
'''simple docstring'''







# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion
import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import SchedulerMixin
from diffusers.utils import BaseOutput, deprecate


@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->DDIM
class 			lowerCAmelCase (				__UpperCAmelCase			):
		a							:					torch.FloatTensor
		a							:					Optional[torch.FloatTensor]       =					None



def 			_a		(	_SCREAMING_SNAKE_CASE		:   Any	,			_SCREAMING_SNAKE_CASE		:   List[str]=0.999	,			_SCREAMING_SNAKE_CASE		:   Tuple="cosine"	,			):
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(_SCREAMING_SNAKE_CASE		:   Union[str, Any]  ):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2  ) ** 2

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(_SCREAMING_SNAKE_CASE		:   List[Any]  ):
																		return math.exp(t * -12.0  )

						else:
												raise ValueError(F'Unsupported alpha_tranform_type: {alpha_transform_type}'  )

						_SCREAMING_SNAKE_CASE				= []
						for i in range(_SCREAMING_SNAKE_CASE  ):
												_SCREAMING_SNAKE_CASE				= i / num_diffusion_timesteps
												_SCREAMING_SNAKE_CASE				= (i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(_SCREAMING_SNAKE_CASE  ) / alpha_bar_fn(_SCREAMING_SNAKE_CASE  )	,			_SCREAMING_SNAKE_CASE  )  )
						return torch.tensor(_SCREAMING_SNAKE_CASE	,			dtype=torch.floataa  )




class 			lowerCAmelCase (				__UpperCAmelCase		,     __UpperCAmelCase			):
		a							:					int       =					1




		@register_to_config
		def __init__(				self					,						UpperCamelCase = 1_000					,						UpperCamelCase = 0.00_01					,						UpperCamelCase = 0.02					,						UpperCamelCase = "linear"					,						UpperCamelCase = None					,						UpperCamelCase = True					,						UpperCamelCase = True					,						UpperCamelCase = 0					,						UpperCamelCase = "epsilon"					,						UpperCamelCase = 1.0					,						**UpperCamelCase					,						):
								if kwargs.get("set_alpha_to_one"					,						UpperCamelCase      ) is not None:
														_SCREAMING_SNAKE_CASE				= (
														    "The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."
														)
														deprecate("set_alpha_to_one"					,						"1.0.0"					,						UpperCamelCase					,						standard_warn=UpperCamelCase      )
														_SCREAMING_SNAKE_CASE				= kwargs["set_alpha_to_one"]
								if trained_betas is not None:
														_SCREAMING_SNAKE_CASE				= torch.tensor(UpperCamelCase					,						dtype=torch.floataa      )
								elif beta_schedule == "linear":
														_SCREAMING_SNAKE_CASE				= torch.linspace(UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						dtype=torch.floataa      )
								elif beta_schedule == "scaled_linear":
														# this schedule is very specific to the latent diffusion model.
														_SCREAMING_SNAKE_CASE				= (
														    torch.linspace(beta_start**0.5					,						beta_end**0.5					,						UpperCamelCase					,						dtype=torch.floataa      ) ** 2
														)
								elif beta_schedule == "squaredcos_cap_v2":
														# Glide cosine schedule
														_SCREAMING_SNAKE_CASE				= betas_for_alpha_bar(UpperCamelCase      )
								else:
														raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'      )

								_SCREAMING_SNAKE_CASE				= 1.0 - self.betas
								_SCREAMING_SNAKE_CASE				= torch.cumprod(self.alphas					,						dim=0      )

								# At every step in inverted ddim, we are looking into the next alphas_cumprod
								# For the final step, there is no next alphas_cumprod, and the index is out of bounds
								# `set_alpha_to_zero` decides whether we set this parameter simply to zero
								# in this case, self.step() just output the predicted noise
								# or whether we use the final alpha of the "non-previous" one.
								_SCREAMING_SNAKE_CASE				= torch.tensor(0.0      ) if set_alpha_to_zero else self.alphas_cumprod[-1]

								# standard deviation of the initial noise distribution
								_SCREAMING_SNAKE_CASE				= 1.0

								# setable values
								_SCREAMING_SNAKE_CASE				= None
								_SCREAMING_SNAKE_CASE				= torch.from_numpy(np.arange(0					,						UpperCamelCase      ).copy().astype(np.intaa      )      )




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase = None      ):
								return sample




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase = None      ):

								if num_inference_steps > self.config.num_train_timesteps:
														raise ValueError(
														    F'`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:'
														    F' {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle'
														    F' maximal {self.config.num_train_timesteps} timesteps.'      )

								_SCREAMING_SNAKE_CASE				= num_inference_steps
								_SCREAMING_SNAKE_CASE				= self.config.num_train_timesteps // self.num_inference_steps
								# creates integer timesteps by multiplying by ratio
								# casting to int to avoid issues when num_inference_step is power of 3
								_SCREAMING_SNAKE_CASE				= (np.arange(0					,						UpperCamelCase      ) * step_ratio).round().copy().astype(np.intaa      )
								_SCREAMING_SNAKE_CASE				= torch.from_numpy(UpperCamelCase      ).to(UpperCamelCase      )
								self.timesteps += self.config.steps_offset




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase = 0.0					,						UpperCamelCase = False					,						UpperCamelCase = None					,						UpperCamelCase = True					,						):
								# 1. get previous step value (=t+1)
								_SCREAMING_SNAKE_CASE				= timestep + self.config.num_train_timesteps // self.num_inference_steps

