Finding Transpose of Matrix in GAMS and solving data reconciliation problem

[suryanarayana kolluri]

Hi All,

I am new to GAMS, I have to solve a DATA RECONCILIATION problem to some chemical engineering example.
My MINLP Optimization Problem is

Min f(x)

Such that,

S_hat = S - SA'PAS
P(ASA') = I

where
A is Matrix came from Material Balance of the System
A' is Transpose of A
S is Co-variance Matrix
P is a Continuous Variable
S_hat is diagonal elements of matrix
I is identity matrix
for example :

A = [1  -1  -1  0;
       0   0   1 -1];

can find transpose of A directly in GAMS?

S = [x1*s1+y1*10, 0,0,0 ;
        0,x2*s2+y2*10,0,0 ;
        0,0,x3*s3+y3*10,0 ;
        0,0,0,x4*s4+y4*10];

 
P = [p11, 0;
       p21,p22];

By matrix multiplication, can i get constraints for expressions S_hat = S - SA'PAS and P(ASA') = I.

I would be great help if anyone can help for giving me an idea.


Thanks and Regards
Suryanarayana
PhD Student
IIT Bombay

[Edson Cordeiro do Valle]

   Hello Suryanarayana

I have some experience with data reconciliation and I would like to know where are your integer variables come from, since in typical Dara reconciliation problems, no integer variables are present, by your formulation I can't see them and why are you trying to use it.

To do matrix multiplications, transposes and inverse other package can be used, as matlab and scilab (the last one is free).
Regarding the use of Scilab, I've developed a framework in this tool for data reconcilation and gross error detection ( https://code.google.com/p/dr-ged-benchmarks/ ), where you can find the implementations and behchmark test problems.
I know this is not a Scilab forum, but I'm suggesting this tool since I've tried to use Gams in the past and found Matlab/Scilab more helpfull.

Any doubts you can contact me by this personal e-mail.

Regards

2012/5/18 suryanarayana kolluri <snk....@gmail.com>

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[yan ren]

> can find transpose of A directly in GAMS?

parameter A(i,j), At(j,i);

...

At(j,i) = A(i.j) should work.

> S = [x1*s1+y1*10, 0,0,0 ;
>         0,x2*s2+y2*10,0,0 ;
>         0,0,x3*s3+y3*10,0 ;
>         0,0,0,x4*s4+y4*10];
>
>
> P = [p11, 0;
>        p21,p22];
>
> By matrix multiplication, can i get constraints for expressions S_hat = S -
> SA'PAS and P(ASA') = I.
>

matrix muliplication for C = A* B
parameter A(i,k) , B(k,j) ,C(i,j) ;

C(i,j ) = sum(k, A(i,k)* B(k,j))


HTH,

Yan

[任彦]

> To do matrix multiplications, transposes and inverse other package can be used, as matlab and scilab (the last one is free).
> Regarding the use of Scilab, I've developed a framework in this tool for data reconcilation and gross error detection ( https://code.google.com/p/dr-ged-benchmarks/ ), where > you can find the implementations and behchmark test problems.
> I know this is not a Scilab forum, but I'm suggesting this tool since I've tried to use Gams in the past and found Matlab/Scilab more helpfull.

I had some terriable experience rewrote in GAMS some reonciliation code written in matlab.
matrix multiplications utillities in GMAS does sucks ... sometimes I have to unload GAMS 2D parameter into gdx file and call lapack myself.

Yan

[Edson Cordeiro do Valle]

   Hello Suryanarayana

As Yan.ren said in the GAMS list, the transpose and the matrix multiplication in GAMS is pretty straightforward.
I think you won't have dificulties in do it. If you have, send me your Gams code.

Regards

2012/5/20 任彦 <yan...@enintech.com>

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[Azadeh Maroufmashat]

Hi Every body!
can we eneter the transpos of one variable in equation set in GAMS?

[Renger van Nieuwkoop]

Hi Azadeh

 

If you want for example to multiply matrix A with the transpose of it you just use PROD()

 

Prod((i,j), A(i,j)*A(j,i))

 

Cheers

Renger

 

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