






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 				__lowerCamelCase     (							__lowerCAmelCase							:					Dict					,							__lowerCAmelCase							:					int=0.999					,							__lowerCAmelCase							:					str="cosine"					,							)     ->  int:
   if alpha_transform_type == "cosine":

      def alpha_bar_fn(__lowerCAmelCase							:					Union[str, Any]							):
         return math.cos((t + 0.008) / 1.008 * math.pi / 2							) ** 2

   elif alpha_transform_type == "exp":

      def alpha_bar_fn(__lowerCAmelCase							:					Union[str, Any]							):
         return math.exp(t * -12.0							)

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

   __UpperCamelCase	:			Any					=					[]
   for i in range(__lowerCAmelCase							):
      __UpperCamelCase	:			Optional[int]					=					i / num_diffusion_timesteps
      __UpperCamelCase	:			List[str]					=					(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 		_A						( UpperCAmelCase_	,				UpperCAmelCase_ ):
  lowercase_						:			int						=					[e.name for e in KarrasDiffusionSchedulers]
  lowercase_						:			List[str]						=					2

  @register_to_config
  def __init__(    self						:	str   ,				lowerCamelCase__						:	int = 10_00   ,				lowerCamelCase__						:	float = 0.0_0085   ,				lowerCamelCase__						:	float = 0.012   ,				lowerCamelCase__						:	str = "linear"   ,				lowerCamelCase__						:	Optional[Union[np.ndarray, List[float]]] = None   ,				lowerCamelCase__						:	str = "epsilon"   ,				lowerCamelCase__						:	str = "linspace"   ,				lowerCamelCase__						:	int = 0   ,				):
     """simple docstring"""

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

     __UpperCamelCase	:			List[Any]					=					1.0 - self.betas
     __UpperCamelCase	:			str					=					torch.cumprod(self.alphas   ,				dim=0			)

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

  def    a					(    self						:	Tuple   ,				lowerCamelCase__						:	Union[str, Any]   ,				lowerCamelCase__						:	Optional[int]=None			):
     """simple docstring"""

     if schedule_timesteps is None:
        __UpperCamelCase	:			Tuple					=					self.timesteps

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

     return indices[pos].item()

  @property
  def    a					(    self						:	Dict			):
     """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						:	int   ,				lowerCamelCase__						:	torch.FloatTensor   ,				lowerCamelCase__						:	Union[float, torch.FloatTensor]   ,				):
     """simple docstring"""

     __UpperCamelCase	:			str					=					self.index_for_timestep(lowerCamelCase__			)

     if self.state_in_first_order:
        __UpperCamelCase	:			Optional[int]					=					self.sigmas[step_index]
     else:
        __UpperCamelCase	:			Any					=					self.sigmas_interpol[step_index]

     __UpperCamelCase	:			Optional[int]					=					sample / ((sigma**2 + 1) ** 0.5)
     return sample

  def    a					(    self						:	List[str]   ,				lowerCamelCase__						:	int   ,				lowerCamelCase__						:	Union[str, torch.device] = None   ,				lowerCamelCase__						:	Optional[int] = None   ,				):
     """simple docstring"""

     __UpperCamelCase	:			Any					=					num_inference_steps

     __UpperCamelCase	:			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":
        __UpperCamelCase	:			Optional[int]					=					np.linspace(0   ,				num_train_timesteps - 1   ,				lowerCamelCase__   ,				dtype=lowerCamelCase__			)[::-1].copy()
     elif self.config.timestep_spacing == "leading":
        __UpperCamelCase	:			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
        __UpperCamelCase	:			int					=					(np.arange(0   ,				lowerCamelCase__			) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__			)
        timesteps += self.config.steps_offset
     elif self.config.timestep_spacing == "trailing":
        __UpperCamelCase	:			Tuple					=					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	:			int					=					(np.arange(lowerCamelCase__   ,				0   ,				-step_ratio			)).round().copy().astype(lowerCamelCase__			)
        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	:			str					=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
     __UpperCamelCase	:			Optional[int]					=					torch.from_numpy(np.log(lowerCamelCase__			)			).to(lowerCamelCase__			)

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

     # interpolate sigmas
     __UpperCamelCase	:			Dict					=					sigmas.log().lerp(sigmas.roll(1			).log()   ,				0.5			).exp()

     __UpperCamelCase	:			int					=					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(lowerCamelCase__			).startswith("""mps"""			):
        # mps does not support float64
        __UpperCamelCase	:			Optional[int]					=					torch.from_numpy(lowerCamelCase__			).to(lowerCamelCase__   ,				dtype=torch.floataa			)
     else:
        __UpperCamelCase	:			Optional[Any]					=					torch.from_numpy(lowerCamelCase__			).to(lowerCamelCase__			)

