Follow-up Comment #1, bug #64777 (group gsl): The LU decomposition of a matrix A is not unique. If the diagonal of L is fixed to contain ones only (which is usually done), the LU decomposition still has the permutation matrix P as degree of freedom (note: PA = LU).
The software you have used to calculate an LU decomposition apparently uses a
different pivoting strategy than GSL does and hence yields a different
permutation matrix P (which is stored in gsl_permutation *perm) and
subsequently different results for L and U.
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