





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       __A							(   tf.keras.optimizers.schedules.LearningRateSchedule	):




      """simple docstring"""







      def __init__(		self   ,				a__   ,				a__   ,				a__   ,				a__ = 1.0   ,				a__ = None   ,				):



             """simple docstring"""





             super().__init__()
             _lowerCamelCase				:  List[Any]						=		initial_learning_rate
             _lowerCamelCase				:  List[Any]						=		warmup_steps
             _lowerCamelCase				:  Tuple						=		power
             _lowerCamelCase				:  List[str]						=		decay_schedule_fn
             _lowerCamelCase				:  Union[str, Any]						=		name


      def __call__(		self   ,				a__):



             """simple docstring"""





             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				:  Dict						=		tf.cast(a__   ,				tf.floataa)
                    _lowerCamelCase				:  int						=		tf.cast(self.warmup_steps   ,				tf.floataa)
                    _lowerCamelCase				:  Optional[int]						=		global_step_float / warmup_steps_float
                    _lowerCamelCase				:  List[str]						=		self.initial_learning_rate * tf.math.pow(a__   ,				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=a__   ,				)



      def 					__snake_case      (		self):



             """simple docstring"""





             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  __UpperCAmelCase(   lowercase_			,     lowercase_			,     lowercase_			,     lowercase_ = 0.0			,     lowercase_ = 0.9			,     lowercase_ = 0.9_9_9			,     lowercase_ = 1e-8			,     lowercase_ = None			,     lowercase_ = None			,     lowercase_ = 0.0			,     lowercase_ = 1.0			,     lowercase_ = None			,     ):
       _lowerCamelCase				:  Dict						=		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				:  List[str]						=		WarmUp(
                  initial_learning_rate=lowercase_			,     decay_schedule_fn=lowercase_			,     warmup_steps=lowercase_			,     )
       if weight_decay_rate > 0.0:
              _lowerCamelCase				:  Tuple						=		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				:  Tuple						=		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       __A							(   lowerCamelCase__	):




      """simple docstring"""







      def __init__(		self   ,				a__ = 0.001   ,				a__ = 0.9   ,				a__ = 0.999   ,				a__ = 1e-7   ,				a__ = False   ,				a__ = 0.0   ,				a__ = None   ,				a__ = None   ,				a__ = "AdamWeightDecay"   ,				**a__   ,				):



             """simple docstring"""





             super().__init__(a__   ,				a__   ,				a__   ,				a__   ,				a__   ,				a__   ,				**a__)
             _lowerCamelCase				:  Union[str, Any]						=		weight_decay_rate
             _lowerCamelCase				:  Any						=		include_in_weight_decay
             _lowerCamelCase				:  Any						=		exclude_from_weight_decay


      @classmethod
      def 					__snake_case      (		cls   ,				a__):



             """simple docstring"""





             _lowerCamelCase				:  Optional[int]						=		{'''WarmUp''': WarmUp}
             return super(a__   ,				cls).from_config(a__   ,				custom_objects=a__)


      def 					__snake_case      (		self   ,				a__   ,				a__   ,				a__):



             """simple docstring"""





             super(a__   ,				self)._prepare_local(a__   ,				a__   ,				a__)
             _lowerCamelCase				:  List[Any]						=		tf.constant(
                 self.weight_decay_rate   ,				name='''adam_weight_decay_rate''')


      def 					__snake_case      (		self   ,				a__   ,				a__   ,				a__):



             """simple docstring"""





             _lowerCamelCase				:  Optional[int]						=		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   ,				a__   ,				a__=None   ,				**a__):



             """simple docstring"""





             _lowerCamelCase,	_lowerCamelCase				:  List[str]						=		list(zip(*a__))
             return super(a__   ,				self).apply_gradients(zip(a__   ,				a__)   ,				name=a__   ,				**a__)


      def 					__snake_case      (		self   ,				a__   ,				a__   ,				a__):



             """simple docstring"""





             if apply_state is None:
                    return self._decayed_lr_t[var_dtype], {}

             _lowerCamelCase				:  Union[str, Any]						=		apply_state or {}
             _lowerCamelCase				:  List[str]						=		apply_state.get((var_device, var_dtype))
             if coefficients is None:
                    _lowerCamelCase				:  Tuple						=		self._fallback_apply_state(a__   ,				a__)
                    _lowerCamelCase				:  Union[str, Any]						=		coefficients

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


      def 					__snake_case      (		self   ,				a__   ,				a__   ,				a__=None):



             """simple docstring"""





