code: 
  
  
  """simple docstring"""
  import numpy as np
  from matplotlib import pyplot as plt
  
  def 							_snake_case			(      __snake_case       :			List[str]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     return 1 / (1 + np.exp(-1 * x      ))
  
  
  
  
  class   lowercase__							:
  
  
  
  
  
     def __init__(       self			,      SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE=None			,      SCREAMING_SNAKE_CASE=None			,      SCREAMING_SNAKE_CASE=False)     ->     str:
        _lowerCamelCase  :				str      =		units
        _lowerCamelCase  :				str      =		None
        _lowerCamelCase  :				Dict      =		None
        _lowerCamelCase  :				List[Any]      =		activation
        if learning_rate is None:
           _lowerCamelCase  :				Tuple      =		0.3
        _lowerCamelCase  :				int      =		learning_rate
        _lowerCamelCase  :				Any      =		is_input_layer
  
  
  
  
  
     def 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE)     ->     Dict:
        _lowerCamelCase  :				List[Any]      =		np.asmatrix(np.random.normal(0			,      0.5			,      (self.units, back_units)))
        _lowerCamelCase  :				Tuple      =		np.asmatrix(np.random.normal(0			,      0.5			,      self.units)).T
        if self.activation is None:
           _lowerCamelCase  :				Tuple      =		sigmoid
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     Optional[Any]:
        # activation function may be sigmoid or linear
        if self.activation == sigmoid:
           _lowerCamelCase  :				Tuple      =		np.dot(self.output			,      (1 - self.output).T)
           _lowerCamelCase  :				Dict      =		np.diag(np.diag(SCREAMING_SNAKE_CASE))
        else:
           _lowerCamelCase  :				str      =		1
        return gradient_activation
  
  
  
  
  
     def 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE)     ->     Any:
        _lowerCamelCase  :				List[Any]      =		xdata
        if self.is_input_layer:
           # input layer
           _lowerCamelCase  :				Tuple      =		xdata
           _lowerCamelCase  :				int      =		xdata
           return xdata
        else:
           _lowerCamelCase  :				List[str]      =		np.dot(self.weight			,      self.xdata) - self.bias
           _lowerCamelCase  :				Optional[Any]      =		self.activation(self.wx_plus_b)
           return self.output
  
  
  
  
  
     def 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE)     ->     List[str]:
        _lowerCamelCase  :				Union[str, Any]      =		self.cal_gradient()  # i * i 维
        _lowerCamelCase  :				Union[str, Any]      =		np.asmatrix(np.dot(gradient.T			,      SCREAMING_SNAKE_CASE))
  
        _lowerCamelCase  :				Optional[int]      =		np.asmatrix(self.xdata)
        _lowerCamelCase  :				str      =		-1
        _lowerCamelCase  :				Optional[int]      =		self.weight
  
        _lowerCamelCase  :				Optional[Any]      =		np.dot(gradient.T			,      self._gradient_weight.T)
        _lowerCamelCase  :				List[Any]      =		gradient * self._gradient_bias
        _lowerCamelCase  :				List[str]      =		np.dot(SCREAMING_SNAKE_CASE			,      self._gradient_x).T
        # upgrade: the Negative gradient direction
        _lowerCamelCase  :				Union[str, Any]      =		self.weight - self.learn_rate * self.gradient_weight
        _lowerCamelCase  :				str      =		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   lowercase__							:
  
  
  
  
  
     def __init__(       self)     ->     Any:
        _lowerCamelCase  :				Union[str, Any]      =		[]
        _lowerCamelCase  :				int      =		[]
        _lowerCamelCase  :				Union[str, Any]      =		plt.figure()
        _lowerCamelCase  :				Optional[int]      =		self.fig_loss.add_subplot(1			,      1			,      1)
  
  
  
