






'''simple docstring'''

import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


A:   str						=					logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class 				__magic_name__  (						UpperCAmelCase_					):







	"""simple docstring"""



	SCREAMING_SNAKE_CASE_       :   torch.FloatTensor
	SCREAMING_SNAKE_CASE_       :   Optional[torch.FloatTensor]   =	None






def 						_UpperCAmelCase     (	a		:						Tuple    ,      a		:						Optional[int]=0.9_99    ,      a		:						Dict="cosine"    ,      )      ->      Optional[Any]:





						"""simple docstring"""
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(a		:						Optional[int]				):
																		return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2				) ** 2

						elif alpha_transform_type == "exp":

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

						else:
												raise ValueError(f"Unsupported alpha_tranform_type: {alpha_transform_type}"				)

						lowercase_   : Tuple   	=      []
						for i in range(a				):
												lowercase_   : str   	=      i / num_diffusion_timesteps
												lowercase_   : Optional[int]   	=      (i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(a				) / alpha_bar_fn(a				)    ,      a				)				)
						return torch.tensor(a    ,      dtype=torch.floataa				)






class 				__magic_name__  (						UpperCAmelCase_,    UpperCAmelCase_					):







	"""simple docstring"""



	SCREAMING_SNAKE_CASE_       :   List[Any]   =	[e.name for e in KarrasDiffusionSchedulers]
	SCREAMING_SNAKE_CASE_       :   List[str]   =	1
	@register_to_config
	def __init__(				self	,   _lowercase = 1000	,   _lowercase = 0.00_01	,   _lowercase = 0.02	,   _lowercase = "linear"	,   _lowercase = None	,   _lowercase = "epsilon"	,   _lowercase = "linear"	,   _lowercase = False	,   _lowercase = "linspace"	,   _lowercase = 0	,   )    ->	Union[str, Any]:
							if trained_betas is not None:
													lowercase_   : List[str]   	=      torch.tensor(_lowercase	,   dtype=torch.floataa							)
							elif beta_schedule == "linear":
													lowercase_   : List[Any]   	=      torch.linspace(_lowercase	,   _lowercase	,   _lowercase	,   dtype=torch.floataa							)
							elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													lowercase_   : List[str]   	=      (
													    torch.linspace(beta_start**0.5	,   beta_end**0.5	,   _lowercase	,   dtype=torch.floataa							) ** 2
													)
							elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													lowercase_   : Union[str, Any]   	=      betas_for_alpha_bar(_lowercase							)
							else:
													raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"							)

							lowercase_   : Tuple   	=      1.0 - self.betas
							lowercase_   : Optional[Any]   	=      torch.cumprod(self.alphas	,   dim=0							)

							lowercase_   : Optional[int]   	=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
							lowercase_   : Union[str, Any]   	=      np.concatenate([sigmas[::-1], [0.0]]							).astype(np.floataa							)
							lowercase_   : Optional[Any]   	=      torch.from_numpy(_lowercase							)

							# setable values
							lowercase_   : Optional[Any]   	=      None
							lowercase_   : Optional[int]   	=      np.linspace(0	,   num_train_timesteps - 1	,   _lowercase	,   dtype=_lowercase							)[::-1].copy()
							lowercase_   : str   	=      torch.from_numpy(_lowercase							)
							lowercase_   : Tuple   	=      False
							lowercase_   : Dict   	=      use_karras_sigmas
	@property
	def 							lowerCamelCase__		(				self							)    ->	List[Any]:
							# standard deviation of the initial noise distribution
							if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

							return (self.sigmas.max() ** 2 + 1) ** 0.5
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase							)    ->	torch.FloatTensor:
							if isinstance(_lowercase	,   torch.Tensor							):
													lowercase_   : Tuple   	=      timestep.to(self.timesteps.device							)
							lowercase_   : Optional[Any]   	=      (self.timesteps == timestep).nonzero().item()
							lowercase_   : List[str]   	=      self.sigmas[step_index]

							lowercase_   : str   	=      sample / ((sigma**2 + 1) ** 0.5)

							lowercase_   : List[str]   	=      True
							return sample
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase = None							)    ->	str:
							lowercase_   : Optional[int]   	=      num_inference_steps

							# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
							if self.config.timestep_spacing == "linspace":
													lowercase_   : Any   	=      np.linspace(0	,   self.config.num_train_timesteps - 1	,   _lowercase	,   dtype=_lowercase							)[
													    ::-1
													].copy()
							elif self.config.timestep_spacing == "leading":
													lowercase_   : List[str]   	=      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
													lowercase_   : List[str]   	=      (np.arange(0	,   _lowercase							) * step_ratio).round()[::-1].copy().astype(_lowercase							)
													timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
													lowercase_   : List[str]   	=      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
													lowercase_   : Optional[Any]   	=      (np.arange(self.config.num_train_timesteps	,   0	,   -step_ratio							)).round().copy().astype(_lowercase							)
													timesteps -= 1
							else:
													raise ValueError(
													    f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."							)

							lowercase_   : Union[str, Any]   	=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
							lowercase_   : Any   	=      np.log(_lowercase							)

							if self.config.interpolation_type == "linear":
													lowercase_   : Dict   	=      np.interp(_lowercase	,   np.arange(0	,   len(_lowercase							)							)	,   _lowercase							)
							elif self.config.interpolation_type == "log_linear":
													lowercase_   : int   	=      torch.linspace(np.log(sigmas[-1]							)	,   np.log(sigmas[0]							)	,   num_inference_steps + 1							).exp()
							else:
													raise ValueError(
													    f"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
													    ' \'linear\' or \'log_linear\''							)

							if self.use_karras_sigmas:
													lowercase_   : List[str]   	=      self._convert_to_karras(in_sigmas=_lowercase	,   num_inference_steps=self.num_inference_steps							)
													lowercase_   : Tuple   	=      np.array([self._sigma_to_t(_lowercase	,   _lowercase							) for sigma in sigmas]							)

							lowercase_   : Any   	=      np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
							lowercase_   : str   	=      torch.from_numpy(_lowercase							).to(device=_lowercase							)
							if str(_lowercase							).startswith('mps'							):
													# mps does not support float64
													lowercase_   : int   	=      torch.from_numpy(_lowercase							).to(_lowercase	,   dtype=torch.floataa							)
							else:
													lowercase_   : List[Any]   	=      torch.from_numpy(_lowercase							).to(device=_lowercase							)
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase							)    ->	List[Any]:
							# get log sigma
							lowercase_   : List[str]   	=      np.log(_lowercase							)

							# get distribution
							lowercase_   : List[str]   	=      log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							lowercase_   : List[Any]   	=      np.cumsum((dists >= 0)	,   axis=0							).argmax(axis=0							).clip(max=log_sigmas.shape[0] - 2							)
							lowercase_   : int   	=      low_idx + 1

							lowercase_   : Optional[int]   	=      log_sigmas[low_idx]
							lowercase_   : Optional[int]   	=      log_sigmas[high_idx]

							# interpolate sigmas
							lowercase_   : str   	=      (low - log_sigma) / (low - high)
							lowercase_   : Any   	=      np.clip(_lowercase	,   0	,   1							)

							# transform interpolation to time range
							lowercase_   : int   	=      (1 - w) * low_idx + w * high_idx
							lowercase_   : List[str]   	=      t.reshape(sigma.shape							)
							return t
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase							)    ->	torch.FloatTensor:
							lowercase_   : float   	=      in_sigmas[-1].item()
							lowercase_   : float   	=      in_sigmas[0].item()

							lowercase_   : Tuple   	=      7.0  # 7.0 is the value used in the paper
							lowercase_   : List[Any]   	=      np.linspace(0	,   1	,   _lowercase							)
							lowercase_   : List[str]   	=      sigma_min ** (1 / rho)
							lowercase_   : List[str]   	=      sigma_max ** (1 / rho)
							lowercase_   : Tuple   	=      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase	,   _lowercase	,   _lowercase = 0.0	,   _lowercase = 0.0	,   _lowercase = float('inf'							)	,   _lowercase = 1.0	,   _lowercase = None	,   _lowercase = True	,   )    ->	Union[EulerDiscreteSchedulerOutput, Tuple]:

