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 @@
+
+