  
  
     def 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE)     ->     int:
        self.layers.append(SCREAMING_SNAKE_CASE)
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     Union[str, Any]:
        for i, layer in enumerate(self.layers[:]):
           if i < 1:
              _lowerCamelCase  :				Optional[int]      =		True
           else:
              layer.initializer(self.layers[i - 1].units)
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     Optional[Any]:
        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 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE)     ->     str:
        _lowerCamelCase  :				int      =		train_round
        _lowerCamelCase  :				List[str]      =		accuracy
  
        self.ax_loss.hlines(self.accuracy			,      0			,      self.train_round * 1.1)
  
        _lowerCamelCase  :				Tuple      =		np.shape(SCREAMING_SNAKE_CASE)
        for _ in range(SCREAMING_SNAKE_CASE):
           _lowerCamelCase  :				List[str]      =		0
           for row in range(x_shape[0]):
              _lowerCamelCase  :				List[Any]      =		np.asmatrix(xdata[row, :]).T
              _lowerCamelCase  :				int      =		np.asmatrix(ydata[row, :]).T
  
              # forward propagation
              for layer in self.layers:
                 _lowerCamelCase  :				Optional[Any]      =		layer.forward_propagation(_xdata)
  
              _lowerCamelCase      ,						_lowerCamelCase  :				List[Any]      =		self.cal_loss(_ydata			,      _xdata)
              _lowerCamelCase  :				str      =		all_loss + loss
  
              # back propagation: the input_layer does not upgrade
              for layer in self.layers[:0:-1]:
                 _lowerCamelCase  :				str      =		layer.back_propagation(SCREAMING_SNAKE_CASE)
  
           _lowerCamelCase  :				Union[str, Any]      =		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 		UpperCamelCase_     (       self			,      SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE)     ->     int:
        _lowerCamelCase  :				List[str]      =		np.sum(np.power((ydata - ydata_)			,      2))
        _lowerCamelCase  :				Optional[int]      =		2 * (ydata_ - ydata)
        # vector (shape is the same as _ydata.shape)
        return self.loss, self.loss_gradient
  
  
  
  
  
     def 		UpperCamelCase_     (       self)     ->     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 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				List[str]      =		np.random.randn(10	,   10      )
     _lowerCamelCase  :				List[Any]      =		np.asarray(
         [
             [0.8, 0.4],
             [0.4, 0.3],
             [0.34, 0.45],
             [0.67, 0.32],
             [0.88, 0.67],
             [0.78, 0.77],
             [0.55, 0.66],
             [0.55, 0.43],
             [0.54, 0.1],
             [0.1, 0.5],
         ]      )
     _lowerCamelCase  :				Dict      =		BPNN()
     for i in (10, 20, 30, 2):
        model.add_layer(DenseLayer(__snake_case      )      )
     model.build()
     model.summary()
     model.train(xdata=__snake_case	,   ydata=__snake_case	,   train_round=100	,   accuracy=0.01      )
  
  
  if __name__ == "__main__":
   example()
  
  
style_context: 
  
  
  """simple docstring"""
  def 							_snake_case			(      __snake_case       :			str	,   __snake_case       :			str	,   __snake_case       :			int	,   __snake_case       :			int	,   __snake_case       :			int	,   __snake_case       :			int	,   ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				Optional[Any]      =		list(__snake_case      )
     _lowerCamelCase  :				Optional[int]      =		list(__snake_case      )
     _lowerCamelCase  :				Union[str, Any]      =		len(__snake_case      )
     _lowerCamelCase  :				Optional[int]      =		len(__snake_case      )
  
     _lowerCamelCase  :				List[str]      =		[
         [0 for _ in range(len_destination_seq + 1      )] for _ in range(len_source_seq + 1      )
     ]
     _lowerCamelCase  :				List[Any]      =		[
         ["""0""" for _ in range(len_destination_seq + 1      )] for _ in range(len_source_seq + 1      )
     ]
  
     for i in range(1	,   len_source_seq + 1      ):
        _lowerCamelCase  :				Optional[Any]      =		i * delete_cost
        _lowerCamelCase  :				Any      =		F'D{source_seq[i - 1]:c}'
  
