Efficient way to insert characters between other characters in a string - string

Question

What is an efficient way in MATLAB to replace/insert one symbol (in series of symbols) with several others that correspond to the one that is being replaced?
For example, consider having a string Eq: Eq = 'A*exp(-((x-xc)/w)^2)'. Is there a way to replace * with .*, / with ./,\ with .\, and ^ with .^ without writing four separate strrep() lines?

Answer 1

Regular expressions will do the job nicely. Regular expressions simply find patterns in text. You specify what kind of pattern you are looking for by a regular expression, and the output gives you the locations of where the pattern occurred.
For our particular case, not only do we want to find where patterns occur, we also want to replace those patterns with something else. Specifically, use the function regexprep from MATLAB to replace matches in a string with something else. What you want to do is replace all *, /, \ and ^ symbols by adding a . in front of each.
How regexprep works is that the first input is the string you're looking at, the second input is a pattern that you're trying to find. In our case, we want to find any of *, /, \ and ^. To specify this pattern, you put those desired symbols in [] brackets. Regular expressions reserve \ as a special symbol to delineate characters that can be parsed as a regular expression but actually aren't. As such, you need to use \\ for the \ character and \^ for the ^ character. The third input is what you want to replace each match with. In our case, we simply want to reuse each matched character, but we add a . at the beginning of the match. This is done by doing \.$0 in the regular expression syntax. $0 means to grab the first token produced by a match... which is essentially the matched symbol from the pattern. . is also a reserved keyword using regular expressions, so we must prepend this symbol with a \ character.
Without further ado:
>> Eq = 'A*exp(-((x-xc)/w)^2)';
>> out = regexprep(Eq, '[*/\\\^]', '\.$0')
out =
A.*exp(-((x-xc)./w).^2)
The pattern we are looking for is [*/\\\^], which means that we want to find any of *, /, \ - denoted as \\ in regex, and \^ - denoted as ^ in regex. We want to find any of these symbols and replace them with the same symbol by adding a . character in front - \.$0.
As a more complicated example, let's make sure that we include all of the symbols you're looking for in a sample equation:
>> A = 'A*exp(-((x-xc)/w)^2) \ b^2';
>> out = regexprep(A, '[*/\\\^]', '\.$0')
out =
A.*exp(-((x-xc)./w).^2) .\ b.^2

Answer 2

I'd go with regexp as in rayryeng's answer. But here's another approach, just to provide an alternative.
ops = '*/\^'; %// operators that need a dot
ii = find(ismember(Eq, ops)); %// find where dots should be inserted
[~, jj] = sort([1:numel(Eq) ii-.5]); %// will be used to properly order the result
result = [Eq repmat('.',1,numel(ii))]; %// insert dots at the end
result = result(jj); %// properly order the result
And a variant:
ops = '*/\^'; %// operators that need a dot
ii = find(ismember(Eq, ops)); %// find where dots should be inserted
jj = sort([1:numel(Eq) ii-.5]); %// dot locations are marked with fractional part
result = Eq(ceil(jj)); %// repeat characters where the dots will be placed
result(mod(jj,1)>0) = '.'; %// place dots at indices with fractional part

Answer 3

The vectorize function already does almost all of what you want except that it does not convert mldivide (\) to ldivide (.\).
By "efficient," do you mean fewer lines of code or faster? Regular expressions are almost always slower than other approaches and less readable. I don't think they're necessary or a good choice in this case. If you only need to convert your string once, then speed is less of a concern than readability (strrep will still be faster). If you need to do it many times, this simple code that you alluded to is 4–5 times faster than regexrep for short strings like your example (and much faster for longer strings):
out = strrep(Eq,'*','.*');
out = strrep(out,'/','./');
out = strrep(out,'\','.\');
out = strrep(out,'^','.^');
If you want one line, use:
out = strrep(strrep(strrep(strrep(Eq,'*','.*'),'/','./'),'\','.\'),'^','.^');
which will also be slightly faster still. Or create your own version of vectorize and call that.
Where regular expressions shine is in more complex cases, e.g., if your string is already partially vectorized: Eq = 'A.*exp(-((x-xc)/w)^2)'. Even still, the vectorize function just uses strrep and then calls strfind to "remove any possible '..*', '../', etc." and replace them with the proper element-wise operators because it's faster (symbolic math strings can get very large, for example).