public List <Point> QuadraticMethod(double h)
{
CheckStep(h);
if (points.Count < 3)
{
throw new Exception("Количество точек в заданном интервале недостаточно.");
}
List <Point> resultPoints = new List <Point>();
for (int k = 0; k < points.Count - 2; k++)
{
double[,] valuesA = new double[3, 3];
double[,] valuesB = new double[3, 1];
for (int i = 0; i < valuesA.GetLength(0); i++)
{
for (int j = 0; j < valuesA.GetLength(1); j++)
{
valuesA[i, j] = Math.Pow(points[k + i].X, 2 - j);
}
valuesB[i, 0] = points[k + i].Y;
}
Matrix A = new Matrix(valuesA);
Matrix B = new Matrix(valuesB);
SystemEquations systemEquations = new SystemEquations(A, B);
double[,] solution = systemEquations.MatrixMethod();
double a, b, c;
a = solution[0, 0];
b = solution[1, 0];
c = solution[2, 0];
if (k == 0)
{
for (double x = points[0].X; x < points[1].X; x += h)
{
double newX = x;
double newY = a * Math.Pow(newX, 2) + b * newX + c;
resultPoints.Add(new Point(newX, newY));
}
}
for (double x = points[k + 1].X; x <= points[k + 2].X; x += h)
{
double newX = x;
double newY = a * Math.Pow(newX, 2) + b * newX + c;
resultPoints.Add(new Point(newX, newY));
}
}
return(resultPoints);
}
public List <Point> SplineMethod(double step)
{
CheckStep(step);
double[,] A = new double[points.Count, points.Count];
double[,] B = new double[points.Count, 1];
double h = points[1].X - points[0].X;
for (int i = 0; i < A.GetLength(0); i++)
{
for (int j = 0; j < A.GetLength(1); j++)
{
if (i == j)
{
A[i, j] = 4 * h / 3;
}
else if (i == j + 1 || i == j - 1)
{
A[i, j] = h / 3;
}
}
}
for (int i = 1; i < B.GetLength(0) - 1; i++)
{
B[i, 0] = (points[i + 1].Y - 2 * points[i].Y + points[i - 1].Y) / h;
}
SystemEquations equations = new SystemEquations(new Matrix(A), new Matrix(B));
double[,] C = equations.GausGordanMethod();
List <Point> resultPoints = new List <Point>();
for (int k = 1; k < points.Count - 1; k++)
{
for (double x = points[k].X; x <= points[k + 1].X; x += step)
{
double a = points[k - 1].Y;
double b = ((points[k].Y - points[k - 1].Y) / h) - (h / 3) * (2 * C[k, 0] + C[k + 1, 0]);
double d = (C[k + 1, 0] - C[k, 0]) / (3 * h);
double c = C[k, 0];
double y = a + b * (x - points[k].X) + c * Math.Pow(x - points[k].X, 2) + d * Math.Pow(x - points[k].X, 3);
resultPoints.Add(new Point(x - h, y));
}
}
return(resultPoints);
}
public DifferentiationResult MethodUndefinedCoefficients(int degreeAccuracy)
{
if (degreeAccuracy >= points.Count)
{
throw new Exception("Порядок точности не может быть больше кол-ва точек.");
}
double[,] matrixC = new double[points.Count, points.Count];
double[,] matrixFreeTerms = new double[points.Count, 1];
for (int i = 0; i < matrixC.GetLength(0); i++)
{
for (int j = 0; j < matrixC.GetLength(1); j++)
{
//Заполнение матрицы коэффицентов C
if ((j == 0) && (i != 0))
{
matrixC[i, j] = 0;
}
else if (i == 0)
{
matrixC[i, j] = 1;
}
else
{
matrixC[i, j] = Math.Pow(j * step, i);
}
//Заполнение матрицы свободных членов
if (j == 0)
{
if (i == 0)
{
matrixFreeTerms[i, j] = i;
}
else if (i == 1)
{
matrixFreeTerms[i, j] = i;
}
else
{
matrixFreeTerms[i, j] = Math.Pow(step, i - 1) * i;
}
}
}
}
//Решение СЛАУ
SystemEquations equations = new SystemEquations(new Matrix(matrixC), new Matrix(matrixFreeTerms));
double[,] res = equations.GausGordanMethod();
//Вычисление производных
List <Point> derivativePoints = new List <Point>();
for (int i = 1; i < res.GetLength(0) - degreeAccuracy; i++)
{
double derivate = 0;
for (int j = 0; j <= degreeAccuracy; j++)
{
derivate += res[j, 0] * points[i - 1 + j].Y;
}
derivativePoints.Add(new Point(points[i].X, derivate));
}
return(new DifferentiationResult(derivativePoints.ToArray(), AbsoluteDeviation(derivativePoints), StandartDeviation(derivativePoints)));
}
