public void SolveWithGaussSeidel_Test()
{
Matrix inputMatrix = new Matrix(new double[3, 3]
{
{ 10, -4, -2 },
{ -4, 10, -4 },
{ -6, -2, 12 }
});
Vector rightSideVector = new Vector(new double[3]
{
2,
3,
1
});
Vector startValue = new Vector(new double[3] {
0, 0, 0
});
LGS lgs = new LGS(inputMatrix, rightSideVector);
Vector result = lgs.Solve(Enums.ESolveAlgorithm.eGaußSeidel, startValue);
Vector expected = new Vector(new double[3] {
0.598, 0.741, 0.506
});
Assert.AreEqual(expected, result);
}
public static Function CreateRegression(List <Point> points, int degreeOfPolynominal)
{
if (degreeOfPolynominal < 1)
{
throw new ArgumentException("Degree of polynominal must be at least 1");
}
Matrix regressionMatrix = CreateRegressionMatrix(points, degreeOfPolynominal + 1);
Vector regressionVector = CreateRegressionVector(points, degreeOfPolynominal + 1);
Parser parser = new Parser();
LGS lgs = new LGS(regressionMatrix, regressionVector);
string function = CreateRegressionFunction(lgs.Solve(Enums.ESolveAlgorithm.eGaussianElimination), degreeOfPolynominal + 1);
return(parser.ParseFunction(function));
}
public void SolveWithGaussianElimination_Test()
{
Matrix m = new Matrix(new double[4, 4] {
{ 1, 1, 1, 1 }, { 1, 1, -1, -1 }, { 1, -1, 1, 1 }, { 1, -1, -1, 1 }
});
Vector v = new Vector(new double[4] {
0, 1, 3, -1
});
LGS lgs = new LGS(m, v);
Vector result = lgs.Solve(Enums.ESolveAlgorithm.eGaussianElimination);
Vector expected = new Vector(new double[6] {
1, -2, 3, 4, 2, -1
});
Assert.AreEqual(expected, result);
}
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));
}
/// <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());
}
/// <summary>
/// Berechnet die Regression für die gegebenen Punkte
/// </summary>
/// <param name="?"></param>
/// <param name="degreeOfPolynominal"></param>
/// <returns></returns>
public static Function CalculateRegression(List <Point> points, int degreeOfPolynominal = 1)
{
if (points == null || points.Count < 2)
{
return(null);
}
Matrix inputMatrix = new Matrix(new double[degreeOfPolynominal + 1, degreeOfPolynominal + 1]);
Math_Collection.LinearAlgebra.Vectors.Vector outputVector =
new Math_Collection.LinearAlgebra.Vectors.Vector(new double[degreeOfPolynominal + 1]);
int maxPower = degreeOfPolynominal * 2;
int actualPower = maxPower;
// Input Matrix aufbauen
for (int i = 0; i < inputMatrix.RowCount; i++)
{
for (int k = 0; k < inputMatrix.ColumnCount; k++)
{
actualPower = maxPower - (i + k);
inputMatrix[i, k] = SumXValues(points, actualPower);
}
}
maxPower = degreeOfPolynominal;
// Output Vector aufbauen
for (int m = 0; m < outputVector.Size; m++)
{
outputVector[m] = SumXYValues(points, maxPower);
maxPower--;
}
// LGS Lösen
LGS lgs = new LGS(inputMatrix, outputVector);
Math_Collection.LinearAlgebra.Vectors.Vector resultVector = lgs.Solve();
// Function aufbauen
// ax^1 + b; ax^2+bx^1+c
string functionString = "";
maxPower = degreeOfPolynominal;
for (int o = 0; o <= degreeOfPolynominal; o++)
{
if (o != degreeOfPolynominal)
{
functionString += string.Format(resultVector[o] + "*x^{0}+", maxPower);
}
else
{
functionString += resultVector[o];
}
maxPower--;
}
functionString = functionString.Replace(",", ".");
Parser parser = new Parser();
return(parser.ParseFunction(functionString));
}