csharpfftfsharpintegrationinterpolationlinear-algebramathdifferentiationmatrixnumericsrandomregressionstatisticsmathnet
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
252 lines
10 KiB
252 lines
10 KiB
// <copyright file="BfgsTest.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) 2009-2016 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 System;
|
|
using MathNet.Numerics.LinearAlgebra.Double;
|
|
using MathNet.Numerics.Optimization;
|
|
using NUnit.Framework;
|
|
using System.Linq;
|
|
using System.Text;
|
|
using System.Collections.Generic;
|
|
using MathNet.Numerics.UnitTests.OptimizationTests.TestFunctions;
|
|
using System.Collections;
|
|
using MathNet.Numerics.Optimization.ObjectiveFunctions;
|
|
|
|
namespace MathNet.Numerics.UnitTests.OptimizationTests
|
|
{
|
|
[TestFixture]
|
|
public class BfgsBMinimizerTests
|
|
{
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_Easy()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer (1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
var lowerBound = new DenseVector(new[]{ -5.0, -5.0 });
|
|
var upperBound = new DenseVector(new[]{ 5.0, 5.0 });
|
|
var initialGuess = new DenseVector(new[] { 1.2, 1.2 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
|
|
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_Hard()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer (1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
|
|
var lowerBound = new DenseVector(new[]{ -5.0, -5.0 });
|
|
var upperBound = new DenseVector(new[]{ 5.0, 5.0 });
|
|
|
|
var initialGuess = new DenseVector (new[]{ -1.2, 1.0 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
|
|
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_Overton()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer (1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
|
|
var lowerBound = new DenseVector(new[]{ -5.0, -5.0 });
|
|
var upperBound = new DenseVector(new[]{ 5.0, 5.0 });
|
|
var initialGuess = new DenseVector (new[]{ -0.9, -0.5 });
|
|
|
|
var result = solver.FindMinimum (obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
|
|
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_Easy_OneBoundary()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer (1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
var lowerBound = new DenseVector(new[]{ 1.0, -5.0 });
|
|
var upperBound = new DenseVector(new[]{ 5.0, 5.0 });
|
|
var initialGuess = new DenseVector(new[] { 1.2, 1.2 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
|
|
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_Easy_TwoBoundaries()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer (1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
var lowerBound = new DenseVector(new[]{ 1.0, 1.0 });
|
|
var upperBound = new DenseVector(new[]{ 5.0, 5.0 });
|
|
var initialGuess = new DenseVector(new[] { 1.2, 1.2 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.That(Math.Abs(result.MinimizingPoint[0] - RosenbrockFunction.Minimum[0]), Is.LessThan(1e-3));
|
|
Assert.That(Math.Abs(result.MinimizingPoint[1] - RosenbrockFunction.Minimum[1]), Is.LessThan(1e-3));
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_MinimumGreateerOrEqualToLowerBoundary()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer(1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
|
|
var lowerBound = new DenseVector(new[] { 2, 2.0 });
|
|
var upperBound = new DenseVector(new[] { 5.0, 5.0 });
|
|
|
|
var initialGuess = new DenseVector(new[] { 2.5, 2.5 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.GreaterOrEqual(result.MinimizingPoint[0],lowerBound[0]);
|
|
Assert.GreaterOrEqual(result.MinimizingPoint[1], lowerBound[1]);
|
|
}
|
|
|
|
[Test]
|
|
