Real valued function for positive x,y returning complex values?

I am getting this error when evaluating my function ff: "Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.467910e-279." The function isn't complex, so I am unsure why it is returning a matrix of 0+0i values. How do I fix this error?

x=[0:0.1:5];
y=[0:0.1:5];
[xx,yy]=meshgrid(x,y);
gg=10*xx*0.5+0.1*xx-10-2*yy;
figure
surf(xx,yy,gg)
xlabel('s1')
ylabel('s2')
zlabel('g(x,y)');
hold on;
q=zeros(51,51);
mesh(xx,yy,q);
ff=10*xx^0.5-3*yy^1.2 +2*yy;

Answer 1

[Geert]

Rob,

I think the problem is that on the last line of your code, i.e.,

ff=10*xx^0.5-3*yy^1.2 +2*yy;

you're taking the matrix square root of xx and not of each matrix element individually. What you probably want to do is the following:

ff=10*xx.^0.5-3*yy.^1.2 +2*yy;

( Notice the point in xx.^0.5. This is an elementwise operation, it basically will take the square root of each individual element, rather than from the entire matrix).

I wrote a little example to explain the difference between elementwise and full matrix operations:

% generate random matrix
A = rand(2,2)

% calculate 2th power of A
A^2

% observe that the same result is produced by A*A
A*A

% observe that the result is different from A.^2
A.^2

% when taking the (1/2)th power (= square root), complex numbers arise
B = A^0.5

% observe that B*B = A
B*B

The warning you get, relates to the matrix xx, which is close to singular. Remember that a matrix is singular iff it has a zero eigenvalue. The fact that xx is close to singular can be observed by having a look at its eigen values:

lambda = eig(xx);
disp(sprintf('The last and smallest eigenvalue is %d', lambda(end)))

You can observe the last (and smallest) eigenvalue is 1.6421e-142. This last eigenvalue is so small, that it renders the square root calculation of xx inaccurate.

[Rob]

Thanks Geert! I forgot all about element-wise operations.