



"""simple docstring"""
import re
from typing import Callable, List, Optional, Union

import tensorflow as tf


try:
			from tensorflow.keras.optimizers.legacy import Adam
except ImportError:
			from tensorflow.keras.optimizers import Adam


class 							lowerCamelCase_(   tf.keras.optimizers.schedules.LearningRateSchedule    ):





					'''simple docstring'''



					def __init__(    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__ = 1.0				,       lowerCamelCase__ = None				,       ):
									super().__init__()
									_lowerCamelCase        =				initial_learning_rate
									_lowerCamelCase        =				warmup_steps
									_lowerCamelCase        =				power
									_lowerCamelCase        =				decay_schedule_fn
									_lowerCamelCase        =				name

					def __call__(    self				,       lowerCamelCase__   ):
									with tf.name_scope(self.name or '''WarmUp'''   ) as name:
													# Implements polynomial warmup. i.e., if global_step < warmup_steps, the
													# learning rate will be `global_step/num_warmup_steps * init_lr`.
													_lowerCamelCase        =				tf.cast(lowerCamelCase__				,       tf.floataa   )
													_lowerCamelCase        =				tf.cast(self.warmup_steps				,       tf.floataa   )
													_lowerCamelCase        =				global_step_float / warmup_steps_float
													_lowerCamelCase        =				self.initial_learning_rate * tf.math.pow(lowerCamelCase__				,       self.power   )
													return tf.cond(
													    global_step_float < warmup_steps_float				,       lambda: warmup_learning_rate				,       lambda: self.decay_schedule_fn(step - self.warmup_steps   )				,       name=lowerCamelCase__				,       )





					def 			snake_case__      (    self   ):
									return {
									    "initial_learning_rate": self.initial_learning_rate,
									    "decay_schedule_fn": self.decay_schedule_fn,
									    "warmup_steps": self.warmup_steps,
									    "power": self.power,
									    "name": self.name,
									}



def        lowerCAmelCase_(   lowercase_     :							float						,   lowercase_     :							int						,   lowercase_     :							int						,   lowercase_     :							float = 0.0						,   lowercase_     :							float = 0.9						,   lowercase_     :							float = 0.9_9_9						,   lowercase_     :							float = 1e-8						,   lowercase_     :							Optional[float] = None						,   lowercase_     :							Optional[float] = None						,   lowercase_     :							float = 0.0						,   lowercase_     :							float = 1.0						,   lowercase_     :							Optional[List[str]] = None						,   )	->       List[Any]:
				_lowerCamelCase        =				tf.keras.optimizers.schedules.PolynomialDecay(
				    initial_learning_rate=lowercase_						,   decay_steps=num_train_steps - num_warmup_steps						,   end_learning_rate=init_lr * min_lr_ratio						,   power=lowercase_						,   )
				if num_warmup_steps:
								_lowerCamelCase        =				WarmUp(
								    initial_learning_rate=lowercase_						,   decay_schedule_fn=lowercase_						,   warmup_steps=lowercase_						,   )
				if weight_decay_rate > 0.0:
								_lowerCamelCase        =				AdamWeightDecay(
								    learning_rate=lowercase_						,   weight_decay_rate=lowercase_						,   beta_a=lowercase_						,   beta_a=lowercase_						,   epsilon=lowercase_						,   clipnorm=lowercase_						,   global_clipnorm=lowercase_						,   exclude_from_weight_decay=['''LayerNorm''', '''layer_norm''', '''bias''']						,   include_in_weight_decay=lowercase_						,   )
				else:
								_lowerCamelCase        =				tf.keras.optimizers.Adam(
								    learning_rate=lowercase_						,   beta_a=lowercase_						,   beta_a=lowercase_						,   epsilon=lowercase_						,   clipnorm=lowercase_						,   global_clipnorm=lowercase_						,   )
				# We return the optimizer and the LR scheduler in order to better track the
				# evolution of the LR independently of the optimizer.
				return optimizer, lr_schedule


class 							lowerCamelCase_(   A__    ):





