'''simple docstring'''




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 SchedulerMixin


__SCREAMING_SNAKE_CASE :  List[Any]  =						logging.get_logger(__name__)  # pylint: disable=invalid-name

@dataclass
class 			lowerCamelCase_			(UpperCamelCase_					):
   '''simple docstring'''

   __UpperCamelCase:						torch.FloatTensor

class 			lowerCamelCase_			(UpperCamelCase_							,				UpperCamelCase_					):
   '''simple docstring'''

   __UpperCamelCase:						Tuple      			=		1




   @register_to_config
   def __init__( self		:       Any		,      A		:       List[Any] = 40		,      A		:       Optional[Any] = 0.002		,      A		:       int = 80.0		,      A		:       Tuple = 0.5		,      A		:       int = 1.0		,      A		:       Optional[int] = 7.0		,      A		:       List[str] = True		,      ):
          # standard deviation of the initial noise distribution
          _UpperCAmelCase  :						Any							   =					sigma_max

          _UpperCAmelCase  :						Tuple							   =					np.linspace(0		,      1		,      __SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						Union[str, Any]							   =					self._convert_to_karras(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						Tuple							   =					self.sigma_to_t(__SCREAMING_SNAKE_CASE )

          # setable values
          _UpperCAmelCase  :						Optional[int]							   =					None
          _UpperCAmelCase  :						Any							   =					torch.from_numpy(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						List[Any]							   =					torch.from_numpy(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						str							   =					False
          _UpperCAmelCase  :						Any							   =					False




   def   _A			( self		:       List[Any]		,      A		:       Any		,      A		:       Optional[int]=None ):
          if schedule_timesteps is None:
                 _UpperCAmelCase  :						Dict							   =					self.timesteps

          _UpperCAmelCase  :						Optional[int]							   =					(schedule_timesteps == timestep).nonzero()
          return indices.item()




   def   _A			( self		:       List[str]		,      A		:       Any		,      A		:       str ):
          # Get sigma corresponding to timestep
          if isinstance(__SCREAMING_SNAKE_CASE		,      torch.Tensor ):
                 _UpperCAmelCase  :						Optional[int]							   =					timestep.to(self.timesteps.device )
          _UpperCAmelCase  :						Optional[int]							   =					self.index_for_timestep(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						str							   =					self.sigmas[step_idx]

          _UpperCAmelCase  :						int							   =					sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)

          _UpperCAmelCase  :						Dict							   =					True
          return sample




   def   _A			( self		:       Optional[Any]		,      A		:       str ):
          if not isinstance(__SCREAMING_SNAKE_CASE		,      np.ndarray ):
                 _UpperCAmelCase  :						Union[str, Any]							   =					np.array(__SCREAMING_SNAKE_CASE		,      dtype=np.floataa )

          _UpperCAmelCase  :						Optional[Any]							   =					1000 * 0.25 * np.log(sigmas + 1E-44 )

          return timesteps




   def   _A			( self		:       Optional[Any]		,      A		:       List[Any] = None		,      A		:       Any = None		,      A		:       Tuple = None		,      ):
          if num_inference_steps is None and timesteps is None:
                 raise ValueError("Exactly one of `num_inference_steps` or `timesteps` must be supplied." )

          if num_inference_steps is not None and timesteps is not None:
                 raise ValueError("Can only pass one of `num_inference_steps` or `timesteps`." )

          # Follow DDPMScheduler custom timesteps logic
          if timesteps is not None:
                 for i in range(1		,      len(__SCREAMING_SNAKE_CASE ) ):
                        if timesteps[i] >= timesteps[i - 1]:
                               raise ValueError("`timesteps` must be in descending order." )

                 if timesteps[0] >= self.config.num_train_timesteps:
                        raise ValueError(
                            F"""`timesteps` must start before `self.config.train_timesteps`:"""
                            F""" {self.config.num_train_timesteps}.""" )

                 _UpperCAmelCase  :						Optional[Any]							   =					np.array(__SCREAMING_SNAKE_CASE		,      dtype=np.intaa )
                 _UpperCAmelCase  :						int							   =					True
          else:
                 if num_inference_steps > self.config.num_train_timesteps:
                        raise ValueError(
                            F"""`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"""
                            F""" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"""
                            F""" maximal {self.config.num_train_timesteps} timesteps.""" )

                 _UpperCAmelCase  :						List[str]							   =					num_inference_steps

                 _UpperCAmelCase  :						List[Any]							   =					self.config.num_train_timesteps // self.num_inference_steps
                 _UpperCAmelCase  :						Any							   =					(np.arange(0		,      __SCREAMING_SNAKE_CASE ) * step_ratio).round()[::-1].copy().astype(np.intaa )
                 _UpperCAmelCase  :						Optional[Any]							   =					False

