// <copyright file="Test.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Linq;
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// ReSharper disable CheckNamespace
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namespace IStation.Numerics
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// ReSharper restore CheckNamespace
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{
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public static class TestFunctions
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{
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/// <summary>
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/// Valley-shaped Rosenbrock function for 2 dimensions: (x,y) -> (1-x)^2 + 100*(y-x^2)^2.
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/// This function has a global minimum at (1,1) with f(1,1) = 0.
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/// Common range: [-5,10] or [-2.048,2.048].
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/// </summary>
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/// <remarks>
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/// https://en.wikipedia.org/wiki/Rosenbrock_function
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/// http://www.sfu.ca/~ssurjano/rosen.html
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/// </remarks>
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public static double Rosenbrock(double x, double y)
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{
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double a = 1.0 - x;
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double b = y - x*x;
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return a*a + 100*b*b;
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}
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/// <summary>
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/// Valley-shaped Rosenbrock function for 2 or more dimensions.
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/// This function have a global minimum of all ones and, for 8 > N > 3, a local minimum at (-1,1,...,1).
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/// </summary>
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/// <remarks>
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/// https://en.wikipedia.org/wiki/Rosenbrock_function
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/// http://www.sfu.ca/~ssurjano/rosen.html
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/// </remarks>
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public static double Rosenbrock(params double[] x)
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{
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double sum = 0;
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for (int i = 1; i < x.Length; i++)
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{
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sum += Rosenbrock(x[i - 1], x[i]);
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}
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return sum;
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}
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/// <summary>
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/// Himmelblau, a multi-modal function: (x,y) -> (x^2+y-11)^2 + (x+y^2-7)^2
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/// This function has 4 global minima with f(x,y) = 0.
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/// Common range: [-6,6].
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/// Named after David Mautner Himmelblau
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/// </summary>
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/// <remarks>
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/// https://en.wikipedia.org/wiki/Himmelblau%27s_function
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/// </remarks>
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public static double Himmelblau(double x, double y)
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{
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double a = x*x + y - 11.0;
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double b = x + y*y - 7.0;
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return a*a + b*b;
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}
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/// <summary>
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/// Rastrigin, a highly multi-modal function with many local minima.
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/// Global minimum of all zeros with f(0) = 0.
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/// Common range: [-5.12,5.12].
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/// </summary>
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/// <remarks>
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/// https://en.wikipedia.org/wiki/Rastrigin_function
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/// http://www.sfu.ca/~ssurjano/rastr.html
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/// </remarks>
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public static double Rastrigin(params double[] x)
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{
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return x.Sum(xi => xi*xi - 10.0*Math.Cos(Constants.Pi2*xi)) + 10.0*x.Length;
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}
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/// <summary>
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/// Drop-Wave, a multi-modal and highly complex function with many local minima.
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/// Global minimum of all zeros with f(0) = -1.
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/// Common range: [-5.12,5.12].
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/// </summary>
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/// <remarks>
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/// http://www.sfu.ca/~ssurjano/drop.html
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/// </remarks>
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public static double DropWave(double x, double y)
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{
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double t = x*x + y*y;
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return -(1.0 + Math.Cos(12.0*Math.Sqrt(t)))/(0.5*t + 2.0);
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}
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/// <summary>
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/// Ackley, a function with many local minima. It is nearly flat in outer regions but has a large hole at the center.
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/// Global minimum of all zeros with f(0) = 0.
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/// Common range: [-32.768, 32.768].
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/// </summary>
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/// <remarks>
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/// http://www.sfu.ca/~ssurjano/ackley.html
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/// </remarks>
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public static double Ackley(params double[] x)
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{
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double u = x.Sum(xi => xi*xi)/x.Length;
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double v = x.Sum(xi => Math.Cos(Constants.Pi2*xi))/x.Length;
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return -20*Math.Exp(-0.2*Math.Sqrt(u)) - Math.Exp(v) + 20 + Math.E;
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}
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/// <summary>
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/// Bowl-shaped first Bohachevsky function.
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/// Global minimum of all zeros with f(0,0) = 0.
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/// Common range: [-100, 100]
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/// </summary>
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/// <remarks>
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/// http://www.sfu.ca/~ssurjano/boha.html
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/// </remarks>
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public static double Bohachevsky1(double x, double y)
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{
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return x*x + 2*y*y - 0.3*Math.Cos(3*Math.PI*x) - 0.4*Math.Cos(4*Math.PI*y);
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}
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/// <summary>
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/// Plate-shaped Matyas function.
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/// Global minimum of all zeros with f(0,0) = 0.
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/// Common range: [-10, 10].
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/// </summary>
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/// <remarks>
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/// http://www.sfu.ca/~ssurjano/matya.html
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/// </remarks>
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public static double Matyas(double x, double y)
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{
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return 0.26*(x*x + y*y) - 0.48*x*y;
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}
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/// <summary>
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/// Valley-shaped six-hump camel back function.
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/// Two global minima and four local minima. Global minima with f(x) ) -1.0316 at (0.0898,-0.7126) and (-0.0898,0.7126).
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/// Common range: x in [-3,3], y in [-2,2].
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/// </summary>
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/// <remarks>
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/// http://www.sfu.ca/~ssurjano/camel6.html
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/// </remarks>
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public static double SixHumpCamel(double x, double y)
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{
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double x2 = x*x;
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double y2 = y*y;
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return (4 - 2.1*x2 + x2*x2/3)*x2 + x*y + (-4 + 4*y2)*y2;
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}
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}
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}
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