Marmot::NumericalAlgorithms::Differentiation::Complex Namespace Reference

Namespaces
	ScalarToTensor
	TensorToScalar
	TensorToTensor

Typedefs
using	scalar_to_scalar_function_type = std::function< complexDouble(const complexDouble x) >
using	vector_to_vector_function_type = std::function< Eigen::VectorXcd(const Eigen::VectorXcd &X) >
using	complexDouble = std::complex< double >
template<size_t dim>
using	tensor_to_scalar_function_type = std::function< std::complex< double >(const Fastor::Tensor< std::complex< double >, dim, dim > &T) >

Functions
double	forwardDifference (const scalar_to_scalar_function_type &f, const double x)
std::tuple< Eigen::VectorXd, Eigen::MatrixXd >	forwardDifference (const vector_to_vector_function_type &F, const Eigen::VectorXd &X)
Eigen::MatrixXd	centralDifference (const vector_to_vector_function_type &F, const Eigen::VectorXd &X)
Eigen::MatrixXd	fourthOrderAccurateDerivative (const vector_to_vector_function_type &F, const Eigen::VectorXd &X)
template<size_t dim>
Fastor::Tensor< double, dim, dim >	forwardDifference (const tensor_to_scalar_function_type< dim > &F, const Fastor::Tensor< double, dim, dim > &T)
std::tuple< VectorXd, MatrixXd >	forwardDifference (const vector_to_vector_function_type &F, const VectorXd &X)
MatrixXd	centralDifference (const vector_to_vector_function_type &F, const VectorXd &X)
MatrixXd	fourthOrderAccurateDerivative (const vector_to_vector_function_type &F, const VectorXd &X)

Variables
static const std::complex< double >	imaginaryUnit = { 0, 1 }
static const std::complex< double >	complexUnit = { 1, 1 }
static const std::complex< double >	i_ = Marmot::Constants::sqrt2 / 2. * complexUnit
static const double	imaginaryPerturbationSize = 1e-20
static const complexDouble	imaginaryPerturbation = imaginaryPerturbationSize * imaginaryUnit

Typedef Documentation

scalar_to_scalar_function_type

using Marmot::NumericalAlgorithms::Differentiation::Complex::scalar_to_scalar_function_type = typedef std::function< complexDouble( const complexDouble x ) >

vector_to_vector_function_type

using Marmot::NumericalAlgorithms::Differentiation::Complex::vector_to_vector_function_type = typedef std::function< Eigen::VectorXcd( const Eigen::VectorXcd& X ) >

complexDouble

using Marmot::NumericalAlgorithms::Differentiation::Complex::complexDouble = typedef std::complex< double >

tensor_to_scalar_function_type

template<size_t dim>

using Marmot::NumericalAlgorithms::Differentiation::Complex::tensor_to_scalar_function_type = typedef std::function< std::complex< double >( const Fastor::Tensor< std::complex< double >, dim, dim >& T ) >

Function Documentation

forwardDifference() [1/4]

double Marmot::NumericalAlgorithms::Differentiation::Complex::forwardDifference	(	const scalar_to_scalar_function_type &	f,
		const double	x
	)

forwardDifference() [2/4]

std::tuple< Eigen::VectorXd, Eigen::MatrixXd > Marmot::NumericalAlgorithms::Differentiation::Complex::forwardDifference	(	const vector_to_vector_function_type &	F,
		const Eigen::VectorXd &	X
	)

centralDifference() [1/2]

Eigen::MatrixXd Marmot::NumericalAlgorithms::Differentiation::Complex::centralDifference	(	const vector_to_vector_function_type &	F,
		const Eigen::VectorXd &	X
	)

fourthOrderAccurateDerivative() [1/2]

Eigen::MatrixXd Marmot::NumericalAlgorithms::Differentiation::Complex::fourthOrderAccurateDerivative	(	const vector_to_vector_function_type &	F,
		const Eigen::VectorXd &	X
	)

forwardDifference() [3/4]

template<size_t dim>

Fastor::Tensor< double, dim, dim > Marmot::NumericalAlgorithms::Differentiation::Complex::forwardDifference	(	const tensor_to_scalar_function_type< dim > &	F,
		const Fastor::Tensor< double, dim, dim > &	T
	)

forwardDifference() [4/4]

std::tuple< VectorXd, MatrixXd > Marmot::NumericalAlgorithms::Differentiation::Complex::forwardDifference	(	const vector_to_vector_function_type &	F,
		const VectorXd &	X
	)

centralDifference() [2/2]

MatrixXd Marmot::NumericalAlgorithms::Differentiation::Complex::centralDifference	(	const vector_to_vector_function_type &	F,
		const VectorXd &	X
	)

fourthOrderAccurateDerivative() [2/2]

MatrixXd Marmot::NumericalAlgorithms::Differentiation::Complex::fourthOrderAccurateDerivative	(	const vector_to_vector_function_type &	F,
		const VectorXd &	X
	)

Variable Documentation

imaginaryUnit

const std::complex< double > Marmot::NumericalAlgorithms::Differentiation::Complex::imaginaryUnit = { 0, 1 }

static

complexUnit

const std::complex< double > Marmot::NumericalAlgorithms::Differentiation::Complex::complexUnit = { 1, 1 }

static

i_

const std::complex< double > Marmot::NumericalAlgorithms::Differentiation::Complex::i_ = Marmot::Constants::sqrt2 / 2. * complexUnit

static

imaginaryPerturbationSize

const double Marmot::NumericalAlgorithms::Differentiation::Complex::imaginaryPerturbationSize = 1e-20

static

imaginaryPerturbation

const complexDouble Marmot::NumericalAlgorithms::Differentiation::Complex::imaginaryPerturbation = imaginaryPerturbationSize * imaginaryUnit

static