Question

I have two floating-point number vectors which contain the same values up to a small error, but not necessarily sorted in the same way; for instance, A=rand(10);a=eig(A);b=eig(A+1e-10); (remember that eig outputs eigenvalues in no specified order).

I need to find a permutation p that matches the corresponding elements, i.e. p=mysterious_function(a,b) such that norm(a-b(p)) is small.

Is there an existing function that does this in a sane and safe way, or do I really need to roll out my own slow and poorly-error-checked implementation?

I need this only for test purposes for now, it need not be excessively optimized. Notice that the solution which involves sorting both vectors with sort fails in case of vectors containing complex equal-modulus arguments, such as the typical output of eig().

Answer 1

You seem to want to solve the linear assignment problem. I haven’t tested it myself, but this piece of code should help you.