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S1=[20 32 44 56 68 80 92 104 116 128 140 152 164 176 188 200];

P=[16.82 26.93 37.01 47.1 57.21 67.32 77.41 87.5 97.54 107.7 117.8 127.9 138 148 158.2 168.3];

X = [0.119 0.191 0.262 0.334 0.405 0.477 0.548 0.620 0.691 0.763 0.835 0.906 0.978 1.049 1.120 1.192];

S = [2.3734 3.6058 5.0256 6.6854 8.6413 10.978 13.897 17.396 21.971 28.040 36.475 49.065 69.736 110.20 224.69 2779.1];



objective=@(x)((1250*x(3)*S(a)-(S(a)+x(2))*(P(a)+x(1)))/(1250*(S(a)+x(2))*(P(a)+x(1)))-x(5))^2+((x(2)*(P(a)^2+x(1)*P(a)))/(1250*x(4)*X(a)*x(3)-P(a)^2-x(1)*P(a))-S(a))^2+(74000/3*((X(a)*x(3)*S(a))/S1(a)*(S(a)+x(2)))-P(a))^2



%x0 = [Kp Ks mu.m Yp mu.d]

x0=[7.347705469 14.88611028 1.19747242 16.65696429 6.01E-03];



x=fminunc(objective,x0);

disp(x)

The code above is used for optimisizing the objective function, so that all the unknown values of the parameters can be found. As you may have seen, the objective function consists of 4 variables (S1, S, P, X), each having 16 data entities. My question is: how to create an objective function, so that all the data entities are utilised?
The final objective function has to be the sum of the objective function (shown above) with a=1:16. Any ideas?

Make the following changes to your code:

1. Replace, e.g. all S(a) variables with S to use the whole vector. Do the same for each of your four variables.




2. Convert all 'scalar' operations in your objective function to 'elementwise' ones, i.e. replace ^, * and / with .^, .* and ./. This produces 16 values, one for each index from 1 to 16 (i.e. what was previously referred to by a).




3. wrap the resulting expression into a sum() function to sum the 16 results into a final value




4. Use your optimiser as normal.

Resulting code:

S1 = [20 32 44 56 68 80 92 104 116 128 140 152 164 176 188 200];

P  = [16.82 26.93 37.01 47.1 57.21 67.32 77.41 87.5 97.54 107.7 117.8 127.9 138 148 158.2 168.3];

X  = [0.119 0.191 0.262 0.334 0.405 0.477 0.548 0.620 0.691 0.763 0.835 0.906 0.978 1.049 1.120 1.192];

S  = [2.3734 3.6058 5.0256 6.6854 8.6413 10.978 13.897 17.396 21.971 28.040 36.475 49.065 69.736 110.20 224.69 2779.1];



objective = @(x) sum( ((1250.*x(3).*S-(S+x(2)).*(P+x(1)))./(1250.*(S+x(2)).*(P+x(1)))-x(5)).^2+((x(2).*(P.^2+x(1).*P))./(1250.*x(4).*X.*x(3)-P.^2-x(1).*P)-S).^2+(74000./3.*((X.*x(3).*S)./S1.*(S+x(2)))-P).^2 );



%x0 = [Kp Ks mu.m Yp mu.d]

x0 = [7.347705469 14.88611028 1.19747242 16.65696429 6.01E-03];

x  = fminunc(objective,x0);

disp(x)

Note that you can make this code a lot clearer to read for humans; I just made the "direct" changes that illustrate conversion from your scalar expression to the desired vectorised one.