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