     for i in range(1	,   len_destination_seq + 1      ):
        _lowerCamelCase  :				Dict      =		i * insert_cost
        _lowerCamelCase  :				List[str]      =		F'I{destination_seq[i - 1]:c}'
  
     for i in range(1	,   len_source_seq + 1      ):
        for j in range(1	,   len_destination_seq + 1      ):
           if source_seq[i - 1] == destination_seq[j - 1]:
              _lowerCamelCase  :				Union[str, Any]      =		costs[i - 1][j - 1] + copy_cost
              _lowerCamelCase  :				Tuple      =		F'C{source_seq[i - 1]:c}'
           else:
              _lowerCamelCase  :				Tuple      =		costs[i - 1][j - 1] + replace_cost
              _lowerCamelCase  :				List[str]      =		F'R{source_seq[i - 1]:c}' + str(destination_seq[j - 1]      )
  
           if costs[i - 1][j] + delete_cost < costs[i][j]:
              _lowerCamelCase  :				Any      =		costs[i - 1][j] + delete_cost
              _lowerCamelCase  :				Any      =		F'D{source_seq[i - 1]:c}'
  
           if costs[i][j - 1] + insert_cost < costs[i][j]:
              _lowerCamelCase  :				Dict      =		costs[i][j - 1] + insert_cost
              _lowerCamelCase  :				Union[str, Any]      =		F'I{destination_seq[j - 1]:c}'
  
     return costs, ops
  
  def 							_snake_case			(      __snake_case       :			list[list[str]]	,   __snake_case       :			int	,   __snake_case       :			int      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if i == 0 and j == 0:
        return []
     else:
        if ops[i][j][0] == "C" or ops[i][j][0] == "R":
           _lowerCamelCase  :				List[Any]      =		assemble_transformation(__snake_case	,   i - 1	,   j - 1      )
           seq.append(ops[i][j]      )
           return seq
        elif ops[i][j][0] == "D":
           _lowerCamelCase  :				Optional[Any]      =		assemble_transformation(__snake_case	,   i - 1	,   __snake_case      )
           seq.append(ops[i][j]      )
           return seq
        else:
           _lowerCamelCase  :				str      =		assemble_transformation(__snake_case	,   __snake_case	,   j - 1      )
           seq.append(ops[i][j]      )
           return seq
  
  
  if __name__ == "__main__":
   UpperCAmelCase ,     UpperCAmelCase   =	compute_transform_tables("""Python""", """Algorithms""", -1, 1, 2, 2)
  
   UpperCAmelCase   =	len(operations)
   UpperCAmelCase   =	len(operations[0])
   UpperCAmelCase   =	assemble_transformation(operations, m - 1, n - 1)
  
   UpperCAmelCase   =	list("""Python""")
   UpperCAmelCase   =	0
   UpperCAmelCase   =	0
  
   with open("""min_cost.txt""", """w""") as file:
    for op in sequence:
     print("""""".join(string))
  
     if op[0] == "C":
      file.write("""%-16s""" % """Copy %c""" % op[1])
      file.write("""\t\t\t""" + """""".join(string))
      file.write("""\r\n""")
  
      cost -= 1
     elif op[0] == "R":
      UpperCAmelCase   =	op[2]
  
      file.write("""%-16s""" % ("""Replace %c""" % op[1] + """ with """ + str(op[2])))
      file.write("""\t\t""" + """""".join(string))
      file.write("""\r\n""")
  
      cost += 1
     elif op[0] == "D":
      string.pop(i)
  
      file.write("""%-16s""" % """Delete %c""" % op[1])
      file.write("""\t\t\t""" + """""".join(string))
      file.write("""\r\n""")
  
      cost += 2
     else:
      string.insert(i, op[1])
  
      file.write("""%-16s""" % """Insert %c""" % op[1])
      file.write("""\t\t\t""" + """""".join(string))
      file.write("""\r\n""")
  
      cost += 2
  
     i += 1
  
    print("""""".join(string))
    print("""Cost: """, cost)
  
    file.write("""\r\nMinimum cost: """ + str(cost))
  
  