code: 
  
  
  '''simple docstring'''
  
  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__			,       __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 sklearn.metrics import mean_absolute_error
  
  import datasets
  
  
  lowerCAmelCase   :Union[str, Any]								=    '''\
  @article{scikit-learn,
   title={Scikit-learn: Machine Learning in {P}ython},
   author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
           and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
           and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
           Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
   journal={Journal of Machine Learning Research},
   volume={12},
   pages={2825--2830},
   year={2011}
  }
  '''
  
  lowerCAmelCase   :int								=    '''\
  Mean Absolute Error (MAE) is the mean of the magnitude of difference between the predicted and actual
  values.
  '''
  
  
  lowerCAmelCase   :Optional[int]								=    '''
  Args:
      predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
          Estimated target values.
      references: array-like of shape (n_samples,) or (n_samples, n_outputs)
          Ground truth (correct) target values.
      sample_weight: array-like of shape (n_samples,), default=None
          Sample weights.
      multioutput: {"raw_values", "uniform_average"} or array-like of shape (n_outputs,), default="uniform_average"
          Defines aggregating of multiple output values. Array-like value defines weights used to average errors.
  
                   "raw_values" : Returns a full set of errors in case of multioutput input.
  
                   "uniform_average" : Errors of all outputs are averaged with uniform weight.
  
  Returns:
      mae : mean absolute error.
          If multioutput is "raw_values", then mean absolute error is returned for each output separately. If multioutput is "uniform_average" or an ndarray of weights, then the weighted average of all output errors is returned.
          MAE output is non-negative floating point. The best value is 0.0.
  Examples:
  
      >>> mae_metric = datasets.load_metric("mae")
      >>> predictions = [2.5, 0.0, 2, 8]
      >>> references = [3, -0.5, 2, 7]
      >>> results = mae_metric.compute(predictions=predictions, references=references)
      >>> print(results)
      {\'mae\': 0.5}
  
      If you\'re using multi-dimensional lists, then set the config as follows :
  
      >>> mae_metric = datasets.load_metric("mae", "multilist")
      >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
      >>> references = [[0, 2], [-1, 2], [8, -5]]
      >>> results = mae_metric.compute(predictions=predictions, references=references)
      >>> print(results)
      {\'mae\': 0.75}
      >>> results = mae_metric.compute(predictions=predictions, references=references, multioutput=\'raw_values\')
      >>> print(results)
      {\'mae\': array([0.5, 1. ])}
  '''
  @datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION	,  _KWARGS_DESCRIPTION							)
  class _lowerCamelCase (		datasets.Metric							):
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Union[str, Any]    )						->				int:
  			return datasets.MetricInfo(
  			    description=_DESCRIPTION						,  citation=_CITATION						,  inputs_description=_KWARGS_DESCRIPTION						,  features=datasets.Features(self._get_feature_types()    )						,  reference_urls=[
  			        'https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_absolute_error.html'
  			    ]						,  )
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Tuple    )						->				List[str]:
  			if self.config_name == "multilist":
  				return {
  				    "predictions": datasets.Sequence(datasets.Value('float'    )    ),
  				    "references": datasets.Sequence(datasets.Value('float'    )    ),
  				}
  			else:
  				return {
  				    "predictions": datasets.Value('float'    ),
  				    "references": datasets.Value('float'    ),
  				}
  
  
  
  
  
  
  
  		def      __lowerCAmelCase	(      self	:		Dict						,  _A	:		Optional[int]						,  _A	:		Optional[Any]						,  _A	:		Optional[Any]=None						,  _A	:		Tuple="uniform_average"    )						->				Any:
  			__magic_name__ :					Optional[Any]  			=  mean_absolute_error(_A						,  _A						,  sample_weight=_A						,  multioutput=_A    )
  
  			return {"mae": mae_score}