Tue May 20 21:35:33 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 : -1.94155 1.21054 1 : 1.38169 -3.63517 2 : -0.139477 1.33663 3 : -0.724668 -1.67851 4 : -2.36069 2.83141 5 : -0.505895 -1.63644 6 : -1.17509 -1.53714 7 : 0.503214 -2.24995 8 : -2.16191 4.79376 9 : 0.261245 1.96776 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 -0.10759 -0.874692 0.0054496 0.0443047 0.360192 -0.000276032 2 2.1241 0.034746 0.514156 0.000713716 0.00814383 0.124945 1.64299e-05 4 2.1241 -0.0863426 -0.578466 0.0116865 0.00632492 0.202629 -0.00128689 8 2.1241 0.0334622 -0.286176 0.0540484 -0.0449203 0.140664 0.00126954 16 2.1241 0.0222346 -0.210375 0.0352667 -0.0168625 0.129417 0.000864334 32 2.1241 -0.0456591 0.118776 0.0325238 -0.0272637 0.135092 -0.00130924 64 2.1241 -0.0687702 0.0507116 0.0274814 -0.0279147 0.135782 -0.00203668 128 2.1241 -0.00750745 -0.00896204 0.0330804 -0.0256742 0.142662 -0.000481442 256 2.1241 0.000894925 0.0217517 0.027391 -0.0237747 0.155876 2.9181e-05 512 2.1241 -0.00363922 0.00381768 0.0299616 -0.026961 0.146282 8.59293e-05 1024 2.1241 0.00644187 -0.00020258 0.0301878 -0.0204789 0.147552 0.000415724 2048 2.1241 -0.00559158 0.00324722 0.0293121 -0.0237814 0.145943 -0.000198433 4096 2.1241 0.00162514 -0.00456608 0.0294486 -0.0231349 0.146056 5.76052e-05 8192 2.1241 -0.00134508 -0.0027843 0.028796 -0.0212074 0.142681 -2.0221e-05 16384 2.1241 0.000533237 0.0011453 0.0296175 -0.0227276 0.141355 3.47392e-05 32768 2.1241 0.00140228 0.000376675 0.0295111 -0.0224597 0.142187 3.86557e-05 65536 2.1241 -0.000272274 -0.00177361 0.0296098 -0.0228875 0.142304 -3.8257e-05 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 : -0.666125 0.0466682 -0.239898 1 : 0.602336 0.548926 0.332253 2 : 0.276442 0.621297 0.0146399 3 : 0.446236 0.527764 0.358627 4 : -0.620112 -0.64711 0.0749138 5 : 0.271263 0.0745238 0.210489 6 : 0.203146 -0.779662 -0.254846 7 : -0.460277 -0.167051 0.608619 8 : 0.583654 0.475801 0.641815 9 : -0.56777 -0.319548 0.455954 ellipse_monte_carlo_test(): Normal end of execution. Tue May 20 21:35:35 2025