					'''simple docstring'''



					def __init__(    self				,       lowerCamelCase__ = 0.0_0_1				,       lowerCamelCase__ = 0.9				,       lowerCamelCase__ = 0.9_9_9				,       lowerCamelCase__ = 1e-7				,       lowerCamelCase__ = False				,       lowerCamelCase__ = 0.0				,       lowerCamelCase__ = None				,       lowerCamelCase__ = None				,       lowerCamelCase__ = "AdamWeightDecay"				,       **lowerCamelCase__				,       ):
									super().__init__(lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       **lowerCamelCase__   )
									_lowerCamelCase        =				weight_decay_rate
									_lowerCamelCase        =				include_in_weight_decay
									_lowerCamelCase        =				exclude_from_weight_decay

					@classmethod
					def 			snake_case__      (    cls				,       lowerCamelCase__   ):
									_lowerCamelCase        =				{'''WarmUp''': WarmUp}
									return super(lowerCamelCase__				,       cls   ).from_config(lowerCamelCase__				,       custom_objects=lowerCamelCase__   )

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   ):
									super(lowerCamelCase__				,       self   )._prepare_local(lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   )
									_lowerCamelCase        =				tf.constant(
									    self.weight_decay_rate				,       name='''adam_weight_decay_rate'''   )

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   ):
									_lowerCamelCase        =				self._do_use_weight_decay(var.name   )
									if do_decay:
													return var.assign_sub(
													    learning_rate * var * apply_state[(var.device, var.dtype.base_dtype)]['''weight_decay_rate''']				,       use_locking=self._use_locking				,       )
									return tf.no_op()

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__=None				,       **lowerCamelCase__   ):
									_lowerCamelCase  ,     _lowerCamelCase        =				list(zip(*lowerCamelCase__   )   )
									return super(lowerCamelCase__				,       self   ).apply_gradients(zip(lowerCamelCase__				,       lowerCamelCase__   )				,       name=lowerCamelCase__				,       **lowerCamelCase__   )

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   ):
									if apply_state is None:
													return self._decayed_lr_t[var_dtype], {}

									_lowerCamelCase        =				apply_state or {}
									_lowerCamelCase        =				apply_state.get((var_device, var_dtype)   )
									if coefficients is None:
													_lowerCamelCase        =				self._fallback_apply_state(lowerCamelCase__				,       lowerCamelCase__   )
													_lowerCamelCase        =				coefficients

									return coefficients["lr_t"], {"apply_state": apply_state}

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__=None   ):
									_lowerCamelCase  ,     _lowerCamelCase        =				self._get_lr(var.device				,       var.dtype.base_dtype				,       lowerCamelCase__   )
									_lowerCamelCase        =				self._decay_weights_op(lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   )
									with tf.control_dependencies([decay]   ):
													return super(lowerCamelCase__				,       self   )._resource_apply_dense(lowerCamelCase__				,       lowerCamelCase__				,       **lowerCamelCase__   )

					def 			snake_case__      (    self				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__=None   ):
									_lowerCamelCase  ,     _lowerCamelCase        =				self._get_lr(var.device				,       var.dtype.base_dtype				,       lowerCamelCase__   )
									_lowerCamelCase        =				self._decay_weights_op(lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__   )
									with tf.control_dependencies([decay]   ):
													return super(lowerCamelCase__				,       self   )._resource_apply_sparse(lowerCamelCase__				,       lowerCamelCase__				,       lowerCamelCase__				,       **lowerCamelCase__   )

					def 			snake_case__      (    self   ):
									_lowerCamelCase        =				super().get_config()
									config.update({'''weight_decay_rate''': self.weight_decay_rate}   )
									return config





					def 			snake_case__      (    self				,       lowerCamelCase__   ):
									if self.weight_decay_rate == 0:
													return False

									if self._include_in_weight_decay:
													for r in self._include_in_weight_decay:
																	if re.search(lowerCamelCase__				,       lowerCamelCase__   ) is not None:
																					return True

									if self._exclude_from_weight_decay:
													for r in self._exclude_from_weight_decay:
																	if re.search(lowerCamelCase__				,       lowerCamelCase__   ) is not None:
																					return False
									return True


class 							lowerCamelCase_(   A__    ):





					'''simple docstring'''



					def __init__(    self   ):
									_lowerCamelCase        =				[]
									_lowerCamelCase        =				None

