brent returns spurious minimum

[bjarthur]

is the following example a limitation of brent's algorithm or a bug in the code? the function to be minimized is a step, so has wonky derivatives. would be nice if it gave a reasonable answer though.

in both cases below the function is -1 for negative input and 1 for positive input. in the first case, which returns 1 as the minimum (a wrong answer), the search interval is -1:2. in the second, which works, the interval is -2:2.

julia> optimize(x->x<0 ? -1 : 1, -1, 2)
Results of Optimization Algorithm
 * Algorithm: Brent's Method
 * Search Interval: [-1.000000, 2.000000]
 * Minimizer: 2.000000e+00
 * Minimum: 1.000000e+00
 * Iterations: 36
 * Convergence: max(|x - x_upper|, |x - x_lower|) <= 2*(1.5e-08*|x|+2.2e-16): true
 * Objective Function Calls: 37

julia> optimize(x->x<0 ? -1 : 1, -2, 2)
Results of Optimization Algorithm
 * Algorithm: Brent's Method
 * Search Interval: [-2.000000, 2.000000]
 * Minimizer: -1.055728e+00
 * Minimum: -1.000000e+00
 * Iterations: 37
 * Convergence: max(|x - x_upper|, |x - x_lower|) <= 2*(1.5e-08*|x|+2.2e-16): true
 * Objective Function Calls: 38

[bjarthur]

for comparison, python gives a valid answer, albeit not within the range specified:

>>> from scipy import optimize
>>> def f(x):
...   return -1 if x<0 else 1
... 
>>> optimize.brent(f,brack=(-1,2))
-5.854101854603439
>>> optimize.brent(f,brack=(-2,2))
-8.472135811722177

but matlab does not:

>> f = @(x) sign(x)

f =

  function_handle with value:

    @(x)sign(x)

>> fminbnd(f,-1,2)

ans =

    2.0000

>> fminbnd(f,-2,2)

ans =

   -1.0557