$title CONVERT test suite - test hessian info correctness (CONVERT7,SEQ=419)

$onText
Do some consistency checks on the full Hessian and the
Hessian-vector products dumped out by CONVERT.

Currently, there are flags to do this for NLP models in gamslib.
Run it like this:
gams convert7.gms
    --gmsName=chenery
    --modelName=chenrad
    --modelType=NLP
    --objName=td

Contributor: Steve Dirkse
$offText

$if not set gmsName   $set gmsName   chenery
$if not set modelName $set modelName chenrad
$if not set modelType $set modelType NLP
$if not set objName   $set objName   td

$call gamslib -q %gmsName%
$if errorlevel 1 $abort 'gamslib %gmsName% failed'
$onEcho > convert.opt
dumpgdx %gmsName%.gdx
gdxhessian 1
gdxquadratic 1
$offEcho

$onEcho > %gmsName%TestHess.gms
$include %gmsName%HessDump.gms
alias(j,jj);
scalar
  tol / 1e-9 /;
parameters
  testW(j,j)     'Hession of the Lagrangian - upper triangle - calculated'
  testFullW(j,j) 'full version of testW'
  testWe(j)      'product testW * e'
  diffW(j,j), errW(j,j)
  diffWe(j),  errWe(j)
  ;

testW(j,jj) = sum(i, h(i,j,jj)* (-e.m(i)));

testFullW(j,jj) = testW(j,jj) + testW(jj,j);  testFullW(j,j) = testW(j,j);
testWe(j) = sum(jj, testFullW(j,jj) * 1);

diffW(j,jj) = testW(j,jj) - W(j,jj);
errW(j,jj) = diffW(j,jj);
errW(j,jj)$[abs(errW(j,jj)) < tol] = 0;

diffWe(j) = testWe(j) - We(j);
errWe(j) = diffWe(j);
errWe(j)$[abs(errWe(j)) < tol] = 0;

execute_unload '%gmsName%HessFinal'

abort$[card(errW ) > 0] 'errors comparing testW and W';
abort$[card(errWe) > 0] 'errors comparing testWe and We';
$offEcho

$include %gmsName%
option %modelType%=convert;
%modelName%.optfile=1;
Solve %modelName% using %modelType% maximizing %objName% ;
abort$(%modelName%.solvestat <> %solveStat.normalCompletion% or %modelName%.modelstat <> %modelStat.noSolutionReturned%) 'wrong status codes';
scalar rc;
execute 'gdxdump %gmsName%.gdx > %gmsName%HessDump.gms';
execute 'gams %gmsName%TestHess.gms lo=%GAMS.lo%';
rc=errorlevel;
display rc;
abort$(rc <> 0) '"gams %gmsName%TestHess.gms" gave nonzero return';