In fact, PDL::Fit::Levmar is based on lourakis's levmar. PDL::Fit::LM uses PDL functions from Perl, including PDL::Slatec LINPACK functions for matrix inversion.

For anyone who looks into this (I assume that in the last 15 years, the OP has either solved their problem, or moved on), reading the Perl source of ::LM and/or the docs of ::Levmar will help. I am not an expert in this field.