code: 
  
  
  
  
  
  
  import numpy as np
  from matplotlib import pyplot as plt
  
  
  
  
  
  
  
  def 			lowercase__  (				A_		)  ->							Tuple:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         return 1 / (1 + np.exp(-1 * x		))
  
  
  
  class 							_A :
      """simple docstring"""
  
      def __init__(							self			:    Tuple   ,    __SCREAMING_SNAKE_CASE			:    Any   ,    __SCREAMING_SNAKE_CASE			:    List[Any]=None   ,    __SCREAMING_SNAKE_CASE			:    List[str]=None   ,    __SCREAMING_SNAKE_CASE			:    List[Any]=False			)			->       Optional[Any]:
             __UpperCAmelCase    							=units
             __UpperCAmelCase    							=None
             __UpperCAmelCase    							=None
             __UpperCAmelCase    							=activation
             if learning_rate is None:
                    __UpperCAmelCase    							=0.3
             __UpperCAmelCase    							=learning_rate
             __UpperCAmelCase    							=is_input_layer
  
  
  
      def _a       (							self			:    List[str]   ,    __SCREAMING_SNAKE_CASE			:    int			)			->       Optional[int]:
             __UpperCAmelCase    							=np.asmatrix(np.random.normal(0   ,    0.5   ,    (self.units, back_units)			)			)
             __UpperCAmelCase    							=np.asmatrix(np.random.normal(0   ,    0.5   ,    self.units			)			).T
             if self.activation is None:
                    __UpperCAmelCase    							=sigmoid
  
  
  
      def _a       (							self			:    Dict			)			->       Union[str, Any]:
             # activation function may be sigmoid or linear
             if self.activation == sigmoid:
                    __UpperCAmelCase    							=np.dot(self.output   ,    (1 - self.output).T			)
                    __UpperCAmelCase    							=np.diag(np.diag(__SCREAMING_SNAKE_CASE			)			)
             else:
                    __UpperCAmelCase    							=1
             return gradient_activation
  
  
  
      def _a       (							self			:    Any   ,    __SCREAMING_SNAKE_CASE			:    str			)			->       List[str]:
             __UpperCAmelCase    							=xdata
             if self.is_input_layer:
                    # input layer
                    __UpperCAmelCase    							=xdata
                    __UpperCAmelCase    							=xdata
                    return xdata
             else:
                    __UpperCAmelCase    							=np.dot(self.weight   ,    self.xdata			) - self.bias
                    __UpperCAmelCase    							=self.activation(self.wx_plus_b			)
                    return self.output
  
  
  
      def _a       (							self			:    int   ,    __SCREAMING_SNAKE_CASE			:    Optional[Any]			)			->       Optional[Any]:
             __UpperCAmelCase    							=self.cal_gradient()  # i * i 维
             __UpperCAmelCase    							=np.asmatrix(np.dot(gradient.T   ,    __SCREAMING_SNAKE_CASE			)			)
  
             __UpperCAmelCase    							=np.asmatrix(self.xdata			)
             __UpperCAmelCase    							=-1
             __UpperCAmelCase    							=self.weight
  
             __UpperCAmelCase    							=np.dot(gradient.T   ,    self._gradient_weight.T			)
             __UpperCAmelCase    							=gradient * self._gradient_bias
             __UpperCAmelCase    							=np.dot(__SCREAMING_SNAKE_CASE   ,    self._gradient_x			).T
             # upgrade: the Negative gradient direction
             __UpperCAmelCase    							=self.weight - self.learn_rate * self.gradient_weight
             __UpperCAmelCase    							=self.bias - self.learn_rate * self.gradient_bias.T
             # updates the weights and bias according to learning rate (0.3 if undefined)
             return self.gradient
  
  
  
  
  class 							_A :
      """simple docstring"""
  
      def __init__(							self			:    Union[str, Any]			)			->       Any:
             __UpperCAmelCase    							=[]
             __UpperCAmelCase    							=[]
             __UpperCAmelCase    							=plt.figure()
             __UpperCAmelCase    							=self.fig_loss.add_subplot(1   ,    1   ,    1			)
  
  
  
      def _a       (							self			:    List[Any]   ,    __SCREAMING_SNAKE_CASE			:    List[str]			)			->       Optional[Any]:
             self.layers.append(__SCREAMING_SNAKE_CASE			)
  
  
  
      def _a       (							self			:    Tuple			)			->       List[str]:
             for i, layer in enumerate(self.layers[:]			):
                    if i < 1:
                           __UpperCAmelCase    							=True
                    else:
                           layer.initializer(self.layers[i - 1].units			)
  
  
  
      def _a       (							self			:    Tuple			)			->       List[str]:
             for i, layer in enumerate(self.layers[:]			):
                    print(f'''------- layer {i} -------'''			)
                    print("""weight.shape """   ,    np.shape(layer.weight			)			)
                    print("""bias.shape """   ,    np.shape(layer.bias			)			)
  
