Need help to form equations

Hello all

I want to form the equations through the matlab commands,I have the matrix of constants....Can anyone guide how can I form the equations. Example equations

1) a1v1^2-a2v2-a3v3^2-a4v4=0

2) a3v3^2-a4v4-a1v1=0

3) a1v1+a4v4-a3v3^2=0

4) a2v2+a1v1+a3v3-a4v4=0

where a's are constant and I have a matrix for a and I have to find v's.

I want to use them in fsolve.

please guide!!!

Regards

Answer 1

[David Sanchez]

a = rand(1,4); % your a matrix
syms v1 v2 v3 v4
S = solve( a(1)*v1^2-a(2)*v2-a(3)*v3^2-a(4)*v4==0,...
 a(3)*v3^2-a(4)*v4-a(1)*v1==0,...
 a(1)*v1+a(4)*v4-a(3)*v3^2==0,...
 a(2)*v2+a(1)*v1+a(3)*v3-a(4)*v4==0)

S = 

      v1: [4x1 sym]
      v2: [4x1 sym]
      v3: [4x1 sym]
      v4: [4x1 sym]

To display the solutions, access the elements of the structure array S

S.v1
ans =

                                                                             0
                                            0.76082746713182598996024745838092
   - 0.38041373356591299498012372919046 - 0.65889591443313132581875790778993*i
   - 0.38041373356591299498012372919046 + 0.65889591443313132581875790778993*i

[Sameer]

Hello...thanks for replying but my concern is that i have plenty of equations,thus i want to generate the equations using a loop,therefore i want to know how can I acheive that...

Awaiting a response

Regards

[Sameer]

To give the more clear idea:

function F = Equation_trial( x )

F= [50-20*x(1)-30*x(2)-40*x(3);

    30*x(2)-50*x(4)-60*x(5);   

    20*x(1)+60*x(5)-70*x(6);    

    70*x(6)+50*x(4)+40*x(3)-80*x(7);   

    50000+20-x(8)-500*x(1)^2;   

    50000+20-x(9)-500*x(2)^2;    

    50000+20-x(10)-500*x(3)^2;  

    500*x(2)^2+x(9)-x(11)-500*x(4)^2;    

    500*x(2)^2+x(9)-x(12)-500*x(5)^2;    

    500*x(6)^2+x(13)-x(8)-500*x(1)^2;  

    500*x(6)^2+x(13)-x(12)-500*x(5)^2;   

    500*x(7)^2+x(14)-x(10)-500*x(3)^2;  

    500*x(7)^2+x(14)-x(11)-500*x(4)^2; 

    500*x(7)^2+x(14)-x(13)-500*x(6)^2];

end

x0=[1,1,1,1,1,1,1,1,1,1,1,1,1,1]'

[x,fval]=fsolve(@Equation_trial,x0)

This is what I have to do but I want these equations to be generated on its own using a loop.

please quide

regards