






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 ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__=0.999 ,			lowerCamelCase__="cosine" ,			)  ->      int:
 if alpha_transform_type == "cosine":

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

 elif alpha_transform_type == "exp":

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

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

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





class 	lowerCamelCase__				(							UpperCAmelCase,   UpperCAmelCase ):
      lowerCamelCase_							:   Optional[int]											=	[e.name for e in KarrasDiffusionSchedulers]
      lowerCamelCase_							:   List[str]											=	2






      @register_to_config
      def __init__(self					:    Tuple		,		_snake_case					:    int = 1000		,		_snake_case					:    float = 0.0_0085		,		_snake_case					:    float = 0.012		,		_snake_case					:    str = "linear"		,		_snake_case					:    Optional[Union[np.ndarray, List[float]]] = None		,		_snake_case					:    str = "epsilon"		,		_snake_case					:    str = "linspace"		,		_snake_case					:    int = 0		,		)       ->   List[Any]:


       """simple docstring"""






       if trained_betas is not None:
        lowerCamelCase_							:    int							=     torch.tensor(_snake_case		,		dtype=torch.floataa		)
       elif beta_schedule == "linear":
        lowerCamelCase_							:    List[str]							=     torch.linspace(_snake_case		,		_snake_case		,		_snake_case		,		dtype=torch.floataa		)
       elif beta_schedule == "scaled_linear":
        # this schedule is very specific to the latent diffusion model.
        lowerCamelCase_							:    List[Any]							=     (
            torch.linspace(beta_start**0.5		,		beta_end**0.5		,		_snake_case		,		dtype=torch.floataa		) ** 2
        )
       elif beta_schedule == "squaredcos_cap_v2":
        # Glide cosine schedule
        lowerCamelCase_							:    List[Any]							=     betas_for_alpha_bar(_snake_case		)
       else:
        raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'		)

       lowerCamelCase_							:    List[str]							=     1.0 - self.betas
       lowerCamelCase_							:    Optional[int]							=     torch.cumprod(self.alphas		,		dim=0		)

       #  set all values
       self.set_timesteps(_snake_case		,		_snake_case		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    int		,		_snake_case					:    Optional[Any]=None		)       ->   Any:


       """simple docstring"""






       if schedule_timesteps is None:
        lowerCamelCase_							:    Dict							=     self.timesteps

       lowerCamelCase_							:    List[str]							=     (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:
        lowerCamelCase_							:    Any							=     1 if len(_snake_case		) > 1 else 0
       else:
        lowerCamelCase_							:    Tuple							=     timestep.cpu().item() if torch.is_tensor(_snake_case		) else timestep
        lowerCamelCase_							:    Optional[Any]							=     self._index_counter[timestep_int]

       return indices[pos].item()






      @property
      def      UpperCAmelCase_     (self					:    Dict		)       ->   Dict:


       """simple docstring"""






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

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






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


       """simple docstring"""






       lowerCamelCase_							:    Union[str, Any]							=     self.index_for_timestep(_snake_case		)

       if self.state_in_first_order:
        lowerCamelCase_							:    Any							=     self.sigmas[step_index]
       else:
        lowerCamelCase_							:    Tuple							=     self.sigmas_interpol[step_index - 1]

       lowerCamelCase_							:    List[str]							=     sample / ((sigma**2 + 1) ** 0.5)
       return sample






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    int		,		_snake_case					:    Union[str, torch.device] = None		,		_snake_case					:    Optional[int] = None		,		)       ->   int:


       """simple docstring"""






       lowerCamelCase_							:    Optional[int]							=     num_inference_steps

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

       lowerCamelCase_							:    Optional[int]							=     np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5		)
       lowerCamelCase_							:    Dict							=     torch.from_numpy(np.log(_snake_case		)		).to(_snake_case		)

       lowerCamelCase_							:    List[Any]							=     np.interp(_snake_case		,		np.arange(0		,		len(_snake_case		)		)		,		_snake_case		)
       lowerCamelCase_							:    Optional[Any]							=     np.concatenate([sigmas, [0.0]]		).astype(np.floataa		)
       lowerCamelCase_							:    Union[str, Any]							=     torch.from_numpy(_snake_case		).to(device=_snake_case		)

       # compute up and down sigmas
       lowerCamelCase_							:    List[str]							=     sigmas.roll(-1		)
       lowerCamelCase_							:    int							=     0.0
       lowerCamelCase_							:    str							=     (sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
       lowerCamelCase_							:    str							=     (sigmas_next**2 - sigmas_up**2) ** 0.5
       lowerCamelCase_							:    Any							=     0.0

