请帮我按要求编写代码 ''' Parameters: x is a two dimensional numpy array. Returns: a two dimensioal array representing the element-wise sigmoid of x. '''

以下是按照要求编写的代码：

import numpy as np

def sigmoid(x):
    """
    Parameters:
    x: a two dimensional numpy array
    
    Returns:
    a two dimensional array representing the element-wise sigmoid of x.
    """
    return 1 / (1 + np.exp(-x))

该函数接收一个二维 numpy 数组 `x` 作为参数，并返回一个二维数组，表示 `x` 中每个元素的 sigmoid 值。sigmoid 函数的公式为：

$$
sigmoid(x) = \frac{1}{1 + e^{-x}}
$$

我们可以使用 numpy 中的 `exp` 函数来计算 $e^{-x}$，然后将其加上 1，并取倒数即可得到 sigmoid 值。

相关问题

def value(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is a two dimensional numpy array. Returns: a two dimensioal array representing the element-wise sigmoid of x. ''' #### write your code below ####

根据这段代码的要求，我们需要在 `value` 方法中编写代码，实现对输入的二维 numpy 数组 `x` 进行 sigmoid 转换，并返回结果。以下是按照要求编写的代码：

import numpy as np

class MyModel:
    def value(self, x: np.ndarray) -> np.ndarray:
        """
        Parameters:
        x: a two dimensional numpy array
        
        Returns:
        a two dimensional array representing the element-wise sigmoid of x.
        """
        return 1 / (1 + np.exp(-x))

该代码定义了一个名为 `MyModel` 的类，其中包含了一个名为 `value` 的方法，它接收一个二维 numpy 数组 `x` 作为参数，并返回一个二维数组，表示 `x` 中每个元素的 sigmoid 值。

在方法中，我们使用了 numpy 中的 `exp` 函数来计算 $e^{-x}$，然后将其加上 1，并取倒数即可得到 sigmoid 值。

class Softmax(Activation): ''' softmax nonlinear function. ''' def __init__(self): ''' There are no parameters in softmax function. ''' super(Softmax, self).__init__() def value(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is the input to the softmax function. x is a two dimensional numpy array. Each row is the input to the softmax function Returns: output of the softmax function. The returned value is with the same shape as that of x. ''' #### write your code below #### return def derivative(self, x: np.ndarray) -> np.ndarray: ''' Parameters: x is the input to the softmax function. x is a two dimensional numpy array. Returns: a two dimensional array representing the derivative of softmax function w.r.t. x. ''' #### write your code below ####

下面是对 `Softmax` 激活函数的实现，你可以将其加入到代码中：

class Softmax(Activation):
    '''
    softmax nonlinear function.
    '''
    def __init__(self):
        '''
        There are no parameters in softmax function.
        '''
        super(Softmax, self).__init__()

    def value(self, x: np.ndarray) -> np.ndarray:
        '''
        Parameters:
          x is the input to the softmax function. x is a two dimensional numpy array. Each row is the input to the softmax function
        Returns:
          output of the softmax function. The returned value is with the same shape as that of x.
        '''
        exp_scores = np.exp(x)
        return exp_scores / np.sum(exp_scores, axis=1, keepdims=True)

    def derivative(self, x: np.ndarray) -> np.ndarray:
        '''
        Parameters:
          x is the input to the softmax function. x is a two dimensional numpy array.
        Returns:
          a two dimensional array representing the derivative of softmax function w.r.t. x.
        '''
        softmax_output = self.value(x)
        return softmax_output * (1 - softmax_output)