%off nat;
on rounded;



procedure delta(ii,jj);
begin 
if ii eq jj then return 1 else return 0; 
end;


DELTA


procedure addone(x); rrr:=x+1;


ADDONE


% random numbers with uniform distribution generated in Mathematica 
%no=Table[Random[Real],{i,1,100 }]

noise:=
{0.7611189572266488, 0.809932949360867, 
  0.32754272053822, 0.3711809230728502, 
  0.2198155852281288, 0.2810910296348176, 
  0.5994259353572776, 0.987082750593675, 
  0.6503306993502929, 0.6922800675720912, 
  0.7549523349478609, 0.445705988068098}$



n:=2;


N := 2

m:=2;


M := 2

%--------------------------------------------------
A(1):=10$


*** A declared operator 
 A(2):=30$


AA:=TP(MAT( (A(1), A(2) )));


      [10]
AA := [  ]
      [30]


%--------------------------------------------------

matrix KM(n,n);


for tt:=1:n do for pp:=1:m do km(tt,pp):=k(tt,pp);


*** K declared operator 


k(1,1):=0.6$

 k(1,2):=0.4$


k(2,1):=0.4$

 k(2,2):=0.6$



%-----------------
RR:=TP(MAT( (R(1), R(2) )));


*** R declared operator 

      [R(1)]
RR := [    ]
      [R(2)]


NNO:=TP(MAT( (NO(1), NO(2) )));


*** NO declared operator 

       [NO(1)]
NNO := [     ]
       [NO(2)]


NO(1):=100;


NO(1) := 100
 NO(2):=20;


NO(2) := 20


RR:= KM*AA + NNO;


      [118.0]
RR := [     ]
      [42.0 ]




%--------------- matrix formulation ---------------------------------
matrix RM(n,n);


for ii:=1:n do rm(ii,ii):=r(ii);




%---- SYMMETRY -------------------------------------
matrix ONE(n,n);


for ii:=1:n do ONE(ii,ii):=1;




matrix SS(n,n);


for tt:=1:n do for pp:=1:m do SS(tt,pp):=S(tt,pp);


*** S declared operator 


S(1,2):= - RR(1,1)*(S(1,1) - 1)/RR(2,1);


S(1,2) :=  - 2.80952380952*S(1,1) + 2.80952380952

S(2,1):= - RR(2,1)*(S(2,2) - 1)/RR(1,1);


S(2,1) :=  - 0.35593220339*S(2,2) + 0.35593220339


S(1,1):=2;


S(1,1) := 2
 S(2,2):=2;


S(2,2) := 2


SS*RR - RR;


[0]
[ ]
[0]



%---- SYMMETRYX -------------------------------------



FACTOR A;



SS;


[       2           - 2.80952380952]
[                                  ]
[ - 0.35593220339         2        ]


SS**-1;


[0.666666666667  0.936507936508]
[                              ]
[0.118644067797  0.666666666667]


                             

SS*KM*AA - KM*AA;


[ - 43.8095238095]
[                ]
[  15.593220339  ]


SS*NNO - NNO;


[ 43.8095238095 ]
[               ]
[ - 15.593220339]



%----------------
SSX:=SS-ONE;


       [       1           - 2.80952380952]
SSX := [                                  ]
       [ - 0.35593220339         1        ]


SSX**-1;


***** Singular matrix 



SSX*KM*AA;


[ - 43.8095238095]
[                ]
[  15.593220339  ]


SSX*NNO;


[ 43.8095238095 ]
[               ]
[ - 15.593220339]



KM*AA;


[18.0]
[    ]
[22.0]


NNO;


[100]
[   ]
[20 ]




YY:=TP(MAT( (Y(1), Y(2) )));


*** Y declared operator 

      [Y(1)]
YY := [    ]
      [Y(2)]



SSX*YY;


[ - 2.80952380952*Y(2) + Y(1)]
[                            ]
[ Y(2) - 0.35593220339*Y(1)  ]



shut aax;