09 April 2020 06:04:58 PM VANDERMONDE_APPROX_1D_TEST: C++ version Test the VANDERMONDE_APPROX_1D library. The R8LIB library is needed. The QR_SOLVE library is needed. The test needs the CONDITION library. The test needs the TEST_INTERP libary. TEST01: Approximate data from TEST_INTERP problem #1 Number of data points = 18 Using polynomial approximant of degree 0 L2 data approximation error = 0.392837 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 1 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 = 0.0613776 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 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 = 0.0374634 Normalized length of piecewise linear interpolant = 3.13553 Normalized length of polynomial interpolant = 3.37935 TEST01: Approximate data from TEST_INTERP problem #2 Number of data points = 18 Using polynomial approximant of degree 0 L2 data approximation error = 2.58162 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 1 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 interpolant = 1 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 = 0.89436 Normalized length of piecewise linear interpolant = 2.66086 Normalized length of polynomial interpolant = 7153.58 TEST01: Approximate data from TEST_INTERP problem #3 Number of data points = 11 Using polynomial approximant of degree 0 L2 data approximation error = 7.87737 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 1 TEST01: Approximate data from TEST_INTERP problem #3 Number of data points = 11 Using polynomial approximant of degree 1 L2 data approximation error = 4.4679 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 interpolant = 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 = 4.77316e-10 Normalized length of piecewise linear interpolant = 1.68472 Normalized length of polynomial interpolant = 3.88345 TEST01: Approximate data from TEST_INTERP problem #4 Number of data points = 8 Using polynomial approximant of degree 0 L2 data approximation error = 0.149984 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 1 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 interpolant = 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 = 0.14598 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 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 = 0.0559589 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 3.3304 TEST01: Approximate data from TEST_INTERP problem #4 Number of data points = 8 Using polynomial approximant of degree 4 L2 data approximation error = 0.0559577 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 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 = 0.00829484 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 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 = 1.14673e-14 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 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 = 5.17323e-15 Normalized length of piecewise linear interpolant = 3.25908 Normalized length of polynomial interpolant = 4.89584 TEST01: Approximate data from TEST_INTERP problem #5 Number of data points = 9 Using polynomial approximant of degree 0 L2 data approximation error = 0.143324 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 1 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 = 3.2218 Normalized length of polynomial interpolant = 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 = 0.13517 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 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 = 0.0717904 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 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 = 0.0391096 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 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 = 0.03589 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 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 = 2.12718e-12 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 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 = 7.5367e-13 Normalized length of piecewise linear interpolant = 3.2218 Normalized length of polynomial interpolant = 125.388 TEST01: Approximate data from TEST_INTERP problem #6 Number of data points = 49 Using polynomial approximant of degree 0 L2 data approximation error = 0.0530251 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 1 TEST01: Approximate data from TEST_INTERP problem #6 Number of data points = 49 Using polynomial approximant of degree 1 L2 data approximation error = 0.0525121 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 1.0062 TEST01: Approximate data from TEST_INTERP problem #6 Number of data points = 49 Using polynomial approximant of degree 2 L2 data approximation error = 0.0473605 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 1.2402 TEST01: Approximate data from TEST_INTERP problem #6 Number of data points = 49 Using polynomial approximant of degree 3 L2 data approximation error = 0.0437687 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 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 = 0.0424429 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 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 = 0.0363054 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 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 = 0.0272317 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 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 = 0.018759 Normalized length of piecewise linear interpolant = 2.68209 Normalized length of polynomial interpolant = 2.9594 TEST01: Approximate data from TEST_INTERP problem #7 Number of data points = 4 Using polynomial approximant of degree 0 L2 data approximation error = 0.25 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 1 TEST01: Approximate data from TEST_INTERP problem #7 Number of data points = 4 Using polynomial approximant of degree 1 L2 data approximation error = 0.25 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 1 TEST01: Approximate data from TEST_INTERP problem #7 Number of data points = 4 Using polynomial approximant of degree 2 L2 data approximation error = 5.43896e-16 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 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 = 3.20093e-16 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 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 = 1.02245e-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 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 = 9.10451e-16 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 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 = 5.31662e-15 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 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 = 2.18769e-14 Normalized length of piecewise linear interpolant = 2.63961 Normalized length of polynomial interpolant = 10.4248 TEST01: Approximate data from TEST_INTERP problem #8 Number of data points = 12 Using polynomial approximant of degree 0 L2 data approximation error = 0.101554 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 1 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 interpolant = 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 = 0.000762201 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 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 = 0.000748027 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 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 = 0.000731706 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 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 = 0.000704364 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 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 = 0.000627667 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 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 = 2.06746e-11 Normalized length of piecewise linear interpolant = 2.31939 Normalized length of polynomial interpolant = 23167 VANDERMONDE_APPROX_1D_TEST: Normal end of execution. 09 April 2020 06:04:58 PM