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基于Pythonfminunc的替代方法-创新互联

最近闲着没事，想把coursera上斯坦福ML课程里面的练习，用Python来实现一下，一是加深ML的基础，二是熟悉一下numpy，matplotlib，scipy这些库。

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在EX2中，优化theta使用了matlab里面的fminunc函数，不知道Python里面如何实现。搜索之后，发现stackflow上有人提到用scipy库里面的minimize函数来替代。我尝试直接调用我的costfunction和grad，程序报错，提示(3,)和(100,1)dim维度不等，gradient vector不对之类的，试了N多次后，终于发现问题何在。。

首先来看看使用np.info(minimize)查看函数的介绍，传入的参数有：

fun : callable
 The objective function to be minimized.
 
  ``fun(x, *args) -> float``
 
 where x is an 1-D array with shape (n,) and `args`
 is a tuple of the fixed parameters needed to completely
 specify the function.
x0 : ndarray, shape (n,)
 Initial guess. Array of real elements of size (n,),
 where 'n' is the number of independent variables.
args : tuple, optional
 Extra arguments passed to the objective function and its
 derivatives (`fun`, `jac` and `hess` functions).
method : str or callable, optional
 Type of solver. Should be one of
 
  - 'Nelder-Mead' :ref:`(see here) `
  - 'Powell'  :ref:`(see here) `
  - 'CG'   :ref:`(see here) `
  - 'BFGS'  :ref:`(see here) `
  - 'Newton-CG' :ref:`(see here) `
  - 'L-BFGS-B' :ref:`(see here) `
  - 'TNC'   :ref:`(see here) `
  - 'COBYLA'  :ref:`(see here) `
  - 'SLSQP'  :ref:`(see here) `
  - 'trust-constr':ref:`(see here) `
  - 'dogleg'  :ref:`(see here) `
  - 'trust-ncg' :ref:`(see here) `
  - 'trust-exact' :ref:`(see here) `
  - 'trust-krylov' :ref:`(see here) `
  - custom - a callable object (added in version 0.14.0),
   see below for description.
 
 If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
 depending if the problem has constraints or bounds.
jac : {callable, '2-point', '3-point', 'cs', bool}, optional
 Method for computing the gradient vector. Only for CG, BFGS,
 Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,
 trust-exact and trust-constr. If it is a callable, it should be a
 function that returns the gradient vector:
 
  ``jac(x, *args) -> array_like, shape (n,)``
 
 where x is an array with shape (n,) and `args` is a tuple with
 the fixed parameters. Alternatively, the keywords
 {'2-point', '3-point', 'cs'} select a finite
 difference scheme for numerical estimation of the gradient. Options
 '3-point' and 'cs' are available only to 'trust-constr'.
 If `jac` is a Boolean and is True, `fun` is assumed to return the
 gradient along with the objective function. If False, the gradient
 will be estimated using '2-point' finite difference estimation.

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