          # Map timesteps to Karras sigmas directly for multistep sampling
          # See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
          _UpperCAmelCase  :						Tuple							   =					self.config.num_train_timesteps
          _UpperCAmelCase  :						List[str]							   =					timesteps[::-1].copy()
          _UpperCAmelCase  :						Tuple							   =					ramp / (num_train_timesteps - 1)
          _UpperCAmelCase  :						int							   =					self._convert_to_karras(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						List[str]							   =					self.sigma_to_t(__SCREAMING_SNAKE_CASE )

          _UpperCAmelCase  :						Dict							   =					np.concatenate([sigmas, [self.sigma_min]] ).astype(np.floataa )
          _UpperCAmelCase  :						List[Any]							   =					torch.from_numpy(__SCREAMING_SNAKE_CASE ).to(device=__SCREAMING_SNAKE_CASE )

          if str(__SCREAMING_SNAKE_CASE ).startswith("mps" ):
                 # mps does not support float64
                 _UpperCAmelCase  :						str							   =					torch.from_numpy(__SCREAMING_SNAKE_CASE ).to(__SCREAMING_SNAKE_CASE		,      dtype=torch.floataa )
          else:
                 _UpperCAmelCase  :						int							   =					torch.from_numpy(__SCREAMING_SNAKE_CASE ).to(device=__SCREAMING_SNAKE_CASE )




   def   _A			( self		:       Dict		,      A		:       Any ):
          _UpperCAmelCase  :						Union[str, Any]							   =					self.config.sigma_min
          _UpperCAmelCase  :						int							   =					self.config.sigma_max

          _UpperCAmelCase  :						str							   =					self.config.rho
          _UpperCAmelCase  :						Any							   =					sigma_min ** (1 / rho)
          _UpperCAmelCase  :						Optional[Any]							   =					sigma_max ** (1 / rho)
          _UpperCAmelCase  :						Union[str, Any]							   =					(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas




   def   _A			( self		:       Union[str, Any]		,      A		:       Dict ):
          _UpperCAmelCase  :						Optional[int]							   =					self.config.sigma_data

          _UpperCAmelCase  :						List[Any]							   =					sigma_data**2 / (sigma**2 + sigma_data**2)
          _UpperCAmelCase  :						Any							   =					sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
          return c_skip, c_out




   def   _A			( self		:       List[str]		,      A		:       Dict ):
          _UpperCAmelCase  :						Tuple							   =					self.config.sigma_min
          _UpperCAmelCase  :						List[Any]							   =					self.config.sigma_data

          _UpperCAmelCase  :						int							   =					sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
          _UpperCAmelCase  :						List[Any]							   =					(sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
          return c_skip, c_out




   def   _A			( self		:       int		,      A		:       List[str]		,      A		:       List[Any]		,      A		:       str		,      A		:       Optional[int] = None		,      A		:       Any = True		,      ):

          if (
              isinstance(__SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE )
              or isinstance(__SCREAMING_SNAKE_CASE		,      torch.IntTensor )
              or isinstance(__SCREAMING_SNAKE_CASE		,      torch.LongTensor )
          ):
                 raise ValueError(
                     (
                         "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                         F""" `{self.__class__}.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(__SCREAMING_SNAKE_CASE		,      torch.Tensor ):
                 _UpperCAmelCase  :						Optional[Any]							   =					timestep.to(self.timesteps.device )

          _UpperCAmelCase  :						List[Any]							   =					self.config.sigma_min
          _UpperCAmelCase  :						str							   =					self.config.sigma_max

          _UpperCAmelCase  :						int							   =					self.index_for_timestep(__SCREAMING_SNAKE_CASE )

          # sigma_next corresponds to next_t in original implementation
          _UpperCAmelCase  :						Dict							   =					self.sigmas[step_index]
          if step_index + 1 < self.config.num_train_timesteps:
                 _UpperCAmelCase  :						Optional[int]							   =					self.sigmas[step_index + 1]
          else:
                 # Set sigma_next to sigma_min
                 _UpperCAmelCase  :						List[Any]							   =					self.sigmas[-1]

          # Get scalings for boundary conditions
          _UpperCAmelCase   ,						_UpperCAmelCase  :						str							   =					self.get_scalings_for_boundary_condition(__SCREAMING_SNAKE_CASE )

          # 1. Denoise model output using boundary conditions
          _UpperCAmelCase  :						List[Any]							   =					c_out * model_output + c_skip * sample
          if self.config.clip_denoised:
                 _UpperCAmelCase  :						int							   =					denoised.clamp(-1		,      1 )

