# 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