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Built-in Mathematica Symbol

SmithWatermanSimilarity

SmithWatermanSimilarity[u, v]
gives a number representing the Smith-Waterman similarity between strings or vectors u and v.

SmithWatermanSimilarity[u, v] finds an optimal local alignment between the elements of u and v, and returns the number of one-element matches.

For strings, setting the option IgnoreCase->True makes SmithWatermanSimilarity treat lowercase and uppercase letters as equivalent.

With the default setting SimilarityRules->Automatic, each match between two characters contributes 1 to the total similarity score, while each mismatch, insertion or deletion contributes -1.

The option GapPenalty specifies an additional cost to be subtracted from the similarity score for any run of insertions or deletions.

Smith-Waterman similarity between two strings:

Smith-Waterman similarity between two vectors:

Smith-Waterman similarity between two strings:

Smith-Waterman similarity between two vectors: