diff --git a/src/Numerics/Differentiation/NumericalHessian.cs b/src/Numerics/Differentiation/NumericalHessian.cs new file mode 100644 index 00000000..6edf6ba9 --- /dev/null +++ b/src/Numerics/Differentiation/NumericalHessian.cs @@ -0,0 +1,119 @@ +// +// 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) 2009-2015 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. +// + +using System; + +namespace MathNet.Numerics.Differentiation +{ + /// + /// Class for evaluating the Hessian of a smooth continuously differentiable function using finite differences. + /// By default, a central 3-point method is used. + /// + public class NumericalHessian + { + /// + /// Number of function evaluations. + /// + public int FunctionEvaluations + { + get { return _df.Evaluations; } + } + + private readonly NumericalDerivative _df; + + /// + /// Creates a numerical Hessian object with a three point central difference method. + /// + public NumericalHessian() : this(3, 1) { } + + /// + /// Creates a numerical Hessian with a specified differentiation scheme. + /// + /// Number of points for Hessian evaluation. + /// Center point for differentiation. + public NumericalHessian(int points, int center) + { + _df = new NumericalDerivative(points, center); + } + + /// + /// Evaluates the Hessian of the scalar univariate function f at points x. + /// + /// Scalar univariate function handle. + /// Point at which to evaluate Hessian. + /// Hessian tensor. + public double[] Evaluate(Func f, double x) + { + return new[] { _df.EvaluateDerivative(f, x, 2) }; + } + + /// + /// Evaluates the Hessian of a multivariate function f at points x. + /// + /// + /// This method of computing the Hessian is only vaid for Lipschitz continuous functions. + /// The function mirrors the Hessian along the diagonal since d2f/dxdy = d2f/dydx for continuously differentiable functions. + /// + /// Multivariate function handle.> + /// Points at which to evaluate Hessian.> + /// Hessian tensor. + public double[,] Evaluate(Func f, double[] x) + { + var hessian = new double[x.Length, x.Length]; + + // Compute diagonal elements + for (var row = 0; row < x.Length; row++) + { + hessian[row, row] = _df.EvaluatePartialDerivative(f, x, row, 2); + } + + // Compute non-diagonal elements + for (var row = 0; row < x.Length; row++) + { + for (var col = 0; col < row; col++) + { + var mixedPartial = _df.EvaluateMixedPartialDerivative(f, x, new[] { row, col }, 2); + + hessian[row, col] = mixedPartial; + hessian[col, row] = mixedPartial; + } + } + return hessian; + } + + /// + /// Resets the function evaluation counter for the Hessian. + /// + public void ResetFunctionEvaluations() + { + _df.ResetEvaluations(); + } + } +} diff --git a/src/Numerics/Differentiation/NumericalJacobian.cs b/src/Numerics/Differentiation/NumericalJacobian.cs new file mode 100644 index 00000000..ec04debc --- /dev/null +++ b/src/Numerics/Differentiation/NumericalJacobian.cs @@ -0,0 +1,172 @@ +// +// 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) 2009-2015 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. +// + +using System; + +namespace MathNet.Numerics.Differentiation +{ + /// + /// Class for evaluating the Jacobian of a function using finite differences. + /// By default, a central 3-point method is used. + /// + public class NumericalJacobian + { + /// + /// Number of function evaluations. + /// + public int FunctionEvaluations + { + get { return _df.Evaluations; } + } + + private readonly NumericalDerivative _df; + + /// + /// Creates a numerical Jacobian object with a three point central difference method. + /// + public NumericalJacobian() : this(3, 1) { } + + /// + /// Creates a numerical Jacobian with a specified differentiation scheme. + /// + /// Number of points for