private Math_Collection.LinearAlgebra.Vectors.Vector GetCoefficientVector(double[] gi)
{
Math_Collection.LinearAlgebra.Vectors.Vector v = new Math_Collection.LinearAlgebra.Vectors.Vector(new double[_amountOfSplineParts + 1]);
for (int i = 2; i <= _amountOfSplineParts; i++)
{
v[i - 1] = gi[i];
}
return(v);
}
private List <double> CalculateD(Math_Collection.LinearAlgebra.Vectors.Vector outcome, List <double> hList)
{
List <double> dList = new List <double>();
for (int i = 0; i < outcome.Size - 1; i++)
{
dList.Add((outcome[i + 1] - outcome[i]) / (3 * hList[i]));
}
return(dList);
}
private List <string> CreateSplineFunctions(List <double> bList, Math_Collection.LinearAlgebra.Vectors.Vector c, List <double> dList)
{
List <string> splineFunctionList = new List <string>();
for (int i = 1; i < pointList.Count; i++)
{
splineFunctionList.Add("" + pointList[i - 1].Y +
(bList[i - 1] < 0 ? "+(" : "+(") + bList[i - 1] + (c[i - 1] < 0 ? "*x)+(" : "*x)+(") +
c[i - 1] + (dList[i - 1] < 0 ? "*(x^2))+(" : "*(x^2))+(") + dList[i - 1] + "*(x^3))");
}
return(splineFunctionList);
}
private List <double> CalculateB(Math_Collection.LinearAlgebra.Vectors.Vector c, List <double> hList)
{
List <double> bList = new List <double>();
for (int i = 1; i < pointList.Count; i++)
{
double b = ((pointList[i].Y - pointList[i - 1].Y) / hList[i - 1])
- ((hList[i - 1] / 3) * ((2 * c[i - 1]) + c[i]));
bList.Add(b);
}
return(bList);
}
private void Plot()
{
//Make asynchronous
List <double> hList = CalculateH();
List <double> gList = CalculateG(hList);
Math_Collection.LinearAlgebra.Matrices.Matrix m = CreateSplineMatrix(hList);
double[] gListAsArray = gList.ToArray();
LGS lgs = new LGS(m, new Math_Collection.LinearAlgebra.Vectors.Vector(gListAsArray));
//Make asynchronous
Math_Collection.LinearAlgebra.Vectors.Vector outcome = lgs.Solve(LGS.SolveAlgorithm.Gauß);
string sOutcome = outcome.ToString();
List <double> bList = CalculateB(outcome, hList);
List <double> dList = CalculateD(outcome, hList);
SolveSplineFunctions(CreateSplineFunctions(bList, outcome, dList));
}
private Math_Collection.LinearAlgebra.Vectors.Vector CopyTo(Math_Collection.LinearAlgebra.Vectors.Vector v, int startIndex, int sizeForNewArray)
{
if (v == null)
{
return(null);
}
if (v.Size == 0)
{
return(v);
}
if (sizeForNewArray < v.Size + startIndex)
{
throw new System.ArgumentException("The new vector must be big enough to old the data from the old vector");
}
double[] newValues = new double[sizeForNewArray];
v.Values.CopyTo(newValues, startIndex);
return(new Math_Collection.LinearAlgebra.Vectors.Vector(newValues));
}
/// <summary>
/// Calculates all polynominal parts of the spline
/// </summary>
/// <returns>A List of Functions that represents all polynominals</returns>
/// <seealso cref="http://www.tm-mathe.de/Themen/html/funnatsplines.html"/>
private List <Function> CalculateSplineParts()
{
if (_sourcePoints != null && _sourcePoints.Count < 3)
{
return(null);
}
// 3.Degree Polynomial := f(x) = a + bx + cx^2 + dx^3
// f'(x) = b + 2cx + 3dx^2
// f''(x) = 2c + 6dx
Parser parser = new Parser();
double[] xs = _sourcePoints.Keys.ToArray();
double[] ys = _sourcePoints.Values.ToArray();
#region Calculate Help Variable hi and gi
double[] hi = CalculateH(xs);
double[] gi = CalcualteG(ys, hi);
#endregion
#region Calculate all c's
Matrix coefficientMatrix = GetCoefficientMatrix(hi);
Math_Collection.LinearAlgebra.Vectors.Vector coefficientVector = GetCoefficientVector(gi);
LGS lgs = new LGS(coefficientMatrix, coefficientVector);
Math_Collection.LinearAlgebra.Vectors.Vector resultFromLGS = lgs.Solve(Math_Collection.Enums.ESolveAlgorithm.eGaussianElimination);
double[] ci = new double[_amountOfSplineParts + 2];
for (int i = 2; i <= _amountOfSplineParts + 1; i++)
{
ci[i] = resultFromLGS[i - 1];
}
#endregion
#region Calculates all a values
// a's = yi-1
double[] ai = new double[_amountOfSplineParts + 1];
for (int i = 1; i <= _amountOfSplineParts; i++)
{
ai[i] = ys[i - 1];
}
#endregion
#region Calculate all b's
// bi = (yi - yi-1) / hi - (hi / 3) * (2*ci + ci+1)
double[] bi = new double[_amountOfSplineParts + 1];
for (int i = 1; i <= _amountOfSplineParts; i++)
{
bi[i] = ((ys[i] - ys[i - 1]) / hi[i]) - (hi[i] / 3) * (2 * ci[i] + ci[i + 1]);
}
#endregion
#region Calculate all d's
// di = (ci+1 - ci) / 3 * hi
double[] di = new double[_amountOfSplineParts + 1];
for (int i = 1; i <= _amountOfSplineParts; i++)
{
di[i] = (ci[i + 1] - ci[i]) / (3 * hi[i]);
}
#endregion
#region Generate all Functions
Function[] functionParts = new Function[_amountOfSplineParts];
for (int i = 1; i <= _amountOfSplineParts; i++)
{
string f = ai[i] + "+" + bi[i] + "*x+" + ci[i] + "*x^2+" + di[i] + "*x^3";
functionParts[i - 1] = parser.ParseFunction(f);
}
#endregion
return(functionParts.ToList());
}
