Calculate Levenshtein distance in MATLAB (words or characters) with Wagner–Fischer algorithm

This is a MATLAB implementation of the Wagner–Fischer algorithm.

function y = lvdistance(sentence1, sentence2, penalties, split_characters)
%LVDISTANCE Calculate Levenshtein distance between two strings
% Uses Wagner–Fischer algorithm
% See https://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm
%
% Arguments:
% sentence1, sentence2: strings, e.g. 'hello world'
% penalties (optional): vector of penalties for deletion, insertion and
% substitution (default: [1 1 1])
% split_characters (optional): split at each character, not only at spaces
% (default: false)
%
% GPL v3, Nicolai Spohrer <nicolai@xeve.de>

switch nargin
    case 2
        penalty_deletion = 1;
        penalty_insertion = 1;
        penalty_substitution = 1;
        split_characters = false;
    case 3
        penalty_deletion = penalties(1);
        penalty_insertion = penalties(2);
        penalty_substitution = penalties(3);
        split_characters = false;
    case 4
        penalty_deletion = penalties(1);
        penalty_insertion = penalties(2);
        penalty_substitution = penalties(3);
    otherwise
        error 'Invalid number of arguments';
end

if split_characters
    % split at each character
    sentence1 = num2cell(sentence1);
    sentence2 = num2cell(sentence2);
else
    % split at spaces
    sentence1 = strsplit(sentence1, ' ');
    sentence2 = strsplit(sentence2, ' ');
end



m = length(sentence1);
n = length(sentence2);

% distance 2D array
d = zeros(m+1, n+1);

for i=1:m+1
    d(i, 1) = i-1;
end

for j=1:n+1
    d(1, j) = j-1;
end

for j=1:n
    for i=1:m
        if strcmp(sentence1{i}, sentence2{j})
            % words are equal, therefore no operation required
            d(i+1, j+1) = d(i, j);
        else
            % words are not equal
            d(i+1, j+1) = min(min(...
                d(i, j+1) + penalty_deletion,...  % deletion
                d(i+1, j) + penalty_insertion),...  % insertion
                d(i, j) + penalty_substitution); % substitution
        end
    end
end

y = d(m+1, n+1);
end