             _lowerCamelCase,	_lowerCamelCase				:  str						=		self._get_lr(var.device   ,				var.dtype.base_dtype   ,				a__)
             _lowerCamelCase				:  Tuple						=		self._decay_weights_op(a__   ,				a__   ,				a__)
             with tf.control_dependencies([decay]):
                    return super(a__   ,				self)._resource_apply_dense(a__   ,				a__   ,				**a__)


      def 					__snake_case      (		self   ,				a__   ,				a__   ,				a__   ,				a__=None):



             """simple docstring"""





             _lowerCamelCase,	_lowerCamelCase				:  List[Any]						=		self._get_lr(var.device   ,				var.dtype.base_dtype   ,				a__)
             _lowerCamelCase				:  str						=		self._decay_weights_op(a__   ,				a__   ,				a__)
             with tf.control_dependencies([decay]):
                    return super(a__   ,				self)._resource_apply_sparse(a__   ,				a__   ,				a__   ,				**a__)


      def 					__snake_case      (		self):



             """simple docstring"""





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



      def 					__snake_case      (		self   ,				a__):



             """simple docstring"""





             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(a__   ,				a__) is not None:
                                  return True

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







class       __A							(   lowerCamelCase__	):




      """simple docstring"""







      def __init__(		self):



             """simple docstring"""





             _lowerCamelCase				:  List[str]						=		[]
             _lowerCamelCase				:  List[Any]						=		None


      @property
      def 					__snake_case      (		self):



             """simple docstring"""





             if self._accum_steps is None:
                    _lowerCamelCase				:  Tuple						=		tf.Variable(
                        tf.constant(0   ,				dtype=tf.intaa)   ,				trainable=a__   ,				synchronization=tf.VariableSynchronization.ON_READ   ,				aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA   ,				)

             return self._accum_steps.value()


      @property
      def 					__snake_case      (		self):



             """simple docstring"""





             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   ,				a__):



             """simple docstring"""





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

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

             self._accum_steps.assign_add(1)



      def 					__snake_case      (		self):



             """simple docstring"""





             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(a__))








from __future__ import annotations

from scipy.special import comb  # type: ignore







class       __A							:




      """simple docstring"""







      def __init__(		self   ,				a__):



             """simple docstring"""





             _lowerCamelCase				:  str						=		list_of_points
             # Degree determines the flexibility of the curve.
             # Degree = 1 will produce a straight line.
             _lowerCamelCase				:  List[Any]						=		len(a__) - 1


      def 					__snake_case      (		self   ,				a__):



             """simple docstring"""





             assert 0 <= t <= 1, "Time t must be between 0 and 1."
             _lowerCamelCase				:  list[float]						=		[]
             for i in range(len(self.list_of_points)):
                    # basis function for each i
                    output_values.append(
                        comb(self.degree   ,				a__) * ((1 - t) ** (self.degree - i)) * (t**i))
             # the basis must sum up to 1 for it to produce a valid Bezier curve.
             assert round(sum(a__)   ,				5) == 1
             return output_values


      def 					__snake_case      (		self   ,				a__):



             """simple docstring"""





             assert 0 <= t <= 1, "Time t must be between 0 and 1."

             _lowerCamelCase				:  Any						=		self.basis_function(a__)
             _lowerCamelCase				:  List[Any]						=		0.0
             _lowerCamelCase				:  List[Any]						=		0.0
             for i in range(len(self.list_of_points)):
                    # For all points, sum up the product of i-th basis function and i-th point.
                    x += basis_function[i] * self.list_of_points[i][0]
                    y += basis_function[i] * self.list_of_points[i][1]
             return (x, y)



      def 					__snake_case      (		self   ,				a__ = 0.01):



             """simple docstring"""





             from matplotlib import pyplot as plt  # type: ignore

             _lowerCamelCase				:  list[float]						=		[]  # x coordinates of points to plot
             _lowerCamelCase				:  list[float]						=		[]  # y coordinates of points to plot

             _lowerCamelCase				:  List[Any]						=		0.0
             while t <= 1:
                    _lowerCamelCase				:  Tuple						=		self.bezier_curve_function(a__)
                    to_plot_x.append(value[0])
                    to_plot_y.append(value[1])
                    t += step_size

             _lowerCamelCase				:  List[Any]						=		[i[0] for i in self.list_of_points]
             _lowerCamelCase				:  Union[str, Any]						=		[i[1] for i in self.list_of_points]

             plt.plot(
                 a__   ,				a__   ,				color='''blue'''   ,				label='''Curve of Degree ''' + str(self.degree)   ,				)
             plt.scatter(a__   ,				a__   ,				color='''red'''   ,				label='''Control Points''')
             plt.legend()
             plt.show()


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
       BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
       BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3

