Tue Oct 19 11:33:43 2021 ellipse_monte_carlo_test(): Python version: 3.6.9 Test ellipse_monte_carlo(). ellipse_area1_test Python version: 3.6.9 ellipse_area1 computes the area of an ellipse. R = 10 Matrix A in ellipse definition x*A*x=r^2 Col: 0 1 Row 0 : 5 1 1 : 1 2 Area = 104.72 ellipse_area1_test Normal end of execution. ellipse_area2_test Python version: 3.6.9 ellipse_area2 computes the area of an ellipse. Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10 Area = 104.72 ellipse_area2_test Normal end of execution. ellipse_sample_test Python version: 3.6.9 ellipse_sample computes points uniformly distributed inside an ellipse x'*A*x=r^2. Random points inside ellipse Row: 0 1 Col 0 : 1.28299 -1.33197 1 : 1.17531 -1.58573 2 : -0.516635 -2.03479 3 : -0.779696 -2.54365 4 : 0.731638 -1.40956 5 : 1.06716 -0.637445 6 : 0.00669391 -3.53896 7 : -0.131582 -3.75443 8 : 2.06492 -4.82182 9 : -1.72947 3.04776 ellipse_sample_test Normal end of execution. ellipse_sample2_test Use ellipse_sample to estimate integrals in the ellipse x * A * x <= r^2. N 1 X Y X^2 XY Y^2 X^3 1 2.1241 -0.0627402 -0.739181 0.00185317 0.0218334 0.257233 -5.47377e-05 2 2.1241 0.0561549 0.49728 0.0130331 -0.0275234 0.259646 0.000955173 4 2.1241 0.146513 0.0894116 0.0690486 0.00455314 0.0221588 0.00197754 8 2.1241 0.0410411 0.102358 0.0306516 -0.0507093 0.168562 0.00209112 16 2.1241 0.00142034 -0.0260806 0.0400184 -0.0160585 0.0717242 0.00203818 32 2.1241 0.00149008 -0.0854268 0.0354443 -0.0274628 0.161799 -0.000854005 64 2.1241 0.0399975 -0.125319 0.0288053 -0.0232495 0.147996 0.00128309 128 2.1241 0.0134336 -0.0145283 0.032769 -0.0205504 0.153086 0.000462069 256 2.1241 -0.0173721 0.0245298 0.0315963 -0.0275271 0.137842 -0.000414788 512 2.1241 0.00798588 -0.0190177 0.0287919 -0.02068 0.14733 0.000184411 1024 2.1241 0.00844082 0.00677976 0.0294218 -0.0232018 0.136969 0.000209816 2048 2.1241 0.00390163 0.00845041 0.0299009 -0.0236992 0.141995 0.00017774 4096 2.1241 -0.0059939 -0.0027995 0.0295358 -0.0223838 0.141677 -0.000261415 8192 2.1241 0.00184005 0.000956073 0.0293581 -0.0218289 0.14043 0.000112679 16384 2.1241 0.000694125 -0.000626313 0.0295017 -0.0224108 0.143884 1.36177e-08 32768 2.1241 0.000418805 -0.000332089 0.0293872 -0.0223632 0.141438 2.01265e-07 65536 2.1241 0.000767348 0.000745469 0.0295547 -0.022678 0.142417 5.94353e-05 ellipse_sample2_test: Normal end of execution. r8po_fa_test Python version: 3.6.9 r8po_fa factors a positive definite symmetric linear system, Matrix order N = 5 The matrix A: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 The factor R (a R8UT matrix): Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 0 1 1 1 1 2 : 0 0 1 1 1 3 : 0 0 0 1 1 4 : 0 0 0 0 1 The product R' * R: Col: 0 1 2 3 4 Row 0 : 1 1 1 1 1 1 : 1 2 2 2 2 2 : 1 2 3 3 3 3 : 1 2 3 4 4 4 : 1 2 3 4 5 r8po_fa_test: Normal end of execution. r8po_sl_test Python version: 3.6.9 r8po_sl solves a linear system with an R8PO matrix after it has been factored by r8po_fa. Matrix order N = 5 Matrix A: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : 0 2 -1 0 0 2 : 0 0 2 -1 0 3 : 0 0 0 2 -1 4 : 0 0 0 0 2 Right hand side b: 0: 0 1: 0 2: 0 3: 0 4: 6 Solution x: 0: 1 1: 2 2: 3 3: 4 4: 5 r8po_sl_test Normal end of execution. uniform_in_sphere01_map_test Python version: 3.6.9 uniform_in_sphere01_map computes points uniformly distributed inside the M-dimensional unit sphere. Random points inside unit 3-sphere Row: 0 1 2 Col 0 : 0.22431 0.520622 0.168713 1 : -0.332604 -0.179675 -0.368818 2 : 0.22165 0.881071 -0.146716 3 : -0.0387888 0.291416 0.727108 4 : 0.949945 -0.117379 -0.0114209 5 : -0.518698 -0.198806 0.118375 6 : 0.0229162 -0.813562 0.102834 7 : -0.47922 -0.540437 0.189967 8 : -0.00200091 0.0293269 -0.198176 9 : -0.342779 -0.019025 -0.543797 uniform_in_sphere01_map_test Normal end of execution. ellipse_monte_carlo_test(): Normal end of execution. Tue Oct 19 11:33:46 2021