Optimization: added trust region Newton-CG minimizer.

src/Numerics.Tests/OptimizationTests/NonLinearCurveFittingTests.cs

@@ -93,8 +93,9 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         }
 
         [Test]
-        public void TRLMDER_FindMinimum_Rosenbrock_Unconstrained()
+        public void TRDLDER_FindMinimum_Rosenbrock_Unconstrained()
         {
+            // DogLeg Minimizer
             var obj = ObjectiveModel.FittingModel(RosenbrockModel, RosenbrockPrime, RosenbrockX, RosenbrockY);
             var solver = new TrustRegionDogLegMinimizer(maximumIterations: 10000);
             var result = solver.FindMinimum(obj, RosenbrockStart1);
@@ -103,10 +104,20 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
             {
                 AssertHelpers.AlmostEqualRelative(RosenbrockPbest[i], result.BestFitParameters[i], 1);
             }
+
+            // NewtonCG Minimizer
+            obj = ObjectiveModel.FittingModel(RosenbrockModel, RosenbrockPrime, RosenbrockX, RosenbrockY);
+            var solverNCG = new TrustRegionNewtonCGMinimizer(maximumIterations: 10000);
+            result = solverNCG.FindMinimum(obj, RosenbrockStart1);
+
+            for (int i = 0; i < result.BestFitParameters.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(RosenbrockPbest[i], result.BestFitParameters[i], 1);
+            }
         }
 
         [Test]
-        public void TRLMDIF_FindMinimum_Rosenbrock_Unconstrained()
+        public void TRDLDIF_FindMinimum_Rosenbrock_Unconstrained()
         {
             var obj = ObjectiveModel.FittingModel(RosenbrockModel, RosenbrockPrime, RosenbrockX, RosenbrockY);
             var solver = new TrustRegionDogLegMinimizer(maximumIterations: 10000);
@@ -118,6 +129,19 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
             }
         }
 
+        [Test]
+        public void TRNCGDER_FindMinimum_Rosenbrock_Unconstrained()
+        {
+            var obj = ObjectiveModel.FittingModel(RosenbrockModel, RosenbrockPrime, RosenbrockX, RosenbrockY);
+            var solver = new TrustRegionNewtonCGMinimizer(maximumIterations: 10000);
+            var result = solver.FindMinimum(obj, RosenbrockStart1);
+
+            for (int i = 0; i < result.BestFitParameters.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(RosenbrockPbest[i], result.BestFitParameters[i], 1);
+            }
+        }
+
         // model: Rat43 (https://www.itl.nist.gov/div898/strd/nls/data/ratkowsky3.shtml)
         //       f(x; a, b, c, d) =  a / ((1 + exp(b - c * x))^(1 / d))
         // best fitted parameters:
@@ -335,7 +359,7 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         }
 
         [Test]
-        public void TRLMDIF_FindMinimum_BoxBod_Unconstrained()
+        public void TRDLDIF_FindMinimum_BoxBod_Unconstrained()
         {
             var obj = ObjectiveModel.FittingModel(BoxBodModel, BoxBodX, BoxBodY, accuracyOrder: 6);
             var solver = new TrustRegionDogLegMinimizer();
@@ -348,6 +372,20 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
             }
         }
 
+        [Test]
+        public void TRNCGDIF_FindMinimum_BoxBod_Unconstrained()
+        {
+            var obj = ObjectiveModel.FittingModel(BoxBodModel, BoxBodX, BoxBodY, accuracyOrder: 6);
+            var solver = new TrustRegionNewtonCGMinimizer();
+            var result = solver.FindMinimum(obj, BoxBodStart1);
+
+            for (int i = 0; i < result.BestFitParameters.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(BoxBodPbest[i], result.BestFitParameters[i], 3);
+                AssertHelpers.AlmostEqualRelative(BoxBodPstd[i], result.StandardErrors[i], 3);
+            }
+        }
+
         // model : Thurber (https://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml)
         //       f(x; b1 ... b7) = (b1 + b2*x + b3*x^2 + b4*x^3) / (1 + b5*x + b6*x^2 + b7*x^3) 
         // derivatives:
@@ -450,7 +488,7 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
         }
         
         [Test]
-        public void TRLMDIF_FindMinimum_Thurber_Scaled()
+        public void TRDLDIF_FindMinimum_Thurber_Scaled()
         {
             var obj = ObjectiveModel.FittingModel(ThurberModel, ThurberX, ThurberY,
                 scales: ThurberScales,
@@ -464,5 +502,21 @@ namespace MathNet.Numerics.UnitTests.OptimizationTests
                 AssertHelpers.AlmostEqualRelative(ThurberPstd[i], result.StandardErrors[i], 3);
             }
         }
+
+        [Test]
+        public void TRNCGDIF_FindMinimum_Thurber_Scaled()
+        {
+            var obj = ObjectiveModel.FittingModel(ThurberModel, ThurberX, ThurberY,
+                scales: ThurberScales,
+                accuracyOrder: 6);
+            var solver = new TrustRegionNewtonCGMinimizer();
+            var result = solver.FindMinimum(obj, ThurberInitialGuess);
+
+            for (int i = 0; i < result.BestFitParameters.Count; i++)
+            {
+                AssertHelpers.AlmostEqualRelative(ThurberPbest[i], result.BestFitParameters[i], 3);
+                AssertHelpers.AlmostEqualRelative(ThurberPstd[i], result.StandardErrors[i], 3);
+            }
+        }
     }
 }

