Description
Test interval evaluators for sin and cos: function and gradient. The test is designed to catch all the interesting combinations of extreme points and inflection points so the implementation gets a full workout. Contributor: Steve, Jan 2017
Small Model of Type : GAMS
Category : GAMS Test library
Main file : fnsincosintrv.gms
$TITLE 'Test sin/cos func/grad interval evals' (FNSINCOSINTRV,SEQ=714)
$ontext
Test interval evaluators for sin and cos: function and gradient.
The test is designed to catch all the interesting combinations of
extreme points and inflection points so the implementation gets a full
workout.
Contributor: Steve, Jan 2017
$offtext
sets
t 'tests cases' / t11*t14, t21*t24, t31*t34, t41*t44 /
v 'values' /
xlo
xup
flo_
fup_
glo_
gup_
flo
fup
glo
gup
flod
fupd
glod
gupd
/;
parameters
eflo(t) 'errors in flo'
efup(t) 'errors in fup'
eglo(t) 'errors in glo'
egup(t) 'errors in gup'
;
file fp /''/; put fp;
table s(t,v) 'sin test data'
xlo xup flo_ fup_ glo_ gup_
t11 [-1/6] [ 2/6] 1.0
t12 [-1/6] [ 5/6] 1.0 1.0
t13 [-1/6] [ 8/6] 1.0 -1.0 1.0
t14 [-1/6] [11/6] -1.0 1.0 -1.0 1.0
t21 [2/6] [ 5/6] 1.0
t22 [2/6] [ 8/6] 1.0 -1.0
t23 [2/6] [11/6] -1.0 1.0 -1.0
t24 [2/6] [14/6] -1.0 1.0 -1.0 1.0
t31 [5/6] [ 8/6] -1.0
t32 [5/6] [11/6] -1.0 -1.0
t33 [5/6] [14/6] -1.0 -1.0 1.0
t34 [5/6] [17/6] -1.0 1.0 -1.0 1.0
t41 [8/6] [11/6] -1.0
t42 [8/6] [14/6] -1.0 1.0
t43 [8/6] [17/6] -1.0 1.0 1.0
t44 [8/6] [20/6] -1.0 1.0 -1.0 1.0
;
s(t,'xlo') = s(t,'xlo') * pi;
s(t,'xup') = s(t,'xup') * pi;
s('t11','flo_') = sin(s('t11','xlo'));
s('t11','fup_') = sin(s('t11','xup'));
s('t11','glo_') = cos(s('t11','xup'));
s('t12','flo_') = sin(s('t12','xlo'));
s('t12','glo_') = cos(s('t12','xup'));
s('t13','flo_') = sin(s('t13','xup'));
s('t21','flo_') = sin(s('t21','xup'));
s('t21','glo_') = cos(s('t21','xup'));
s('t21','gup_') = cos(s('t21','xlo'));
s('t22','flo_') = sin(s('t22','xup'));
s('t22','gup_') = cos(s('t22','xlo'));
s('t23','gup_') = cos(s('t23','xup'));
s('t31','flo_') = sin(s('t31','xup'));
s('t31','fup_') = sin(s('t31','xlo'));
s('t31','gup_') = cos(s('t31','xup'));
s('t32','fup_') = sin(s('t32','xlo'));
s('t32','gup_') = cos(s('t32','xup'));
s('t33','fup_') = sin(s('t33','xup'));
s('t41','fup_') = sin(s('t41','xup'));
s('t41','glo_') = cos(s('t41','xlo'));
s('t41','gup_') = cos(s('t41','xup'));
s('t42','fup_') = sin(s('t42','xup'));
s('t42','glo_') = cos(s('t42','xlo'));
s('t43','glo_') = cos(s('t43','xup'));
s(t,'flo') = sin.low (s(t,'xlo'):s(t,'xup'));
s(t,'fup') = sin.high (s(t,'xlo'):s(t,'xup'));
s(t,'glo') = sin.gradL(s(t,'xlo'):s(t,'xup'));
s(t,'gup') = sin.gradH(s(t,'xlo'):s(t,'xup'));
s(t,'flod') = s(t,'flo') - s(t,'flo_');
s(t,'fupd') = s(t,'fup') - s(t,'fup_');
s(t,'glod') = s(t,'glo') - s(t,'glo_');
