Description
sqlog10(x,S) = log_10(x) if x >= S (1/log 10) (ln(S) + r/S - 1/S^2) otherwise, r = x - S for S >= 1e-150, default S = 1e-150. Contributor: Steve, Mar 2017
Small Model of Type : GAMS
Category : GAMS Test library
Main file : fnsqlog102.gms includes : fnset_xy.inc [html] fntest_xy.inc [html]
$title 'Test correctness of sqlog10 intrinsic' (FNSQLOG102,SEQ=724)
$onText
sqlog10(x,S) = log_10(x) if x >= S
(1/log 10) (ln(S) + r/S - 1/S^2) otherwise, r = x - S
for S >= 1e-150, default S = 1e-150.
Contributor: Steve, Mar 2017
$offText
$include fnset_xy.inc
reps = 8e-16;
sets
T /
t1 * t6,
t11 * t16
t21 * t26
/
torig(t) 'unsmoothed inputs'
;
* doing anything with y = 1e-150 is pretty useless: the 2nd deriv is
* so large
table data(T,V)
x y f_ fx_ fxx_ rc_ ec_
t1 1 1e-140
t2 1e-136 1e-140
t3 1e-139 1e-140
t4 1e-160 1e-140
t5 EPS 1e-140
t6 -1e1 1e-140
t11 1 1e-20
t12 1e-19 1e-20
t13 1e-20 1e-20
t14 1e-120 1e-20
t15 EPS 1e-20
t16 -1e40 1e-20
t21 4000 2000
t22 2001 2000
t23 2000 2000
t24 1999.999 2000
t25 EPS 2000
t26 -1e100 2000
;
scalars
r
L10
lnS
;
* problematic to test exactly at the breakpoint: should 2nd deriv be 0
* or taken from the smooth part?
loop{T$[data(T,'x') = data(T,'y')],
data(T,'x') = (1+4e-16) * data(T,'x');
};
torig(t) = [data(T,'x') > data(T,'y')];
L10 = log(10);
loop{torig(T),
data(T, 'f_') = log(data(T,'x')) / L10;
data(T, 'fx_') = 1 / (data(T,'x') * L10);
data(T,'fxx_') = (-1 / data(T,'x')) / (data(T,'x')*L10);
};
loop{t$[not torig(t)],
lnS = log(data(t,'y'));
r = data(t,'x') - data(t,'y');
data(t, 'f_') = (lnS + r/data(t,'y') - 0.5*sqr(r/data(t,'y'))) / L10;
data(t, 'fx_') = (1 - r/data(t,'y')) / (data(t,'y')*L10);
data(T,'fxx_') = (-1 / data(t,'y')) / (data(t,'y')*L10);
};
loop {T,
data(T,'fyx_') = data(T,'fxy_');
data(T, 'f') = sqlog10.value( data(T,'x'),data(T,'y'));
data(T, 'fx') = sqlog10.grad(1: data(T,'x'),data(T,'y'));
data(T, 'fy') = sqlog10.grad(2: data(T,'x'),data(T,'y'));
data(T,'fxx') = sqlog10.hess(1:1:data(T,'x'),data(T,'y'));
data(T,'fxy') = sqlog10.hess(1:2:data(T,'x'),data(T,'y'));
data(T,'fyx') = sqlog10.hess(2:1:data(T,'x'),data(T,'y'));
data(T,'fyy') = sqlog10.hess(2:2:data(T,'x'),data(T,'y'));
data(T, 'rc') = mathlastrc;
data(T, 'ec') = mathlastec;
};
display data;
$include fntest_xy.inc