Description
LSE max is defined as: LSEMax(x) := log(exp(x1)+exp(x2)+...) LSE min is defined as: LSEMin(x) := -LSEMax(-x) = -log(exp(-x1)+exp(-x2)+...) scaled LSE max is defined as: LSEMaxSc(t,x) := LSEMax(tx) / t scaled LSE min is defined as: LSEMinSc(t,x) := LSEMin(tx) / t This is not a very precise test: we simply verify that the direct/naive computation of the function is pretty close to what the intrinsics produce, and that the numerical gradients and Hessians are pretty close to what the intrinsics produce.
Small Model of Type : GAMS
Category : GAMS Test library
Main file : fnlse.gms
$title 'Rough correctness test for LSE max/min intrinsics' (FNLSE,SEQ=912)
$ontext
LSE max is defined as: LSEMax(x) := log(exp(x1)+exp(x2)+...)
LSE min is defined as: LSEMin(x) := -LSEMax(-x) = -log(exp(-x1)+exp(-x2)+...)
scaled LSE max is defined as: LSEMaxSc(t,x) := LSEMax(tx) / t
scaled LSE min is defined as: LSEMinSc(t,x) := LSEMin(tx) / t
This is not a very precise test: we simply verify that the direct/naive
computation of the function is pretty close to what the intrinsics produce,
and that the numerical gradients and Hessians are pretty close to
what the intrinsics produce.
$offtext
Sets
arg / n00*n19 /
P / p1*p1000 /;
alias (arg,argp);
singleton set PP(P);
scalars
t
aErr0
aTol0 / 3e-14 /
aTol1 / 4e-7 /
aTol2 / 1e-4 /
rTol2 'numerical Hessians are not very precise' / .9 /
;
Parameters
data(arg)
gotFunc
wantFunc
gotGrad(arg)
wantGrad(arg)
aErr1(arg)
gotHess(arg,arg)
wantHess(arg,arg)
aErr2(arg,arg)
mx2(arg,argp)
rErr2(arg,argp)
;
execseed = 20021215;
option fdDelta = 1.0e-5;
* ------------------------ LSEMax -------------------------
loop {P,
PP(P) = yes;
data(arg) = uniform(-10,10);
gotFunc = LSEMax.value(data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantFunc = log(sum(arg, exp(data(arg))));
loop{arg,
gotGrad(arg) = LSEMax.grad(ord(arg): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantGrad(arg) = LSEMax.gradn(ord(arg): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
loop{(arg,argp),
gotHess(arg,argp) = LSEMax.hess(ord(arg):ord(argp): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantHess(arg,argp) = LSEMax.hessn(ord(arg):ord(argp): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
aErr0 = abs(gotFunc-wantFunc);
abort$[aErr0 > aTol0] 'wrong function value in LSEMax', PP, data, gotFunc, wantFunc, aErr0;
aErr1(arg) = abs(gotGrad(arg)-wantGrad(arg));
aErr1(arg)$[aErr1(arg) <= aTol1] = 0;
abort$[card(aErr1) > 0] 'wrong gradient value in LSEMax', PP, data, gotGrad, wantGrad, aErr1;
aErr2(arg,argp) = abs(gotHess(arg,argp)-wantHess(arg,argp));
aErr2(arg,argp)$[aErr2(arg,argp) <= aTol2] = 0;
repeat {
break$[card(aErr2) = 0];
mx2(arg,argp) = max(abs(gotHess(arg,argp)),abs(wantHess(arg,argp)));
rErr2(arg,argp) = [aErr2(arg,argp) / mx2(arg,argp)]$aErr2(arg,argp);
rErr2(arg,argp)$[rErr2(arg,argp) <= rTol2] = 0;
break$[card(rErr2) = 0];
abort 'wrong Hessian value in LSEMax', PP, data, gothess, wantHess, aErr2, rErr2;
until yes };
};
gotGrad(arg) = 0;
wantGrad(arg) = 0;
gotHess(arg,argp) = 0;
wantHess(arg,argp) = 0;
* ------------------------ LSEMaxSc -------------------------
loop {P,
PP(P) = yes;
t = uniform(-1,2); t = 10**t;
data(arg) = uniform(-15,7); data('n00') = 0;
gotFunc = LSEMaxSc.value( t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantFunc = log(sum(arg$[ord(arg) > 1], exp(t*data(arg)))) / t;
loop{arg$[ord(arg) > 1],
gotGrad(arg) = LSEMaxSc.grad(ord(arg): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantGrad(arg) = LSEMaxSc.gradn(ord(arg): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
loop{(arg,argp)$[(ord(arg) > 1) and (ord(argp) > 1)],
gotHess(arg,argp) = LSEMaxSc.hess(ord(arg):ord(argp): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantHess(arg,argp) = LSEMaxSc.hessn(ord(arg):ord(argp): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
aErr0 = abs(gotFunc-wantFunc);
