11 June 2014 10:14:44.422 AM PADUA_PRB FORTRAN77 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 1 2 Col 1: 0.00000 0.00000 Level 1 Padua points: Row 1 2 Col 1: 1.00000 0.00000 2: -1.00000 1.00000 3: -1.00000 -1.00000 Level 2 Padua points: Row 1 2 Col 1: 1.00000 0.500000 2: 1.00000 -1.00000 3: 0.00000 1.00000 4: 0.00000 -0.500000 5: -1.00000 0.500000 6: -1.00000 -1.00000 Level 3 Padua points: Row 1 2 Col 1: 1.00000 0.707107 2: 1.00000 -0.707107 3: 0.500000 1.00000 4: 0.500000 0.00000 5: 0.500000 -1.00000 6: -0.500000 0.707107 7: -0.500000 -0.707107 8: -1.00000 1.00000 9: -1.00000 0.00000 10: -1.00000 -1.00000 Level 4 Padua points: Row 1 2 Col 1: 1.00000 0.809017 2: 1.00000 -0.309017 3: 1.00000 -1.00000 4: 0.707107 1.00000 5: 0.707107 0.309017 6: 0.707107 -0.809017 7: 0.00000 0.809017 8: 0.00000 -0.309017 9: 0.00000 -1.00000 10: -0.707107 1.00000 11: -0.707107 0.309017 12: -0.707107 -0.809017 13: -1.00000 0.809017 14: -1.00000 -0.309017 15: -1.00000 -1.00000 Level 5 Padua points: Row 1 2 Col 1: 1.00000 0.866025 2: 1.00000 0.00000 3: 1.00000 -0.866025 4: 0.809017 1.00000 5: 0.809017 0.500000 6: 0.809017 -0.500000 7: 0.809017 -1.00000 8: 0.309017 0.866025 9: 0.309017 0.00000 10: 0.309017 -0.866025 11: -0.309017 1.00000 12: -0.309017 0.500000 13: -0.309017 -0.500000 14: -0.309017 -1.00000 15: -0.809017 0.866025 16: -0.809017 0.00000 17: -0.809017 -0.866025 18: -1.00000 1.00000 19: -1.00000 0.500000 20: -1.00000 -0.500000 21: -1.00000 -1.00000 Level 6 Padua points: Row 1 2 Col 1: 1.00000 0.900969 2: 1.00000 0.222521 3: 1.00000 -0.623490 4: 1.00000 -1.00000 5: 0.866025 1.00000 6: 0.866025 0.623490 7: 0.866025 -0.222521 8: 0.866025 -0.900969 9: 0.500000 0.900969 10: 0.500000 0.222521 11: 0.500000 -0.623490 12: 0.500000 -1.00000 13: 0.00000 1.00000 14: 0.00000 0.623490 15: 0.00000 -0.222521 16: 0.00000 -0.900969 17: -0.500000 0.900969 18: -0.500000 0.222521 19: -0.500000 -0.623490 20: -0.500000 -1.00000 21: -0.866025 1.00000 22: -0.866025 0.623490 23: -0.866025 -0.222521 24: -0.866025 -0.900969 25: -1.00000 0.900969 26: -1.00000 0.222521 27: -1.00000 -0.623490 28: -1.00000 -1.00000 Level 7 Padua points: Row 1 2 Col 1: 1.00000 0.923880 2: 1.00000 0.382683 3: 1.00000 -0.382683 4: 1.00000 -0.923880 5: 0.900969 1.00000 6: 0.900969 0.707107 7: 0.900969 0.00000 8: 0.900969 -0.707107 9: 0.900969 -1.00000 10: 0.623490 0.923880 11: 0.623490 0.382683 12: 0.623490 -0.382683 13: 0.623490 -0.923880 14: 0.222521 1.00000 15: 0.222521 0.707107 16: 0.222521 0.00000 17: 0.222521 -0.707107 18: 0.222521 -1.00000 19: -0.222521 0.923880 20: -0.222521 0.382683 21: -0.222521 -0.382683 22: -0.222521 -0.923880 23: -0.623490 1.00000 24: -0.623490 0.707107 25: -0.623490 0.00000 26: -0.623490 -0.707107 27: -0.623490 -1.00000 28: -0.900969 0.923880 29: -0.900969 0.382683 30: -0.900969 -0.382683 31: -0.900969 -0.923880 32: -1.00000 1.00000 33: -1.00000 0.707107 