title: SciPy optimize.fmin ValueError: zero-size array to reduction operation maximum which has no identity
body: <p>UPDATE2: A better title (now that I understand the problem) would be:
  What is the proper syntax for input in scipy optimize.fmin?</p>
  
  <p>UPDATE: runnable code was requested, so the function definitions have been replaced with runnable code. Sample input data has been hard-encoded as the numpy array 'data'. </p>
  
  <p>I'm trying to optimize a function with scipy, but am really stuck, and must beg for help. A zero-length array is being passed to a method in the optimizer, and I cannot understand why, nor how to overcome this problem. </p>
  
  <p>A brief outline of what this code is trying to do:</p>
  
  <ul>
  <li>Given data set "data" composed of individual observations "r" </li>
  <li>Estimate a value of parameter "m" which is most likely to have given rise to "data"
  <ul>
  <li>For a given m, calculate the probability p(r|m) for observing each "r" in "data"</li>
  <li>For a given m, calculate the probability P(m|data) that "m" generated the data. </li>
  </ul></li>
  <li>Define a helper function for use with optimize.fmin. </li>
  <li>Use SciPy optimize.fmin to determine the m for which helper(m|data) is maximized.</li>
  </ul>
  
  <p>The error I get when I run this code is:
      ValueError: zero-size array to reduction operation maximum which has no identity</p>
  
  <p>Here is a runnable snippet of code which generates the error on my machine. </p>
  
  <pre><code>#!/usr/bin/env python2.7
  
  import numpy as np
  from scipy import optimize
  
  def p_of_r(m, r): ## this calculates p(r|m) for each datum r
      r_range = np.arange(0, r+1, 1, dtype='int')
      p_r = []
      p_r = np.array([0.0 for a in r_range])
      for x in r_range:
          if x == 0:
              p_r[x] = np.exp(-1 * m)
          else:
              total = 0.0
              for y in np.arange(0, x, 1, dtype='int'):
                  current = ( p_r[y] ) / (x - y  + 1)
                  total = current + total
              p_r[x] = ( m / x ) * total
      return p_r
  
  def likelihood_function(m, *data): # calculates P(m|data) using entire data set
      p_r = p_of_r(m, np.ma.max(data))
      p_r_m = np.array([p_r[y] for y in data])
      bigP = np.prod(p_r_m)
      return bigP
  
  def main():
      data = np.array( [10, 10, 7, 19, 9, 23, 26, 7, 164, 16 ] )
      median_r = np.median(data)
      def Drake(m):
          return median_r / m - np.log(m)
      m_initial = optimize.broyden1(Drake, 1) 
      def helper(x, *args):
          helper_value = -1 * likelihood_function(x, *args)
          return helper_value 
  
      # here is the actual optimize.fmin    
      fmin_result = optimize.fmin(helper, x0=[m_initial], args=data)
      print fmin_result
  
  #    for i in np.arange(0.0, 25.0, 0.1):
  #        print i, helper(i, data)
  if __name__ == "__main__" : main()
  </code></pre>
  
  <p>The error itself: 
  ValueError: zero-size array to reduction operation maximum which has no identity</p>
  
  <p>The traceback is provided below. </p>
  
  <pre><code>ValueError                                Traceback (most recent call last)
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/IPython/utils/py3compat.pyc in execfile(fname, *where)
      176             else:
      177                 filename = fname
  --&gt; 178             __builtin__.execfile(filename, *where)
  
  /Users/deyler/bin/MSS-likelihood-minimal.py in &lt;module&gt;()
       43     print fmin_result
       44 
  ---&gt; 45 if __name__ == "__main__" : main()
  
  /Users/deyler/bin/MSS-likelihood-minimal.py in main()
       40 
       41 
  ---&gt; 42     fmin_result = optimize.fmin(helper, x0=[m_initial], args=data)
       43     print fmin_result
       44 
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in fmin(func, x0, args, xtol, ftol, maxiter, maxfun, full_output, disp, retall, callback)
      371             'return_all': retall}
      372 
  --&gt; 373     res = _minimize_neldermead(func, x0, args, callback=callback, **opts)
      374     if full_output:
      375         retlist = res['x'], res['fun'], res['nit'], res['nfev'], res['status']
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in _minimize_neldermead(func, x0, args, callback, xtol, ftol, maxiter, maxfev, disp, return_all, **unknown_options)
      436     if retall:
      437         allvecs = [sim[0]]
  --&gt; 438     fsim[0] = func(x0)
      439     nonzdelt = 0.05
      440     zdelt = 0.00025
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in function_wrapper(*wrapper_args)
      279     def function_wrapper(*wrapper_args):
      280         ncalls[0] += 1
  --&gt; 281         return function(*(wrapper_args + args))
      282 
      283     return ncalls, function_wrapper
  
  /Users/deyler/bin/MSS-likelihood-minimal.py in helper(x, *args)
       33     m_initial = optimize.broyden1(Drake, 1)
       34     def helper(x, *args):
  ---&gt; 35         helper_value = -1 * likelihood_function(x, *args)
       36         return helper_value
       37 
  
  /Users/deyler/bin/MSS-likelihood-minimal.py in likelihood_function(m, *data)
       21 
       22 def likelihood_function(m, *data):
  ---&gt; 23     p_r = p_of_r(m, np.ma.max(data))
       24     p_r_m = np.array([p_r[y] for y in data])
       25     bigP = np.prod(p_r_m)
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/ma/core.pyc in max(obj, axis, out, fill_value)
     5899         # If obj doesn't have a max method,
     5900         # ...or if the method doesn't accept a fill_value argument
  -&gt; 5901         return asanyarray(obj).max(axis=axis, fill_value=fill_value, out=out)
     5902 max.__doc__ = MaskedArray.max.__doc__
     5903 
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/ma/core.pyc in max(self, axis, out, fill_value)
     5159         # No explicit output
     5160         if out is None:
  -&gt; 5161             result = self.filled(fill_value).max(axis=axis, out=out).view(type(self))
     5162             if result.ndim:
     5163                 # Set the mask
  
  /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/core/_methods.pyc in _amax(a, axis, out, keepdims)
        8 def _amax(a, axis=None, out=None, keepdims=False):
        9     return um.maximum.reduce(a, axis=axis,
  ---&gt; 10                             out=out, keepdims=keepdims)
       11 
       12 def _amin(a, axis=None, out=None, keepdims=False):
  
  ValueError: zero-size array to reduction operation maximum which has no identity
  </code></pre>