private static BoundaryConditions GetBoundaryConditions_m_i()
{
Func fSecondDerivative =
LagrangePolynomial.Calculate(X, Y)
.FindDerivative()
.FindDerivative()
.Calculate;
double freeElem_1 = 3.0 * (Y[1] - Y[0]) / H(0)
- H(0) * fSecondDerivative(X[0]) / 2.0;
double freeElem_2 = 3.0 * (Y[X.Length - 1] - Y[X.Length - 2]) / H(X.Length - 2)
- H(X.Length - 2) * fSecondDerivative(X[X.Length - 2]) / 2.0;
BoundaryConditions boundaryConditions = new BoundaryConditions()
{
first = new VectorRow(X.Length + 1),
second = new VectorRow(X.Length + 1)
};
boundaryConditions.first[0] = 2.0;
boundaryConditions.first[1] = 1.0;
boundaryConditions.first[X.Length] = freeElem_1;
boundaryConditions.second[X.Length - 2] = 1.0;
boundaryConditions.second[X.Length - 1] = 2.0;
boundaryConditions.second[X.Length] = freeElem_2;
return(boundaryConditions);
}
private static LSystem BuildSystem(Matrix mainEquations, BoundaryConditions boundaryConditions)
{
if (boundaryConditions.first.Length != X.Length + 1 ||
boundaryConditions.second.Length != X.Length + 1 ||
mainEquations.Rows != X.Length - 2 ||
mainEquations.Columns != X.Length + 1)
{
throw new ArgumentException();
}
SquareMatrix matrix = new SquareMatrix(X.Length);
VectorColumn freeElems = new VectorColumn(X.Length);
for (int row = 1; row < X.Length - 1; row++)
{
for (int column = 0; column < X.Length; column++)
{
matrix[row, column] = mainEquations[row - 1, column];
}
freeElems[row] = mainEquations[row - 1, X.Length];
}
for (int column = 0; column < X.Length; column++)
{
matrix[0, column] = boundaryConditions.first[column];
matrix[X.Length - 1, column] = boundaryConditions.second[column];
}
freeElems[0] = boundaryConditions.first[X.Length];
freeElems[X.Length - 1] = boundaryConditions.second[X.Length];
return(new LSystem(matrix, freeElems));
}
private static BoundaryConditions GetBoundaryConditions_M_i()
{
BoundaryConditions boundaryConditions = new BoundaryConditions()
{
first = new VectorRow(X.Length + 1),
second = new VectorRow(X.Length + 1)
};
boundaryConditions.first[0] = 1.0;
boundaryConditions.second[X.Length - 1] = 1.0;
return(boundaryConditions);
}
public static Spline Calculate_M_i(double[] x, double[] y)
{
if (x.Length != y.Length)
{
throw new ArgumentException("y", "Array of function's values must has same length as array of arguments.");
}
X = x;
Y = y;
Matrix mainEquations = PrepareEquations_M_i();
BoundaryConditions boundaryConditions = GetBoundaryConditions_M_i();
LSystem system = BuildSystem(mainEquations, boundaryConditions);
VectorColumn solutions = Tridiagonal.Calculate(system);
return(new Spline(BuildSpline_M_i(solutions), X));
}
