/// <summary>
/// Creates a continuous piece-linear function from the points list.
/// The user should also specify a default value to return
/// when the function argument is out of the interpolation area bounds.
/// </summary>
/// <param name="points"></param>
/// <param name="defaultValue"></param>
/// <returns></returns>
public static PieceFunction <T, C> CreatePieceLinearFunction(IList <Point <T> > points, T defaultValue)
{
BoundedInterval <T, C>[] intervals = new BoundedInterval <T, C> [points.Count - 1];
IFunction <T, T>[] functions = new IFunction <T, T> [points.Count - 1];
for (int i = 0; i < points.Count - 1; i++)
{
intervals[i] = new BoundedInterval <T, C>(points[i].X, points[i + 1].X, true, false);
functions[i] = new LinearFunction <T, C>(points[i], points[i + 1]);
}
PieceFunction <T, C> fun = new PieceFunction <T, C>(intervals, functions, defaultValue);
fun.Type = PieceFunctionType.PieceLinearFunction;
return(fun);
}
/// <summary>
/// Creates a continuous natural cubic spline of defect 1.
/// Max. continuous derivative of the spline is second.
/// </summary>
/// <param name="points"></param>
/// <param name="defaultValue"></param>
/// <returns></returns>
public static PieceFunction <T, C> CreateNaturalCubicSpline(IList <Point <T> > points, T defaultValue)
{
int n = points.Count - 1; // количество точек
Numeric <T, C>[] a = new Numeric <T, C> [n];
Numeric <T, C>[] c = new Numeric <T, C> [n];
DefaultList <Numeric <T, C> > b = new DefaultList <Numeric <T, C> >(new Numeric <T, C> [n], Numeric <T, C> .Zero);
Numeric <T, C>[] delta = new Numeric <T, C> [n];
Numeric <T, C>[] lambda = new Numeric <T, C> [n];
Numeric <T, C>[] h = new Numeric <T, C> [n];
Numeric <T, C>[] fDiv = new Numeric <T, C> [n];
KeyValuePair <BoundedInterval <T, C>, IFunction <T, T> >[] pieces = new KeyValuePair <BoundedInterval <T, C>, IFunction <T, T> > [n];
// count h and fDiv
for (int i = 0; i < n; i++)
{
h[i] = calc.dif(points[i + 1].X, points[i].X);
fDiv[i] = calc.dif(points[i + 1].Y, points[i].Y) / h[i];
}
// h идут не от 1 до n
// а от 0 до n-1.
delta[0] = (Numeric <T, C>)(-0.5) * h[1] / (h[0] + h[1]);
lambda[0] = (Numeric <T, C>)(1.5) * (fDiv[1] - fDiv[0]) / (h[0] + h[1]);
// calculating lambda
Numeric <T, C> two = (Numeric <T, C>) 2;
Numeric <T, C> three = (Numeric <T, C>) 3;
for (int i = 2; i < n; i++)
{
delta[i - 1] = -h[i] / (two * (h[i - 1] + h[i]) + h[i - 1] * delta[i - 2]);
lambda[i - 1] = (three * (fDiv[i] - fDiv[i - 1]) - h[i - 1] * lambda[i - 2]) / (two * (h[i - 1] + h[i]) + h[i - 1] * delta[i - 2]);
}
// calculating b
b[n - 1] = Numeric <T, C> .Zero;
for (int i = n - 1; i > 0; i--)
{
b[i - 1] = delta[i - 1] * b[i] + lambda[i - 1];
}
// calculating others
for (int i = 0; i < n; i++)
{
a[i] = (b[i] - b[i - 1]) / (three * h[i]);
c[i] = fDiv[i] + two * h[i] * b[i] / three + h[i] * b[i - 1] / three;
pieces[i] = new KeyValuePair <BoundedInterval <T, C>, IFunction <T, T> >(
new BoundedInterval <T, C>(points[i].X, points[i + 1].X, true, false),
new CubicFunction <T, C> (a[i], b[i], c[i], points[i + 1].Y, points[i + 1].X));
}
PieceFunction <T, C> function = new PieceFunction <T, C>(defaultValue, pieces);
function.Type = PieceFunctionType.NaturalCubicSpline;
return(new PieceFunction <T, C>(defaultValue, pieces));
}