abort$[aErr0 > aTol0] 'wrong function value in LSEMaxSc', PP, data, gotFunc, wantFunc, aErr0;
aErr1(arg) = abs(gotGrad(arg)-wantGrad(arg));
aErr1(arg)$[aErr1(arg) <= aTol1] = 0;
abort$[card(aErr1) > 0] 'wrong gradient value in LSEMaxSc', PP, data, gotGrad, wantGrad, aErr1;
aErr2(arg,argp) = abs(gotHess(arg,argp)-wantHess(arg,argp));
aErr2(arg,argp)$[aErr2(arg,argp) <= aTol2] = 0;
repeat {
break$[card(aErr2) = 0];
mx2(arg,argp) = max(abs(gotHess(arg,argp)),abs(wantHess(arg,argp)));
rErr2(arg,argp) = [aErr2(arg,argp) / mx2(arg,argp)]$aErr2(arg,argp);
rErr2(arg,argp)$[rErr2(arg,argp) <= rTol2] = 0;
break$[card(rErr2) = 0];
abort 'wrong Hessian value in LSEMaxSc', PP, data, gothess, wantHess, aErr2, rErr2;
until yes };
};
* ------------------------ LSEMin -------------------------
loop {P,
PP(P) = yes;
data(arg) = uniform(-10,10);
gotFunc = LSEMin.value(data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantFunc = -log(sum(arg, exp(-data(arg))));
loop{arg,
gotGrad(arg) = LSEMin.grad(ord(arg): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantGrad(arg) = LSEMin.gradn(ord(arg): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
loop{(arg,argp),
gotHess(arg,argp) = LSEMin.hess(ord(arg):ord(argp): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantHess(arg,argp) = LSEMin.hessn(ord(arg):ord(argp): data('n00'),data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
aErr0 = abs(gotFunc-wantFunc);
abort$[aErr0 > aTol0] 'wrong function value in LSEMin', PP, data, gotFunc, wantFunc, aErr0;
aErr1(arg) = abs(gotGrad(arg)-wantGrad(arg));
aErr1(arg)$[aErr1(arg) <= aTol1] = 0;
abort$[card(aErr1) > 0] 'wrong gradient value in LSEMin', PP, data, gotGrad, wantGrad, aErr1;
aErr2(arg,argp) = abs(gotHess(arg,argp)-wantHess(arg,argp));
aErr2(arg,argp)$[aErr2(arg,argp) <= aTol2] = 0;
repeat {
break$[card(aErr2) = 0];
mx2(arg,argp) = max(abs(gotHess(arg,argp)),abs(wantHess(arg,argp)));
rErr2(arg,argp) = [aErr2(arg,argp) / mx2(arg,argp)]$aErr2(arg,argp);
rErr2(arg,argp)$[rErr2(arg,argp) <= rTol2] = 0;
break$[card(rErr2) = 0];
abort 'wrong Hessian value in LSEMin', PP, data, gothess, wantHess, aErr2, rErr2;
until yes };
};
gotGrad(arg) = 0;
wantGrad(arg) = 0;
gotHess(arg,argp) = 0;
wantHess(arg,argp) = 0;
* ------------------------ LSEMinSc -------------------------
loop {P,
PP(P) = yes;
t = uniform(-1,2); t = 10**t;
data(arg) = uniform(-7,15); data('n00') = 0;
gotFunc = LSEMinSc.value( t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantFunc = -log(sum(arg$[ord(arg) > 1], exp(-t*data(arg)))) / t;
loop{arg$[ord(arg) > 1],
gotGrad(arg) = LSEMinSc.grad(ord(arg): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantGrad(arg) = LSEMinSc.gradn(ord(arg): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
loop{(arg,argp)$[(ord(arg) > 1) and (ord(argp) > 1)],
gotHess(arg,argp) = LSEMinSc.hess(ord(arg):ord(argp): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
wantHess(arg,argp) = LSEMinSc.hessn(ord(arg):ord(argp): t,data('n01'),data('n02'),data('n03'),data('n04'),
data('n05'),data('n06'),data('n07'),data('n08'),data('n09'),
data('n10'),data('n11'),data('n12'),data('n13'),data('n14'),
data('n15'),data('n16'),data('n17'),data('n18'),data('n19') );
};
aErr0 = abs(gotFunc-wantFunc);
abort$[aErr0 > aTol0] 'wrong function value in LSEMinSc', PP, data, gotFunc, wantFunc, aErr0;
aErr1(arg) = abs(gotGrad(arg)-wantGrad(arg));
aErr1(arg)$[aErr1(arg) <= aTol1] = 0;
abort$[card(aErr1) > 0] 'wrong gradient value in LSEMinSc', PP, data, gotGrad, wantGrad, aErr1;
aErr2(arg,argp) = abs(gotHess(arg,argp)-wantHess(arg,argp));
aErr2(arg,argp)$[aErr2(arg,argp) <= aTol2] = 0;
repeat {
break$[card(aErr2) = 0];
mx2(arg,argp) = max(abs(gotHess(arg,argp)),abs(wantHess(arg,argp)));
rErr2(arg,argp) = [aErr2(arg,argp) / mx2(arg,argp)]$aErr2(arg,argp);
rErr2(arg,argp)$[rErr2(arg,argp) <= rTol2] = 0;
break$[card(rErr2) = 0];
abort 'wrong Hessian value in LSEMinSc', PP, data, gothess, wantHess, aErr2, rErr2;
until yes };
};