python - python计算梯度错误？

Question

我正在尝试遵循此处的类(class) http://cs231n.github.io/optimization-1/ ，在用有限差分数值计算梯度部分中，他们提供了一个代码片段，用于计算给定函数和数组的梯度。我尝试使用我自己的函数和 numpy 数组作为输入来运行它，但出现以下错误:

ValueError                                Traceback (most recent call last)
<ipython-input-18-31c1f1d6169c> in <module>()
      2     return a
      3 
----> 4 eval_numerical_gradient(f,np.array([1,2,3,4,5]))

<ipython-input-12-d6bea4220895> in eval_numerical_gradient(f, x)
     28     print(x[ix])
     29     # compute the partial derivative
---> 30     grad[ix] = (fxh - fx) / h # the slope
     31     it.iternext() # step to next dimension
     32 

ValueError: setting an array element with a sequence.

我知道错误是因为它无法为 grad[ix] 分配一个序列，我也尝试使用列数组并得到相同的错误。

这是代码:

def eval_numerical_gradient(f, x):
  """ 
  a naive implementation of numerical gradient of f at x 
  - f should be a function that takes a single argument
  - x is the point (numpy array) to evaluate the gradient at
  """ 

  fx = f(x) # evaluate function value at original point
  print(x)
  print(fx)
  grad = np.zeros(x.shape)
  h = 0.00001

  # iterate over all indexes in x
  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
  while not it.finished:
    print(it)
    # evaluate function at x+h
    ix = it.multi_index
    print(ix)
    old_value = x[ix]
    print(old_value)
    x[ix] = old_value + h # increment by h
    print(x)
    fxh = f(x) # evalute f(x + h)
    print(fxh)
    x[ix] = old_value # restore to previous value (very important!)
    print(x[ix])
    # compute the partial derivative
    grad[ix] = (fxh - fx) / h # the slope
    it.iternext() # step to next dimension

  return grad

我的问题是:我输入的 numpy 数组(行和列)是否错误？有人可以解释为什么会发生这种情况吗？

示例输入:

def f(a):
    return a

eval_numerical_gradient(f,np.array([[1],[2],[3]]))

和

def f(a):
    return a

eval_numerical_gradient(f,np.array([1,2,3]))

Answer 1

我建议对 eval_numerical_gradient(f, x) 进行以下修复:

• 第 25 行:将 fxh = f(x) 替换为 fxh = f(x[ix])
• 第 30 行:将 grad[ix] = (fxh - fx)/h 替换为 grad[ix] = (fxh - fx[ix])/h

并使用 float 条目创建输入矩阵，例如，

eval_numerical_gradient(f,np.array([[1],[2],[3]], dtype=np.float))