34: -1.00000 0.00000 35: -1.00000 -0.707107 36: -1.00000 -1.00000 Level 8 Padua points: Row 1 2 Col 1: 1.00000 0.939693 2: 1.00000 0.500000 3: 1.00000 -0.173648 4: 1.00000 -0.766044 5: 1.00000 -1.00000 6: 0.923880 1.00000 7: 0.923880 0.766044 8: 0.923880 0.173648 9: 0.923880 -0.500000 10: 0.923880 -0.939693 11: 0.707107 0.939693 12: 0.707107 0.500000 13: 0.707107 -0.173648 14: 0.707107 -0.766044 15: 0.707107 -1.00000 16: 0.382683 1.00000 17: 0.382683 0.766044 18: 0.382683 0.173648 19: 0.382683 -0.500000 20: 0.382683 -0.939693 21: 0.00000 0.939693 22: 0.00000 0.500000 23: 0.00000 -0.173648 24: 0.00000 -0.766044 25: 0.00000 -1.00000 26: -0.382683 1.00000 27: -0.382683 0.766044 28: -0.382683 0.173648 29: -0.382683 -0.500000 30: -0.382683 -0.939693 31: -0.707107 0.939693 32: -0.707107 0.500000 33: -0.707107 -0.173648 34: -0.707107 -0.766044 35: -0.707107 -1.00000 36: -0.923880 1.00000 37: -0.923880 0.766044 38: -0.923880 0.173648 39: -0.923880 -0.500000 40: -0.923880 -0.939693 41: -1.00000 0.939693 42: -1.00000 0.500000 43: -1.00000 -0.173648 44: -1.00000 -0.766044 45: -1.00000 -1.00000 Level 9 Padua points: Row 1 2 Col 1: 1.00000 0.951057 2: 1.00000 0.587785 3: 1.00000 0.00000 4: 1.00000 -0.587785 5: 1.00000 -0.951057 6: 0.939693 1.00000 7: 0.939693 0.809017 8: 0.939693 0.309017 9: 0.939693 -0.309017 10: 0.939693 -0.809017 11: 0.939693 -1.00000 12: 0.766044 0.951057 13: 0.766044 0.587785 14: 0.766044 0.00000 15: 0.766044 -0.587785 16: 0.766044 -0.951057 17: 0.500000 1.00000 18: 0.500000 0.809017 19: 0.500000 0.309017 20: 0.500000 -0.309017 21: 0.500000 -0.809017 22: 0.500000 -1.00000 23: 0.173648 0.951057 24: 0.173648 0.587785 25: 0.173648 0.00000 26: 0.173648 -0.587785 27: 0.173648 -0.951057 28: -0.173648 1.00000 29: -0.173648 0.809017 30: -0.173648 0.309017 31: -0.173648 -0.309017 32: -0.173648 -0.809017 33: -0.173648 -1.00000 34: -0.500000 0.951057 35: -0.500000 0.587785 36: -0.500000 0.00000 37: -0.500000 -0.587785 38: -0.500000 -0.951057 39: -0.766044 1.00000 40: -0.766044 0.809017 41: -0.766044 0.309017 42: -0.766044 -0.309017 43: -0.766044 -0.809017 44: -0.766044 -1.00000 45: -0.939693 0.951057 46: -0.939693 0.587785 47: -0.939693 0.00000 48: -0.939693 -0.587785 49: -0.939693 -0.951057 50: -1.00000 1.00000 51: -1.00000 0.809017 52: -1.00000 0.309017 53: -1.00000 -0.309017 54: -1.00000 -0.809017 55: -1.00000 -1.00000 Level 10 Padua points: Row 1 2 Col 1: 1.00000 0.959493 2: 1.00000 0.654861 3: 1.00000 0.142315 4: 1.00000 -0.415415 5: 1.00000 -0.841254 6: 1.00000 -1.00000 7: 0.951057 1.00000 8: 0.951057 0.841254 9: 0.951057 0.415415 10: 0.951057 -0.142315 11: 0.951057 -0.654861 12: 0.951057 -0.959493 13: 0.809017 0.959493 14: 0.809017 0.654861 15: 0.809017 0.142315 16: 0.809017 -0.415415 17: 0.809017 -0.841254 18: 0.809017 -1.00000 19: 0.587785 1.00000 20: 0.587785 0.841254 21: 0.587785 0.415415 22: 0.587785 -0.142315 23: 0.587785 -0.654861 24: 0.587785 -0.959493 25: 0.309017 0.959493 26: 0.309017 0.654861 27: 0.309017 0.142315 28: 0.309017 -0.415415 29: 0.309017 -0.841254 30: 0.309017 -1.00000 31: 0.00000 1.00000 32: 0.00000 0.841254 33: 0.00000 0.415415 34: 0.00000 -0.142315 35: 0.00000 -0.654861 36: 0.00000 -0.959493 37: -0.309017 0.959493 38: -0.309017 0.654861 39: -0.309017 0.142315 40: -0.309017 -0.415415 41: -0.309017 -0.841254 42: -0.309017 -1.00000 43: -0.587785 1.00000 44: -0.587785 0.841254 45: -0.587785 0.415415 46: -0.587785 -0.142315 47: -0.587785 -0.654861 48: -0.587785 -0.959493 49: -0.809017 0.959493 50: -0.809017 0.654861 51: -0.809017 0.142315 52: -0.809017 -0.415415 53: -0.809017 -0.841254 54: -0.809017 -1.00000 55: -0.951057 1.00000 56: -0.951057 0.841254 57: -0.951057 0.415415 58: -0.951057 -0.142315 59: -0.951057 -0.654861 60: -0.951057 -0.959493 61: -1.00000 0.959493 62: -1.00000 0.654861 63: -1.00000 0.142315 64: -1.00000 -0.415415 65: -1.00000 -0.841254 66: -1.00000 -1.00000 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 1 1.00000 0.707107 1.00000 0.707107 2 1.00000 -0.707107 1.00000 -0.707107 3 0.500000 1.00000 0.500000 1.00000 4 0.500000 0.00000 0.500000 0.00000 5 0.500000 -1.00000 0.500000 -1.00000 6 -0.500000 0.707107 -0.500000 0.707107 7 -0.500000 -0.707107 -0.500000 -0.707107 8 -1.00000 1.00000 -1.00000 1.00000 9 -1.00000 0.00000 -1.00000 0.00000 10 -1.00000 -1.00000 -1.00000 -1.00000 Level 4 Padua points 1 1.00000 0.809017 1.00000 0.809017 2 1.00000 -0.309017 1.00000 -0.309017 3 1.00000 -1.00000 1.00000 -1.00000 4 0.707107 1.00000 0.707107 1.00000 5 0.707107 0.309017 0.707107 0.309017 6 0.707107 -0.809017 0.707107 -0.809017 7 0.00000 0.809017 0.00000 0.809017 8 0.00000 -0.309017 0.00000 -0.309017 9 0.00000 -1.00000 0.00000 -1.00000 10 -0.707107 1.00000 -0.707107 1.00000 11 -0.707107 0.309017 -0.707107 0.309017 12 -0.707107 -0.809017 -0.707107 -0.809017 13 -1.00000 0.809017 -1.00000 0.809017 14 -1.00000 -0.309017 -1.00000 -0.309017 15 -1.00000 -1.00000 -1.00000 -1.00000 TEST05 PADUA_WEIGHTS computes Padua quadrature weights. PADUA_WEIGHT_SET looks them up in a table. Level 3 Padua points 1 0.111111 0.111111 2 0.111111 0.111111 3 0.222222 0.222222 4 1.33333 1.33333 5 0.222222 0.222222 6 0.888889 0.888889 7 0.888889 0.888889 8 -0.555556E-01 -0.555556E-01 9 0.333333 0.333333 10 -0.555556E-01 -0.555556E-01 Maximum difference = 0.78E-15 Level 4 Padua points 1 0.611730E-01 0.611730E-01 2 0.810492E-01 0.810492E-01 3 -0.888889E-02 -0.888889E-02 4 0.533333E-01 0.533333E-01 5 0.625924 0.625924 6 0.387410 0.387410 7 0.545807 0.545807 8 0.983082 0.983082 9 0.711111E-01 0.711111E-01 10 0.533333E-01 0.533333E-01 11 0.625924 0.625924 12 0.387410 0.387410 13 0.611730E-01 0.611730E-01 14 0.810492E-01 0.810492E-01 15 -0.888889E-02 -0.888889E-02 Maximum difference = 0.12E-14 PADUA_PRB Normal end of execution. 11 June 2014 10:14:44.666 AM