UPDATE2：更好的标题（现在我理解了这个问题）是：scipy optimize.fmin中输入的正确语法是什么？
UPDATE：请求了可运行代码，因此函数定义已被可运行代码所取代。示例输入数据已硬编码为numpy数组"data"。
我正试图用scipy优化一个函数，但真的被卡住了，必须寻求帮助。一个零长度数组被传递给优化器中的一个方法，我不明白为什么，也不明白如何克服这个问题。
这个代码尝试做什么的简要概述：
- 给定的数据集"数据"由单个观测值"r"组成
- 估计最有可能产生"数据"的参数"m"的值
- 对于给定的m，计算观察"数据"中每个"r"的概率p（r|m）
- 对于给定的m，计算"m"生成数据的概率P（m|data）
- 定义一个用于optimize.fmin的辅助函数
- 使用SciPy optimize.fmin来确定帮助对象（m|data）最大化的m
运行此代码时出现的错误为：ValueError：零大小数组到没有标识的缩减操作最大值
下面是一段可运行的代码片段，它在我的机器上生成了错误。
#!/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()
错误本身：ValueError：零大小数组到没有标识的缩减操作最大值
下文提供了回溯。
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
正确的fmin语法是：
args:tuple，可选
Extra arguments passed to func, i.e. f(x,*args).
fmin_result = optimize.fmin(helper, x0=[m_initial], args=(data,))
预计会有下一个结果吗？
Optimization terminated successfully.
Current function value: -0.000000
Iterations: 16
Function evaluations: 32
[ 5.53610656]