Tue Oct 19 17:10:59 2021 square_minimal_rule_test Python version Test the square_minimal_rule library. square_minimal_rule_print_test square_minimal_rule_print prints a quadrature rule for the symmetric unit square. Minimal quadrature rule for a square. Polynomial exactness degree DEGREE = 8 Number of nodes N = 16 J X Y W 0 0.920023 -0.106181 0.206685 1 0.893085 0.753846 0.163708 2 0.667537 -0.660277 0.344873 3 0.973684 -0.941891 0.0415499 4 0.463406 0.971315 0.12077 5 0.525725 0.328438 0.476161 6 -0.317191 0.843165 0.0871456 7 -0.0618911 0.685323 0.375508 8 0.0672083 -0.265414 0.593949 9 0.195748 -0.953138 0.157682 10 -0.728059 0.924562 0.126175 11 -0.553878 0.184945 0.496842 12 -0.444845 -0.741792 0.361102 13 -0.942108 0.565276 0.141357 14 -0.890011 -0.362633 0.236319 15 -0.884156 -0.941851 0.0701717 Sum 4 Area 4 square_minimal_rule_order_test Print the order (number of points) for each minimal square rule. Degree Order 0 1 1 1 2 3 3 4 4 6 5 7 6 10 7 12 8 16 9 17 10 22 11 24 12 31 13 33 14 40 15 43 16 52 17 54 18 64 19 67 20 78 21 81 22 93 23 96 24 109 25 113 26 127 27 132 28 146 29 153 30 167 31 172 32 189 33 197 34 211 35 220 36 238 37 245 38 265 39 274 40 296 41 303 42 326 43 331 44 353 45 359 46 387 47 396 48 417 49 427 50 454 51 462 52 493 53 498 54 530 55 536 square_minimal_rule_error_max_test square_minimal_rule_error_max computes the maximum error for a rule that should be exact for all monomials up to a given value of DEGREE. Degree Monomials Error Max 0 1 0 1 3 0 2 6 1.11022e-15 3 10 0 4 15 8.88178e-16 5 21 6.66134e-16 6 28 8.88178e-16 7 36 2.22045e-16 8 45 3.33067e-16 9 55 8.88178e-16 10 66 1.33227e-15 11 78 8.88178e-16 12 91 3.33067e-16 13 105 4.44089e-16 14 120 1.77636e-15 15 136 8.88178e-16 16 153 8.50015e-16 17 171 6.66134e-16 18 190 8.88178e-16 19 210 4.44089e-16 20 231 2.22045e-16 21 253 1.33227e-15 22 276 1.33227e-15 23 300 4.44089e-16 24 325 6.66134e-16 25 351 4.44089e-16 26 378 8.88178e-16 27 406 2.22045e-15 28 435 7.29668e-16 29 465 8.88178e-16 30 496 8.88178e-16 31 528 8.88178e-16 32 561 8.88178e-16 33 595 1.77636e-15 34 630 1.77636e-15 35 666 8.88178e-16 36 703 6.66134e-16 37 741 3.55271e-15 38 780 8.88178e-16 39 820 8.88178e-16 40 861 1.55431e-15 41 903 5.55112e-16 42 946 8.67145e-16 43 990 1.33227e-15 44 1035 5.55112e-16 45 1081 1.33227e-15 46 1128 1.33227e-15 47 1176 6.66134e-16 48 1225 8.88178e-16 49 1275 8.88178e-16 50 1326 2.88658e-15 51 1378 8.88178e-16 52 1431 1.77636e-15 53 1485 8.88178e-16 54 1540 1.55431e-15 55 1596 1.9984e-15 square_minimal_rule_test Normal end of execution. Tue Oct 19 17:11:11 2021