






"""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


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




@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class  lowercase_     (_UpperCAmelCase  ):
      A__						:		torch.FloatTensor
      A__						:		Optional[torch.FloatTensor]							      =					None







def 							lowerCAmelCase			(   UpperCamelCase_:				str  ,			UpperCamelCase_:				List[Any]=0.999  ,			UpperCamelCase_:				Optional[Any]="cosine"  ,			)							->				Optional[Any]:







  '''simple docstring'''







  if alpha_transform_type == "cosine":

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

  elif alpha_transform_type == "exp":

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

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

  _a					      =						[]
  for i in range(UpperCamelCase_       ):
    _a					      =						i / num_diffusion_timesteps
    _a					      =						(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__						:		List[str]							      =					1






      @register_to_config
      def __init__(     self  ,  a_ = 1_0_0_0  ,  a_ = 0.0_001  ,  a_ = 0.02  ,  a_ = "linear"  ,  a_ = None  ,  a_ = "epsilon"  ,  a_ = "linear"  ,  a_ = False  ,  a_ = "linspace"  ,  a_ = 0  ,  )						->List[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       lowerCamelCase__     (     self						)						->Optional[int]:







        '''simple docstring'''


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

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






      def       lowerCamelCase__     (     self  ,  a_  ,  a_						)						->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       lowerCamelCase__     (     self  ,  a_  ,  a_ = None						)						->Tuple:







        '''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       lowerCamelCase__     (     self  ,  a_  ,  a_						)						->str:







        '''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       lowerCamelCase__     (     self  ,  a_  ,  a_						)						->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       lowerCamelCase__     (     self  ,  a_  ,  a_  ,  a_  ,  a_ = 0.0  ,  a_ = 0.0  ,  a_ = float("inf"						)  ,  a_ = 1.0  ,  a_ = None  ,  a_ = 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       lowerCamelCase__     (     self  ,  a_  ,  a_  ,  a_  ,  )						->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						)						->int:







        '''simple docstring'''


        return self.config.num_train_timesteps










"""simple docstring"""




UpperCamelCase											=     [
    [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
    [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
]






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				int       )							->				bool:







  '''simple docstring'''







  return 0 <= row < rows and 0 <= col < cols






def 							lowerCAmelCase			(   UpperCamelCase_:				int  ,			UpperCamelCase_:				int  ,			UpperCamelCase_:				set  ,			UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						len(UpperCamelCase_       )
  _a					      =						len(mat[0]       )
  if is_safe(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       ) and (row, col) not in seen and mat[row][col] == 1:
    seen.add((row, col)       )
    return (
        1
        + depth_first_search(row + 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(row - 1  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col + 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
        + depth_first_search(UpperCamelCase_  ,			col - 1  ,			UpperCamelCase_  ,			UpperCamelCase_       )
    )
  else:
    return 0






def 							lowerCAmelCase			(   UpperCamelCase_:				list[list[int]]       )							->				int:







  '''simple docstring'''







  _a					      =						set()

  _a					      =						0
  for row, line in enumerate(UpperCamelCase_       ):
    for col, item in enumerate(UpperCamelCase_       ):
      if item == 1 and (row, col) not in seen:
        # Maximizing the area
        _a					      =						max(UpperCamelCase_  ,			depth_first_search(UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_  ,			UpperCamelCase_       )       )
  return max_area


if __name__ == "__main__":
     import doctest

     print(find_max_area(matrix))  # Output -> 6
     doctest.testmod()


