When you grow an array incrementally as you are doing with DE, MATLAB is forced to reallocate the entire array at EVERY iteration, copying over the entire mess just to add ONE element. This will cause the operation to get slower, and the time required will grow quadratically. SO it will get SLOW.
You know in the end EXACTLY how large DE will be. So just add ONE extra line before the loop.
DE = zeros(length(X),length(X_inv));
This essentially creates the array in advance, filling it with zeros. It need no longer reallocated at each iteration, because it will no longer need to change size at every step.
Much of the time, preallocation is not needed. MATLAB is not a language where you need to initialize/allocate every array. Variables that are scalars, and will remain so are never an issue. It is only when an array is dynamically grown that preallocation is important. A problem arises when you don't know the final size of your array. Even there, there are tricks that one can do. I posted a submission to the FEX long ago that allows the user to store information in a form that can be more efficiently grown, then at the end, you can unpack the object into a regular array.
