


"""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_											=     logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class snake_case   (	_UpperCamelCase):
		__UpperCamelCase							     =      42
		__UpperCamelCase							     =      None






def   a__			(					__lowercase  ,      __lowercase=0.999  ,      __lowercase="cosine"  ,      )						->						Optional[Any]:
				if alpha_transform_type == "cosine":

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

				elif alpha_transform_type == "exp":

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

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

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




class snake_case   (	_UpperCamelCase  ,					_UpperCamelCase):
		__UpperCamelCase							     =      [e.name for e in KarrasDiffusionSchedulers]
		__UpperCamelCase							     =      1







		@register_to_config
		def __init__(       self   :							Dict     , a__   :							int = 10_00     , a__   :							float = 0.0_0_0_1     , a__   :							float = 0.0_2     , a__   :							str = "linear"     , a__   :							Optional[Union[np.ndarray, List[float]]] = None     , a__   :							str = "epsilon"     , a__   :							str = "linear"     , a__   :							Optional[bool] = False     , a__   :							str = "linspace"     , a__   :							int = 0     , )							->    Any:





						'''simple docstring'''







						if trained_betas is not None:
										_A       	=      torch.tensor(a__     , dtype=torch.floataa		)
						elif beta_schedule == "linear":
										_A       	=      torch.linspace(a__     , a__     , a__     , dtype=torch.floataa		)
						elif beta_schedule == "scaled_linear":
										# this schedule is very specific to the latent diffusion model.
										_A       	=      (
										    torch.linspace(beta_start**0.5     , beta_end**0.5     , a__     , dtype=torch.floataa		) ** 2
										)
						elif beta_schedule == "squaredcos_cap_v2":
										# Glide cosine schedule
										_A       	=      betas_for_alpha_bar(a__		)
						else:
										raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""		)

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

						_A       	=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
						_A       	=      np.concatenate([sigmas[::-1], [0.0]]		).astype(np.floataa		)
						_A       	=      torch.from_numpy(a__		)

						# setable values
						_A       	=      None
						_A       	=      np.linspace(0     , num_train_timesteps - 1     , a__     , dtype=a__		)[::-1].copy()
						_A       	=      torch.from_numpy(a__		)
						_A       	=      False
						_A       	=      use_karras_sigmas







		@property
		def 			a_			(       self   :							Dict		)							->    str:





						'''simple docstring'''







						if self.config.timestep_spacing in ["linspace", "trailing"]:
										return self.sigmas.max()

						return (self.sigmas.max() ** 2 + 1) ** 0.5







		def 			a_			(       self   :							Optional[Any]     , a__   :							torch.FloatTensor     , a__   :							Union[float, torch.FloatTensor]		)							->    torch.FloatTensor:





						'''simple docstring'''







						if isinstance(a__     , torch.Tensor		):
										_A       	=      timestep.to(self.timesteps.device		)
						_A       	=      (self.timesteps == timestep).nonzero().item()
						_A       	=      self.sigmas[step_index]

						_A       	=      sample / ((sigma**2 + 1) ** 0.5)

						_A       	=      True
						return sample







		def 			a_			(       self   :							Optional[int]     , a__   :							int     , a__   :							Union[str, torch.device] = None		)							->    Dict:





						'''simple docstring'''







						_A       	=      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":
										_A       	=      np.linspace(0     , self.config.num_train_timesteps - 1     , a__     , dtype=a__		)[
										    ::-1
										].copy()
						elif self.config.timestep_spacing == "leading":
										_A       	=      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
										_A       	=      (np.arange(0     , a__		) * step_ratio).round()[::-1].copy().astype(a__		)
										timesteps += self.config.steps_offset
						elif self.config.timestep_spacing == "trailing":
										_A       	=      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
										_A       	=      (np.arange(self.config.num_train_timesteps     , 0     , -step_ratio		)).round().copy().astype(a__		)
										timesteps -= 1
						else:
										raise ValueError(
										    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""		)

						_A       	=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
						_A       	=      np.log(a__		)

						if self.config.interpolation_type == "linear":
										_A       	=      np.interp(a__     , np.arange(0     , len(a__		)		)     , a__		)
						elif self.config.interpolation_type == "log_linear":
										_A       	=      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:
										_A       	=      self._convert_to_karras(in_sigmas=a__     , num_inference_steps=self.num_inference_steps		)
										_A       	=      np.array([self._sigma_to_t(a__     , a__		) for sigma in sigmas]		)

						_A       	=      np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)
						_A       	=      torch.from_numpy(a__		).to(device=a__		)
						if str(a__		).startswith("mps"		):
										# mps does not support float64
										_A       	=      torch.from_numpy(a__		).to(a__     , dtype=torch.floataa		)
						else:
										_A       	=      torch.from_numpy(a__		).to(device=a__		)







		def 			a_			(       self   :							Dict     , a__   :							List[Any]     , a__   :							str		)							->    int:





						'''simple docstring'''







						_A       	=      np.log(a__		)

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

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

						_A       	=      log_sigmas[low_idx]
						_A       	=      log_sigmas[high_idx]

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

						# transform interpolation to time range
						_A       	=      (1 - w) * low_idx + w * high_idx
						_A       	=      t.reshape(sigma.shape		)
						return t







		def 			a_			(       self   :							List[Any]     , a__   :							torch.FloatTensor     , a__   :							Tuple		)							->    torch.FloatTensor:





						'''simple docstring'''







						_A       	=      in_sigmas[-1].item()
						_A       	=      in_sigmas[0].item()

						_A       	=      7.0  # 7.0 is the value used in the paper
						_A       	=      np.linspace(0     , 1     , a__		)
						_A       	=      sigma_min ** (1 / rho)
						_A       	=      sigma_max ** (1 / rho)
						_A       	=      (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
						return sigmas







		def 			a_			(       self   :							Any     , a__   :							torch.FloatTensor     , a__   :							Union[float, torch.FloatTensor]     , a__   :							torch.FloatTensor     , a__   :							float = 0.0     , a__   :							float = 0.0     , a__   :							float = float("inf"		)     , a__   :							float = 1.0     , a__   :							Optional[torch.Generator] = None     , a__   :							bool = True     , )							->    Union[EulerDiscreteSchedulerOutput, Tuple]:





						'''simple docstring'''







						if (
						    isinstance(a__     , a__		)
						    or isinstance(a__     , torch.IntTensor		)
						    or isinstance(a__     , 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(a__     , torch.Tensor		):
										_A       	=      timestep.to(self.timesteps.device		)

						_A       	=      (self.timesteps == timestep).nonzero().item()
						_A       	=      self.sigmas[step_index]

						_A       	=      min(s_churn / (len(self.sigmas		) - 1)     , 2**0.5 - 1		) if s_tmin <= sigma <= s_tmax else 0.0

						_A       	=      randn_tensor(
						    model_output.shape     , dtype=model_output.dtype     , device=model_output.device     , generator=a__		)

						_A       	=      noise * s_noise
						_A       	=      sigma * (gamma + 1)

						if gamma > 0:
										_A       	=      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":
										_A       	=      model_output
						elif self.config.prediction_type == "epsilon":
										_A       	=      sample - sigma_hat * model_output
						elif self.config.prediction_type == "v_prediction":
										# * c_out + input * c_skip
										_A       	=      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
						_A       	=      (sample - pred_original_sample) / sigma_hat

						_A       	=      self.sigmas[step_index + 1] - sigma_hat

						_A       	=      sample + derivative * dt

						if not return_dict:
										return (prev_sample,)

						return EulerDiscreteSchedulerOutput(prev_sample=a__     , pred_original_sample=a__		)







		def 			a_			(       self   :							List[str]     , a__   :							torch.FloatTensor     , a__   :							torch.FloatTensor     , a__   :							torch.FloatTensor     , )							->    torch.FloatTensor:





						'''simple docstring'''







						_A       	=      self.sigmas.to(device=original_samples.device     , dtype=original_samples.dtype		)
						if original_samples.device.type == "mps" and torch.is_floating_point(a__		):
										# mps does not support float64
										_A       	=      self.timesteps.to(original_samples.device     , dtype=torch.floataa		)
										_A       	=      timesteps.to(original_samples.device     , dtype=torch.floataa		)
						else:
										_A       	=      self.timesteps.to(original_samples.device		)
										_A       	=      timesteps.to(original_samples.device		)

						_A       	=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

						_A       	=      original_samples + noise * sigma
						return noisy_samples







		def __len__(       self   :							Any		)							->    List[Any]:





						'''simple docstring'''







						return self.config.num_train_timesteps



"""simple docstring"""


def   a__			(					__lowercase )						->						bool:
				# must be
				_A       	=      [list(__lowercase ) for row in matrix]
				if matrix and isinstance(__lowercase  ,      __lowercase ):
								if isinstance(matrix[0]  ,      __lowercase ):
												_A       	=      0
												for row in matrix:
																if prev_len == 0:
																				_A       	=      len(__lowercase )
																				_A       	=      True
																else:
																				_A       	=      prev_len == len(__lowercase )
								else:
												_A       	=      True
				else:
								_A       	=      False

				return result






def   a__			(					__lowercase )						->						None:
				if check_matrix(__lowercase ) and len(__lowercase ) > 0:
								_A       	=      [list(__lowercase ) for row in a]
								_A       	=      len(__lowercase )
								if isinstance(a[0]  ,      __lowercase ):
												_A       	=      len(a[0] )
								else:
												for dat in a:
																print(__lowercase )
												return

								# horizotal printing increasing
								for i in range(0  ,      __lowercase ):
												print(a[0][i] )
								# vertical printing down
								for i in range(1  ,      __lowercase ):
												print(a[i][mat_col - 1] )
								# horizotal printing decreasing
								if mat_row > 1:
												for i in range(mat_col - 2  ,      -1  ,      -1 ):
																print(a[mat_row - 1][i] )
        # vertical printing up
								for i in range(mat_row - 2  ,      0  ,      -1 ):
												print(a[i][0] )
								_A       	=      [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
								if len(__lowercase ) > 0:
												spiral_print_clockwise(__lowercase )
								else:
												return
				else:
								print("Not a valid matrix" )
								return






def   a__			(					__lowercase )						->						list[int]:
				if matrix:
								return list(matrix.pop(0 ) ) + spiral_traversal(list(zip(*__lowercase ) )[::-1] )
				else:
								return []


# driver code
if __name__ == "__main__":
		import doctest

		doctest.testmod()

		a_											=     [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
		spiral_print_clockwise(a)