Question

According to the python-Levenshtein.ratio source:

https://github.com/miohtama/python-Levenshtein/blob/master/Levenshtein.c#L722

it’s computed as (lensum - ldist) / lensum. This works for

# pip install python-Levenshtein
import Levenshtein
Levenshtein.distance('ab', 'a') # returns 1
Levenshtein.ratio('ab', 'a')    # returns 0.666666

However, it seems to break with

Levenshtein.distance('ab', 'ac')  # returns 1
Levenshtein.ratio('ab', 'ac')     # returns 0.5

I feel I must be missing something very simple.. but why not 0.75?

Answer 1

By looking more carefully at the C code, I found that this apparent contradiction is due to the fact that ratio treats the “replace” edit operation differently than the other operations (i.e. with a cost of 2), whereas distance treats them all the same with a cost of 1.

This can be seen in the calls to the internal levenshtein_common function made within ratio_py function:

---

https://github.com/miohtama/python-Levenshtein/blob/master/Levenshtein.c#L727

static PyObject*
ratio_py(PyObject *self, PyObject *args)
{
  size_t lensum;
  long int ldist;

  if ((ldist = levenshtein_common(args, "ratio", 1, &lensum)) < 0) //Call
    return NULL;

  if (lensum == 0)
    return PyFloat_FromDouble(1.0);

  return PyFloat_FromDouble((double)(lensum - ldist)/(lensum));
}

---

and by distance_py function:

https://github.com/miohtama/python-Levenshtein/blob/master/Levenshtein.c#L715

static PyObject*
distance_py(PyObject *self, PyObject *args)
{
  size_t lensum;
  long int ldist;

  if ((ldist = levenshtein_common(args, "distance", 0, &lensum)) < 0)
    return NULL;

  return PyInt_FromLong((long)ldist);
}

---

which ultimately results in different cost arguments being sent to another internal function, lev_edit_distance, which has the following doc snippet:

@xcost: If nonzero, the replace operation has weight 2, otherwise all
        edit operations have equal weights of 1.

Code of lev_edit_distance():

/**
 * lev_edit_distance:
 * @len1: The length of @string1.
 * @string1: A sequence of bytes of length @len1, may contain NUL characters.
 * @len2: The length of @string2.
 * @string2: A sequence of bytes of length @len2, may contain NUL characters.
 * @xcost: If nonzero, the replace operation has weight 2, otherwise all
 *         edit operations have equal weights of 1.
 *
 * Computes Levenshtein edit distance of two strings.
 *
 * Returns: The edit distance.
 **/
_LEV_STATIC_PY size_t
lev_edit_distance(size_t len1, const lev_byte *string1,
                  size_t len2, const lev_byte *string2,
                  int xcost)
{
  size_t i;

---

[ANSWER]

So in my example,

ratio('ab', 'ac') implies a replacement operation (cost of 2), over the total length of the strings (4), hence 2/4 = 0.5.

That explains the “how”, I guess the only remaining aspect would be the “why”, but for the moment I’m satisfied with this understanding.