



"""simple docstring"""







from __future__ import annotations

from typing import Any
class        __A       :







		'''simple docstring'''





		def __init__(	self						:  Optional[Any]			,_snake_case						:  int			,_snake_case						:  int			,_snake_case						:  float = 0						)					->		None:






				"""simple docstring"""



				lowercase__		,			lowercase__   :    int				=			row, column
				lowercase__   :    Any				=			[[default_value for c in range(_snake_case						)] for r in range(_snake_case						)]







		def __str__(	self						:  Dict						)					->		str:






				"""simple docstring"""



				lowercase__   :    List[str]				=			f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

				# Make string identifier
				lowercase__   :    Optional[int]				=			0
				for row_vector in self.array:
						for obj in row_vector:
								lowercase__   :    str				=			max(_snake_case			,len(str(_snake_case						)						)						)
				lowercase__   :    Tuple				=			f"""%{max_element_length}s"""

				# Make string and return
				def single_line(_snake_case						:  list[float]						) -> str:
						nonlocal string_format_identifier
						lowercase__   :    Dict				=			'''['''
						line += ", ".join(string_format_identifier % (obj,) for obj in row_vector						)
						line += "]"
						return line

				s += "\n".join(single_line(_snake_case						) for row_vector in self.array						)
				return s







		def __repr__(	self						:  Optional[Any]						)					->		str:






				"""simple docstring"""



				return str(self						)







		def 					UpperCAmelCase    (	self						:  Tuple			,_snake_case						:  tuple[int, int]						)					->		bool:






				"""simple docstring"""



				if not (isinstance(_snake_case			,(list, tuple)						) and len(_snake_case						) == 2):
						return False
				elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
						return False
				else:
						return True







		def __getitem__(	self						:  Optional[int]			,_snake_case						:  tuple[int, int]						)					->		Any:






				"""simple docstring"""



				assert self.validate_indicies(_snake_case						)
				return self.array[loc[0]][loc[1]]







		def __setitem__(	self						:  Union[str, Any]			,_snake_case						:  tuple[int, int]			,_snake_case						:  float						)					->		None:






				"""simple docstring"""



				assert self.validate_indicies(_snake_case						)
				lowercase__   :    Any				=			value







		def __add__(	self						:  int			,_snake_case						:  Matrix						)					->		Matrix:






				"""simple docstring"""



				assert isinstance(_snake_case			,_snake_case						)
				assert self.row == another.row and self.column == another.column

				# Add
				lowercase__   :    List[Any]				=			Matrix(self.row			,self.column						)
				for r in range(self.row						):
						for c in range(self.column						):
								lowercase__   :    Any				=			self[r, c] + another[r, c]
				return result







		def __neg__(	self						:  Dict						)					->		Matrix:






				"""simple docstring"""



				lowercase__   :    Dict				=			Matrix(self.row			,self.column						)
				for r in range(self.row						):
						for c in range(self.column						):
								lowercase__   :    List[str]				=			-self[r, c]
				return result







		def __sub__(	self						:  int			,_snake_case						:  Matrix						)					->		Matrix:






				"""simple docstring"""



				return self + (-another)







		def __mul__(	self						:  int			,_snake_case						:  int | float | Matrix						)					->		Matrix:






				"""simple docstring"""



				if isinstance(_snake_case			,(int, float)						):  # Scalar multiplication
						lowercase__   :    str				=			Matrix(self.row			,self.column						)
						for r in range(self.row						):
								for c in range(self.column						):
										lowercase__   :    Tuple				=			self[r, c] * another
						return result
				elif isinstance(_snake_case			,_snake_case						):  # Matrix multiplication
						assert self.column == another.row
						lowercase__   :    Any				=			Matrix(self.row			,another.column						)
						for r in range(self.row						):
								for c in range(another.column						):
										for i in range(self.column						):
												result[r, c] += self[r, i] * another[i, c]
						return result
				else:
						lowercase__   :    Union[str, Any]				=			f"""Unsupported type given for another ({type(_snake_case						)})"""
						raise TypeError(_snake_case						)







		def 					UpperCAmelCase    (	self						:  Dict						)					->		Matrix:






