16 October 2012 9:33:07.173 AM VANDERMONDE_APPROX_1D_TEST: FORTRAN77 version Test the VANDERMONDE_APPROX_1D library. The QR_SOLVE library is needed. The R8LIB library is needed. This test needs the TEST_INTERP libary as well. TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.392837 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 1 L2 data approximation error = 0.350074 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.08357 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 2 L2 data approximation error = 0.344057 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.12211 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 3 L2 data approximation error = 0.332868 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 1.31026 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 4 L2 data approximation error = 0.199123 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 2.51647 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 5 L2 data approximation error = 0.190907 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 2.60932 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 9 L2 data approximation error = 0.613776E-01 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 3.22044 TEST01: Approximate data from TEST_INTERP problem # 1 Number of data points = 18 Using polynomial approximant of degree 12 L2 data approximation error = 0.374634E-01 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial approximant = 3.37935 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 2.58162 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 1 L2 data approximation error = 2.58162 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 2 L2 data approximation error = 1.80946 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.88131 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 3 L2 data approximation error = 1.80946 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.88131 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 4 L2 data approximation error = 1.76341 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.90124 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 5 L2 data approximation error = 1.76341 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 1.90124 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 9 L2 data approximation error = 1.30404 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 8.90486 TEST01: Approximate data from TEST_INTERP problem # 2 Number of data points = 18 Using polynomial approximant of degree 12 L2 data approximation error = 0.894360 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial approximant = 7153.58 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 7.87737 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 1 L2 data approximation error = 4.46790 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.28026 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 2 L2 data approximation error = 2.59431 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.48631 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 3 L2 data approximation error = 1.74627 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.58943 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 4 L2 data approximation error = 1.68297 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.61226 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 5 L2 data approximation error = 1.66663 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 1.59507 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 9 L2 data approximation error = 0.328589 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 3.28924 TEST01: Approximate data from TEST_INTERP problem # 3 Number of data points = 11 Using polynomial approximant of degree 12 L2 data approximation error = 0.324433E-09 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial approximant = 3.88345 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.149984 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 1 L2 data approximation error = 0.146011 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.02803 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 2 L2 data approximation error = 0.145980 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 1.03194 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 3 L2 data approximation error = 0.559589E-01 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.33040 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 4 L2 data approximation error = 0.559577E-01 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.32957 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 5 L2 data approximation error = 0.829484E-02 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 3.58478 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 9 L2 data approximation error = 0.177715E-13 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 4.81669 TEST01: Approximate data from TEST_INTERP problem # 4 Number of data points = 8 Using polynomial approximant of degree 12 L2 data approximation error = 0.651592E-14 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial approximant = 4.89584 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.143324 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 1 L2 data approximation error = 0.143322 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.00003 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 2 L2 data approximation error = 0.135170 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 1.31038 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 3 L2 data approximation error = 0.717904E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.05546 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 4 L2 data approximation error = 0.391096E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.42544 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 5 L2 data approximation error = 0.358900E-01 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 3.41454 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 9 L2 data approximation error = 0.199908E-11 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 47.9536 TEST01: Approximate data from TEST_INTERP problem # 5 Number of data points = 9 Using polynomial approximant of degree 12 L2 data approximation error = 0.615052E-12 Normalized length of piecewise linear interpolant = 3.22180 Normalized length of polynomial approximant = 125.388 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.530251E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 1 L2 data approximation error = 0.525121E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.00620 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 2 L2 data approximation error = 0.473605E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.24020 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 3 L2 data approximation error = 0.437687E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.43902 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 4 L2 data approximation error = 0.424429E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.51608 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 5 L2 data approximation error = 0.363054E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 1.97702 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 9 L2 data approximation error = 0.272317E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 2.51535 TEST01: Approximate data from TEST_INTERP problem # 6 Number of data points = 49 Using polynomial approximant of degree 12 L2 data approximation error = 0.187600E-01 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial approximant = 2.95947 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.250000 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 1 L2 data approximation error = 0.250000 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 2 L2 data approximation error = 0.590092E-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.36731 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 3 L2 data approximation error = 0.235514E-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.36731 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 4 L2 data approximation error = 0.101829E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.58258 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 5 L2 data approximation error = 0.129235E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 3.90825 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 9 L2 data approximation error = 0.534437E-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 6.52763 TEST01: Approximate data from TEST_INTERP problem # 7 Number of data points = 4 Using polynomial approximant of degree 12 L2 data approximation error = 0.216022E-13 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial approximant = 10.4248 TEST01: Approximate 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 Using polynomial approximant of degree 0 L2 data approximation error = 0.101554 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 1.00000 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 1 L2 data approximation error = 0.101522 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 1.00042 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 2 L2 data approximation error = 0.762201E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.31944 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 3 L2 data approximation error = 0.748027E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.31959 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 4 L2 data approximation error = 0.731706E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32028 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 5 L2 data approximation error = 0.704364E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32052 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 9 L2 data approximation error = 0.627667E-03 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 2.32096 TEST01: Approximate data from TEST_INTERP problem # 8 Number of data points = 12 Using polynomial approximant of degree 12 L2 data approximation error = 0.591022E-10 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial approximant = 23167.0 VANDERMONDE_APPROX_1D_TEST: Normal end of execution. 16 October 2012 9:33:07.179 AM