07-Jan-2022 15:21:19 annulus_rule_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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 ( 3.147237, 4.057919) 0.126987 1.040363 3.349657 ( 1.323592,-4.024596) 0.278498 0.825380 1.896549 ( 4.575068, 4.648885) 0.157613 1.128206 3.920728 ( 4.571669,-0.146244) 0.800280 0.942167 0.776694 (-0.782387, 4.157355) 0.792207 1.751700 7.668187 ( 1.557407,-4.642883) 0.849129 1.783123 7.723623 ( 1.787352, 2.577401) 0.743132 1.135359 2.314711 ( 1.554779,-3.288133) 0.706046 0.737879 0.144401 (-2.230770,-4.538286) 0.097132 0.920590 2.632814 ( 1.948286,-1.829005) 0.950222 0.984668 0.209385 ANNULUS_RULE_COMPUTE_TEST: MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test ANNULUS_RULE_COMPUTE. W, X, Y for annulus quadrature: 1: 0.0545415 0.578382 0 2: 0.0872665 0.790569 0 3: 0.0545415 0.956804 0 4: 0.0545415 0.500894 0.289191 5: 0.0872665 0.684653 0.395285 6: 0.0545415 0.828617 0.478402 7: 0.0545415 0.289191 0.500894 8: 0.0872665 0.395285 0.684653 9: 0.0545415 0.478402 0.828617 10: 0.0545415 3.54157e-17 0.578382 11: 0.0872665 4.84084e-17 0.790569 12: 0.0545415 5.85873e-17 0.956804 13: 0.0545415 -0.289191 0.500894 14: 0.0872665 -0.395285 0.684653 15: 0.0545415 -0.478402 0.828617 16: 0.0545415 -0.500894 0.289191 17: 0.0872665 -0.684653 0.395285 18: 0.0545415 -0.828617 0.478402 19: 0.0545415 -0.578382 7.08314e-17 20: 0.0872665 -0.790569 9.68168e-17 21: 0.0545415 -0.956804 1.17175e-16 22: 0.0545415 -0.500894 -0.289191 23: 0.0872665 -0.684653 -0.395285 24: 0.0545415 -0.828617 -0.478402 25: 0.0545415 -0.289191 -0.500894 26: 0.0872665 -0.395285 -0.684653 27: 0.0545415 -0.478402 -0.828617 28: 0.0545415 -1.06247e-16 -0.578382 29: 0.0872665 -1.45225e-16 -0.790569 30: 0.0545415 -1.75762e-16 -0.956804 31: 0.0545415 0.289191 -0.500894 32: 0.0872665 0.395285 -0.684653 33: 0.0545415 0.478402 -0.828617 34: 0.0545415 0.500894 -0.289191 35: 0.0872665 0.684653 -0.395285 36: 0.0545415 0.828617 -0.478402 ANNULUS_RULE_COMPUTE_TEST: Normal end of execution. ANNULUS_RULE_PLOT_TEST: ANNULUS_RULE_PLOT plots annulus quadrature rule points. Graphics saved as "annulus_rule_plot_test.png" ANNULUS_RULE_PLOT_TEST: Normal end of execution. ANNULUS_RULE_MONOMIAL_TEST 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 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 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_test(): Normal end of execution. 07-Jan-2022 15:21:23