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88 lines
2.1 KiB
88 lines
2.1 KiB
/*
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* Work in this file is derived from code originally written by Hans-Peter Moser:
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* http://www.mosismath.com/NaturalSplines/NaturalSplines.html
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*/
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namespace Connected.Components;
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public class NaturalSpline : SplineInterpolator
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{
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/// <summary>
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/// Natural Spline data interpolator
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/// </summary>
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public NaturalSpline(double[] xs, double[] ys, int resolution = 10) : base(xs, ys, resolution)
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{
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m = new Matrix(n - 2);
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gauss = new MatrixSolver(n - 2, m);
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a = new double[n];
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b = new double[n];
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c = new double[n];
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d = new double[n];
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h = new double[n - 1];
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CalcParameters();
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Integrate();
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Interpolate();
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}
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public void CalcParameters()
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{
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for (int i = 0; i < n; i++)
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a[i] = GivenYs[i];
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for (int i = 0; i < n - 1; i++)
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h[i] = GivenXs[i + 1] - GivenXs[i];
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for (int i = 0; i < n - 2; i++)
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{
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for (int k = 0; k < n - 2; k++)
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{
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m.a[i, k] = 0.0;
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m.y[i] = 0.0;
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m.x[i] = 0.0;
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}
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}
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for (int i = 0; i < n - 2; i++)
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{
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if (i == 0)
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{
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m.a[i, 0] = 2.0 * (h[0] + h[1]);
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m.a[i, 1] = h[1];
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}
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else
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{
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m.a[i, i - 1] = h[i];
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m.a[i, i] = 2.0 * (h[i] + h[i + 1]);
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if (i < n - 3)
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m.a[i, i + 1] = h[i + 1];
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}
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if ((h[i] != 0.0) && (h[i + 1] != 0.0))
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m.y[i] = ((a[i + 2] - a[i + 1]) / h[i + 1] - (a[i + 1] - a[i]) / h[i]) * 3.0;
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else
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m.y[i] = 0.0;
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}
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if (gauss.Eliminate() == false)
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throw new InvalidOperationException("error in matrix calculation");
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gauss.Solve();
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c[0] = 0.0;
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c[n - 1] = 0.0;
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for (int i = 1; i < n - 1; i++)
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c[i] = m.x[i - 1];
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for (int i = 0; i < n - 1; i++)
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{
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if (h[i] != 0.0)
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{
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d[i] = 1.0 / 3.0 / h[i] * (c[i + 1] - c[i]);
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b[i] = 1.0 / h[i] * (a[i + 1] - a[i]) - h[i] / 3.0 * (c[i + 1] + 2 * c[i]);
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}
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}
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}
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}
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