\$title 'Test invert utility on rank-deficient inputs' (INVERT02,SEQ=392) \$ontext Test the invert utility on rank-deficient inputs. Given an n-dimensional matrix n of rank r, invert should return n-r. Note that DGESV is checking for an exact zero so it will over-estimate the rank in general. We use the identity matrix in this test so we should get the correct rank from invert. Contributor: Erwin Kalvelagen and Steve Dirkse, July 2008. \$offtext set i /i1*i5 /; alias (i,j,k,r); scalar rc; parameter A(i,j) rankDeficient(i,j) inv(i,j) 'inverse matrix' chk(i,j) 'check the product' ; A(i,i) = 1; execute_unload 'tmp.gdx', i, A; execute 'invert tmp.gdx i A tmp2.gdx inv >invert.log'; rc=errorlevel; abort\$(rc > 0) 'Nonzero return code from invert', rc; execute_load 'tmp2.gdx',inv; rc=errorlevel; abort\$(rc > 0) 'Error loading inverse from b.gdx', rc; chk(i,j) = sum{k, A(i,k)*inv(k,j)}; chk(i,j) = round(chk(i,j),14); display A,inv,chk; chk(i,i) = chk(i,i) - 1; abort\$[card(chk)] 'A * inv <> identity'; loop {r, * create a rank-r matrix from A, and check that we get the right * return code from invert rankDeficient(i,j) = A(i,j)\$[ord(j) <= ord(r)]; execute_unload 'tmp.gdx', i, rankDeficient; execute 'invert tmp.gdx i rankDeficient tmp2.gdx inv >invert.log'; rc=errorlevel; abort\$(ord(r) + rc <> card(i)) 'Bad rank-deficiency returned from invert', rc, rankDeficient, r; };