GaussOptimization.cs

usingSystem;
usingSystem.Collections.Generic;
usingSystem.Linq;

namespaceAlgorithms.Other;

/// <summary>
/// The Gaussian method (coordinate descent method) refers to zero-order methods in which only the value
/// of the function Q(X) at different points in the space of variables is used to organize the search
/// for the extremum. This reduces the overall computational cost of finding the extremum. Also in
/// the Gaussian method, the procedures for finding and moving the operating point are simplified as
/// much as possible.
/// </summary>
publicclassGaussOptimization
{
/// <summary>
/// Implementation of function extremum search by the Gauss optimization algorithm.
/// </summary>
/// <param name="func">Function for which extremum has to be found.</param>
/// <param name="n">This parameter identifies how much step size will be decreased each iteration.</param>
/// <param name="step">The initial shift step.</param>
/// <param name="eps">This value is used to control the accuracy of the optimization. In case if the error is less than eps,
/// optimization will be stopped.</param>
/// <param name="x1">The first function parameter.</param>
/// <param name="x2">The second function parameter.</param>
/// <returns>A tuple of coordinates of function extremum.</returns>
public(doubleX1,doubleX2)Optimize(
Func<double,double,double>func,
doublen,
doublestep,
doubleeps,
doublex1,
doublex2)
{
// The initial value of the error
doubleerror=1;

while(Math.Abs(error)>eps)
{
// Calculation of the function with coordinates that are calculated with shift
doublebottom=func(x1,x2-step);
doubletop=func(x1,x2+step);
doubleleft=func(x1-step,x2);
doubleright=func(x1+step,x2);

// Determination of the best option.
varpossibleFunctionValues=newList<double>{bottom,top,left,right};
doublemaxValue=possibleFunctionValues.Max();
doublemaxValueIndex=possibleFunctionValues.IndexOf(maxValue);

// Error evaluation
error=maxValue-func(x1,x2);

// Coordinates update for the best option
switch(maxValueIndex)
{
case0:
x2-=step;
break;
case1:
x2+=step;
break;
case2:
x1-=step;
break;
default:
x1+=step;
break;
}

// Step reduction
step/=n;
}

return(x1,x2);
}
}