11 June 2014 10:29:15 AM PADUA_PRB C++ version Test the PADUA library. TEST01 PADUA_ORDER converts the level L into the order N of any Padua rule. L N 0 1 1 3 2 6 3 10 4 15 5 21 6 28 7 36 8 45 9 55 10 66 TEST02 PADUA_POINTS returns the points of a Padua rule. Level 0 Padua points: Row: 0 1 Col 0: 0 0 Level 1 Padua points: Row: 0 1 Col 0: 1 0 1: -1 1 2: -1 -1 Level 2 Padua points: Row: 0 1 Col 0: 1 0.5 1: 1 -1 2: 0 1 3: 0 -0.5 4: -1 0.5 5: -1 -1 Level 3 Padua points: Row: 0 1 Col 0: 1 0.707107 1: 1 -0.707107 2: 0.5 1 3: 0.5 0 4: 0.5 -1 5: -0.5 0.707107 6: -0.5 -0.707107 7: -1 1 8: -1 0 9: -1 -1 Level 4 Padua points: Row: 0 1 Col 0: 1 0.809017 1: 1 -0.309017 2: 1 -1 3: 0.707107 1 4: 0.707107 0.309017 5: 0.707107 -0.809017 6: 0 0.809017 7: 0 -0.309017 8: 0 -1 9: -0.707107 1 10: -0.707107 0.309017 11: -0.707107 -0.809017 12: -1 0.809017 13: -1 -0.309017 14: -1 -1 Level 5 Padua points: Row: 0 1 Col 0: 1 0.866025 1: 1 0 2: 1 -0.866025 3: 0.809017 1 4: 0.809017 0.5 5: 0.809017 -0.5 6: 0.809017 -1 7: 0.309017 0.866025 8: 0.309017 0 9: 0.309017 -0.866025 10: -0.309017 1 11: -0.309017 0.5 12: -0.309017 -0.5 13: -0.309017 -1 14: -0.809017 0.866025 15: -0.809017 0 16: -0.809017 -0.866025 17: -1 1 18: -1 0.5 19: -1 -0.5 20: -1 -1 Level 6 Padua points: Row: 0 1 Col 0: 1 0.900969 1: 1 0.222521 2: 1 -0.62349 3: 1 -1 4: 0.866025 1 5: 0.866025 0.62349 6: 0.866025 -0.222521 7: 0.866025 -0.900969 8: 0.5 0.900969 9: 0.5 0.222521 10: 0.5 -0.62349 11: 0.5 -1 12: 0 1 13: 0 0.62349 14: 0 -0.222521 15: 0 -0.900969 16: -0.5 0.900969 17: -0.5 0.222521 18: -0.5 -0.62349 19: -0.5 -1 20: -0.866025 1 21: -0.866025 0.62349 22: -0.866025 -0.222521 23: -0.866025 -0.900969 24: -1 0.900969 25: -1 0.222521 26: -1 -0.62349 27: -1 -1 Level 7 Padua points: Row: 0 1 Col 0: 1 0.92388 1: 1 0.382683 2: 1 -0.382683 3: 1 -0.92388 4: 0.900969 1 5: 0.900969 0.707107 6: 0.900969 0 7: 0.900969 -0.707107 8: 0.900969 -1 9: 0.62349 0.92388 10: 0.62349 0.382683 11: 0.62349 -0.382683 12: 0.62349 -0.92388 13: 0.222521 1 14: 0.222521 0.707107 15: 0.222521 0 16: 0.222521 -0.707107 17: 0.222521 -1 18: -0.222521 0.92388 19: -0.222521 0.382683 20: -0.222521 -0.382683 21: -0.222521 -0.92388 22: -0.62349 1 23: -0.62349 0.707107 24: -0.62349 0 25: -0.62349 -0.707107 26: -0.62349 -1 27: -0.900969 0.92388 28: -0.900969 0.382683 29: -0.900969 -0.382683 30: -0.900969 -0.92388 31: -1 1 32: -1 0.707107 33: -1 0 34: -1 -0.707107 35: -1 -1 Level 8 Padua points: Row: 0 1 Col 0: 1 0.939693 1: 1 0.5 2: 1 -0.173648 3: 1 -0.766044 4: 1 -1 5: 0.92388 1 6: 0.92388 0.766044 7: 0.92388 0.173648 8: 0.92388 -0.5 9: 0.92388 -0.939693 10: 0.707107 0.939693 11: 0.707107 0.5 12: 0.707107 -0.173648 13: 0.707107 -0.766044 14: 0.707107 -1 15: 0.382683 1 16: 0.382683 