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#region Copyright © 2009, De Santiago-Castillo JA. All rights reserved.
//Copyright © 2009 Jose Antonio De Santiago-Castillo
//E-mail:JAntonioDeSantiago@gmail.com
//Web: www.DotNumerics.com
//
#endregion
using System;
using System.Collections.Generic;
using System.Text;
using DotNumerics.Optimization.Cobyla;
using DotNumerics.Optimization.NelderMead;
namespace DotNumerics.Optimization
{
/// <summary>
/// Class used to minimizes a function of several variables by using the Nelder-Mead (Simplex) method. This class can be used for unconstrained and bounded constrained minimization.
/// </summary>
public class Simplex : xMinimizationBase
{
#region Fields
CobylaDriver _CobylaDriver;
DownhillDirver _AmoebaDirver;
//COBYLA MeCOBYLA;
//private OptMultivariateFunction Function;
//private OptBoundVariable[] MeSimplexBoundVariableList;
//private int MeNumBoundVariables = 0;
//private double MeInitialStep = 1;
//double[] W;
//int[] IACT;
#endregion
#region Constructor
/// <summary>
/// Initializes a new instance of the Simplex class.
/// </summary>
public Simplex()
{
}
#endregion
#region Public methods
#region double
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="initialGuess">Array of size N containing the initial guess. N is the number of variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, double[] initialGuess)
{
if (initialGuess == null) return new double[0];
if (initialGuess.Length == 0) return new double[0];
OptSimplexVariable[] variables = this.GetVariables(initialGuess);
double initialStep = this.GetAutomaticInitialStep(variables);
int maxFunc= this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="initialGuess">Array of size N containing the initial guess. N is the number of variables.</param>
/// <param name="initialStep">The initial change of the variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, double[] initialGuess, double initialStep)
{
if (initialGuess == null) return new double[0];
if (initialGuess.Length == 0) return new double[0];
OptSimplexVariable[] variables = this.GetVariables(initialGuess);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
#endregion
#region OptSimplexVariable
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptSimplexVariable[] variables)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
double initialStep = this.GetAutomaticInitialStep(variables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <param name="initialStep">The initial change of the variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptSimplexVariable[] variables, float initialStep)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
#endregion
#region OptVariable
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the initial guess. N is the number of variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptVariable[] variables)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
OptSimplexVariable[] simplexVariables = this.GetVariables(variables);
double initialStep = this.GetAutomaticInitialStep(simplexVariables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, simplexVariables, initialStep, this._Tolerance, ref maxFunc);
}
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the initial guess. N is the number of variables.</param>
/// <param name="initialStep">The initial change of the variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptVariable[] variables, double initialStep)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
OptSimplexVariable[] simplexVariables = this.GetVariables(variables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, simplexVariables, initialStep, this._Tolerance, ref maxFunc);
}
#endregion
#region OptSimplexBoundVariable
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptSimplexBoundVariable[] variables)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
double initialStep = this.GetAutomaticInitialStep(variables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <param name="initialStep">The initial change of the variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptSimplexBoundVariable[] variables, float initialStep)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, variables, initialStep, this._Tolerance, ref maxFunc);
}
#endregion
#region OptBoundVariable
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptBoundVariable[] variables)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
OptSimplexBoundVariable[] simplexVariables = this.GetVariables(variables);
double initialStep = this.GetAutomaticInitialStep(simplexVariables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, simplexVariables, initialStep, this._Tolerance, ref maxFunc);
}
/// <summary>
/// Computes the minimum point of a function of several variables.
