UPDATE2: A better title (now that I understand the problem) would be: What is the proper syntax for input in scipy optimize.fmin?
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'.
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.
A brief outline of what this code is trying to do:
- Given data set "data" composed of individual observations "r"
- Estimate a value of parameter "m" which is most likely to have given rise to "data"
- For a given m, calculate the probability p(r|m) for observing each "r" in "data"
- For a given m, calculate the probability P(m|data) that "m" generated the data.
- Define a helper function for use with optimize.fmin.
- Use SciPy optimize.fmin to determine the m for which helper(m|data) is maximized.
The error I get when I run this code is: ValueError: zero-size array to reduction operation maximum which has no identity
Here is a runnable snippet of code which generates the error on my machine.
#!/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()
The error itself: ValueError: zero-size array to reduction operation maximum which has no identity
The traceback is provided below.
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
--> 178 __builtin__.execfile(filename, *where)
/Users/deyler/bin/MSS-likelihood-minimal.py in <module>()
43 print fmin_result
44
---> 45 if __name__ == "__main__" : main()
/Users/deyler/bin/MSS-likelihood-minimal.py in main()
40
41
---> 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
--> 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]]
--> 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
--> 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):
---> 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):
---> 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
-> 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:
-> 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,
---> 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
datais empty. Unfortunately, we can't tell wheredatais coming from. Also, your error message does not match your code. When stripping down or simplifying code, please do your best to construct a minimal, runnable example that demonstrates your posted error when you run it. If you can't do that, please at least make it consistent with the error message.datais explicitly defined. Ifdatalooks empty, then I am doing something wrong with my inputs to the optimizer.