       # compute interpolated sigmas
       lowerCamelCase_							:    Any							=     sigmas.log().lerp(sigmas_down.log()		,		0.5		).exp()
       lowerCamelCase_							:    Union[str, Any]							=     0.0

       # set sigmas
       lowerCamelCase_							:    Any							=     torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2		), sigmas[-1:]]		)
       lowerCamelCase_							:    int							=     torch.cat(
           [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2		), sigmas_interpol[-1:]]		)
       lowerCamelCase_							:    str							=     torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2		), sigmas_up[-1:]]		)
       lowerCamelCase_							:    Tuple							=     torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2		), sigmas_down[-1:]]		)

       if str(_snake_case		).startswith('mps'		):
        # mps does not support float64
        lowerCamelCase_							:    List[Any]							=     torch.from_numpy(_snake_case		).to(_snake_case		,		dtype=torch.floataa		)
       else:
        lowerCamelCase_							:    Tuple							=     torch.from_numpy(_snake_case		).to(_snake_case		)

       lowerCamelCase_							:    Union[str, Any]							=     self.sigma_to_t(_snake_case		).to(_snake_case		,		dtype=timesteps.dtype		)
       lowerCamelCase_							:    str							=     torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])		,		dim=-1		).flatten()

       lowerCamelCase_							:    Optional[int]							=     torch.cat([timesteps[:1], interleaved_timesteps]		)

       lowerCamelCase_							:    str							=     None

       # for exp beta schedules, such as the one for `pipeline_shap_e.py`
       # we need an index counter
       lowerCamelCase_							:    List[Any]							=     defaultdict(_snake_case		)






      def      UpperCAmelCase_     (self					:    str		,		_snake_case					:    Union[str, Any]		)       ->   Dict:


       """simple docstring"""






       lowerCamelCase_							:    List[str]							=     sigma.log()

       # get distribution
       lowerCamelCase_							:    Dict							=     log_sigma - self.log_sigmas[:, None]

       # get sigmas range
       lowerCamelCase_							:    Dict							=     dists.ge(0		).cumsum(dim=0		).argmax(dim=0		).clamp(max=self.log_sigmas.shape[0] - 2		)
       lowerCamelCase_							:    Optional[int]							=     low_idx + 1

       lowerCamelCase_							:    Dict							=     self.log_sigmas[low_idx]
       lowerCamelCase_							:    Any							=     self.log_sigmas[high_idx]

       # interpolate sigmas
       lowerCamelCase_							:    List[str]							=     (low - log_sigma) / (low - high)
       lowerCamelCase_							:    Dict							=     w.clamp(0		,		1		)

       # transform interpolation to time range
       lowerCamelCase_							:    Optional[Any]							=     (1 - w) * low_idx + w * high_idx
       lowerCamelCase_							:    List[Any]							=     t.view(sigma.shape		)
       return t






      @property
      def      UpperCAmelCase_     (self					:    List[Any]		)       ->   str:


       """simple docstring"""






       return self.sample is None






      def      UpperCAmelCase_     (self					:    Dict		,		_snake_case					:    Union[torch.FloatTensor, np.ndarray]		,		_snake_case					:    Union[float, torch.FloatTensor]		,		_snake_case					:    Union[torch.FloatTensor, np.ndarray]		,		_snake_case					:    Optional[torch.Generator] = None		,		_snake_case					:    bool = True		,		)       ->   Union[SchedulerOutput, Tuple]:


       """simple docstring"""






       lowerCamelCase_							:    Union[str, Any]							=     self.index_for_timestep(_snake_case		)

       # advance index counter by 1
       lowerCamelCase_							:    str							=     timestep.cpu().item() if torch.is_tensor(_snake_case		) else timestep
       self._index_counter[timestep_int] += 1

       if self.state_in_first_order:
        lowerCamelCase_							:    Dict							=     self.sigmas[step_index]
        lowerCamelCase_							:    str							=     self.sigmas_interpol[step_index]
        lowerCamelCase_							:    Optional[int]							=     self.sigmas_up[step_index]
        lowerCamelCase_							:    Union[str, Any]							=     self.sigmas_down[step_index - 1]
       else:
        # 2nd order / KPDM2's method
        lowerCamelCase_							:    Tuple							=     self.sigmas[step_index - 1]
        lowerCamelCase_							:    List[str]							=     self.sigmas_interpol[step_index - 1]
        lowerCamelCase_							:    int							=     self.sigmas_up[step_index - 1]
        lowerCamelCase_							:    List[Any]							=     self.sigmas_down[step_index - 1]

