Orthogonal polynomial evaluation, spectral nodes, weights, and differentiation matrices. More...

#include "janus/core/JanusError.hpp"
#include "janus/core/JanusTypes.hpp"
#include <cmath>
#include <limits>
#include <utility>

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Namespaces
namespace	janus
namespace	janus::detail
	Smooth approximation of ReLU function: softplus(x) = (1/beta) * log(1 + exp(beta * x)).

Functions
std::pair< double, double >	janus::legendre_poly (int n, double x)
	Evaluate Legendre polynomial P_n(x) and derivative P'_n(x).
std::pair< NumericVector, NumericVector >	janus::detail::gauss_legendre_rule (int n)
std::pair< NumericVector, NumericVector >	janus::gauss_legendre_rule (int n)
	Gauss-Legendre nodes and weights on [-1, 1].
NumericVector	janus::legendre_poly_vec (int n, const NumericVector &x)
	Evaluate P_n(x) at each x in vector.
NumericVector	janus::lgl_nodes (int N)
	Compute Legendre-Gauss-Lobatto nodes on [-1, 1].
NumericVector	janus::cgl_nodes (int N)
	Compute Chebyshev-Gauss-Lobatto nodes on [-1, 1].
NumericVector	janus::lgl_weights (int N, const NumericVector &nodes)
	LGL quadrature weights.
NumericVector	janus::cgl_weights (int N, const NumericVector &nodes)
	CGL (Clenshaw-Curtis) quadrature weights on [-1, 1].
NumericVector	janus::barycentric_weights (const NumericVector &nodes)
	Compute barycentric interpolation weights for the given nodes.
double	janus::barycentric_basis_eval (const NumericVector &nodes, const NumericVector &bary_w, int j, double s)
	Evaluate the j-th Lagrange basis polynomial at s using barycentric form.
NumericMatrix	janus::birkhoff_integration_matrix (const NumericVector &nodes)
	Compute Birkhoff integration matrix B^a for the node set.
NumericMatrix	janus::spectral_diff_matrix (const NumericVector &nodes)
	Spectral differentiation matrix using barycentric weights.

Variables
constexpr double	janus::detail::polynomial_root_tolerance = 1e-15
	Tolerance for zero-length integration intervals in Birkhoff matrix.

Detailed Description

Orthogonal polynomial evaluation, spectral nodes, weights, and differentiation matrices.

Namespaces