src/Numerics/Optimization/Subproblems/DogLegSubproblem.cs

@@ -13,7 +13,6 @@ namespace MathNet.Numerics.Optimization.Subproblems
             var Jacobian = objective.Jacobian;
             var Gradient = objective.Gradient;
             var Hessian = objective.Hessian;
-            var RSS = objective.Residue;
 
             // newton point
             // the Gauss–Newton step by solving the normal equations

src/Numerics/Optimization/Subproblems/NewtonCGSubproblem.cs

@@ -0,0 +1,65 @@
+using MathNet.Numerics.LinearAlgebra;
+using System;
+
+namespace MathNet.Numerics.Optimization.Subproblems
+{
+    internal class NewtonCGSubproblem : ITrustRegionSubproblem
+    {
+        public Vector<double> Pstep { get; private set; }
+
+        public bool HitBoundary { get; private set; }
+
+        public void Solve(IObjectiveModel objective, double delta)
+        {
+            var Jacobian = objective.Jacobian;
+            var Gradient = objective.Gradient;
+            var Hessian = objective.Hessian;
+
+            // define tolerance
+            var tolerance = Math.Min(0.5, Math.Sqrt(Gradient.L2Norm())) * Gradient.L2Norm();
+
+            // initialize internal variables
+            var z = Vector<double>.Build.Dense(Hessian.RowCount);
+            var r = -Gradient;
+            var d = -r;
+
+            while (true)
+            {
+                var Bd = Hessian * d;
+                var dBd = d.DotProduct(Bd);
+
+                if (dBd <= 0)
+                {
+                    var t = Util.FindBeta(1, z, d, delta);
+                    Pstep = z + t.Item1 * d;
+                    HitBoundary = true;
+                    return;
+                }
+
+                var r_sq = r.DotProduct(r);
+                var alpha = r_sq / dBd;
+                var znext = z + alpha * d;
+                if(znext.L2Norm() >= delta)
+                {
+                    var t = Util.FindBeta(1, z, d, delta);
+                    Pstep = z + t.Item2 * d;
+                    HitBoundary = true;
+                    return;
+                }
+
+                var rnext = r + alpha * Bd;
+                var rnext_sq = rnext.DotProduct(rnext);
+                if (Math.Sqrt(rnext_sq) < tolerance)
+                {
+                    Pstep = znext;
+                    HitBoundary = false;
+                    return;
+                }
+
+                z = znext;
+                r = rnext;
+                d = -rnext + rnext_sq / r_sq * d; ;
+            }
+        }
+    }
+}

src/Numerics/Optimization/TrustRegionDogLegMinimizer.cs

@@ -1,10 +1,10 @@
-using MathNet.Numerics.LinearAlgebra;
-using System;
-
-namespace MathNet.Numerics.Optimization
+namespace MathNet.Numerics.Optimization
 {
     public sealed class TrustRegionDogLegMinimizer : TrustRegionMinimizerBase
     {
+        /// <summary>
+        /// Non-linear least square fitting by the trust region dogleg algorithm.
+        /// </summary>
         public TrustRegionDogLegMinimizer(double gradientTolerance = 1E-8, double stepTolerance = 1E-8, double functionTolerance = 1E-8, double radiusTolerance = 1E-8, int maximumIterations = -1)
             : base(TrustRegionSubproblem.DogLeg(), gradientTolerance, stepTolerance, functionTolerance, radiusTolerance, maximumIterations)
         { }

src/Numerics/Optimization/TrustRegionNewtonCGMinimizer.cs

@@ -0,0 +1,13 @@
+namespace MathNet.Numerics.Optimization
+{
+    public sealed class TrustRegionNewtonCGMinimizer : TrustRegionMinimizerBase
+    {
+        /// <summary>
+        /// Non-linear least square fitting by the trust region Newton-Conjugate-Gradient algorithm.
+        /// </summary>
+        public TrustRegionNewtonCGMinimizer(double gradientTolerance = 1E-8, double stepTolerance = 1E-8, double functionTolerance = 1E-8, double radiusTolerance = 1E-8, int maximumIterations = -1)
+            : base(TrustRegionSubproblem.NewtonCG(), gradientTolerance, stepTolerance, functionTolerance, radiusTolerance, maximumIterations)
+        { }
+    }
+}
+

src/Numerics/Optimization/TrustRegionSubProblem.cs

@@ -8,5 +8,10 @@ namespace MathNet.Numerics.Optimization
         {
             return new DogLegSubproblem();
         }
+
+        public static ITrustRegionSubproblem NewtonCG()
+        {
+            return new NewtonCGSubproblem();
+        }
     }
 }