# This file was automatically generated by SWIG (http://www.swig.org).
# Version 4.0.2
#
# 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
if _swig_python_version_info < (2, 7, 0):
raise RuntimeError("Python 2.7 or later required")
# Pull in all the attributes from the low-level C/C++ module
if __package__ or "." in __name__:
from ._sum import *
else:
from _sum import *
try:
import builtins as __builtin__
except ImportError:
import __builtin__
def _swig_repr(self):
try:
strthis = "proxy of " + self.this.__repr__()
except __builtin__.Exception:
strthis = ""
return "<%s.%s; %s >" % (self.__class__.__module__, self.__class__.__name__, strthis,)
def _swig_setattr_nondynamic_instance_variable(set):
def set_instance_attr(self, name, value):
if name == "thisown":
self.this.own(value)
elif name == "this":
set(self, name, value)
elif hasattr(self, name) and isinstance(getattr(type(self), name), property):
set(self, name, value)
else:
raise AttributeError("You cannot add instance attributes to %s" % self)
return set_instance_attr
def _swig_setattr_nondynamic_class_variable(set):
def set_class_attr(cls, name, value):
if hasattr(cls, name) and not isinstance(getattr(cls, name), property):
set(cls, name, value)
else:
raise AttributeError("You cannot add class attributes to %s" % cls)
return set_class_attr
def _swig_add_metaclass(metaclass):
"""Class decorator for adding a metaclass to a SWIG wrapped class - a slimmed down version of six.add_metaclass"""
def wrapper(cls):
return metaclass(cls.__name__, cls.__bases__, cls.__dict__.copy())
return wrapper
class _SwigNonDynamicMeta(type):
"""Meta class to enforce nondynamic attributes (no new attributes) for a class"""
__setattr__ = _swig_setattr_nondynamic_class_variable(type.__setattr__)
[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 = 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