/// <summary>
/// Create a linear spline interpolation based on arbitrary points (sorted ascending).
/// </summary>
/// <param name="points">The sample points t, sorted ascending. Supports both lists and arrays.</param>
/// <param name="values">The sample point values x(t). Supports both lists and arrays.</param>
/// <returns>
/// An interpolation scheme optimized for the given sample points and values,
/// which can then be used to compute interpolations and extrapolations
/// on arbitrary points.
/// </returns>
public static IInterpolation LinearBetweenPoints(IList <double> points, IList <double> values)
{
var method = new LinearSplineInterpolation();
method.Initialize(points, values);
return(method);
}
/// <summary>
/// Interpolation of the interface points onto the equidistant Fourier points
/// </summary>
protected void InterpolateOntoFourierPoints(MultidimensionalArray interP, double[] samplP)
{
int numP = interP.Lengths[0];
// set interpolation data
double[] independentVal = new double[numP + 2];
double[] dependentVal = new double[numP + 2];
for (int sp = 1; sp <= numP; sp++)
{
independentVal[sp] = interP[sp - 1, 0];
dependentVal[sp] = interP[sp - 1, 1];
}
// extend the interpolation data for sample points at the boundary of the domain
independentVal[0] = interP[numP - 1, 0] - DomainSize;
dependentVal[0] = interP[numP - 1, 1];
independentVal[numP + 1] = interP[0, 0] + DomainSize;
dependentVal[numP + 1] = interP[0, 1];
switch (this.InterpolationType)
{
case Interpolationtype.LinearSplineInterpolation:
LinearSplineInterpolation LinSpline = new LinearSplineInterpolation();
LinSpline.Initialize(independentVal, dependentVal);
for (int sp = 0; sp < numFp; sp++)
{
samplP[sp] = LinSpline.Interpolate(FourierP[sp]);
//invDFT_coeff[sp] = (Complex)samplP[sp];
}
break;
case Interpolationtype.CubicSplineInterpolation:
CubicSplineInterpolation CubSpline = new CubicSplineInterpolation();
CubSpline.Initialize(independentVal, dependentVal);
for (int sp = 0; sp < numFp; sp++)
{
samplP[sp] = CubSpline.Interpolate(FourierP[sp]);
//invDFT_coeff[sp] = (Complex)samplP[sp];
}
break;
default:
throw new NotImplementedException();
}
}
/// <summary>
/// Interpolation of no equidistant sample point onto equidistant Fourier points
/// </summary>
public static void InterpolateOntoFourierPoints(MultidimensionalArray samplP, double DomainSize, double[] samplFp)
{
int numSp = samplP.Lengths[0];
// set interpolation data (delete multiple independent values)
ArrayList independentList = new ArrayList();
ArrayList dependentList = new ArrayList();
for (int sp = 0; sp < numSp; sp++)
{
if (independentList.Contains(samplP[sp, 0]) == false)
{
independentList.Add(samplP[sp, 0]);
dependentList.Add(samplP[sp, 1]);
}
}
// extend the interpolation data for sample points at the boundary of the domain
independentList.Insert(0, samplP[numSp - 1, 0] - DomainSize);
independentList.Insert(independentList.Count, samplP[0, 0] + DomainSize);
dependentList.Insert(0, samplP[numSp - 1, 1]);
dependentList.Insert(dependentList.Count, samplP[0, 1]);
double[] independentVal = (double[])independentList.ToArray(typeof(double));
double[] dependentVal = (double[])dependentList.ToArray(typeof(double));
// set Fourier points
int numSFp = samplFp.Length;
double[] FourierP = new double[numSFp];
for (int i = 0; i < numSFp; i++)
{
FourierP[i] = (DomainSize / numSFp) * i;
}
switch (InterpolationType)
{
case Interpolationtype.LinearSplineInterpolation:
LinearSplineInterpolation LinSpline = new LinearSplineInterpolation();
LinSpline.Initialize(independentVal, dependentVal);
for (int Fp = 0; Fp < numSFp; Fp++)
{
samplFp[Fp] = LinSpline.Interpolate(FourierP[Fp]);
}
break;
case Interpolationtype.CubicSplineInterpolation:
CubicSplineInterpolation CubSpline = new CubicSplineInterpolation();
CubSpline.Initialize(independentVal, dependentVal);
for (int Fp = 0; Fp < numSFp; Fp++)
{
samplFp[Fp] = CubSpline.Interpolate(FourierP[Fp]);
}
break;
default:
throw new NotImplementedException();
}
}
