Tue Oct 19 11:33:11 2021 disk_rule_test(): Python version: 3.6.9 Test disk_rule(). disk_rule_compute_test Python version: 3.6.9 disk_rule_compute can compute a rule Q(f) for a general disk centered at (XC,YC) with radius RC, using NT equally spaced angles and NR radial distances. NT = 8 NR = 4 Estimate integrals I(f) where f = x^ex * y^ey. Ex Ey I(f) Q(f) 0 0 28.2743 28.2743 1 0 28.2743 28.2743 0 1 56.5487 56.5487 2 0 91.8916 91.8916 1 1 56.5487 56.5487 0 2 176.715 176.715 3 0 219.126 219.126 2 1 183.783 183.783 1 2 176.715 176.715 0 3 607.898 607.898 4 0 696.255 696.255 3 1 438.252 438.252 2 2 526.609 526.609 1 3 607.898 607.898 0 4 2265.48 2265.48 disk_rule_compute_test: Normal end of execution. disk01_area_test Python version: 3.6.9 disk01_area returns the area of the unit disk. disk01_area() = 3.14159 disk01_area_test Normal end of execution. disk01_monomial_integral_test Python version: 3.6.9 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 4 2 0.0477076 0.0490874 0.0014 0 0 3.14159 3.14159 4.4e-16 6 0 0.248671 0.245437 0.0032 4 6 0.00603266 0.00613592 0.0001 4 2 0.0477076 0.0490874 0.0014 2 4 0.0490202 0.0490874 6.7e-05 0 4 0.397132 0.392699 0.0044 8 0 0.174843 0.171806 0.003 8 8 0.000353144 0.000372843 2e-05 4 4 0.0142999 0.0147262 0.00043 6 4 0.00584325 0.00613592 0.00029 8 0 0.174843 0.171806 0.003 2 2 0.129166 0.1309 0.0017 4 0 0.395353 0.392699 0.0027 2 4 0.0490202 0.0490874 6.7e-05 6 8 0.000929153 0.000958738 3e-05 8 4 0.00287573 0.00306796 0.00019 0 4 0.397132 0.392699 0.0044 0 6 0.251626 0.245437 0.0062 0 4 0.397132 0.392699 0.0044 disk01_monomial_integral_test: Normal end of execution. disk01_rule_test Python version: 3.6.9 disk01_rule can compute 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_rule_test: Normal end of execution. disk01_sample_test Python version: 3.6.9 disk01_sample samples the unit disk. Sample points in the unit disk. Row: 0 1 Col 0 : -0.123601 0.0341284 1 : -0.450292 0.859153 2 : 0.282034 0.467059 3 : -0.142576 -0.800371 4 : -0.313456 -0.56944 5 : -0.878579 -0.465535 6 : -0.788814 -0.4537 7 : 0.250679 -0.0306695 8 : 0.00300473 -0.910106 9 : 0.246824 -0.0437641 disk01_sample_test Normal end of execution. imtqlx_test Python version: 3.6.9 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 imtqlx_test: Normal end of execution. legendre_ek_compute_test Python version: 3.6.9 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 legendre_ek_compute_test: Normal end of execution. disk_rule_test(): Normal end of execution. Tue Oct 19 11:33:12 2021