code: 
  
  
  import numpy as np
  from matplotlib import pyplot as plt
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	return 1 / (1 + np.exp(-1 * x	))
  class _lowerCamelCase :
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(      self	:		str						,  _A	:		List[Any]						,  _A	:		Optional[Any]=None						,  _A	:		Any=None						,  _A	:		List[Any]=False    )						->				int:
  			__magic_name__ :					Union[str, Any]  			=  units
  			__magic_name__ :					Any  			=  None
  			__magic_name__ :					Tuple  			=  None
  			__magic_name__ :					Union[str, Any]  			=  activation
  			if learning_rate is None:
  				__magic_name__ :					Dict  			=  0.3
  			__magic_name__ :					Optional[int]  			=  learning_rate
  			__magic_name__ :					Optional[Any]  			=  is_input_layer
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Optional[Any]						,  _A	:		Optional[Any]    )						->				Optional[Any]:
  			__magic_name__ :					str  			=  np.asmatrix(np.random.normal(0						,  0.5						,  (self.units, back_units)    )    )
  			__magic_name__ :					Optional[int]  			=  np.asmatrix(np.random.normal(0						,  0.5						,  self.units    )    ).T
  			if self.activation is None:
  				__magic_name__ :					int  			=  sigmoid
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str    )						->				Dict:
  			# activation function may be sigmoid or linear
  			if self.activation == sigmoid:
  				__magic_name__ :					Union[str, Any]  			=  np.dot(self.output						,  (1 - self.output).T    )
  				__magic_name__ :					Optional[int]  			=  np.diag(np.diag(_A    )    )
  			else:
  				__magic_name__ :					Optional[Any]  			=  1
  			return gradient_activation
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple						,  _A	:		int    )						->				Optional[Any]:
  			__magic_name__ :					str  			=  xdata
  			if self.is_input_layer:
  				# input layer
  				__magic_name__ :					Any  			=  xdata
  				__magic_name__ :					Dict  			=  xdata
  				return xdata
  			else:
  				__magic_name__ :					int  			=  np.dot(self.weight						,  self.xdata    ) - self.bias
  				__magic_name__ :					Any  			=  self.activation(self.wx_plus_b    )
  				return self.output
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Any						,  _A	:		int    )						->				Any:
  			__magic_name__ :					int  			=  self.cal_gradient()  # i * i 维
  			__magic_name__ :					List[str]  			=  np.asmatrix(np.dot(gradient.T						,  _A    )    )
  
  			__magic_name__ :					Tuple  			=  np.asmatrix(self.xdata    )
  			__magic_name__ :					Union[str, Any]  			=  -1
  			__magic_name__ :					List[str]  			=  self.weight
  
  			__magic_name__ :					Dict  			=  np.dot(gradient.T						,  self._gradient_weight.T    )
  			__magic_name__ :					Dict  			=  gradient * self._gradient_bias
  			__magic_name__ :					Optional[Any]  			=  np.dot(_A						,  self._gradient_x    ).T
  			# upgrade: the Negative gradient direction
  			__magic_name__ :					Tuple  			=  self.weight - self.learn_rate * self.gradient_weight
  			__magic_name__ :					Optional[int]  			=  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 _lowerCamelCase :
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(      self	:		int    )						->				Optional[Any]:
  			__magic_name__ :					int  			=  []
  			__magic_name__ :					int  			=  []
  			__magic_name__ :					Tuple  			=  plt.figure()
  			__magic_name__ :					int  			=  self.fig_loss.add_subplot(1						,  1						,  1    )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Union[str, Any]						,  _A	:		Dict    )						->				Any:
  			self.layers.append(_A    )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Dict    )						->				int:
  			for i, layer in enumerate(self.layers[:]    ):
  				if i < 1:
  					__magic_name__ :					Optional[Any]  			=  True
  				else:
  					layer.initializer(self.layers[i - 1].units    )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		str    )						->				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      __lowerCAmelCase	(      self	:		Optional[int]						,  _A	:		int						,  _A	:		int						,  _A	:		List[Any]						,  _A	:		Optional[Any]    )						->				Union[str, Any]:
  			__magic_name__ :					Optional[Any]  			=  train_round
  			__magic_name__ :					Tuple  			=  accuracy
  
  			self.ax_loss.hlines(self.accuracy						,  0						,  self.train_round * 1.1    )
  
