19 January 2017 08:20:40 PM PADUA_PRB C version Test the PADUA library. PADUA_ORDER_TEST 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 PADUA_PLOT_TEST 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'. PADUA_POINTS_TEST 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 PADUA_POINTS_SET_TEST PADUA_POINTS_SET looks up Padua points 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 0.707107 5 -0.5 0.707107 0.5 -1 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 PADUA_WEIGHTS_TEST PADUA_WEIGHTS returns the weights of a Padua rule. Level 0 Padua weights: 0: 4 Level 1 Padua weights: 0: 2 1: 1 2: 1 Level 2 Padua weights: 0: 0.666667 1: 3.70074e-17 2: 0.444444 3: 2.22222 4: 0.666667 5: 3.70074e-17 Level 3 Padua weights: 0: 0.111111 1: 0.111111 2: 0.222222 3: 1.33333 4: 0.222222 5: 0.888889 6: 0.888889 7: -0.0555556 8: 0.333333 9: -0.0555556 Level 4 Padua weights: 0: 0.061173 1: 0.0810492 2: -0.00888889 3: 0.0533333 4: 0.625924 5: 0.38741 6: 0.545807 7: 0.983082 8: 0.0711111 9: 0.0533333 10: 0.625924 11: 0.38741 12: 0.061173 13: 0.0810492 14: -0.00888889 Level 5 Padua weights: 0: 0.0207407 1: 0.0385185 2: 0.0207407 3: 0.0318931 4: 0.32885 5: 0.32885 6: 0.0318931 7: 0.280452 8: 0.63761 9: 0.280452 10: 0.0451439 11: 0.554113 12: 0.554113 13: 0.0451439 14: 0.187696 15: 0.346093 16: 0.187696 17: -0.0103704 18: 0.0503704 19: 0.0503704 20: -0.0103704 Level 6 Padua weights: 0: 0.0142543 1: 0.0263393 2: 0.0195727 3: -0.00302343 4: 0.0120937 5: 0.174314 6: 0.22089 7: 0.100638 8: 0.167723 9: 0.402706 10: 0.324506 11: 0.01935 12: 0.0247921 13: 0.372182 14: 0.448963 15: 0.195332 16: 0.167723 17: 0.402706 18: 0.324506 19: 0.01935 20: 0.0120937 21: 0.174314 22: 0.22089 23: 0.100638 24: 0.0142543 25: 0.0263393 26: 0.0195727 27: -0.00302343 Level 7 Padua weights: 0: 0.00635588 1: 0.0140523 2: 0.0140523 3: 0.00635588 4: 0.00864992 5: 0.106201 6: 0.150581 7: 0.106201 8: 0.00864992 9: 0.0964699 10: 0.255773 11: 0.255773 12: 0.0964699 13: 0.0177137 14: 0.249093 15: 0.340804 16: 0.249093 17: 0.0177137 18: 0.122182 19: 0.315027 20: 0.315027 21: 0.122182 22: 0.0126387 23: 0.197994 24: 0.283218 25: 0.197994 26: 0.0126387 27: 0.0594932 28: 0.130648 29: 0.130648 30: 0.0594932 31: -0.00328798 32: 0.0133787 33: 0.0206349 34: 0.0133787 35: -0.00328798 Level 8 Padua weights: 0: 0.00493068 1: 0.0102646 2: 0.0111146 3: 0.00670609 4: -0.00126984 5: 0.00406163 6: 0.0640019 7: 0.0996591 8: 0.0883832 9: 0.0363315 10: 0.063426 11: 0.169947 12: 0.19275 13: 0.125834 14: 0.00677249 15: 0.0100477 16: 0.16481 17: 0.247731 18: 0.217084 19: 0.0837633 20: 0.0893669 21: 0.236402 22: 0.272941 23: 0.178433 24: 0.0101587 25: 0.0100477 26: 0.16481 27: 0.247731 28: 0.217084 29: 0.0837633 30: 0.063426 31: 0.169947 32: 0.19275 33: 0.125834 34: 0.00677249 35: 0.00406163 36: 0.0640019 37: 0.0996591 38: 0.0883832 39: 0.0363315 40: 0.00493068 41: 0.0102646 42: 0.0111146 43: 0.00670609 44: -0.00126984 Level 9 Padua weights: 0: 0.00255069 1: 0.00608423 2: 0.00742152 3: 0.00608423 4: 0.00255069 5: 0.00323908 6: 0.0431759 7: 0.0701525 8: 0.0701525 9: 0.0431759 10: 0.00323908 11: 0.040319 12: 0.114298 13: 0.141335 14: 0.114298 15: 0.040319 16: 0.00750617 17: 0.114216 18: 0.180218 19: 0.180218 20: 0.114216 21: 0.00750617 22: 0.0623497 23: 0.173042 24: 0.216942 25: 0.173042 26: 0.0623497 27: 0.00818618 28: 0.129536 29: 0.206141 30: 0.206141 31: 0.129536 32: 0.00818618 33: 0.0556455 34: 0.152439 35: 0.187711 36: 0.152439 37: 0.0556455 38: 0.0046594 39: 0.0835452 40: 0.13708 41: 0.13708 42: 0.0835452 43: 0.0046594 44: 0.0242529 45: 0.0572733 46: 0.0700826 47: 0.0572733 48: 0.0242529 49: -0.00136861 50: 0.00483798 51: 0.00887631 52: 0.00887631 53: 0.00483798 54: -0.00136861 Level 10 Padua weights: 0: 0.00213535 1: 0.00470574 2: 0.00589175 3: 0.00525003 4: 0.00284323 5: -0.000624076 6: 0.00171962 7: 0.0284347 8: 0.0486334 9: 0.053265 10: 0.040996 11: 0.0161094 12: 0.0285577 13: 0.0806621 14: 0.105321 15: 0.0965987 16: 0.0572471 17: 0.00288377 18: 0.0046107 19: 0.0793285 20: 0.131369 21: 0.143017 22: 0.109039 23: 0.0398129 24: 0.0460306 25: 0.128358 26: 0.169606 27: 0.156232 28: 0.0931136 29: 0.0050865 30: 0.00570484 31: 0.0982275 32: 0.163504 33: 0.176419 34: 0.134728 35: 0.0489489 36: 0.0460306 37: 0.128358 38: 0.169606 39: 0.156232 40: 0.0931136 41: 0.0050865 42: 0.0046107 43: 0.0793285 44: 0.131369 45: 0.143017 46: 0.109039 47: 0.0398129 48: 0.0285577 49: 0.0806621 50: 0.105321 51: 0.0965987 52: 0.0572471 53: 0.00288377 54: 0.00171962 55: 0.0284347 56: 0.0486334 57: 0.053265 58: 0.040996 59: 0.0161094 60: 0.00213535 61: 0.00470574 62: 0.00589175 63: 0.00525003 64: 0.00284323 65: -0.000624076 PADUA_WEIGHTS_SET_TEST PADUA_WEIGHTS_SET looks up Padua weights in a table. Level 3 Padua weights Computed Lookup 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 weights Computed Lookup 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. 19 January 2017 08:20:40 PM