pg_utils.numerics.special

Computation of special functions, mostly the Jacobi polynomial

This module is for efficient evaluation of the special functions, as this will be a computation-/memory-intensive part in quadratures

Functions

eval_jacobi_nrange(n_min, n_max, alpha, beta, z)	Evaluate Jacobi polynomials for a range of degrees
eval_jacobi_recur(Nmesh, alpha, beta, zmesh)	Evaluate Jacobi polynomials using recurrence relations
eval_jacobi_recur_Nmax(Nmax, alpha, beta, z)	Evaluate Jacobi polynomials with recurrence relation up to a degree
eval_jacobi_recur_gmpy2(Nmax, alpha, beta, z)	Evaluate Jacobi polynomials with recurrence relation up to a degree, to (arbitrary) multi-precision, array operations using gmpy2.
eval_jacobi_recur_mp(Nmesh, alpha, beta, zmesh)	Evaluate Jacobi polynomials using recurrence relations to arb prec
eval_jacobi_recur_mpmath(Nmax, alpha, beta, z)	Evaluate Jacobi polynomials with recurrence relation up to a degree, to (arbitrary) multi-precision.
roots_jacobi_mp(n, alpha, beta[, n_dps, ...])	Multi-precision Jacobi root calculation.

Classes

RootsJacobiResult(xi, wt, flag, msg)

Result object of root-finding routine for Jacobi polynomials