Detailed Description

template<typename DerivativeStrategy>
struct NumLib::NumericalDerivative< DerivativeStrategy >

Computes numerical derivatives of almost arbitrary function (objects) with respect to scalar or vectorial (Eigen vectors) variables.

Template Parameters

DerivativeStrategy compute central or forward differences

Definition at line 208 of file NumericalDifferentiation.h.

#include <NumericalDifferentiation.h>

Collaboration diagram for NumLib::NumericalDerivative< DerivativeStrategy >:

[legend]

Public Member Functions
	NumericalDerivative (RelativeEpsilon const &rel_eps, MinimumPerturbation const &min_pert)

template<typename Function , typename... Args>
auto	operator() (Function const &f, Args const &... args) const

Private Member Functions
template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs>
auto	differentiate (Function const &f, TupleOfArgs const &args, DByDScalar const &d_by_dScalar, std::index_sequence< AllArgIdcs... > all_arg_idcs) const

template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>
auto	differentiateWrtScalarOrVectorialArgument (std::true_type, Function const &f, TupleOfArgs const &args, DByDScalar const &d_by_dScalar, std::integral_constant< std::size_t, PerturbedArgIdx > perturbed_arg_idx, std::index_sequence< AllArgIdcs... > all_arg_idcs) const

template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>
auto	differentiateWrtScalarOrVectorialArgument (std::false_type, Function const &f, TupleOfArgs const &args, DByDScalar const &d_by_dScalar, std::integral_constant< std::size_t, PerturbedArgIdx > perturbed_arg_idx, std::index_sequence< AllArgIdcs... > all_arg_idcs) const

template<typename Function , typename TupleOfArgs , typename DByDScalar , Eigen::Index... PerturbedArgComponents, std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>
auto	differentiateWrtAllVectorComponents (Function const &f, TupleOfArgs const &args, DByDScalar const &d_by_dScalar, std::integer_sequence< Eigen::Index, PerturbedArgComponents... >, std::integral_constant< std::size_t, PerturbedArgIdx > perturbed_arg_idx, std::index_sequence< AllArgIdcs... > all_arg_idcs) const

Private Attributes
detail::DefaultPerturbationStrategy	pert_strat_

Constructor & Destructor Documentation

◆ NumericalDerivative()

template<typename DerivativeStrategy >

NumLib::NumericalDerivative< DerivativeStrategy >::NumericalDerivative	(	RelativeEpsilon const &	rel_eps,
		MinimumPerturbation const &	min_pert )

inline

Definition at line 210 of file NumericalDifferentiation.h.

        : pert_strat_{rel_eps, min_pert}
    {
    }

Member Function Documentation

◆ differentiate()

template<typename DerivativeStrategy >

template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs>

auto NumLib::NumericalDerivative< DerivativeStrategy >::differentiate	(	Function const &	f,
		TupleOfArgs const &	args,
		DByDScalar const &	d_by_dScalar,
		std::index_sequence< AllArgIdcs... >	all_arg_idcs ) const

inlineprivate

Definition at line 232 of file NumericalDifferentiation.h.

    {
        return std::tuple{differentiateWrtScalarOrVectorialArgument(
            detail::IsScalar<std::remove_cvref_t<
                std::tuple_element_t<AllArgIdcs, TupleOfArgs>>>{},
            f, args, d_by_dScalar,
            std::integral_constant<std::size_t, AllArgIdcs>{},
            all_arg_idcs)... /* "for each function argument" */};
    }

References NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtScalarOrVectorialArgument().

Referenced by NumLib::NumericalDerivative< DerivativeStrategy >::operator()().