/// </summary>
/// <param name="function">The function to minimize.</param>
/// <param name="variables">Array of size N containing the varaibles.</param>
/// <param name="initialStep">The initial change of the variables.</param>
/// <returns>Array containing the solution.</returns>
public double[] ComputeMin(OptMultivariateFunction function, OptBoundVariable[] variables, float initialStep)
{
if (variables == null) return new double[0];
if (variables.Length == 0) return new double[0];
OptSimplexBoundVariable[] simplexVariables = this.GetVariables(variables);
int maxFunc = this._MaxFunEvaluations;
return this.GetMinimum(function, simplexVariables, initialStep, this._Tolerance, ref maxFunc);
}
#endregion
#endregion
#region Private Methods
private double[] GetMinimum(OptMultivariateFunction function, OptSimplexVariable[] variables, double initialStep, double ftol, ref int nMax)
{
if (this._AmoebaDirver == null) this._AmoebaDirver = new DownhillDirver();
double[] minimum = this._AmoebaDirver.ComputeMin(function, variables, initialStep, ftol, ref nMax);
this.FunEvaluations = nMax;
return minimum;
}
private double[] GetMinimum(OptMultivariateFunction function, OptSimplexBoundVariable[] variables, double initialStep, double tolerance, ref int MAXFUN)
{
if (this._CobylaDriver == null) this._CobylaDriver = new CobylaDriver();
double[] minimum = this._CobylaDriver.ComputeMin(function, variables, initialStep, tolerance, ref MAXFUN);
this.FunEvaluations = MAXFUN;
return minimum;
}
private OptSimplexVariable[] GetVariables(double[] variablesArray)
{
OptSimplexVariable[] vars = new OptSimplexVariable[variablesArray.Length];
for (int i = 0; i < variablesArray.Length; i++)
{
vars[i] = new OptSimplexVariable(variablesArray[i]);
}
return vars;
}
private OptSimplexVariable[] GetVariables(OptVariable[] variablesArray)
{
OptSimplexVariable[] vars = new OptSimplexVariable[variablesArray.Length];
for (int i = 0; i < variablesArray.Length; i++)
{
OptVariable var = variablesArray[i];
vars[i] = new OptSimplexVariable(var.Name, var.InitialGuess, var.Fixed);
}
return vars;
}
private OptSimplexBoundVariable[] GetVariables(OptBoundVariable[] variablesArray)
{
OptSimplexBoundVariable[] vars = new OptSimplexBoundVariable[variablesArray.Length];
for (int i = 0; i < variablesArray.Length; i++)
{
OptBoundVariable var = variablesArray[i];
vars[i] = new OptSimplexBoundVariable(var.Name, var.InitialGuess, var.Fixed, var.LowerBound, var.UpperBound);
}
return vars;
}
private double GetAutomaticInitialStep(OptSimplexBoundVariable[] variables)
{
int numFreeVariables = this.GetNumFreeVariable(variables);
if (numFreeVariables == 0) return 1;
double step = 0;
double sum = 0;
foreach (OptSimplexBoundVariable var in variables)
{
if (var.Fixed == false)
{
//mod
sum += Math.Abs(var.InitialGuess / var.ScaleFactor);
}
}
if (sum != 0)
{
step = sum / (2.0 * numFreeVariables);
}
else
{
step = 1;
}
return step;
}
private double GetAutomaticInitialStep(OptSimplexVariable[] variables)
{
int numFreeVariables = this.GetNumFreeVariable(variables);
if (numFreeVariables == 0) return 1;
double step = 0;
double sum = 0;
foreach (OptSimplexVariable var in variables)
{
if (var.Fixed == false)
{
//mod
sum += Math.Abs(var.InitialGuess / var.ScaleFactor);
}
}
if (sum != 0)
{
step = sum / (2.0 * numFreeVariables);
}
else
{
step = 1;
}
return step;
}
private int GetNumFreeVariable(OptSimplexBoundVariable[] variables)
{
int numFreeVariables = 0;
foreach (OptSimplexBoundVariable var in variables)
{
if (var.Fixed == false) numFreeVariables++;
}
return numFreeVariables;
}
private int GetNumFreeVariable(OptSimplexVariable[] variables)
{
int numFreeVariables = 0;
foreach (OptSimplexVariable var in variables)
{
if (var.Fixed == false) numFreeVariables++;
}
return numFreeVariables;
}
#endregion
}
}
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