Tue Oct 19 11:33:46 2021 ellipsoid_monte_carlo_test(): Python version: 3.6.9 Test ellipsoid_monte_carlo(). ellipsoid_monte_carlo_test01 Use ellipsoid_sample to estimate integrals in a 2D ellipse x * A * x <= r^2. Ellipsoid radius R = 2 Ellipsoid center V: 0: 0 1: 0 Ellipsoid matrix A: Col: 0 1 Row 0 : 9 1 1 : 1 4 Ellipsoid volume = 2.1241 N 1 X Y X^2 XY Y^2 X^3 1 2.1241 -0.305762 0.0615156 0.044014 -0.00885509 0.00178154 -0.00633575 2 2.1241 -0.0757202 -0.28009 0.0623356 -0.0820849 0.179075 -0.00647398 4 2.1241 -0.0239841 0.378416 0.0323777 0.0207476 0.0967515 -0.00162397 8 2.1241 0.0691337 -0.136564 0.0468192 -0.0181949 0.0614318 0.00497667 16 2.1241 -0.0281885 0.335797 0.0437229 -0.0231907 0.133503 0.000865719 32 2.1241 0.0291108 -0.076941 0.0195218 -0.0129631 0.18609 -0.00019235 64 2.1241 0.0301266 0.00686615 0.0370522 -0.0306043 0.157937 0.00126108 128 2.1241 0.0220941 -0.0242779 0.0271906 -0.024053 0.1412 0.000593154 256 2.1241 0.00653531 -0.0184321 0.0271392 -0.026336 0.151643 0.00042724 512 2.1241 -0.00925636 0.026095 0.0289995 -0.0221801 0.144118 -0.000256262 1024 2.1241 0.00489363 0.0174424 0.0299868 -0.020288 0.140106 0.000187813 2048 2.1241 -0.00507412 -0.000148249 0.0289503 -0.0205501 0.139995 -0.000125816 4096 2.1241 -0.00506877 0.00997929 0.0298444 -0.0231523 0.138865 -5.96749e-05 8192 2.1241 0.00169278 0.00341428 0.0290993 -0.0217622 0.139496 1.50305e-05 16384 2.1241 -0.00146052 -0.00350096 0.0290056 -0.0217015 0.14277 -3.60304e-05 32768 2.1241 -0.00124181 0.0100566 0.0291828 -0.0221405 0.14064 -5.10749e-05 65536 2.1241 -0.00108781 0.00550429 0.0296502 -0.022659 0.141131 -2.23332e-05 ellipsoid_monte_carlo_test01 Normal end of execution. ellipsoid_monte_carlo_test02 Use ellipsoid_sample to estimate integrals in a 2D ellipse (x-v) * A * (x-v) <= r^2. Ellipsoid radius R = 0.5 Ellipsoid center V: 0: 2 1: 3 Ellipsoid matrix A: Col: 0 1 Row 0 : 9 1 1 : 1 4 Ellipsoid volume = 0.132757 N 1 X Y X^2 XY Y^2 X^3 1 0.132757 0.268412 0.38659 0.542685 0.781621 1.12576 1.09722 2 0.132757 0.261999 0.39638 0.517089 0.782158 1.18398 1.02059 4 0.132757 0.266729 0.395842 0.536088 0.795292 1.18039 1.07784 8 0.132757 0.267641 0.39817 0.539651 0.802644 1.19448 1.08827 16 0.132757 0.265114 0.399035 0.529507 0.796827 1.20005 1.05773 32 0.132757 0.264385 0.397966 0.526613 0.792453 1.19368 1.04911 64 0.132757 0.265942 0.397932 0.532882 0.797034 1.1932 1.06804 128 0.132757 0.265391 0.398482 0.53064 0.796532 1.19659 1.0612 256 0.132757 0.265415 0.398628 0.53075 0.796893 1.19754 1.06157 512 0.132757 0.265678 0.398394 0.531804 0.797209 1.1961 1.06474 1024 0.132757 0.265438 0.398266 0.53084 0.796223 1.19533 1.06184 2048 0.132757 0.265567 0.398132 0.531359 0.796339 1.19452 1.0634 4096 0.132757 0.265362 0.398381 0.530535 0.796216 1.19605 1.06092 8192 0.132757 0.265554 0.39818 0.531303 0.796397 1.19482 1.06323 16384 0.132757 0.265537 0.398193 0.531236 0.796368 1.1949 1.06302 32768 0.132757 0.265533 0.398257 0.531219 0.796486 1.19529 1.06297 65536 0.132757 0.265529 0.398228 0.531203 0.796414 1.19511 1.06293 ellipsoid_monte_carlo_test02 Normal end of execution. ellipsoid_monte_carlo_test03 Use ellipsoid_sample to estimate integrals in a 3D ellipse (x-v) * A * (x-v) <= r^2. Ellipsoid radius