
import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_=0.999	,	UpperCamelCase_="cosine"	,	)		->		Any:
					'''simple docstring'''


					if alpha_transform_type == "cosine":

										def alpha_bar_fn(UpperCamelCase_		):
															return math.cos((t + 0.008) / 1.008 * math.pi / 2		) ** 2

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(UpperCamelCase_		):
															return math.exp(t * -12.0		)

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

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




class 						lowercase__  (						_UpperCAmelCase     ,       _UpperCAmelCase  ):
	A__    :   Optional[Any]				       =[e.name for e in KarrasDiffusionSchedulers]
	A__    :   Optional[Any]				       =2
	@register_to_config
	def __init__(			self							:   Tuple       ,   UpperCAmelCase_							:   int = 1000       ,   UpperCAmelCase_							:   float = 0.00_085       ,   UpperCAmelCase_							:   float = 0.012       ,   UpperCAmelCase_							:   str = "linear"       ,   UpperCAmelCase_							:   Optional[Union[np.ndarray, List[float]]] = None       ,   UpperCAmelCase_							:   str = "epsilon"       ,   UpperCAmelCase_							:   Optional[bool] = False       ,   UpperCAmelCase_							:   Optional[bool] = False       ,   UpperCAmelCase_							:   float = 1.0       ,   UpperCAmelCase_							:   str = "linspace"       ,   UpperCAmelCase_							:   int = 0       ,   ):
						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_       ,   alpha_transform_type='cosine'							)
						elif beta_schedule == "exp":
											SCREAMING_SNAKE_CASE__													= betas_for_alpha_bar(UpperCAmelCase_       ,   alpha_transform_type='exp'							)
						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							)

						#  set all values
						self.set_timesteps(UpperCAmelCase_       ,   UpperCAmelCase_       ,   UpperCAmelCase_							)
						SCREAMING_SNAKE_CASE__													= use_karras_sigmas
	def      A_				(			self							:   List[Any]       ,   UpperCAmelCase_							:   Optional[int]       ,   UpperCAmelCase_							:   Tuple=None							):
						if schedule_timesteps is None:
											SCREAMING_SNAKE_CASE__													= self.timesteps

						SCREAMING_SNAKE_CASE__													= (schedule_timesteps == timestep).nonzero()

						# The sigma index that is taken for the **very** first `step`
						# is always the second index (or the last index if there is only 1)
						# This way we can ensure we don't accidentally skip a sigma in
						# case we start in the middle of the denoising schedule (e.g. for image-to-image)
						if len(self._index_counter							) == 0:
											SCREAMING_SNAKE_CASE__													= 1 if len(UpperCAmelCase_							) > 1 else 0
						else:
											SCREAMING_SNAKE_CASE__													= timestep.cpu().item() if torch.is_tensor(UpperCAmelCase_							) else timestep
											SCREAMING_SNAKE_CASE__													= self._index_counter[timestep_int]

						return indices[pos].item()
	@property
	def      A_				(			self							:   Optional[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      A_				(			self							:   Dict       ,   UpperCAmelCase_							:   torch.FloatTensor       ,   UpperCAmelCase_							:   Union[float, torch.FloatTensor]       ,   ):
						SCREAMING_SNAKE_CASE__													= self.index_for_timestep(UpperCAmelCase_							)

						SCREAMING_SNAKE_CASE__													= self.sigmas[step_index]
						SCREAMING_SNAKE_CASE__													= sample / ((sigma**2 + 1) ** 0.5)
						return sample
	def      A_				(			self							:   str       ,   UpperCAmelCase_							:   int       ,   UpperCAmelCase_							:   Union[str, torch.device] = None       ,   UpperCAmelCase_							:   Optional[int] = None       ,   ):
						SCREAMING_SNAKE_CASE__													= num_inference_steps

						SCREAMING_SNAKE_CASE__													= num_train_timesteps or self.config.num_train_timesteps

