Warning: X does not support locale en_US.UTF-8 09-Jun-2023 17:22:07 triangle_symq_rule_test() MATLAB/Octave version 9.14.0.2206163 (R2023a) Test triangle_symq_rule() triangle_symq_rule_test01(): Map points from one triangle to another. R = reference triangle S = simplex T = user-defined triangle. ref_to_triangle(): r => t simplex_to_triangle(): s => t triangle_to_ref(): t => r triangle_to_simplex(): t => s SP1: 0.1853 0.0942 TP1: 1.4616 1.0237 RP1: -0.5352 -0.4142 TP2: 1.4616 1.0237 SP2: 0.1853 0.0942 SP1: 0.8730 0.0866 TP1: 3.5324 3.7519 RP1: 0.8327 -0.4273 TP2: 3.5324 3.7519 SP2: 0.8730 0.0866 SP1: 0.6324 0.0975 TP1: 2.7995 2.8221 RP1: 0.3623 -0.4084 TP2: 2.7995 2.8221 SP2: 0.6324 0.0975 SP1: 0.2785 0.5469 TP1: 1.2886 2.7546 RP1: 0.1039 0.3699 TP2: 1.2886 2.7546 SP2: 0.2785 0.5469 SP1: 0.0425 0.0351 TP1: 1.0924 0.2753 RP1: -0.8799 -0.5165 TP2: 1.0924 0.2753 SP2: 0.0425 0.0351 Region is user-defined triangle. Triangle: 1.0000 0.0000 4.0000 4.0000 0.0000 3.0000 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 8 NUMNODES = 16 J W X Y 1 0.670913 1.34114 1.19399 2 0.670913 2.80601 3.14715 3 0.670913 0.852847 2.65886 4 0.618096 2.29646 2.08141 5 0.618096 1.91859 3.21505 6 0.618096 0.784952 1.70354 7 0.938051 1.66667 2.33333 8 0.21098 1.10109 0.353831 9 0.21098 3.64617 3.74726 10 0.21098 0.252736 2.89891 11 0.176997 1.78094 1.07764 12 0.176997 2.92236 3.70331 13 0.176997 0.296692 2.21906 14 0.176997 3.17708 2.93915 15 0.176997 1.06085 3.23793 16 0.176997 0.762072 0.822918 Weight sum 6.5 Area 6.5 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 8 Number of nodes = 16 Graphics saved as "user08.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 8 Quadrature rule written to file "user08.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 2.75098e-16 Region is standard equilateral triangle. Triangle: -1.0000 -0.5774 1.0000 -0.5774 0.0000 1.1547 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 8 NUMNODES = 16 J W X Y 1 0.178778 -0.488292 -0.281916 2 0.178778 0.488292 -0.281916 3 0.178778 4.44089e-16 0.563831 4 0.164704 0 -0.436336 5 0.164704 0.377878 0.218168 6 0.164704 -0.377878 0.218168 7 0.249962 0 2.22045e-16 8 0.0562198 -0.848358 -0.4898 9 0.0562198 0.848358 -0.4898 10 0.0562198 6.66134e-16 0.9796 11 0.0471643 -0.46538 -0.56281 12 0.0471643 0.720098 -0.121625 13 0.0471643 -0.254718 0.684436 14 0.0471643 0.46538 -0.56281 15 0.0471643 0.254718 0.684436 16 0.0471643 -0.720098 -0.121625 Weight sum 1.73205 Area 1.73205 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 8 Number of nodes = 16 Graphics saved as "equi08.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 8 Quadrature rule written to file "equi08.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 8 RMS integration error = 1.39354e-16 Region is the simplex (0,0),(1,0),(0,1). Triangle: 0.0000 0.0000 1.0000 0.0000 0.0000 1.0000 triangle_symq_rule_test02(): Symmetric quadrature rule for a triangle. Polynomial exactness degree = 4 NUMNODES = 6 J W X Y 1 0.111691 0.445948 0.108103 2 0.111691 0.445948 0.445948 3 0.111691 0.108103 0.445948 4 0.0549759 0.0915762 0.0915762 5 0.0549759 0.816848 0.0915762 6 0.0549759 0.0915762 0.816848 Weight sum 0.5 Area 0.5 triangle_symq_rule_test03(): triasymq_gnuplot() creates gnuplot graphics files. Polynomial exactness degree = 4 Number of nodes = 6 Graphics saved as "simp04.png" triangle_symq_rule_test04(): Get a quadrature rule for a triangle. Then write it to a file. Polynomial exactness degree = 4 Quadrature rule written to file "simp04.txt". triangle_symq_rule_test05(): Compute a quadrature rule for a triangle. Check it by integrating orthonormal polynomials. Polynomial exactness degree DEGREE = 4 RMS integration error = 7.87137e-17 triangle_symq_rule_test(): Normal end of execution. 09-Jun-2023 17:22:12