15 December 2008 8:50:38.067 AM TEST_APPROX_PRB FORTRAN90 version Demonstrate the TEST_APPROX test interpolation and approximation functions. TEST001 Demonstrate some of the bookkeeping routines. GET_PROB_NUM returns the number of problems. P00_TITLE returns the problem title. P00_TYPE returns the problem type. P00_LIMIT returns the problem limits. Number of problems = 11 Problem 1 Problem TITLE = "Runge example, 1 / ( x * x + 1 ), [-5,5]". Problem TYPE = 0 Problem lower limit A = -5.00000 Problem upper limit B = 5.00000 Problem 2 Problem TITLE = "Bernstein example, abs ( x ), [-1,1]". Problem TYPE = 0 Problem lower limit A = -1.00000 Problem upper limit B = 1.00000 Problem 3 Problem TITLE = "DeBoor example, Mars position, data vector". Problem TYPE = 1 Problem 4 Problem TITLE = "DeBoor example, roughly linear data". Problem TYPE = 1 Problem 5 Problem TITLE = "The pulse data, 0 0 0 0 0 1 0 0 0 0 0". Problem TYPE = 1 Problem 6 Problem TITLE = "The jump data, 0 0 0 0 0 1/2 1 1 1 1 1". Problem TYPE = 1 Problem 7 Problem TITLE = "DeBoor's Titanium Property". Problem TYPE = 1 Problem 8 Problem TITLE = "The Sawtooth". Problem TYPE = 1 Problem 9 Problem TITLE = "Concavity test". Problem TYPE = 1 Problem 10 Problem TITLE = "Extrapolation test.". Problem TYPE = 1 Problem 11 Problem TITLE = "Sunspot Data, 1700-1960.". Problem TYPE = 1 TEST002 P00_STORY prints the problem "story". Problem 1 This is a famous example, due to Runge. If equally spaced abscissas are used, the sequence of interpolating polynomials Pn(X) diverges, in the sense that the max norm of the difference between Pn(X) and F(X) becomes arbitrarily large as N increases. Problem 2 This example is due to Bernstein. If equally spaced abscissas are used, the sequence of interpolating polynomials Pn(X) only converges to F(X) at -1, 0, and 1. Problem 3 This example is due to deBoor. For this example, X is measured in days, and Y records the observed position of Mars in a heliocentric coordinate system. Problem 4 This example is due to deBoor. The data lies roughly along a straight line. Polynomial interpolation is inappropriate. Instead, a least squares approximation should be sought, of the form: F(X) = A + B * X Problem 5 The data is all zero except for a single value of 1 in the center. This data set is interesting because an interpolation method that is "local" will produce an interpolating curve that is exactly zero over most of the outlying intervals, whereas a nonlocal interpolation method may produce a curve that "wiggles" over the entire interpolation interval. Problem 6 Theoretically, the data is a step, 0 to the left of 5, and 1 to the right. To keep things simple, the data is defined to be 0 up to 5 - RADIUS, 1/2 at 5, 1 at 5 + RADIUS and beyond, with RADIUS set to a "small" value, currently 0.01. Some interpolation methods will violently overreact to this jump. Problem 7 This example is due to deBoor. This data represents a property of titanium as a function of temperature. Problem 8 This is a data vector. Problem 9 This is a data vector. Problem 10 This example is due to Pierre Blais. Data is only available over the interval [0, 238], but extrapolation is to be used to extend the approximate function to a maximum argument of 1023. The behavior of the extrapolated curve is of great interest. Problem 11 This example is due to Max Waldmeier. This data represents a measure of sunspot activity over the years 1700 to 1960. The X value is the year, and the Y value is a measure of the sunspot activity, which is usually, but not always, an integer. TEST01 Equally spaced polynomial interpolation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] Interpolating polynomial order = 2 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.384615E-01 0.20E-01 -3.00000 0.100000 0.384615E-01 0.62E-01 -2.00000 0.200000 0.384615E-01 0.16 -1.00000 0.500000 0.384615E-01 0.46 0.00000 1.00000 0.384615E-01 0.96 1.00000 0.500000 0.384615E-01 0.46 2.00000 0.200000 0.384615E-01 0.16 3.00000 0.100000 0.384615E-01 0.62E-01 4.00000 0.588235E-01 0.384615E-01 0.20E-01 5.00000 0.384615E-01 0.384615E-01 0.0 Interpolating polynomial order = 3 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.384615 -0.33 -3.00000 0.100000 0.653846 -0.55 -2.00000 0.200000 0.846154 -0.65 -1.00000 0.500000 0.961538 -0.46 0.00000 1.00000 1.00000 0.0 1.00000 0.500000 0.961538 -0.46 2.00000 0.200000 0.846154 -0.65 3.00000 0.100000 0.653846 -0.55 4.00000 0.588235E-01 0.384615 -0.33 5.00000 0.384615E-01 0.384615E-01 0.0 Interpolating polynomial order = 4 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.130090 -0.71E-01 -3.00000 0.100000 0.201357 -0.10 -2.00000 0.200000 0.252262 -0.52E-01 -1.00000 0.500000 0.282805 0.22 0.00000 1.00000 0.292986 0.71 1.00000 0.500000 0.282805 0.22 2.00000 0.200000 0.252262 -0.52E-01 3.00000 0.100000 0.201357 -0.10 4.00000 0.588235E-01 0.130090 -0.71E-01 5.00000 0.384615E-01 0.384615E-01 0.0 Interpolating polynomial order = 5 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 -0.379310 0.44 -3.00000 0.100000 -0.110080 0.21 -2.00000 0.200000 0.400531 -0.20 -1.00000 0.500000 0.834218 -0.33 0.00000 1.00000 1.00000 0.11E-15 1.00000 0.500000 0.834218 -0.33 2.00000 0.200000 0.400531 -0.20 3.00000 0.100000 -0.110080 0.21 4.00000 0.588235E-01 -0.379310 0.44 5.00000 0.384615E-01 0.384615E-01 -0.69E-16 Interpolating polynomial order = 6 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 -0.480769E-01 0.11 -3.00000 0.100000 0.100000 0.0 -2.00000 0.200000 0.321154 -0.12 -1.00000 0.500000 0.500000 0.0 0.00000 1.00000 0.567308 0.43 1.00000 0.500000 0.500000 0.0 2.00000 0.200000 0.321154 -0.12 3.00000 0.100000 0.100000 0.0 4.00000 0.588235E-01 -0.480769E-01 0.11 5.00000 0.384615E-01 0.384615E-01 0.0 Interpolating polynomial order = 7 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.519117 -0.46 -3.00000 0.100000 -0.590103E-01 0.16 -2.00000 0.200000 0.772552E-01 0.12 -1.00000 0.500000 0.681328 -0.18 0.00000 1.00000 1.00000 0.0 1.00000 0.500000 0.681328 -0.18 2.00000 0.200000 0.772552E-01 0.12 3.00000 0.100000 -0.590103E-01 0.16 4.00000 0.588235E-01 0.519117 -0.46 5.00000 0.384615E-01 0.384615E-01 -0.11E-14 Interpolating polynomial order = 8 X Y(X) Y_Interp Error -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.159338 -0.10 -3.00000 0.100000 0.255492E-01 0.74E-01 -2.00000 0.200000 0.225147 -0.25E-01 -1.00000 0.500000 0.582170 -0.82E-01 0.00000 1.00000 0.752641 0.25 1.00000 0.500000 0.582170 -0.82E-01 2.00000 0.200000 0.225147 -0.25E-01 3.00000 0.100000 0.255492E-01 0.74E-01 4.00000 0.588235E-01 0.159338 -0.10 5.00000 0.384615E-01 0.384615E-01 -0.82E-14 Problem 2 Bernstein example, abs ( x ), [-1,1] Interpolating polynomial order = 2 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 1.00000 -0.20 -0.600000 0.600000 1.00000 -0.40 -0.400000 0.400000 1.00000 -0.60 -0.200000 0.200000 1.00000 -0.80 0.00000 0.00000 1.00000 -1.0 0.200000 0.200000 1.00000 -0.80 0.400000 0.400000 1.00000 -0.60 0.600000 0.600000 1.00000 -0.40 0.800000 0.800000 1.00000 -0.20 1.00000 1.00000 1.00000 0.0 Interpolating polynomial order = 3 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.640000 0.16 -0.600000 0.600000 0.360000 0.24 -0.400000 0.400000 0.160000 0.24 -0.200000 0.200000 0.400000E-01 0.16 0.00000 0.00000 0.00000 0.0 0.200000 0.200000 0.400000E-01 0.16 0.400000 0.400000 0.160000 0.24 0.600000 0.600000 0.360000 0.24 0.800000 0.800000 0.640000 0.16 1.00000 1.00000 1.00000 0.0 Interpolating polynomial order = 4 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.730000 0.70E-01 -0.600000 0.600000 0.520000 0.80E-01 -0.400000 0.400000 0.370000 0.30E-01 -0.200000 0.200000 0.280000 -0.80E-01 0.00000 0.00000 0.250000 -0.25 0.200000 0.200000 0.280000 -0.80E-01 0.400000 0.400000 0.370000 0.30E-01 0.600000 0.600000 0.520000 0.80E-01 0.800000 0.800000 0.730000 0.70E-01 1.00000 1.00000 1.00000 0.0 Interpolating polynomial order = 5 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.947200 -0.15 -0.600000 0.600000 0.667200 -0.67E-01 -0.400000 0.400000 0.339200 0.61E-01 -0.200000 0.200000 0.912000E-01 0.11 0.00000 0.00000 0.00000 0.0 0.200000 0.200000 0.912000E-01 0.11 0.400000 0.400000 0.339200 0.61E-01 0.600000 0.600000 0.667200 -0.67E-01 0.800000 0.800000 0.947200 -0.15 1.00000 1.00000 1.00000 0.0 Interpolating polynomial order = 6 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.840625 -0.41E-01 -0.600000 0.600000 0.600000 0.0 -0.400000 0.400000 0.365625 0.34E-01 -0.200000 0.200000 0.200000 0.56E-16 0.00000 0.00000 0.140625 -0.14 0.200000 0.200000 0.200000 -0.17E-15 0.400000 0.400000 0.365625 0.34E-01 0.600000 0.600000 0.600000 -0.11E-15 0.800000 0.800000 0.840625 -0.41E-01 1.00000 1.00000 1.00000 0.0 Interpolating polynomial order = 7 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.664883 0.14 -0.600000 0.600000 0.646157 -0.46E-01 -0.400000 0.400000 0.435789 -0.36E-01 -0.200000 0.200000 0.137459 0.63E-01 0.00000 0.00000 0.00000 0.0 0.200000 0.200000 0.137459 0.63E-01 0.400000 0.400000 0.435789 -0.36E-01 0.600000 0.600000 0.646157 -0.46E-01 0.800000 0.800000 0.664883 0.14 1.00000 1.00000 1.00000 0.13E-14 Interpolating polynomial order = 8 X Y(X) Y_Interp Error -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.775587 0.24E-01 -0.600000 0.600000 0.617050 -0.17E-01 -0.400000 0.400000 0.394735 0.53E-02 -0.200000 0.200000 0.184102 0.16E-01 0.00000 0.00000 0.976563E-01 -0.98E-01 0.200000 0.200000 0.184102 0.16E-01 0.400000 0.400000 0.394735 0.53E-02 0.600000 0.600000 0.617050 -0.17E-01 0.800000 0.800000 0.775587 0.24E-01 1.00000 1.00000 1.00000 0.44E-15 Skipped problem 3 Wrong type. Skipped problem 4 Wrong type. Skipped problem 5 Wrong type. Skipped problem 6 Wrong type. Skipped problem 7 Wrong type. Skipped problem 8 Wrong type. Skipped problem 9 Wrong type. Skipped problem 10 Wrong type. Skipped problem 11 Wrong type. TEST02 Polynomial interpolation to a vector of data. Skipped problem 1 Wrong type. Skipped problem 2 Wrong type. Problem 3 DeBoor example, Mars position, data vector Interpolating polynomial order = 10 * 1250.50 1.39140 1255.50 1.38606 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13958 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957057 * 1330.50 0.905530 1335.50 0.851920 * 1340.50 0.796420 Problem 4 DeBoor example, roughly linear data Interpolating polynomial order = 11 * 1.00000 0.00000 1.50000 -4.83067 * 2.00000 0.600000 2.50000 2.39480 * 3.00000 1.77000 3.50000 1.37568 * 4.00000 1.92000 4.50000 2.78486 * 5.00000 3.31000 5.50000 3.42747 * 6.00000 3.52000 6.50000 3.92580 * 7.00000 4.59000 7.50000 5.14001 * 8.00000 5.31000 8.50000 5.32911 * 9.00000 5.79000 9.50000 6.80032 * 10.0000 7.06000 10.5000 5.07361 * 11.0000 7.17000 Problem 5 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 Interpolating polynomial order = 11 * 0.00000 0.00000 0.500000 4.93352 * 1.00000 0.00000 1.50000 -1.00154 * 2.00000 0.00000 2.50000 0.412399 * 3.00000 0.00000 3.50000 -0.320755 * 4.00000 0.00000 4.50000 0.666183 * 5.00000 1.00000 5.50000 0.666183 * 6.00000 0.00000 6.50000 -0.320755 * 7.00000 0.00000 7.50000 0.412399 * 8.00000 0.116573E-13 8.50000 -1.00154 * 9.00000 0.262290E-13 9.50000 4.93352 * 10.0000 0.209832E-12 Problem 6 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 Skipped problem 6 Too big. Problem 7 DeBoor's Titanium Property Skipped problem 7 Too big. Problem 8 The Sawtooth Skipped problem 8 Too big. Problem 9 Concavity test Interpolating polynomial order = 9 * 0.00000 0.00000 0.500000E-01 