

"""simple docstring"""





import numpy as np
from matplotlib import pyplot as plt



def        _lowerCAmelCase      (						UpperCAmelCase     :							List[Any]				):


					'''simple docstring'''






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

class     __a   :

			"""simple docstring"""

			def __init__(							self     :					List[str]						,  lowercase_     :					Tuple						,  lowercase_     :					str=None						,  lowercase_     :					Optional[Any]=None						,  lowercase_     :					Optional[Any]=False						):
								UpperCamelCase__		:    Optional[Any]         =units
								UpperCamelCase__		:    int         =None
								UpperCamelCase__		:    Optional[Any]         =None
								UpperCamelCase__		:    str         =activation
								if learning_rate is None:
													UpperCamelCase__		:    Union[str, Any]         =0.3
								UpperCamelCase__		:    Union[str, Any]         =learning_rate
								UpperCamelCase__		:    str         =is_input_layer






			def    _lowerCAmelCase			(							self     :					Dict						,  lowercase_     :					Optional[int]						):
								UpperCamelCase__		:    List[Any]         =np.asmatrix(np.random.normal(0						,  0.5						,  (self.units, back_units)						)						)
								UpperCamelCase__		:    Optional[Any]         =np.asmatrix(np.random.normal(0						,  0.5						,  self.units						)						).T
								if self.activation is None:
													UpperCamelCase__		:    List[Any]         =sigmoid






			def    _lowerCAmelCase			(							self     :					Optional[int]						):
								# activation function may be sigmoid or linear
								if self.activation == sigmoid:
													UpperCamelCase__		:    Union[str, Any]         =np.dot(self.output						,  (1 - self.output).T						)
													UpperCamelCase__		:    Union[str, Any]         =np.diag(np.diag(lowercase_						)						)
								else:
													UpperCamelCase__		:    List[str]         =1
								return gradient_activation






			def    _lowerCAmelCase			(							self     :					Tuple						,  lowercase_     :					Optional[Any]						):
								UpperCamelCase__		:    Tuple         =xdata
								if self.is_input_layer:
													# input layer
													UpperCamelCase__		:    int         =xdata
													UpperCamelCase__		:    Union[str, Any]         =xdata
													return xdata
								else:
													UpperCamelCase__		:    int         =np.dot(self.weight						,  self.xdata						) - self.bias
													UpperCamelCase__		:    List[Any]         =self.activation(self.wx_plus_b						)
													return self.output






			def    _lowerCAmelCase			(							self     :					Optional[int]						,  lowercase_     :					Dict						):
								UpperCamelCase__		:    Optional[int]         =self.cal_gradient()  # i * i 维
								UpperCamelCase__		:    List[str]         =np.asmatrix(np.dot(gradient.T						,  lowercase_						)						)

								UpperCamelCase__		:    List[str]         =np.asmatrix(self.xdata						)
								UpperCamelCase__		:    List[str]         =-1
								UpperCamelCase__		:    Any         =self.weight

								UpperCamelCase__		:    Tuple         =np.dot(gradient.T						,  self._gradient_weight.T						)
								UpperCamelCase__		:    Any         =gradient * self._gradient_bias
								UpperCamelCase__		:    Optional[int]         =np.dot(lowercase_						,  self._gradient_x						).T
								# upgrade: the Negative gradient direction
								UpperCamelCase__		:    int         =self.weight - self.learn_rate * self.gradient_weight
								UpperCamelCase__		:    Optional[Any]         =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     :					List[Any]						):
								UpperCamelCase__		:    List[str]         =[]
								UpperCamelCase__		:    Optional[int]         =[]
								UpperCamelCase__		:    int         =plt.figure()
								UpperCamelCase__		:    Dict         =self.fig_loss.add_subplot(1						,  1						,  1						)






			def    _lowerCAmelCase			(							self     :					List[str]						,  lowercase_     :					List[Any]						):
								self.layers.append(lowercase_						)






			def    _lowerCAmelCase			(							self     :					Dict						):
								for i, layer in enumerate(self.layers[:]						):
													if i < 1:
																		UpperCamelCase__		:    int         =True
													else:
																		layer.initializer(self.layers[i - 1].units						)






			def    _lowerCAmelCase			(							self     :					int						):
								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     :					Dict						,  lowercase_     :					List[str]						,  lowercase_     :					str						,  lowercase_     :					List[Any]						,  lowercase_     :					int						):
								UpperCamelCase__		:    Union[str, Any]         =train_round
								UpperCamelCase__		:    Any         =accuracy