          # 2. Sample z ~ N(0, s_noise^2 * I)
          # Noise is not used for onestep sampling.
          if len(self.timesteps ) > 1:
                 _UpperCAmelCase  :						List[str]							   =					randn_tensor(
                     model_output.shape		,      dtype=model_output.dtype		,      device=model_output.device		,      generator=__SCREAMING_SNAKE_CASE )
          else:
                 _UpperCAmelCase  :						int							   =					torch.zeros_like(__SCREAMING_SNAKE_CASE )
          _UpperCAmelCase  :						Any							   =					noise * self.config.s_noise

          _UpperCAmelCase  :						Union[str, Any]							   =					sigma_next.clamp(min=__SCREAMING_SNAKE_CASE		,      max=__SCREAMING_SNAKE_CASE )

          # 3. Return noisy sample
          # tau = sigma_hat, eps = sigma_min
          _UpperCAmelCase  :						Union[str, Any]							   =					denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5

          if not return_dict:
                 return (prev_sample,)

          return CMStochasticIterativeSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE )




   def   _A			( self		:       List[str]		,      A		:       Dict		,      A		:       int		,      A		:       str		,      ):
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          _UpperCAmelCase  :						List[Any]							   =					self.sigmas.to(device=original_samples.device		,      dtype=original_samples.dtype )
          if original_samples.device.type == "mps" and torch.is_floating_point(__SCREAMING_SNAKE_CASE ):
                 # mps does not support float64
                 _UpperCAmelCase  :						int							   =					self.timesteps.to(original_samples.device		,      dtype=torch.floataa )
                 _UpperCAmelCase  :						List[Any]							   =					timesteps.to(original_samples.device		,      dtype=torch.floataa )
          else:
                 _UpperCAmelCase  :						Any							   =					self.timesteps.to(original_samples.device )
                 _UpperCAmelCase  :						List[Any]							   =					timesteps.to(original_samples.device )

          _UpperCAmelCase  :						str							   =					[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

          _UpperCAmelCase  :						int							   =					original_samples + noise * sigma
          return noisy_samples





   def __len__( self		:       Optional[Any] ):
          return self.config.num_train_timesteps


'''simple docstring'''




from typing import Any

import numpy as np

class 			lowerCamelCase_			:
      '''simple docstring'''

      def __init__( self		:       Optional[int]		,      A		:       np.ndarray		,      A		:       int ):
             # Check if RHS is negative
             if np.any(tableau[:, -1]		,      where=tableau[:, -1] < 0 ):
                    raise ValueError("RHS must be > 0" )

             _UpperCAmelCase  :						Union[str, Any]							   =					tableau
             _UpperCAmelCase   ,						_UpperCAmelCase  :						str							   =					tableau.shape

             # Number of decision variables x1, x2, x3...
             _UpperCAmelCase  :						Any							   =					n_vars

             # Number of artificial variables to be minimised
             _UpperCAmelCase  :						List[str]							   =					len(np.where(tableau[self.n_vars : -1] == -1 )[0] )

             # 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
             _UpperCAmelCase  :						List[Any]							   =					(self.n_art_vars > 0) + 1

             # Number of slack variables added to make inequalities into equalities
             _UpperCAmelCase  :						int							   =					self.n_rows - self.n_stages

             # Objectives for each stage
             _UpperCAmelCase  :						Optional[Any]							   =					["max"]

             # In two stage simplex, first minimise then maximise
             if self.n_art_vars:
                    self.objectives.append("min" )

             _UpperCAmelCase  :						Any							   =					[""]

             # Index of current pivot row and column
             _UpperCAmelCase  :						Optional[Any]							   =					None
             _UpperCAmelCase  :						Dict							   =					None

             # Does objective row only contain (non)-negative values?
             _UpperCAmelCase  :						List[str]							   =					False




      @staticmethod
      def   _A			( *A		:       int ):
             if len(A ) != 3:
                    raise ValueError("Must provide n_vars, n_slack, and n_art_vars" )

             if not all(x >= 0 and isinstance(A		,      A ) for x in args ):
                    raise ValueError("All arguments must be non-negative integers" )

             # decision | slack | artificial
             _UpperCAmelCase  :						Optional[Any]							   =					["x", "s", "a"]
             _UpperCAmelCase  :						int							   =					[]
             for i in range(3 ):
                    for j in range(args[i] ):
                           titles.append(string_starts[i] + str(j + 1 ) )
             titles.append("RHS" )
             return titles




      def   _A			( self		:       List[str]		,      A		:       np.ndarray ):
             _UpperCAmelCase  :						str							   =					self.objectives[-1]

             # Find entries of highest magnitude in objective rows
             _UpperCAmelCase  :						List[str]							   =					(objective == "min") - (objective == "max")
             _UpperCAmelCase  :						Optional[Any]							   =					np.argmax(sign * tableau[0, : self.n_vars] )

             # Choice is only valid if below 0 for maximise, and above for minimise
             if sign * self.tableau[0, col_idx] <= 0:
                    _UpperCAmelCase  :						Dict							   =					True
                    return 0, 0