1.32484 * 0.100000 0.900000 0.150000 0.752561 * 0.200000 0.950000 0.250000 1.07856 * 0.300000 0.900000 0.350000 0.489281 * 0.400000 0.100000 0.450000 -0.517323E-01 * 0.500000 0.500000E-01 0.550000 0.190582 * 0.600000 0.500000E-01 0.700000 -1.36104 * 0.800000 0.200000 0.900000 11.7975 * 1.00000 1.00000 Problem 10 Extrapolation test. Interpolating polynomial order = 12 * 0.00000 0.00000 35.5000 53263.6 * 71.0000 7.75540 87.5000 -365.169 * 104.000 19.7062 119.500 52.6291 * 135.000 35.5379 140.000 38.2108 * 145.000 42.9154 152.500 50.0208 * 160.000 54.7752 170.500 59.3723 * 181.000 66.7587 187.000 72.5336 * 193.000 78.4929 199.000 84.1117 * 205.000 89.7683 210.000 95.2479 * 215.000 101.746 220.000 108.479 * 225.000 113.482 231.500 116.128 * 238.000 135.457 Problem 11 Sunspot Data, 1700-1960. Skipped problem 11 Too big. TEST03 Bernstein polynomial approximation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] Approximating polynomial degree = 2 -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.211538 -0.15 -3.00000 0.100000 0.346154 -0.25 -2.00000 0.200000 0.442308 -0.24 -1.00000 0.500000 0.500000 -0.11E-15 0.00000 1.00000 0.519231 0.48 1.00000 0.500000 0.500000 -0.11E-15 2.00000 0.200000 0.442308 -0.24 3.00000 0.100000 0.346154 -0.25 4.00000 0.588235E-01 0.211538 -0.15 5.00000 0.384615E-01 0.384615E-01 0.0 Approximating polynomial degree = 3 -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.995475E-01 -0.41E-01 -3.00000 0.100000 0.147059 -0.47E-01 -2.00000 0.200000 0.180995 0.19E-01 -1.00000 0.500000 0.201357 0.30 0.00000 1.00000 0.208145 0.79 1.00000 0.500000 0.201357 0.30 2.00000 0.200000 0.180995 0.19E-01 3.00000 0.100000 0.147059 -0.47E-01 4.00000 0.588235E-01 0.995475E-01 -0.41E-01 5.00000 0.384615E-01 0.384615E-01 0.0 Approximating polynomial degree = 4 -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.114556 -0.56E-01 -3.00000 0.100000 0.229443 -0.13 -2.00000 0.200000 0.341346 -0.14 -1.00000 0.500000 0.420424 0.80E-01 0.00000 1.00000 0.448773 0.55 1.00000 0.500000 0.420424 0.80E-01 2.00000 0.200000 0.341346 -0.14 3.00000 0.100000 0.229443 -0.13 4.00000 0.588235E-01 0.114556 -0.56E-01 5.00000 0.384615E-01 0.384615E-01 0.0 Approximating polynomial degree = 5 -5.00000 0.384615E-01 0.384615E-01 0.0 -4.00000 0.588235E-01 0.960615E-01 -0.37E-01 -3.00000 0.100000 0.182215 -0.82E-01 -2.00000 0.200000 0.265908 -0.66E-01 -1.00000 0.500000 0.324985 0.18 0.00000 1.00000 0.346154 0.65 1.00000 0.500000 0.324985 0.18 2.00000 0.200000 0.265908 -0.66E-01 3.00000 0.100000 0.182215 -0.82E-01 4.00000 0.588235E-01 0.960615E-01 -0.37E-01 5.00000 0.384615E-01 0.384615E-01 0.0 Problem 2 Bernstein example, abs ( x ), [-1,1] Approximating polynomial degree = 2 -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.820000 -0.20E-01 -0.600000 0.600000 0.680000 -0.80E-01 -0.400000 0.400000 0.580000 -0.18 -0.200000 0.200000 0.520000 -0.32 0.00000 0.00000 0.500000 -0.50 0.200000 0.200000 0.520000 -0.32 0.400000 0.400000 0.580000 -0.18 0.600000 0.600000 0.680000 -0.80E-01 0.800000 0.800000 0.820000 -0.20E-01 1.00000 1.00000 1.00000 0.0 Approximating polynomial degree = 3 -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.820000 -0.20E-01 -0.600000 0.600000 0.680000 -0.80E-01 -0.400000 0.400000 0.580000 -0.18 -0.200000 0.200000 0.520000 -0.32 0.00000 0.00000 0.500000 -0.50 0.200000 0.200000 0.520000 -0.32 0.400000 0.400000 0.580000 -0.18 0.600000 0.600000 0.680000 -0.80E-01 0.800000 0.800000 0.820000 -0.20E-01 1.00000 1.00000 1.00000 0.0 Approximating polynomial degree = 4 -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.803800 -0.38E-02 -0.600000 0.600000 0.628800 -0.29E-01 -0.400000 0.400000 0.491800 -0.92E-01 -0.200000 0.200000 0.404800 -0.20 0.00000 0.00000 0.375000 -0.38 0.200000 0.200000 0.404800 -0.20 0.400000 0.400000 0.491800 -0.92E-01 0.600000 0.600000 0.628800 -0.29E-01 0.800000 0.800000 0.803800 -0.38E-02 1.00000 1.00000 1.00000 0.0 Approximating polynomial degree = 5 -1.00000 1.00000 1.00000 0.0 -0.800000 0.800000 0.803800 -0.38E-02 -0.600000 0.600000 0.628800 -0.29E-01 -0.400000 0.400000 0.491800 -0.92E-01 -0.200000 0.200000 0.404800 -0.20 0.00000 0.00000 0.375000 -0.38 0.200000 0.200000 0.404800 -0.20 0.400000 0.400000 0.491800 -0.92E-01 0.600000 0.600000 0.628800 -0.29E-01 0.800000 0.800000 0.803800 -0.38E-02 1.00000 1.00000 1.00000 0.0 Skipped problem 3 Wrong type. Skipped problem 4 Wrong type. Skipped problem 5 Wrong type. Skipped problem 6 Wrong type. Skipped problem 7 Wrong type. Skipped problem 8 Wrong type. Skipped problem 9 Wrong type. Skipped problem 10 Wrong type. Skipped problem 11 Wrong type. TEST04 Linear spline interpolation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] X Y Y' * -5.00000 0.384615E-01 0.203620E-01 -4.50000 0.486425E-01 0.203620E-01 * -4.00000 0.588235E-01 0.411765E-01 -3.50000 0.794118E-01 0.411765E-01 * -3.00000 0.100000 0.100000 -2.50000 0.150000 0.100000 * -2.00000 0.200000 0.300000 -1.50000 0.350000 0.300000 * -1.00000 0.500000 0.500000 -0.500000 0.750000 0.500000 * 0.00000 1.00000 -0.500000 0.500000 0.750000 -0.500000 * 1.00000 0.500000 -0.300000 1.50000 0.350000 -0.300000 * 2.00000 0.200000 -0.100000 2.50000 0.150000 -0.100000 * 3.00000 0.100000 -0.411765E-01 3.50000 0.794118E-01 -0.411765E-01 * 4.00000 0.588235E-01 -0.203620E-01 4.50000 0.486425E-01 -0.203620E-01 * 5.00000 0.384615E-01 -0.203620E-01 Problem 2 Bernstein example, abs ( x ), [-1,1] X Y Y' * -1.00000 1.00000 -1.00000 -0.900000 0.900000 -1.00000 * -0.800000 0.800000 -1.00000 -0.700000 0.700000 -1.00000 * -0.600000 0.600000 -1.00000 -0.500000 0.500000 -1.00000 * -0.400000 0.400000 -1.00000 -0.300000 0.300000 -1.00000 * -0.200000 0.200000 -1.00000 -0.100000 0.100000 -1.00000 * 0.00000 0.00000 1.00000 0.100000 0.100000 1.00000 * 0.200000 0.200000 1.00000 0.300000 0.300000 1.00000 * 0.400000 0.400000 1.00000 0.500000 0.500000 1.00000 * 0.600000 0.600000 1.00000 0.700000 0.700000 1.00000 * 0.800000 0.800000 1.00000 0.900000 0.900000 1.00000 * 1.00000 1.00000 1.00000 Problem 3 DeBoor example, Mars position, data vector X Y Y' * 1250.50 1.39140 -0.144400E-02 1255.50 1.38418 -0.144400E-02 * 1260.50 1.37696 -0.291300E-02 1265.50 1.36240 -0.291300E-02 * 1270.50 1.34783 -0.432700E-02 1275.50 1.32620 -0.432700E-02 * 1280.50 1.30456 -0.566900E-02 1285.50 1.27622 -0.566900E-02 * 1290.50 1.24787 -0.692500E-02 1295.50 1.21325 -0.692500E-02 * 1300.50 1.17862 -0.808600E-02 1305.50 1.13819 -0.808600E-02 * 1310.50 1.09776 -0.914000E-02 1315.50 1.05206 -0.914000E-02 * 1320.50 1.00636 -0.100830E-01 1325.50 0.955945 -0.100830E-01 * 1330.50 0.905530 -0.109110E-01 1335.50 0.850975 -0.109110E-01 * 1340.50 0.796420 -0.109110E-01 Problem 4 DeBoor example, roughly linear data X Y Y' * 1.00000 0.00000 0.600000 1.50000 0.300000 0.600000 * 2.00000 0.600000 1.17000 2.50000 1.18500 1.17000 * 3.00000 1.77000 0.150000 3.50000 1.84500 0.150000 * 4.00000 1.92000 1.39000 4.50000 2.61500 1.39000 * 5.00000 3.31000 0.210000 5.50000 3.41500 0.210000 * 6.00000 3.52000 1.07000 6.50000 4.05500 1.07000 * 7.00000 4.59000 0.720000 7.50000 4.95000 0.720000 * 8.00000 5.31000 0.480000 8.50000 5.55000 0.480000 * 9.00000 5.79000 1.27000 9.50000 6.42500 1.27000 * 10.0000 7.06000 0.110000 10.5000 7.11500 0.110000 * 11.0000 7.17000 0.110000 Problem 5 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y Y' * 0.00000 0.00000 0.00000 0.500000 0.00000 0.00000 * 1.00000 0.00000 0.00000 1.50000 0.00000 0.00000 * 2.00000 0.00000 0.00000 2.50000 0.00000 0.00000 * 3.00000 0.00000 0.00000 3.50000 0.00000 0.00000 * 4.00000 0.00000 1.00000 4.50000 0.500000 1.00000 * 5.00000 1.00000 -1.00000 5.50000 0.500000 -1.00000 * 6.00000 0.00000 0.00000 6.50000 0.00000 0.00000 * 7.00000 0.00000 0.00000 7.50000 0.00000 0.00000 * 8.00000 0.00000 0.00000 8.50000 0.00000 0.00000 * 9.00000 0.00000 0.00000 9.50000 0.00000 0.00000 * 10.0000 0.00000 0.00000 Problem 6 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y Y' * 0.00000 0.00000 0.00000 0.416667 0.00000 0.00000 * 0.833333 0.00000 0.00000 1.25000 0.00000 0.00000 * 1.66667 0.00000 0.00000 2.08333 0.00000 0.00000 * 2.50000 0.00000 0.00000 2.91667 0.00000 0.00000 * 3.33333 0.00000 0.00000 3.75000 0.00000 0.00000 * 4.16667 0.00000 0.00000 4.58333 0.00000 0.00000 * 5.00000 0.500000 50.0000 5.41667 1.00000 0.00000 * 5.83333 1.00000 0.00000 6.25000 1.00000 0.00000 * 6.66667 1.00000 0.00000 7.08333 1.00000 0.00000 * 7.50000 1.00000 0.00000 7.91667 1.00000 0.00000 * 8.33333 1.00000 0.00000 8.75000 1.00000 0.00000 * 9.16667 1.00000 0.00000 9.58333 1.00000 0.00000 * 10.0000 1.00000 0.00000 Problem 7 DeBoor's Titanium Property X Y Y' * 595.000 0.644000 -0.220000E-02 600.000 0.633000 -0.220000E-02 * 605.000 0.622000 0.160000E-02 610.000 0.630000 0.160000E-02 * 615.000 0.638000 0.110000E-02 620.000 0.643500 0.110000E-02 * 625.000 0.649000 0.300000E-03 630.000 0.650500 0.300000E-03 * 635.000 0.652000 -0.130000E-02 640.000 0.645500 -0.130000E-02 * 645.000 0.639000 0.700000E-03 650.000 0.642500 0.700000E-03 * 655.000 0.646000 0.110000E-02 660.000 0.651500 0.110000E-02 * 665.000 0.657000 -0.500000E-03 670.000 0.654500 -0.500000E-03 * 675.000 0.652000 0.300000E-03 680.000 0.653500 0.300000E-03 * 685.000 0.655000 -0.110000E-02 690.000 0.649500 -0.110000E-02 * 695.000 0.644000 0.190000E-02 700.000 0.653500 0.190000E-02 * 705.000 0.663000 0.00000 710.000 0.663000 0.00000 * 715.000 0.663000 0.500000E-03 720.000 0.665500 0.500000E-03 * 725.000 0.668000 0.800000E-03 730.000 0.672000 0.800000E-03 * 735.000 0.676000 0.00000 740.000 0.676000 0.00000 * 745.000 0.676000 0.100000E-02 750.000 0.681000 0.100000E-02 * 755.000 0.686000 -0.700000E-03 760.000 0.682500 -0.700000E-03 * 765.000 0.679000 -0.100000E-03 770.000 0.678500 -0.100000E-03 * 775.000 0.678000 0.500000E-03 780.000 0.680500 0.500000E-03 * 785.000 0.683000 0.110000E-02 790.000 0.688500 0.110000E-02 * 795.000 0.694000 0.500000E-03 800.000 0.696500 0.500000E-03 * 805.000 0.699000 0.110000E-02 810.000 0.704500 0.110000E-02 * 815.000 0.710000 0.200000E-02 820.000 0.720000 0.200000E-02 * 825.000 0.730000 0.330000E-02 830.000 0.746500 0.330000E-02 * 835.000 0.763000 0.490000E-02 840.000 0.787500 0.490000E-02 * 845.000 0.812000 0.950000E-02 850.000 0.859500 0.950000E-02 * 855.000 0.907000 0.137000E-01 860.000 0.975500 0.137000E-01 * 865.000 1.04400 0.292000E-01 870.000 1.19000 0.292000E-01 * 875.000 1.33600 0.545000E-01 880.000 1.60850 0.545000E-01 * 885.000 1.88100 0.288000E-01 890.000 2.02500 0.288000E-01 * 895.000 2.16900 -0.940000E-02 900.000 2.12200 -0.940000E-02 * 905.000 2.07500 -0.477000E-01 910.000 1.83650 -0.477000E-01 * 915.000 1.59800 -0.387000E-01 920.000 1.40450 -0.387000E-01 * 925.000 1.21100 -0.295000E-01 930.000 1.06350 -0.295000E-01 * 935.000 0.916000 -0.170000E-01 940.000 0.831000 -0.170000E-01 * 945.000 0.746000 -0.740000E-02 950.000 0.709000 -0.740000E-02 * 955.000 0.672000 -0.450000E-02 960.000 0.649500 -0.450000E-02 * 965.000 0.627000 -0.120000E-02 970.000 0.621000 -0.120000E-02 * 975.000 0.615000 -0.800000E-03 980.000 0.611000 -0.800000E-03 * 985.000 0.607000 -0.100000E-03 990.000 0.606500 -0.100000E-03 * 995.000 0.606000 0.300000E-03 1000.00 0.607500 0.300000E-03 * 1005.00 0.609000 -0.600000E-03 1010.00 0.606000 -0.600000E-03 * 1015.00 0.603000 -0.200000E-03 1020.00 0.602000 -0.200000E-03 * 1025.00 0.601000 0.200000E-03 1030.00 0.602000 0.200000E-03 * 1035.00 0.603000 -0.200000E-03 1040.00 0.602000 -0.200000E-03 * 1045.00 0.601000 0.100000E-02 1050.00 0.606000 0.100000E-02 * 1055.00 0.611000 -0.100000E-02 1060.00 