Wed Oct 8 07:44:20 2025 ellipse_monte_carlo_test(): python version: 3.10.12 numpy version: 1.26.4 Test ellipse_monte_carlo(). ellipse_area1_test(): 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_area2_test(): ellipse_area2() computes the area of an ellipse. Ellipse: 5 * x^2 + 2 * xy + 2 * y^2 = 10 Area = 104.72 ellipse_sample_test(): ellipse_sample() computes points uniformly distributed inside an ellipse x'*A*x=r^2. Random points inside ellipse Row: 0 1 Col 0 : -1.48682 0.910993 1 : 1.63336 0.773842 2 : -1.59554 1.4997 3 : -1.21161 4.44958 4 : -0.647128 1.33731 5 : -1.6172 3.65704 6 : 1.57109 -5.52069 7 : -1.80097 4.11886 8 : -0.922868 0.462347 9 : 1.05625 -1.48976 ellipse_sample2_test(): ellipse_sample() estimates integrals in the ellipse x * A * x <= r^2. N 1 X Y X^2 XY Y^2 X^3 1 2.1241 -0.360768 -0.0845277 0.0612746 0.0143566 0.00336374 -0.0104072 2 2.1241 -0.250532 -0.424985 0.0329815 0.0393877 0.118626 -0.00469966 4 2.1241 -0.217177 -0.157155 0.0772246 -0.0660296 0.185187 -0.0104215 8 2.1241 -0.0143556 0.257507 0.022378 -0.0115418 0.0680555 -0.00134978 16 2.1241 -0.103919 -0.165168 0.0271992 -0.0298945 0.196804 -0.00369885 32 2.1241 0.0139111 -0.0984802 0.0275694 -0.0210632 0.190579 -0.000653406 64 2.1241 0.0374574 -0.0313062 0.0302656 -0.0245916 0.130025 0.00074925 128 2.1241 0.0155911 0.04022 0.0348392 -0.0245687 0.130909 8.89119e-05 256 2.1241 -0.0242743 0.0176298 0.0280594 -0.0221727 0.134252 -0.000568299 512 2.1241 -0.00832125 -5.75974e-06 0.0306061 -0.0225339 0.130915 -0.0001539 1024 2.1241 -0.00510352 0.00704099 0.0289884 -0.0245821 0.148222 -6.15053e-05 2048 2.1241 0.00343215 0.0143497 0.0285445 -0.0210065 0.143801 7.78617e-05 4096 2.1241 -0.00267942 0.00376916 0.0289913 -0.0214201 0.141409 -6.52794e-05 8192 2.1241 0.0054182 -0.00800347 0.0290323 -0.0221955 0.143454 0.000220192 16384 2.1241 -0.00121868 0.000206526 0.0294525 -0.0224561 0.143576 -1.84608e-05 32768 2.1241 -0.000501158 -3.10465e-05 0.0295312 -0.0225726 0.14199 -3.15232e-05 65536 2.1241 0.000739768 -0.00219128 0.0296558 -0.0226479 0.142032 8.92289e-06 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(): Python version: 3.10.12 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 : 0.232412 0.748004 -0.200198 1 : -0.33827 -0.523159 0.734406 2 : 0.359041 0.458353 0.172167 3 : -0.381942 0.517317 0.585933 4 : 0.136698 0.30573 0.615432 5 : -0.105122 0.532203 -0.482892 6 : -0.231717 -0.14121 -0.855745 7 : 0.801217 -0.00957964 -0.207509 8 : 0.741644 0.145587 -0.175778 9 : -0.7174 0.157478 -0.0402613 ellipse_monte_carlo_test(): Normal end of execution. Wed Oct 8 07:44:22 2025