Bsxfun And Faster

Matlab introduces bsxfun (binary singleton expansion) since 2007, which made matrix-vector operation easier when the vector is going to be applied to each row.

In fact, bsxfun works with all binary operations, if it needs to be done element-wisely.

Usually, when mxArray A and mxArray B are going to take operation op(A, B), but the dimension does not match, it might need repmat to reallocate memory.

>> a = rand(40);
>> a - mean(a); % matrix - vector, error
Error using -
Matrix dimensions must agree.

>> a = rand(40);
>> bsxfun(@minus, a, mean(a)); % runs fine

Refer to official site.

fun can also be a handle to any binary element-wise function not listed above. A binary element-wise function of the form C = fun(A,B) accepts arrays Aand B of arbitrary, but equal size and returns output of the same size. Each element in the output array C is the result of an operation on the corresponding elements of A and B only.

The corresponding dimensions of A and B must be equal to each other or equal to one. Whenever a dimension of A or B is singleton (equal to one), bsxfun virtually replicates the array along that dimension to match the other array. In the case where a dimension of A or B is singleton, and the corresponding dimension in the other array is zero, bsxfun virtually diminishes the singleton dimension to zero.

The size of the output array C is equal to: max(size(A),size(B)).*(size(A)>0 & size(B)>0).

This technique vectorizes the binary operation, and skip the overhead of allocation of memory as repmat does.