  
  
      def _a       (							self			:    int   ,    __SCREAMING_SNAKE_CASE			:    Any   ,    __SCREAMING_SNAKE_CASE			:    str   ,    __SCREAMING_SNAKE_CASE			:    Union[str, Any]   ,    __SCREAMING_SNAKE_CASE			:    List[str]			)			->       Union[str, Any]:
             __UpperCAmelCase    							=train_round
             __UpperCAmelCase    							=accuracy
  
             self.ax_loss.hlines(self.accuracy   ,    0   ,    self.train_round * 1.1			)
  
             __UpperCAmelCase    							=np.shape(__SCREAMING_SNAKE_CASE			)
             for _ in range(__SCREAMING_SNAKE_CASE			):
                    __UpperCAmelCase    							=0
                    for row in range(x_shape[0]			):
                           __UpperCAmelCase    							=np.asmatrix(xdata[row, :]			).T
                           __UpperCAmelCase    							=np.asmatrix(ydata[row, :]			).T
  
                           # forward propagation
                           for layer in self.layers:
                                  __UpperCAmelCase    							=layer.forward_propagation(_xdata			)
  
                           __UpperCAmelCase							,   __UpperCAmelCase    							=self.cal_loss(_ydata   ,    _xdata			)
                           __UpperCAmelCase    							=all_loss + loss
  
                           # back propagation: the input_layer does not upgrade
                           for layer in self.layers[:0:-1]:
                                  __UpperCAmelCase    							=layer.back_propagation(__SCREAMING_SNAKE_CASE			)
  
                    __UpperCAmelCase    							=all_loss / x_shape[0]
                    self.train_mse.append(__SCREAMING_SNAKE_CASE			)
  
                    self.plot_loss()
  
                    if mse < self.accuracy:
                           print("""----达到精度----"""			)
                           return mse
             return None
  
  
  
      def _a       (							self			:    Any   ,    __SCREAMING_SNAKE_CASE			:    Tuple   ,    __SCREAMING_SNAKE_CASE			:    List[Any]			)			->       int:
             __UpperCAmelCase    							=np.sum(np.power((ydata - ydata_)   ,    2			)			)
             __UpperCAmelCase    							=2 * (ydata_ - ydata)
             # vector (shape is the same as _ydata.shape)
             return self.loss, self.loss_gradient
  
  
  
      def _a       (							self			:    Optional[int]			)			->       Tuple:
             if self.ax_loss.lines:
                    self.ax_loss.lines.remove(self.ax_loss.lines[0]			)
             self.ax_loss.plot(self.train_mse   ,    """r-"""			)
             plt.ion()
             plt.xlabel("""step"""			)
             plt.ylabel("""loss"""			)
             plt.show()
             plt.pause(0.1			)
  
  
  
  
  
  
  
  def 			lowercase__  (				)  ->							str:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=np.random.randn(10     ,			10		)
         __UpperCAmelCase    							=np.asarray(
             [
                 [0.8, 0.4],
                 [0.4, 0.3],
                 [0.3_4, 0.4_5],
                 [0.6_7, 0.3_2],
                 [0.8_8, 0.6_7],
                 [0.7_8, 0.7_7],
                 [0.5_5, 0.6_6],
                 [0.5_5, 0.4_3],
                 [0.5_4, 0.1],
                 [0.1, 0.5],
             ]		)
         __UpperCAmelCase    							=BPNN()
         for i in (10, 20, 30, 2):
                model.add_layer(DenseLayer(A_		)		)
         model.build()
         model.summary()
         model.train(xdata=A_     ,			ydata=A_     ,			train_round=100     ,			accuracy=0.0_1		)
  
  
  if __name__ == "__main__":
     example()
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
  from numpy import divide, inta, multiply, ravel, sort, zeros_like
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	int     ,			A_:	Any=3		)  ->							Dict:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=int(mask / 2		)
         # copy image size
         __UpperCAmelCase    							=zeros_like(A_		)
         for i in range(A_     ,			gray_img.shape[0] - bd		):
                for j in range(A_     ,			gray_img.shape[1] - bd		):
                       # get mask according with mask
                       __UpperCAmelCase    							=ravel(gray_img[i - bd : i + bd + 1, j - bd : j + bd + 1]		)
                       # calculate mask median
                       __UpperCAmelCase    							=sort(A_		)[inta(divide((multiply(A_     ,			A_		))     ,			2		) + 1		)]
                       __UpperCAmelCase    							=median
         return median_img
  
  
  if __name__ == "__main__":
     # read original image
     __A  							=  imread("../image_data/lena.jpg")
     # turn image in gray scale value
     __A  							=  cvtColor(img, COLOR_BGR2GRAY)
  
     # get values with two different mask size
     __A  							=  median_filter(gray, 3)
     __A  							=  median_filter(gray, 5)
  
     # show result images
     imshow("median filter with 3x3 mask", medianaxa)
     imshow("median filter with 5x5 mask", medianaxa)
     waitKey(0)
  
  
  
  
  