								# 2. compute alphas, betas
								# change original implementation to exactly match noise levels for analogous forward process
								_SCREAMING_SNAKE_CASE				= self.alphas_cumprod[timestep]
								_SCREAMING_SNAKE_CASE				= (
								    self.alphas_cumprod[prev_timestep]
								    if prev_timestep < self.config.num_train_timesteps
								    else self.final_alpha_cumprod
								)

								_SCREAMING_SNAKE_CASE				= 1 - alpha_prod_t

								# 3. compute predicted original sample from predicted noise also called
								# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
								if self.config.prediction_type == "epsilon":
														_SCREAMING_SNAKE_CASE				= (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
														_SCREAMING_SNAKE_CASE				= model_output
								elif self.config.prediction_type == "sample":
														_SCREAMING_SNAKE_CASE				= model_output
														_SCREAMING_SNAKE_CASE				= (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
								elif self.config.prediction_type == "v_prediction":
														_SCREAMING_SNAKE_CASE				= (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
														_SCREAMING_SNAKE_CASE				= (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
								else:
														raise ValueError(
														    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'
														    " `v_prediction`"      )

								# 4. Clip or threshold "predicted x_0"
								if self.config.clip_sample:
														_SCREAMING_SNAKE_CASE				= pred_original_sample.clamp(
														    -self.config.clip_sample_range					,						self.config.clip_sample_range      )

								# 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
								_SCREAMING_SNAKE_CASE				= (1 - alpha_prod_t_prev) ** 0.5 * pred_epsilon

								# 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
								_SCREAMING_SNAKE_CASE				= alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

								if not return_dict:
														return (prev_sample, pred_original_sample)
								return DDIMSchedulerOutput(prev_sample=UpperCamelCase					,						pred_original_sample=UpperCamelCase      )




		def __len__(				self      ):
								return self.config.num_train_timesteps

'''simple docstring'''







import numpy

# List of input, output pairs
_snake_case				:   Optional[Any]     =				(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
_snake_case				:   Any     =				(((515, 22, 13), 555), ((61, 35, 49), 150))
_snake_case				:   Any     =				[2, 4, 1, 5]
_snake_case				:   str     =				len(train_data)
_snake_case				:   int     =				0.009



def 			_a		(	_SCREAMING_SNAKE_CASE		:   List[Any]	,			_SCREAMING_SNAKE_CASE		:   List[Any]="train"  ):
						return calculate_hypothesis_value(_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  ) - output(
						    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  )



def 			_a		(	_SCREAMING_SNAKE_CASE		:   List[Any]  ):
						_SCREAMING_SNAKE_CASE				= 0
						for i in range(len(_SCREAMING_SNAKE_CASE  ) - 1  ):
												hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
						hyp_val += parameter_vector[0]
						return hyp_val



def 			_a		(	_SCREAMING_SNAKE_CASE		:   str	,			_SCREAMING_SNAKE_CASE		:   Union[str, Any]  ):
						if data_set == "train":
												return train_data[example_no][1]
						elif data_set == "test":
												return test_data[example_no][1]
						return None



def 			_a		(	_SCREAMING_SNAKE_CASE		:   Any	,			_SCREAMING_SNAKE_CASE		:   str  ):
						if data_set == "train":
												return _hypothesis_value(train_data[example_no][0]  )
						elif data_set == "test":
												return _hypothesis_value(test_data[example_no][0]  )
						return None



def 			_a		(	_SCREAMING_SNAKE_CASE		:   Union[str, Any]	,			_SCREAMING_SNAKE_CASE		:   Optional[int]=m  ):
						_SCREAMING_SNAKE_CASE				= 0
						for i in range(_SCREAMING_SNAKE_CASE  ):
												if index == -1:
																		summation_value += _error(_SCREAMING_SNAKE_CASE  )
												else:
																		summation_value += _error(_SCREAMING_SNAKE_CASE  ) * train_data[i][0][index]
						return summation_value



def 			_a		(	_SCREAMING_SNAKE_CASE		:   Optional[Any]  ):
						_SCREAMING_SNAKE_CASE				= summation_of_cost_derivative(_SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE  ) / m
						return cost_derivative_value



def 			_a		(	):
						global parameter_vector
						# Tune these values to set a tolerance value for predicted output
						_SCREAMING_SNAKE_CASE				= 0.000_002
						_SCREAMING_SNAKE_CASE				= 0
						_SCREAMING_SNAKE_CASE				= 0
						while True:
												j += 1
												_SCREAMING_SNAKE_CASE				= [0, 0, 0, 0]
												for i in range(0	,			len(_SCREAMING_SNAKE_CASE  )  ):
																		_SCREAMING_SNAKE_CASE				= get_cost_derivative(i - 1  )
																		_SCREAMING_SNAKE_CASE				= (
																		    parameter_vector[i] - LEARNING_RATE * cost_derivative
																		)
												if numpy.allclose(
												    _SCREAMING_SNAKE_CASE	,			_SCREAMING_SNAKE_CASE	,			atol=_SCREAMING_SNAKE_CASE	,			rtol=_SCREAMING_SNAKE_CASE	,			):
																		break
												_SCREAMING_SNAKE_CASE				= temp_parameter_vector
						print(("Number of iterations:", j)  )



def 			_a		(	):
						for i in range(len(_SCREAMING_SNAKE_CASE  )  ):
												print(("Actual output value:", output(_SCREAMING_SNAKE_CASE	,			"test"  ))  )
												print(("Hypothesis output:", calculate_hypothesis_value(_SCREAMING_SNAKE_CASE	,			"test"  ))  )


if __name__ == "__main__":
						run_gradient_descent()
						print("""\nTesting gradient descent for a linear hypothesis function.\n""")
						test_gradient_descent()