Solve for two 1024x1024 variables using two equations.

      pic1 = double (Pic1);
      pic3 = double(Pic3);
      pic4 = double(Pic4);
      ILE = 1;
      E = pic1./ILE;
      VT = 0.025;
      IL = 1;
      I1 = pic3 - B*IL;
      I2 = pic4 - B*IL;
      jp=0.038;    
      V1(1:1024,1:1024)=0.616185;
      V2(1:1024,1:1024)=0.575044;
    %Equation 1
    %(V1-VT.*log(I1)) = -((VT).*log(A)) -(jp.*B)+ (I1.*(V1 - VT.*log(I1)+ jp.*B +VT.*log(A)));
    equation1 = (V1-VT.*log(I1))+((VT).*log(A)) +(jp.*B)- (I1.*(V1 + VT.*log(I1)- jp.*B - VT.*log(A)));

      %Equation 2
    %V2-VT.*log(I2) = -((VT).*log(A)) -(jp.*B) + (I2.*(V2 - VT.*log(I2)+ jp.*B +VT.*log(A)));
    equation2 = V2-VT.*log(I2)+((VT).*log(A)) +(jp.*B) - (I2.*(V2 + VT.*log(I2)- jp.*B - VT.*log(A)));

I want to solve for the variables A and B (1024x1024) from the two equations? need guidance in coding using the two equations.

Answer 1

[Torsten]

Your equations are linear in log(A). So first solve (taking paper and pencil) for log(A) as an expression depending on B. Then insert this expression for log(A) e.g. in equation 1. You've now reduced your problem to solving one (nonlinear) equation in B. I'd suggest you solve this one element after the other for B using MATLAB's "fzero". This may take a while since you have 1024x1024 single equations to solve.

Best wishes

Torsten.

[shoba]

@Torsten

I have solved for log(A).

 log(A) = (V1-(VT.*log(I1))+(jp.*B)-(V1*I1+I1.*VT.*log(I1))- (I1.*jp.*B))./(VT.*(I1-1));

how to substitute into equation 1 via MATLAB? and use "fzero"?

[Torsten]

I get another expression for log(A) from your first equation, but however ...

You have to insert the correct expression manually into equation (2) and solve for the elements of B one element after the other using MATLAB's "fzero".

Best wishes

Torsten.

[John D'Errico]

I missed the dependence on B in I1 and I2.