Finding best combination matlab with formula - matlab

Question

I have a formula here:
E = T*(1-W)*U + X*W*F + S*W*C*D
Lets say T, W,S,X and D are all constants, while U, F and C are variables and F and C are related to each other.
Now my aim is to find different values of E based on different combinations of U, F and C.
For example I have values for these variables:
U = 2.02, 1, 3, 4
F = 6, 4, 3.03
C = 0.5, 0.4, 0.3
Noting that F and C are related to each other e.g. when F=6 then C=0.5 or if F=4 then C=0.4 and so on.
Can anyone help me how to execute this on matlab so that matlab will calculate the value for E for all possible combinations of variables.

Answer 1

I found a relation
F = 10*(exp(C)-1.06);
from your data. I don't know if that is consistent with your expectations. Regardless, once you choose the range of C,F, and U and the size of the steps to sample the individual variables, you can compute the phase space of your function like this:
%%%% modify me %%%%
T = 1;
W = 1;
S = 1;
X = 1;
D = 1;
%%%%%%%%%%%%%
Nstep = 10;
U = [2.02, 1, 3 , 4];
F = [6, 4, 3.03];
C = [0.5, 0.4, 0.3];
Umin = min(U);
Umax = max(U);
Cmin = min(C);
Cmax = max(C);
Fmin = min(F);
Fmax = max(F);
Ustep = (Umax-Umin)/Nstep;
Fstep = (Fmax-Fmin)/Nstep;
Cstep = (Cmax-Cmin)/Nstep;
U = [Umin:Ustep:Umax];
C = [Cmin:Cstep:Cmax];
F = [Fmin:Fstep:Fmax];
[C,F,U] = MESHGRID(C,F,U);
E = T.*(1-W).*U + X.*W.*F + S.*W.*C.*D;
If the remaining variables T, W, S, X, D are not scalars you'll need to adjust the size of the arrays holding them.

Answer 2

I'm not sure if I understood correctly your question. If you just want to loop through 3 variables with known values, where two of them are correlated, you can use for example:
U = [2.02 1 3 4];
F = [6 4 3.03];
C = [0.5 0.4 0.3];
T = 1; W = 2; S = 3; X = 4; D = 5; %example values
for j=1:size(U,2)
for i=1:size(F,2)
E = T*(1-W)*U(j) + X*W*F(i) + S*W*C(i)*D; disp (E);
end
end
Otherwise, we need probably a bit more details about the relation between F and C.

Answer 3

I think you want to do this, it is not very optimized but should be easy to understand.
U = [2.02 1 3 4];
F = [6 4 3.03];
C = [0.5 0.4 0.3];
[W, T, D, X, S] = deal(1); %Assign dummy values for now
minLength = min(min(numel(U),numel(F)),numel(C)); %As U is not the same length as F and C here
E = zeros(minLength,1);
for k = 1:minLength
E(k) = T*(1-W)*U(k) + X*W*F(k) + S*W*C(k)*D;
end
You can now find the lowest value by doing:
find(E == min(E))