numericdifferentiation.hh

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#ifndef DUMUX_NUMERIC_DIFFERENTIATION_HH
#define DUMUX_NUMERIC_DIFFERENTIATION_HH
 
#include <cmath>
#include <limits>
 
namespace Dumux {
 
class NumericDifferentiation
{
public:
 
    template<class Scalar>
    static Scalar epsilon(const Scalar value, const Scalar baseEps = 1e-10)
    {
        assert(std::numeric_limits<Scalar>::epsilon()*1e4 < baseEps);
        // the epsilon value used for the numeric differentiation is
        // now scaled by the absolute value of the primary variable...
        using std::abs;
        return baseEps*(abs(value) + 1.0);
    }
 
    template<class Function, class Scalar, class FunctionEvalType>
    static void partialDerivative(const Function& function, Scalar x0,
                                  FunctionEvalType& derivative,
                                  const FunctionEvalType& fx0,
                                  const int numericDifferenceMethod = 1)
    { partialDerivative(function, x0, derivative, fx0, epsilon(x0), numericDifferenceMethod); }
 
    template<class Function, class Scalar, class FunctionEvalType>
    static void partialDerivative(const Function& function, Scalar x0,
                                  FunctionEvalType& derivative,
                                  const FunctionEvalType& fx0,
                                  const Scalar eps,
                                  const int numericDifferenceMethod = 1)
    {
        Scalar delta = 0.0;
        // we are using forward or central differences, i.e. we need to calculate f(x + \epsilon)
        if (numericDifferenceMethod >= 0)
        {
            delta += eps;
            // calculate the function evaluated with the deflected variable
            derivative = function(x0 + eps);
        }
 
        // we are using backward differences,
        // i.e. we don't need to calculate f(x + \epsilon)
        // we can recycle the (possibly cached) f(x)
        else derivative = fx0;
 
        // we are using backward or central differences,
        // i.e. we need to calculate f(x - \epsilon)
        if (numericDifferenceMethod <= 0)
        {
            delta += eps;
            // subtract the function evaluated with the deflected variable
            derivative -= function(x0 - eps);
        }
 
        // we are using forward differences,
        // i.e. we don't need to calculate f(x - \epsilon)
        // we can recycle the (possibly cached) f(x)
        else derivative -= fx0;
 
        // divide difference in residuals by the magnitude of the
        // deflections between the two function evaluation
        derivative /= delta;
    }
};
 
} // end namespace Dumux
 
#endif