public void CubicPolynomialFunctionValueTest()
{
Func<double, double> f = x => 3 * Math.Pow(x, 3) + 2 * x - 6;
var current = f(2);
var df = new NumericalDerivative(3, 0);
Assert.AreEqual(38, df.EvaluateDerivative(f, 2, 1, current), 1e-8);
}
public void CreateDerivativeFunctionHandleTest()
{
Func<double, double> f = x => 3 * Math.Pow(x, 3) + 2 * x - 6;
var nd = new NumericalDerivative(5, 2);
var df = nd.CreateDerivativeFunctionHandle(f, 3);
Assert.AreEqual(18, df(0));
// Test new function with same nd class
Func<double, double> f2 = x => 2 * Math.Pow(x, 3) + 2 * x - 6;
var df2 = nd.CreateDerivativeFunctionHandle(f2, 3);
Assert.AreEqual(12, df2(0));
// Original delegate not changed
Assert.AreEqual(18, df(0));
}
public Surface(VectorFunction r)
{
this.r = r;
List<CommonFunction> components = r.components;
List<DefinedCommonFunction> derivativesU = new List<DefinedCommonFunction>();
List<DefinedCommonFunction> derivativesV = new List<DefinedCommonFunction>();
NumericalDerivative derivative = new NumericalDerivative();
derivativesU.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[0].getCommonFunction(), 0, 1)));
derivativesV.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[0].getCommonFunction(), 1, 1)));
derivativesU.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[1].getCommonFunction(), 0, 1)));
derivativesV.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[1].getCommonFunction(), 1, 1)));
derivativesU.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[2].getCommonFunction(), 0, 1)));
derivativesV.Add(new DefinedCommonFunction(derivative.CreatePartialDerivativeFunctionHandle(components[2].getCommonFunction(), 1, 1)));
VectorFunction v1 = new VectorFunction(derivativesU);
VectorFunction v2 = new VectorFunction(derivativesV);
VectorFunction normalLength = new Vector3Mul(v1, v2);
CommonFunction length = new Length(normalLength);
List<bool> normalPow = new List<bool>();
normalPow.Add(true); normalPow.Add(false);
List<CommonFunction> normalx = new List<CommonFunction>();
normalx.Add(normalLength.components[0]); normalx.Add(length);
List<CommonFunction> normaly = new List<CommonFunction>();
normaly.Add(normalLength.components[1]); normaly.Add(length);
List<CommonFunction> normalz = new List<CommonFunction>();
normalz.Add(normalLength.components[2]); normalz.Add(length);
List<CommonFunction> normalCoordinates = new List<CommonFunction>();
normalCoordinates.Add(new Mul(normalx, normalPow));
normalCoordinates.Add(new Mul(normaly, normalPow));
normalCoordinates.Add(new Mul(normalz, normalPow));
normal = new VectorFunction(normalCoordinates);
}
public void CubicPolynomialThirdDerivativeAtAnyValTest()
{
Func<double, double> f = x => 3 * Math.Pow(x, 3) + 2 * x - 6;
var df = new NumericalDerivative(5, 2);
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
df.Center = 0;
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
df.Center = 1;
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
df.Center = 2;
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
df.Center = 3;
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
df.Center = 4;
Assert.AreEqual(18, df.EvaluateDerivative(f, 0, 3));
Assert.AreEqual(18, df.EvaluateDerivative(f, 10, 3));
}
/// <summary>
/// Creates a numerical Jacobian with a specified differentiation scheme.
/// </summary>
/// <param name="points">Number of points for Jacobian evaluation.</param>
/// <param name="center">Center point for differentiation.</param>
public NumericalJacobian(int points, int center)
{
_df = new NumericalDerivative(points, center);
}
/// <summary>
/// Creates a numerical Hessian with a specified differentiation scheme.
