Python / Scipy "invalid index to scalar variable"

Question

I am using the Scipy optimization module, specifically fmin_tnc and fmin_l_bfgs_b. However, I am receiving the message "IndexError: invalid index to scalar variable" when using either one.

What is the cause of this error?

And what is the meaning of this error message?

My practice code:

def f01(para):
    para1, para2 = para
    return 1+ (para1 -1)**2 + (para2 -2)**2

para0 = np.array([10, 10]) 
mybounds = [(-40,30),(-20,15)]

opt.fmin_l_bfgs_b(f01, para0,  bounds = mybounds )

Which returns:

Traceback (most recent call last):
  File "C:\Python27\mystuff\practice_optimize01.py", line 78, in <module>
    opt.fmin_l_bfgs_b(f01, para0,  bounds = mybounds )

  File "C:\Python27\lib\site-packages\scipy\optimize\lbfgsb.py", line 174, in fm
in_l_bfgs_b
**opts)

  File "C:\Python27\lib\site-packages\scipy\optimize\lbfgsb.py", line 294, in _m
 inimize_lbfgsb
    f, g = func_and_grad(x)

  File "C:\Python27\lib\site-packages\scipy\optimize\lbfgsb.py", line 249, in fu
nc_and_grad
    f = fun(x, *args)

  File "C:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 55, in _
_call__
    self.jac = fg[1]
IndexError: invalid index to scalar variable.

Python 2.7.3, 32-bit. Numpy 1.6.2. Scipy 0.11.0b1. Windows XP and Vista.

Answer 1

fmin_l_bfgs_b expects that your function returns the function value and the gradient. You return only the function value.

If you only return the function value and don't provide a gradient, then you need to set approx_grad=True so that fmin_l_bfgs_b uses a numerical approximation to it.

See the description of the options in the docstring.

From my reading of the documentation, fmin_tnc has the same pattern, and same problem in your case.