Why am I getting complex values from the following anonymous function?

I'm trying to build a function to be used with lsqnonlin(), it should pull data from 3 arrays of doubles and output a value. When I call it though, I get a 10x10 complex double.

Here's my function:

fun = @(consumption1,leisure1,pollution1)

(((leisure1.^-2.5).*((.5*consumption1.^-1.5)+(.5*imag(pollution1.^1.5))))/

((consumption1.^-2.5).*((.5*leisure1.^-1.5)+(.5*imag(pollution1.^1.5)))))

and here's the result of the first 10 values:

Columns 1 through 4

   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i

Columns 5 through 8

   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i

Columns 9 through 10

-0.0000 + 0.2777i   0.0000 + 0.0000i
-0.0000 - 0.0000i   0.0000 + 0.0000i
 0.4205 + 0.0000i   0.0000 + 0.0000i
-0.0000 - 0.0000i   0.0000 + 0.0000i
-0.0000 + 0.0198i   0.0000 + 0.0000i
-0.0000 - 0.0000i   0.0000 + 0.0000i
 0.0000 - 0.0000i   0.0000 + 0.0000i
 0.0000 - 0.0000i   0.0000 + 0.0000i
 1.2943 + 0.0001i   0.0000 + 0.0000i
 0.0000 - 0.0000i   0.0000 + 0.0000i

Any ideas or insight would be greatly appreciated, I was previously running into the same problem when I would do pollution1.^1.5, which is why I added(imag(pollution1.^1.5) which gave the correct value.

Answer 1

[Star Strider]

My guess is that one of your variables has at least one negative number. Raising them to a non-integer power produces a complex value. Note that not all of them are complex, but MATLAB produces complex representation for them all.

Example:

x = [1 2 3 -4 5]';
y = x.^-1.5

y =

              1 +          0i
        0.35355 +          0i
        0.19245 +          0i
              0 +      0.125i
       0.089443 +          0i