0.606000 -0.100000E-02 * 1065.00 0.601000 0.700000E-03 1070.00 0.604500 0.700000E-03 * 1075.00 0.608000 0.700000E-03 Problem 8 The Sawtooth X Y Y' * 0.00000 0.00000 2.00000 0.833333E-01 0.166667 2.00000 * 0.166667 0.333333 2.00000 0.250000 0.500000 2.00000 * 0.333333 0.666667 2.00000 0.416667 0.833333 2.00000 * 0.500000 1.00000 -2.00000 0.583333 0.833333 -2.00000 * 0.666667 0.666667 -2.00000 0.750000 0.500000 -2.00000 * 0.833333 0.333333 -2.00000 0.916667 0.166667 -2.00000 * 1.00000 0.00000 2.00000 1.08333 0.166667 2.00000 * 1.16667 0.333333 2.00000 1.25000 0.500000 2.00000 * 1.33333 0.666667 2.00000 1.41667 0.833333 2.00000 * 1.50000 1.00000 -2.00000 1.58333 0.833333 -2.00000 * 1.66667 0.666667 -2.00000 1.75000 0.500000 -2.00000 * 1.83333 0.333333 -2.00000 1.91667 0.166667 -2.00000 * 2.00000 0.00000 2.00000 2.08333 0.166667 2.00000 * 2.16667 0.333333 2.00000 2.25000 0.500000 2.00000 * 2.33333 0.666667 2.00000 2.41667 0.833333 2.00000 * 2.50000 1.00000 -2.00000 2.58333 0.833333 -2.00000 * 2.66667 0.666667 -2.00000 2.75000 0.500000 -2.00000 * 2.83333 0.333333 -2.00000 2.91667 0.166667 -2.00000 * 3.00000 0.00000 2.00000 3.08333 0.166667 2.00000 * 3.16667 0.333333 2.00000 3.25000 0.500000 2.00000 * 3.33333 0.666667 2.00000 3.41667 0.833333 2.00000 * 3.50000 1.00000 -2.00000 3.58333 0.833333 -2.00000 * 3.66667 0.666667 -2.00000 3.75000 0.500000 -2.00000 * 3.83333 0.333333 -2.00000 3.91667 0.166667 -2.00000 * 4.00000 0.00000 2.00000 4.08333 0.166667 2.00000 * 4.16667 0.333333 2.00000 4.25000 0.500000 2.00000 * 4.33333 0.666667 2.00000 4.41667 0.833333 2.00000 * 4.50000 1.00000 -2.00000 4.58333 0.833333 -2.00000 * 4.66667 0.666667 -2.00000 4.75000 0.500000 -2.00000 * 4.83333 0.333333 -2.00000 4.91667 0.166667 -2.00000 * 5.00000 0.00000 -2.00000 Problem 9 Concavity test X Y Y' * 0.00000 0.00000 9.00000 0.625000E-01 0.562500 9.00000 * 0.125000 0.912500 0.500000 0.187500 0.943750 0.500000 * 0.250000 0.925000 -0.500000 0.312500 0.800000 -8.00000 * 0.375000 0.300000 -8.00000 0.437500 0.812500E-01 -0.500000 * 0.500000 0.500000E-01 0.00000 0.562500 0.500000E-01 0.00000 * 0.625000 0.687500E-01 0.750000 0.687500 0.115625 0.750000 * 0.750000 0.162500 0.750000 0.812500 0.250000 4.00000 * 0.875000 0.500000 4.00000 0.937500 0.750000 4.00000 * 1.00000 1.00000 4.00000 Problem 10 Extrapolation test. X Y Y' * 0.00000 0.00000 0.109231 46.5000 5.07924 0.109231 * 93.0000 15.7226 0.362145 139.500 38.8577 0.737751 * 186.000 71.6479 0.977851 232.500 126.160 1.69032 * 279.000 204.760 1.69032 325.500 283.360 1.69032 * 372.000 361.960 1.69032 418.500 440.560 1.69032 * 465.000 519.160 1.69032 511.500 597.760 1.69032 * 558.000 676.360 1.69032 604.500 754.960 1.69032 * 651.000 833.560 1.69032 697.500 912.160 1.69032 * 744.000 990.760 1.69032 790.500 1069.36 1.69032 * 837.000 1147.96 1.69032 883.500 1226.56 1.69032 * 930.000 1305.16 1.69032 976.500 1383.76 1.69032 * 1023.00 1462.36 1.69032 Problem 11 Sunspot Data, 1700-1960. X Y Y' * 1700.00 5.00000 6.00000 1700.50 8.00000 6.00000 * 1701.00 11.0000 5.00000 1701.50 13.5000 5.00000 * 1702.00 16.0000 7.00000 1702.50 19.5000 7.00000 * 1703.00 23.0000 13.0000 1703.50 29.5000 13.0000 * 1704.00 36.0000 22.0000 1704.50 47.0000 22.0000 * 1705.00 58.0000 -29.0000 1705.50 43.5000 -29.0000 * 1706.00 29.0000 -9.00000 1706.50 24.5000 -9.00000 * 1707.00 20.0000 -10.0000 1707.50 15.0000 -10.0000 * 1708.00 10.0000 -2.00000 1708.50 9.00000 -2.00000 * 1709.00 8.00000 -5.00000 1709.50 5.50000 -5.00000 * 1710.00 3.00000 -3.00000 1710.50 1.50000 -3.00000 * 1711.00 0.00000 0.00000 1711.50 0.00000 0.00000 * 1712.00 0.00000 2.00000 1712.50 1.00000 2.00000 * 1713.00 2.00000 9.00000 1713.50 6.50000 9.00000 * 1714.00 11.0000 16.0000 1714.50 19.0000 16.0000 * 1715.00 27.0000 20.0000 1715.50 37.0000 20.0000 * 1716.00 47.0000 16.0000 1716.50 55.0000 16.0000 * 1717.00 63.0000 -3.00000 1717.50 61.5000 -3.00000 * 1718.00 60.0000 -21.0000 1718.50 49.5000 -21.0000 * 1719.00 39.0000 -11.0000 1719.50 33.5000 -11.0000 * 1720.00 28.0000 -2.00000 1720.50 27.0000 -2.00000 * 1721.00 26.0000 -4.00000 1721.50 24.0000 -4.00000 * 1722.00 22.0000 -11.0000 1722.50 16.5000 -11.0000 * 1723.00 11.0000 10.0000 1723.50 16.0000 10.0000 * 1724.00 21.0000 19.0000 1724.50 30.5000 19.0000 * 1725.00 40.0000 38.0000 1725.50 59.0000 38.0000 * 1726.00 78.0000 44.0000 1726.50 100.000 44.0000 * 1727.00 122.000 -19.0000 1727.50 112.500 -19.0000 * 1728.00 103.000 -30.0000 1728.50 88.0000 -30.0000 * 1729.00 73.0000 -26.0000 1729.50 60.0000 -26.0000 * 1730.00 47.0000 -12.0000 1730.50 41.0000 -12.0000 * 1731.00 35.0000 -24.0000 1731.50 23.0000 -24.0000 * 1732.00 11.0000 -6.00000 1732.50 8.00000 -6.00000 * 1733.00 5.00000 11.0000 1733.50 10.5000 11.0000 * 1734.00 16.0000 18.0000 1734.50 25.0000 18.0000 * 1735.00 34.0000 36.0000 1735.50 52.0000 36.0000 * 1736.00 70.0000 11.0000 1736.50 75.5000 11.0000 * 1737.00 81.0000 30.0000 1737.50 96.0000 30.0000 * 1738.00 111.000 -10.0000 1738.50 106.000 -10.0000 * 1739.00 101.000 -28.0000 1739.50 87.0000 -28.0000 * 1740.00 73.0000 -33.0000 1740.50 56.5000 -33.0000 * 1741.00 40.0000 -20.0000 1741.50 30.0000 -20.0000 * 1742.00 20.0000 -4.00000 1742.50 18.0000 -4.00000 * 1743.00 16.0000 -11.0000 1743.50 10.5000 -11.0000 * 1744.00 5.00000 6.00000 1744.50 8.00000 6.00000 * 1745.00 11.0000 11.0000 1745.50 16.5000 11.0000 * 1746.00 22.0000 18.0000 1746.50 31.0000 18.0000 * 1747.00 40.0000 20.0000 1747.50 50.0000 20.0000 * 1748.00 60.0000 20.9000 1748.50 70.4500 20.9000 * 1749.00 80.9000 2.50000 1749.50 82.1500 2.50000 * 1750.00 83.4000 -35.7000 1750.50 65.5500 -35.7000 * 1751.00 47.7000 0.100000 1751.50 47.7500 0.100000 * 1752.00 47.8000 -17.1000 1752.50 39.2500 -17.1000 * 1753.00 30.7000 -18.5000 1753.50 21.4500 -18.5000 * 1754.00 12.2000 -2.60000 1754.50 10.9000 -2.60000 * 1755.00 9.60000 0.600000 1755.50 9.90000 0.600000 * 1756.00 10.2000 22.2000 1756.50 21.3000 22.2000 * 1757.00 32.4000 15.2000 1757.50 40.0000 15.2000 * 1758.00 47.6000 6.40000 1758.50 50.8000 6.40000 * 1759.00 54.0000 8.90000 1759.50 58.4500 8.90000 * 1760.00 62.9000 23.0000 1760.50 74.4000 23.0000 * 1761.00 85.9000 -24.7000 1761.50 73.5500 -24.7000 * 1762.00 61.2000 -16.1000 1762.50 53.1500 -16.1000 * 1763.00 45.1000 -8.70000 1763.50 40.7500 -8.70000 * 1764.00 36.4000 -15.5000 1764.50 28.6500 -15.5000 * 1765.00 20.9000 -9.50000 1765.50 16.1500 -9.50000 * 1766.00 11.4000 26.4000 1766.50 24.6000 26.4000 * 1767.00 37.8000 32.0000 1767.50 53.8000 32.0000 * 1768.00 69.8000 36.3000 1768.50 87.9500 36.3000 * 1769.00 106.100 -5.30000 1769.50 103.450 -5.30000 * 1770.00 100.800 -19.2000 1770.50 91.2000 -19.2000 * 1771.00 81.6000 -15.1000 1771.50 74.0500 -15.1000 * 1772.00 66.5000 -31.7000 1772.50 50.6500 -31.7000 * 1773.00 34.8000 -4.20000 1773.50 32.7000 -4.20000 * 1774.00 30.6000 -23.6000 1774.50 18.8000 -23.6000 * 1775.00 7.00000 12.8000 1775.50 13.4000 12.8000 * 1776.00 19.8000 72.7000 1776.50 56.1500 72.7000 * 1777.00 92.5000 61.9000 1777.50 123.450 61.9000 * 1778.00 154.400 -28.5000 1778.50 140.150 -28.5000 * 1779.00 125.900 -41.1000 1779.50 105.350 -41.1000 * 1780.00 84.8000 -16.7000 1780.50 76.4500 -16.7000 * 1781.00 68.1000 -29.6000 1781.50 53.3000 -29.6000 * 1782.00 38.5000 -15.7000 1782.50 30.6500 -15.7000 * 1783.00 22.8000 -12.6000 1783.50 16.5000 -12.6000 * 1784.00 10.2000 13.9000 1784.50 17.1500 13.9000 * 1785.00 24.1000 58.8000 1785.50 53.5000 58.8000 * 1786.00 82.9000 49.1000 1786.50 107.450 49.1000 * 1787.00 132.000 -1.10000 1787.50 131.450 -1.10000 * 1788.00 130.900 -12.8000 1788.50 124.500 -12.8000 * 1789.00 118.100 -28.2000 1789.50 104.000 -28.2000 * 1790.00 89.9000 -23.3000 1790.50 78.2500 -23.3000 * 1791.00 66.6000 -6.60000 1791.50 63.3000 -6.60000 * 1792.00 60.0000 -13.1000 1792.50 53.4500 -13.1000 * 1793.00 46.9000 -5.90000 1793.50 43.9500 -5.90000 * 1794.00 41.0000 -19.7000 1794.50 31.1500 -19.7000 * 1795.00 21.3000 -5.30000 1795.50 18.6500 -5.30000 * 1796.00 16.0000 -9.60000 1796.50 11.2000 -9.60000 * 1797.00 6.40000 -2.30000 1797.50 5.25000 -2.30000 * 1798.00 4.10000 2.70000 1798.50 5.45000 2.70000 * 1799.00 6.80000 7.70000 1799.50 10.6500 7.70000 * 1800.00 14.5000 19.5000 1800.50 24.2500 19.5000 * 1801.00 34.0000 11.0000 1801.50 39.5000 11.0000 * 1802.00 45.0000 -1.90000 1802.50 44.0500 -1.90000 * 1803.00 43.1000 4.40000 1803.50 45.3000 4.40000 * 1804.00 47.5000 -5.30000 1804.50 44.8500 -5.30000 * 1805.00 42.2000 -14.1000 1805.50 35.1500 -14.1000 * 1806.00 28.1000 -18.0000 1806.50 19.1000 -18.0000 * 1807.00 10.1000 -2.00000 1807.50 9.10000 -2.00000 * 1808.00 8.10000 -5.60000 1808.50 5.30000 -5.60000 * 1809.00 2.50000 -2.50000 1809.50 1.25000 -2.50000 * 1810.00 0.00000 1.40000 1810.50 0.700000 1.40000 * 1811.00 1.40000 3.60000 1811.50 3.20000 3.60000 * 1812.00 5.00000 7.20000 1812.50 8.60000 7.20000 * 1813.00 12.2000 1.70000 1813.50 13.0500 1.70000 * 1814.00 13.9000 21.5000 1814.50 24.6500 21.5000 * 1815.00 35.4000 10.4000 1815.50 40.6000 10.4000 * 1816.00 45.8000 -4.70000 1816.50 43.4500 -4.70000 * 1817.00 41.1000 -11.0000 1817.50 35.6000 -11.0000 * 1818.00 30.1000 -6.20000 1818.50 27.0000 -6.20000 * 1819.00 23.9000 -8.30000 1819.50 19.7500 -8.30000 * 1820.00 15.6000 -9.00000 1820.50 11.1000 -9.00000 * 1821.00 6.60000 -2.60000 1821.50 5.30000 -2.60000 * 1822.00 4.00000 -2.20000 1822.50 2.90000 -2.20000 * 1823.00 1.80000 6.70000 1823.50 5.15000 6.70000 * 1824.00 8.50000 8.10000 1824.50 12.5500 8.10000 * 1825.00 16.6000 19.7000 1825.50 26.4500 19.7000 * 1826.00 36.3000 13.3000 1826.50 42.9500 13.3000 * 1827.00 49.6000 14.6000 1827.50 56.9000 14.6000 * 1828.00 64.2000 2.80000 1828.50 65.6000 2.80000 * 1829.00 67.0000 3.90000 1829.50 68.9500 3.90000 * 1830.00 70.9000 -23.1000 1830.50 59.3500 -23.1000 * 1831.00 47.8000 -20.3000 1831.50 37.6500 -20.3000 * 1832.00 27.5000 -19.0000 1832.50 18.0000 -19.0000 * 1833.00 8.50000 4.70000 1833.50 10.8500 4.70000 * 1834.00 13.2000 43.7000 1834.50 35.0500 43.7000 * 1835.00 56.9000 64.6000 1835.50 89.2000 64.6000 * 1836.00 121.500 16.8000 1836.50 129.900 16.8000 * 1837.00 138.300 -35.1000 1837.50 120.750 -35.1000 * 1838.00 103.200 -17.5000 1838.50 94.4500 -17.5000 * 1839.00 85.7000 -21.1000 1839.50 75.1500 -21.1000 * 1840.00 64.6000 -27.9000 1840.50 50.6500 -27.9000 * 1841.00 36.7000 -12.5000 1841.50 30.4500 -12.5000 * 1842.00 24.2000 -13.5000 1842.50 17.4500 -13.5000 * 1843.00 10.7000 4.30000 1843.50 12.8500 4.30000 * 1844.00 15.0000 25.1000 1844.50 27.5500 25.1000 * 1845.00 40.1000 21.4000 1845.50 50.8000 21.4000 * 1846.00 61.5000 37.0000 1846.50 80.0000 37.0000 * 1847.00 98.5000 26.2000 1847.50 111.600 26.2000 * 1848.00 124.700 -28.4000 1848.50 110.500 -28.4000 * 1849.00 96.3000 -29.7000 1849.50 81.4500 -29.7000 * 1850.00 66.6000 -2.10000 1850.50 65.5500 -2.10000 * 1851.00 64.5000 -10.4000 1851.50 59.3000 -10.4000 * 1852.00 54.1000 -15.1000 1852.50 46.5500 -15.1000 * 1853.00 39.0000 -18.4000 1853.50 29.8000 -18.4000 * 1854.00 20.6000 -13.9000 1854.50 13.6500 -13.9000 * 1855.00 6.70000 -2.40000 1855.50 5.50000 -2.40000 * 1856.00 4.30000 18.4000 1856.50 13.5000 18.4000 * 1857.00 22.7000 32.1000 1857.50 38.7500 32.1000 * 1858.00 54.8000 39.0000 1858.50 74.3000 39.0000 * 1859.00 93.8000 2.00000 1859.50 94.8000 2.00000 * 1860.00 95.8000 -18.6000 1860.50 86.5000 -18.6000 * 1861.00 77.2000 -18.1000 1861.50 68.1500 -18.1000 * 1862.00 59.1000 -15.1000 1862.50 51.5500 -15.1000 * 1863.00 44.0000 3.00000 1863.50 45.5000 3.00000 * 1864.00 47.0000 -16.5000 1864.50 38.7500 -16.5000 * 1865.00 30.5000 -14.2000 1865.50 23.4000 -14.2000 * 1866.00 16.3000 -9.00000 1866.50 