Using optimisation function "fminunc" for nth number of time

I aim trying to optimise some functions at a goal. The have common expressions but the constant value changes on every instsance. I tried using for loop, but the code give same output everytime.

clc
clear all
x0 = [1;1;1];

freq=xlsread('data.xlsx', 'Sheet1', 'A1:A3026');
T1 =xlsread('data.xlsx', 'Sheet1', 'B1:B3026');
T2=xlsread('data.xlsx', 'Sheet1', 'C1:C3026');
Y = [T1 T2];
n = 1:15;
for n = 1:15

objfun = @(x)objectiveFcn(x,Y,freq,n);


% options = optimoptions("fminunc","Display","iter","PlotFcn",...
    % ["optimplotfunccount","optimplotfval","optimplotfirstorderopt"]);


[solution,objectiveValue] = fminunc(objfun,x0);


% Clear variables
% clearvars objfun options
solution
end 

% objectiveValue
% solution

function f = objectiveFcn(x,Y,freq,n)



for n= 1:15

% f= cell(1,3);
f = (Y(n,1) - real(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2 + ...
    (Y(n,2) - imag(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2;
   

end

end

[Torsten]

I cannot make sense of your code. Maybe you could try again to state your problem in a mathematical manner.

[OLUWAFEMI AKINMOLAYAN]

I am trying to minimise the function "f"' using three parameters. However the function "f" is nth number of functions. Hence, i should have nth number of parameters x(n,3) after optimsation. I only chose n to be 15 as an example.

I believe i have to find a way to index each objective function with its nth value in other to find solution assign to each index. but dont know how?

Answer 1

[Walter Roberson]

Do not use a for loop inside the objective. Each iteration of the for loop, you are overwriting all of f so the result is the same as if you had done only the final iteration of the loop.

Instead, have the for loop be outside and have the call to the function pass in the "current" value of the parameter to the objective function; see http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[OLUWAFEMI AKINMOLAYAN]

do you think this works?

clc
clear all
x0 = [1;1;1];

freq=xlsread('data.xlsx', 'Sheet1', 'A1:A3026');
T1 =xlsread('data.xlsx', 'Sheet1', 'B1:B3026');
T2=xlsread('data.xlsx', 'Sheet1', 'C1:C3026');
Y = [T1 T2];
n = 1:15;

for n = 1 :15
a1= Y(n,1);
a2= Y(n,2);
b= freq(n);



objfun = @(x)objectiveFcn(x,a1,a2,b);

[solution,objectiveValue] = fminunc(objfun,x0);

solution
end 


function f = objectiveFcn(x,a1,a2,b)
f = (a1 - real(cos((1+1i*x(1))*(2*pi*b*0.002/(1600))+x(2)+x(3)))).^2 + ...
    (a2 - imag(cos((1+1i*x(1))*(2*pi*b*0.002/(1600))+x(2)+x(3)))).^2;
   
end

[Walter Roberson]

x0 = [1;1;1];

for n = 1 :15
    a1 = Y(n,1);
    a2 = Y(n,2);
    b = freq(n);
    gf(n,:) = fminunc(@(x) objectiveFcn(x,a,b), x0);
end

function f = objectiveFcn(x,a1,a2,b)
  f = (a1 - real(cos((1+1i*x(1))*(2*pi*b*0.002/(1600))+x(2)+x(3)))).^2 + ...
      (a2 - imag(cos((1+1i*x(1))*(2*pi*b*0.002/(1600))+x(2)+x(3)))).^2;
   
end

[Walter Roberson]

However you should also consider

function f = objectiveFcn(x,a1,a2,b)
  expr = cos((1+1i*x(1))*(2*pi*b*0.002/(1600))+x(2)+x(3));
  f = (a1 - real(expr)).^2 + (a2 - imag(expr)).^2; 
end

[OLUWAFEMI AKINMOLAYAN]

Thanks @Walter Roberson

Answer 2

[Matt J]

It is because the n that you pass to objectiveFcn(x,Y,freq,n) is being overwritten by n=3 inside your objective function code.

function f = objectiveFcn(x,Y,freq,n)   % n is given as input here


 for n= 1:3  %n is overwritten here 
             %(also, note that the first two iterations n=1 and n=2 don't do anything)

         f = (Y(n,1) - real(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2 + ...
             (Y(n,2) - imag(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2;
   
  end
end

[OLUWAFEMI AKINMOLAYAN]

Does that mean the for loop does nothing in the objective fn?

[Matt J]

Each iteration overwrites the current f with the value on the right-hand side. Perhaps you meant to sum the expressions in the loop like below. However, it is still not clear what you want to do with the input argument n.

function f = objectiveFcn(x,Y,freq,n)   % n is given as input here

 f=0;

 for j= 1:3  %n is overwritten here 
             %(also, note that the first two iterations n=1 and n=2 don't do anything)

         f = f + (Y(j,1) - real(cos((1+1i*x(1))*(2*pi*freq(j)*0.002/(1600))+x(2)+x(3)))).^2 + ...
                 (Y(j,2) - imag(cos((1+1i*x(1))*(2*pi*freq(j)*0.002/(1600))+x(2)+x(3)))).^2;
   
  end
end

[OLUWAFEMI AKINMOLAYAN]

I dont intend to sum the expression. The n input just serve purpose of iteration

[Walter Roberson]

If I understand correctly, you want to minimize once for freq(1), then minimize for freq(2), then for freq(3), and so on, with each minimization not affecting the rest. If that is correct then use the strategy I indicated in my Answer.

If the information about the different frequencies is required all in the same call, to do some kind of composite minimization, then what I outlined would not be appropriate.

[Matt J]

I dont intend to sum the expression. The n input just serve purpose of iteration

Then it's not clear why you have a for-loop in your objectiveFcn. Possibly, this is what you want is,

function f = objectiveFcn(x,Y,freq,n)

  f = (Y(n,1) - real(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2 + ...
      (Y(n,2) - imag(cos((1+1i*x(1))*(2*pi*freq(n)*0.002/(1600))+x(2)+x(3)))).^2;
   

end