RootFinding: merge Broyden's method from 'taschna/master'

src/Numerics/Numerics.csproj

@@ -111,6 +111,7 @@
     <Compile Include="LinearAlgebra\Generic\Matrix.BCL.cs" />
     <Compile Include="LinearAlgebra\Generic\Vector.BCL.cs" />
     <Compile Include="NonConvergenceException.cs" />
+    <Compile Include="RootFinding\Broyden.cs" />
     <Compile Include="RootFinding\NewtonRaphson.cs" />
     <Compile Include="RootFinding\RobustNewtonRaphson.cs" />
     <Compile Include="RootFinding\ZeroCrossingBracketing.cs" />

src/Numerics/RootFinding/Broyden.cs

@@ -0,0 +1,147 @@
+// <copyright file="Broyden.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+// http://mathnetnumerics.codeplex.com
+// 
+// Copyright (c) 2009-2013 Math.NET
+// 
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+// 
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+// 
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+using MathNet.Numerics.LinearAlgebra.Double;
+using MathNet.Numerics.LinearAlgebra.Generic;
+using System;
+
+namespace MathNet.Numerics.RootFinding
+{
+    /// <summary>
+    /// Algorithm by Broyden.
+    /// Implementation inspired by Press, Teukolsky, Vetterling, and Flannery, "Numerical Recipes in C", 2nd edition, Cambridge University Press
+    /// </summary>
+    public static class Broyden
+    {
+        /// <summary>Find a solution of the equation f(x)=0.</summary>
+        /// <param name="f">The function to find roots from.</param>
+        /// <param name="initialGuess">Initial guess of the root.</param>
+        /// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Default 1e-8.</param>
+        /// <param name="maxIterations">Maximum number of iterations. Default 100.</param>
+        /// <returns>Returns the root with the specified accuracy.</returns>
+        /// <exception cref="NonConvergenceException"></exception>
+        public static double[] FindRoot(Func<double[], double[]> f, double[] initialGuess, double accuracy = 1e-8, int maxIterations = 100)
+        {
+            double[] root;
+            if (TryFindRoot(f, initialGuess, accuracy, maxIterations, out root))
+            {
+                return root;
+            }
+            throw new NonConvergenceException("The algorithm has exceeded the number of iterations allowed");
+        }
+
+        /// <summary>Find a solution of the equation f(x)=0.</summary>
+        /// <param name="f">The function to find roots from.</param>
+        /// <param name="initialGuess">The low value of the range where the root is supposed to be.</param>
+        /// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached.</param>
+        /// <param name="maxIterations">Maximum number of iterations. Usually 100.</param>
+        /// <param name="root">The root that was found, if any. Undefined if the function returns false.</param>
+        /// <returns>True if a root with the specified accuracy was found, else false.</returns>
+        public static bool TryFindRoot(Func<double[], double[]> f, double[] initialGuess, double accuracy, int maxIterations, out double[] root)
+        {
+            double[] F = f(initialGuess);
+            DenseVector FVect = new DenseVector(F);
+            double g = FVect.Norm(2);
+
+            Matrix<double> B = CalculateApproximateJacobian(f, initialGuess, F);
+
+            Vector<double> x = new DenseVector(initialGuess);
+
+            for (int i = 0; i <= maxIterations; i++)
+            {
+                Vector<double> dx = -B.LU().Solve(FVect);
+                Vector<double> xnew = x + dx;
+                double[] FNew = f(xnew.ToArray());
+                DenseVector FNewVect = new DenseVector(FNew);
+                double gNew = FNewVect.Norm(2);
+                if (gNew > g)
+                {
+                    double g2 = g * g;
+                    double scale = g2 / (g2 + gNew * gNew);
+                    if (scale == 0.0) scale = 1.0e-4;
+                    dx = scale * dx;
+                    xnew = x + dx;
+                    FNew = f(xnew.ToArray());
+                    FNewVect = new DenseVector(FNew);
+                    gNew = FNewVect.Norm(2);
+                }
+
+                if (gNew < accuracy)
+                {
+                    root = xnew.ToArray();
+                    return true;
+                }
+
+                // update Jacobian B
+                DenseVector dF = FNewVect - FVect;
+                Matrix<double> dB = (dF - B.Multiply(dx)).ToColumnMatrix() * dx.Multiply(1.0 / Math.Pow(dx.Norm(2),2)).ToRowMatrix();
+                B = B + dB;
+
+                x = xnew;
+                FVect = FNewVect;
+                g = gNew;
+            }
+
+            root = null;
+            return false;
+        }
+
+        /// <summary>
+        /// Helper method to calculate an approxiamtion of the Jacobian.
+        /// </summary>
+        /// <param name="f">The function.</param>
+        /// <param name="x0">The argument.</param>
+        /// <returns></returns>
+        private static Matrix<double> CalculateApproximateJacobian(Func<double[], double[]> f, double[] x0, double[] F0)
+        {
+            int dim = x0.Length;
+            double[] xpos = new double[dim];
+            DenseMatrix B = new DenseMatrix(dim);
+
+            for (int j = 0; j < dim; j++)
+            {
+                Array.Copy(x0, xpos, dim);
+
+                double h = Math.Abs(x0[j]) * 1.0e-4;
+                if (h == 0.0) h = 1.0e-4;
+                xpos[j] += h;
+
+                double[] Fpos = f(xpos);
+
+                for (int i = 0; i < dim; i++)
+                {
+                    B[i, j] = (Fpos[i] - F0[i]) / h;
+                }
+            }
+
+            return B;
+        }
+    }
+}

src/UnitTests/UnitTests.csproj

@@ -773,6 +773,7 @@
     <Compile Include="Random\WH2006Tests.cs" />
     <Compile Include="Random\XorshiftTests.cs" />
     <Compile Include="RootFindingTests\BrentTest.cs" />
+    <Compile Include="RootFindingTests\BroydenTest.cs" />
     <Compile Include="RootFindingTests\FindRootsTest.cs" />
     <Compile Include="RootFindingTests\RobustNewtonRaphsonTest.cs" />
     <Compile Include="RootFindingTests\NewtonRaphsonTest.cs" />