pg_utils.numerics.special.eval_jacobi_recur

pg_utils.numerics.special.eval_jacobi_recur(Nmesh: ndarray, alpha: float, beta: float, zmesh: ndarray) → ndarray

Evaluate Jacobi polynomials using recurrence relations

This function is intended to maintain the same signature as scipy.special.eval_jacobi and sympy.jacobi, albeit several restrictions regarding the input params (see note)

Parameters:

• Nmesh (np.ndarray) – mesh for degrees (N,Nz)

• alpha (float) – alpha index

• beta (float) – beta index

• zmesh (np.ndarray) – mesh for evaluation grid (N,Nz)

Note

This function is designed in such a way that the Jacobi polynomial is evaluated on a grid that remains the same for all degrees. Denoting the total number of degrees with N and total number of grid points Nz, the standard for input parameter is as follows * Param Nmesh is of shape (N,Nz); first index changes deg * Param zmesh is of shape (N,Nz); second index changes z