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

     __UpperCamelCase	:			str					=					torch.cat([timesteps[:1], interleaved_timesteps]			)

     __UpperCamelCase	:			List[Any]					=					None

     # for exp beta schedules, such as the one for `pipeline_shap_e.py`
     # we need an index counter
     __UpperCamelCase	:			Union[str, Any]					=					defaultdict(lowerCamelCase__			)

  def    a					(    self						:	Union[str, Any]   ,				lowerCamelCase__						:	List[Any]			):
     """simple docstring"""

     __UpperCamelCase	:			Optional[Any]					=					sigma.log()

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

     # get sigmas range
     __UpperCamelCase	:			Union[str, Any]					=					dists.ge(0			).cumsum(dim=0			).argmax(dim=0			).clamp(max=self.log_sigmas.shape[0] - 2			)
     __UpperCamelCase	:			List[Any]					=					low_idx + 1

     __UpperCamelCase	:			List[str]					=					self.log_sigmas[low_idx]
     __UpperCamelCase	:			str					=					self.log_sigmas[high_idx]

     # interpolate sigmas
     __UpperCamelCase	:			Union[str, Any]					=					(low - log_sigma) / (low - high)
     __UpperCamelCase	:			Optional[Any]					=					w.clamp(0   ,				1			)

     # transform interpolation to time range
     __UpperCamelCase	:			int					=					(1 - w) * low_idx + w * high_idx
     __UpperCamelCase	:			int					=					t.view(sigma.shape			)
     return t

  @property
  def    a					(    self						:	Optional[Any]			):
     """simple docstring"""

     return self.sample is None

  def    a					(    self						:	Any   ,				lowerCamelCase__						:	Union[torch.FloatTensor, np.ndarray]   ,				lowerCamelCase__						:	Union[float, torch.FloatTensor]   ,				lowerCamelCase__						:	Union[torch.FloatTensor, np.ndarray]   ,				lowerCamelCase__						:	bool = True   ,				):
     """simple docstring"""

     __UpperCamelCase	:			List[Any]					=					self.index_for_timestep(lowerCamelCase__			)

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

     if self.state_in_first_order:
        __UpperCamelCase	:			Tuple					=					self.sigmas[step_index]
        __UpperCamelCase	:			Any					=					self.sigmas_interpol[step_index + 1]
        __UpperCamelCase	:			Any					=					self.sigmas[step_index + 1]
     else:
        # 2nd order / KDPM2's method
        __UpperCamelCase	:			Union[str, Any]					=					self.sigmas[step_index - 1]
        __UpperCamelCase	:			Dict					=					self.sigmas_interpol[step_index]
        __UpperCamelCase	:			str					=					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	:			Any					=					0
     __UpperCamelCase	:			List[str]					=					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	:			List[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	:			Optional[Any]					=					sigma_hat if self.state_in_first_order else sigma_interpol
        __UpperCamelCase	:			Dict					=					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	:			str					=					sigma_interpol - sigma_hat

        # store for 2nd order step
        __UpperCamelCase	:			Optional[int]					=					sample
     else:
        # DPM-Solver-2
        # 2. Convert to an ODE derivative for 2nd order
        __UpperCamelCase	:			Optional[Any]					=					(sample - pred_original_sample) / sigma_interpol

        # 3. delta timestep
        __UpperCamelCase	:			Optional[int]					=					sigma_next - sigma_hat

        __UpperCamelCase	:			Optional[int]					=					self.sample
        __UpperCamelCase	:			str					=					None

     __UpperCamelCase	:			Union[str, Any]					=					sample + derivative * dt

     if not return_dict:
        return (prev_sample,)

     return SchedulerOutput(prev_sample=lowerCamelCase__			)

  def    a					(    self						:	Optional[int]   ,				lowerCamelCase__						:	torch.FloatTensor   ,				lowerCamelCase__						:	torch.FloatTensor   ,				lowerCamelCase__						:	torch.FloatTensor   ,				):
     """simple docstring"""

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

     __UpperCamelCase	:			Optional[int]					=					[self.index_for_timestep(lowerCamelCase__   ,				lowerCamelCase__			) for t in timesteps]

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

     __UpperCamelCase	:			int					=					original_samples + noise * sigma
     return noisy_samples

  def __len__(    self						:	str			):
     """simple docstring"""

     return self.config.num_train_timesteps











from __future__ import annotations

from typing import Any







class 		_A						:

  def __init__(    self						:	List[Any]   ,				lowerCamelCase__						:	int   ,				lowerCamelCase__						:	int   ,				lowerCamelCase__						:	float = 0			):
     """simple docstring"""

