Some points:
- Your rmse function is not returning any value
- You need to pass a function to the optimization function that takes only the variables that can be optimized
- Since you're optimizing a,b,c,d all the calculations related to those variables should stay in the optimization function
Taking those points in consideration you can do something like this:
x0 = [1,1,1,1]; % you can give a reasonable value here
[x,fval] = fminsearch(@(x)rmse(x,experimental_values),x0) % I', assuming experimental_values is on your workspace
% The rmse function is:
function r = rmse (x,experimental_values)
a = x(1);
b = x(2);
c = x(3);
d = x(4);
c6=1*a+4*b+1*d;
c8=1*a+6*b+1*d;
c10=1*a+8*b+1*d;
c12=1*a+10*b+1*d;
c14=1*a+12*b+1*d;
c14_1=1*a+10*b+2*c+1*d;
c15=1*a+13*b+1*d;
c16=1*a+14*b+1*d;
c16_1=1*a+12*b+2*c+1*d;
c17=1*a+15*b+1*d;
c17_1=1*a+13*b+2*c+1*d;
c18=1*a+16*b+1*d;
c18_1=1*a+14*b+2*c+1*d;
c18_2=1*a+12*b+4*c+1*d;
c18_3=1*a+10*b+6*c+1*d;
c20=1*a+18*b+1*d;
c20_1=1*a+16*b+2*c+1*d;
c20_2=1*a+14*b+4*c+1*d;
c20_4=1*a+10*b+8*c+1*d;
c22=1*a+20*b+1*d;
c22_1=1*a+18*b+2*c+1*d;
c24=1*a+22*b+1*d;
c24_1=1*a+20*b+2*c+1*d;
%%%%%%% with the 23 equations above, a column 23 x 1 is created:
CFPPi=[c6;c8;c10;c12;c14;c14_1;c15;c16;c16_1;c17;c17_1;c18;c18_1;c18_2;c18_3;c20;c20_1;c20_2;c20_4;c22;c22_1;c24;c24_1];
%%% the column above is multiplied with a matrix of 23x63 (biodiesel_composition) data base and it creates a new matrix.
prediction=CFPPi.*biodiesel_composicion;
% Lately each column of the the prediction matrix is sum to create a row of 1x69
biodisel_cfpp=sum(prediccion,1);
r = sqrt(sum((experimental_values(:)-biodisel_cfpp(:)).^2/numel(experimental_values)));
end
