How to find number of common decimal digits of two arrays element wise?

Question

I have a complex function I want to approximate, and I use np.polyfit to find the polynomial to approximate it.

And I want to find the statistics of correct decimal places to determine the quality of the approximation.

But it is hard to do efficiently. Currently I just convert the elements to strings and find the longest common prefix length element by element, needless to say this is inefficient.

import numpy as np
from collections import Counter

x = np.linspace(1, 2, 4096)
exp = np.exp(x)
poly = np.polyfit(x, exp, 6)
approx = np.polyval(poly, x)

def LCP(s1, s2):
    c = 0
    for a, b in zip(s1, s2):
        if a != b:
            break
        c += 1
    return c

def leading_digits(f1, f2):
    l = LCP(str(f1), str(f2)) - 1
    return max(l, 0)

correct_places = Counter()
for a, b in zip(approx, exp):
    correct_places[leading_digits(a, b)] += 1

Counter({7: 2014, 8: 1699, 6: 207, 9: 135, 5: 27, 10: 12, 11: 2})

What is a more efficient way?

Asked By: Ξένη Γήινος

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Source

Answer 1

So I’m not exactly sure why you’re wanting to compare digits for accuracy, there are a lot of other well known stats to determine the efficacy of an approximation. I would start with r-squared. If you do want to compare digits you could do something like the following:

a = 10.1234567891
b = 10.1234567890

c = a-b

digits = 0
while c < 1:
    digits += 1
    c *= 10
    
print(digits)

# digits = 10

digits would be how many decimal places they have in common

Answered By: CumminUp07

Answer 2

Comparing the number of equal leading digits doesn’t seem like a good approach. 1.01 and 1.09 have 2 leading digits in common, 1.09 and 1.10 only 1, but the second pair has a smaller absolute difference.

I would compute the absolute difference and get the order of magnitude of it using logarithms:

diff = abs(approx-exp)
Counter(-np.floor(np.where(diff>0, np.log10(diff), 0)).astype(int))

Output:

Counter({8: 3488, 7: 307, 9: 272, 10: 26, 11: 2, 12: 1})

Answered By: mozway

How to find number of common decimal digits of two arrays element wise?

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