11 September 2021 2:14:16.198 PM VANDERMONDE_INTERP_1D_TEST: FORTRAN90 version Test the VANDERMONDE_INTERP_1D library. The QR_SOLVE library is needed. The R8LIB library is needed. This test needs the CONDITION library. This test needs the TEST_INTERP library. VANDERMONDE_COEF_1D_TEST VANDERMONDE_COEF_1D sets the Vandermonde coefficients for 1D interpolation. Interpolation data: 1 0.00000 24.0000 2 1.00000 0.00000 3 2.00000 0.00000 4 3.00000 0.00000 5 4.00000 0.00000 Vandermonde interpolant coefficients: 1: 24.000000 2: -50.000000 3: 35.000000 4: -10.000000 5: 1.0000000 Vandermonde interpolant polynomial: p(x) = 1.00000 * x ^ 4 - 10.0000 * x ^ 3 + 35.0000 * x ^ 2 - 50.0000 * x + 24.0000 VANDERMONDE_MATRIX_1D_TEST VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation. Vandermonde matrix: Col 1 2 3 4 Row 1: 1.00000 -1.00000 1.00000 -1.00000 2: 1.00000 2.00000 4.00000 8.00000 3: 1.00000 3.00000 9.00000 27.0000 4: 1.00000 5.00000 25.0000 125.000 VANDERMONDE_VALUE_1D_TEST VANDERMONDE_VALUE_1D evaluates a Vandermonde interpolant. The polynomial coefficients: p(x) = 1.00000 * x ^ 4 - 10.0000 * x ^ 3 + 35.0000 * x ^ 2 - 50.0000 * x + 24.0000 X, P(X) 1 0.00000 24.0000 2 0.333333 10.8642 3 0.666667 3.45679 4 1.00000 0.00000 5 1.33333 -0.987654 6 1.66667 -0.691358 7 2.00000 0.00000 8 2.33333 0.493827 9 2.66667 0.493827 10 3.00000 0.00000 11 3.33333 -0.691358 12 3.66667 -0.987654 13 4.00000 0.00000 14 4.33333 3.45679 15 4.66667 10.8642 16 5.00000 24.0000 TEST01: Interpolate data from TEST_INTERP problem # 1 Number of data points = 18 Condition of Vandermonde matrix is 0.477869E+27 L2 interpolation error averaged per interpolant node = 0.759901E-04 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 559.092 TEST01: Interpolate data from TEST_INTERP problem # 2 Number of data points = 18 Condition of Vandermonde matrix is 0.181734E+35 L2 interpolation error averaged per interpolant node = 1408.99 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 0.883740E+10 TEST01: Interpolate data from TEST_INTERP problem # 3 Number of data points = 11 Condition of Vandermonde matrix is 0.249182E+15 L2 interpolation error averaged per interpolant node = 0.611492E-09 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 4.30657 TEST01: Interpolate data from TEST_INTERP problem # 4 Number of data points = 8 Condition of Vandermonde matrix is 735473. L2 interpolation error averaged per interpolant node = 0.790641E-13 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 5.38186 TEST01: Interpolate data from TEST_INTERP problem # 5 Number of data points = 9 Condition of Vandermonde matrix is 0.115830E+08 L2 interpolation error averaged per interpolant node = 0.547696E-11 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial interpolant = 37.1961 TEST01: Interpolate data from TEST_INTERP problem # 6 Number of data points = 49 Condition of Vandermonde matrix is 0.164361+160 L2 interpolation error averaged per interpolant node = 4.47823 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 1057.25 TEST01: Interpolate data from TEST_INTERP problem # 7 Number of data points = 4 Condition of Vandermonde matrix is 475.000 L2 interpolation error averaged per interpolant node = 0.235514E-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 3.36731 TEST01: Interpolate data from TEST_INTERP problem # 8 Number of data points = 12 Condition of Vandermonde matrix is 0.364961E+10 L2 interpolation error averaged per interpolant node = 0.389812E-10 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 23167.0 TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 1 Number of data points = 18 Data array: Row 1 2 Col 1: 0.00000 4.00000 2: 1.00000 5.00000 3: 2.00000 6.00000 4: 4.00000 6.00000 5: 5.00000 5.00000 6: 6.00000 3.00000 7: 7.00000 1.00000 8: 8.00000 1.00000 9: 9.00000 1.00000 10: 10.0000 3.00000 11: 11.0000 4.00000 12: 12.0000 4.00000 13: 13.0000 3.00000 14: 14.0000 3.00000 15: 15.0000 4.00000 16: 16.0000 4.00000 17: 17.0000 3.00000 18: 18.0000 0.00000 Created graphics data file "data01.txt". Created graphics interp file "interp01.txt". Created graphics command file "commands01.