// <copyright file="NewtonMinimizer.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) 2009-2017 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 IStation.Numerics.LinearAlgebra;
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using IStation.Numerics.Optimization.LineSearch;
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namespace IStation.Numerics.Optimization
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{
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public sealed class NewtonMinimizer : IUnconstrainedMinimizer
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{
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public double GradientTolerance { get; set; }
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public int MaximumIterations { get; set; }
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public bool UseLineSearch { get; set; }
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public NewtonMinimizer(double gradientTolerance, int maximumIterations, bool useLineSearch = false)
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{
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GradientTolerance = gradientTolerance;
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MaximumIterations = maximumIterations;
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UseLineSearch = useLineSearch;
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}
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public MinimizationResult FindMinimum(IObjectiveFunction objective, Vector<double> initialGuess)
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{
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return Minimum(objective, initialGuess, GradientTolerance, MaximumIterations, UseLineSearch);
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}
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public static MinimizationResult Minimum(IObjectiveFunction objective, Vector<double> initialGuess, double gradientTolerance=1e-8, int maxIterations=1000, bool useLineSearch=false)
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{
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if (!objective.IsGradientSupported)
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{
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throw new IncompatibleObjectiveException("Gradient not supported in objective function, but required for Newton minimization.");
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}
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if (!objective.IsHessianSupported)
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{
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throw new IncompatibleObjectiveException("Hessian not supported in objective function, but required for Newton minimization.");
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}
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// Check that we're not already done
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objective.EvaluateAt(initialGuess);
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ValidateGradient(objective);
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if (objective.Gradient.Norm(2.0) < gradientTolerance)
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{
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return new MinimizationResult(objective, 0, ExitCondition.AbsoluteGradient);
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}
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// Set up line search algorithm
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var lineSearcher = new WeakWolfeLineSearch(1e-4, 0.9, 1e-4, maxIterations: 1000);
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// Subsequent steps
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int iterations = 0;
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int totalLineSearchSteps = 0;
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int iterationsWithNontrivialLineSearch = 0;
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bool tmpLineSearch = false;
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while (objective.Gradient.Norm(2.0) >= gradientTolerance && iterations < maxIterations)
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{
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ValidateHessian(objective);
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var searchDirection = objective.Hessian.LU().Solve(-objective.Gradient);
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if (searchDirection * objective.Gradient >= 0)
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{
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searchDirection = -objective.Gradient;
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tmpLineSearch = true;
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}
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if (useLineSearch || tmpLineSearch)
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{
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LineSearchResult result;
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try
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{
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result = lineSearcher.FindConformingStep(objective, searchDirection, 1.0);
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}
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catch (Exception e)
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{
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throw new InnerOptimizationException("Line search failed.", e);
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}
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iterationsWithNontrivialLineSearch += result.Iterations > 0 ? 1 : 0;
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totalLineSearchSteps += result.Iterations;
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objective = result.FunctionInfoAtMinimum;
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}
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else
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{
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objective.EvaluateAt(objective.Point + searchDirection);
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}
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ValidateGradient(objective);
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tmpLineSearch = false;
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iterations += 1;
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}
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if (iterations == maxIterations)
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{
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throw new MaximumIterationsException(FormattableString.Invariant($"Maximum iterations ({maxIterations}) reached."));
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}
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return new MinimizationWithLineSearchResult(objective, iterations, ExitCondition.AbsoluteGradient, totalLineSearchSteps, iterationsWithNontrivialLineSearch);
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}
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static void ValidateGradient(IObjectiveFunctionEvaluation eval)
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{
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foreach (var x in eval.Gradient)
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{
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if (Double.IsNaN(x) || Double.IsInfinity(x))
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{
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throw new EvaluationException("Non-finite gradient returned.", eval);
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}
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}
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}
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static void ValidateHessian(IObjectiveFunctionEvaluation eval)
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{
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for (int ii = 0; ii < eval.Hessian.RowCount; ++ii)
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{
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for (int jj = 0; jj < eval.Hessian.ColumnCount; ++jj)
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{
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if (Double.IsNaN(eval.Hessian[ii, jj]) || Double.IsInfinity(eval.Hessian[ii, jj]))
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{
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throw new EvaluationException("Non-finite Hessian returned.", eval);
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}
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}
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}
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}
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}
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}
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