fnlse.gms : Rough correctness test for LSE max/min intrinsics

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 };
};