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

						SCREAMING_SNAKE_CASE__													= np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
						SCREAMING_SNAKE_CASE__													= np.log(UpperCAmelCase_							)
						SCREAMING_SNAKE_CASE__													= np.interp(UpperCAmelCase_       ,   np.arange(0       ,   len(UpperCAmelCase_							)							)       ,   UpperCAmelCase_							)

						if self.config.use_karras_sigmas:
											SCREAMING_SNAKE_CASE__													= self._convert_to_karras(in_sigmas=UpperCAmelCase_       ,   num_inference_steps=self.num_inference_steps							)
											SCREAMING_SNAKE_CASE__													= np.array([self._sigma_to_t(UpperCAmelCase_       ,   UpperCAmelCase_							) for sigma in sigmas]							)

						SCREAMING_SNAKE_CASE__													= np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
						SCREAMING_SNAKE_CASE__													= torch.from_numpy(UpperCAmelCase_							).to(device=UpperCAmelCase_							)
						SCREAMING_SNAKE_CASE__													= torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2							), sigmas[-1:]]							)

						SCREAMING_SNAKE_CASE__													= torch.from_numpy(UpperCAmelCase_							)
						SCREAMING_SNAKE_CASE__													= torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2							)]							)

						if str(UpperCAmelCase_							).startswith('mps'							):
											# mps does not support float64
											SCREAMING_SNAKE_CASE__													= timesteps.to(UpperCAmelCase_       ,   dtype=torch.floataa							)
						else:
											SCREAMING_SNAKE_CASE__													= timesteps.to(device=UpperCAmelCase_							)

						# empty dt and derivative
						SCREAMING_SNAKE_CASE__													= None
						SCREAMING_SNAKE_CASE__													= None

						# for exp beta schedules, such as the one for `pipeline_shap_e.py`
						# we need an index counter
						SCREAMING_SNAKE_CASE__													= defaultdict(UpperCAmelCase_							)
	def      A_				(			self							:   List[str]       ,   UpperCAmelCase_							:   Any       ,   UpperCAmelCase_							:   Dict							):
						# get log sigma
						SCREAMING_SNAKE_CASE__													= np.log(UpperCAmelCase_							)

						# get distribution
						SCREAMING_SNAKE_CASE__													= log_sigma - log_sigmas[:, np.newaxis]

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

						SCREAMING_SNAKE_CASE__													= log_sigmas[low_idx]
						SCREAMING_SNAKE_CASE__													= log_sigmas[high_idx]

						# interpolate sigmas
						SCREAMING_SNAKE_CASE__													= (low - log_sigma) / (low - high)
						SCREAMING_SNAKE_CASE__													= np.clip(UpperCAmelCase_       ,   0       ,   1							)

						# transform interpolation to time range
						SCREAMING_SNAKE_CASE__													= (1 - w) * low_idx + w * high_idx
						SCREAMING_SNAKE_CASE__													= t.reshape(sigma.shape							)
						return t
	def      A_				(			self							:   int       ,   UpperCAmelCase_							:   torch.FloatTensor       ,   UpperCAmelCase_							:   Dict							):
						SCREAMING_SNAKE_CASE__													= in_sigmas[-1].item()
						SCREAMING_SNAKE_CASE__													= in_sigmas[0].item()

						SCREAMING_SNAKE_CASE__													= 7.0  # 7.0 is the value used in the paper
						SCREAMING_SNAKE_CASE__													= np.linspace(0       ,   1       ,   UpperCAmelCase_							)
						SCREAMING_SNAKE_CASE__													= sigma_min ** (1 / rho)
						SCREAMING_SNAKE_CASE__													= sigma_max ** (1 / rho)
						SCREAMING_SNAKE_CASE__													= (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
						return sigmas
	@property
	def      A_				(			self							:   Optional[Any]							):
						return self.dt is None
	def      A_				(			self							:   Any       ,   UpperCAmelCase_							:   Union[torch.FloatTensor, np.ndarray]       ,   UpperCAmelCase_							:   Union[float, torch.FloatTensor]       ,   UpperCAmelCase_							:   Union[torch.FloatTensor, np.ndarray]       ,   UpperCAmelCase_							:   bool = True       ,   ):
						SCREAMING_SNAKE_CASE__													= self.index_for_timestep(UpperCAmelCase_							)