11.8000 -9.00000 * 1867.00 7.30000 30.3000 1867.50 22.4500 30.3000 * 1868.00 37.6000 36.4000 1868.50 55.8000 36.4000 * 1869.00 74.0000 65.0000 1869.50 106.500 65.0000 * 1870.00 139.000 -27.8000 1870.50 125.100 -27.8000 * 1871.00 111.200 -9.60000 1871.50 106.400 -9.60000 * 1872.00 101.600 -35.4000 1872.50 83.9000 -35.4000 * 1873.00 66.2000 -21.5000 1873.50 55.4500 -21.5000 * 1874.00 44.7000 -27.7000 1874.50 30.8500 -27.7000 * 1875.00 17.0000 -5.70000 1875.50 14.1500 -5.70000 * 1876.00 11.3000 1.10000 1876.50 11.8500 1.10000 * 1877.00 12.4000 -9.00000 1877.50 7.90000 -9.00000 * 1878.00 3.40000 2.60000 1878.50 4.70000 2.60000 * 1879.00 6.00000 26.3000 1879.50 19.1500 26.3000 * 1880.00 32.3000 22.0000 1880.50 43.3000 22.0000 * 1881.00 54.3000 5.40000 1881.50 57.0000 5.40000 * 1882.00 59.7000 4.00000 1882.50 61.7000 4.00000 * 1883.00 63.7000 -0.200000 1883.50 63.6000 -0.200000 * 1884.00 63.5000 -11.3000 1884.50 57.8500 -11.3000 * 1885.00 52.2000 -26.8000 1885.50 38.8000 -26.8000 * 1886.00 25.4000 -12.3000 1886.50 19.2500 -12.3000 * 1887.00 13.1000 -6.30000 1887.50 9.95000 -6.30000 * 1888.00 6.80000 -0.500000 1888.50 6.55000 -0.500000 * 1889.00 6.30000 0.800000 1889.50 6.70000 0.800000 * 1890.00 7.10000 28.5000 1890.50 21.3500 28.5000 * 1891.00 35.6000 37.4000 1891.50 54.3000 37.4000 * 1892.00 73.0000 12.1000 1892.50 79.0500 12.1000 * 1893.00 85.1000 -7.10000 1893.50 81.5500 -7.10000 * 1894.00 78.0000 -14.0000 1894.50 71.0000 -14.0000 * 1895.00 64.0000 -22.2000 1895.50 52.9000 -22.2000 * 1896.00 41.8000 -15.6000 1896.50 34.0000 -15.6000 * 1897.00 26.2000 0.500000 1897.50 26.4500 0.500000 * 1898.00 26.7000 -14.6000 1898.50 19.4000 -14.6000 * 1899.00 12.1000 -2.60000 1899.50 10.8000 -2.60000 * 1900.00 9.50000 -6.80000 1900.50 6.10000 -6.80000 * 1901.00 2.70000 2.30000 1901.50 3.85000 2.30000 * 1902.00 5.00000 19.4000 1902.50 14.7000 19.4000 * 1903.00 24.4000 17.6000 1903.50 33.2000 17.6000 * 1904.00 42.0000 21.5000 1904.50 52.7500 21.5000 * 1905.00 63.5000 -9.70000 1905.50 58.6500 -9.70000 * 1906.00 53.8000 8.20000 1906.50 57.9000 8.20000 * 1907.00 62.0000 -13.5000 1907.50 55.2500 -13.5000 * 1908.00 48.5000 -4.60000 1908.50 46.2000 -4.60000 * 1909.00 43.9000 -25.3000 1909.50 31.2500 -25.3000 * 1910.00 18.6000 -12.9000 1910.50 12.1500 -12.9000 * 1911.00 5.70000 -2.10000 1911.50 4.65000 -2.10000 * 1912.00 3.60000 -2.20000 1912.50 2.50000 -2.20000 * 1913.00 1.40000 8.20000 1913.50 5.50000 8.20000 * 1914.00 9.60000 37.8000 1914.50 28.5000 37.8000 * 1915.00 47.4000 9.70000 1915.50 52.2500 9.70000 * 1916.00 57.1000 46.8000 1916.50 80.5000 46.8000 * 1917.00 103.900 -23.3000 1917.50 92.2500 -23.3000 * 1918.00 80.6000 -17.0000 1918.50 72.1000 -17.0000 * 1919.00 63.6000 -26.0000 1919.50 50.6000 -26.0000 * 1920.00 37.6000 -11.5000 1920.50 31.8500 -11.5000 * 1921.00 26.1000 -11.9000 1921.50 20.1500 -11.9000 * 1922.00 14.2000 -8.40000 1922.50 10.0000 -8.40000 * 1923.00 5.80000 10.9000 1923.50 11.2500 10.9000 * 1924.00 16.7000 27.6000 1924.50 30.5000 27.6000 * 1925.00 44.3000 19.6000 1925.50 54.1000 19.6000 * 1926.00 63.9000 5.10000 1926.50 66.4500 5.10000 * 1927.00 69.0000 8.80000 1927.50 73.4000 8.80000 * 1928.00 77.8000 -12.9000 1928.50 71.3500 -12.9000 * 1929.00 64.9000 -29.2000 1929.50 50.3000 -29.2000 * 1930.00 35.7000 -14.5000 1930.50 28.4500 -14.5000 * 1931.00 21.2000 -10.1000 1931.50 16.1500 -10.1000 * 1932.00 11.1000 -5.40000 1932.50 8.40000 -5.40000 * 1933.00 5.70000 3.00000 1933.50 7.20000 3.00000 * 1934.00 8.70000 27.4000 1934.50 22.4000 27.4000 * 1935.00 36.1000 43.6000 1935.50 57.9000 43.6000 * 1936.00 79.7000 34.7000 1936.50 97.0500 34.7000 * 1937.00 114.400 -4.80000 1937.50 112.000 -4.80000 * 1938.00 109.600 -20.8000 1938.50 99.2000 -20.8000 * 1939.00 88.8000 -21.0000 1939.50 78.3000 -21.0000 * 1940.00 67.8000 -20.3000 1940.50 57.6500 -20.3000 * 1941.00 47.5000 -16.9000 1941.50 39.0500 -16.9000 * 1942.00 30.6000 -14.3000 1942.50 23.4500 -14.3000 * 1943.00 16.3000 -6.70000 1943.50 12.9500 -6.70000 * 1944.00 9.60000 23.6000 1944.50 21.4000 23.6000 * 1945.00 33.2000 59.4000 1945.50 62.9000 59.4000 * 1946.00 92.6000 59.0000 1946.50 122.100 59.0000 * 1947.00 151.600 -15.3000 1947.50 143.950 -15.3000 * 1948.00 136.300 -1.60000 1948.50 135.500 -1.60000 * 1949.00 134.700 -50.8000 1949.50 109.300 -50.8000 * 1950.00 83.9000 -14.5000 1950.50 76.6500 -14.5000 * 1951.00 69.4000 -37.9000 1951.50 50.4500 -37.9000 * 1952.00 31.5000 -17.6000 1952.50 22.7000 -17.6000 * 1953.00 13.9000 -9.50000 1953.50 9.15000 -9.50000 * 1954.00 4.40000 33.6000 1954.50 21.2000 33.6000 * 1955.00 38.0000 103.700 1955.50 89.8500 103.700 * 1956.00 141.700 48.5000 1956.50 165.950 48.5000 * 1957.00 190.200 -5.40000 1957.50 187.500 -5.40000 * 1958.00 184.800 -25.8000 1958.50 171.900 -25.8000 * 1959.00 159.000 -46.7000 1959.50 135.650 -46.7000 * 1960.00 112.300 -46.7000 TEST05 Overhauser spline interpolation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] X Y * -5.00000 0.384615E-01 -4.50000 0.460407E-01 * -4.00000 0.588235E-01 -3.50000 0.744344E-01 * -3.00000 0.100000 -2.50000 0.133824 * -2.00000 0.200000 -1.50000 0.325000 * -1.00000 0.500000 -0.500000 0.800000 * 0.00000 1.00000 0.500000 0.800000 * 1.00000 0.500000 1.50000 0.325000 * 2.00000 0.200000 2.50000 0.133824 * 3.00000 0.100000 3.50000 0.744344E-01 * 4.00000 0.588235E-01 4.50000 0.460407E-01 * 5.00000 0.384615E-01 Problem 2 Bernstein example, abs ( x ), [-1,1] X Y * -1.00000 1.00000 -0.900000 0.900000 * -0.800000 0.800000 -0.700000 0.700000 * -0.600000 0.600000 -0.500000 0.500000 * -0.400000 0.400000 -0.300000 0.300000 * -0.200000 0.200000 -0.100000 0.750000E-01 * 0.00000 0.00000 0.100000 0.750000E-01 * 0.200000 0.200000 0.300000 0.300000 * 0.400000 0.400000 0.500000 0.500000 * 0.600000 0.600000 0.700000 0.700000 * 0.800000 0.800000 0.900000 0.900000 * 1.00000 1.00000 Problem 3 DeBoor example, Mars position, data vector X Y * 1250.50 1.39140 1255.50 1.38602 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13957 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957052 * 1330.50 0.905530 1335.50 0.852010 * 1340.50 0.796420 Problem 4 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.228750 * 2.00000 0.600000 2.50000 1.21313 * 3.00000 1.77000 3.50000 1.83125 * 4.00000 1.92000 4.50000 2.61125 * 5.00000 3.31000 5.50000 3.43500 * 6.00000 3.52000 6.50000 4.02313 * 7.00000 4.59000 7.50000 4.98687 * 8.00000 5.31000 8.50000 5.51563 * 9.00000 5.79000 9.50000 6.44812 * 10.0000 7.06000 10.5000 7.26000 * 11.0000 7.17000 Problem 5 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 -0.625000E-01 * 4.00000 0.00000 4.50000 0.562500 * 5.00000 1.00000 5.50000 0.562500 * 6.00000 0.00000 6.50000 -0.625000E-01 * 7.00000 0.00000 7.50000 0.00000 * 8.00000 0.00000 8.50000 0.00000 * 9.00000 0.00000 9.50000 0.00000 * 10.0000 0.00000 Problem 6 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.00000 * 4.00000 0.00000 4.49500 -6.12563 * 4.99000 0.00000 4.99500 0.249375 * 5.00000 0.500000 5.00500 0.750625 * 5.01000 1.00000 5.50500 7.12563 * 6.00000 1.00000 6.50000 1.00000 * 7.00000 1.00000 7.50000 1.00000 * 8.00000 1.00000 8.50000 1.00000 * 9.00000 1.00000 9.50000 1.00000 * 10.0000 1.00000 Problem 7 DeBoor's Titanium Property X Y * 595.000 0.644000 600.000 0.628250 * 605.000 0.622000 610.000 0.627938 * 615.000 0.638000 620.000 0.644313 * 625.000 0.649000 630.000 0.652000 * 635.000 0.652000 640.000 0.645250 * 645.000 0.639000 650.000 0.641000 * 655.000 0.646000 660.000 0.652250 * 665.000 0.657000 670.000 0.655000 * 675.000 0.652000 680.000 0.653875 * 685.000 0.655000 690.000 0.648500 * 695.000 0.644000 700.000 0.652813 * 705.000 0.663000 710.000 0.663875 * 715.000 0.663000 720.000 0.665000 * 725.000 0.668000 730.000 0.672313 * 735.000 0.676000 740.000 0.675875 * 745.000 0.676000 750.000 0.681438 * 755.000 0.686000 760.000 0.683188 * 765.000 0.679000 770.000 0.677750 * 775.000 0.678000 780.000 0.679750 * 785.000 0.683000 790.000 0.688500 * 795.000 0.694000 800.000 0.696500 * 805.000 0.699000 810.000 0.703562 * 815.000 0.710000 820.000 0.718625 * 825.000 0.730000 830.000 0.744687 * 835.000 0.763000 840.000 0.783625 * 845.000 0.812000 850.000 0.854000 * 855.000 0.907000 860.000 0.963188 * 865.000 1.04400 870.000 1.16450 * 875.000 1.33600 880.000 1.60875 * 885.000 1.88100 890.000 2.06494 * 895.000 2.16900 900.000 2.16981 * 905.000 2.07500 910.000 1.85481 * 915.000 1.59800 920.000 1.39313 * 925.000 1.21100 930.000 1.04994 * 935.000 0.916000 940.000 0.817187 * 945.000 0.746000 950.000 0.701188 * 955.000 0.672000 960.000 0.645625 * 965.000 0.627000 970.000 0.618687 * 975.000 0.615000 980.000 0.610313 * 985.000 0.607000 990.000 0.605812 * 995.000 0.606000 1000.00 0.607812 * 1005.00 0.609000 1010.00 0.606313 * 1015.00 0.603000 1020.00 0.601500 * 1025.00 0.601000 1030.00 0.602000 * 1035.00 0.603000 1040.00 0.601500 * 1045.00 0.601000 1050.00 0.606500 * 1055.00 0.611000 1060.00 0.606188 * 1065.00 0.601000 1070.00 0.602375 * 1075.00 0.608000 Problem 8 The Sawtooth X Y * 0.00000 0.00000 0.250000 0.750000 * 0.500000 1.00000 0.750000 0.458333 * 1.00000 0.00000 1.12500 0.208333 * 1.25000 0.500000 1.37500 0.812500 * 1.50000 1.00000 1.62500 0.812500 * 1.75000 0.500000 1.87500 0.175000 * 2.00000 0.00000 2.08333 0.133333 * 2.16667 0.333333 2.25000 0.500000 * 2.33333 0.666667 2.41667 0.875000 * 2.50000 1.00000 2.58333 0.875000 * 2.66667 0.666667 2.75000 0.500000 * 2.83333 0.333333 2.91667 0.119048 * 3.00000 -0.555112E-16 3.06250 0.982143E-01 * 3.12500 0.250000 3.18750 0.375000 * 3.25000 0.500000 3.31250 0.625000 * 3.37500 0.750000 3.43750 0.906250 * 3.50000 1.00000 3.56250 0.906250 * 3.62500 0.750000 3.68750 0.625000 * 3.75000 0.500000 3.81250 0.375000 * 3.87500 0.250000 3.93750 0.902778E-01 * 4.00000 0.00000 4.05000 0.777778E-01 * 4.10000 0.200000 4.15000 0.300000 * 4.20000 0.400000 4.25000 0.500000 * 4.30000 0.600000 4.35000 0.700000 * 4.40000 0.800000 4.45000 0.925000 * 4.50000 1.00000 4.55000 0.925000 * 4.60000 0.800000 4.65000 0.700000 * 4.70000 0.600000 4.75000 0.500000 * 4.80000 0.400000 4.85000 0.300000 * 4.90000 0.200000 4.95000 0.100000 * 5.00000 0.00000 Problem 9 Concavity test X Y * 0.00000 0.00000 0.500000E-01 0.556250 * 0.100000 0.900000 0.150000 0.984375 * 0.200000 0.950000 0.250000 0.978125 * 0.300000 0.900000 0.350000 0.500000 * 0.400000 0.100000 0.450000 0.250000E-01 * 0.500000 0.500000E-01 0.550000 0.437500E-01 * 0.600000 0.500000E-01 0.700000 0.718750E-01 * 0.800000 0.200000 0.900000 0.518750 * 1.00000 1.00000 Problem 10 Extrapolation test. X Y * 0.00000 0.00000 35.5000 0.812936 * 71.0000 7.75540 87.5000 13.0838 * 104.000 19.7062 119.500 26.6780 * 135.000 35.5379 140.000 39.1309 * 145.000 42.9154 152.500 48.9577 * 160.000 54.7752 170.500 60.4236 * 181.000 66.7587 187.000 72.4323 * 193.000 78.4929 199.000 83.9481 * 205.000 89.7683 210.000 95.6256 * 215.000 101.746 220.000 107.348 * 225.000 113.482 231.500 123.520 * 238.000 135.457 Problem 11 Sunspot Data, 1700-1960. X Y * 1700.00 5.00000 1700.50 8.12500 * 1701.00 11.0000 1701.50 13.4375 * 1702.00 16.0000 1702.50 19.0000 * 1703.00 23.0000 1703.50 28.5625 * 1704.00 36.0000 1704.50 49.6250 * 1705.00 58.0000 1705.50 45.4375 * 1706.00 29.0000 1706.50 23.3125 * 1707.00 20.0000 1707.50 14.5625 * 1708.00 10.0000 1708.50 8.68750 * 1709.00 8.00000 1709.50 5.56250 * 1710.00 3.00000 1710.50 1.18750 * 1711.00 0.00000 1711.50 -0.312500 * 1712.00 0.00000 1712.50 0.437500 * 1713.00 2.00000 1713.50 5.62500 * 1714.00 11.0000 1714.50 18.3125 * 1715.00 27.0000 1715.50 37.0000 * 1716.00 47.0000 1716.50 56.4375 * 1717.00 63.0000 