PetscDTJacobiEvalJet#
Evaluate the jet (function and derivatives) of the Jacobi polynomials basis up to a given degree.
Synopsis#
#include "petscdt.h"
PetscErrorCode PetscDTJacobiEvalJet(PetscReal alpha, PetscReal beta, PetscInt npoints, const PetscReal points[], PetscInt degree, PetscInt k, PetscReal p[])
Input Parameters#
alpha - the left exponent of the weight
beta - the right exponetn of the weight
npoints - the number of points to evaluate the polynomials at
points - [npoints] array of point coordinates
degree - the maximm degree polynomial space to evaluate, (degree + 1) will be evaluated total.
k - the maximum derivative to evaluate in the jet, (k + 1) will be evaluated total.
Output Parameter#
p - an array containing the evaluations of the Jacobi polynomials’s jets on the points. the size is (degree + 1) x (k + 1) x npoints, which also describes the order of the dimensions of this three-dimensional array: the first (slowest varying) dimension is polynomial degree; the second dimension is derivative order; the third (fastest varying) dimension is the index of the evaluation point.
Notes#
The Jacobi polynomials with indices \(\alpha\) and \(\beta\) are orthogonal with respect to the weighted inner product \(\langle f, g \rangle = \int_{-1}^1 (1+x)^{\alpha} (1-x)^{\beta} f(x) g(x) dx\).
See Also#
Level#
advanced
Location#
Index of all DT routines
Table of Contents for all manual pages
Index of all manual pages