
'''simple docstring'''

import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


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



def 		_UpperCAmelCase			(					_lowerCamelCase  :    Tuple					, _lowerCamelCase  :    List[Any]=0.999					, _lowerCamelCase  :    Dict="cosine"					, )      ->  Optional[int]:



		if alpha_transform_type == "cosine":

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

		elif alpha_transform_type == "exp":

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

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

		_lowerCAmelCase    :					Optional[int]							=   []
		for i in range(_lowerCamelCase						):
				_lowerCAmelCase    :					Dict							=   i / num_diffusion_timesteps
				_lowerCAmelCase    :					Dict							=   (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      ):
							__lowerCAmelCase      :			Dict      = [e.name for e in KarrasDiffusionSchedulers]
							__lowerCAmelCase      :			List[Any]      = 1




							@register_to_config
							def __init__(       self				,				snake_case_ = 1_0_0_0				,				snake_case_ = 0.0001				,				snake_case_ = 0.02				,				snake_case_ = "linear"				,				snake_case_ = None				,				snake_case_ = False				,				snake_case_ = "epsilon"				,				snake_case_ = "linspace"				,				snake_case_ = 0				,				):


									if trained_betas is not None:
											_lowerCAmelCase    :					str							=   torch.tensor(lowerCAmelCase__				,				dtype=torch.floataa					)
									elif beta_schedule == "linear":
											_lowerCAmelCase    :					str							=   torch.linspace(lowerCAmelCase__				,				lowerCAmelCase__				,				lowerCAmelCase__				,				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				,				lowerCAmelCase__				,				dtype=torch.floataa					) ** 2
											)
									elif beta_schedule == "squaredcos_cap_v2":
											# Glide cosine schedule
											_lowerCAmelCase    :					Tuple							=   betas_for_alpha_bar(lowerCAmelCase__					)
									else:
											raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'					)

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

									_lowerCAmelCase    :					Dict							=   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
									_lowerCAmelCase    :					Optional[Any]							=   np.concatenate([sigmas[::-1], [0.0]]					).astype(np.floataa					)
									_lowerCAmelCase    :					Optional[int]							=   torch.from_numpy(lowerCAmelCase__					)

									# setable values
									_lowerCAmelCase    :					str							=   None
									_lowerCAmelCase    :					Any							=   use_karras_sigmas
									self.set_timesteps(lowerCAmelCase__				,				lowerCAmelCase__					)
									_lowerCAmelCase    :					Union[str, Any]							=   []
									_lowerCAmelCase    :					Union[str, Any]							=   False




							@property
							def 							__UpperCamelCase    (       self					):


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

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




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_					):


									if isinstance(lowerCAmelCase__				,				torch.Tensor					):
											_lowerCAmelCase    :					List[str]							=   timestep.to(self.timesteps.device					)
									_lowerCAmelCase    :					Dict							=   (self.timesteps == timestep).nonzero().item()
									_lowerCAmelCase    :					str							=   self.sigmas[step_index]
									_lowerCAmelCase    :					Tuple							=   sample / ((sigma**2 + 1) ** 0.5)
									_lowerCAmelCase    :					str							=   True
									return sample




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_				,				snake_case_					):


									def lms_derivative(snake_case_					):
											_lowerCAmelCase    :					List[Any]							=   1.0
											for k in range(lowerCAmelCase__					):
													if current_order == k:
															continue
													prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
											return prod

									_lowerCAmelCase    :					Union[str, Any]							=   integrate.quad(lowerCAmelCase__				,				self.sigmas[t]				,				self.sigmas[t + 1]				,				epsrel=1E-4					)[0]

									return integrated_coeff




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_ = None					):
									_lowerCAmelCase    :					Optional[int]							=   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":
											_lowerCAmelCase    :					Dict							=   np.linspace(0				,				self.config.num_train_timesteps - 1				,				lowerCAmelCase__				,				dtype=lowerCAmelCase__					)[
											    ::-1
											].copy()
									elif self.config.timestep_spacing == "leading":
											_lowerCAmelCase    :					Optional[Any]							=   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
											_lowerCAmelCase    :					List[str]							=   (np.arange(0				,				lowerCAmelCase__					) * step_ratio).round()[::-1].copy().astype(lowerCAmelCase__					)
											timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
											_lowerCAmelCase    :					List[Any]							=   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
											_lowerCAmelCase    :					List[str]							=   (np.arange(self.config.num_train_timesteps				,				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\'.'					)