0.766044 17: 0.382683 0.173648 18: 0.382683 -0.5 19: 0.382683 -0.939693 20: 0 0.939693 21: 0 0.5 22: 0 -0.173648 23: 0 -0.766044 24: 0 -1 25: -0.382683 1 26: -0.382683 0.766044 27: -0.382683 0.173648 28: -0.382683 -0.5 29: -0.382683 -0.939693 30: -0.707107 0.939693 31: -0.707107 0.5 32: -0.707107 -0.173648 33: -0.707107 -0.766044 34: -0.707107 -1 35: -0.92388 1 36: -0.92388 0.766044 37: -0.92388 0.173648 38: -0.92388 -0.5 39: -0.92388 -0.939693 40: -1 0.939693 41: -1 0.5 42: -1 -0.173648 43: -1 -0.766044 44: -1 -1 Level 9 Padua points: Row: 0 1 Col 0: 1 0.951057 1: 1 0.587785 2: 1 0 3: 1 -0.587785 4: 1 -0.951057 5: 0.939693 1 6: 0.939693 0.809017 7: 0.939693 0.309017 8: 0.939693 -0.309017 9: 0.939693 -0.809017 10: 0.939693 -1 11: 0.766044 0.951057 12: 0.766044 0.587785 13: 0.766044 0 14: 0.766044 -0.587785 15: 0.766044 -0.951057 16: 0.5 1 17: 0.5 0.809017 18: 0.5 0.309017 19: 0.5 -0.309017 20: 0.5 -0.809017 21: 0.5 -1 22: 0.173648 0.951057 23: 0.173648 0.587785 24: 0.173648 0 25: 0.173648 -0.587785 26: 0.173648 -0.951057 27: -0.173648 1 28: -0.173648 0.809017 29: -0.173648 0.309017 30: -0.173648 -0.309017 31: -0.173648 -0.809017 32: -0.173648 -1 33: -0.5 0.951057 34: -0.5 0.587785 35: -0.5 0 36: -0.5 -0.587785 37: -0.5 -0.951057 38: -0.766044 1 39: -0.766044 0.809017 40: -0.766044 0.309017 41: -0.766044 -0.309017 42: -0.766044 -0.809017 43: -0.766044 -1 44: -0.939693 0.951057 45: -0.939693 0.587785 46: -0.939693 0 47: -0.939693 -0.587785 48: -0.939693 -0.951057 49: -1 1 50: -1 0.809017 51: -1 0.309017 52: -1 -0.309017 53: -1 -0.809017 54: -1 -1 Level 10 Padua points: Row: 0 1 Col 0: 1 0.959493 1: 1 0.654861 2: 1 0.142315 3: 1 -0.415415 4: 1 -0.841254 5: 1 -1 6: 0.951057 1 7: 0.951057 0.841254 8: 0.951057 0.415415 9: 0.951057 -0.142315 10: 0.951057 -0.654861 11: 0.951057 -0.959493 12: 0.809017 0.959493 13: 0.809017 0.654861 14: 0.809017 0.142315 15: 0.809017 -0.415415 16: 0.809017 -0.841254 17: 0.809017 -1 18: 0.587785 1 19: 0.587785 0.841254 20: 0.587785 0.415415 21: 0.587785 -0.142315 22: 0.587785 -0.654861 23: 0.587785 -0.959493 24: 0.309017 0.959493 25: 0.309017 0.654861 26: 0.309017 0.142315 27: 0.309017 -0.415415 28: 0.309017 -0.841254 29: 0.309017 -1 30: 0 1 31: 0 0.841254 32: 0 0.415415 33: 0 -0.142315 34: 0 -0.654861 35: 0 -0.959493 36: -0.309017 0.959493 37: -0.309017 0.654861 38: -0.309017 0.142315 39: -0.309017 -0.415415 40: -0.309017 -0.841254 41: -0.309017 -1 42: -0.587785 1 43: -0.587785 0.841254 44: -0.587785 0.415415 45: -0.587785 -0.142315 46: -0.587785 -0.654861 47: -0.587785 -0.959493 48: -0.809017 0.959493 49: -0.809017 0.654861 50: -0.809017 0.142315 51: -0.809017 -0.415415 52: -0.809017 -0.841254 53: -0.809017 -1 54: -0.951057 1 55: -0.951057 0.841254 56: -0.951057 