09 April 2020 08:24:58 PM VANDERMONDE_INTERP_1D_TEST: C++ 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: 0: 0 24 1: 1 0 2: 2 0 3: 3 0 4: 4 0 Vandermonde interpolant coefficients: 0: 24 1: -50 2: 35 3: -10 4: 1 Vandermonde interpolant polynomial: p(x) = 1 * x ^ 4 - 10 * x ^ 3 + 35 * x ^ 2 - 50 * x + 24 VANDERMONDE_MATRIX_1D_TEST VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation. Vandermonde matrix: Col: 0 1 2 3 Row 0: 1 -1 1 -1 1: 1 2 4 8 2: 1 3 9 27 3: 1 5 25 125 VANDERMONDE_VALUE_1D_TEST VANDERMONDE_VALUE_1D evaluates a Vandermonde interpolant. The polynomial: p(x) = 1 * x ^ 4 - 10 * x ^ 3 + 35 * x ^ 2 - 50 * x + 24 X, P(X): 0: 0 24 1: 0.333333 10.8642 2: 0.666667 3.45679 3: 1 0 4: 1.33333 -0.987654 5: 1.66667 -0.691358 6: 2 0 7: 2.33333 0.493827 8: 2.66667 0.493827 9: 3 0 10: 3.33333 -0.691358 11: 3.66667 -0.987654 12: 4 0 13: 4.33333 3.45679 14: 4.66667 10.8642 15: 5 24 TEST01: Interpolate data from TEST_INTERP problem #1 Number of data points = 18 Condition of Vandermonde matrix is 4.77869e+26 L2 interpolation error averaged per interpolant node = 7.59901e-05 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 1.81734e+34 L2 interpolation error averaged per interpolant node = 1408.99 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 8.8374e+09 TEST01: Interpolate data from TEST_INTERP problem #3 Number of data points = 11 Condition of Vandermonde matrix is 2.49182e+14 L2 interpolation error averaged per interpolant node = 4.43613e-10 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 = 6.98598e-14 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 1.1583e+07 L2 interpolation error averaged per interpolant node = 5.47696e-12 Normalized length of piecewise linear interpolant = 3.2218 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 1.64361e+159 L2 interpolation error averaged per interpolant node = 124.311 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 21692.6 TEST01: Interpolate data from TEST_INTERP problem #7 Number of data points = 4 Condition of Vandermonde matrix is 475 L2 interpolation error averaged per interpolant node = 2.35514e-16 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 3.64961e+09 L2 interpolation error averaged per interpolant node = 4.73764e-11 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 23167 TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #1 Number of data points = 18 Data array: Row: 0 1 Col 0: 0 4 1: 1 5 2: 2 6 3: 4 6 4: 5 5 5: 6 3 6: 7 1 7: 8 1 8: 9 1 9: 10 3 10: 11 4 11: 12 4 12: 13 3 13: 14 3 14: 15 4 15: 16 4 16: 17 3 17: 18 0 Created graphics data file "data1.txt". Created graphics interp file "interp1.txt". Created graphics command file "commands1.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #2 Number of data points = 18 Data array: Row: 0 1 Col 0: 0 0 1: 1.34 5 2: 5 8.66 3: 10 10 4: 10.6 10.4 5: 10.7 12 6: 10.705 28.6 7: 10.8 30.2 8: 11.4 30.6 9: 19.6 30.6 10: 20.2 30.2 11: 20.295 28.6 12: 20.3 12 13: 20.4 10.4 14: 21 10 15: 26 8.66 16: 29.66 5 17: 31 0 Created graphics data file "data2.txt". Created graphics interp file "interp2.txt". Created graphics command file "commands2.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #3 Number of data points = 11 Data array: Row: 0 1 Col 0: 0 0 1: 2 10 2: 3 10 3: 5 10 4: 6 10 5: 8 10 6: 9 10.5 7: 11 15 8: 12 50 9: 14 60 10: 15 85 Created graphics data file "data3.txt". Created graphics interp file "interp3.txt". Created graphics command file "commands3.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #4 Number of data points = 8 Data array: Row: 0 1 Col 0: 0 0 1: 0.05 0.7 2: 0.1 1 3: 0.2 1 4: 0.8 0.3 5: 0.85 0.05 6: 0.9 0.1 7: 1 1 Created graphics data file "data4.txt". Created graphics interp file "interp4.txt". Created graphics command file "commands4.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #5 Number of data points = 9 Data array: Row: 0 1 Col 0: 0 0 1: 0.1 0.9 2: 0.2 0.95 3: 0.3 0.9 4: 0.4 0.1 5: 0.5 0.05 6: 0.6 0.05 7: 0.8 0.2 8: 1 1 Created graphics data file "data5.txt". Created graphics interp file "interp5.txt". Created graphics command file "commands5.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #6 Number of data points = 49 Data array: Row: 0 1 Col 0: 595 0.644 1: 605 0.622 2: 615 0.638 3: 625 0.649 4: 635 0.652 5: 645 0.639 6: 655 0.646 7: 665 0.657 8: 675 0.652 9: 685 0.655 10: 695 0.644 11: 705 0.663 12: 715 0.663 13: 725 0.668 14: 735 0.676 15: 745 0.676 16: 755 0.686 17: 765 0.679 18: 775 0.678 19: 785 0.683 20: 795 0.694 21: 805 0.699 22: 815 0.71 23: 825 0.73 24: 835 0.763 25: 845 0.812 26: 855 0.907 27: 865 1.044 28: 875 1.336 29: 885 1.881 30: 895 2.169 31: 905 2.075 32: 915 1.598 33: 925 1.211 34: 935 0.916 35: 945 0.746 36: 955 0.672 37: 965 0.627 38: 975 0.615 39: 985 0.607 40: 995 0.606 41: 1005 0.609 42: 1015 0.603 43: 1025 0.601 44: 1035 0.603 45: 1045 0.601 46: 1055 0.611 47: 1065 0.601 48: 1075 0.608 Created graphics data file "data6.txt". Created graphics interp file "interp6.txt". Created graphics command file "commands6.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #7 Number of data points = 4 Data array: Row: 0 1 Col 0: 0 1 1: 1 2 2: 4 2 3: 5 1 Created graphics data file "data7.txt". Created graphics interp file "interp7.txt". Created graphics command file "commands7.txt". TEST02: VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system for the interpolating polynomial. Interpolate data from TEST_INTERP problem #8 Number of data points = 12 Data array: Row: 0 1 Col 0: -1 1 1: -0.8 0.64 2: -0.6 0.36 3: -0.4 0.16 4: -0.2 0.04 5: 0 0 6: 0.2 0.04 7: 0.20001 0.05 8: 0.4 0.16 9: 0.6 0.36 10: 0.8 0.64 11: 1 1 Created graphics data file "data8.txt". Created graphics interp file "interp8.txt". Created graphics command file "commands8.txt". VANDERMONDE_INTERP_1D_TEST: Normal end of execution. 09 April 2020 08:24:58 PM