C# One Variable Minimization Example

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using System;

using CenterSpace.NMath.Core;
using CenterSpace.NMath.Analysis;

namespace CenterSpace.NMath.Analysis.Examples.CSharp
{
  class OneVariableMinimizationExample
  {
    /// <summary>
    /// A .NET example in C# showing how to find a minimum of a univariate function
    /// using a golden minimizer and Brent's method.
    /// </summary>
    static void Main( string[] args )
    {
      // Create a one-variable function.
      OneVariableFunction function = new Func<double, double>( f );

      // Use golden section search to find the minimum of the function
      // in the interval -10000 to 10000.
      int lower = -10000;
      int upper = 10000;

      // Create the minimizer with default tolerance and default maximum iterations.
      var golden = new GoldenMinimizer();

      // Perform the minimization.
      double min = golden.Minimize( function, lower, upper );

      Console.WriteLine();

      Console.WriteLine( "GoldenMinimizer found a minimum of " + function.Evaluate( min ) );
      Console.WriteLine( "at " + min + " in " + golden.Iterations + " iterations." );

      if ( golden.ToleranceMet )
      {
        // Error is less than desired tolerance
        Console.Write( "Error of " + golden.Error + " is within tolerance of " );
        Console.WriteLine( golden.Tolerance + "." );
      }
      else
      {
        // Minimization ended because maximum iterations was reached
        Console.WriteLine( "Ended with maximum iterations." );
      }
      Console.WriteLine();

      // Try Brent's Method for better efficiency.
      var brent = new BrentMinimizer();
      min = brent.Minimize( function, lower, upper );

      Console.WriteLine( "BrentMinimizer found a minimum of " + function.Evaluate( min ) );
      Console.WriteLine( "at " + min + " in " + brent.Iterations + " iterations." );
      if ( brent.ToleranceMet )
      {
        // Error is less than desired tolerance
        Console.Write( "Error of " + brent.Error + " is within tolerance of " );
        Console.WriteLine( brent.Tolerance + "." );
      }
      else
      {
        // Minimization ended because maximum iterations was reached
        Console.WriteLine( "Ended with maximum iterations." );
      }
      Console.WriteLine();

      // If the derivative is known, we can utilize a better Brent's
      // algorithm.

      // Create the derivative function.
      OneVariableFunction derivative = new Func<double, double>( df );

      // Instantiate a DBrentMinimizer.
      var dbrent = new DBrentMinimizer();
      min = dbrent.Minimize( function, derivative, lower, upper );

      Console.WriteLine( "DBrentMinimizer found a minimum of " + function.Evaluate( min ) );
      Console.WriteLine( "at " + min + " in " + dbrent.Iterations + " iterations." );
      if ( dbrent.ToleranceMet )
      {
        // Error is less than desired tolerance
        Console.Write( "Error of " + dbrent.Error + " is within tolerance of " );
        Console.WriteLine( dbrent.Tolerance + "." );
      }
      else
      {
        // Minimization ended because maximum iterations was reached
        Console.WriteLine( "Ended with maximum iterations." );
      }
      Console.WriteLine();

      // Increase the tolerance to 0.1
      dbrent.Tolerance = 0.1;
      min = dbrent.Minimize( function, derivative, lower, upper );

      Console.WriteLine( "DBrentMinimizer found a minimum of " + function.Evaluate( min ) );
      Console.WriteLine( "at " + min + " in " + dbrent.Iterations + " iterations." );
      if ( dbrent.ToleranceMet )
      {
        // Error is less than desired tolerance
        Console.Write( "Error of " + dbrent.Error + " is within tolerance of " );
        Console.WriteLine( dbrent.Tolerance + "." );
      }
      else
      {
        // Minimization ended because maximum iterations was reached
        Console.WriteLine( "Ended with maximum iterations." );
      }
      Console.WriteLine();

      // Decrease tolerance to 1e-13 and increase the interval.
      dbrent.Tolerance = 1e-13;
      min = dbrent.Minimize( function, derivative, lower * 100, upper * 100 );

      Console.WriteLine( "DBrentMinimizer found a minimum of " + function.Evaluate( min ) );
      Console.WriteLine( "at " + min + " in " + dbrent.Iterations + " iterations." );
      if ( dbrent.ToleranceMet )
      {
        Console.Write( "Error of " + dbrent.Error + " is within tolerance of " );
        Console.WriteLine( dbrent.Tolerance + "." );
      }
      else
      {
        Console.WriteLine( "Ended with maximum iterations." );
      }
      Console.WriteLine();

      Console.WriteLine();
      Console.WriteLine( "Press Enter Key" );
      Console.Read();
    }

    private static double df( double x )
    {
      return 8 * Math.Cos( x ) + 6 * x - 5;
    }

    private static double f( double x )
    {
      return 8 * Math.Sin( x ) + 3 * x * x - 5 * x;
    }

  } // class

} // namepace
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