Version:

ex2.gms : External Equation - Example 2

**Description**

This is the second in a sequence of examples that show how to use the external equations (=X=) facility with GAMS/CONOPT. The second model is also simple unconstrained quadratic model and the quadratic function is defined in an external equation. But this time we communicate the data from GAMS via a put file including information on the size of the model. We can now change the data in GAMS without reprogramming the Fortran or C routine. The model is slightly convoluted. We want to be able to solve it for different subsets I of the Domain D.

**Small Model of Type : ** GAMS

**Category :** GAMS Test library

**Main file : ** ex2.gms

```
$Title External Equation - Example 2 (EX2,SEQ=565)
$offsymlist offsymxref
$ontext
This is the second in a sequence of examples that show how to
use the external equations (=X=) facility with GAMS/CONOPT.
The second model is also simple unconstrained quadratic model
and the quadratic function is defined in an external equation.
But this time we communicate the data from GAMS via a put file
including information on the size of the model. We can now change
the data in GAMS without reprogramming the Fortran or C routine.
The model is slightly convoluted. We want to be able to solve
it for different subsets I of the Domain D.
$offtext
set D Domain for the variables / i1*i14 /;
set I(D) Subset for actual optimization;
alias (D,E), (i,j);
Parameter Q(D,D) Covariance Matrix
X0(D) Targets;
Q(D,E) = power(0.5, abs(ord(D)-ord(E)) );
X0(D) = ord(D) / card(D);
display Q, x0;
variable x(D), z;
equation zdef, zdefX;
* Define I for the first solve to hold 7 elements
I(D) = yes$(ord(D) le 7);
* The desired equation, implemented in GAMS, is
zdef.. sum {(i,j),
(x(i)-x0(i)) * Q(i,j) * (x(j)-x0(j)) }
=e= z;
* It is implemented as an external equation as:
zdefX.. sum {D$I(D), ord(D)*x(D) } + (card(I)+1)* z =X= 1;
$ontext
See the comments in ex1.gms for further details.
We use D instead of I in the equation since I is now a dynamic
set and we cannot use ord(I).
The size of the set I and the model data is now written to
the file ex2.put using PUT statements. Note that we end with
a putclose statement so the file is closed when we read it
in the external module.
$offtext
file f / ex2.put /; f.nw = 0; f.nd = 13;
f.nr = 0; put f card(i):0:0 /; f.nr = 2;
loop {i,
put x0(i) /;
loop {j,
put q(i,j) /;
};
};
putclose f;
$ set pre
$ifi %system.filesys%==unix $set pre 'lib'
$ set suf '64'
$set N ex2
$set c_cbN %pre%%N%c_cb%suf%
$set d_cbN %pre%%N%d_cb%suf%
$set f_cbN %pre%%N%f_cb%suf%
model %N% 'GAMS implementation' / zdef /;
model %c_cbN% 'External equations in C, with callbacks' / zdefX /;
model %d_cbN% 'External equations in Delphi with callbacks' / zdefX /;
model %f_cbN% 'External equations in F77, with callbacks' / zdefX /;
option limcol = 0;
$ontext
Create a summary table where we compare the expected results,
x0 with the actual results, x.l, to ensure that data have been
communicated correctly to the external equation.
$offtext
parameter report(*,*,*) 'Solution Summary';
option report:5;
scalar totdist /0/;
* reuse the same code several times
$onechoV > runme.gms
z.l = 0;
z.m = 0;
x.l(i) = 0;
x.m(i) = 0;
zdef.l = 0;
zdef.m = 0;
solve %1 using nlp minimizing z;
abort$(%1.solvestat %2) 'problems running model %1';
execerror = 0;
report('Solve ','Stat', '%1') = %1.solvestat;
report('Model ','Stat', '%1') = %1.modelstat;
report(i,'Target', '%1') = x0(i);
report(i,'Value', '%1') = x.l(i);
report(i,'Distance','%1') = abs(x.l(i) - x0(i));
totdist = totdist + sum(i,abs(x.l(i) - x0(i)));
$offecho
$ set ext '.dll'
$ifi %system.filesys%==unix $set ext '.so'
$ifi %system.platform%==dex $set ext '.dylib'
$ifi %system.platform%==dax $set ext '.dylib'
$ set eq
$ifi %system.filesys%==unix $set eq "'"
$if set runall $set runC_cb '1' set runD_cb '1' set runF_cb '1'
$ifthen not set nocomp
$ ifi set runC_cb $call gams complink lo=%gams.lo% --lang=c --files=ex2c_cb.c --libname=%c_cbN%%ext%
$ if errorlevel 1 $abort Error compiling C Library
$ ifi set runD_cb $call gams complink lo=%gams.lo% --lang=Delphi --files=ex2d_cb.dpr
$ if errorlevel 1 $abort Error compiling Delphi Library
$ ifi set runF_cb $call gams complink lo=%gams.lo% --lang=fortran90 --files=%eq%"gehelper.f90 msg2_f.f90 ex2f_cb.f90"%eq% --libname=%f_cbN%%ext%
$ if errorlevel 1 $abort Error compiling Fortran90 Library
$endif
$ batinclude runme %N% '<> 1'
$if set runC_cb $batinclude runme %c_cbN% '<> 1'
$if set runD_cb $batinclude runme %d_cbN% '<> 1'
$if set runF_cb $batinclude runme %f_cbN% '<> 1'
display report;
if ((totdist < 1.0E-6),
display "@@@@ #Test passed.";
else
abort totdist, "@@@@ #Test not passed. Inspect ex2.lst for details.";
);
$ontext
Now define I to hold all 14 elements. This should give rise to an
error since we have only allocated space for 10 elements in the
Fortran and Delphi routine.
The C-version allocates memory dynamically and will work correctly.
$offtext
I(D) = yes;
$ontext
When we open the PUT file again for writing it will by default
be overwritten, which is what we need:
$offtext
* start over with new data and empty report
f.nr = 0; put f card(i):0:0 /; f.nr = 2;
loop {i,
put x0(i) /;
loop {j,
put q(i,j) /;
};
};
putclose f;
option clear = report;
totdist = 0;
$ batinclude runme %N% '<> 1'
$if set runC_cb $batinclude runme %c_cbN% '<> 1'
$if set runD_cb $batinclude runme %d_cbN% ' = 1'
$if set runF_cb $batinclude runme %f_cbN% ' = 1'
display report;
```