01 April 2023 4:40:54.856 PM padua_test(): FORTRAN90 version Test padua(). 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 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 PADUA_POINTS_SET_TEST PADUA_POINTS_SET looks up Padua points 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 PADUA_WEIGHTS_TEST PADUA_WEIGHTS returns the weights of a Padua rule. Level 0 Padua weights: 1: 4.0000000 Level 1 Padua weights: 1: 2.0000000 2: 1.0000000 3: 1.0000000 Level 2 Padua weights: 1: 0.66666667 2: 0.37007434E-16 3: 0.44444444 4: 2.2222222 5: 0.66666667 6: 0.37007434E-16 Level 3 Padua weights: 1: 0.11111111 2: 0.11111111 3: 0.22222222 4: 1.3333333 5: 0.22222222 6: 0.88888889 7: 0.88888889 8: -0.55555556E-01 9: 0.33333333 10: -0.55555556E-01 Level 4 Padua weights: 1: 0.61173031E-01 2: 0.81049191E-01 3: -0.88888889E-02 4: 0.53333333E-01 5: 0.62592363 6: 0.38740971 7: 0.54580669 8: 0.98308220 9: 0.71111111E-01 10: 0.53333333E-01 11: 0.62592363 12: 0.38740971 13: 0.61173031E-01 14: 0.81049191E-01 15: -0.88888889E-02 Level 5 Padua weights: 1: 0.20740741E-01 2: 0.38518519E-01 3: 0.20740741E-01 4: 0.31893132E-01 5: 0.32884991 6: 0.32884991 7: 0.31893132E-01 8: 0.28045178 9: 0.63761036 10: 0.28045178 11: 0.45143905E-01 12: 0.55411305 13: 0.55411305 14: 0.45143905E-01 15: 0.18769637 16: 0.34609335 17: 0.18769637 18: -0.10370370E-01 19: 0.50370370E-01 20: 0.50370370E-01 21: -0.10370370E-01 Level 6 Padua weights: 1: 0.14254319E-01 2: 0.26339293E-01 3: 0.19572676E-01 4: -0.30234316E-02 5: 0.12093726E-01 6: 0.17431446 7: 0.22089002 8: 0.10063830 9: 0.16772342 10: 0.40270585 11: 0.32450648 12: 0.19349962E-01 13: 0.24792139E-01 14: 0.37218246 15: 0.44896331 16: 0.19533194 17: 0.16772342 18: 0.40270585 19: 0.32450648 20: 0.19349962E-01 21: 0.12093726E-01 22: 0.17431446 23: 0.22089002 24: 0.10063830 25: 0.14254319E-01 26: 0.26339293E-01 27: 0.19572676E-01 28: -0.30234316E-02 Level 7 Padua weights: 1: 0.63558815E-02 2: 0.14052282E-01 3: 0.14052282E-01 4: 0.63558815E-02 5: 0.86499231E-02 6: 0.10620079 7: 0.15058058 8: 0.10620079 9: 0.86499231E-02 10: 0.96469863E-01 11: 0.25577256 12: 0.25577256 13: 0.96469863E-01 14: 0.17713654E-01 15: 0.24909270 16: 0.34080411 17: 0.24909270 18: 0.17713654E-01 19: 0.12218180 20: 0.31502661 21: 0.31502661 22: 0.12218180 23: 0.12638691E-01 24: 0.19799449 25: 0.28321848 26: 0.19799449 27: 0.12638691E-01 28: 0.59493247E-01 29: 0.13064776 30: 0.13064776 31: 0.59493247E-01 32: -0.32879819E-02 33: 0.13378685E-01 34: 0.20634921E-01 35: 0.13378685E-01 36: -0.32879819E-02 Level 8 Padua weights: 1: 0.49306787E-02 2: 0.10264550E-01 3: 0.11114554E-01 4: 0.67060896E-02 5: -0.12698413E-02 6: 0.40616291E-02 7: 0.64001855E-01 8: 0.99659118E-01 9: 0.88383228E-01 10: 0.36331469E-01 11: 0.63425995E-01 12: 0.16994709 13: 0.19275014 14: 0.12583445 15: 0.67724868E-02 16: 0.10047718E-01 17: 0.16480980 18: 