Optimization: Finish implementation of Golden Section minimum search

src/Numerics/Numerics.csproj

@@ -264,6 +264,7 @@
     <Compile Include="Optimization\BfgsMinimizer.cs" />
     <Compile Include="Optimization\ConjugateGradientMinimizer.cs" />
     <Compile Include="Optimization\GoldenSectionMinimizer.cs" />
+    <Compile Include="Optimization\MinimizationResult1D.cs" />
     <Compile Include="Optimization\NewtonMinimizer.cs" />
     <Compile Include="Optimization\ObjectiveFunction.cs" />
     <Compile Include="Optimization\ObjectiveFunction1D.cs" />

src/Numerics/Optimization/GoldenSectionMinimizer.cs

@@ -13,7 +13,7 @@ namespace MathNet.Numerics.Optimization
             MaximumIterations = maxIterations;
         }
 
-        public MinimizationResult FindMinimum(IObjectiveFunction1D objective, double lowerBound, double upperBound)
+        public MinimizationResult1D FindMinimum(IObjectiveFunction1D objective, double lowerBound, double upperBound)
         {
             double middlePointX = lowerBound + (upperBound - lowerBound) / (1 + Constants.GoldenRatio);
             IEvaluation1D lower = objective.Evaluate(lowerBound);
@@ -37,19 +37,29 @@ namespace MathNet.Numerics.Optimization
                 var test = objective.Evaluate(testX);
                 ValueChecker(test.Value, testX);
 
-                if (test.Value > middle.Value)
+                if (test.Point < middle.Point)
                 {
-                    if (test.Point < middle.Point)
+                    if (test.Value > middle.Value)
+                    {
                         lower = test;
+                    }
                     else
-                        upper = test;
+                    {
+                        upper = middle;
+                        middle = test;
+                    }
                 }
                 else
                 {
-                    if (test.Point < middle.Point)
-                        upper = middle;
+                    if (test.Value > middle.Value)
+                    {
+                        upper = test;
+                    }
                     else
+                    {
                         lower = middle;
+                        middle = test;
+                    }
                 }
 
                 iterations += 1;
@@ -58,7 +68,7 @@ namespace MathNet.Numerics.Optimization
             if (iterations == MaximumIterations)
                 throw new MaximumIterationsException("Max iterations reached.");
 
-            return null;
+            return new MinimizationResult1D(middle, iterations, MinimizationResult.ExitCondition.BoundTolerance);
         }
 
         private void ValueChecker(double value, double point)

src/Numerics/Optimization/MinimizationResult1D.cs

@@ -0,0 +1,17 @@
+namespace MathNet.Numerics.Optimization
+{
+    public class MinimizationResult1D
+    {
+        public double MinimizingPoint { get { return FunctionInfoAtMinimum.Point; } }
+        public IEvaluation1D FunctionInfoAtMinimum { get; private set; }
+        public int Iterations { get; private set; }
+        public MinimizationResult.ExitCondition ReasonForExit { get; private set; }
+
+        public MinimizationResult1D(IEvaluation1D functionInfo, int iterations, MinimizationResult.ExitCondition reasonForExit)
+        {
+            FunctionInfoAtMinimum = functionInfo;
+            Iterations = iterations;
+            ReasonForExit = reasonForExit;
+        }
+    }
+}

src/UnitTests/OptimizationTests/TestBfgsMinimizer.cs

@@ -12,7 +12,7 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         public void FindMinimum_Rosenbrock_Easy()
         {
             var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
-            var solver = new BfgsMinimizer(1e-5, 1000);
+            var solver = new BfgsMinimizer(1e-5, 1e-5, 1000);
             var result = solver.FindMinimum(obj, new DenseVector(new[] { 1.2, 1.2 }));
 
             Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
@@ -23,7 +23,7 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         public void FindMinimum_Rosenbrock_Hard()
         {
             var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
-            var solver = new BfgsMinimizer(1e-5, 1000);
+            var solver = new BfgsMinimizer(1e-5, 1e-5, 1000);
             var result = solver.FindMinimum(obj, new DenseVector(new[] { -1.2, 1.0 }));
 
             Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));
@@ -34,7 +34,7 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         public void FindMinimum_Rosenbrock_Overton()
         {
             var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
-            var solver = new BfgsMinimizer(1e-5, 1000);
+            var solver = new BfgsMinimizer(1e-5, 1e-5, 1000);
             var result = solver.FindMinimum(obj, new DenseVector(new[] { -0.9, -0.5 }));
 
             Assert.That(Math.Abs(result.MinimizingPoint[0] - 1.0), Is.LessThan(1e-3));

src/UnitTests/OptimizationTests/TestConjugateGradientMinimizer.cs

@@ -8,7 +8,6 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
     [TestFixture]
     public class TestConjugateGradientMinimizer
     {
-
         [Test]
         public void FindMinimum_Rosenbrock_Easy()
         {

src/UnitTests/OptimizationTests/TestGoldenSectionMinimizer.cs

@@ -0,0 +1,32 @@
+using System;
+using MathNet.Numerics.Optimization;
+using NUnit.Framework;
+
+namespace MathNet.Numerics.UnitTests.OptimizationTests
+{
+    [TestFixture]
+    public class TestGoldenSectionMinimizer
+    {
+        [Test]
+        public void Test_Works()
+        {
+            var algorithm = new GoldenSectionMinimizer(1e-5, 1000);
+            var f1 = new Func<double, double>(x => (x - 3)*(x - 3));
+            var obj = new SimpleObjectiveFunction1D(f1);
+            var r1 = algorithm.FindMinimum(obj, -100, 100);
+
+            Assert.That(Math.Abs(r1.MinimizingPoint - 3.0), Is.LessThan(1e-4));
+        }
+
+        [Test]
+        public void Test_ExpansionWorks()
+        {
+            var algorithm = new GoldenSectionMinimizer(1e-5, 1000);
+            var f1 = new Func<double, double>(x => (x - 3) * (x - 3));
+            var obj = new SimpleObjectiveFunction1D(f1);
+            var r1 = algorithm.FindMinimum(obj, -5, 5);
+
+            Assert.That(Math.Abs(r1.MinimizingPoint - 3.0), Is.LessThan(1e-4));
+        }
+    }
+}

src/UnitTests/UnitTests.csproj

@@ -368,6 +368,7 @@
     <Compile Include="Random\RandomSerializationTests.cs" />
     <Compile Include="OptimizationTests\RosenbrockFunction.cs" />
     <Compile Include="OptimizationTests\TestNewtonMinimizer.cs" />
+    <Compile Include="OptimizationTests\TestGoldenSectionMinimizer.cs" />
     <Compile Include="Random\SystemRandomSourceTests.cs" />
     <Compile Include="OptimizationTests\BfgsTest.cs" />
     <Compile Include="RootFindingTests\BisectionTest.cs" />