     __UpperCamelCase	,     __UpperCamelCase	:			Tuple					=					row, column
     __UpperCamelCase	:			Tuple					=					[[default_value for c in range(lowerCamelCase__			)] for r in range(lowerCamelCase__			)]

  def __str__(    self						:	List[Any]			):
     """simple docstring"""

     __UpperCamelCase	:			Dict					=					f'Matrix consist of {self.row} rows and {self.column} columns\n'

     # Make string identifier
     __UpperCamelCase	:			Optional[int]					=					0
     for row_vector in self.array:
        for obj in row_vector:
           __UpperCamelCase	:			int					=					max(lowerCamelCase__   ,				len(str(lowerCamelCase__			)			)			)
     __UpperCamelCase	:			Union[str, Any]					=					f'%{max_element_length}s'

     # Make string and return
     def single_line(lowerCamelCase__						:	list[float]			) -> str:
        nonlocal string_format_identifier
        __UpperCamelCase	:			List[Any]					=					"""["""
        line += ", ".join(string_format_identifier % (obj,) for obj in row_vector			)
        line += "]"
        return line

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

  def __repr__(    self						:	Any			):
     """simple docstring"""

     return str(self			)

  def    a					(    self						:	str   ,				lowerCamelCase__						:	tuple[int, int]			):
     """simple docstring"""

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

  def __getitem__(    self						:	Union[str, Any]   ,				lowerCamelCase__						:	tuple[int, int]			):
     """simple docstring"""

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

  def __setitem__(    self						:	Union[str, Any]   ,				lowerCamelCase__						:	tuple[int, int]   ,				lowerCamelCase__						:	float			):
     """simple docstring"""

     assert self.validate_indicies(lowerCamelCase__			)
     __UpperCamelCase	:			str					=					value

  def __add__(    self						:	int   ,				lowerCamelCase__						:	Matrix			):
     """simple docstring"""

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

     # Add
     __UpperCamelCase	:			Tuple					=					Matrix(self.row   ,				self.column			)
     for r in range(self.row			):
        for c in range(self.column			):
           __UpperCamelCase	:			Optional[int]					=					self[r, c] + another[r, c]
     return result

  def __neg__(    self						:	Optional[int]			):
     """simple docstring"""

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

  def __sub__(    self						:	Tuple   ,				lowerCamelCase__						:	Matrix			):
     """simple docstring"""

     return self + (-another)

  def __mul__(    self						:	Tuple   ,				lowerCamelCase__						:	int | float | Matrix			):
     """simple docstring"""

     if isinstance(lowerCamelCase__   ,				(int, float)			):  # Scalar multiplication
        __UpperCamelCase	:			List[str]					=					Matrix(self.row   ,				self.column			)
        for r in range(self.row			):
           for c in range(self.column			):
              __UpperCamelCase	:			Tuple					=					self[r, c] * another
        return result
     elif isinstance(lowerCamelCase__   ,				lowerCamelCase__			):  # Matrix multiplication
        assert self.column == another.row
        __UpperCamelCase	:			List[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:
        __UpperCamelCase	:			Any					=					f'Unsupported type given for another ({type(lowerCamelCase__			)})'
        raise TypeError(lowerCamelCase__			)

  def    a					(    self						:	Union[str, Any]			):
     """simple docstring"""

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

  def    a					(    self						:	Any   ,				lowerCamelCase__						:	Matrix   ,				lowerCamelCase__						:	Matrix			):
     """simple docstring"""

     assert isinstance(lowerCamelCase__   ,				lowerCamelCase__			) and isinstance(lowerCamelCase__   ,				lowerCamelCase__			)
     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
     __UpperCamelCase	:			Optional[int]					=					v.transpose()
     __UpperCamelCase	:			Tuple					=					(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 				__lowerCamelCase     (							)     ->  None:
          # a^(-1)
          __UpperCamelCase	:			str					=					Matrix(3					,							3					,							0							)
          for i in range(3							):
             __UpperCamelCase	:			List[str]					=					1
          print(f'a^(-1) is {ainv}'							)
          # u, v
          __UpperCamelCase	:			Any					=					Matrix(3					,							1					,							0							)
          __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	:			Any					=					1, 2, -3
          __UpperCamelCase	:			int					=					Matrix(3					,							1					,							0							)
          __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	:			Dict					=					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 				__lowerCamelCase     (							)     ->  None:
          import doctest

          doctest.testmod()



       testa()



