Hello! I believe that I have found the bug and fixed it. The bug was pertaining to the variable dpel in the function: francis_search_subdiag_small_elements.
I have attached a corrected version with comments to show where the issue was. I have tested this version of francis.c against the matrix submitted by Dmitry Cheshkov and also checked it against test.c, both were successful. Thanks, Michael Dunlap
francis.c
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