public static Result Evaluate(FittingFunction function, float a, float b, float accuracy)
{
float width = b - a;
if (!Converge(function, a, b))
{
return(Evaluate(function,
a + (function(a) > 0 ? -width : width) * precentage,
b + (function(a) > 0 ? -width : width) * precentage,
accuracy));
}
float center = (a + b) / 2.0f;
int iterationCount = 0;
do
{
iterationCount++;
center = (a + b) / 2.0f;
var result = function(center);
if (function(a) * result <= 0)
{
b = center;
}
else
{
a = center;
}
} while (Math.Abs(b - a) > accuracy);
return(new Result(iterationCount, center));
}
public static float[] Approximate(float a, float b, int degree, FittingFunction fittingFunction)
{
int n = degree + 1;
float[] result = new float[n];
var u = ChebyshevSpace(n);
float[] xs = new float[n];
float[] ys = new float[n];
for (int j = 0; j < n; j++)
{
xs[j] = Expand(u[j], a, b);
ys[j] = Convert.ToSingle(fittingFunction(xs[j]));
}
for (int j = 0; j < n; j++)
{
float c = 0;
for (int i = 0; i < n; i++)
{
var f = ys[i];
var t = CalculatePolynom(j, u[i]);
c += f * t;
}
result[j] = (2.0f / n) * c;
}
result[0] /= 2.0f;
return(result);
}
private static bool Converge(FittingFunction function, double x)
{
var value = function(x);
var derivative = (function(x + h) - 2 * function(x) + function(x - h)) / (h * h);
return(value * derivative > 0);
}
/// <summary>
/// Check if convergention condition is achieved
/// </summary>
/// <param name="function">Function to evaluate</param>
/// <param name="a">Left border</param>
/// <param name="b">Right border</param>
/// <returns></returns>
public static bool Converge(FittingFunction function, float a, float b)
{
var aValue = function(a);
var bValue = function(b);
return((aValue * bValue) <= 0);
}
private void DrawBasePoints(FittingFunction fittingFunction)
{
var points = new List <Point>();
var xValues = ChebyshevApproximation.GenerateX(a, b, step);
for (int i = 0; i < xValues.Length; i++)
{
points.Add(new Point(xValues[i], fittingFunction(xValues[i])));
}
RealDataPlotFor1.ItemsSource = RealDataPlotFor2.ItemsSource = RealDataPlotFor3.ItemsSource
= RealDataPlotFor4.ItemsSource = RealDataPlotFor5.ItemsSource = RealDataPlotFor6.ItemsSource
= RealDataPlotFor7.ItemsSource = RealDataPlotFor8.ItemsSource = RealDataPlotFor9.ItemsSource
= points;
}
public static Result Evaluate(FittingFunction function, float a, float b, float accuracy)
{
double x0 = SetStartPoint(function, a, b);
int iterationCount = 0;
double x = x0 - (function(x0) / FirstDerivative(function, x0, h));
while (IsAccuracyReached(function, x0, x, accuracy))
{
x0 = x;
iterationCount++;
x = x0 - (function(x0) / FirstDerivative(function, x0, h));
}
return(new Result(iterationCount, x));
}
private static double SetStartPoint(FittingFunction function, float a, float b)
{
if (Converge(function, a))
{
return(a);
}
if (Converge(function, b))
{
return(b);
}
float width = b - a;
return(SetStartPoint(function,
a + (function(a) > 0 ? -width : width) * percentage,
b + (function(a) > 0 ? -width : width) * percentage));
}
private static double FirstDerivative(FittingFunction function, double x, double epsilon)
{
return((function(x + epsilon) - function(x)) / epsilon);
}
private static bool IsAccuracyReached(FittingFunction function, double oldValue, double newValue, float accuracy)
{
return(Math.Abs(function(oldValue) - function(newValue)) > accuracy);
}