							if (
							    isinstance(_lowercase	,   _lowercase							)
							    or isinstance(_lowercase	,   torch.IntTensor							)
							    or isinstance(_lowercase	,   torch.LongTensor							)
							):
													raise ValueError(
													    (
													        'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
													        ' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'
													        ' one of the `scheduler.timesteps` as a timestep.'
													    )	,   )

							if not self.is_scale_input_called:
													logger.warning(
													    'The `scale_model_input` function should be called before `step` to ensure correct denoising. '
													    'See `StableDiffusionPipeline` for a usage example.'							)

							if isinstance(_lowercase	,   torch.Tensor							):
													lowercase_   : List[str]   	=      timestep.to(self.timesteps.device							)

							lowercase_   : Union[str, Any]   	=      (self.timesteps == timestep).nonzero().item()
							lowercase_   : Union[str, Any]   	=      self.sigmas[step_index]

							lowercase_   : List[str]   	=      min(s_churn / (len(self.sigmas							) - 1)	,   2**0.5 - 1							) if s_tmin <= sigma <= s_tmax else 0.0

							lowercase_   : Any   	=      randn_tensor(
							    model_output.shape	,   dtype=model_output.dtype	,   device=model_output.device	,   generator=_lowercase							)

							lowercase_   : Any   	=      noise * s_noise
							lowercase_   : Optional[int]   	=      sigma * (gamma + 1)

							if gamma > 0:
													lowercase_   : Union[str, Any]   	=      sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							# NOTE: "original_sample" should not be an expected prediction_type but is left in for
							# backwards compatibility
							if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
													lowercase_   : Optional[Any]   	=      model_output
							elif self.config.prediction_type == "epsilon":
													lowercase_   : str   	=      sample - sigma_hat * model_output
							elif self.config.prediction_type == "v_prediction":
													# * c_out + input * c_skip
													lowercase_   : Dict   	=      model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
							else:
													raise ValueError(
													    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"							)

							# 2. Convert to an ODE derivative
							lowercase_   : Optional[Any]   	=      (sample - pred_original_sample) / sigma_hat

							lowercase_   : Optional[int]   	=      self.sigmas[step_index + 1] - sigma_hat

							lowercase_   : List[Any]   	=      sample + derivative * dt

							if not return_dict:
													return (prev_sample,)

							return EulerDiscreteSchedulerOutput(prev_sample=_lowercase	,   pred_original_sample=_lowercase							)
	def 							lowerCamelCase__		(				self	,   _lowercase	,   _lowercase	,   _lowercase	,   )    ->	torch.FloatTensor:
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							lowercase_   : List[Any]   	=      self.sigmas.to(device=original_samples.device	,   dtype=original_samples.dtype							)
							if original_samples.device.type == "mps" and torch.is_floating_point(_lowercase							):
													# mps does not support float64
													lowercase_   : Optional[Any]   	=      self.timesteps.to(original_samples.device	,   dtype=torch.floataa							)
													lowercase_   : str   	=      timesteps.to(original_samples.device	,   dtype=torch.floataa							)
							else:
													lowercase_   : Dict   	=      self.timesteps.to(original_samples.device							)
													lowercase_   : Union[str, Any]   	=      timesteps.to(original_samples.device							)

							lowercase_   : Any   	=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

							lowercase_   : Union[str, Any]   	=      sigmas[step_indices].flatten()
							while len(sigma.shape							) < len(original_samples.shape							):
													lowercase_   : Any   	=      sigma.unsqueeze(-1							)

							lowercase_   : Any   	=      original_samples + noise * sigma
							return noisy_samples







	def __len__(				self							)    ->	Dict:
							return self.config.num_train_timesteps








