23-Feb-2019 09:16:25 vandermonde_interp_1d_test: MATLAB version Test vandermonde_interp_1d. The R8LIB library is needed. This test needs the TEST_INTERP library as well. VANDERMONDE_COEF_1D_TEST VANDERMONDE_COEF_1D sets the Vandermonde coefficients for 1D interpolation. Interpolation data: 1: 0 24 2: 1 0 3: 2 0 4: 3 0 5: 4 0 Vandermonde interpolant coefficients: 1: 24 2: -50 3: 35 4: -10 5: 1 Vandermonde interpolant polynomial: p(x) = 1.000000 * x^4 - 10.000000 * x^3 + 35.000000 * x^2 - 50.000000 * x + 24.000000 VANDERMONDE_MATRIX_1D_TEST VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation. Vandermonde matrix: Col: 1 2 3 4 Row 1 : 1 -1 1 -1 2 : 1 2 4 8 3 : 1 3 9 27 4 : 1 5 25 125 VANDERMONDE_VALUE_1D_TEST VANDERMONDE_VALUE_1D evaluates a Vandermonde interpolant. The Vandermonde interpolant: p(x) = 1.000000 * x^4 - 10.000000 * x^3 + 35.000000 * x^2 - 50.000000 * x + 24.000000 Vandermonde interpolant values: 1: 0 24 2: 0.333333 10.8642 3: 0.666667 3.45679 4: 1 0 5: 1.33333 -0.987654 6: 1.66667 -0.691358 7: 2 0 8: 2.33333 0.493827 9: 2.66667 0.493827 10: 3 0 11: 3.33333 -0.691358 12: 3.66667 -0.987654 13: 4 0 14: 4.33333 3.45679 15: 4.66667 10.8642 16: 5 24 VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #1. Number of data points = 18 Data array: Row: 1 2 Col 1: 0.000000 4.000000 2: 1.000000 5.000000 3: 2.000000 6.000000 4: 4.000000 6.000000 5: 5.000000 5.000000 6: 6.000000 3.000000 7: 7.000000 1.000000 8: 8.000000 1.000000 9: 9.000000 1.000000 10: 10.000000 3.000000 11: 11.000000 4.000000 12: 12.000000 4.000000 13: 13.000000 3.000000 14: 14.000000 3.000000 15: 15.000000 4.000000 16: 16.000000 4.000000 17: 17.000000 3.000000 18: 18.000000 0.000000 Condition of Vandermonde matrix is 1.3693e+23 L2 interpolation error averaged per interpolant node = 0.656266 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 8.13383 Created plot file "p01_data.png". Created plot file "p01_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #2. Number of data points = 18 Data array: Row: 1 2 Col 1: 0.000000 0.000000 2: 1.340000 5.000000 3: 5.000000 8.660000 4: 10.000000 10.000000 5: 10.600000 10.400000 6: 10.700000 12.000000 7: 10.705000 28.600000 8: 10.800000 30.200000 9: 11.400000 30.600000 10: 19.600000 30.600000 11: 20.200000 30.200000 12: 20.295000 28.600000 13: 20.300000 12.000000 14: 20.400000 10.400000 15: 21.000000 10.000000 16: 26.000000 8.660000 17: 29.660000 5.000000 18: 31.000000 0.000000 Condition of Vandermonde matrix is 3.75525e+26 L2 interpolation error averaged per interpolant node = 1.44334 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 60.0939 Created plot file "p02_data.png". Created plot file "p02_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #3. Number of data points = 11 Data array: Row: 1 2 Col 1: 0.000000 0.000000 2: 2.000000 10.000000 3: 3.000000 10.000000 4: 5.000000 10.000000 5: 6.000000 10.000000 6: 8.000000 10.000000 7: 9.000000 10.500000 8: 11.000000 15.000000 9: 12.000000 50.000000 10: 14.000000 60.000000 11: 15.000000 85.000000 Condition of Vandermonde matrix is 1.6913e+14 L2 interpolation error averaged per interpolant node = 6.09582e-10 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 4.30657 Created plot file "p03_data.png". Created plot file "p03_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #4. Number of data points = 8 Data array: Row: 1 2 Col 1: 0.000000 0.000000 2: 0.050000 0.700000 3: 0.100000 1.000000 4: 0.200000 1.000000 5: 0.800000 