Source code for pygsl.sum

# This file was automatically generated by SWIG (https://www.swig.org).
# Version 4.3.1
#
# Do not make changes to this file unless you know what you are doing - modify
# the SWIG interface file instead.

"""
Sum modul for Levin u-transform

This module provides a function for accelerating the convergence of
series based on the Levin u-transform.  This method takes a small
number of terms from the start of a series and uses a systematic
approximation to compute an extrapolated value and an estimate of its
error. The u-transform works for both convergent and divergent
series, including asymptotic series.
"""

from sys import version_info as _swig_python_version_info
# Pull in all the attributes from the low-level C/C++ module
if __package__ or "." in __name__:
    from ._sum import *
else:
    from _sum import *


[docs] def levin_sum(a, truncate=False, info_dict=None): """Return (sum(a), err) where sum(a) is the extrapolated sum of the infinite series a and err is an error estimate. Uses the Levin u-transform method. Parameters: a : A list or array of floating point numbers assumed to be the first terms in a series. truncate: If True, then use a more efficient algorithm, but with a less accurate error estimate info_dict: If info_dict is provided, then two entries will be added: 'terms_used' will be the number of terms used and 'sum_plain' will be the sum of these terms without acceleration. Notes: The error estimate is made assuming that the terms a are computed to machined precision. Example: Computing the zeta function zeta(2) = 1/1**2 + 1/2**2 + 1/3**2 + ... = pi**2/6 >>> from math import pi >>> zeta_2 = pi**2/6 >>> a = [1.0/n**2 for n in range(1,21)] >>> info_dict = {} >>> (ans, err_est) = levin_sum(a, info_dict=info_dict) >>> ans, zeta_2 # doctest: +ELLIPSIS 1.644934066..., 1.644934066... >>> err = abs(ans - zeta_2) >>> err < err_est True >>> (ans, err_est) = levin_sum(a, truncate=False) >>> ans # doctest: +ELLIPSIS 1.644934066... """ if truncate: l = _levin_utrunc(len(a)) else: l = _levin(len(a)) ans, err_est = l.accel(a) if info_dict is not None: info_dict['sum_plain'] = l.sum_plain() info_dict['terms_used'] = l.get_terms_used() del l return ans, err_est