				"""simple docstring"""



				lowercase__   :    int				=			Matrix(self.column			,self.row						)
				for r in range(self.row						):
						for c in range(self.column						):
								lowercase__   :    Dict				=			self[r, c]
				return result







		def 					UpperCAmelCase    (	self						:  int			,_snake_case						:  Matrix			,_snake_case						:  Matrix						)					->		Any:






				"""simple docstring"""



				assert isinstance(_snake_case			,_snake_case						) and isinstance(_snake_case			,_snake_case						)
				assert self.row == self.column == u.row == v.row  # u, v should be column vector
				assert u.column == v.column == 1  # u, v should be column vector

				# Calculate
				lowercase__   :    Dict				=			v.transpose()
				lowercase__   :    Union[str, Any]				=			(v_t * self * u)[0, 0] + 1
				if numerator_factor == 0:
						return None  # It's not invertable
				return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":



							def      __UpperCAmelCase      (    )							->      None:
									# a^(-1)
									lowercase__   :    Tuple				=			Matrix(3						,     3						,     0	)
									for i in range(3	):
											lowercase__   :    List[Any]				=			1
									print(f"""a^(-1) is {ainv}"""	)
									# u, v
									lowercase__   :    Tuple				=			Matrix(3						,     1						,     0	)
									lowercase__		,			lowercase__		,			lowercase__   :    Dict				=			1, 2, -3
									lowercase__   :    List[Any]				=			Matrix(3						,     1						,     0	)
									lowercase__		,			lowercase__		,			lowercase__   :    str				=			4, -2, 5
									print(f"""u is {u}"""	)
									print(f"""v is {v}"""	)
									print(f"""uv^T is {u * v.transpose()}"""	)
									# Sherman Morrison
									print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowerCamelCase						,     __lowerCamelCase	)}"""	)



							def      __UpperCAmelCase      (    )							->      None:
									import doctest

									doctest.testmod()





							testa()





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 		UpperCamelCase	(   snake_case__       :    Dict       ,     snake_case__       :    Any=0.999       ,     snake_case__       :    List[Any]="cosine"       ,     )	->     Optional[int]:
   if alpha_transform_type == "cosine":

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

   elif alpha_transform_type == "exp":

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

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

   UpperCamelCase    :  List[Any]							=	[]
   for i in range(snake_case__	):
      UpperCamelCase    :  Optional[Any]							=	i / num_diffusion_timesteps
      UpperCamelCase    :  Union[str, Any]							=	(i + 1) / num_diffusion_timesteps
      betas.append(min(1 - alpha_bar_fn(snake_case__	) / alpha_bar_fn(snake_case__	)       ,     snake_case__	)	)
   return torch.tensor(snake_case__       ,     dtype=torch.floataa	)



class 				lowerCAmelCase_		(  a__       ,    a__							):
       UpperCAmelCase__				:					List[Any]        =  [e.name for e in KarrasDiffusionSchedulers]
       UpperCAmelCase__				:					List[str]        =  2
       @register_to_config
       def __init__(			self,			SCREAMING_SNAKE_CASE_ = 1000,			SCREAMING_SNAKE_CASE_ = 0.0_00_85,			SCREAMING_SNAKE_CASE_ = 0.0_12,			SCREAMING_SNAKE_CASE_ = "linear",			SCREAMING_SNAKE_CASE_ = None,			SCREAMING_SNAKE_CASE_ = "epsilon",			SCREAMING_SNAKE_CASE_ = "linspace",			SCREAMING_SNAKE_CASE_ = 0,			)     ->		List[str]:
          if trained_betas is not None:
             UpperCamelCase    :  Union[str, Any]							=	torch.tensor(SCREAMING_SNAKE_CASE_,			dtype=torch.floataa       )
          elif beta_schedule == "linear":
             UpperCamelCase    :  List[Any]							=	torch.linspace(SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			dtype=torch.floataa       )
          elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
             UpperCamelCase    :  int							=	(
                 torch.linspace(beta_start**0.5,			beta_end**0.5,			SCREAMING_SNAKE_CASE_,			dtype=torch.floataa       ) ** 2
             )
          elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             UpperCamelCase    :  Optional[int]							=	betas_for_alpha_bar(SCREAMING_SNAKE_CASE_       )
          else:
             raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}"""       )

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

          #  set all values
          self.set_timesteps(SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_       )
       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_=None       )     ->		str:
          if schedule_timesteps is None:
             UpperCamelCase    :  Union[str, Any]							=	self.timesteps

