pg_utils.numerics.special.eval_jacobi_recur_gmpy2

pg_utils.numerics.special.eval_jacobi_recur_gmpy2(Nmax: int, alpha: mpfr, beta: mpfr, z: ndarray, prec: int = 113) → ndarray[source]

Evaluate Jacobi polynomials with recurrence relation up to a degree, to (arbitrary) multi-precision, array operations using gmpy2.

This functions generates values for Jacobi polynomials from degree 0 up to a specified degree, using recurrence relations.

Parameters:

Nmax (int) – maximum degree, required to be >= 1
alpha (gmpy2.mpfr) – alpha index for Jacobi polynomials
beta (gmpy2.mpfr) – beta index for Jacobi polynomials
z (np.ndarray) – 1-D array of grid points where the Jacobi polynomials are to be evaluated; assumed to be within interval [-1, +1]
prec (int) – precision (no. of binary digits) for calculation

Returns:

Array with shape (Nmax + 1, z.size), values for Jacobi polynomials at grid points specified in z.

Note

The input parameters alpha and beta as well as z need to at least match the precision of the desired output, otherwise the multi-precision evaluation is meaningless.