Matlab: Nonlinear Eq: error - matlab

Question

I have the code from a previous question, however, this one is similar, just more equations added. However, I get an error and I'm not sure how to fix it.
Link to my previous question: Matlab: Nonlinear equation solver
function F = fcn(x)
F=[x(6) + x(7) + x(8) + x(9) + x(10) - 2 ;
x(6)*x(1) + x(7)*x(2) + x(8)*x(3) + x(9)*x(4) + x(10)*x(5) ;
x(6)*x(1)^2 + x(7)*x(2)^2 + x(8)*x(3)^2 + x(9)*x(4)^2 + x(10)*x(5) - 2/3 ;
x(6)*x(1)^3 + x(7)*x(2)^3 + x(8)*x(3)^3 + x(9)*x(4)^3 + x(10)*x(5) ;
x(6)*x(1)^4 + x(7)*x(2)^4 + x(8)*x(3)^4 + x(9)*x(4)^4 + x(10)*x(5) -2/5 ;
x(6)*x(1)^5 + x(7)*x(2)^5 + x(8)*x(3)^5 + x(9)*x(4)^5 + x(10)*x(5) ;
x(6)*x(1)^6 + x(7)*x(2)^6 + x(8)*x(3)^6 + x(9)*x(4)^6 + x(10)*x(5) -2/7 ;
x(6)*x(1)^7 + x(7)*x(2)^7 + x(8)*x(3)^7 + x(9)*x(4)^7 + x(10)*x(5) ;
x(6)*x(1)^8 + x(7)*x(2)^8 + x(8)*x(3)^8 + x(9)*x(4)^8 + x(10)*x(5) -2/9 ;
x(6)*x(1)^9 + x(7)*x(2)^9 + x(8)*x(3)^9 + x(9)*x(4)^9 + x(10)*x(5)
];
end
clc
clear all;
format long
x0 = [0.9; 0.5; 0.1; -0.5; -0.9; 0.2; 0.4; 0.5; 0.4; 0.2]; %Guess
F0 = fcn(x0);
[x,fval]=fsolve(#fcn, x0) %solve without optimization
options = optimset('MaxFunEvals',10000, 'MaxIter', 10000); %optimization criteria
[x,fval]=fsolve(#fcn, x0, options) %solve with optimization
The error that I get are:
Error using vertcat
Dimensions of matrices being concatenated are not consistent.
Error in fcn(line 4) %This is from the function script
F=[x(6) + x(7) + x(8) + x(9) + x(10)
- 2 ;
Error in fcncall (line 7) %This is from the main script
F0 = fcn(x0);

Answer 1

This is a very subtle error I've encountered before. When creating an array literal as you are doing fcn, negative signs that are directly attached to numbers and preceded by a space, as in rows 5, 7, and 9 of your array literal, are viewed as unary operators (i.e., the - makes the number negative and does not act as a binary minus operation). Therefore, because Matlab allows the delimiting of columns to be made with spaces, the indicated rows are interpreted to have two columns; row 5 column 1 is x(6)*x(1)^4 ... x(10)*x(5), and row 5 column 2 is -2/5.
So, either put a space between the three numbers or eliminate all spaces between the minus signs. For example:
x(6)*x(1)^4 + x(7)*x(2)^4 + x(8)*x(3)^4 + x(9)*x(4)^4 + x(10)*x(5) - 2/5;
or
x(6)*x(1)^4 + x(7)*x(2)^4 + x(8)*x(3)^4 + x(9)*x(4)^4 + x(10)*x(5)-2/5;

Answer 2

That problem wasn't easy to find. Not using a blank before the minus at the end of the rows, you created a row with two elements instead of one. For a simplified example compare this:
>> [2 - 2]
ans =
0
>> [2 -2]
ans =
2 -2
>> [(2 -2)]
ans =
0
Now the corrected version of your code:
F=[x(6) + x(7) + x(8) + x(9) + x(10) - 2 ;
x(6)*x(1) + x(7)*x(2) + x(8)*x(3) + x(9)*x(4) + x(10)*x(5) ;
x(6)*x(1)^2 + x(7)*x(2)^2 + x(8)*x(3)^2 + x(9)*x(4)^2 + x(10)*x(5) - 2/3 ; ...either set a space
x(6)*x(1)^3 + x(7)*x(2)^3 + x(8)*x(3)^3 + x(9)*x(4)^3 + x(10)*x(5) ;
(x(6)*x(1)^4 + x(7)*x(2)^4 + x(8)*x(3)^4 + x(9)*x(4)^4 + x(10)*x(5) -2/5); ...or use brackets
x(6)*x(1)^5 + x(7)*x(2)^5 + x(8)*x(3)^5 + x(9)*x(4)^5 + x(10)*x(5) ; ...both fixes the problem
x(6)*x(1)^6 + x(7)*x(2)^6 + x(8)*x(3)^6 + x(9)*x(4)^6 + x(10)*x(5) - 2/7 ;
x(6)*x(1)^7 + x(7)*x(2)^7 + x(8)*x(3)^7 + x(9)*x(4)^7 + x(10)*x(5) ;
x(6)*x(1)^8 + x(7)*x(2)^8 + x(8)*x(3)^8 + x(9)*x(4)^8 + x(10)*x(5) - 2/9 ;
x(6)*x(1)^9 + x(7)*x(2)^9 + x(8)*x(3)^9 + x(9)*x(4)^9 + x(10)*x(5) ];