petsc-3.14.6 2021-03-30
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Evaluate the jet (function and derivatives) of the Jacobi polynomials basis up to a given degree. The Jacobi polynomials with indices $\alpha$ and $\beta$ are orthogonal with respect to the weighted inner product $\langle f, g \rangle = \int_{-1}^1 (1+x)^{\alpha} (1-x)^{\beta) f(x) g(x) dx$.


#include "petscdt.h" 
PetscErrorCode PetscDTJacobiEvalJet(PetscReal alpha, PetscReal beta, PetscInt npoints, const PetscReal points[], PetscInt degree, PetscInt k, PetscReal p[])

Input Arguments

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 Argments

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.

See Also

PetscDTJacobiEval(), PetscDTPKDEvalJet()




Index of all DT routines
Table of Contents for all manual pages
Index of all manual pages