1717.50 63.8125 * 1718.00 60.0000 1718.50 50.0000 * 1719.00 39.0000 1719.50 32.3125 * 1720.00 28.0000 1720.50 26.5625 * 1721.00 26.0000 1721.50 24.5625 * 1722.00 22.0000 1722.50 15.6250 * 1723.00 11.0000 1723.50 14.1250 * 1724.00 21.0000 1724.50 28.7500 * 1725.00 40.0000 1725.50 57.4375 * 1726.00 78.0000 1726.50 103.563 * 1727.00 122.000 1727.50 117.125 * 1728.00 103.000 1728.50 88.4375 * 1729.00 73.0000 1729.50 58.8750 * 1730.00 47.0000 1730.50 40.8750 * 1731.00 35.0000 1731.50 22.6250 * 1732.00 11.0000 1732.50 5.81250 * 1733.00 5.00000 1733.50 9.00000 * 1734.00 16.0000 1734.50 23.4375 * 1735.00 34.0000 1735.50 52.4375 * 1736.00 70.0000 1736.50 75.8750 * 1737.00 81.0000 1737.50 97.3125 * 1738.00 111.000 1738.50 109.625 * 1739.00 101.000 1739.50 88.4375 * 1740.00 73.0000 1740.50 56.0000 * 1741.00 40.0000 1741.50 28.1875 * 1742.00 20.0000 1742.50 17.4375 * 1743.00 16.0000 1743.50 9.87500 * 1744.00 5.00000 1744.50 6.62500 * 1745.00 11.0000 1745.50 15.7500 * 1746.00 22.0000 1746.50 30.4375 * 1747.00 40.0000 1747.50 49.8188 * 1748.00 60.0000 1748.50 71.5438 * 1749.00 80.9000 1749.50 85.6875 * 1750.00 83.4000 1750.50 65.7000 * 1751.00 47.7000 1751.50 46.5875 * 1752.00 47.8000 1752.50 40.4125 * 1753.00 30.7000 1753.50 20.5438 * 1754.00 12.2000 1754.50 9.70625 * 1755.00 9.60000 1755.50 8.35000 * 1756.00 10.2000 1756.50 20.3875 * 1757.00 32.4000 1757.50 40.9875 * 1758.00 47.6000 1758.50 51.1938 * 1759.00 54.0000 1759.50 57.4125 * 1760.00 62.9000 1760.50 76.5000 * 1761.00 85.9000 1761.50 75.9938 * 1762.00 61.2000 1762.50 52.1500 * 1763.00 45.1000 1763.50 40.7125 * 1764.00 36.4000 1764.50 28.7000 * 1765.00 20.9000 1765.50 13.5313 * 1766.00 11.4000 1766.50 22.0062 * 1767.00 37.8000 1767.50 53.1812 * 1768.00 69.8000 1768.50 90.2813 * 1769.00 106.100 1769.50 106.919 * 1770.00 100.800 1770.50 91.8125 * 1771.00 81.6000 1771.50 74.8312 * 1772.00 66.5000 1772.50 49.9688 * 1773.00 34.8000 1773.50 32.1937 * 1774.00 30.6000 1774.50 17.7375 * 1775.00 7.00000 1775.50 7.38125 * 1776.00 19.8000 1776.50 53.0812 * 1777.00 92.5000 1777.50 129.775 * 1778.00 154.400 1778.50 146.587 * 1779.00 125.900 1779.50 104.613 * 1780.00 84.8000 1780.50 75.7312 * 1781.00 68.1000 1781.50 53.2375 * 1782.00 38.5000 1782.50 29.5875 * 1783.00 22.8000 1783.50 14.6500 * 1784.00 10.2000 1784.50 12.6875 * 1785.00 24.1000 1785.50 51.3000 * 1786.00 82.9000 1786.50 111.194 * 1787.00 132.000 1787.50 135.319 * 1788.00 130.900 1788.50 126.194 * 1789.00 118.100 1789.50 104.656 * 1790.00 89.9000 1790.50 76.9000 * 1791.00 66.6000 1791.50 62.6625 * 1792.00 60.0000 1792.50 53.4063 * 1793.00 46.9000 1793.50 44.3625 * 1794.00 41.0000 1794.50 31.1125 * 1795.00 21.3000 1795.50 18.0187 * 1796.00 16.0000 1796.50 11.0125 * 1797.00 6.40000 1797.50 4.48125 * 1798.00 4.10000 1798.50 4.82500 * 1799.00 6.80000 1799.50 9.60000 * 1800.00 14.5000 1800.50 24.0438 * 1801.00 34.0000 1801.50 40.8375 * 1802.00 45.0000 1802.50 44.4625 * 1803.00 43.1000 1803.50 45.5125 * 1804.00 47.5000 1804.50 46.0063 * 1805.00 42.2000 1805.50 35.9438 * 1806.00 28.1000 1806.50 18.3438 * 1807.00 10.1000 1807.50 8.32500 * 1808.00 8.10000 1808.50 5.33125 * 1809.00 2.50000 1809.50 0.812500 * 1810.00 0.00000 1810.50 0.318750 * 1811.00 1.40000 1811.50 2.83750 * 1812.00 5.00000 1812.50 8.71875 * 1813.00 12.2000 1813.50 12.1563 * 1814.00 13.9000 1814.50 24.1063 * 1815.00 35.4000 1815.50 42.2375 * 1816.00 45.8000 1816.50 44.7875 * 1817.00 41.1000 1817.50 35.6938 * 1818.00 30.1000 1818.50 26.8312 * 1819.00 23.9000 1819.50 19.9250 * 1820.00 15.6000 1820.50 10.7438 * 1821.00 6.60000 1821.50 4.87500 * 1822.00 4.00000 1822.50 2.31875 * 1823.00 1.80000 1823.50 4.50625 * 1824.00 8.50000 1824.50 11.7375 * 1825.00 16.6000 1825.50 26.1250 * 1826.00 36.3000 1826.50 43.2687 * 1827.00 49.6000 1827.50 57.5563 * 1828.00 64.2000 1828.50 66.2688 * 1829.00 67.0000 1829.50 70.5687 * 1830.00 70.9000 1830.50 60.8625 * 1831.00 47.8000 1831.50 37.3937 * 1832.00 27.5000 1832.50 16.4375 * 1833.00 8.50000 1833.50 6.93125 * 1834.00 13.2000 1834.50 31.3062 * 1835.00 56.9000 1835.50 90.8812 * 1836.00 121.500 1836.50 136.131 * 1837.00 138.300 1837.50 122.894 * 1838.00 103.200 1838.50 93.5750 * 1839.00 85.7000 1839.50 75.8000 * 1840.00 64.6000 1840.50 50.1125 * 1841.00 36.7000 1841.50 29.5500 * 1842.00 24.2000 1842.50 16.4000 * 1843.00 10.7000 1843.50 10.4375 * 1844.00 15.0000 1844.50 26.4813 * 1845.00 40.1000 1845.50 50.0563 * 1846.00 61.5000 1846.50 79.7000 * 1847.00 98.5000 1847.50 115.688 * 1848.00 124.700 1848.50 113.994 * 1849.00 96.3000 1849.50 79.8063 * 1850.00 66.6000 1850.50 64.3438 * 1851.00 64.5000 1851.50 60.1125 * 1852.00 54.1000 1852.50 47.0500 * 1853.00 39.0000 1853.50 29.7250 * 1854.00 20.6000 1854.50 12.6500 * 1855.00 6.70000 1855.50 3.48125 * 1856.00 4.30000 1856.50 11.3437 * 1857.00 22.7000 1857.50 37.4625 * 1858.00 54.8000 1858.50 76.1813 * 1859.00 93.8000 1859.50 98.4000 * 1860.00 95.8000 1860.50 87.7562 * 1861.00 77.2000 1861.50 67.9313 * 1862.00 59.1000 1862.50 50.2313 * 1863.00 44.0000 1863.50 45.5875 * 1864.00 47.0000 1864.50 39.8250 * 1865.00 30.5000 1865.50 22.9312 * 1866.00 16.3000 1866.50 9.01875 * 1867.00 7.30000 1867.50 19.6125 * 1868.00 37.6000 1868.50 53.6313 * 1869.00 74.0000 1869.50 110.512 * 1870.00 139.000 1870.50 129.762 * 1871.00 111.200 1871.50 106.875 * 1872.00 101.600 1872.50 84.6437 * 1873.00 66.2000 1873.50 54.9688 * 1874.00 44.7000 1874.50 29.8625 * 1875.00 17.0000 1875.50 12.3500 * 1876.00 11.3000 1876.50 12.0563 * 1877.00 12.4000 1877.50 7.80625 * 1878.00 3.40000 1878.50 2.49375 * 1879.00 6.00000 1879.50 17.9375 * 1880.00 32.3000 1880.50 44.6063 * 1881.00 54.3000 1881.50 58.1250 * 1882.00 59.7000 1882.50 62.0500 * 1883.00 63.7000 1883.50 64.5563 * 1884.00 63.5000 1884.50 59.5125 * 1885.00 52.2000 1885.50 38.8625 * 1886.00 25.4000 1886.50 17.9688 * 1887.00 13.1000 1887.50 9.21250 * 1888.00 6.80000 1888.50 6.10625 * 1889.00 6.30000 1889.50 4.88750 * 1890.00 7.10000 1890.50 19.0625 * 1891.00 35.6000 1891.50 55.3250 * 1892.00 73.0000 1892.50 81.8312 * 1893.00 85.1000 1893.50 83.1812 * 1894.00 78.0000 1894.50 71.9437 * 1895.00 64.0000 1895.50 53.0000 * 1896.00 41.8000 1896.50 32.5812 * 1897.00 26.2000 1897.50 26.3875 * 1898.00 26.7000 1898.50 19.5938 * 1899.00 12.1000 1899.50 10.3125 * 1900.00 9.50000 1900.50 5.79375 * 1901.00 2.70000 1901.50 2.21250 * 1902.00 5.00000 1902.50 13.7437 * 1903.00 24.4000 1903.50 33.0687 * 1904.00 42.0000 1904.50 54.4562 * 1905.00 63.5000 1905.50 59.4812 * 1906.00 53.8000 1906.50 58.1375 * 1907.00 62.0000 1907.50 56.0500 * 1908.00 48.5000 1908.50 46.9375 * 1909.00 43.9000 1909.50 31.7687 * 1910.00 18.6000 1910.50 10.7000 * 1911.00 5.70000 1911.50 3.98125 * 1912.00 3.60000 1912.50 1.85625 * 1913.00 1.40000 1913.50 3.00000 * 1914.00 9.60000 1914.50 28.4062 * 1915.00 47.4000 1915.50 51.6875 * 1916.00 57.1000 1916.50 82.5625 * 1917.00 103.900 1917.50 96.2375 * 1918.00 80.6000 1918.50 72.2687 * 1919.00 63.6000 1919.50 50.2563 * 1920.00 37.6000 1920.50 30.9688 * 1921.00 26.1000 1921.50 19.9562 * 1922.00 14.2000 1922.50 8.57500 * 1923.00 5.80000 1923.50 9.00000 * 1924.00 16.7000 1924.50 29.9562 * 1925.00 44.3000 1925.50 55.5063 * 1926.00 63.9000 1926.50 67.1250 * 1927.00 69.0000 1927.50 74.5250 * 1928.00 77.8000 1928.50 73.7250 * 1929.00 64.9000 1929.50 50.4000 * 1930.00 35.7000 1930.50 27.2563 * 1931.00 21.2000 1931.50 15.5813 * 1932.00 11.1000 1932.50 7.58125 * 1933.00 5.70000 1933.50 5.15000 * 1934.00 8.70000 1934.50 19.8625 * 1935.00 36.1000 1935.50 57.4438 * 1936.00 79.7000 1936.50 100.075 * 1937.00 114.400 1937.50 115.469 * 1938.00 109.600 1938.50 100.212 * 1939.00 88.8000 1939.50 78.2687 * 1940.00 67.8000 1940.50 57.3937 * 1941.00 47.5000 1941.50 38.6750 * 1942.00 30.6000 1942.50 22.8125 * 1943.00 16.3000 1943.50 10.5813 * 1944.00 9.60000 1944.50 17.2688 * 1945.00 33.2000 1945.50 60.6875 * 1946.00 92.6000 1946.50 126.769 * 1947.00 151.600 1947.50 147.738 * 1948.00 136.300 1948.50 137.719 * 1949.00 134.700 1949.50 110.106 * 1950.00 83.9000 1950.50 75.8438 * 1951.00 69.4000 1951.50 50.6437 * 1952.00 31.5000 1952.50 20.9250 * 1953.00 13.9000 1953.50 5.95000 * 1954.00 4.40000 1954.50 14.1250 * 1955.00 38.0000 1955.50 88.9188 * 1956.00 141.700 1956.50 172.769 * 1957.00 190.200 1957.50 192.144 * 1958.00 184.800 1958.50 174.481 * 1959.00 159.000 1959.50 138.262 * 1960.00 112.300 TEST06 Cubic spline interpolation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] X Y * -5.00000 0.384615E-01 -4.50000 0.470256E-01 * -4.00000 0.588235E-01 -3.50000 0.748403E-01 * -3.00000 0.100000 -2.50000 0.140039 * -2.00000 0.200000 -1.50000 0.297358 * -1.00000 0.500000 -0.500000 0.820528 * 0.00000 1.00000 0.500000 0.820528 * 1.00000 0.500000 1.50000 0.297358 * 2.00000 0.200000 2.50000 0.140039 * 3.00000 0.100000 3.50000 0.748403E-01 * 4.00000 0.588235E-01 4.50000 0.470256E-01 * 5.00000 0.384615E-01 Problem 2 Bernstein example, abs ( x ), [-1,1] X Y * -1.00000 1.00000 -0.900000 0.899673 * -0.800000 0.800000 -0.700000 0.700654 * -0.600000 0.600000 -0.500000 0.497712 * -0.400000 0.400000 -0.300000 0.308497 * -0.200000 0.200000 -0.100000 0.683007E-01 * 0.00000 0.00000 0.100000 0.683007E-01 * 0.200000 0.200000 0.300000 0.308497 * 0.400000 0.400000 0.500000 0.497712 * 0.600000 0.600000 0.700000 0.700654 * 0.800000 0.800000 0.900000 0.899673 * 1.00000 1.00000 Problem 3 DeBoor example, Mars position, data vector X Y * 1250.50 1.39140 1255.50 1.38603 * 1260.50 1.37696 1265.50 1.36420 * 1270.50 1.34783 1275.50 1.32792 * 1280.50 1.30456 1285.50 1.27784 * 1290.50 1.24787 1295.50 1.21476 * 1300.50 1.17862 1305.50 1.13958 * 1310.50 1.09776 1315.50 1.05331 * 1320.50 1.00636 1325.50 0.957041 * 1330.50 0.905530 1335.50 0.851979 * 1340.50 0.796420 Problem 4 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.147883 * 2.00000 0.600000 2.50000 1.27548 * 3.00000 1.77000 3.50000 1.80393 * 4.00000 1.92000 4.50000 2.60628 * 5.00000 3.31000 5.50000 3.46843 * 6.00000 3.52000 6.50000 3.96999 * 7.00000 4.59000 7.50000 5.04535 * 8.00000 5.31000 8.50000 5.47486 * 9.00000 5.79000 9.50000 6.42397 * 10.0000 7.06000 10.5000 7.33302 * 11.0000 7.17000 Problem 5 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.490196E-02 * 1.00000 0.00000 1.50000 -0.980392E-02 * 2.00000 0.00000 2.50000 0.343137E-01 * 3.00000 0.00000 3.50000 -0.127451 * 4.00000 0.00000 4.50000 0.600490 * 5.00000 1.00000 5.50000 0.600490 * 6.00000 0.00000 6.50000 -0.127451 * 7.00000 0.00000 7.50000 0.343137E-01 * 8.00000 0.00000 8.50000 -0.980392E-02 * 9.00000 0.00000 9.50000 0.490196E-02 * 10.0000 0.00000 Problem 6 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 -0.811346E-01 * 1.00000 0.00000 1.50000 0.162269 * 2.00000 0.00000 2.50000 -0.567942 * 3.00000 0.00000 3.50000 2.10950 * 4.00000 0.00000 4.49500 -7.76284 * 4.99000 0.00000 4.99500 0.248920 * 5.00000 0.500000 5.00500 0.751080 * 5.01000 1.00000 5.50500 8.76284 * 6.00000 1.00000 6.50000 -1.10950 * 7.00000 1.00000 7.50000 1.56794 * 8.00000 1.00000 8.50000 0.837731 * 9.00000 1.00000 9.50000 1.08113 * 10.0000 1.00000 Problem 7 DeBoor's Titanium Property X Y * 595.000 0.644000 600.000 0.626793 * 605.000 0.622000 610.000 0.628164 * 615.000 0.638000 620.000 0.644675 * 625.000 0.649000 630.000 0.652511 * 635.000 0.652000 640.000 0.645281 * 645.000 0.639000 650.000 0.639864 * 655.000 0.646000 660.000 0.653263 * 665.000 0.657000 670.000 0.654584 * 675.000 0.652000 680.000 0.654400 * 685.000 0.655000 690.000 0.648067 * 695.000 0.644000 700.000 0.652333 * 705.000 0.663000 710.000 0.664977 * 715.000 0.663000 720.000 0.664011 * 725.000 0.668000 730.000 0.672980 * 