Jacobian evaluation. + /// Center point for differentation. + public NumericalJacobian(int points, int center) + { + _df = new NumericalDerivative(points, center); + } + + /// + /// Evaluates the Jacbian of scalar univariate function f at point x. + /// + /// Scalar univariate function handle. + /// Point at which to evaluate Jacobian. + /// Jacobian vector. + public double[] Evaluate(Func f, double x) + { + return new[] { _df.EvaluateDerivative(f, x, 1) }; + } + + /// + /// Evaluates the Jacobian of a multivariate function f at vector x. + /// + /// + /// This function assumes that the length of vector x consistent with the argument count of f. + /// + /// Multivariate function handle. + /// Points at which to evaluate Jacobian. + /// Jacobian vector. + public double[] Evaluate(Func f, double[] x) + { + var jacobian = new double[x.Length]; + + for (var i = 0; i < jacobian.Length; i++) + jacobian[i] = _df.EvaluatePartialDerivative(f, x, i, 1); + + return jacobian; + } + + /// + /// Evaluates the Jacobian of a multivariate function f at vector x given a current function value. + /// + /// + /// To minimize the number of function evaluations, a user can supply the current value of the function + /// to be used in computing the Jacobian. This value must correspond to the "center" location for the + /// finite differencing. If a scheme is used where the center value is not evaluated, this will provide no + /// added efficiency. This method also assumes that the length of vector x consistent with the argument count of f. + /// + /// Multivariate function handle. + /// Points at which to evaluate Jacobian. + /// Current function value at finite difference center. + /// Jacobian vector. + public double[] Evaluate(Func f, double[] x, double currentValue) + { + var jacobian = new double[x.Length]; + + for (var i = 0; i < jacobian.Length; i++) + jacobian[i] = _df.EvaluatePartialDerivative(f, x, i, 1, currentValue); + + return jacobian; + } + + /// + /// Evaluates the Jacobian of a multivariate function array f at vector x. + /// + /// Multivariate function array handle. + /// Vector at which to evaluate Jacobian. + /// Jacobian matrix. + public double[,] Evaluate(Func[] f, double[] x) + { + var jacobian = new double[f.Length, x.Length]; + for (int i = 0; i < f.Length; i++) + { + var gradient = Evaluate(f[i], x); + for (int j = 0; j < gradient.Length; j++) + jacobian[i, j] = gradient[j]; + } + + return jacobian; + } + + /// + /// Evaluates the Jacobian of a multivariate function array f at vector x given a vector of current function values. + /// + /// + /// To minimize the number of function evaluations, a user can supply a vector of current values of the functions + /// to be used in computing the Jacobian. These value must correspond to the "center" location for the + /// finite differencing. If a scheme is used where the center value is not evaluated, this will provide no + /// added efficiency. This method also assumes that the length of vector x consistent with the argument count of f. + /// + /// Multivariate function array handle. + /// Vector at which to evaluate Jacobian. + /// Vector of current function values. + /// Jacobian matrix. + public double[,] Evaluate(Func[] f, double[] x, double[] currentValues) + { + var jacobian = new double[f.Length, x.Length]; + for (int i = 0; i < f.Length; i++) + { + var gradient = Evaluate(f[i], x, currentValues[i]); + for (int j = 0; j < gradient.Length; j++) + jacobian[i, j] = gradient[j]; + } + + return jacobian; + } + + /// + /// Resets the function evaluation counter for the Jacobian. + /// + public void ResetFunctionEvaluations() + { + _df.ResetEvaluations(); + } + } +} diff --git a/src/Numerics/Numerics.csproj b/src/Numerics/Numerics.csproj index 166b4258..2172e7d4 