Tue May 20 21:35:05 2025 disk01_rule_test python version: 3.10.12 numpy version: 1.26.4 Test disk01_rule(). disk01_area_test(): disk01_area() returns the area of the unit disk. disk01_area() = 3.141592653589793 disk01_monomial_integral_test(): disk01_monomial_integral() computes monomial integrals over the interior of the unit disk in 2D. Compare with a Monte Carlo value. Number of sample points used is 4192 If any exponent is odd, the integral is zero. We will restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 0 8 0.164707 0.171806 0.0071 0 2 0.774998 0.785398 0.01 0 0 3.14159 3.14159 4.4e-16 4 0 0.400955 0.392699 0.0083 2 8 0.0141428 0.0143172 0.00017 8 8 0.000381817 0.000372843 9e-06 4 4 0.0149193 0.0147262 0.00019 8 0 0.173876 0.171806 0.0021 4 4 0.0149193 0.0147262 0.00019 2 4 0.0490577 0.0490874 3e-05 0 6 0.237021 0.245437 0.0084 2 4 0.0490577 0.0490874 3e-05 0 0 3.14159 3.14159 4.4e-16 4 0 0.400955 0.392699 0.0083 2 0 0.800096 0.785398 0.015 6 6 0.00223127 0.0021914 4e-05 2 2 0.132059 0.1309 0.0012 0 8 0.164707 0.171806 0.0071 4 2 0.050257 0.0490874 0.0012 4 4 0.0149193 0.0147262 0.00019 disk01_rule_compute_test(): disk01_rule_compute() computes a rule Q(f) for the unit disk using NT equally spaced angles and NR radial distances. NT = 8 NR = 4 Estimate integrals I(f) where f = x^e(1) * y^e(2). E(1) E(2) I(f) Q(f) 0 0 3.14159 3.14159 0 2 0.785398 0.785398 0 4 0.392699 0.392699 0 6 0.245437 0.245437 2 2 0.1309 0.1309 2 4 0.0490874 0.0490874 2 6 0.0245437 0.019635 4 4 0.0147262 0.019635 4 6 0.00613592 0.00818123 6 6 0.0021914 0.00350624 disk01_sample_test(): disk01_sample() samples the unit disk. Sample points in the unit disk. Row: 0 1 Col 0 : -0.189792 0.210975 1 : -0.170855 0.118463 2 : 0.80944 -0.00123204 3 : 0.634584 0.368751 4 : 0.00216127 -0.995877 5 : -0.731051 0.251771 6 : -0.730574 0.157193 7 : 0.064795 0.369252 8 : 0.793149 0.256747 9 : -0.915099 -0.256003 imtqlx_test(): imtqlx() takes a symmetric tridiagonal matrix A and computes its eigenvalues LAM. It also accepts a vector Z and computes Q'*Z, where Q is the matrix that diagonalizes A. Computed eigenvalues: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Exact eigenvalues: 0: 0.267949 1: 1 2: 2 3: 3 4: 3.73205 Vector Z: 0: 1 1: 1 2: 1 3: 1 4: 1 Vector Q*Z: 0: -2.1547 1: -1.8855e-16 2: 0.57735 3: 1.66533e-16 4: -0.154701 legendre_ek_compute_test(): legendre_ek_compute() computes a Legendre quadrature rule using the Elhay-Kautsky algorithm. Index X W 0 0 2 0 -0.5773502691896256 1 1 0.5773502691896256 1 0 -0.7745966692414832 0.5555555555555559 1 -6.466579952145703e-17 0.8888888888888886 2 0.7745966692414834 0.5555555555555554 0 -0.8611363115940526 0.3478548451374537 1 -0.3399810435848563 0.6521451548625463 2 0.3399810435848564 0.6521451548625459 3 0.8611363115940522 0.347854845137454 0 -0.9061798459386641 0.2369268850561892 1 -0.538469310105683 0.4786286704993667 2 -3.478412152580952e-17 0.5688888888888882 3 0.5384693101056829 0.478628670499367 4 0.9061798459386642 0.2369268850561892 0 -0.9324695142031522 0.1713244923791701 1 -0.6612093864662647 0.3607615730481389 2 -0.2386191860831971 0.4679139345726916 3 0.2386191860831969 0.4679139345726918 4 0.6612093864662648 0.3607615730481388 5 0.9324695142031524 0.1713244923791705 0 -0.9491079123427583 0.1294849661688696 1 -0.7415311855993943 0.2797053914892763 2 -0.4058451513773971 0.381830050505119 3 4.452841060583418e-17 0.4179591836734696 4 0.4058451513773971 0.3818300505051177 5 0.7415311855993941 0.2797053914892761 6 0.9491079123427584 0.1294849661688694 0 -0.9602898564975358 0.101228536290376 1 -0.7966664774136267 0.2223810344533742 2 -0.5255324099163291 0.3137066458778873 3 -0.1834346424956499 0.3626837833783611 4 0.1834346424956497 0.3626837833783627 5 0.5255324099163293 0.3137066458778878 6 0.7966664774136266 0.2223810344533745 7 0.9602898564975362 0.1012285362903759 0 -0.9681602395076263 0.08127438836157426 1 -0.836031107326636 0.1806481606948577 2 -0.6133714327005901 0.2606106964029359 3 -0.3242534234038091 0.3123470770400025 4 1.604668093316319e-16 0.3302393550012599 5 0.324253423403809 0.3123470770400033 6 0.6133714327005904 0.2606106964029349 7 0.836031107326636 0.180648160694857 8 0.9681602395076262 0.08127438836157452 0 -0.973906528517172 0.06667134430868817 1 -0.8650633666889845 0.1494513491505806 2 -0.6794095682990243 0.2190863625159822 3 -0.4333953941292472 0.2692667193099962 4 -0.1488743389816309 0.2955242247147525 5 0.148874338981631 0.2955242247147538 6 0.4333953941292469 0.2692667193099955 7 0.6794095682990243 0.2190863625159825 8 0.8650633666889844 0.14945134915058 9 0.973906528517172 0.06667134430868776 disk01_rule_test(): Normal end of execution. Tue May 20 21:35:05 2025