Tue Oct 19 11:23:51 2021 annulus_rule_test(): Python version: 3.6.9 Test annulus_rule(). annulus_area_test(): annulus_area() computes the area of an annulus with center = (CX,CY), inner radius R1 and outer radius R2. ( CX CY ) R1 R2 Area ( 4.961068, 3.007902) 0.073543 0.443297 0.600369 (-1.288772,-4.789833) 0.596772 1.317019 4.330380 ( 2.042371, 1.481353) 0.434194 0.546804 0.347054 (-3.485537,-2.846751) 0.987734 1.360746 2.752073 (-2.972910,-3.165973) 0.103651 0.170445 0.057517 (-3.909518,-4.084640) 0.671798 1.205466 3.147359 (-3.226315, 1.072783) 0.526928 0.768488 0.983069 (-1.193186,-4.074319) 0.521893 0.847648 1.401575 ( 4.148368, 2.725034) 0.021310 0.196807 0.120257 (-0.846386,-1.877768) 0.666979 0.977833 1.606286 annulus_area_test(): Normal end of execution. annulus_rule_compute_test(): Python version: 3.6.9 Test annulus_rule_compute(). W, X, Y for annulus quadrature: 0: 0.0545415 0.578382 0 1: 0.0872665 0.790569 0 2: 0.0545415 0.956804 0 3: 0.0545415 0.500894 0.289191 4: 0.0872665 0.684653 0.395285 5: 0.0545415 0.828617 0.478402 6: 0.0545415 0.289191 0.500894 7: 0.0872665 0.395285 0.684653 8: 0.0545415 0.478402 0.828617 9: 0.0545415 3.54157e-17 0.578382 10: 0.0872665 4.84084e-17 0.790569 11: 0.0545415 5.85873e-17 0.956804 12: 0.0545415 -0.289191 0.500894 13: 0.0872665 -0.395285 0.684653 14: 0.0545415 -0.478402 0.828617 15: 0.0545415 -0.500894 0.289191 16: 0.0872665 -0.684653 0.395285 17: 0.0545415 -0.828617 0.478402 18: 0.0545415 -0.578382 7.08314e-17 19: 0.0872665 -0.790569 9.68168e-17 20: 0.0545415 -0.956804 1.17175e-16 21: 0.0545415 -0.500894 -0.289191 22: 0.0872665 -0.684653 -0.395285 23: 0.0545415 -0.828617 -0.478402 24: 0.0545415 -0.289191 -0.500894 25: 0.0872665 -0.395285 -0.684653 26: 0.0545415 -0.478402 -0.828617 27: 0.0545415 -1.06247e-16 -0.578382 28: 0.0872665 -1.45225e-16 -0.790569 29: 0.0545415 -1.75762e-16 -0.956804 30: 0.0545415 0.289191 -0.500894 31: 0.0872665 0.395285 -0.684653 32: 0.0545415 0.478402 -0.828617 33: 0.0545415 0.500894 -0.289191 34: 0.0872665 0.684653 -0.395285 35: 0.0545415 0.828617 -0.478402 annulus_rule_compute_test(): Normal end of execution. annulus_rule_monomial_test(): Python version: 3.6.9 annulus_rule_compute() can supply a quadrature rule for the annulus centered at (0,0) with R1 = 0, R2 = 1 Apply this rule to a variety of monomials. NR NT 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 4 16 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 8 32 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 16 64 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 32 128 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 64 256 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 Exact 3.14159 0.785398 0.785398 0.392699 0.1309 0.392699 0.245437 annulus_rule_monomial_test(): Normal end of execution. annulus_rule_monomial_test(): Python version: 3.6.9 annulus_rule_compute() can supply a quadrature rule for the annulus centered at (0,0) with R1 = 0.5, R2 = 1 Apply this rule to a variety of monomials. NR NT 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 4 16 2.35619 0.736311 0.736311 0.386563 0.128854 0.386563 0.244478 8 32 2.35619 0.736311 0.736311 0.386563 0.128854 0.386563 0.244478 16 64 2.35619 0.736311 0.736311 0.386563 0.128854 0.386563 0.244478 32 128 2.35619 0.736311 0.736311 0.386563 0.128854 0.386563 0.244478 64 256 2.35619 0.736311 0.736311 0.386563 0.128854 0.386563 0.244478 annulus_rule_monomial_test(): Normal end of execution. annulus_rule_monomial_test(): Python version: 3.6.9 annulus_rule_compute() can supply a quadrature rule for the annulus centered at (1,0) with R1 = 0, R2 = 1 Apply this rule to a variety of monomials. NR NT 1 X^2 Y^2 X^4 X^2Y^2 Y^4 X^6 4 16 3.14159 3.92699 0.785398 8.24668 0.916298 0.392699 21.0585 8 32 3.14159 3.92699 0.785398 8.24668 0.916298 0.392699 21.0585 16 64 3.14159 3.92699 0.785398 8.24668 0.916298 0.392699 21.0585 32 128 3.14159 3.92699 0.785398 8.24668 0.916298 0.392699 21.0585 64 256 3.14159 3.92699 0.785398 8.24668 0.916298 0.392699 21.0585 annulus_rule_monomial_test(): Normal end of execution. rule_adjust_test(): Python version: 3.6.9 rule_adjust() adjusts a quadrature rule from [A,B] to [C,D]. W, X defined on [-1,+1] 0: 0.0575094 -0.92388 1: 0.19635 -0.707107 2: 0.33519 -0.382683 3: 0.392699 6.12323e-17 4: 0.33519 0.382683 5: 0.19635 0.707107 6: 0.0575094 0.92388 W, X adjusted to [0,1] 0: 0.0287547 0.0380602 1: 0.0981748 0.146447 2: 0.167595 0.308658 3: 0.19635 0.5 4: 0.167595 0.691342 5: 0.0981748 0.853553 6: 0.0287547 0.96194 rule_adjust_test(): Normal end of execution. annulus_rule_test(): Normal end of execution. Tue Oct 19 11:23:52 2021