Wed Oct 8 07:44:23 2025 ellipsoid_monte_carlo_test(): python version: 3.10.12 numpy version: 1.26.4 Test ellipsoid_monte_carlo(). ellipsoid_monte_carlo_test01() ellipsoid_sample() estimates 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 -0.0740596 -0.434071 0.00258218 0.0151345 0.0887046 -9.00312e-05 2 2.1241 -0.198331 0.744052 0.0408842 -0.0659852 0.261178 -0.00799407 4 2.1241 0.176074 -0.0506375 0.0304436 -0.0319058 0.156704 0.00433931 8 2.1241 0.0412733 0.120662 0.0116978 -0.00335977 0.120999 0.00127505 16 2.1241 0.0858032 0.094638 0.0342004 -0.00117 0.166433 0.00169452 32 2.1241 -0.0149087 -0.0538876 0.0315377 -0.024532 0.141359 0.0010839 64 2.1241 0.0104243 -0.0339602 0.0290807 -0.0142867 0.137424 0.000817088 128 2.1241 0.00546704 -0.0189816 0.0283563 -0.0227819 0.147712 0.000188451 256 2.1241 0.00262791 -0.0127417 0.0254306 -0.0205966 0.156942 -2.42674e-05 512 2.1241 -0.00715683 -0.0461213 0.0287534 -0.0187803 0.143741 -0.000236421 1024 2.1241 -0.000720638 0.0202513 0.0299647 -0.0226434 0.144749 -3.91617e-05 2048 2.1241 -0.00369549 -0.0083466 0.0321006 -0.0241651 0.140922 -7.78538e-05 4096 2.1241 -0.00297889 0.00757619 0.0302872 -0.0239925 0.140321 -4.38524e-05 8192 2.1241 -5.62145e-05 -0.0068815 0.0292067 -0.0211606 0.142077 1.49542e-05 16384 2.1241 -0.00310869 0.00135681 0.0292896 -0.0221983 0.142425 -0.000116228 32768 2.1241 -0.000759374 -0.00143477 0.0296331 -0.0226492 0.142474 -6.15659e-05 65536 2.1241 0.000409767 -0.000950306 0.0294604 -0.0224214 0.141307 2.47416e-05 ellipsoid_monte_carlo_test02(): ellipsoid_sample() estimates 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 0.263354 0.413025 0.522425 0.819332 1.28498 1.03635 2 0.132757 0.262315 0.389528 0.51836 0.769587 1.14308 1.02443 4 0.132757 0.264938 0.396489 0.528784 0.791289 1.1849 1.0555 8 0.132757 0.263618 0.401049 0.523508 0.796356 1.21201 1.03969 16 0.132757 0.265425 0.397571 0.53078 0.794887 1.19104 1.06164 32 0.132757 0.267561 0.395608 0.539333 0.797281 1.1794 1.08731 64 0.132757 0.26543 0.397846 0.530807 0.795385 1.19277 1.06174 128 0.132757 0.265143 0.398165 0.529669 0.795144 1.19468 1.05835 256 0.132757 0.26536 0.398989 0.530535 0.797424 1.19966 1.06094 512 0.132757 0.265307 0.398481 0.530309 0.796256 1.19666 1.06022 1024 0.132757 0.265705 0.397978 0.531913 0.796453 1.19358 1.06507 2048 0.132757 0.265519 0.398499 0.531165 0.796923 1.19674 1.06282 4096 0.132757 0.2655 0.398241 0.531093 0.796354 1.1952 1.06261 8192 0.132757 0.265539 0.398272 0.531247 0.796534 1.19538 1.06306 16384 0.132757 0.265534 0.398404 0.531226 0.796783 1.19617 1.063 32768 0.132757 0.265511 0.398274 0.531135 0.796455 1.19539 1.06273 65536 0.132757 0.265495 0.398258 0.53107 0.796374 1.19529 1.06253 ellipsoid_monte_carlo_test03(): ellipsoid_sample() estimates 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 0.10299 0.151026 0.262925 0.121546 2.3726 2.38672 2 0.0872665 0.0734004 0.194001 0.259566 0.0686789 3.84648 2.31025 4 0.0872665 0.0957104 0.159672 0.266997 0.115628 2.84164 2.5237 8 0.0872665 0.0970656 0.159779 0.264925 0.115289 2.77555 2.45111 16 0.0872665 0.078107 0.192057 0.256697 0.0776657 3.71416 2.23061 32 0.0872665 0.089985 0.169853 0.263166 0.101733 3.09377 2.40729 64 0.0872665 0.0837918 0.181744 0.259425 0.0888142 3.40835 2.30613 128 0.0872665 0.0833828 0.181155 0.260004 0.0896592 3.42155 2.32435 256 0.0872665 0.087244 0.174276 0.261967 0.0967352 3.21798 2.37583 512 0.0872665 0.090718 0.168627 0.26319 0.103729 3.05041 2.40916 1024 0.0872665 0.0891674 0.171287 0.262543 0.100471 3.12764 2.3912 2048 0.0872665 0.0860602 0.176553 0.261317 0.093944 3.28078 2.35796 4096 0.0872665 0.0874643 0.17419 0.261941 0.0966916 3.21172 2.37466 8192 0.0872665 0.0869644 0.175001 0.261683 0.095808 3.23524 2.368 16384 0.0872665 0.0866943 0.175453 0.261577 0.0950816 3.24689 2.36492 32768 0.0872665 0.0873839 0.174356 0.261831 0.0966527 3.21663 2.37197 65536 0.0872665 0.0873055 0.174453 0.261816 0.09641 3.21881 2.37139 ellipsoid_sample_test(): 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 : 1.82398 2.36211 2.0806 1 : 1.98266 3.05849 0.785068 2 : 1.91491 2.47673 1.85555 3 : 1.83104 2.90048 1.4751 4 : 2.07545 2.6798 1.29967 5 : 1.92553 2.51336 1.77597 6 : 2.0797 3.5153 0.310814 7 : 2.11599 3.11876 0.627808 8 : 2.0363 3.07316 1.00846 9 : 2.11144 3.44774 0.376895 10 : 1.96393 2.57878 1.53367 11 : 1.8333 2.82583 1.58389 12 : 1.96987 2.96495 1.21869 13 : 1.97765 2.55588 1.54721 14 : 1.91931 2.78262 1.48229 15 : 2.1132 3.25436 0.598479 16 : 2.05322 2.66569 1.34132 17 : 1.98129 2.51264 1.52225 18 : 1.90421 3.16802 0.841977 19 : 1.91819 3.06644 1.03699 ellipsoid_volume_test(): 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 hypersphere_unit_volume_test(): 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 r8po_fa_test(): 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_sl_test(): 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 uniform_in_sphere01_map_test(): 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 : -0.56972 0.181282 -0.448503 1 : -0.636888 0.415132 0.600767 2 : 0.43967 -0.263065 0.0899045 3 : -0.0495243 0.237947 0.0225655 4 : -0.341022 0.758339 0.444983 5 : 0.471883 0.546211 0.38893 6 : -0.125251 0.134053 -0.926016 7 : -0.490439 -0.265606 -0.247131 8 : 0.383766 -0.193367 0.552812 9 : 0.231209 0.505416 -0.208672 ellipsoid_monte_carlo_test(): Normal end of execution. Wed Oct 8 07:44:29 2025