       # 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
       lowerCamelCase_							:    Any							=     0
       lowerCamelCase_							:    List[Any]							=     sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

       lowerCamelCase_							:    List[Any]							=     model_output.device
       lowerCamelCase_							:    Optional[int]							=     randn_tensor(model_output.shape		,		dtype=model_output.dtype		,		device=_snake_case		,		generator=_snake_case		)

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
        lowerCamelCase_							:    str							=     sigma_hat if self.state_in_first_order else sigma_interpol
        lowerCamelCase_							:    str							=     sample - sigma_input * model_output
       elif self.config.prediction_type == "v_prediction":
        lowerCamelCase_							:    Dict							=     sigma_hat if self.state_in_first_order else sigma_interpol
        lowerCamelCase_							:    Tuple							=     model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
            sample / (sigma_input**2 + 1)
        )
       elif self.config.prediction_type == "sample":
        raise NotImplementedError('prediction_type not implemented yet: sample'		)
       else:
        raise ValueError(
            f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'		)

       if self.state_in_first_order:
        # 2. Convert to an ODE derivative for 1st order
        lowerCamelCase_							:    List[Any]							=     (sample - pred_original_sample) / sigma_hat
        # 3. delta timestep
        lowerCamelCase_							:    Optional[int]							=     sigma_interpol - sigma_hat

        # store for 2nd order step
        lowerCamelCase_							:    Optional[int]							=     sample
        lowerCamelCase_							:    Dict							=     dt
        lowerCamelCase_							:    Any							=     sample + derivative * dt
       else:
        # DPM-Solver-2
        # 2. Convert to an ODE derivative for 2nd order
        lowerCamelCase_							:    Any							=     (sample - pred_original_sample) / sigma_interpol
        # 3. delta timestep
        lowerCamelCase_							:    Dict							=     sigma_down - sigma_hat

        lowerCamelCase_							:    Dict							=     self.sample
        lowerCamelCase_							:    Dict							=     None

        lowerCamelCase_							:    Tuple							=     sample + derivative * dt
        lowerCamelCase_							:    int							=     prev_sample + noise * sigma_up

       if not return_dict:
        return (prev_sample,)

       return SchedulerOutput(prev_sample=_snake_case		)






      def      UpperCAmelCase_     (self					:    Any		,		_snake_case					:    torch.FloatTensor		,		_snake_case					:    torch.FloatTensor		,		_snake_case					:    torch.FloatTensor		,		)       ->   torch.FloatTensor:


       """simple docstring"""






       lowerCamelCase_							:    int							=     self.sigmas.to(device=original_samples.device		,		dtype=original_samples.dtype		)
       if original_samples.device.type == "mps" and torch.is_floating_point(_snake_case		):
        # mps does not support float64
        lowerCamelCase_							:    Optional[Any]							=     self.timesteps.to(original_samples.device		,		dtype=torch.floataa		)
        lowerCamelCase_							:    List[str]							=     timesteps.to(original_samples.device		,		dtype=torch.floataa		)
       else:
        lowerCamelCase_							:    Any							=     self.timesteps.to(original_samples.device		)
        lowerCamelCase_							:    Optional[Any]							=     timesteps.to(original_samples.device		)

       lowerCamelCase_							:    Union[str, Any]							=     [self.index_for_timestep(_snake_case		,		_snake_case		) for t in timesteps]

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

       lowerCamelCase_							:    str							=     original_samples + noise * sigma
       return noisy_samples






      def __len__(self					:    Optional[Any]		)       ->   int:


       """simple docstring"""






       return self.config.num_train_timesteps








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       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      bool:
 return 0 <= row < rows and 0 <= col < cols




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      int:
 lowerCamelCase_							:    Tuple							=     len(lowerCamelCase__				)
 lowerCamelCase_							:    Tuple							=     len(mat[0]				)
 if is_safe(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				) and (row, col) not in seen and mat[row][col] == 1:
  seen.add((row, col)				)
  return (
      1
      + depth_first_search(row + 1 ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
      + depth_first_search(row - 1 ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
      + depth_first_search(lowerCamelCase__ ,			col + 1 ,			lowerCamelCase__ ,			lowerCamelCase__				)
      + depth_first_search(lowerCamelCase__ ,			col - 1 ,			lowerCamelCase__ ,			lowerCamelCase__				)
  )
 else:
  return 0




def       _a   (							lowerCamelCase__				)  ->      int:
 lowerCamelCase_							:    set							=     set()

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


if __name__ == "__main__":
       import doctest

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