735.000 0.676000 740.000 0.675444 * 745.000 0.676000 750.000 0.681492 * 755.000 0.686000 760.000 0.683711 * 765.000 0.679000 770.000 0.677287 * 775.000 0.678000 780.000 0.679639 * 785.000 0.683000 790.000 0.688656 * 795.000 0.694000 800.000 0.696736 * 805.000 0.699000 810.000 0.703400 * 815.000 0.710000 820.000 0.718538 * 825.000 0.730000 830.000 0.745198 * 835.000 0.763000 840.000 0.783294 * 845.000 0.812000 850.000 0.854375 * 855.000 0.907000 860.000 0.967208 * 865.000 1.04400 870.000 1.15442 * 875.000 1.33600 880.000 1.60611 * 885.000 1.88100 890.000 2.07163 * 895.000 2.16900 900.000 2.17749 * 905.000 2.07500 910.000 1.85478 * 915.000 1.59800 920.000 1.38578 * 925.000 1.21100 930.000 1.05186 * 935.000 0.916000 940.000 0.814898 * 945.000 0.746000 950.000 0.702172 * 955.000 0.672000 960.000 0.646039 * 965.000 0.627000 970.000 0.618420 * 975.000 0.615000 980.000 0.610904 * 985.000 0.607000 990.000 0.605339 * 995.000 0.606000 1000.00 0.608116 * 1005.00 0.609000 1010.00 0.606571 * 1015.00 0.603000 1020.00 0.600976 * 1025.00 0.601000 1030.00 0.602524 * 1035.00 0.603000 1040.00 0.600928 * 1045.00 0.601000 1050.00 0.606765 * 1055.00 0.611000 1060.00 0.607014 * 1065.00 0.601000 1070.00 0.600806 * 1075.00 0.608000 Problem 8 The Sawtooth X Y * 0.00000 0.00000 0.250000 0.927655 * 0.500000 1.00000 0.750000 0.394689 * 1.00000 0.00000 1.12500 0.167009 * 1.25000 0.500000 1.37500 0.839404 * 1.50000 1.00000 1.62500 0.850375 * 1.75000 0.500000 1.87500 0.134096 * 2.00000 0.00000 2.08333 0.131345 * 2.16667 0.333333 2.25000 0.496036 * 2.33333 0.666667 2.41667 0.884509 * 2.50000 1.00000 2.58333 0.882595 * 2.66667 0.666667 2.75000 0.501777 * 2.83333 0.333333 2.91667 0.110298 * 3.00000 0.00000 3.06250 0.895875E-01 * 3.12500 0.250000 3.18750 0.387114 * 3.25000 0.500000 3.31250 0.611956 * 3.37500 0.750000 3.43750 0.915063 * 3.50000 1.00000 3.56250 0.915292 * 3.62500 0.750000 3.68750 0.611267 * 3.75000 0.500000 3.81250 0.389639 * 3.87500 0.250000 3.93750 0.801769E-01 * 4.00000 0.00000 4.05000 0.721362E-01 * 4.10000 0.200000 4.15000 0.306900 * 4.20000 0.400000 4.25000 0.500264 * 4.30000 0.600000 4.35000 0.692046 * 4.40000 0.800000 4.45000 0.931554 * 4.50000 1.00000 4.55000 0.931738 * 4.60000 0.800000 4.65000 0.691493 * 4.70000 0.600000 4.75000 0.502290 * 4.80000 0.400000 4.85000 0.299346 * 4.90000 0.200000 4.95000 0.100327 * 5.00000 0.00000 Problem 9 Concavity test X Y * 0.00000 0.00000 0.500000E-01 0.591250 * 0.100000 0.900000 0.150000 0.961249 * 0.200000 0.950000 0.250000 0.995003 * 0.300000 0.900000 0.350000 0.502489 * 0.400000 0.100000 0.450000 -0.495861E-02 * 0.500000 0.500000E-01 0.550000 0.673455E-01 * 0.600000 0.500000E-01 0.700000 0.615748E-01 * 0.800000 0.200000 0.900000 0.509838 * 1.00000 1.00000 Problem 10 Extrapolation test. X Y * 0.00000 0.00000 35.5000 0.617949 * 71.0000 7.75540 87.5000 13.2257 * 104.000 19.7062 119.500 26.6483 * 135.000 35.5379 140.000 39.0471 * 145.000 42.9154 152.500 49.1626 * 160.000 54.7752 170.500 60.2921 * 181.000 66.7587 187.000 72.4146 * 193.000 78.4929 199.000 83.9544 * 205.000 89.7683 210.000 95.6326 * 215.000 101.746 220.000 107.445 * 225.000 113.482 231.500 123.250 * 238.000 135.457 Problem 11 Sunspot Data, 1700-1960. X Y * 1700.00 5.00000 1700.50 8.24884 * 1701.00 11.0000 1701.50 13.3773 * 1702.00 16.0000 1702.50 19.3669 * 1703.00 23.0000 1703.50 27.1552 * 1704.00 36.0000 1704.50 50.8874 * 1705.00 58.0000 1705.50 46.0451 * 1706.00 29.0000 1706.50 22.0573 * 1707.00 20.0000 1707.50 15.1009 * 1708.00 10.0000 1708.50 8.41414 * 1709.00 8.00000 1709.50 5.86754 * 1710.00 3.00000 1710.50 0.990688 * 1711.00 0.00000 1711.50 -0.205296 * 1712.00 0.00000 1712.50 0.455495 * 1713.00 2.00000 1713.50 5.50831 * 1714.00 11.0000 1714.50 18.2612 * 1715.00 27.0000 1715.50 36.8217 * 1716.00 47.0000 1716.50 56.4520 * 1717.00 63.0000 1717.50 64.4955 * 1718.00 60.0000 1718.50 49.9411 * 1719.00 39.0000 1719.50 31.7402 * 1720.00 28.0000 1720.50 26.4732 * 1721.00 26.0000 1721.50 25.2419 * 1722.00 22.0000 1722.50 15.4342 * 1723.00 11.0000 1723.50 13.7712 * 1724.00 21.0000 1724.50 29.2310 * 1725.00 40.0000 1725.50 55.8047 * 1726.00 78.0000 1726.50 104.675 * 1727.00 122.000 1727.50 118.370 * 1728.00 103.000 1728.50 87.5966 * 1729.00 73.0000 1729.50 58.3689 * 1730.00 47.0000 1730.50 41.1778 * 1731.00 35.0000 1731.50 23.1701 * 1732.00 11.0000 1732.50 4.89200 * 1733.00 5.00000 1733.50 9.63693 * 1734.00 16.0000 1734.50 22.5603 * 1735.00 34.0000 1735.50 53.2469 * 1736.00 70.0000 1736.50 75.5769 * 1737.00 81.0000 1737.50 96.6953 * 1738.00 111.000 1738.50 111.017 * 1739.00 101.000 1739.50 87.9879 * 1740.00 73.0000 1740.50 56.1566 * 1741.00 40.0000 1741.50 27.3857 * 1742.00 20.0000 1742.50 17.9258 * 1743.00 16.0000 1743.50 10.0363 * 1744.00 5.00000 1744.50 6.17897 * 1745.00 11.0000 1745.50 15.9978 * 1746.00 22.0000 1746.50 30.3298 * 1747.00 40.0000 1747.50 49.8081 * 1748.00 60.0000 1748.50 70.8004 * 1749.00 80.9000 1749.50 87.5030 * 1750.00 83.4000 1750.50 65.0127 * 1751.00 47.7000 1751.50 45.4462 * 1752.00 47.8000 1752.50 42.0275 * 1753.00 30.7000 1753.50 19.6188 * 1754.00 12.2000 1754.50 10.0097 * 1755.00 9.60000 1755.50 8.12986 * 1756.00 10.2000 1756.50 19.9708 * 1757.00 32.4000 1757.50 41.6118 * 1758.00 47.6000 1758.50 51.6070 * 1759.00 54.0000 1759.50 55.9725 * 1760.00 62.9000 1760.50 77.2779 * 1761.00 85.9000 1761.50 77.1161 * 1762.00 61.2000 1762.50 50.6704 * 1763.00 45.1000 1763.50 41.1022 * 1764.00 36.4000 1764.50 29.4957 * 1765.00 20.9000 1765.50 12.7150 * 1766.00 11.4000 1766.50 21.7818 * 1767.00 37.8000 1767.50 52.9452 * 1768.00 69.8000 1768.50 90.4749 * 1769.00 106.100 1769.50 108.193 * 1770.00 100.800 1770.50 90.5164 * 1771.00 81.6000 1771.50 75.7167 * 1772.00 66.5000 1772.50 49.3542 * 1773.00 34.8000 1773.50 32.1290 * 1774.00 30.6000 1774.50 19.3423 * 1775.00 7.00000 1775.50 5.42689 * 1776.00 19.8000 1776.50 51.3876 * 1777.00 92.5000 1777.50 132.060 * 1778.00 154.400 1778.50 148.422 * 1779.00 125.900 1779.50 102.276 * 1780.00 84.8000 1780.50 76.0493 * 1781.00 68.1000 1781.50 53.6646 * 1782.00 38.5000 1782.50 29.2173 * 1783.00 22.8000 1783.50 15.4912 * 1784.00 10.2000 1784.50 11.5180 * 1785.00 24.1000 1785.50 50.2617 * 1786.00 82.9000 1786.50 112.835 * 1787.00 132.000 1787.50 135.610 * 1788.00 130.900 1788.50 125.688 * 1789.00 118.100 1789.50 105.249 * 1790.00 89.9000 1790.50 76.0028 * 1791.00 66.6000 1791.50 62.9396 * 1792.00 60.0000 1792.50 53.3136 * 1793.00 46.9000 1793.50 44.5933 * 1794.00 41.0000 1794.50 31.1882 * 1795.00 21.3000 1795.50 17.6287 * 1796.00 16.0000 1796.50 11.4593 * 1797.00 6.40000 1797.50 4.10918 * 1798.00 4.10000 1798.50 5.14150 * 1799.00 6.80000 1799.50 9.27481 * 1800.00 14.5000 1800.50 23.7593 * 1801.00 34.0000 1801.50 41.6006 * 1802.00 45.0000 1802.50 44.1632 * 1803.00 43.1000 1803.50 45.2215 * 1804.00 47.5000 1804.50 46.3257 * 1805.00 42.2000 1805.50 36.2630 * 1806.00 28.1000 1806.50 17.9348 * 1807.00 10.1000 1807.50 8.11043 * 1808.00 8.10000 1808.50 5.77351 * 1809.00 2.50000 1809.50 0.533046 * 1810.00 0.00000 1810.50 0.469309 * 1811.00 1.40000 1811.50 2.55222 * 1812.00 5.00000 1812.50 9.24682 * 1813.00 12.2000 1813.50 11.8230 * 1814.00 13.9000 1814.50 23.5487 * 1815.00 35.4000 1815.50 42.9696 * 1816.00 45.8000 1816.50 44.8978 * 1817.00 41.1000 1817.50 35.4642 * 1818.00 30.1000 1818.50 26.6579 * 1819.00 23.9000 1819.50 20.2416 * 1820.00 15.6000 1820.50 10.5255 * 1821.00 6.60000 1821.50 4.96881 * 1822.00 4.00000 1822.50 2.24924 * 1823.00 1.80000 1823.50 4.59673 * 1824.00 8.50000 1824.50 11.5514 * 1825.00 16.6000 1825.50 26.1229 * 1826.00 36.3000 1826.50 43.3072 * 1827.00 49.6000 1827.50 57.7109 * 1828.00 64.2000 1828.50 65.9365 * 1829.00 67.0000 1829.50 70.8054 * 1830.00 70.9000 1830.50 61.3043 * 1831.00 47.8000 1831.50 37.0525 * 1832.00 27.5000 1832.50 16.8983 * 1833.00 8.50000 1833.50 6.47926 * 1834.00 13.2000 1834.50 30.1221 * 1835.00 56.9000 1835.50 90.8197 * 1836.00 121.500 1836.50 138.437 * 1837.00 138.300 1837.50 122.371 * 1838.00 103.200 1838.50 92.2907 * 1839.00 85.7000 1839.50 76.9158 * 1840.00 64.6000 1840.50 49.6460 * 1841.00 36.7000 1841.50 29.4753 * 1842.00 24.2000 1842.50 16.9527 * 1843.00 10.7000 1843.50 9.51387 * 1844.00 15.0000 1844.50 26.9168 * 1845.00 40.1000 1845.50 50.2564 * 1846.00 61.5000 1846.50 78.3451 * 1847.00 98.5000 1847.50 116.963 * 1848.00 124.700 1848.50 115.228 * 1849.00 96.3000 1849.50 78.1392 * 1850.00 66.6000 1850.50 64.2030 * 1851.00 64.5000 1851.50 60.7612 * 1852.00 54.1000 1852.50 46.9272 * 1853.00 39.0000 1853.50 29.8299 * 1854.00 20.6000 1854.50 12.7032 * 1855.00 6.70000 1855.50 3.25735 * 1856.00 4.30000 1856.50 11.3049 * 1857.00 22.7000 1857.50 36.8355 * 1858.00 54.8000 1858.50 76.4279 * 1859.00 93.8000 1859.50 99.4903 * 1860.00 95.8000 1860.50 87.2108 * 1861.00 77.2000 1861.50 68.1539 * 1862.00 59.1000 1862.50 49.5112 * 1863.00 44.0000 1863.50 45.7387 * 1864.00 47.0000 1864.50 40.3588 * 1865.00 30.5000 1865.50 23.1760 * 1866.00 16.3000 1866.50 8.27460 * 1867.00 7.30000 1867.50 20.0881 * 1868.00 37.6000 1868.50 51.7481 * 1869.00 74.0000 1869.50 112.057 * 1870.00 139.000 1870.50 130.999 * 1871.00 111.200 1871.50 105.223 * 1872.00 101.600 1872.50 85.5611 * 1873.00 66.2000 1873.50 54.4457 * 1874.00 44.7000 1874.50 30.3186 * 1875.00 17.0000 1875.50 11.3548 * 1876.00 11.3000 1876.50 12.7622 * 1877.00 12.4000 1877.50 8.28376 * 1878.00 3.40000 1878.50 1.69021 * 1879.00 6.00000 1879.50 17.5679 * 1880.00 32.3000 1880.50 45.3632 * 1881.00 54.3000 1881.50 58.1670 * 1882.00 59.7000 1882.50 61.7190 * 1883.00 63.7000 1883.50 64.4571 * 1884.00 63.5000 1884.50 60.1400 * 1885.00 52.2000 1885.50 38.7577 * 1886.00 25.4000 1886.50 17.5042 * 1887.00 13.1000 1887.50 9.28796 * 1888.00 6.80000 1888.50 6.51894 * 1889.00 6.30000 1889.50 4.82378 * 1890.00 7.10000 1890.50 18.0109 * 1891.00 35.6000 1891.50 55.8075 * 1892.00 73.0000 1892.50 82.5092 * 1893.00 85.1000 1893.50 82.8933 * 1894.00 78.0000 1894.50 71.9552 * 1895.00 64.0000 1895.50 53.3986 * 1896.00 41.8000 1896.50 31.6505 * 1897.00 26.2000 1897.50 26.8371 * 1898.00 26.7000 1898.50 19.8263 * 1899.00 12.1000 1899.50 9.87011 * 1900.00 9.50000 1900.50 6.46822 * 1901.00 2.70000 1901.50 1.46950 * 1902.00 5.00000 1902.50 14.0288 * 1903.00 24.4000 1903.50 32.5279 * 1904.00 42.0000 1904.50 55.3220 * 1905.00 63.5000 1905.50 59.2716 * 1906.00 53.8000 1906.50 57.8292 * 1907.00 62.0000 1907.50 56.3365 * 1908.00 48.5000 1908.50 46.7247 * 1909.00 43.9000 1909.50 32.4897 * 1910.00 18.6000 1910.50 9.77882 * 1911.00 5.70000 1911.50 4.19495 * 1912.00 3.60000 1912.50 2.67886 * 1913.00 1.40000 1913.50 1.37711 * 1914.00 9.60000 1914.50 29.8127 * 1915.00 47.4000 1915.50 50.5596 * 1916.00 57.1000 1916.50 82.5738 * 1917.00 103.900 1917.50 98.0203 * 1918.00 80.6000 1918.50 70.8702 * 1919.00 63.6000 1919.50 50.7615 * 1920.00 37.6000 1920.50 30.3712 * 1921.00 26.1000 1921.50 20.6162 * 1922.00 14.2000 1922.50 8.45157 * 1923.00 5.80000 1923.50 8.42755 * 1924.00 16.7000 1924.50 29.8382 * 1925.00 44.3000 1925.50 56.3070 * 1926.00 63.9000 1926.50 66.7214 * 1927.00 69.0000 1927.50 74.1575 * 1928.00 77.8000 1928.50 74.7984 * 1929.00 64.9000 1929.50 49.9987 * 1930.00 35.7000 1930.50 26.8067 * 1931.00 21.2000 1931.50 15.8619 * 1932.00 11.1000 1932.50 7.78318 * 1933.00 5.70000 1933.50 5.04289 * 1934.00 8.70000 1934.50 19.3453 * 1935.00 36.1000 1935.50 57.0511 * 1936.00 79.7000 1936.50 100.763 * 1937.00 114.400 1937.50 116.147 * 1938.00 109.600 1938.50 99.7100 * 1939.00 88.8000 1939.50 78.1875 * 1940.00 67.8000 1940.50 57.4023 * 1941.00 47.5000 1941.50 38.6157 * 1942.00 30.6000 1942.50 23.1849 * 1943.00 