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

								UpperCamelCase__		:    int         =np.shape(lowercase_						)
								for _ in range(lowercase_						):
													UpperCamelCase__		:    Any         =0
													for row in range(x_shape[0]						):
																		UpperCamelCase__		:    Dict         =np.asmatrix(xdata[row, :]						).T
																		UpperCamelCase__		:    Union[str, Any]         =np.asmatrix(ydata[row, :]						).T

																		# forward propagation
																		for layer in self.layers:
																							UpperCamelCase__		:    Optional[int]         =layer.forward_propagation(_xdata						)

																		UpperCamelCase__  ,			UpperCamelCase__		:    Optional[int]         =self.cal_loss(_ydata						,  _xdata						)
																		UpperCamelCase__		:    Union[str, Any]         =all_loss + loss

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

													UpperCamelCase__		:    Dict         =all_loss / x_shape[0]
													self.train_mse.append(lowercase_						)

													self.plot_loss()

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






			def    _lowerCAmelCase			(							self     :					Optional[Any]						,  lowercase_     :					Union[str, Any]						,  lowercase_     :					str						):
								UpperCamelCase__		:    Any         =np.sum(np.power((ydata - ydata_)						,  2						)						)
								UpperCamelCase__		:    Optional[int]         =2 * (ydata_ - ydata)
								# vector (shape is the same as _ydata.shape)
								return self.loss, self.loss_gradient






			def    _lowerCAmelCase			(							self     :					Union[str, 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'''






					UpperCamelCase__		:    List[Any]         =np.random.randn(10      ,							10				)
					UpperCamelCase__		:    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],
					    ]				)
					UpperCamelCase__		:    Tuple         =BPNN()
					for i in (10, 20, 30, 2):
										model.add_layer(DenseLayer(UpperCAmelCase				)				)
					model.build()
					model.summary()
					model.train(xdata=UpperCAmelCase      ,							ydata=UpperCAmelCase      ,							train_round=100      ,							accuracy=0.01				)


if __name__ == "__main__":
				example()





"""simple docstring"""





import math as m



def        _lowerCAmelCase      (						UpperCAmelCase     :							Optional[int]      ,							UpperCAmelCase     :							Optional[Any]      ,							UpperCAmelCase     :							Optional[Any]=0.001				):


					'''simple docstring'''






					return (f(a + h				) - f(a - h				)) / (2 * h)



def        _lowerCAmelCase      (						UpperCAmelCase     :							List[str]      ,							UpperCAmelCase     :							Optional[Any]=0      ,							UpperCAmelCase     :							Optional[int]=100      ,							UpperCAmelCase     :							Union[str, Any]=0.0001      ,							UpperCAmelCase     :							Dict=1E-6      ,							UpperCAmelCase     :							Any=False				):


					'''simple docstring'''






					UpperCamelCase__		:    Optional[Any]         =xa  # set the initial guess
					UpperCamelCase__		:    List[Any]         =[a]
					UpperCamelCase__		:    Optional[Any]         =abs(f(UpperCAmelCase				)				)
					UpperCamelCase__		:    List[str]         =lambda UpperCAmelCase				: calc_derivative(UpperCAmelCase      ,							UpperCAmelCase      ,							h=UpperCAmelCase				)  # noqa: E731  Derivative of f(x)
					for _ in range(UpperCAmelCase				):
										if fa(UpperCAmelCase				) == 0:
															raise ValueError('''No converging solution found'''				)
										UpperCamelCase__		:    Any         =a - f(UpperCAmelCase				) / fa(UpperCAmelCase				)  # Calculate the next estimate
										if logsteps:
															steps.append(UpperCAmelCase				)
										if error < maxerror:
															break
					else:
										raise ValueError('''Iteration limit reached, no converging solution found'''				)
					if logsteps:
										# If logstep is true, then log intermediate steps
										return a, error, steps
					return a, error


if __name__ == "__main__":
				from matplotlib import pyplot as plt

				_SCREAMING_SNAKE_CASE       :  str        = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				_SCREAMING_SNAKE_CASE       ,       _SCREAMING_SNAKE_CASE       ,       _SCREAMING_SNAKE_CASE       :  Any        = newton_raphson(
				    f, xa=1_0, maxiter=1_0_0_0, step=1e-6, logsteps=True
				)
				plt.plot([abs(f(x)) for x in steps])
				plt.xlabel("""step""")
				plt.ylabel("""error""")
				plt.show()
				print(F'''solution = {{{solution:f}}}, error = {{{error:f}}}''')