100644 --- a/src/Numerics/Numerics.csproj +++ b/src/Numerics/Numerics.csproj @@ -82,6 +82,8 @@ + + diff --git a/src/UnitTests/DifferentiationTests/NumericalHessianTests.cs b/src/UnitTests/DifferentiationTests/NumericalHessianTests.cs new file mode 100644 index 00000000..a833a3a3 --- /dev/null +++ b/src/UnitTests/DifferentiationTests/NumericalHessianTests.cs @@ -0,0 +1,76 @@ +// +// 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) 2009-2015 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. +// + +namespace MathNet.Numerics.UnitTests.DifferentiationTests +{ + using System; + using Differentiation; + using NUnit.Framework; + + [TestFixture, Category("Differentiation")] + class NumericalHessianTests + { + [Test] + public void ScalarFunctonSecondDerivativeTest() + { + // d2/dx2((2x)^2) = 8 + Func f = x => Math.Pow(2 * x, 2); + var J = new NumericalHessian(); + var jeval = J.Evaluate(f, 2); + Assert.AreEqual((double)8, jeval[0], 1e-7); + } + + [Test] + public void OneEquationTwoVarVectorFunctionTest() + { + Func f = x => 4 * Math.Pow(x[0], 2) + 3 * Math.Pow(x[1], 3); + var H = new NumericalHessian(); + var heval = H.Evaluate(f, new double[] { 1, 1 }); + var solution = new double[,] { { 8, 0 }, { 0, 18 } }; + Assert.AreEqual(solution, heval); + Assert.AreEqual(12, H.FunctionEvaluations); + H.ResetFunctionEvaluations(); + Assert.AreEqual(0, H.FunctionEvaluations); + } + + [Test] + public void RosenbrockFunctionHessianTest() + { + Func f = x => Math.Pow((1 - x[0]), 2) + 100 * Math.Pow(x[1] - Math.Pow(x[0], 2), 2); + var H = new NumericalHessian(5, 2); + var heval = H.Evaluate(f, new double[] { 2, 3 }); + var solution = new double[,] { { 3602, -800 }, { -800, 200 } }; + for (int row = 0; row < solution.Rank; row++) + { + for (int col = 0; col < solution.Rank; col++) + { + Assert.AreEqual(solution[row, col], heval[row, col], 1e-7); + } + } + + } + } +} diff --git a/src/UnitTests/DifferentiationTests/NumericalJacobianTests.cs b/src/UnitTests/DifferentiationTests/NumericalJacobianTests.cs new file mode 100644 index 00000000..c9833070 --- /dev/null +++ b/src/UnitTests/DifferentiationTests/NumericalJacobianTests.cs @@ -0,0 +1,75 @@ +// +// 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) 2009-2015 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. +// + +namespace MathNet.Numerics.UnitTests.DifferentiationTests +{ + using System; + using Differentiation; + using NUnit.Framework; + + [TestFixture, Category("Differentiation")] + class NumericalJacobianTests + { + [Test] + public void OneEquationVectorFunctionTest() + { + Func f = x => Math.Sin(x[0] * x[1]) * Math.Exp(-x[0] / 2) + x[1] / x[0]; + var J = new NumericalJacobian(); + var jeval = J.Evaluate(f, new double[] { 1, 1 }); + Assert.AreEqual(-0.92747906175, jeval[0], 1e-9); + Assert.AreEqual(1.32770991402, jeval[1], 1e-9); + Assert.AreEqual(4, J.FunctionEvaluations); + J.ResetFunctionEvaluations(); + Assert.AreEqual(0, J.FunctionEvaluations); + } + + [Test] + public void ScalarFunctonDerivativeTest() + { + Func f = x => 1 / x; + var J = new NumericalJacobian(); + var jeval = J.Evaluate(f, 2); + Assert.AreEqual((double)-1 / 4, jeval[0], 1e-7); + } + + [Test] + public void VectorFunctionJacobianTest() + { + Func[] f = + { + (x) => Math.Pow(x[0], 2)*x[1], + (x) => 5*x[0] + Math.Sin(x[1]) + }; + var j = new NumericalJacobian(); + var jeval = j.Evaluate(f, new double[] { 1, 1 }); + Assert.AreEqual(2, jeval[0, 0]); + Assert.AreEqual(1, jeval[0, 1]); + Assert.AreEqual(5, jeval[1, 0]); + Assert.AreEqual(Math.Cos(1), jeval[1, 1], 1e-7); + + } + } +} diff --git a/src/UnitTests/UnitTests.csproj b/src/UnitTests/UnitTests.csproj index 1ac8eb41..54482cd3 100644 --- a/src/UnitTests/UnitTests.csproj +++ b/src/UnitTests/UnitTests.csproj @@ -79,6 +79,8 @@ + +