Tue May 20 21:35:36 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 -0.120034 0.796991 0.00678322 -0.0450384 0.299041 -0.000383324 2 2.1241 0.127434 -0.161294 0.00765858 -0.0112732 0.204014 0.000461065 4 2.1241 -0.0769808 0.0111807 0.0462789 -0.0074253 0.0486568 -0.00233154 8 2.1241 0.149257 -0.485727 0.0352449 -0.052231 0.164275 0.00435015 16 2.1241 -0.077134 0.14649 0.0323501 -0.0327285 0.162352 -0.00244851 32 2.1241 0.0384385 -0.0196381 0.0379231 -0.0167997 0.123361 0.00097919 64 2.1241 -0.0174937 -0.0171265 0.0311142 -0.0283649 0.15434 -0.00106276 128 2.1241 0.00242528 -0.0538154 0.0263249 -0.0201449 0.168451 0.000159878 256 2.1241 0.0105574 -0.0175218 0.0290326 -0.0249121 0.153081 0.000533502 512 2.1241 0.0135 -0.0334667 0.0278754 -0.0206137 0.144877 0.000386116 1024 2.1241 0.00281334 -0.0172429 0.030685 -0.0242109 0.141293 -2.1576e-05 2048 2.1241 -0.00906117 0.0228592 0.0301297 -0.0228436 0.146621 -0.000157467 4096 2.1241 0.00130406 0.00560594 0.0293705 -0.022774 0.142692 -8.09999e-06 8192 2.1241 0.000653856 0.00414943 0.0299993 -0.022539 0.141296 5.11772e-05 16384 2.1241 0.00198729 0.00257746 0.0292432 -0.0218359 0.141869 4.18533e-05 32768 2.1241 0.00206658 -0.0014339 0.0292554 -0.0228603 0.142308 6.59273e-05 65536 2.1241 -0.0016771 -0.000171568 0.0296736 -0.0227237 0.141736 -4.36669e-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 0.267002 0.384647 0.536998 0.773608 1.11447 1.08002 2 0.132757 0.272016 0.397265 0.557357 0.813987 1.18883 1.14202 4 0.132757 0.264243 0.395184 0.526002 0.786692 1.17668 1.04715 8 0.132757 0.264411 0.399413 0.526697 0.79549 1.20193 1.04929 16 0.132757 0.267367 0.397847 0.538508 0.80119 1.19277 1.0847 32 0.132757 0.265924 0.396166 0.532794 0.793486 1.18269 1.06773 64 0.132757 0.265576 0.399311 0.531375 0.798735 1.20166 1.06339 128 0.132757 0.265217 0.397515 0.529956 0.794068 1.19079 1.05918 256 0.132757 0.265238 0.398723 0.53003 0.796541 1.19812 1.05938 512 0.132757 0.265514 0.398365 0.531142 0.796643 1.19596 1.06273 1024 0.132757 0.265639 0.39804 0.531645 0.796377 1.19396 1.06425 2048 0.132757 0.265708 0.397799 0.53192 0.796088 1.19256 1.06508 4096 0.132757 0.265579 0.398335 0.531402 0.796771 1.19577 1.06352 8192 0.132757 0.265419 0.39843 0.530765 0.796489 1.19634 1.06161 16384 0.132757 0.265501 0.398299 0.531093 0.796473 1.19555 1.0626 32768 0.132757 0.265497 0.398218 0.531075 0.7963 1.19505 1.06254 65536 0.132757 0.26553 0.398261 0.53121 0.796485 1.19531 1.06295 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 0.09277 0.159619 0.271034 0.0986206 2.81626 2.61442 2 0.0872665 0.0742063 0.195415 0.255466 0.0632552 3.75264 2.18977 4 0.0872665 0.0680952 0.207019 0.253957 0.0630713 4.20218 2.16953 8 0.0872665 0.0999786 0.154528 0.266688 0.1288 2.68388 2.51204 16 0.0872665 0.0925751 0.165254 0.264336 0.108381 2.96109 2.44414 32 0.0872665 0.0932762 0.164628 0.263983 0.108354 2.92437 2.42966 64 0.0872665 0.0880027 0.174172 0.2615 0.0981709 3.19727 2.36363 128 0.0872665 0.0914503 0.167321 0.263869 0.104204 3.01006 2.42664 256 0.0872665 0.0888432 0.171863 0.262463 0.099622 3.14199 2.38906 512 0.0872665 0.087538 0.17363 0.2623 0.0959201 3.19366 2.38298 1024 0.0872665 0.0884639 0.172625 0.262286 0.0987529 3.16618 2.38404 2048 0.0872665 0.0872978 0.174407 0.261825 0.0963982 3.21781 2.37174 4096 0.0872665 0.0880032 0.173342 0.262104 0.0977255 3.18573 2.37882 8192 0.0872665 0.0868946 0.175185 0.261589 0.0956785 3.24054 2.36533 16384 0.0872665 0.0872588 0.1746 0.261763 0.0964179 3.22351 2.37015 32768 0.0872665 0.0872174 0.174639 0.261786 0.0961071 3.22363 2.37039 65536 0.0872665 0.0872255 0.174578 0.261802 0.0962292 3.22274 2.37102 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 : 2.1564 3.40167 0.253724 1 : 2.06982 3.52532 0.293235 2 : 2.01277 3.0533 1.04758 3 : 2.1462 3.46406 0.148782 4 : 1.91443 2.74331 1.56321 5 : 1.93889 2.57635 1.7221 6 : 2.0433 3.3318 0.690389 7 : 2.03493 3.10571 0.887166 8 : 1.88964 2.78155 1.59908 9 : 2.18165 3.15768 0.468811 10 : 1.94795 2.73072 1.26489 11 : 1.83984 2.65479 1.57195 12 : 2.11295 3.25748 0.403234 13 : 1.84045 2.92485 1.46738 14 : 2.01744 3.56544 0.19963 15 : 2.01639 2.93452 0.98143 16 : 1.93784 3.05344 1.0491 17 : 2.01178 3.3846 0.65208 18 : 2.16775 2.98673 0.664272 19 : 1.95301 2.72593 1.30446 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 : -0.434195 -0.394873 0.4329 1 : 0.733123 -0.227884 -0.587981 2 : 0.402441 -0.343721 -0.465041 3 : -0.098021 -0.728222 -0.338298 4 : 0.255638 0.482851 0.591775 5 : 0.157314 -0.463075 0.252767 6 : -0.288237 0.631637 0.213664 7 : -0.0950202 -0.163296 0.690316 8 : -0.85036 -0.117147 -0.0191208 9 : -0.326762 0.332613 -0.315138 ellipsoid_monte_carlo_test(): Normal end of execution. Tue May 20 21:35:42 2025