0.24773073 19: 0.21708414 20: 0.83763325E-01 21: 0.89366892E-01 22: 0.23640212 23: 0.27294095 24: 0.17843290 25: 0.10158730E-01 26: 0.10047718E-01 27: 0.16480980 28: 0.24773073 29: 0.21708414 30: 0.83763325E-01 31: 0.63425995E-01 32: 0.16994709 33: 0.19275014 34: 0.12583445 35: 0.67724868E-02 36: 0.40616291E-02 37: 0.64001855E-01 38: 0.99659118E-01 39: 0.88383228E-01 40: 0.36331469E-01 41: 0.49306787E-02 42: 0.10264550E-01 43: 0.11114554E-01 44: 0.67060896E-02 45: -0.12698413E-02 Level 9 Padua weights: 1: 0.25506906E-02 2: 0.60842301E-02 3: 0.74215168E-02 4: 0.60842301E-02 5: 0.25506906E-02 6: 0.32390756E-02 7: 0.43175876E-01 8: 0.70152505E-01 9: 0.70152505E-01 10: 0.43175876E-01 11: 0.32390756E-02 12: 0.40319010E-01 13: 0.11429762 14: 0.14133538 15: 0.11429762 16: 0.40319010E-01 17: 0.75061728E-02 18: 0.11421620 19: 0.18021767 20: 0.18021767 21: 0.11421620 22: 0.75061728E-02 23: 0.62349690E-01 24: 0.17304190 25: 0.21694182 26: 0.17304190 27: 0.62349690E-01 28: 0.81861762E-02 29: 0.12953556 30: 0.20614077 31: 0.20614077 32: 0.12953556 33: 0.81861762E-02 34: 0.55645456E-01 35: 0.15243920 36: 0.18771076 37: 0.15243920 38: 0.55645456E-01 39: 0.46594043E-02 40: 0.83545220E-01 41: 0.13707970 42: 0.13707970 43: 0.83545220E-01 44: 0.46594043E-02 45: 0.24252859E-01 46: 0.57273308E-01 47: 0.70082579E-01 48: 0.57273308E-01 49: 0.24252859E-01 50: -0.13686067E-02 51: 0.48379774E-02 52: 0.88763083E-02 53: 0.88763083E-02 54: 0.48379774E-02 55: -0.13686067E-02 Level 10 Padua weights: 1: 0.21353546E-02 2: 0.47057365E-02 3: 0.58917462E-02 4: 0.52500319E-02 5: 0.28432271E-02 6: -0.62407626E-03 7: 0.17196192E-02 8: 0.28434747E-01 9: 0.48633385E-01 10: 0.53265009E-01 11: 0.40995952E-01 12: 0.16109397E-01 13: 0.28557657E-01 14: 0.80662125E-01 15: 0.10532103 16: 0.96598728E-01 17: 0.57247117E-01 18: 0.28837697E-02 19: 0.46106970E-02 20: 0.79328509E-01 21: 0.13136863 22: 0.14301690 23: 0.10903907 24: 0.39812860E-01 25: 0.46030595E-01 26: 0.12835814 27: 0.16960572 28: 0.15623203 29: 0.93113564E-01 30: 0.50864957E-02 31: 0.57048406E-02 32: 0.98227492E-01 33: 0.16350375 34: 0.17641935 35: 0.13472815 36: 0.48948888E-01 37: 0.46030595E-01 38: 0.12835814 39: 0.16960572 40: 0.15623203 41: 0.93113564E-01 42: 0.50864957E-02 43: 0.46106970E-02 44: 0.79328509E-01 45: 0.13136863 46: 0.14301690 47: 0.10903907 48: 0.39812860E-01 49: 0.28557657E-01 50: 0.80662125E-01 51: 0.10532103 52: 0.96598728E-01 53: 0.57247117E-01 54: 0.28837697E-02 55: 0.17196192E-02 56: 0.28434747E-01 57: 0.48633385E-01 58: 0.53265009E-01 59: 0.40995952E-01 60: 0.16109397E-01 61: 0.21353546E-02 62: 0.47057365E-02 63: 0.58917462E-02 64: 0.52500319E-02 65: 0.28432271E-02 66: -0.62407626E-03 PADUA_WEIGHTS_SET_TEST PADUA_WEIGHTS_SET looks up Padua weights 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_TEST Normal end of execution. 01 April 2023 4:40:54.858 PM