# Copyright (C) 2020 Andreas Kloeckner # #

# ## MIT License

# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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# THE SOFTWARE.
#

# In[4]:
import numpy as np
import matplotlib.pyplot as pt
# What this demo does is sum the series
# $$
# \exp(x) \approx \sum_{i=0}^n \frac{x^i}{i!},
# $$
# for varying $n$, and varying $x$. It then prints the partial sum, the true value, and the final term of the series.
# In[5]:
a = 0.0
x = 1e0 # flip sign
true_f = np.exp(x)
e = []
for i in range(0, 10): # crank up
d = np.prod(
np.arange(1, i+1).astype(np.float))
# series for exp
a += x**i / d
print(a, np.exp(x), x**i / d)
e.append(abs(true_f-a)/true_f)
# In[6]:
pt.semilogy(e)
# In[3]: