exp_errors.py

# Script to investigate exp errors
from __future__ import print_function, division

import numpy as np

import sympy.mpmath as mp

mp.mp.dps = 100
EPS = np.finfo(np.float64).eps

N = 100000
until = 20.
vals = np.arange(N) * until / N
exact_exp = np.zeros_like(vals)

for i, val in enumerate(vals):
    mp_val = mp.mpf(val)
    mp_exp = mp.exp(mp_val)
    exact_exp[i] = float(str(mp_exp))

errors = exact_exp - np.exp(vals)
rel_errs = errors / exact_exp

print("Proportion of zeros:", np.sum(errors == 0) / N)
print("Sum of error:", np.sum(errors))
print("Sum of squared error:", np.sum(errors ** 2))
print("Max / min error:", np.max(errors), np.min(errors))
print("Sum of squared relative error:", np.sum(rel_errs ** 2))
print("Max / min relative error:", np.max(rel_errs), np.min(rel_errs))
print("eps: ", EPS)
print("Proportion of relative err >= eps:", np.sum(np.abs(rel_errs) >= EPS) / N)