						# advance index counter by 1
						SCREAMING_SNAKE_CASE__													= timestep.cpu().item() if torch.is_tensor(UpperCAmelCase_							) else timestep
						self._index_counter[timestep_int] += 1

						if self.state_in_first_order:
											SCREAMING_SNAKE_CASE__													= self.sigmas[step_index]
											SCREAMING_SNAKE_CASE__													= self.sigmas[step_index + 1]
						else:
											# 2nd order / Heun's method
											SCREAMING_SNAKE_CASE__													= self.sigmas[step_index - 1]
											SCREAMING_SNAKE_CASE__													= self.sigmas[step_index]

						# currently only gamma=0 is supported. This usually works best anyways.
						# We can support gamma in the future but then need to scale the timestep before
						# passing it to the model which requires a change in API
						SCREAMING_SNAKE_CASE__													= 0
						SCREAMING_SNAKE_CASE__													= sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
											SCREAMING_SNAKE_CASE__													= sigma_hat if self.state_in_first_order else sigma_next
											SCREAMING_SNAKE_CASE__													= sample - sigma_input * model_output
						elif self.config.prediction_type == "v_prediction":
											SCREAMING_SNAKE_CASE__													= sigma_hat if self.state_in_first_order else sigma_next
											SCREAMING_SNAKE_CASE__													= model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
											    sample / (sigma_input**2 + 1)
											)
						elif self.config.prediction_type == "sample":
											SCREAMING_SNAKE_CASE__													= model_output
						else:
											raise ValueError(
											    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'							)

						if self.config.clip_sample:
											SCREAMING_SNAKE_CASE__													= pred_original_sample.clamp(
											    -self.config.clip_sample_range       ,   self.config.clip_sample_range							)

						if self.state_in_first_order:
											# 2. Convert to an ODE derivative for 1st order
											SCREAMING_SNAKE_CASE__													= (sample - pred_original_sample) / sigma_hat
											# 3. delta timestep
											SCREAMING_SNAKE_CASE__													= sigma_next - sigma_hat

											# store for 2nd order step
											SCREAMING_SNAKE_CASE__													= derivative
											SCREAMING_SNAKE_CASE__													= dt
											SCREAMING_SNAKE_CASE__													= sample
						else:
											# 2. 2nd order / Heun's method
											SCREAMING_SNAKE_CASE__													= (sample - pred_original_sample) / sigma_next
											SCREAMING_SNAKE_CASE__													= (self.prev_derivative + derivative) / 2

											# 3. take prev timestep & sample
											SCREAMING_SNAKE_CASE__													= self.dt
											SCREAMING_SNAKE_CASE__													= self.sample

											# free dt and derivative
											# Note, this puts the scheduler in "first order mode"
											SCREAMING_SNAKE_CASE__													= None
											SCREAMING_SNAKE_CASE__													= None
											SCREAMING_SNAKE_CASE__													= None

						SCREAMING_SNAKE_CASE__													= sample + derivative * dt

						if not return_dict:
											return (prev_sample,)

						return SchedulerOutput(prev_sample=UpperCAmelCase_							)
	def      A_				(			self							:   Union[str, Any]       ,   UpperCAmelCase_							:   torch.FloatTensor       ,   UpperCAmelCase_							:   torch.FloatTensor       ,   UpperCAmelCase_							:   torch.FloatTensor       ,   ):
						# Make sure sigmas and timesteps have the same device and dtype as original_samples
						SCREAMING_SNAKE_CASE__													= self.sigmas.to(device=original_samples.device       ,   dtype=original_samples.dtype							)
						if original_samples.device.type == "mps" and torch.is_floating_point(UpperCAmelCase_							):
											# mps does not support float64
											SCREAMING_SNAKE_CASE__													= self.timesteps.to(original_samples.device       ,   dtype=torch.floataa							)
											SCREAMING_SNAKE_CASE__													= timesteps.to(original_samples.device       ,   dtype=torch.floataa							)
						else:
											SCREAMING_SNAKE_CASE__													= self.timesteps.to(original_samples.device							)
											SCREAMING_SNAKE_CASE__													= timesteps.to(original_samples.device							)

						SCREAMING_SNAKE_CASE__													= [self.index_for_timestep(UpperCAmelCase_       ,   UpperCAmelCase_							) for t in timesteps]