          UpperCamelCase    :  Dict							=	(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:
             UpperCamelCase    :  Optional[int]							=	1 if len(SCREAMING_SNAKE_CASE_       ) > 1 else 0
          else:
             UpperCamelCase    :  str							=	timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE_       ) else timestep
             UpperCamelCase    :  int							=	self._index_counter[timestep_int]

          return indices[pos].item()
       @property
       def 					snake_case_       (			self       )     ->		List[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 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			)     ->		torch.FloatTensor:
          UpperCamelCase    :  Optional[int]							=	self.index_for_timestep(SCREAMING_SNAKE_CASE_       )

          if self.state_in_first_order:
             UpperCamelCase    :  Dict							=	self.sigmas[step_index]
          else:
             UpperCamelCase    :  int							=	self.sigmas_interpol[step_index]

          UpperCamelCase    :  Any							=	sample / ((sigma**2 + 1) ** 0.5)
          return sample
       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_ = None,			SCREAMING_SNAKE_CASE_ = None,			)     ->		Optional[int]:
          UpperCamelCase    :  Dict							=	num_inference_steps

          UpperCamelCase    :  List[Any]							=	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":
             UpperCamelCase    :  int							=	np.linspace(0,			num_train_timesteps - 1,			SCREAMING_SNAKE_CASE_,			dtype=SCREAMING_SNAKE_CASE_       )[::-1].copy()
          elif self.config.timestep_spacing == "leading":
             UpperCamelCase    :  List[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
             UpperCamelCase    :  Optional[Any]							=	(np.arange(0,			SCREAMING_SNAKE_CASE_       ) * step_ratio).round()[::-1].copy().astype(SCREAMING_SNAKE_CASE_       )
             timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
             UpperCamelCase    :  Optional[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
             UpperCamelCase    :  Any							=	(np.arange(SCREAMING_SNAKE_CASE_,			0,			-step_ratio       )).round().copy().astype(SCREAMING_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'."""       )

          UpperCamelCase    :  Tuple							=	np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
          UpperCamelCase    :  Optional[int]							=	torch.from_numpy(np.log(SCREAMING_SNAKE_CASE_       )       ).to(SCREAMING_SNAKE_CASE_       )

          UpperCamelCase    :  Optional[int]							=	np.interp(SCREAMING_SNAKE_CASE_,			np.arange(0,			len(SCREAMING_SNAKE_CASE_       )       ),			SCREAMING_SNAKE_CASE_       )
          UpperCamelCase    :  Dict							=	np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )
          UpperCamelCase    :  Optional[int]							=	torch.from_numpy(SCREAMING_SNAKE_CASE_       ).to(device=SCREAMING_SNAKE_CASE_       )

          # interpolate sigmas
          UpperCamelCase    :  Union[str, Any]							=	sigmas.log().lerp(sigmas.roll(1       ).log(),			0.5       ).exp()

          UpperCamelCase    :  Any							=	torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2       ), sigmas[-1:]]       )
          UpperCamelCase    :  Optional[Any]							=	torch.cat(
              [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2       ), sigmas_interpol[-1:]]       )

          if str(SCREAMING_SNAKE_CASE_       ).startswith('mps'       ):
             # mps does not support float64
             UpperCamelCase    :  Any							=	torch.from_numpy(SCREAMING_SNAKE_CASE_       ).to(SCREAMING_SNAKE_CASE_,			dtype=torch.floataa       )
          else:
             UpperCamelCase    :  Dict							=	torch.from_numpy(SCREAMING_SNAKE_CASE_       ).to(SCREAMING_SNAKE_CASE_       )

          # interpolate timesteps
          UpperCamelCase    :  int							=	self.sigma_to_t(SCREAMING_SNAKE_CASE_       ).to(SCREAMING_SNAKE_CASE_,			dtype=timesteps.dtype       )
          UpperCamelCase    :  List[str]							=	torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None]),			dim=-1       ).flatten()

          UpperCamelCase    :  Optional[Any]							=	torch.cat([timesteps[:1], interleaved_timesteps]       )

