pg_utils.numerics.special.roots_jacobi_mp

pg_utils.numerics.special.roots_jacobi_mp(n: int, alpha: mpf, beta: mpf, n_dps: int = 33, extra_dps: int = 8, max_iter: int = 10) → RootsJacobiResult[source]

Multi-precision Jacobi root calculation.

Calculates the nodes (=roots of Jacobi polynomial) and weights for Gauss-Jacobi quadrature to arbitrary precision.

Parameters:

  • n (int) – number of nodes / degree of Jacobi polynomial

  • alpha (mpmath.mpf) – alpha value, with precision that is consistent with the desired precision of output

  • beta (mpmath.mpf) – beta value, with precision that is consistent with the desired precision of output

  • n_dps (int) – number of decimal digits, default=33, i.e. approx. quadruple precision

  • extra_dps (int) – additional decimal digits during calculation

  • max_iter (int) – maximum iteration, default=10

Returns:

RootsJacobiResult object, containing the calculated quadrature nodes and weights, as mpmath.mpf wrapped in numpy.ndarray