






"""simple docstring"""
import random



class 					UpperCamelCase__   :







    """simple docstring"""







    def __init__(		self   :  List[str]							,						UpperCamelCase_   :  float							,						UpperCamelCase_   :  float   ):





           '''simple docstring'''

           __magic_name__										=						x
           __magic_name__										=						y







    def 							a__ (		self   :  Optional[Any]   ):





           '''simple docstring'''

           return (self.x**2 + self.y**2) <= 1







    @classmethod
    def 							a__ (		cls   :  int   ):





           '''simple docstring'''

           return cls(x=random.random()							,						y=random.random()   )


def        A	(							__snake_case:   Union[str, Any]     )						->		Optional[Any]:

       """simple docstring"""





       if number_of_simulations < 1:
              raise ValueError('At least one simulation is necessary to estimate PI.'     )

       __magic_name__										=						0
       for _ in range(__snake_case     ):
              __magic_name__										=						Point.random_unit_square()

              if random_point.is_in_unit_circle():
                     number_in_unit_circle += 1

       return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
 # import doctest

 # doctest.testmod()
 from math import pi

 snake_case   :   Dict    		=		"""Please enter the desired number of Monte Carlo simulations: """
 snake_case   :   Union[str, Any]    		=		estimate_pi(int(input(prompt).strip()))
 print(f"""An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}""")







"""simple docstring"""
import numpy as np
from matplotlib import pyplot as plt


def        A	(							__snake_case:   List[Any]     )						->		Union[str, Any]:

       """simple docstring"""





       return 1 / (1 + np.exp(-1 * x     ))



class 					UpperCamelCase__   :







    """simple docstring"""







    def __init__(		self   :  Tuple							,						UpperCamelCase_   :  List[Any]							,						UpperCamelCase_   :  Optional[int]=None							,						UpperCamelCase_   :  List[str]=None							,						UpperCamelCase_   :  Tuple=False   ):





           '''simple docstring'''

           __magic_name__										=						units
           __magic_name__										=						None
           __magic_name__										=						None
           __magic_name__										=						activation
           if learning_rate is None:
                  __magic_name__										=						0.3
           __magic_name__										=						learning_rate
           __magic_name__										=						is_input_layer







    def 							a__ (		self   :  str							,						UpperCamelCase_   :  List[str]   ):





           '''simple docstring'''

           __magic_name__										=						np.asmatrix(np.random.normal(0							,						0.5							,						(self.units, back_units)   )   )
           __magic_name__										=						np.asmatrix(np.random.normal(0							,						0.5							,						self.units   )   ).T
           if self.activation is None:
                  __magic_name__										=						sigmoid







    def 							a__ (		self   :  Optional[int]   ):





           '''simple docstring'''

           if self.activation == sigmoid:
                  __magic_name__										=						np.dot(self.output							,						(1 - self.output).T   )
                  __magic_name__										=						np.diag(np.diag(UpperCamelCase_   )   )
           else:
                  __magic_name__										=						1
           return gradient_activation







    def 							a__ (		self   :  Optional[Any]							,						UpperCamelCase_   :  Any   ):





           '''simple docstring'''

           __magic_name__										=						xdata
           if self.is_input_layer:
                  # input layer
                  __magic_name__										=						xdata
                  __magic_name__										=						xdata
                  return xdata
           else:
                  __magic_name__										=						np.dot(self.weight							,						self.xdata   ) - self.bias
                  __magic_name__										=						self.activation(self.wx_plus_b   )
                  return self.output







    def 							a__ (		self   :  str							,						UpperCamelCase_   :  Optional[int]   ):





           '''simple docstring'''

           __magic_name__										=						self.cal_gradient()  # i * i 维
           __magic_name__										=						np.asmatrix(np.dot(gradient.T							,						UpperCamelCase_   )   )

           __magic_name__										=						np.asmatrix(self.xdata   )
           __magic_name__										=						-1
           __magic_name__										=						self.weight

           __magic_name__										=						np.dot(gradient.T							,						self._gradient_weight.T   )
           __magic_name__										=						gradient * self._gradient_bias
           __magic_name__										=						np.dot(UpperCamelCase_							,						self._gradient_x   ).T
           # upgrade: the Negative gradient direction
           __magic_name__										=						self.weight - self.learn_rate * self.gradient_weight
           __magic_name__										=						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 					UpperCamelCase__   :







    """simple docstring"""







    def __init__(		self   :  List[Any]   ):





           '''simple docstring'''

           __magic_name__										=						[]
           __magic_name__										=						[]
           __magic_name__										=						plt.figure()
           __magic_name__										=						self.fig_loss.add_subplot(1							,						1							,						1   )







    def 							a__ (		self   :  List[str]							,						UpperCamelCase_   :  Any   ):





           '''simple docstring'''

           self.layers.append(UpperCamelCase_   )







    def 							a__ (		self   :  Any   ):





           '''simple docstring'''

           for i, layer in enumerate(self.layers[:]   ):
                  if i < 1:
                         __magic_name__										=						True
                  else:
                         layer.initializer(self.layers[i - 1].units   )







    def 							a__ (		self   :  Any   ):





           '''simple docstring'''

           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   :  str							,						UpperCamelCase_   :  Any							,						UpperCamelCase_   :  Tuple							,						UpperCamelCase_   :  Any							,						UpperCamelCase_   :  Union[str, Any]   ):





           '''simple docstring'''

           __magic_name__										=						train_round
           __magic_name__										=						accuracy

           self.ax_loss.hlines(self.accuracy							,						0							,						self.train_round * 1.1   )

           __magic_name__										=						np.shape(UpperCamelCase_   )
           for _ in range(UpperCamelCase_   ):
                  __magic_name__										=						0
                  for row in range(x_shape[0]   ):
                         __magic_name__										=						np.asmatrix(xdata[row, :]   ).T
                         __magic_name__										=						np.asmatrix(ydata[row, :]   ).T

                         # forward propagation
                         for layer in self.layers:
                                __magic_name__										=						layer.forward_propagation(_xdata   )

                         __magic_name__							,     __magic_name__										=						self.cal_loss(_ydata							,						_xdata   )
                         __magic_name__										=						all_loss + loss

                         # back propagation: the input_layer does not upgrade
                         for layer in self.layers[:0:-1]:
                                __magic_name__										=						layer.back_propagation(UpperCamelCase_   )

                  __magic_name__										=						all_loss / x_shape[0]
                  self.train_mse.append(UpperCamelCase_   )

                  self.plot_loss()

                  if mse < self.accuracy:
                         print('----达到精度----'   )
                         return mse
           return None







    def 							a__ (		self   :  Union[str, Any]							,						UpperCamelCase_   :  str							,						UpperCamelCase_   :  Union[str, Any]   ):





           '''simple docstring'''

           __magic_name__										=						np.sum(np.power((ydata - ydata_)							,						2   )   )
           __magic_name__										=						2 * (ydata_ - ydata)
           # vector (shape is the same as _ydata.shape)
           return self.loss, self.loss_gradient







    def 							a__ (		self   :  str   ):





           '''simple docstring'''

           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        A	(							)						->		Dict:

       """simple docstring"""





       __magic_name__										=						np.random.randn(1_0   ,    1_0     )
       __magic_name__										=						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__										=						BPNN()
       for i in (1_0, 2_0, 3_0, 2):
              model.add_layer(DenseLayer(__snake_case     )     )
       model.build()
       model.summary()
       model.train(xdata=__snake_case   ,    ydata=__snake_case   ,    train_round=1_0_0   ,    accuracy=0.01     )


if __name__ == "__main__":
 example()