Calculus.hpp File Reference

Numerical differentiation and integration (gradient, trapz, cumtrapz, diff). More...

#include "janus/core/JanusConcepts.hpp"
#include "janus/core/JanusError.hpp"
#include "janus/math/Arithmetic.hpp"
#include <Eigen/Dense>
#include <optional>
#include <type_traits>
#include <utility>

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Namespaces
namespace	janus

Functions
template<typename Derived>
auto	janus::diff (const Eigen::MatrixBase< Derived > &v)
	Computes adjacent differences of a vector Returns a vector of size N-1 where out[i] = v[i+1] - v[i].
template<typename DerivedY, typename DerivedX>
auto	janus::trapz (const Eigen::MatrixBase< DerivedY > &y, const Eigen::MatrixBase< DerivedX > &x)
	Computes trapezoidal integration Approximation of integral of y(x) using trapezoidal rule.
template<typename DerivedY, typename DerivedX>
auto	janus::cumtrapz (const Eigen::MatrixBase< DerivedY > &y, const Eigen::MatrixBase< DerivedX > &x)
	Computes the cumulative trapezoidal integral.
template<typename DerivedY, JanusScalar Spacing = double>
auto	janus::cumtrapz (const Eigen::MatrixBase< DerivedY > &y, const Spacing &dx=1.0)
	Computes the cumulative trapezoidal integral with uniform spacing.
template<typename DerivedY, typename DerivedX>
auto	janus::gradient_1d (const Eigen::MatrixBase< DerivedY > &y, const Eigen::MatrixBase< DerivedX > &x)
	Computes gradient of 1D data using central differences.
template<typename DerivedF, typename Spacing = double>
auto	janus::gradient (const Eigen::MatrixBase< DerivedF > &f, const Spacing &dx=1.0, int edge_order=1, int n=1)
	Computes gradient using second-order accurate central differences.
template<typename DerivedF, typename Spacing = double, typename Period>
auto	janus::gradient_periodic (const Eigen::MatrixBase< DerivedF > &f, const Spacing &dx, const Period &period, int edge_order=1, int n=1)
	Computes gradient with periodic boundary conditions.

Detailed Description

Numerical differentiation and integration (gradient, trapz, cumtrapz, diff).

See also

FiniteDifference.hpp, IntegrateDiscrete.hpp