0.300000 6: 0.850000 0.050000 7: 0.900000 0.100000 8: 1.000000 1.000000 Condition of Vandermonde matrix is 356159 L2 interpolation error averaged per interpolant node = 3.37227e-14 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 5.38186 Created plot file "p04_data.png". Created plot file "p04_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #5. Number of data points = 9 Data array: Row: 1 2 Col 1: 0.000000 0.000000 2: 0.100000 0.900000 3: 0.200000 0.950000 4: 0.300000 0.900000 5: 0.400000 0.100000 6: 0.500000 0.050000 7: 0.600000 0.050000 8: 0.800000 0.200000 9: 1.000000 1.000000 Condition of Vandermonde matrix is 4.06242e+06 L2 interpolation error averaged per interpolant node = 3.51826e-12 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 37.1961 Created plot file "p05_data.png". Created plot file "p05_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #6. Number of data points = 49 Data array: Row: 1 2 Col 1: 595.000000 0.644000 2: 605.000000 0.622000 3: 615.000000 0.638000 4: 625.000000 0.649000 5: 635.000000 0.652000 6: 645.000000 0.639000 7: 655.000000 0.646000 8: 665.000000 0.657000 9: 675.000000 0.652000 10: 685.000000 0.655000 11: 695.000000 0.644000 12: 705.000000 0.663000 13: 715.000000 0.663000 14: 725.000000 0.668000 15: 735.000000 0.676000 16: 745.000000 0.676000 17: 755.000000 0.686000 18: 765.000000 0.679000 19: 775.000000 0.678000 20: 785.000000 0.683000 21: 795.000000 0.694000 22: 805.000000 0.699000 23: 815.000000 0.710000 24: 825.000000 0.730000 25: 835.000000 0.763000 26: 845.000000 0.812000 27: 855.000000 0.907000 28: 865.000000 1.044000 29: 875.000000 1.336000 30: 885.000000 1.881000 31: 895.000000 2.169000 32: 905.000000 2.075000 33: 915.000000 1.598000 34: 925.000000 1.211000 35: 935.000000 0.916000 36: 945.000000 0.746000 37: 955.000000 0.672000 38: 965.000000 0.627000 39: 975.000000 0.615000 40: 985.000000 0.607000 41: 995.000000 0.606000 42: 1005.000000 0.609000 43: 1015.000000 0.603000 44: 1025.000000 0.601000 45: 1035.000000 0.603000 46: 1045.000000 0.601000 47: 1055.000000 0.611000 48: 1065.000000 0.601000 49: 1075.000000 0.608000 Condition of Vandermonde matrix is 1.934e+147 L2 interpolation error averaged per interpolant node = 0.109701 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 2.94461 Created plot file "p06_data.png". Created plot file "p06_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #7. Number of data points = 4 Data array: Row: 1 2 Col 1: 0.000000 1.000000 2: 1.000000 2.000000 3: 4.000000 2.000000 4: 5.000000 1.000000 Condition of Vandermonde matrix is 367.189 L2 interpolation error averaged per interpolant node = 0 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 3.36731 Created plot file "p07_data.png". Created plot file "p07_poly.png". VANDERMONDE_INTERP_1D_TEST01: Interpolate data from TEST_INTERP problem #8. Number of data points = 12 Data array: Row: 1 2 Col 1: -1.000000 1.000000 2: -0.800000 0.640000 3: -0.600000 0.360000 4: -0.400000 0.160000 5: -0.200000 0.040000 6: 0.000000 0.000000 7: 0.200000 0.040000 8: 0.200010 0.050000 9: 0.400000 0.160000 10: 0.600000 0.360000 11: 0.800000 0.640000 12: 1.000000 1.000000 Condition of Vandermonde matrix is 1.01468e+09 L2 interpolation error averaged per interpolant node = 2.92709e-11 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 23167 Created plot file "p08_data.png". Created plot file "p08_poly.png". vandermonde_interp_1d_test: Normal end of execution. 23-Feb-2019 09:16:30