						SCREAMING_SNAKE_CASE__													= sigmas[step_indices].flatten()
						while len(sigma.shape							) < len(original_samples.shape							):
											SCREAMING_SNAKE_CASE__													= sigma.unsqueeze(-1							)

						SCREAMING_SNAKE_CASE__													= original_samples + noise * sigma
						return noisy_samples





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







def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					def update_area_of_max_square(UpperCamelCase_	,	UpperCamelCase_		) -> int:
										# BASE CASE
										if row >= rows or col >= cols:
															return 0

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(UpperCamelCase_	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	col + 1		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square(row + 1	,	UpperCamelCase_		)

										if mat[row][col]:
															SCREAMING_SNAKE_CASE__													= 1 + min([right, diagonal, down]		)
															SCREAMING_SNAKE_CASE__													= max(largest_square_area[0]	,	UpperCamelCase_		)
															return sub_problem_sol
										else:
															return 0

					SCREAMING_SNAKE_CASE__													= [0]
					update_area_of_max_square(0	,	0		)
					return largest_square_area[0]






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					def update_area_of_max_square_using_dp_array(
					    UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		) -> int:
										if row >= rows or col >= cols:
															return 0
										if dp_array[row][col] != -1:
															return dp_array[row][col]

										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(UpperCamelCase_	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	col + 1	,	UpperCamelCase_		)
										SCREAMING_SNAKE_CASE__													= update_area_of_max_square_using_dp_array(row + 1	,	UpperCamelCase_	,	UpperCamelCase_		)

										if mat[row][col]:
															SCREAMING_SNAKE_CASE__													= 1 + min([right, diagonal, down]		)
															SCREAMING_SNAKE_CASE__													= max(largest_square_area[0]	,	UpperCamelCase_		)
															SCREAMING_SNAKE_CASE__													= sub_problem_sol
															return sub_problem_sol
										else:
															return 0

					SCREAMING_SNAKE_CASE__													= [0]
					SCREAMING_SNAKE_CASE__													= [[-1] * cols for _ in range(UpperCamelCase_		)]
					update_area_of_max_square_using_dp_array(0	,	0	,	UpperCamelCase_		)

					return largest_square_area[0]






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					SCREAMING_SNAKE_CASE__													= [[0] * (cols + 1) for _ in range(rows + 1		)]
					SCREAMING_SNAKE_CASE__													= 0
					for row in range(rows - 1	,	-1	,	-1		):
										for col in range(cols - 1	,	-1	,	-1		):
															SCREAMING_SNAKE_CASE__													= dp_array[row][col + 1]
															SCREAMING_SNAKE_CASE__													= dp_array[row + 1][col + 1]
															SCREAMING_SNAKE_CASE__													= dp_array[row + 1][col]

															if mat[row][col] == 1:
																				SCREAMING_SNAKE_CASE__													= 1 + min(UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)
																				SCREAMING_SNAKE_CASE__													= max(dp_array[row][col]	,	UpperCamelCase_		)
															else:
																				SCREAMING_SNAKE_CASE__													= 0

					return largest_square_area






def 							_lowercase							(     UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)		->		int:
					'''simple docstring'''


					SCREAMING_SNAKE_CASE__													= [0] * (cols + 1)
					SCREAMING_SNAKE_CASE__													= [0] * (cols + 1)
					SCREAMING_SNAKE_CASE__													= 0
					for row in range(rows - 1	,	-1	,	-1		):
										for col in range(cols - 1	,	-1	,	-1		):
															SCREAMING_SNAKE_CASE__													= current_row[col + 1]
															SCREAMING_SNAKE_CASE__													= next_row[col + 1]
															SCREAMING_SNAKE_CASE__													= next_row[col]

															if mat[row][col] == 1:
																				SCREAMING_SNAKE_CASE__													= 1 + min(UpperCamelCase_	,	UpperCamelCase_	,	UpperCamelCase_		)
																				SCREAMING_SNAKE_CASE__													= max(current_row[col]	,	UpperCamelCase_		)
															else:
																				SCREAMING_SNAKE_CASE__													= 0
										SCREAMING_SNAKE_CASE__													= current_row

					return largest_square_area


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))