s(t,'gupd') = s(t,'gup') - s(t,'gup_');
eflo(t) = round(abs(s(t,'flod')),12);
efup(t) = round(abs(s(t,'fupd')),12);
eglo(t) = round(abs(s(t,'glod')),12);
egup(t) = round(abs(s(t,'gupd')),12);
if {[card(eflo)+card(efup)+card(eglo)+card(egup)] > 0,
execute_unload 'stResults';
execute_unload 'stErrs', eflo, efup, eglo, egup;
putclose ' ' / '** SINE ERRORS FOUND **'/' '/;
abort$1 'aborting';
};
* ------------------------------------------------------
table c(t,v) 'cos test data'
xlo xup flo_ fup_ glo_ gup_
t11 [-1/6] [ 2/6] 1.0
t12 [-1/6] [ 5/6] 1.0 -1.0
t13 [-1/6] [ 8/6] -1.0 1.0 -1.0
t14 [-1/6] [11/6] -1.0 1.0 -1.0 1.0
t21 [2/6] [ 5/6] -1.0
t22 [2/6] [ 8/6] -1.0 -1.0
t23 [2/6] [11/6] -1.0 -1.0 1.0
t24 [2/6] [14/6] -1.0 1.0 -1.0 1.0
t31 [5/6] [ 8/6] -1.0
t32 [5/6] [11/6] -1.0 1.0
t33 [5/6] [14/6] -1.0 1.0 1.0
t34 [5/6] [17/6] -1.0 1.0 -1.0 1.0
t41 [8/6] [11/6] 1.0
t42 [8/6] [14/6] 1.0 1.0
t43 [8/6] [17/6] 1.0 -1.0 1.0
t44 [8/6] [20/6] -1.0 1.0 -1.0 1.0
;
c(t,'xlo') = c(t,'xlo') * pi;
c(t,'xup') = c(t,'xup') * pi;
c('t11','flo_') = cos(c('t11','xup'));
c('t11','glo_') = -sin(c('t11','xup'));
c('t11','gup_') = -sin(c('t11','xlo'));
c('t12','flo_') = cos(c('t12','xup'));
c('t12','gup_') = -sin(c('t12','xlo'));
c('t13','gup_') = -sin(c('t13','xup'));
c('t21','flo_') = cos(c('t21','xup'));
c('t21','fup_') = cos(c('t21','xlo'));
c('t21','gup_') = -sin(c('t21','xup'));
c('t22','fup_') = cos(c('t22','xlo'));
c('t22','gup_') = -sin(c('t22','xup'));
c('t23','fup_') = cos(c('t23','xup'));
c('t31','fup_') = cos(c('t31','xup'));
c('t31','glo_') = -sin(c('t31','xlo'));
c('t31','gup_') = -sin(c('t31','xup'));
c('t32','fup_') = cos(c('t32','xup'));
c('t32','glo_') = -sin(c('t32','xlo'));
c('t33','glo_') = -sin(c('t33','xup'));
c('t41','flo_') = cos(c('t41','xlo'));
c('t41','fup_') = cos(c('t41','xup'));
c('t41','glo_') = -sin(c('t41','xup'));
c('t42','flo_') = cos(c('t42','xlo'));
c('t42','glo_') = -sin(c('t42','xup'));
c('t43','flo_') = cos(c('t43','xup'));
c(t,'flo') = cos.low (c(t,'xlo'):c(t,'xup'));
c(t,'fup') = cos.high (c(t,'xlo'):c(t,'xup'));
c(t,'glo') = cos.gradL(c(t,'xlo'):c(t,'xup'));
c(t,'gup') = cos.gradH(c(t,'xlo'):c(t,'xup'));
c(t,'flod') = c(t,'flo') - c(t,'flo_');
c(t,'fupd') = c(t,'fup') - c(t,'fup_');
c(t,'glod') = c(t,'glo') - c(t,'glo_');
c(t,'gupd') = c(t,'gup') - c(t,'gup_');
eflo(t) = round(abs(c(t,'flod')),12);
efup(t) = round(abs(c(t,'fupd')),12);
eglo(t) = round(abs(c(t,'glod')),12);
egup(t) = round(abs(c(t,'gupd')),12);
if {[card(eflo)+card(efup)+card(eglo)+card(egup)] > 0,
execute_unload 'ctResults';
execute_unload 'ctErrs', eflo, efup, eglo, egup;
putclose ' ' / '** COSINE ERRORS FOUND **'/' '/;
abort$1 'aborting';
else
putclose ' ' / '** TEST OK **'/' '/;
};