I want to calculate the determinant of a matrix by LU-decomposition with ?getrf. Since ?getrf does not compute the decomposition of the original matrix but of a matrix obtained by row permutations of the original one, the sign of the determinant depends on the number of those permutations. The MKL reference tells me that this information is contained in the array 'ipiv' where the pivot indices mean: row i was interchanged with row ipiv(i). So when ipiv(i)==j with i/=j this means that the rows i and j have been exchanged. As far as I understand this also means that ipiv(j)==i. However I checked this and this is not the case. So what's the meaning of this 'ipiv' array?