Created
February 22, 2020 17:29
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Numerically evaluate sine integral $ Si(x) $
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#!/usr/bin/env python3 | |
from itertools import count | |
# This is stable up to about x=34. | |
# Above that, reimplement with rational arithmetic. | |
def Si(x): | |
"""Sine integral. Numerically stable up to about x=34.""" | |
sign = +1 | |
fact = 1 | |
numerator = x | |
acc = 0 | |
for n in count(): | |
tnp1 = 2 * n + 1 | |
if n: | |
fact *= 2 * n * tnp1 | |
abs_term = numerator / (tnp1 * fact) | |
if acc - abs_term == acc: | |
# further terms won't affect the result. | |
break | |
acc += sign * abs_term | |
numerator *= x**2 | |
sign = -sign | |
return acc | |
if __name__ == '__main__': | |
import numpy as np | |
import matplotlib.pyplot as plt | |
x = np.linspace(0, 15, 500) | |
y = np.array([Si(xx) for xx in x]) | |
plt.plot(x, y) | |
plt.show() | |
Author
kbob
commented
Feb 22, 2020
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