Description
scaled LSE min LSEMinSc is defined as f := LSEMin(t*x) / t = -log(exp(-t*x1)+exp(-t*x2)+...) / t
Small Model of Type : GAMS
Category : GAMS Test library
Main file : fnlseminsc.gms
$title 'Test correctness of LSEMinSc intrinsic' (FNLSEMINSC,SEQ=916)
$onText
scaled LSE min LSEMinSc is defined as
f := LSEMin(t*x) / t
= -log(exp(-t*x1)+exp(-t*x2)+...) / t
$offText
Sets
P
V
arg 'expected content of set V' / v00*v19 /
tst(*)
;
alias (V,Vp);
alias (u,*);
scalars
t
aErr0
mx0
rErr0
;
parameters
xIn(P,V)
x(V)
wantFunc(P)
wntFunc
gotFunc
wantGrad(P,V)
wntGrad(V)
gotGrad(V)
wantHess(P,V,V)
wntHess(V,V)
gotHess(V,V)
aErr1(V)
aErr1Show(V)
mx1(V)
rErr1(V)
rErr1Show(V)
aErr2(V,V)
aErr2Show(V,V)
mx2(V,V)
rErr2(V,V)
rErr2Show(V,V)
;
$gdxIn fnlseminsc.gdx
$load P V xIn wantFunc wantGrad wantHess
$gdxIn
abort$[card(arg) <> card(V)] 'sets arg and V are not equal';
tst(arg) = yes;
tst(V) = no;
abort$[card(tst)] 'sets arg and V are not equal', tst;
* ------------------------ LSEMinSc -------------------------
loop {P,
x(V) = xIn(P,V);
t = x('v00');
x('v00') = 0;
wntFunc = wantFunc(P);
gotFunc = LSEMinSc.value( t,x('v01'),x('v02'),x('v03'),x('v04'),
x('v05'),x('v06'),x('v07'),x('v08'),x('v09'),
x('v10'),x('v11'),x('v12'),x('v13'),x('v14'),
x('v15'),x('v16'),x('v17'),x('v18'),x('v19') );
wntGrad(V) = wantGrad(P,V);
loop{V,
gotGrad(V) = LSEMinSc.grad(ord(V): t,x('v01'),x('v02'),x('v03'),x('v04'),
x('v05'),x('v06'),x('v07'),x('v08'),x('v09'),
x('v10'),x('v11'),x('v12'),x('v13'),x('v14'),
x('v15'),x('v16'),x('v17'),x('v18'),x('v19') );
};
wntHess(V,Vp) = wantHess(P,V,Vp);
loop{(V,Vp),
gotHess(V,Vp) = LSEMinSc.hess(ord(V):ord(Vp): t,x('v01'),x('v02'),x('v03'),x('v04'),
x('v05'),x('v06'),x('v07'),x('v08'),x('v09'),
x('v10'),x('v11'),x('v12'),x('v13'),x('v14'),
x('v15'),x('v16'),x('v17'),x('v18'),x('v19') );
};
aErr0 = abs(gotFunc-wntFunc);
repeat {
break$[aErr0 <= 1e-200];
mx0 = max(abs(gotFunc),abs(wntFunc));
rErr0 = aErr0 / mx0;
break$[rErr0 <= 5e-16];
abort 'wrong function value in LSEMinSc', t, x, gotFunc, wntFunc, aErr0, rErr0;
until yes };
aErr1(V) = abs(gotGrad(V)-wntGrad(V));
aErr1Show(V) = aErr1(V)$[aErr1(V) > 1e-200];
repeat {
break$[card(aErr1Show) = 0];
mx1(V) = max(abs(gotGrad(V)),abs(wntGrad(V)));
rErr1(V) = [aErr1(V) / mx1(V)]$aErr1Show(V);
rErr1Show(V) = rErr1(V)$[rErr1(V) > 5e-16];
break$[card(rErr1Show) = 0];
abort 'wrong gradient value in LSEMinSc', t, x, gotGrad, wntGrad, aErr1Show, rErr1Show;
until yes };
aErr2(V,Vp) = abs(gotHess(V,Vp)-wntHess(V,Vp));
aErr2Show(V,Vp) = aErr2(V,Vp)$[aErr2(V,Vp) > 1e-200];
repeat {
break$[card(aErr2Show) = 0];
mx2(V,Vp) = max(abs(gotHess(V,Vp)),abs(wntHess(V,Vp)));
rErr2(V,Vp) = [aErr2(V,Vp) / mx2(V,Vp)]$aErr2Show(V,Vp);
rErr2Show(V,Vp) = rErr2(V,Vp)$[rErr2(V,Vp) > 1e-15];
break$[card(rErr2Show) = 0];
abort 'wrong Hessian value in LSEMinSc', t, x, gotHess, wntHess, aErr2Show, rErr2Show;
until yes };
};