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uni-m.cds-num-met/week1/ex1.py

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#!/usr/bin/env python3
# Truncation of Euler's Constant
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def mainA():
e_OEIS = 2.7182818284590452353
N_max = 25
N_range = np.arange(0, N_max)
# a) Simple Relative Error Determination
e_approx = np.empty(N_max)
rel_err = np.empty(N_max)
prev_e = 0
for i, n in enumerate(N_range):
e_approx[i] = prev_e + 1/np.math.factorial(n)
rel_err[i] = abs( e_approx[i] - e_OEIS ) / e_OEIS
prev_e = e_approx[i]
## Plot it all
fig, ax = plt.subplots()
ax.set_title("Relative Error for std float")
ax.plot(N_range, rel_err)
ax.set_yscale('log')
ax.grid()
ax.set_ylabel("Relative Error")
ax.set_xlabel("N")
plt.show()
def mainB():
# b) Varying Floating Point Precision
e_OEIS = 2.7182818284590452353
N_max = 25
N_range = np.arange(0, N_max)
e_approx = np.zeros(N_max)
rel_err = np.zeros(N_max)
series_element_64 = np.empty(N_max, dtype=np.float64)
series_element_32 = np.empty(N_max, dtype=np.float32)
series64_diff = np.empty(N_max, dtype=np.float64)
series32_diff = np.empty(N_max, dtype=np.float64)
## Determine the coefficients
for i,n in enumerate(N_range):
e_n = 1/np.math.factorial(n)
series_element_64[i] = e_n # auto casts to float64
series_element_32[i] = e_n # auto casts to float32
## Make a Cumulative Sum of the elements
series64 = np.cumsum(series_element_64)
series32 = np.cumsum(series_element_32)
## Determine the relative errror
for i,n in enumerate(N_range):
series64_diff[i] = abs( series64[i] - e_OEIS ) / e_OEIS
series32_diff[i] = abs( series32[i] - e_OEIS ) / e_OEIS
## Plot it all
fig, ax = plt.subplots()
ax.set_title("Relative Error for float64 and float32")
ax.plot(N_range, series64_diff, label="float64")
ax.plot(N_range, series32_diff, label="float32")
ax.set_yscale('log')
ax.grid()
ax.legend()
ax.set_ylabel("Relative Error")
ax.set_xlabel("N")
plt.show()
def mainC():
# c) Relative errors for different rounding accuracies
round_accuracies = np.arange(1,6)
e_OEIS = 2.7182818284590452353
N_max = 25
N_range = np.arange(0, N_max)
# a) Simple Relative Error Determination
e_approx = np.empty(N_max)
rel_err = np.empty( (len(round_accuracies), N_max) )
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for i,d in enumerate(round_accuracies):
prev_e = 0
for j, n in enumerate(N_range):
e_approx[i] = prev_e + round(1/np.math.factorial(n), d)
rel_err[i,j] = abs( e_approx[i] - e_OEIS ) / e_OEIS
prev_e = e_approx[i]
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## Plot it all
fig, ax = plt.subplots()
ax.set_title("Relative Errors for std float with rounding at various digits d")
for i,d in enumerate(round_accuracies):
ax.plot(N_range, rel_err[i], label="d = {}".format(d))
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ax.set_yscale('log')
ax.grid()
ax.set_ylabel("Relative Error")
ax.set_xlabel("N")
ax.legend()
plt.show()
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if __name__ == "__main__":
import numpy as np
import matplotlib.pyplot as plt
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mainA()
mainB()
mainC()