'''simple docstring'''

from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar






def 						_UpperCAmelCase     (	a		:						float    ,      a		:						float    ,      a		:						int				)      ->      list:





						"""simple docstring"""
						seed(1				)
						return [gauss(a    ,      a				) for _ in range(a				)]






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						list				)      ->      list:





						"""simple docstring"""
						return [k for k in range(a				) for _ in range(instance_count[k]				)]






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						list				)      ->      float:





						"""simple docstring"""
						return sum(a				) / instance_count






def 						_UpperCAmelCase     (	a		:						int    ,      a		:						int				)      ->      float:





						"""simple docstring"""
						return instance_count / total_count






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list    ,      a		:						int				)      ->      float:





						"""simple docstring"""
						lowercase_   : str   	=      []  # An empty list to store all squared differences
						# iterate over number of elements in items
						for i in range(len(a				)				):
												# for loop iterates over number of elements in inner layer of items
												for j in range(len(items[i]				)				):
																		# appending squared differences to 'squared_diff' list
																		squared_diff.append((items[i][j] - means[i]) ** 2				)

    # one divided by (the number of all instances - number of classes) multiplied by
    # sum of all squared differences
						lowercase_   : Tuple   	=      len(a				)  # Number of classes in dataset
						return 1 / (total_count - n_classes) * sum(a				)






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list    ,      a		:						float    ,      a		:						list				)      ->      list:





						"""simple docstring"""
						lowercase_   : str   	=      []
						# for loop iterates over number of elements in list
						for i in range(len(a				)				):
												# for loop iterates over number of inner items of each element
												for j in range(len(x_items[i]				)				):
																		lowercase_   : Any   	=      []  # to store all discriminant values of each item as a list
																		# for loop iterates over number of classes we have in our dataset
																		for k in range(len(a				)				):
																								# appending values of discriminants for each class to 'temp' list
																								temp.append(
																								    x_items[i][j] * (means[k] / variance)
																								    - (means[k] ** 2 / (2 * variance))
																								    + log(probabilities[k]				)				)
																		# appending discriminant values of each item to 'results' list
																		results.append(a				)

						return [result.index(max(a				)				) for result in results]






def 						_UpperCAmelCase     (	a		:						list    ,      a		:						list				)      ->      float:





						"""simple docstring"""
						lowercase_   : Optional[Any]   	=      sum(1 for i, j in zip(a    ,      a				) if i == j				)
						# percentage of accuracy equals to number of correct predictions divided by number
						# of all data and multiplied by 100
						return (correct / len(a				)) * 1_0_0


A:   Union[str, Any]						=					TypeVar("num")






def 						_UpperCAmelCase     (	a		:						Callable[[object], num]    ,      a		:						str    ,      a		:						str    ,      a		:						Callable[[num], bool] = lambda a				: True    ,      a		:						str | None = None    ,      )      ->      num:





						"""simple docstring"""
						while True:
												try:
																		lowercase_   : int   	=      input_type(input(a				).strip() or default				)
																		if condition(a				):
																								return user_input
																		else:
																								print(f"{user_input}: {err_msg}"				)
																								continue
												except ValueError:
																		print(
																		    f"{user_input}: Incorrect input type, expected {input_type.__name__!r}"				)






def 						_UpperCAmelCase     (	)      ->      List[str]:





						"""simple docstring"""
						while True:
												print(' Linear Discriminant Analysis '.center(5_0    ,      '*'				)				)
												print('*' * 5_0    ,      '\n'				)
												print('First of all we should specify the number of classes that'				)
												print('we want to generate as training dataset'				)
												# Trying to get number of classes
												lowercase_   : Dict   	=      valid_input(
												    input_type=a    ,      condition=lambda a				: x > 0    ,      input_msg='Enter the number of classes (Data Groupings): '    ,      err_msg='Number of classes should be positive!'    ,      )

												print('-' * 1_0_0				)

												# Trying to get the value of standard deviation
												lowercase_   : List[Any]   	=      valid_input(
												    input_type=a    ,      condition=lambda a				: x >= 0    ,      input_msg=(
												        'Enter the value of standard deviation'
												        '(Default value is 1.0 for all classes): '
												    )    ,      err_msg='Standard deviation should not be negative!'    ,      default='1.0'    ,      )

												print('-' * 1_0_0				)

												# Trying to get number of instances in classes and theirs means to generate
												# dataset
												lowercase_   : Any   	=      []  # An empty list to store instance counts of classes in dataset
												for i in range(a				):
																		lowercase_   : Union[str, Any]   	=      valid_input(
																		    input_type=a    ,      condition=lambda a				: x > 0    ,      input_msg=(f"Enter The number of instances for class_{i+1}: ")    ,      err_msg='Number of instances should be positive!'    ,      )
																		counts.append(a				)
												print('-' * 1_0_0				)

												# An empty list to store values of user-entered means of classes
												lowercase_   : int   	=      []
												for a in range(a				):
																		lowercase_   : Union[str, Any]   	=      valid_input(
																		    input_type=a    ,      input_msg=(f"Enter the value of mean for class_{a+1}: ")    ,      err_msg='This is an invalid value.'    ,      )
																		user_means.append(a				)
												print('-' * 1_0_0				)

												print('Standard deviation: '    ,      a				)
												# print out the number of instances in classes in separated line
												for i, count in enumerate(a    ,      1				):
																		print(f"Number of instances in class_{i} is: {count}"				)
												print('-' * 1_0_0				)

												# print out mean values of classes separated line
												for i, user_mean in enumerate(a    ,      1				):
																		print(f"Mean of class_{i} is: {user_mean}"				)
												print('-' * 1_0_0				)

												# Generating training dataset drawn from gaussian distribution
												lowercase_   : Optional[int]   	=      [
												    gaussian_distribution(user_means[j]    ,      a    ,      counts[j]				)
												    for j in range(a				)
												]
												print('Generated Normal Distribution: \n'    ,      a				)
												print('-' * 1_0_0				)

												# Generating Ys to detecting corresponding classes
												lowercase_   : Optional[int]   	=      y_generator(a    ,      a				)
												print('Generated Corresponding Ys: \n'    ,      a				)
												print('-' * 1_0_0				)

												# Calculating the value of actual mean for each class
												lowercase_   : str   	=      [calculate_mean(counts[k]    ,      x[k]				) for k in range(a				)]
												# for loop iterates over number of elements in 'actual_means' list and print
												# out them in separated line
												for i, actual_mean in enumerate(a    ,      1				):
																		print(f"Actual(Real) mean of class_{i} is: {actual_mean}"				)
												print('-' * 1_0_0				)

												# Calculating the value of probabilities for each class
												lowercase_   : Union[str, Any]   	=      [
												    calculate_probabilities(counts[i]    ,      sum(a				)				) for i in range(a				)
												]

												# for loop iterates over number of elements in 'probabilities' list and print
												# out them in separated line
												for i, probability in enumerate(a    ,      1				):
																		print(f"Probability of class_{i} is: {probability}"				)
												print('-' * 1_0_0				)

												# Calculating the values of variance for each class
												lowercase_   : List[str]   	=      calculate_variance(a    ,      a    ,      sum(a				)				)
												print('Variance: '    ,      a				)
												print('-' * 1_0_0				)

												# Predicting Y values
												# storing predicted Y values in 'pre_indexes' variable
												lowercase_   : Tuple   	=      predict_y_values(a    ,      a    ,      a    ,      a				)
												print('-' * 1_0_0				)

												# Calculating Accuracy of the model
												print(f"Accuracy: {accuracy(a    ,      a				)}"				)
												print('-' * 1_0_0				)
												print(' DONE '.center(1_0_0    ,      '+'				)				)

												if input('Press any key to restart or \'q\' for quit: '				).strip().lower() == "q":
																		print('\n' + 'GoodBye!'.center(1_0_0    ,      '-'				) + '\n'				)
																		break
												system('cls' if name == 'nt' else 'clear'				)  # noqa: S605


if __name__ == "__main__":
						main()