0.415415 57: -0.951057 -0.142315 58: -0.951057 -0.654861 59: -0.951057 -0.959493 60: -1 0.959493 61: -1 0.654861 62: -1 0.142315 63: -1 -0.415415 64: -1 -0.841254 65: -1 -1 TEST03 PADUA_PLOT plots the Padua points. Created data file 'padua_00_data.txt'. Created command file 'padua_00_commands.txt'. Created data file 'padua_01_data.txt'. Created command file 'padua_01_commands.txt'. Created data file 'padua_02_data.txt'. Created command file 'padua_02_commands.txt'. Created data file 'padua_03_data.txt'. Created command file 'padua_03_commands.txt'. Created data file 'padua_04_data.txt'. Created command file 'padua_04_commands.txt'. Created data file 'padua_05_data.txt'. Created command file 'padua_05_commands.txt'. Created data file 'padua_06_data.txt'. Created command file 'padua_06_commands.txt'. Created data file 'padua_07_data.txt'. Created command file 'padua_07_commands.txt'. Created data file 'padua_08_data.txt'. Created command file 'padua_08_commands.txt'. Created data file 'padua_09_data.txt'. Created command file 'padua_09_commands.txt'. Created data file 'padua_10_data.txt'. Created command file 'padua_10_commands.txt'. TEST04 PADUA_POINTS computes the points of a Padua rule. PADUA_POINT_SET looks them up in a table. Level 3 Padua points. 0 1 0.707107 1 0.707107 1 1 -0.707107 1 -0.707107 2 0.5 1 0.5 1 3 0.5 0 0.5 0 4 0.5 -1 0.5 -1 5 -0.5 0.707107 -0.5 0.707107 6 -0.5 -0.707107 -0.5 -0.707107 7 -1 1 -1 1 8 -1 0 -1 0 9 -1 -1 -1 -1 Level 4 Padua points. 0 1 0.809017 1 0.809017 1 1 -0.309017 1 -0.309017 2 1 -1 1 -1 3 0.707107 1 0.707107 1 4 0.707107 0.309017 0.707107 0.309017 5 0.707107 -0.809017 0.707107 -0.809017 6 0 0.809017 0 0.809017 7 0 -0.309017 0 -0.309017 8 0 -1 0 -1 9 -0.707107 1 -0.707107 1 10 -0.707107 0.309017 -0.707107 0.309017 11 -0.707107 -0.809017 -0.707107 -0.809017 12 -1 0.809017 -1 0.809017 13 -1 -0.309017 -1 -0.309017 14 -1 -1 -1 -1 TEST05 PADUA_WEIGHTS computes quadrature points of a Padua rule. PADUA_WEIGHT_SET looks them up in a table. Level 3 Padua quadrature weights. 0 0.111111 0.111111 1 0.111111 0.111111 2 0.222222 0.222222 3 1.33333 1.33333 4 0.222222 0.222222 5 0.888889 0.888889 6 0.888889 0.888889 7 -0.0555556 -0.0555556 8 0.333333 0.333333 9 -0.0555556 -0.0555556 Maximum difference = 7.77156e-16 Level 4 Padua quadrature weights. 0 0.061173 0.061173 1 0.0810492 0.0810492 2 -0.00888889 -0.00888889 3 0.0533333 0.0533333 4 0.625924 0.625924 5 0.38741 0.38741 6 0.545807 0.545807 7 0.983082 0.983082 8 0.0711111 0.0711111 9 0.0533333 0.0533333 10 0.625924 0.625924 11 0.38741 0.38741 12 0.061173 0.061173 13 0.0810492 0.0810492 14 -0.00888889 -0.00888889 Maximum difference = 1.22125e-15 PADUA_PRB Normal end of execution. 11 June 2014 10:29:15 AM