/// </summary>
/// <param name="points">Number of points for Hessian evaluation.</param>
/// <param name="center">Center point for differentiation.</param>
public NumericalHessian(int points, int center)
{
_df = new NumericalDerivative(points, center);
}
public void VectorFunctionMixedPartialDerivativeTest()
{
Func<double[], double>[] f =
{
(x) => Math.Pow(x[0],2) - 3*x[1],
(x) => x[1]*x[1] + 2*x[0]*x[1]
};
var x0 = new double[] { 2, 2 };
var df = new NumericalDerivative();
Assert.AreEqual(new double[] { 0, 2 }, df.EvaluateMixedPartialDerivative(f, x0, new int[] { 0, 1 }, 2));
Assert.AreEqual(new double[] { 0, 2 }, df.EvaluateMixedPartialDerivative(f, x0, new int[] { 1, 0 }, 2));
}
public void SinFirstDerivativeAtZeroTest()
{
Func<double, double> f = Math.Sin;
var df = new NumericalDerivative();
Assert.AreEqual(1, df.EvaluateDerivative(f, 0, 1), 1e-10);
}
public void VectorFunction1PartialDerivativeTest()
{
Func<double[], double>[] f =
{
(x) => Math.Pow(x[0],2) - 3*x[1],
(x) => x[1]*x[1] + 2*x[0]*x[1]
};
var x0 = new double[] { 2, 2 };
var g = new double[] { 4, 4 };
var df = new NumericalDerivative();
Assert.AreEqual(g, df.EvaluatePartialDerivative(f, x0, 0, 1));
Assert.AreEqual(new double[] { 2, 0 }, df.EvaluatePartialDerivative(f, x0, 0, 2));
Assert.AreEqual(new double[] { -3, 8 }, df.EvaluatePartialDerivative(f, x0, 1, 1));
}
public void RosenbrockFunctionMixedDerivativeTwoVariableSecondOrderTest()
{
Func<double[], double> f = x => Math.Pow(1 - x[0], 2) + 100 * Math.Pow(x[1] - Math.Pow(x[0], 2), 2);
var df = new NumericalDerivative();
var x0 = new double[] { 2, 2 };
var parameterIndex = new[] { 0, 1 };
Assert.AreEqual(-800, df.EvaluateMixedPartialDerivative(f, x0, parameterIndex, 2));
}
public void RosenbrockFunctionMixedDerivativeOneVariableSecondOrderTest()
{
Func<double[], double> f = x => Math.Pow(1 - x[0], 2) + 100 * Math.Pow(x[1] - Math.Pow(x[0], 2), 2);
var df = new NumericalDerivative();
var x0 = new double[] { 2, 2 };
var parameterindex = new int[] { 0, 0 };
Assert.AreEqual(1602, df.EvaluatePartialDerivative(f, x0, 0, 1), 1e-6);
Assert.AreEqual(4002, df.EvaluateMixedPartialDerivative(f, x0, parameterindex, 2));
}
public void ExponentialFunctionPartialDerivativeCurrentValueTest()
{
//Test Function
Func<double[], double> f = (x) => Math.Sin(x[0] * x[1]) + Math.Exp(-x[0] / 2) + x[1] / x[0];
//Analytical partial dfdx
Func<double[], double> dfdx =
(x) => Math.Cos(x[0] * x[1]) * x[1] - Math.Exp(-x[0] / 2) / 2 - x[1] / Math.Pow(x[0], 2);
//Analytical partial dfdy
Func<double[], double> dfdy = (x) => Math.Cos(x[0] * x[1]) * x[0] + 1 / x[0];
// Current value
var x1 = new double[] { 3, 3 };
var current = f(x1);
var df = new NumericalDerivative(5, 2);
Assert.AreEqual(dfdx(x1), df.EvaluatePartialDerivative(f, x1, 0, 1, current), 1e-8);
Assert.AreEqual(dfdy(x1), df.EvaluatePartialDerivative(f, x1, 1, 1, current), 1e-8);
}
public void ExponentialFunctionPartialDerivativeTest()
{
//Test Function
Func<double[], double> f = (x) => Math.Sin(x[0] * x[1]) + Math.Exp(-x[0] / 2) + x[1] / x[0];
//Analytical partial dfdx
Func<double[], double> dfdx =
(x) => Math.Cos(x[0] * x[1]) * x[1] - Math.Exp(-x[0] / 2) / 2 - x[1] / Math.Pow(x[0], 2);
//Analytical partial dfdy
Func<double[], double> dfdy = (x) => Math.Cos(x[0] * x[1]) * x[0] + 1 / x[0];
var df = new NumericalDerivative(3, 1);
var x1 = new double[] { 3, 3 };
Assert.AreEqual(dfdx(x1), df.EvaluatePartialDerivative(f, x1, 0, 1), 1e-8);
Assert.AreEqual(dfdy(x1), df.EvaluatePartialDerivative(f, x1, 1, 1), 1e-8);
var x2 = new double[] { 300, -50 };
df.StepType = StepType.Absolute;
Assert.AreEqual(dfdx(x2), df.EvaluatePartialDerivative(f, x2, 0, 1), 1e-5);
Assert.AreEqual(dfdy(x2), df.EvaluatePartialDerivative(f, x2, 1, 1), 1e-2);
}