          UpperCamelCase    :  Optional[Any]							=	None

          # for exp beta schedules, such as the one for `pipeline_shap_e.py`
          # we need an index counter
          UpperCamelCase    :  Dict							=	defaultdict(SCREAMING_SNAKE_CASE_       )
       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_       )     ->		Union[str, Any]:
          # get log sigma
          UpperCamelCase    :  List[Any]							=	sigma.log()

          # get distribution
          UpperCamelCase    :  Optional[int]							=	log_sigma - self.log_sigmas[:, None]

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

          UpperCamelCase    :  List[str]							=	self.log_sigmas[low_idx]
          UpperCamelCase    :  Optional[Any]							=	self.log_sigmas[high_idx]

          # interpolate sigmas
          UpperCamelCase    :  int							=	(low - log_sigma) / (low - high)
          UpperCamelCase    :  Tuple							=	w.clamp(0,			1       )

          # transform interpolation to time range
          UpperCamelCase    :  List[str]							=	(1 - w) * low_idx + w * high_idx
          UpperCamelCase    :  Dict							=	t.view(sigma.shape       )
          return t
       @property
       def 					snake_case_       (			self       )     ->		Optional[int]:
          return self.sample is None
       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_ = True,			)     ->		Union[SchedulerOutput, Tuple]:
          UpperCamelCase    :  str							=	self.index_for_timestep(SCREAMING_SNAKE_CASE_       )

          # advance index counter by 1
          UpperCamelCase    :  Optional[int]							=	timestep.cpu().item() if torch.is_tensor(SCREAMING_SNAKE_CASE_       ) else timestep
          self._index_counter[timestep_int] += 1

          if self.state_in_first_order:
             UpperCamelCase    :  Tuple							=	self.sigmas[step_index]
             UpperCamelCase    :  Dict							=	self.sigmas_interpol[step_index + 1]
             UpperCamelCase    :  Optional[int]							=	self.sigmas[step_index + 1]
          else:
             # 2nd order / KDPM2's method
             UpperCamelCase    :  str							=	self.sigmas[step_index - 1]
             UpperCamelCase    :  Dict							=	self.sigmas_interpol[step_index]
             UpperCamelCase    :  Any							=	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
          UpperCamelCase    :  Dict							=	0
          UpperCamelCase    :  Any							=	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":
             UpperCamelCase    :  Any							=	sigma_hat if self.state_in_first_order else sigma_interpol
             UpperCamelCase    :  List[Any]							=	sample - sigma_input * model_output
          elif self.config.prediction_type == "v_prediction":
             UpperCamelCase    :  Union[str, Any]							=	sigma_hat if self.state_in_first_order else sigma_interpol
             UpperCamelCase    :  Optional[int]							=	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
             UpperCamelCase    :  int							=	(sample - pred_original_sample) / sigma_hat
             # 3. delta timestep
             UpperCamelCase    :  Any							=	sigma_interpol - sigma_hat

             # store for 2nd order step
             UpperCamelCase    :  Tuple							=	sample
          else:
             # DPM-Solver-2
             # 2. Convert to an ODE derivative for 2nd order
             UpperCamelCase    :  Union[str, Any]							=	(sample - pred_original_sample) / sigma_interpol

             # 3. delta timestep
             UpperCamelCase    :  Dict							=	sigma_next - sigma_hat

             UpperCamelCase    :  Any							=	self.sample
             UpperCamelCase    :  str							=	None

          UpperCamelCase    :  Any							=	sample + derivative * dt

          if not return_dict:
             return (prev_sample,)

          return SchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE_       )
       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_,			)     ->		torch.FloatTensor:
          # Make sure sigmas and timesteps have the same device and dtype as original_samples
          UpperCamelCase    :  Optional[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    :  List[str]							=	self.timesteps.to(original_samples.device,			dtype=torch.floataa       )
             UpperCamelCase    :  str							=	timesteps.to(original_samples.device,			dtype=torch.floataa       )
          else:
             UpperCamelCase    :  Dict							=	self.timesteps.to(original_samples.device       )
             UpperCamelCase    :  int							=	timesteps.to(original_samples.device       )

          UpperCamelCase    :  str							=	[self.index_for_timestep(SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_       ) for t in timesteps]

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

          UpperCamelCase    :  Any							=	original_samples + noise * sigma
          return noisy_samples






       def __len__(			self       )     ->		Optional[int]:
          return self.config.num_train_timesteps



