/// <summary>
/// Determine the center of gravity (centroid) of a function's curve
/// </summary>
/// <param name="function">Function object</param>
/// <param name="step">Distance between domain's values</param>
/// <returns>Numeric value representing the domain's value which approximately corresponds to the centroid</returns>
public static double Centroid(FunctionBase function, double step = 0.1)
{
var points = function.Points(step);
(double num, double den) = (0, 0);
foreach (var(x, y) in points)
{
num += x * y;
den += y;
}
return(num / den);
}
/// <summary>
/// Determine the center of area (splits the curve in two pices with the same area) (bisecter) of a function
/// </summary>
/// <param name="function">Function object</param>
/// <param name="step">Distance between domain's values</param>
/// <returns>Numeric value representing the domain's value which approximately corresponds to the bisecter</returns>
public static double Bisecter(FunctionBase function, double step = 0.1)
{
var points = function.Points(step);
double area = points.Select((x, y) => y).Sum();
double current = 0.0;
foreach (var(x, y) in points)
{
current += y;
if (current >= area / 2.0)
{
return(x);
}
}
throw new Exception("There is some error");
}
/// <summary>
/// Determine the point which corresponds with the mean of the function's maximums
/// </summary>
/// <param name="func">Function object</param>
/// <param name="step">Distance between domain's values</param>
/// <returns>Numeric value representing the domain's value which approximately corresponds to the mean of maximums</returns>
public static double MeanMax(FunctionBase function, double step = 0.1)
{
var points = function.Points(step);
var maximums = new List <double>();
double k = 0;
foreach (var(x, y) in points)
{
if (Math.Abs(y - k) < 1e-6)
{
maximums.Add(x);
}
else if (y > k)
{
k = y;
maximums.Clear();
maximums.Add(x);
}
}
return(maximums.Sum() / maximums.Count());
}