             # Pivot row is chosen as having the lowest quotient when elements of
             # the pivot column divide the right-hand side

             # Slice excluding the objective rows
             _UpperCAmelCase  :						Any							   =					slice(self.n_stages		,      self.n_rows )

             # RHS
             _UpperCAmelCase  :						Optional[Any]							   =					tableau[s, -1]

             # Elements of pivot column within slice
             _UpperCAmelCase  :						Optional[Any]							   =					tableau[s, col_idx]

             # Array filled with nans
             _UpperCAmelCase  :						List[Any]							   =					np.full(self.n_rows - self.n_stages		,      np.nan )

             # If element in pivot column is greater than zeron_stages, return
             # quotient or nan otherwise
             _UpperCAmelCase  :						str							   =					np.divide(A		,      A		,      out=A		,      where=divisor > 0 )

             # Arg of minimum quotient excluding the nan values. n_stages is added
             # to compensate for earlier exclusion of objective columns
             _UpperCAmelCase  :						Optional[Any]							   =					np.nanargmin(A ) + self.n_stages
             return row_idx, col_idx




      def   _A			( self		:       List[Any]		,      A		:       np.ndarray		,      A		:       int		,      A		:       int ):
             _UpperCAmelCase  :						Union[str, Any]							   =					tableau[row_idx].copy()

             _UpperCAmelCase  :						Optional[Any]							   =					piv_row[col_idx]

             # Entry becomes 1
             piv_row *= 1 / piv_val

             # Variable in pivot column becomes basic, ie the only non-zero entry
             for idx, coeff in enumerate(tableau[:, col_idx] ):
                    tableau[idx] += -coeff * piv_row
             _UpperCAmelCase  :						Optional[Any]							   =					piv_row
             return tableau




      def   _A			( self		:       Optional[Any]		,      A		:       np.ndarray ):
             self.objectives.pop()

             if not self.objectives:
                    return tableau

             # Slice containing ids for artificial columns
             _UpperCAmelCase  :						Union[str, Any]							   =					slice(-self.n_art_vars - 1		,      -1 )

             # Delete the artificial variable columns
             _UpperCAmelCase  :						List[Any]							   =					np.delete(A		,      A		,      axis=1 )

             # Delete the objective row of the first stage
             _UpperCAmelCase  :						Union[str, Any]							   =					np.delete(A		,      0		,      axis=0 )

             _UpperCAmelCase  :						Any							   =					1
             self.n_rows -= 1
             _UpperCAmelCase  :						Dict							   =					0
             _UpperCAmelCase  :						List[str]							   =					False
             return tableau




      def   _A			( self		:       Optional[Any] ):
             # Stop simplex algorithm from cycling.
             for _ in range(100 ):
                    # Completion of each stage removes an objective. If both stages
                    # are complete, then no objectives are left
                    if not self.objectives:
                           _UpperCAmelCase  :						Any							   =					self.generate_col_titles(
                               self.n_vars		,      self.n_slack		,      self.n_art_vars )

                           # Find the values of each variable at optimal solution
                           return self.interpret_tableau(self.tableau		,      self.col_titles )

                    _UpperCAmelCase   ,						_UpperCAmelCase  :						List[str]							   =					self.find_pivot(self.tableau )

                    # If there are no more negative values in objective row
                    if self.stop_iter:
                           # Delete artificial variable columns and rows. Update attributes
                           _UpperCAmelCase  :						int							   =					self.change_stage(self.tableau )
                    else:
                           _UpperCAmelCase  :						Optional[Any]							   =					self.pivot(self.tableau		,      A		,      A )
             return {}





      def   _A			( self		:       List[Any]		,      A		:       np.ndarray		,      A		:       list[str] ):
             _UpperCAmelCase  :						str							   =					{"P": abs(tableau[0, -1] )}

             for i in range(self.n_vars ):
                    # Gives ids of nonzero entries in the ith column
                    _UpperCAmelCase  :						Dict							   =					np.nonzero(tableau[:, i] )
                    _UpperCAmelCase  :						Dict							   =					len(nonzero[0] )

                    # First entry in the nonzero ids
                    _UpperCAmelCase  :						str							   =					nonzero[0][0]
                    _UpperCAmelCase  :						str							   =					tableau[nonzero_rowidx, i]

                    # If there is only one nonzero value in column, which is one
                    if n_nonzero == nonzero_val == 1:
                           _UpperCAmelCase  :						Optional[Any]							   =					tableau[nonzero_rowidx, -1]
                           _UpperCAmelCase  :						Any							   =					rhs_val

        # Check for basic variables
             for title in col_titles:
                    # Don't add RHS or slack variables to output dict
                    if title[0] not in "R-s-a":
                           output_dict.setdefault(A		,      0 )
             return output_dict


if __name__ == "__main__":
  import doctest

  doctest.testmod()