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 2 Number of data points = 18 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 1.34000 5.00000 3: 5.00000 8.66000 4: 10.0000 10.0000 5: 10.6000 10.4000 6: 10.7000 12.0000 7: 10.7050 28.6000 8: 10.8000 30.2000 9: 11.4000 30.6000 10: 19.6000 30.6000 11: 20.2000 30.2000 12: 20.2950 28.6000 13: 20.3000 12.0000 14: 20.4000 10.4000 15: 21.0000 10.0000 16: 26.0000 8.66000 17: 29.6600 5.00000 18: 31.0000 0.00000 Created graphics data file "data02.txt". Created graphics interp file "interp02.txt". Created graphics command file "commands02.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 3 Number of data points = 11 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 2.00000 10.0000 3: 3.00000 10.0000 4: 5.00000 10.0000 5: 6.00000 10.0000 6: 8.00000 10.0000 7: 9.00000 10.5000 8: 11.0000 15.0000 9: 12.0000 50.0000 10: 14.0000 60.0000 11: 15.0000 85.0000 Created graphics data file "data03.txt". Created graphics interp file "interp03.txt". Created graphics command file "commands03.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 4 Number of data points = 8 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 0.500000E-01 0.700000 3: 0.100000 1.00000 4: 0.200000 1.00000 5: 0.800000 0.300000 6: 0.850000 0.500000E-01 7: 0.900000 0.100000 8: 1.00000 1.00000 Created graphics data file "data04.txt". Created graphics interp file "interp04.txt". Created graphics command file "commands04.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 5 Number of data points = 9 Data array: Row 1 2 Col 1: 0.00000 0.00000 2: 0.100000 0.900000 3: 0.200000 0.950000 4: 0.300000 0.900000 5: 0.400000 0.100000 6: 0.500000 0.500000E-01 7: 0.600000 0.500000E-01 8: 0.800000 0.200000 9: 1.00000 1.00000 Created graphics data file "data05.txt". Created graphics interp file "interp05.txt". Created graphics command file "commands05.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 6 Number of data points = 49 Data array: Row 1 2 Col 1: 595.000 0.644000 2: 605.000 0.622000 3: 615.000 0.638000 4: 625.000 0.649000 5: 635.000 0.652000 6: 645.000 0.639000 7: 655.000 0.646000 8: 665.000 0.657000 9: 675.000 0.652000 10: 685.000 0.655000 11: 695.000 0.644000 12: 705.000 0.663000 13: 715.000 0.663000 14: 725.000 0.668000 15: 735.000 0.676000 16: 745.000 0.676000 17: 755.000 0.686000 18: 765.000 0.679000 19: 775.000 0.678000 20: 785.000 0.683000 21: 795.000 0.694000 22: 805.000 0.699000 23: 815.000 0.710000 24: 825.000 0.730000 25: 835.000 0.763000 26: 845.000 0.812000 27: 855.000 0.907000 28: 865.000 1.04400 29: 875.000 1.33600 30: 885.000 1.88100 31: 895.000 2.16900 32: 905.000 2.07500 33: 915.000 1.59800 34: 925.000 1.21100 35: 935.000 0.916000 36: 945.000 0.746000 37: 955.000 0.672000 38: 965.000 0.627000 39: 975.000 0.615000 40: 985.000 0.607000 41: 995.000 0.606000 42: 1005.00 0.609000 43: 1015.00 0.603000 44: 1025.00 0.601000 45: 1035.00 0.603000 46: 1045.00 0.601000 47: 1055.00 0.611000 48: 1065.00 0.601000 49: 1075.00 0.608000 Created graphics data file "data06.txt". Created graphics interp file "interp06.txt". Created graphics command file "commands06.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 7 Number of data points = 4 Data array: Row 1 2 Col 1: 0.00000 1.00000 2: 1.00000 2.00000 3: 4.00000 2.00000 4: 5.00000 1.00000 Created graphics data file "data07.txt". Created graphics interp file "interp07.txt". Created graphics command file "commands07.txt". TEST02: VANDERMONDE_MATRIX_1D sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem # 8 Number of data points = 12 Data array: Row 1 2 Col 1: -1.00000 1.00000 2: -0.800000 0.640000 3: -0.600000 0.360000 4: -0.400000 0.160000 5: -0.200000 0.400000E-01 6: 0.00000 0.00000 7: 0.200000 0.400000E-01 8: 0.200010 0.500000E-01 9: 0.400000 0.160000 10: 0.600000 0.360000 11: 0.800000 0.640000 12: 1.00000 1.00000 Created graphics data file "data08.txt". Created graphics interp file "interp08.txt". Created graphics command file "commands08.txt". VANDERMONDE_INTERP_1D_TEST: Normal end of execution. 11 September 2021 2:14:16.208 PM