53388e-08 2.54e-09 2 4 0 4 6 0 9.47199e-06 9.01178e-06 4.60e-07 4 6 2 0 6 0 1.98882e-06 2.04813e-06 5.93e-08 0 2 2 2 0 6 0.000369649 0.000360471 9.18e-06 2 0 6 0 6 6 4.02629e-07 4.26694e-07 2.41e-08 0 0 4 6 4 4 1.05238e-06 1.22888e-06 1.76e-07 0 0 2 4 6 2 5.15405e-05 6.00785e-05 8.54e-06 6 2 6 6 6 2 8.39922e-12 9.15809e-12 7.59e-13 HYPERSPHERE_MONTE_CARLO_PRB Normal end of execution. 26 February 2022 07:22:22 PM