SciPy的optimize.fmin ValueError異常：零大小的數組還原操作的最大不具有身份

Question

UPDATE2：一個更好的標題（現在我明白這個問題）是： 哪些是SciPy的optimize.fmin輸入正確的語法？

更新：請求可運行代碼，因此函數定義已被替換爲可運行代碼。樣本輸入數據已經被硬編碼爲numpy數組'data'。

我想用scipy優化一個函數，但是我確實卡住了，並且必須求助。一個零長度的數組正在傳遞給優化器中的一個方法，我不明白爲什麼，也不知道如何解決這個問題。

的這是什麼代碼是試圖做一個簡要介紹：

• 定數據集的「數據」由單獨的意見「R」
• 估計的參數「M」，這是最可能的值已經引起了「數據」
  • 對於給定的米，計算的概率P（R | M），用於在「數據」
  • 對於給定的米觀察每個「R」，計算的概率P（米|數據）「m」生成數據。
• 定義一個輔助函數，用於optimize.fmin。
• 使用SciPy optimize.fmin確定助手（m |數據）最大化的m。

當我運行這段代碼我得到的錯誤是： ValueError異常：零大小的數組還原操作的最大不具有身份

這裏是一個代碼運行的片段產生在我的機器上的錯誤。

#!/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() 

錯誤本身： ValueError異常：零大小的數組到歸約運算最大具有

回溯下面提供沒有標識。

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 

Answer 1

正確fmin syntax是：

args: tuple, optional

Extra arguments passed to func, i.e. f(x,*args). 

fmin_result = optimize.fmin(helper, x0=[m_initial], args=(data,)) 

旁邊結果預期？

Optimization terminated successfully. 
     Current function value: -0.000000 
     Iterations: 16 
     Function evaluations: 32 
[ 5.53610656]