public void FindMinimum_Rosenbrock_MinimumLesserOrEqualToUpperBoundary()
|
|
{
|
|
var obj = ObjectiveFunction.Gradient(RosenbrockFunction.Value, RosenbrockFunction.Gradient);
|
|
var solver = new BfgsBMinimizer(1e-5, 1e-5, 1e-5, maximumIterations: 1000);
|
|
|
|
var lowerBound = new DenseVector(new[] { -2.0, -2.0 });
|
|
var upperBound = new DenseVector(new[] { 0.5, 0.5 });
|
|
|
|
var initialGuess = new DenseVector(new[] { -0.9, -0.5 });
|
|
|
|
var result = solver.FindMinimum(obj, lowerBound, upperBound, initialGuess);
|
|
|
|
Assert.LessOrEqual(result.MinimizingPoint[0],upperBound[0]);
|
|
Assert.LessOrEqual(result.MinimizingPoint[1],upperBound[1]);
|
|
}
|
|
|
|
[Test]
|
|
[TestCaseSource(typeof(MghTestCaseEnumerator))]
|
|
public void Mgh_Tests(TestFunctions.TestCase test_case)
|
|
{
|
|
var obj = new MghObjectiveFunction(test_case.Function, true, true);
|
|
var solver = new BfgsBMinimizer(1e-8, 1e-8, 1e-8, 1000);
|
|
|
|
var result = solver.FindMinimum(obj, test_case.LowerBound, test_case.UpperBound, test_case.InitialGuess);
|
|
|
|
if (test_case.MinimizingPoint != null)
|
|
{
|
|
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
|
|
}
|
|
|
|
var val1 = result.FunctionInfoAtMinimum.Value;
|
|
var val2 = test_case.MinimalValue;
|
|
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
|
|
var abs_err = Math.Abs(val1 - val2);
|
|
var rel_err = abs_err / abs_min;
|
|
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
|
|
Assert.That(success, "Minimal function value is not as expected.");
|
|
}
|
|
|
|
[Test]
|
|
[TestCaseSource(typeof(FdMghTestCaseEnumerator))]
|
|
public void Mgh_FiniteDifference_Tests(TestFunctions.TestCase test_case)
|
|
{
|
|
var obj1 = new MghObjectiveFunction(test_case.Function, true, true);
|
|
var obj = new ForwardDifferenceGradientObjectiveFunction(obj1, test_case.LowerBound, test_case.UpperBound, 1e-10, 1e-10);
|
|
var solver = new BfgsBMinimizer(1e-8, 1e-8, 1e-8, 1000);
|
|
|
|
var result = solver.FindMinimum(obj, test_case.LowerBound, test_case.UpperBound, test_case.InitialGuess);
|
|
|
|
if (test_case.MinimizingPoint != null)
|
|
{
|
|
Assert.That((result.MinimizingPoint - test_case.MinimizingPoint).L2Norm(), Is.LessThan(1e-3));
|
|
}
|
|
|
|
var val1 = result.FunctionInfoAtMinimum.Value;
|
|
var val2 = test_case.MinimalValue;
|
|
var abs_min = Math.Min(Math.Abs(val1), Math.Abs(val2));
|
|
var abs_err = Math.Abs(val1 - val2);
|
|
var rel_err = abs_err / abs_min;
|
|
var success = (abs_min <= 1 && abs_err < 1e-3) || (abs_min > 1 && rel_err < 1e-3);
|
|
Assert.That(success, "Minimal function value is not as expected.");
|
|
}
|
|
|
|
|
|
private class BaseMghTestCaseEnumerator : IEnumerable<ITestCaseData>
|
|
{
|
|
private string _prefix = "";
|
|
|
|
public BaseMghTestCaseEnumerator(string prefix)
|
|
{
|
|
if (prefix.EndsWith(" "))
|
|
_prefix = prefix;
|
|
else
|
|
_prefix = prefix + " ";
|
|
}
|
|
public IEnumerator<ITestCaseData> GetEnumerator()
|
|
{
|
|
return
|
|
RosenbrockFunction2.TestCases
|
|
.Concat(BealeFunction.TestCases)
|
|
.Concat(HelicalValleyFunction.TestCases)
|
|
.Concat(MeyerFunction.TestCases)
|
|
.Concat(PowellSingularFunction.TestCases)
|
|
.Concat(WoodFunction.TestCases)
|
|
.Concat(BrownAndDennisFunction.TestCases)
|
|
.Where(x => x.IsBounded)
|
|
.Select(x => new TestCaseData(x)
|
|
.SetName(_prefix + x.FullName)
|
|
)
|
|
.GetEnumerator();
|
|
}
|
|
|
|
IEnumerator IEnumerable.GetEnumerator()
|
|
{
|
|
return this.GetEnumerator();
|
|
}
|
|
}
|
|
|
|
private class MghTestCaseEnumerator : BaseMghTestCaseEnumerator
|
|
{
|
|
public MghTestCaseEnumerator() : base("") { }
|
|
}
|
|
|
|
private class FdMghTestCaseEnumerator : BaseMghTestCaseEnumerator
|
|
{
|
|
public FdMghTestCaseEnumerator() : base("FD") { }
|
|
}
|
|
}
|
|
}
|
|
|
|
|