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#

PetscDTJacobiEval(), PetscDTPKDEvalJet()

Level#

advanced

Location#

src/dm/dt/interface/dt.c

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Index of all manual pages