R = 0.5 Ellipsoid center V: 0: 1 1: 2 2: 3 Ellipsoid matrix A: Col: 0 1 2 Row 0 : 9 6 3 1 : 6 5 4 2 : 3 4 9 Ellipsoid volume = 0.0872665 N 1 X Y Z X^2 YZ Z^3 1 0.0872665 0.0528437 0.227672 0.250719 0.0319993 4.90288 2.06952 2 0.0872665 0.0828652 0.184928 0.258769 0.0788141 3.4462 2.27531 4 0.0872665 0.0918273 0.168176 0.262505 0.108888 3.05101 2.39859 8 0.0872665 0.0841879 0.178372 0.260685 0.089901 3.33811 2.3399 16 0.0872665 0.0891726 0.171331 0.261729 0.0983116 3.09754 2.36646 32 0.0872665 0.0823975 0.182758 0.259958 0.0861177 3.46294 2.32238 64 0.0872665 0.0903243 0.169635 0.262599 0.102292 3.06633 2.39278 128 0.0872665 0.0851956 0.177929 0.261048 0.0934633 3.33178 2.35235 256 0.0872665 0.0873487 0.174259 0.262061 0.0962694 3.21534 2.37774 512 0.0872665 0.088115 0.173341 0.262001 0.0977173 3.18068 2.37612 1024 0.0872665 0.0862742 0.176312 0.261379 0.0942952 3.27365 2.35955 2048 0.0872665 0.0882249 0.173095 0.262126 0.0982336 3.17838 2.37974 4096 0.0872665 0.0874324 0.174302 0.261824 0.096455 3.21143 2.37138 8192 0.0872665 0.087925 0.17344 0.262041 0.0975703 3.1878 2.3775 16384 0.0872665 0.0873849 0.174351 0.261839 0.0966597 3.21649 2.3722 32768 0.0872665 0.0875088 0.174154 0.261882 0.0967895 3.2096 2.3731 65536 0.0872665 0.0873682 0.174383 0.261826 0.0965123 3.21637 2.3716 ellipsoid_monte_carlo_test03 Normal end of execution. ellipsoid_sample_test Python version: 3.6.9 ellipsoid_sample samples the ellipsoid (X-V)' * A * (X-V) <= R * R. M = 3 A: Col: 0 1 2 Row 0 : 9 3 3 1 : 3 5 3 2 : 3 3 3 V: 0: 2 1: 3 2: 1 Ellipsoid sample points: Row: 0 1 2 Col 0 : 1.97412 2.85184 1.11282 1 : 2.03659 3.6044 0.218284 2 : 1.86979 2.37327 1.90824 3 : 1.96449 2.66638 1.31672 4 : 1.975 3.15854 0.82372 5 : 2.0134 2.82995 1.21123 6 : 1.86398 2.54174 1.84234 7 : 1.85804 2.3168 2.05589 8 : 2.02206 3.3761 0.418117 9 : 2.10737 3.32518 0.497504 10 : 1.96043 2.68308 1.28826 11 : 2.15018 3.53942 0.147384 12 : 1.81397 2.95395 1.34129 13 : 2.03702 3.0434 0.920512 14 : 2.0841 3.38741 0.40508 15 : 2.10272 2.78874 0.975316 16 : 2.05108 3.20842 0.841246 17 : 2.02342 3.43287 0.322087 18 : 2.17446 3.31589 0.325886 19 : 2.15796 3.43876 0.191772 ellipsoid_sample_test Normal end of execution. ellipsoid_volume_test Python version: 3.6.9 ellipsoid_volume computes the volume of the ellipsoid (X-V)' * A * (X-V) <= R * R. M = 3 A: Col: 0 1 2 Row 0 : 9 3 3 1 : 3 5 3 2 : 3 3 3 V: 0: 2 1: 3 2: 1 Volume = 0.698132 ellipsoid_volume_test Normal end of execution. hypersphere_unit_volume_test Python version: 3.6.9 hypersphere_unit_volume computes the volume of the unit hypersphere in M dimensions. M Volume 1 2 2 3.14159 3 4.18879 4 4.9348 5 5.26379 6 5.16771 7 4.72477 8 4.05871 9 3.29851 10 2.55016 hypersphere_unit_volume_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 : 0.39318 -0.301144 -0.539253 1 : 0.692086 0.166939 -0.629952 2 : 0.497152 0.120565 -0.638802 3 : 0.860611 -0.186783 0.417184 4 : 0.216073 0.0585538 0.707437 5 : 0.585396 0.749281 -0.067271 6 : 0.644278 0.626568 -0.247373 7 : -0.807279 0.236167 -0.201845 8 : -0.829485 0.133953 0.389654 9 : 0.401737 -0.556249 -0.293858 uniform_in_sphere01_map_test Normal end of execution. ellipsoid_monte_carlo_test Normal end of execution. Tue Oct 19 11:33:55 2021