16.3000 1943.50 10.6198 * 1944.00 9.60000 1944.50 16.7735 * 1945.00 33.2000 1945.50 58.9488 * 1946.00 92.6000 1946.50 129.256 * 1947.00 151.600 1947.50 147.288 * 1948.00 136.300 1948.50 137.715 * 1949.00 134.700 1949.50 110.415 * 1950.00 83.9000 1950.50 74.8125 * 1951.00 69.4000 1951.50 51.8475 * 1952.00 31.5000 1952.50 20.1099 * 1953.00 13.9000 1953.50 7.46279 * 1954.00 4.40000 1954.50 11.3389 * 1955.00 38.0000 1955.50 88.5315 * 1956.00 141.700 1956.50 175.497 * 1957.00 190.200 1957.50 191.541 * 1958.00 184.800 1958.50 174.051 * 1959.00 159.000 1959.50 138.493 * 1960.00 112.300 TEST07 Plot an Overhauser spline interpolant. Data points: 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 Problem 9 Concavity test XMIN, XMAX = 0.00000 1.00000 YMIN, YMAX = -0.100000 1.10000 Plot points: 1 0.00000 0.00000 2 0.166667E-01 0.209028 3 0.333333E-01 0.394444 4 0.500000E-01 0.556250 5 0.666667E-01 0.694444 6 0.833333E-01 0.809028 7 0.100000 0.900000 8 0.116667 0.958681 9 0.133333 0.983333 10 0.150000 0.984375 11 0.166667 0.972222 12 0.183333 0.957292 13 0.200000 0.950000 14 0.216667 0.956134 15 0.233333 0.968519 16 0.250000 0.978125 17 0.266667 0.975926 18 0.283333 0.952894 19 0.300000 0.900000 20 0.316667 0.801389 21 0.333333 0.661111 22 0.350000 0.500000 23 0.366667 0.338889 24 0.383333 0.198611 25 0.400000 0.100000 26 0.416667 0.476852E-01 27 0.433333 0.259259E-01 28 0.450000 0.250000E-01 29 0.466667 0.351852E-01 30 0.483333 0.467593E-01 31 0.500000 0.500000E-01 32 0.516667 0.465278E-01 33 0.533333 0.444444E-01 34 0.550000 0.437500E-01 35 0.566667 0.444444E-01 36 0.583333 0.465278E-01 37 0.600000 0.500000E-01 38 0.633333 0.559028E-01 39 0.666667 0.611111E-01 40 0.700000 0.718750E-01 41 0.733333 0.944444E-01 42 0.766667 0.135069 43 0.800000 0.200000 44 0.833333 0.288194 45 0.866667 0.394444 46 0.900000 0.518750 47 0.933333 0.661111 48 0.966667 0.821528 49 1.00000 1.00000 DEBUG: About to call PS_PAGE_HEAD DEBUG: About to call PS_LINE_OPEN TEST08 Plot a cubic spline interpolant. Problem 9 Concavity test Plot points: 1 0.00000 0.00000 2 0.166667E-01 0.228472 3 0.333333E-01 0.425556 4 0.500000E-01 0.591250 5 0.666667E-01 0.725556 6 0.833333E-01 0.828472 7 0.100000 0.900000 8 0.116667 0.941435 9 0.133333 0.959259 10 0.150000 0.961249 11 0.166667 0.955184 12 0.183333 0.948842 13 0.200000 0.950000 14 0.216667 0.963427 15 0.233333 0.981854 16 0.250000 0.995003 17 0.266667 0.992596 18 0.283333 0.964354 19 0.300000 0.900000 20 0.316667 0.793515 21 0.333333 0.655918 22 0.350000 0.502489 23 0.366667 0.348507 24 0.383333 0.209251 25 0.400000 0.100000 26 0.416667 0.319586E-01 27 0.433333 0.297089E-04 28 0.450000 -0.495861E-02 29 0.466667 0.782165E-02 30 0.483333 0.291985E-01 31 0.500000 0.500000E-01 32 0.516667 0.629102E-01 33 0.533333 0.680373E-01 34 0.550000 0.673455E-01 35 0.566667 0.627992E-01 36 0.583333 0.563626E-01 37 0.600000 0.500000E-01 38 0.633333 0.430647E-01 39 0.666667 0.462628E-01 40 0.700000 0.615748E-01 41 0.733333 0.909814E-01 42 0.766667 0.136463 43 0.800000 0.200000 44 0.833333 0.283243 45 0.866667 0.386522 46 0.900000 0.509838 47 0.933333 0.653189 48 0.966667 0.816576 49 1.00000 1.00000 TEST09 B spline approximation. Problem 1 Runge example, 1 / ( x * x + 1 ), [-5,5] X Y * -5.00000 0.384615E-01 -4.50000 0.490762E-01 * -4.00000 0.622926E-01 -3.50000 0.810709E-01 * -3.00000 0.109804 -2.50000 0.155392 * -2.00000 0.233333 -1.50000 0.358333 * -1.00000 0.533333 -0.500000 0.733333 * 0.00000 0.833333 0.500000 0.733333 * 1.00000 0.533333 1.50000 0.358333 * 2.00000 0.233333 2.50000 0.155392 * 3.00000 0.109804 3.50000 0.810709E-01 * 4.00000 0.622926E-01 4.50000 0.490762E-01 * 5.00000 0.384615E-01 Problem 2 Bernstein example, abs ( x ), [-1,1] X Y * -1.00000 1.00000 -0.900000 0.900000 * -0.800000 0.800000 -0.700000 0.700000 * -0.600000 0.600000 -0.500000 0.500000 * -0.400000 0.400000 -0.300000 0.300000 * -0.200000 0.200000 -0.100000 0.108333 * 0.00000 0.666667E-01 0.100000 0.108333 * 0.200000 0.200000 0.300000 0.300000 * 0.400000 0.400000 0.500000 0.500000 * 0.600000 0.600000 0.700000 0.700000 * 0.800000 0.800000 0.900000 0.900000 * 1.00000 1.00000 Problem 3 DeBoor example, Mars position, data vector X Y * 1250.50 1.39140 1255.50 1.38387 * 1260.50 1.37451 1265.50 1.36179 * 1270.50 1.34547 1275.50 1.32562 * 1280.50 1.30232 1285.50 1.27567 * 1290.50 1.24578 1295.50 1.21274 * 1300.50 1.17668 1305.50 1.13773 * 1310.50 1.09600 1315.50 1.05164 * 1320.50 1.00479 1325.50 0.955576 * 1330.50 0.904150 1335.50 0.850803 * 1340.50 0.796420 Problem 4 DeBoor example, roughly linear data X Y * 1.00000 0.00000 1.50000 0.311875 * 2.00000 0.695000 2.50000 1.17563 * 3.00000 1.60000 3.50000 1.84958 * 4.00000 2.12667 4.50000 2.61625 * 5.00000 3.11333 5.50000 3.40833 * 6.00000 3.66333 6.50000 4.06562 * 7.00000 4.53167 7.50000 4.93771 * 8.00000 5.27000 8.50000 5.56146 * 9.00000 5.92167 9.50000 6.41729 * 10.0000 6.86667 10.5000 7.09083 * 11.0000 7.17000 Problem 5 The pulse data, 0 0 0 0 0 1 0 0 0 0 0 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.208333E-01 * 4.00000 0.166667 4.50000 0.479167 * 5.00000 0.666667 5.50000 0.479167 * 6.00000 0.166667 6.50000 0.208333E-01 * 7.00000 0.00000 7.50000 0.00000 * 8.00000 0.00000 8.50000 0.00000 * 9.00000 0.00000 9.50000 0.00000 * 10.0000 0.00000 Problem 6 The jump data, 0 0 0 0 0 1/2 1 1 1 1 1 X Y * 0.00000 0.00000 0.500000 0.00000 * 1.00000 0.00000 1.50000 0.00000 * 2.00000 0.00000 2.50000 0.00000 * 3.00000 0.00000 3.50000 0.00000 * 4.00000 0.00000 4.49500 0.104167E-01 * 4.99000 0.833333E-01 4.99500 0.260417 * 5.00000 0.500000 5.00500 0.739583 * 5.01000 0.916667 5.50500 0.989583 * 6.00000 1.00000 6.50000 1.00000 * 7.00000 1.00000 7.50000 1.00000 * 8.00000 1.00000 8.50000 1.00000 * 9.00000 1.00000 9.50000 1.00000 * 10.0000 1.00000 Problem 7 DeBoor's Titanium Property X Y * 595.000 0.644000 600.000 0.633792 * 605.000 0.628333 610.000 0.630687 * 615.000 0.637167 620.000 0.643229 * 625.000 0.647667 630.000 0.650000 * 635.000 0.649333 640.000 0.645583 * 645.000 0.642333 650.000 0.643000 * 655.000 0.646667 660.000 0.651250 * 665.000 0.654333 670.000 0.654333 * 675.000 0.653333 680.000 0.653375 * 685.000 0.652667 690.000 0.649833 * 695.000 0.649000 700.000 0.653729 * 705.000 0.659833 710.000 0.662708 * 715.000 0.663833 720.000 0.665667 * 725.000 0.668500 730.000 0.671896 * 735.000 0.674667 740.000 0.676042 * 745.000 0.677667 750.000 0.680854 * 755.000 0.683167 760.000 0.682271 * 765.000 0.680000 770.000 0.678750 * 775.000 0.679000 780.000 0.680750 * 785.000 0.684000 790.000 0.688500 * 795.000 0.693000 800.000 0.696500 * 805.000 0.700000 810.000 0.704813 * 815.000 0.711500 820.000 0.720458 * 825.000 0.732167 830.000 0.747104 * 835.000 0.765667 840.000 0.788792 * 845.000 0.819667 850.000 0.861333 * 855.000 0.914000 860.000 0.979604 * 865.000 1.06983 870.000 1.19850 * 875.000 1.37817 880.000 1.60842 * 885.000 1.83817 890.000 2.01169 * 895.000 2.10533 900.000 2.10606 * 905.000 2.01117 910.000 1.83040 * 915.000 1.61300 920.000 1.40829 * 925.000 1.22633 930.000 1.06802 * 935.000 0.936833 940.000 0.835604 * 945.000 0.762000 950.000 0.711604 * 955.000 0.676833 960.000 0.650792 * 965.000 0.632500 970.000 0.621771 * 975.000 0.615667 980.000 0.611229 * 985.000 0.608167 990.000 0.606729 * 995.000 0.606667 1000.00 0.607396 * 1005.00 0.607500 1010.00 0.605896 * 1015.00 0.603667 1020.00 0.602167 * 1025.00 0.601667 1030.00 0.602000 * 1035.00 0.602333 1040.00 0.602167 * 1045.00 0.603000 1050.00 0.605833 * 1055.00 0.607667 1060.00 0.605938 * 1065.00 0.603833 1070.00 0.604854 * 1075.00 0.608000 Problem 8 The Sawtooth X Y * 0.00000 0.00000 0.250000 0.458333 * 0.500000 0.666667 0.750000 0.489583 * 1.00000 0.250000 1.12500 0.281250 * 1.25000 0.500000 1.37500 0.729167 * 1.50000 0.833333 1.62500 0.729167 * 1.75000 0.500000 1.87500 0.267361 * 2.00000 0.138889 2.08333 0.184028 * 2.16667 0.333333 2.25000 0.500000 * 2.33333 0.666667 2.41667 0.819444 * 2.50000 0.888889 2.58333 0.819444 * 2.66667 0.666667 2.75000 0.500000 * 2.83333 0.333333 2.91667 0.178819 * 3.00000 0.972222E-01 3.06250 0.137153 * 3.12500 0.250000 3.18750 0.375000 * 3.25000 0.500000 3.31250 0.625000 * 3.37500 0.750000 3.43750 0.864583 * 3.50000 0.916667 3.56250 0.864583 * 3.62500 0.750000 3.68750 0.625000 * 3.75000 0.500000 3.81250 0.375000 * 3.87500 0.250000 3.93750 0.134375 * 4.00000 0.750000E-01 4.05000 0.109375 * 4.10000 0.200000 4.15000 0.300000 * 4.20000 0.400000 4.25000 0.500000 * 4.30000 0.600000 4.35000 0.700000 * 4.40000 0.800000 4.45000 0.891667 * 4.50000 0.933333 4.55000 0.891667 * 4.60000 0.800000 4.65000 0.700000 * 4.70000 0.600000 4.75000 0.500000 * 4.80000 0.400000 4.85000 0.300000 * 4.90000 0.200000 4.95000 0.100000 * 5.00000 0.00000 Problem 9 Concavity test X Y * 0.00000 0.00000 0.500000E-01 0.432292 * 0.100000 0.758333 0.150000 0.905208 * 0.200000 0.933333 0.250000 0.907292 * 0.300000 0.775000 0.350000 0.500000 * 0.400000 0.225000 0.450000 0.916667E-01 * 0.500000 0.583333E-01 0.550000 0.541667E-01 * 0.600000 0.750000E-01 0.700000 0.141667 * 0.800000 0.308333 0.900000 0.613542 * 1.00000 1.00000 Problem 10 Extrapolation test. X Y * 0.00000 0.00000 35.5000 3.96510 * 71.0000 8.45463 87.5000 13.8991 * 104.000 20.3530 119.500 27.5268 * 135.000 34.1288 140.000 39.1439 * 145.000 43.6624 152.500 48.9412 * 160.000 54.7958 170.500 60.7643 * 181.000 66.7171 187.000 72.6110 * 193.000 78.4164 199.000 84.1357 * 205.000 89.8854 210.000 95.7668 * 215.000 101.706 220.000 107.822 * 225.000 115.189 231.500 124.683 * 238.000 135.457 Problem 11 Sunspot Data, 1700-1960. X Y * 1700.00 5.00000 1700.50 7.97917 * 1701.00 10.8333 1701.50 13.5208 * 1702.00 16.3333 1702.50 19.6667 * 1703.00 24.0000 1703.50 29.8125 * 1704.00 37.5000 1704.50 46.1250 * 1705.00 49.5000 1705.50 42.8542 * 1706.00 32.3333 1706.50 24.8958 * 1707.00 19.8333 1707.50 15.1458 * 1708.00 11.3333 1708.50 9.10417 * 1709.00 7.50000 1709.50 5.47917 * 1710.00 3.33333 1710.50 1.60417 * 1711.00 0.500000 1711.50 0.104167 * 1712.00 0.333333 1712.50 1.18750 * 1713.00 3.16667 1713.50 6.79167 * 1714.00 12.1667 1714.50 19.2292 * 1715.00 27.6667 1715.50 37.0000 * 1716.00 46.3333 1716.50 54.5208 * 1717.00 59.8333 1717.50 60.7292 * 1718.00 57.0000 1718.50 49.3333 * 1719.00 40.6667 1719.50 33.8958 * 1720.00 29.5000 1720.50 27.1458 * 1721.00 25.6667 1721.50 23.8125 * 1722.00 20.8333 1722.50 16.7917 * 1723.00 14.5000 1723.50 16.6250 * 1724.00 22.5000 1724.50 31.0833 * 1725.00 43.1667 1725.50 59.5208 * 1726.00 79.0000 1726.50 98.8125 * 1727.00 111.500 1727.50 110.958 * 1728.00 101.167 1728.50 87.8542 * 1729.00 73.6667 1729.50 60.3750 * 1730.00 49.3333 1730.50 41.0417 * 1731.00 33.0000 1731.50 23.1250 * 1732.00 14.0000 1732.50 8.72917 * 1733.00 7.83333 1733.50 11.0000 * 1734.00 17.1667 1734.50 25.5208 * 1735.00 37.0000 1735.50 51.8542 * 1736.00 65.8333 1736.50 75.3750 * 1737.00 84.1667 1737.50 95.5625 * 1738.00 104.333 1738.50 104.792 * 1739.00 98.0000 1739.50 86.5208 * 1740.00 72.1667 1740.50 56.6667 * 1741.00 42.1667 1741.50 30.6042 * 1742.00 22.6667 1742.50 18.1875 * 1743.00 14.8333 1743.50 10.7083 * 1744.00 7.83333 1744.50 8.45833 * 1745.00 11.8333 1745.50 16.7500 * 1746.00 23.1667 1746.50 31.1875 * 1747.00 40.3333 1747.50 50.0604 * 1748.00 60.1500 1748.50 70.0854 * 1749.00 77.8333 1749.50 80.9708 * 1750.00 77.0333 1750.50 65.5000 * 1751.00 53.6667 1751.50 48.1375 * 1752.00 44.9333 1752.50 38.8625 * 1753.00 30.4667 1753.50 21.7521 * 1754.00 14.8500 1754.50 11.2979 * 1755.00 10.1333 1755.50 10.4167 * 1756.00 13.8000 1756.50 21.6042 * 1757.00 31.2333 1757.50 39.6708 * 1758.00 