					@property
					def 			snake_case__      (    self   ):
									if self._accum_steps is None:
													_lowerCamelCase        =				tf.Variable(
													    tf.constant(0				,       dtype=tf.intaa   )				,       trainable=lowerCamelCase__				,       synchronization=tf.VariableSynchronization.ON_READ				,       aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA				,       )

									return self._accum_steps.value()

					@property
					def 			snake_case__      (    self   ):
									if not self._gradients:
													raise ValueError('''The accumulator should be called first to initialize the gradients'''   )
									return [gradient.value() if gradient is not None else gradient for gradient in self._gradients]

					def __call__(    self				,       lowerCamelCase__   ):
									if not self._gradients:
													_lowerCamelCase        =				self.step  # Create the step variable.
													self._gradients.extend(
													    [
													        tf.Variable(
													            tf.zeros_like(lowerCamelCase__   )				,       trainable=lowerCamelCase__				,       synchronization=tf.VariableSynchronization.ON_READ				,       aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA				,       )
													        if gradient is not None
													        else gradient
													        for gradient in gradients
													    ]   )
									if len(lowerCamelCase__   ) != len(self._gradients   ):
													raise ValueError(F"""Expected {len(self._gradients   )} gradients, but got {len(lowerCamelCase__   )}"""   )

									for accum_gradient, gradient in zip(self._gradients				,       lowerCamelCase__   ):
													if accum_gradient is not None and gradient is not None:
																	accum_gradient.assign_add(lowerCamelCase__   )

									self._accum_steps.assign_add(1   )





					def 			snake_case__      (    self   ):
									if not self._gradients:
													return
									self._accum_steps.assign(0   )
									for gradient in self._gradients:
													if gradient is not None:
																	gradient.assign(tf.zeros_like(lowerCamelCase__   )   )





"""simple docstring"""
from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
__SCREAMING_SNAKE_CASE  :						List[str]    							=      numpy.array([0, 0])
__SCREAMING_SNAKE_CASE  :						Optional[Any]    							=      numpy.array([0.5, 0.866_0254])
__SCREAMING_SNAKE_CASE  :						Tuple    							=      numpy.array([1, 0])
__SCREAMING_SNAKE_CASE  :						List[Any]    							=      [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]						,   lowercase_     :							int							)	->       list[numpy.ndarray]:
				_lowerCamelCase        =				initial_vectors
				for _ in range(lowercase_							):
								_lowerCamelCase        =				iteration_step(lowercase_							)
				return vectors



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]							)	->       list[numpy.ndarray]:
				_lowerCamelCase        =				[]
				for i, start_vector in enumerate(vectors[:-1]							):
								_lowerCamelCase        =				vectors[i + 1]
								new_vectors.append(lowercase_							)
								_lowerCamelCase        =				end_vector - start_vector
								new_vectors.append(start_vector + difference_vector / 3							)
								new_vectors.append(
								    start_vector + difference_vector / 3 + rotate(difference_vector / 3						,   60							)							)
								new_vectors.append(start_vector + difference_vector * 2 / 3							)
				new_vectors.append(vectors[-1]							)
				return new_vectors



def        lowerCAmelCase_(   lowercase_     :							numpy.ndarray						,   lowercase_     :							float							)	->       numpy.ndarray:
				_lowerCamelCase        =				numpy.radians(lowercase_							)
				_lowerCamelCase  ,     _lowerCamelCase        =				numpy.cos(lowercase_							), numpy.sin(lowercase_							)
				_lowerCamelCase        =				numpy.array(((c, -s), (s, c))							)
				return numpy.dot(lowercase_						,   lowercase_							)



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]							)	->       None:
				_lowerCamelCase        =				plt.gca()
				axes.set_aspect('''equal'''							)

				# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
				# y-coordinates as inputs, which are constructed from the vector-list using
				# zip()
				_lowerCamelCase  ,     _lowerCamelCase        =				zip(*lowercase_							)
				plt.plot(lowercase_						,   lowercase_							)
				plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			__SCREAMING_SNAKE_CASE  :						str    							=      iterate(INITIAL_VECTORS, 5)
			plot(processed_vectors)
