Writing a function, when each argument is dependent on previous argument while the first argument is known

Hello,

I am new to MATLAB and not able to troubleshoot my attached code. I initially received the error “conversion to cell from function_handle is not possible” and I believe I managed to resolve that error. Below is part of the script:

% Main optimization and parameter fitting starts here:

% Boundary conditions for parameters C (constant(1)) and D (constant(2)):
lb = [0.000000000001,0.05]; ub = [1,50]; constant0 = [0.0000000031,15];

i_dt=zeros(n,length(S)); % S dimensions are (2,145)
i_dt(:,2:length(S))=dt.*hg_new;

L=zeros(n,length(S)); % Height of elements
L(:,1)=Linitial; % Height of elements for day zero

for jj=1:length(S)
   if jj==1
       continue
   end
       
    for j=1:n % n is 101 (previously defined...)
    
     L = @(constant,i_dt) L(j,jj-1)-(i_dt.*constant(1).*((L(j,jj-1)./hs)-1)^constant(2)); %i_dt is (101,145)
     
    end
   height_pred = @(constant,i_dt) sum(L(jj)); %heigh_pred(1) is known and previously defined
      
end


options = optimoptions('lsqcurvefit','FinDiffType','central',...
    'TolFun',1e-10);
constant = lsqcurvefit(height_pred,constant0,i_dt,height_meas,lb,ub,options);

Currently I receive error “Index exceeds matrix dimensions.” for below line:

L = @(constant,i_dt) L(j,jj-1)-(i_dt.*constant(1).*((L(j,jj-1)./hs)-1)^constant(2));

My guess is that I have not defined the function properly and thus MATLAB cannot proceed.

The main script is much longer and I only copied the problematic section, so please let me know if more of the main script is needed. As you can see, I am trying to fit two parameters into an equation using lsqcurvefit function. The functionheight_pred is sum of L function. In L function, each argument is relying on the value from the previous argument while the first argument is known.

I am stuck at getting this code work or at least knowing where the problem is coming from. Any help is much appreciated.

Answer 1

[Steven Lord]

You start off with L being a matrix but then you turn it into an anonymous function. Which should it be?

If it should be a matrix, have the line where you currently make it an anonymous function instead compute what the next iteration's L matrix should be and assign to it.

L = 1;
while L < 100
    L = 2*L; % Not L = @(something) 2*L;
end

If it should always be an anonymous function you probably want to rename your L matrix.

[Neelufar Aghazamani]

Thank you very much Steven Lord for your quick reply.

L is a 101 by 145 matrix that only its first column is known. The rest of columns are unknown and can be calculated using the formula:

L = @(constant,i_dt) L(j,jj-1)-(i_dt.*constant(1).*((L(j,jj-1)./hs)-1)^constant(2)); %i_dt is (101,145)

As you see, value of argument L(j,jj) depends on the value of argument L(j,jj-1).

However, to calculate L values (using above formula, I need to optimize two constants (constant(1) and constant(2)). That is why I wrote L in a function, to be able to use lsqcurvefit.

I am confused how to code this.