The function is based on the paper by Held and Karp from 1962. The DP is guaranteed to provide the accurate (optimal) result to the TSP, but the time complexity of this algorithm is O(2^n n^2), which limits the use of this algorithm to 15 cities or less.
NOTE: For reasonable runtime, please do not try to calculate a tour of more than 13 cities. DP is not for large sets of cities.
As I said, I haven't tested it for an asymmetric TSP. You will need to pass a list of cities with n rows and 2 columns. This list will not be used in calculating the Dmatrix, but will be used for knowing the number of cities.
You know, it's a MATLAB code that you could modify and try to run your own versions...