/// <summary>
/// Evaluates the Jacobian of a multivariate function f at vector x.
/// </summary>
/// <remarks>
/// This function assumes that the length of vector x consistent with the argument count of f.
/// </remarks>
/// <param name="f">Multivariate function handle.</param>
/// <param name="x">Points at which to evaluate Jacobian.</param>
/// <returns>Jacobian vector.</returns>
public double[] Evaluate(Func <double[], double> 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);
}
/// <summary>
/// Evaluates the Hessian of a multivariate function f at points x.
/// </summary>
/// <remarks>
/// 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.
/// </remarks>
/// <param name="f">Multivariate function handle.></param>
/// <param name="x">Points at which to evaluate Hessian.></param>
/// <returns>Hessian tensor.</returns>
public double[,] Evaluate(Func <double[], double> 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);
}