# Calculates the Hamming distance between two DArT trimmed DNA sequences

`utils.hamming.Rd`

Hamming distance is calculated as the number of base differences between two sequences which can be expressed as a count or a proportion. Typically, it is calculated between two sequences of equal length. In the context of DArT trimmed sequences, which differ in length but which are anchored to the left by the restriction enzyme recognition sequence, it is sensible to compare the two trimmed sequences starting from immediately after the common recognition sequence and terminating at the last base of the shorter sequence.

## Arguments

- str1
String containing the first sequence [required].

- str2
String containing the second sequence [required].

- r
Number of bases in the restriction enzyme recognition sequence [default 4].

## Details

The Hamming distance between the rows of a matrix can be computed quickly by exploiting the fact that the dot product of two binary vectors x and (1-y) counts the corresponding elements that are different between x and y. This matrix multiplication can also be used for matrices with more than two possible values, and different types of elements, such as DNA sequences.

The function calculates the Hamming distance between all columns of a matrix X, or two matrices X and Y. Again matrix multiplication is used, this time for counting, between two columns x and y, the number of cases in which corresponding elements have the same value (e.g. A, C, G or T). This counting is done for each of the possible values individually, while iteratively adding the results. The end result of the iterative adding is the sum of all corresponding elements that are the same, i.e. the inverse of the Hamming distance. Therefore, the last step is to subtract this end result H from the maximum possible distance, which is the number of rows of matrix X.

If the two DNA sequences are of differing length, the longer is truncated. The initial common restriction enzyme recognition sequence is ignored.

The algorithm is that of Johann de Jong https://johanndejong.wordpress.com/2015/10/02/faster-hamming-distance-in-r-2/

## Author

Custodian: Arthur Georges (Post to https://groups.google.com/d/forum/dartr)