// sum(S^T * (x - y)) = [what we calculated] - (µ1 - µ2) sum(S^T)
//
// so we can just subtract away the mean difference here.
// sum(S^T * (x - y)) = [what we calculated] - (µ1 - µ2) sum(S^T)
//
// so we can just subtract away the mean difference here.