◆ differentiateWrtAllVectorComponents()

template<typename DerivativeStrategy >

template<typename Function , typename TupleOfArgs , typename DByDScalar , Eigen::Index... PerturbedArgComponents, std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>

auto NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtAllVectorComponents	(	Function const &	f,
		TupleOfArgs const &	args,
		DByDScalar const &	d_by_dScalar,
		std::integer_sequence< Eigen::Index, PerturbedArgComponents... >	,
		std::integral_constant< std::size_t, PerturbedArgIdx >	perturbed_arg_idx,
		std::index_sequence< AllArgIdcs... >	all_arg_idcs ) const

inlineprivate

Definition at line 287 of file NumericalDifferentiation.h.

    {
        return std::array{
            d_by_dScalar(f, args, pert_strat_, perturbed_arg_idx,
                         PerturbedArgComponents, all_arg_idcs)...
            /* "for each component of the vectorial function argument being
               perturbed" */
        };
    }

References NumLib::NumericalDerivative< DerivativeStrategy >::pert_strat_.

Referenced by NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtScalarOrVectorialArgument().

◆ differentiateWrtScalarOrVectorialArgument() [1/2]

template<typename DerivativeStrategy >

template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>

auto NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtScalarOrVectorialArgument	(	std::false_type	,
		Function const &	f,
		TupleOfArgs const &	args,
		DByDScalar const &	d_by_dScalar,
		std::integral_constant< std::size_t, PerturbedArgIdx >	perturbed_arg_idx,
		std::index_sequence< AllArgIdcs... >	all_arg_idcs ) const

inlineprivate

Definition at line 262 of file NumericalDifferentiation.h.

    {
        using VectorialArg = std::remove_cvref_t<
            std::tuple_element_t<PerturbedArgIdx, TupleOfArgs>>;
        constexpr int N = VectorialArg::RowsAtCompileTime;
 
        static_assert(N != Eigen::Dynamic);
        static_assert(VectorialArg::ColsAtCompileTime == 1,
                      "Row vectors are not supported, yet. If you implement "
                      "support for them, make sure to test your implementation "
                      "thoroughly.");
 
        return differentiateWrtAllVectorComponents(
            f, args, d_by_dScalar,
            std::make_integer_sequence<Eigen::Index, N>{}, perturbed_arg_idx,
            all_arg_idcs);
    }

References NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtAllVectorComponents(), and NumLib::N.

◆ differentiateWrtScalarOrVectorialArgument() [2/2]

template<typename DerivativeStrategy >

template<typename Function , typename TupleOfArgs , typename DByDScalar , std::size_t... AllArgIdcs, std::size_t PerturbedArgIdx>

auto NumLib::NumericalDerivative< DerivativeStrategy >::differentiateWrtScalarOrVectorialArgument	(	std::true_type	,
		Function const &	f,
		TupleOfArgs const &	args,
		DByDScalar const &	d_by_dScalar,
		std::integral_constant< std::size_t, PerturbedArgIdx >	perturbed_arg_idx,
		std::index_sequence< AllArgIdcs... >	all_arg_idcs ) const

inlineprivate

Definition at line 247 of file NumericalDifferentiation.h.

    {
        constexpr Eigen::Index component_does_not_matter = -1;
 
        return d_by_dScalar(f, args, pert_strat_, perturbed_arg_idx,
                            component_does_not_matter, all_arg_idcs);
    }

References NumLib::NumericalDerivative< DerivativeStrategy >::pert_strat_.

Referenced by NumLib::NumericalDerivative< DerivativeStrategy >::differentiate().

◆ operator()()

template<typename DerivativeStrategy >

template<typename Function , typename... Args>

auto NumLib::NumericalDerivative< DerivativeStrategy >::operator()	(	Function const &	f,
		Args const &...	args ) const

inline

Definition at line 217 of file NumericalDifferentiation.h.

    {
        auto const d_by_dScalar =
            DerivativeStrategy::createDByDScalar(f, args...);
 
        // TODO also return value from the function, not only the derivatives?
        return differentiate(f,
                             std::forward_as_tuple(args...),
                             d_by_dScalar,
                             std::make_index_sequence<sizeof...(Args)>{});
    }