  			__magic_name__ :					Union[str, Any]  			=  np.shape(_A    )
  			for _ in range(_A    ):
  				__magic_name__ :					Any  			=  0
  				for row in range(x_shape[0]    ):
  					__magic_name__ :					List[str]  			=  np.asmatrix(xdata[row, :]    ).T
  					__magic_name__ :					Dict  			=  np.asmatrix(ydata[row, :]    ).T
  
  					# forward propagation
  					for layer in self.layers:
  						__magic_name__ :					Dict  			=  layer.forward_propagation(_xdata    )
  
  					__magic_name__ :					Tuple  			=  self.cal_loss(_ydata						,  _xdata    )
  					__magic_name__ :					List[str]  			=  all_loss + loss
  
  					# back propagation: the input_layer does not upgrade
  					for layer in self.layers[:0:-1]:
  						__magic_name__ :					str  			=  layer.back_propagation(_A    )
  
  				__magic_name__ :					str  			=  all_loss / x_shape[0]
  				self.train_mse.append(_A    )
  
  				self.plot_loss()
  
  				if mse < self.accuracy:
  					print('----达到精度----'    )
  					return mse
  			return None
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Union[str, Any]						,  _A	:		Tuple						,  _A	:		Optional[Any]    )						->				Any:
  			__magic_name__ :					Dict  			=  np.sum(np.power((ydata - ydata_)						,  2    )    )
  			__magic_name__ :					List[Any]  			=  2 * (ydata_ - ydata)
  			# vector (shape is the same as _ydata.shape)
  			return self.loss, self.loss_gradient
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		List[str]    )						->				Optional[Any]:
  			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 lowerCamelCase    (    ):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	__magic_name__ :					List[str]  			=  np.random.randn(10	,	10	)
  	__magic_name__ :					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],
  	    ]	)
  	__magic_name__ :					int  			=  BPNN()
  	for i in (10, 20, 30, 2):
  		model.add_layer(DenseLayer(lowerCAmelCase	)	)
  	model.build()
  	model.summary()
  	model.train(xdata=lowerCAmelCase	,	ydata=lowerCAmelCase	,	train_round=100	,	accuracy=0.01	)
  
  
  if __name__ == "__main__":
  							example()
style_context: 
  
  
  '''simple docstring'''
  
  from __future__ import annotations
  
  
  
  
  
  def lowerCamelCase    (    lowerCAmelCase       :			list[int | float]	,	lowerCAmelCase       :			int	,	lowerCAmelCase       :			int	):
  
  
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	if len(lowerCAmelCase	) == 0:
  		raise ValueError('find_min() arg is an empty sequence'	)
  	if (
  	    left >= len(lowerCAmelCase	)
  	    or left < -len(lowerCAmelCase	)
  	    or right >= len(lowerCAmelCase	)
  	    or right < -len(lowerCAmelCase	)
  	):
  		raise IndexError('list index out of range'	)
  	if left == right:
  		return nums[left]
  	__magic_name__ :					Tuple  			=  (left + right) >> 1  # the middle
  	__magic_name__ :					str  			=  find_min(lowerCAmelCase	,	lowerCAmelCase	,	lowerCAmelCase	)  # find min in range[left, mid]
  	__magic_name__ :					Optional[Any]  			=  find_min(lowerCAmelCase	,	mid + 1	,	lowerCAmelCase	)  # find min in range[mid + 1, right]
  
  	return left_min if left_min <= right_min else right_min
  
  
  if __name__ == "__main__":
  							import doctest
  
  							doctest.testmod(verbose=True)