Question

What is the problem with this code?

function F = Final_Project_2(x)
 F = [(1/x(1)) + (1/x(2))- (2/(7*x(3)));
       (x(3)+2*x(4))*(15*x(2))/((x(1)+x(2))*x(3)-0.7/x(3))-14;
       (x(3)*((0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)))/(x(3)+(0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)) -20;
       ((0.576*x(2)*x(3)/(x(1)+x(2))*x(3)) - 0.27*x(4)/x(3))-100];

And here is the workspace code:

x0 = [1; 1; 1; 1];           % Make a starting guess at the solution
options=optimset('Display','iter');   % Option to display output
[x,fval] = fsolve(@Final_Project_2,x0,options)  % Call optimizer
??? Error using ==> vertcat
CAT arguments dimensions are not consistent.

Error in ==> Final_Project_2 at 5
F = [(1/x(1)) + (1/x(2))- (2/(7*x(3)));

Error in ==> fsolve at 254
            fuser = feval(funfcn{3},x,varargin{:});

Caused by:
    Failure in initial user-supplied objective function evaluation. FSOLVE cannot
    continue.

Answer 1

Matlab fails to concatenate the following array:

F = [(1/x(1)) + (1/x(2))- (2/(7*x(3)));
       (x(3)+2*x(4))*(15*x(2))/((x(1)+x(2))*x(3)-0.7/x(3))-14;
       (x(3)*((0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)))/(x(3)+(0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)) -20;
       ((0.576*x(2)*x(3)/(x(1)+x(2))*x(3)) - 0.27*x(4)/x(3))-100];

The problem occurs in the third row where the last -20 is interpreted as a single value in a vector rather than a part of the term you are calculating. To demonstrate this, you can bracket each row of this array and have a look at the results:

x = [1 2 3 4]; % just for demonstration purpuse

[(1/x(1)) + (1/x(2))- (2/(7*x(3)));]
[       (x(3)+2*x(4))*(15*x(2))/((x(1)+x(2))*x(3)-0.7/x(3))-14;]
[       (x(3)*((0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)))/(x(3)+(0.576*x(2)/(x(1)+x(2))*x(3)) - 0.27/x(3)) - 20;]
[       ((0.576*x(2)*x(3)/(x(1)+x(2))*x(3)) - 0.27*x(4)/x(3))-100]

This results in

ans =
    1.4048

ans =
   23.6426

ans =
    0.7843  -20.0000

ans =
  -96.9040

Please note the 1×2 vector in the third row.

To solve your problem, either put more emphasis on placing spaces in your calculation (i.e., omit all spaces, or write - 20 instead of -20 in your example), or put everything that belongs to one term in parentheses.