46.1333 1758.50 50.6688 * 1759.00 54.4167 1759.50 58.7958 * 1760.00 65.2500 1760.50 73.7000 * 1761.00 77.9500 1761.50 72.7354 * 1762.00 62.6333 1762.50 53.4833 * 1763.00 46.3333 1763.50 40.7625 * 1764.00 35.2667 1764.50 28.6333 * 1765.00 21.9000 1765.50 17.0229 * 1766.00 17.3833 1766.50 25.4646 * 1767.00 38.7333 1767.50 54.0063 * 1768.00 70.5167 1768.50 87.1729 * 1769.00 99.1667 1769.50 102.294 * 1770.00 98.4833 1770.50 90.9958 * 1771.00 82.2833 1771.50 73.7896 * 1772.00 63.7333 1772.50 50.8771 * 1773.00 39.3833 1773.50 32.8688 * 1774.00 27.3667 1774.50 19.1542 * 1775.00 13.0667 1775.50 15.4063 * 1776.00 29.7833 1776.50 57.1729 * 1777.00 90.7000 1777.50 121.342 * 1778.00 139.333 1778.50 138.004 * 1779.00 123.800 1779.50 105.596 * 1780.00 88.8667 1780.50 76.6896 * 1781.00 65.9500 1781.50 53.3208 * 1782.00 40.8167 1782.50 31.0042 * 1783.00 23.3167 1783.50 17.1167 * 1784.00 14.6167 1784.50 18.6375 * 1785.00 31.5833 1785.50 54.2333 * 1786.00 81.2833 1786.50 106.202 * 1787.00 123.633 1787.50 130.160 * 1788.00 128.950 1788.50 123.935 * 1789.00 115.533 1789.50 103.781 * 1790.00 90.7167 1790.50 78.7000 * 1791.00 69.3833 1791.50 63.5125 * 1792.00 58.9167 1792.50 53.4646 * 1793.00 48.1000 1793.50 43.8125 * 1794.00 38.7000 1794.50 31.1625 * 1795.00 23.7000 1795.50 18.8604 * 1796.00 15.2833 1796.50 11.2625 * 1797.00 7.61667 1797.50 5.50625 * 1798.00 4.93333 1798.50 5.65833 * 1799.00 7.63333 1799.50 11.0000 * 1800.00 16.4667 1800.50 24.3188 * 1801.00 32.5833 1801.50 39.0542 * 1802.00 42.8500 1802.50 43.9125 * 1803.00 44.1500 1803.50 45.2292 * 1804.00 45.8833 1804.50 44.4646 * 1805.00 40.7333 1805.50 34.8854 * 1806.00 27.4500 1806.50 19.3521 * 1807.00 12.7667 1807.50 9.35833 * 1808.00 7.50000 1808.50 5.28958 * 1809.00 3.01667 1809.50 1.39583 * 1810.00 0.650000 1810.50 0.827083 * 1811.00 1.76667 1811.50 3.32083 * 1812.00 5.60000 1812.50 8.56042 * 1813.00 11.2833 1813.50 13.3479 * 1814.00 17.2000 1814.50 24.8312 * 1815.00 33.5500 1815.50 40.0542 * 1816.00 43.2833 1816.50 43.0042 * 1817.00 40.0500 1817.50 35.5688 * 1818.00 30.9000 1818.50 27.0562 * 1819.00 23.5500 1819.50 19.6917 * 1820.00 15.4833 1820.50 11.2188 * 1821.00 7.66667 1821.50 5.44167 * 1822.00 4.06667 1822.50 3.09375 * 1823.00 3.28333 1823.50 5.36458 * 1824.00 8.73333 1824.50 12.8208 * 1825.00 18.5333 1825.50 26.5583 * 1826.00 35.2333 1826.50 42.8438 * 1827.00 49.8167 1827.50 56.6813 * 1828.00 62.2333 1828.50 65.3771 * 1829.00 67.1833 1829.50 68.4104 * 1830.00 66.4000 1830.50 58.8458 * 1831.00 48.2667 1831.50 37.7354 * 1832.00 27.7167 1832.50 18.5208 * 1833.00 12.4500 1833.50 12.1563 * 1834.00 19.7000 1834.50 36.2979 * 1835.00 60.3833 1835.50 88.6396 * 1836.00 113.533 1836.50 127.823 * 1837.00 129.650 1837.50 120.035 * 1838.00 106.133 1838.50 94.7417 * 1839.00 85.1000 1839.50 74.9333 * 1840.00 63.4667 1840.50 50.8292 * 1841.00 39.2667 1841.50 30.7500 * 1842.00 24.0333 1842.50 17.8000 * 1843.00 13.6667 1843.50 13.6542 * 1844.00 18.4667 1844.50 27.9063 * 1845.00 39.4833 1845.50 51.0479 * 1846.00 64.1000 1846.50 80.1000 * 1847.00 96.7000 1847.50 110.238 * 1848.00 115.600 1848.50 109.335 * 1849.00 96.0833 1849.50 81.9979 * 1850.00 71.2000 1850.50 65.9521 * 1851.00 63.1167 1851.50 59.0292 * 1852.00 53.3167 1852.50 46.3833 * 1853.00 38.4500 1853.50 29.8250 * 1854.00 21.3500 1854.50 13.9833 * 1855.00 8.61667 1855.50 6.17292 * 1856.00 7.76667 1856.50 14.2188 * 1857.00 24.9833 1857.50 39.1792 * 1858.00 55.9500 1858.50 73.6729 * 1859.00 87.6333 1859.50 93.6000 * 1860.00 92.3667 1860.50 86.0812 * 1861.00 77.2833 1861.50 68.2229 * 1862.00 59.6000 1862.50 51.9896 * 1863.00 47.0167 1863.50 45.4708 * 1864.00 43.7500 1864.50 38.3917 * 1865.00 30.8833 1865.50 23.5563 * 1866.00 17.1667 1866.50 12.7271 * 1867.00 13.8500 1867.50 23.3958 * 1868.00 38.6167 1868.50 56.5229 * 1869.00 78.7667 1869.50 105.162 * 1870.00 123.533 1870.50 123.546 * 1871.00 114.233 1871.50 106.242 * 1872.00 97.3000 1872.50 83.6521 * 1873.00 68.5167 1873.50 55.6104 * 1874.00 43.6667 1874.50 31.1792 * 1875.00 20.6667 1875.50 14.7500 * 1876.00 12.4333 1876.50 11.7813 * 1877.00 10.7167 1877.50 7.93125 * 1878.00 5.33333 1878.50 5.43542 * 1879.00 9.95000 1879.50 19.5542 * 1880.00 31.5833 1880.50 42.8646 * 1881.00 51.5333 1881.50 56.6250 * 1882.00 59.4667 1882.50 61.5833 * 1883.00 63.0000 1883.50 63.2813 * 1884.00 61.6500 1884.50 57.2958 * 1885.00 49.6167 1885.50 38.7792 * 1886.00 27.8167 1886.50 19.6771 * 1887.00 14.1000 1887.50 10.1958 * 1888.00 7.76667 1888.50 6.69792 * 1889.00 6.51667 1889.50 7.30417 * 1890.00 11.7167 1890.50 22.1125 * 1891.00 37.0833 1891.50 53.9583 * 1892.00 68.7833 1892.50 78.1229 * 1893.00 81.9000 1893.50 81.0062 * 1894.00 76.8500 1894.50 70.6854 * 1895.00 62.6333 1895.50 52.8667 * 1896.00 42.9000 1896.50 34.4729 * 1897.00 28.8833 1897.50 26.4708 * 1898.00 24.1833 1898.50 19.3354 * 1899.00 14.1000 1899.50 10.9625 * 1900.00 8.80000 1900.50 6.20208 * 1901.00 4.21667 1901.50 4.39583 * 1902.00 7.85000 1902.50 15.0188 * 1903.00 24.1000 1903.50 33.2437 * 1904.00 42.6500 1904.50 52.1812 * 1905.00 58.3000 1905.50 58.3729 * 1906.00 56.7833 1906.50 57.8208 * 1907.00 58.3833 1907.50 54.9833 * 1908.00 49.9833 1908.50 45.9542 * 1909.00 40.4500 1909.50 31.0771 * 1910.00 20.6667 1910.50 12.6333 * 1911.00 7.50000 1911.50 4.87292 * 1912.00 3.58333 1912.50 2.71458 * 1913.00 3.13333 1913.50 6.33333 * 1914.00 14.5333 1914.50 28.5313 * 1915.00 42.7167 1915.50 52.4375 * 1916.00 63.2833 1916.50 79.8125 * 1917.00 92.2167 1917.50 90.9208 * 1918.00 81.6500 1918.50 72.0437 * 1919.00 62.1000 1919.50 50.7146 * 1920.00 40.0167 1920.50 32.1438 * 1921.00 26.0333 1921.50 20.2146 * 1922.00 14.7833 1922.50 10.4750 * 1923.00 9.01667 1923.50 12.0000 * 1924.00 19.4833 1924.50 30.6813 * 1925.00 42.9667 1925.50 53.6313 * 1926.00 61.4833 1926.50 66.2250 * 1927.00 69.6167 1927.50 73.0250 * 1928.00 74.1833 1928.50 70.5583 * 1929.00 62.1833 1929.50 50.2667 * 1930.00 38.1500 1930.50 28.8479 * 1931.00 21.9333 1931.50 16.3396 * 1932.00 11.8833 1932.50 8.67292 * 1933.00 7.10000 1933.50 7.88333 * 1934.00 12.7667 1934.50 23.2458 * 1935.00 38.8000 1935.50 58.0521 * 1936.00 78.2167 1936.50 96.0417 * 1937.00 107.817 1937.50 110.844 * 1938.00 106.933 1938.50 98.8625 * 1939.00 88.7667 1939.50 78.3104 * 1940.00 67.9167 1940.50 57.7354 * 1941.00 48.0667 1941.50 39.1750 * 1942.00 31.0333 1942.50 23.6625 * 1943.00 17.5667 1943.50 13.7396 * 1944.00 14.6500 1944.50 22.7771 * 1945.00 39.1667 1945.50 63.6375 * 1946.00 92.5333 1946.50 120.544 * 1947.00 139.217 1947.50 142.688 * 1948.00 138.583 1948.50 134.760 * 1949.00 126.500 1949.50 109.031 * 1950.00 89.9500 1950.50 76.9188 * 1951.00 65.5000 1951.50 50.3854 * 1952.00 34.8833 1952.50 23.2917 * 1953.00 15.2500 1953.50 10.2167 * 1954.00 11.5833 1954.50 23.5583 * 1955.00 49.6833 1955.50 90.1604 * 1956.00 132.500 1956.50 163.677 * 1957.00 181.217 1957.50 185.952 * 1958.00 181.400 1958.50 171.040 * 1959.00 155.517 1959.50 135.215 * 1960.00 112.300 TEST10 Plot a B spline approximant. Data points: 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 Problem 9 Concavity test Plot points: 1 0.00000 0.00000 2 0.166667E-01 0.149344 3 0.333333E-01 0.294753 4 0.500000E-01 0.432292 5 0.666667E-01 0.558025 6 0.833333E-01 0.668017 7 0.100000 0.758333 8 0.116667 0.826273 9 0.133333 0.874074 10 0.150000 0.905208 11 0.166667 0.923148 12 0.183333 0.931366 13 0.200000 0.933333 14 0.216667 0.931443 15 0.233333 0.923765 16 0.250000 0.907292 17 0.266667 0.879012 18 0.283333 0.835918 19 0.300000 0.775000 20 0.316667 0.694907 21 0.333333 0.600926 22 0.350000 0.500000 23 0.366667 0.399074 24 0.383333 0.305093 25 0.400000 0.225000 26 0.416667 0.164043 27 0.433333 0.120679 28 0.450000 0.916667E-01 29 0.466667 0.737654E-01 30 0.483333 0.637346E-01 31 0.500000 0.583333E-01 32 0.516667 0.549383E-01 33 0.533333 0.533951E-01 34 0.550000 0.541667E-01 35 0.566667 0.577160E-01 36 0.583333 0.645062E-01 37 0.600000 0.750000E-01 38 0.633333 0.899691E-01 39 0.666667 0.111420 40 0.700000 0.141667 41 0.733333 0.183025 42 0.766667 0.237809 43 0.800000 0.308333 44 0.833333 0.396026 45 0.866667 0.498765 46 0.900000 0.613542 47 0.933333 0.737346 48 0.966667 0.867168 49 1.00000 1.00000 TEST11 Plot a beta spline approximant. BETA1 = 100.000 BETA2 = 0.00000 Data points: 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 Problem 9 Concavity test Plot points: 1 0.00000 -0.882178 2 0.166667E-01 -0.509781 3 0.333333E-01 -0.258687 4 0.500000E-01 -0.104637 5 0.666667E-01 -0.233736E-01 6 0.833333E-01 0.935977E-02 7 0.100000 0.178209E-01 8 0.116667 0.389521 9 0.133333 0.638764 10 0.150000 0.790041 11 0.166667 0.867843 12 0.183333 0.896663 13 0.200000 0.900990 14 0.216667 0.921597 15 0.233333 0.935329 16 0.250000 0.943561 17 0.266667 0.947668 18 0.283333 0.949026 19 0.300000 0.949009 20 0.316667 0.927705 21 0.333333 0.912122 22 0.350000 0.901117 23 0.366667 0.893549 24 0.383333 0.888277 25 0.400000 0.884159 26 0.416667 0.553755 27 0.433333 0.332193 28 0.450000 0.197707 29 0.466667 0.128526 30 0.483333 0.102883 31 0.500000 0.990100E-01 32 0.516667 0.783622E-01 33 0.533333 0.645215E-01 34 0.550000 0.561263E-01 35 0.566667 0.518152E-01 36 0.583333 0.502270E-01 37 0.600000 0.500001E-01 38 0.633333 0.501232E-01 39 0.666667 0.504500E-01 40 0.700000 0.509394E-01 41 0.733333 0.515502E-01 42 0.766667 0.522411E-01 43 0.800000 0.529709E-01 44 0.833333 0.115570 45 0.866667 0.158835 46 0.900000 0.186631 47 0.933333 0.202821 48 0.966667 0.211270 49 1.00000 0.215842 TEST12 Plot a cubic spline interpolant. Problem 10 Extrapolation test. Plot points: 1 0.00000 0.00000 2 2.75000 -0.185085 3 5.50000 -0.331049 4 8.25000 -0.437890 5 11.0000 -0.505609 6 13.7500 -0.534206 7 16.5000 -0.523680 8 19.2500 -0.474033 9 22.0000 -0.385263 10 24.7500 -0.257371 11 27.5000 -0.903567E-01 12 30.2500 0.115780 13 33.0000 0.361038 14 35.7500 0.645419 15 38.5000 0.968922 16 41.2500 1.33155 17 44.0000 1.73329 18 46.7500 2.17416 19 49.5000 2.65415 20 52.2500 3.17327 21 55.0000 3.73150 22 57.7500 4.32886 23 60.5000 4.96534 24 63.2500 5.64095 25 66.0000 6.35567 26 68.7500 7.10952 27 71.5000 7.90248 28 74.2500 8.73407 29 77.0000 9.60260 30 79.7500 10.5062 31 82.5000 11.4431 32 85.2500 12.4114 33 88.0000 13.4093 34 90.7500 14.4349 35 93.5000 15.4863 36 96.2500 16.5618 37 99.0000 17.6595 38 101.750 18.7776 39 104.500 19.9141 40 107.250 21.0700 41 110.000 22.2522 42 112.750 23.4685 43 115.500 24.7268 44 118.250 26.0350 45 121.000 27.4009 46 123.750 28.8324 47 126.500 30.3374 48 129.250 31.9237 49 132.000 33.5992 50 134.750 35.3716 51 137.500 37.2482 52 140.250 39.2319 53 143.000 41.3244 54 145.750 43.5269 55 148.500 45.8166 56 151.250 48.1259 57 154.000 50.3828 58 156.750 52.5149 59 159.500 54.4501 60 162.250 56.1312 61 165.000 57.6046 62 167.750 58.9613 63 170.500 60.2921 64 173.250 61.6881 65 176.000 63.2401 66 178.750 65.0393 67 181.500 67.1762 68 184.250 69.6769 69 187.000 72.4146 70 189.750 75.2410 71 192.500 78.0078 72 195.250 80.5930 73 198.000 83.0594 74 200.750 85.5483 75 203.500 88.2013 76 206.250 91.1554 77 209.000 94.4072 78 211.750 97.7960 79 214.500 101.152 80 217.250 104.340 81 220.000 107.445 82 222.750 110.653 83 225.500 114.147 84 228.250 118.061 85 231.000 122.412 86 233.750 127.199 87 236.500 132.423 88 239.250 138.084 89 242.000 144.181 90 244.750 150.716 91 247.500 157.687 92 250.250 165.095 93 253.000 172.939 94 255.750 181.220 95 258.500 189.939 96 261.250 199.093 97 264.000 208.685 98 266.750 218.713 99 269.500 229.178 100 272.250 240.080 101 275.000 251.418 TEST_APPROX_PRB Normal end of execution. 15 December 2008 8:50:38.178 AM