Fuzzy regex (e.g. {e<=2}) correct usage in Python

Let's check this snippet for fuzzy counts:

>>> pattern_string = 'ATAGGAGAAGATGATGTATA'
>>> query_string = 'ATAGAGCAAGATGATGTATA'
>>> r = regex.compile('(%s){e<=2}' % pattern_string)
>>> r.match(query_string)
<regex.Match object; span=(0, 20), match='ATAGAGCAAGATGATGTATA', fuzzy_counts=(0, 1, 1)>

fuzzy_counts=(0, 1, 1) means that in this case, we get no substitutions, 1 insertion, and 1 deletion. So your filter works because the total count of errors is 2.

But it seems that you need to filter only by substitutions count, so you can modify the regex:

import regex
res = regex.findall("(ATAGGAGAAGATGATGTATA){s<=2}", "ATAGAGCAAGATGATGTATA", overlapped=True)
print res

Check this great example from docs:

• {i<=3} permit at most 3 insertions, but no other types
• {d<=3} permit at most 3 deletions, but no other types
• {s<=3} permit at most 3 substitutions, but no other types
• {i<=1,s<=2} permit at most 1 insertion and at most 2 substitutions, but no deletions
• {e<=3} permit at most 3 errors

• {1<=e<=3} permit at least 1 and at most 3 errors

• {i<=2,d<=2,e<=3} permit at most 2 insertions, at most 2 deletions, at most 3 errors in total, but no substitutions

Your mistake is to assume that "errors" are the same thing as "substitutions", when this is not the case.

The regex package's fuzzy matching understands three kinds of errors - insertions, deletions, and substitutions. An error distance specified with e, as you've used, can be made up of any combination of those errors. And ATAGGAGAAGATGATGTATA can be edited into ATAGAGCAAGATGATGTATA with only two such operations (1 deletion and 1 insertion), as shown by the sequence alignment below:

ATAGGAG-AAGATGATGTATA
ATAG-AGCAAGATGATGTATA

is there any way of getting this to find only strings within the Hamming 2-ball of the given pattern?

Yes. Note that Hamming distance is a kind of edit distance that measures the minimum number of substitutions required to edit one string to another of equal length. So to only match strings within the Hamming 2-ball of pattern, we need to tell regex to match anything within 2 substitutions, which we can do by using the s error type instead of e:

import regex
res = regex.findall("(ATAGGAGAAGATGATGTATA){s<=2}", "ATAGAGCAAGATGATGTATA", overlapped=True)
print res

Is it possible that a swap of letters is considered to be only one change?

Not in the regex package as it currently stands. The standard term of art for a "swap" of two characters is a "transposition". Edit distances that include transpositions as a possible edit (e.g. Dameau-Levenshtein distance, in which edits can be insertions, substitutions, deletions, or transpositions of adjacent characters) do exist and are useful for some applications (e.g. typo correction). However, at the time of writing, the fuzzy matching in the regex package does not have any support for them at all.