									_lowerCAmelCase    :					int							=   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5					)
									_lowerCAmelCase    :					Optional[int]							=   np.log(lowerCAmelCase__					)
									_lowerCAmelCase    :					int							=   np.interp(lowerCAmelCase__				,				np.arange(0				,				len(lowerCAmelCase__					)					)				,				lowerCAmelCase__					)

									if self.use_karras_sigmas:
											_lowerCAmelCase    :					List[str]							=   self._convert_to_karras(in_sigmas=lowerCAmelCase__					)
											_lowerCAmelCase    :					Tuple							=   np.array([self._sigma_to_t(lowerCAmelCase__				,				lowerCAmelCase__					) for sigma in sigmas]					)

									_lowerCAmelCase    :					Union[str, Any]							=   np.concatenate([sigmas, [0.0]]					).astype(np.floataa					)

									_lowerCAmelCase    :					Union[str, Any]							=   torch.from_numpy(lowerCAmelCase__					).to(device=lowerCAmelCase__					)
									if str(lowerCAmelCase__					).startswith("""mps"""					):
											# mps does not support float64
											_lowerCAmelCase    :					Any							=   torch.from_numpy(lowerCAmelCase__					).to(lowerCAmelCase__				,				dtype=torch.floataa					)
									else:
											_lowerCAmelCase    :					Any							=   torch.from_numpy(lowerCAmelCase__					).to(device=lowerCAmelCase__					)

									_lowerCAmelCase    :					List[str]							=   []




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_					):
									_lowerCAmelCase    :					Optional[Any]							=   np.log(lowerCAmelCase__					)

									# get distribution
									_lowerCAmelCase    :					Dict							=   log_sigma - log_sigmas[:, np.newaxis]

									# get sigmas range
									_lowerCAmelCase    :					Union[str, Any]							=   np.cumsum((dists >= 0)				,				axis=0					).argmax(axis=0					).clip(max=log_sigmas.shape[0] - 2					)
									_lowerCAmelCase    :					Dict							=   low_idx + 1

									_lowerCAmelCase    :					Optional[Any]							=   log_sigmas[low_idx]
									_lowerCAmelCase    :					int							=   log_sigmas[high_idx]

									# interpolate sigmas
									_lowerCAmelCase    :					Optional[Any]							=   (low - log_sigma) / (low - high)
									_lowerCAmelCase    :					Any							=   np.clip(lowerCAmelCase__				,				0				,				1					)

									# transform interpolation to time range
									_lowerCAmelCase    :					Union[str, Any]							=   (1 - w) * low_idx + w * high_idx
									_lowerCAmelCase    :					str							=   t.reshape(sigma.shape					)
									return t




							def 							__UpperCamelCase    (       self				,				snake_case_					):
									_lowerCAmelCase    :					str							=   in_sigmas[-1].item()
									_lowerCAmelCase    :					Optional[int]							=   in_sigmas[0].item()

									_lowerCAmelCase    :					int							=   7.0  # 7.0 is the value used in the paper
									_lowerCAmelCase    :					Tuple							=   np.linspace(0				,				1				,				self.num_inference_steps					)
									_lowerCAmelCase    :					Optional[Any]							=   sigma_min ** (1 / rho)
									_lowerCAmelCase    :					str							=   sigma_max ** (1 / rho)
									_lowerCAmelCase    :					int							=   (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_				,				snake_case_				,				snake_case_ = 4				,				snake_case_ = True				,				):


									if not self.is_scale_input_called:
											warnings.warn(
											    """The `scale_model_input` function should be called before `step` to ensure correct denoising. """
											    """See `StableDiffusionPipeline` for a usage example."""					)

									if isinstance(lowerCAmelCase__				,				torch.Tensor					):
											_lowerCAmelCase    :					Optional[Any]							=   timestep.to(self.timesteps.device					)
									_lowerCAmelCase    :					Optional[Any]							=   (self.timesteps == timestep).nonzero().item()
									_lowerCAmelCase    :					List[str]							=   self.sigmas[step_index]

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									if self.config.prediction_type == "epsilon":
											_lowerCAmelCase    :					List[str]							=   sample - sigma * model_output
									elif self.config.prediction_type == "v_prediction":
											# * c_out + input * c_skip
											_lowerCAmelCase    :					Tuple							=   model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
									elif self.config.prediction_type == "sample":
											_lowerCAmelCase    :					int							=   model_output
									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
									_lowerCAmelCase    :					str							=   (sample - pred_original_sample) / sigma
									self.derivatives.append(lowerCAmelCase__					)
									if len(self.derivatives					) > order:
											self.derivatives.pop(0					)

									# 3. Compute linear multistep coefficients
									_lowerCAmelCase    :					int							=   min(step_index + 1				,				lowerCAmelCase__					)
									_lowerCAmelCase    :					Optional[int]							=   [self.get_lms_coefficient(lowerCAmelCase__				,				lowerCAmelCase__				,				lowerCAmelCase__					) for curr_order in range(lowerCAmelCase__					)]

									# 4. Compute previous sample based on the derivatives path
									_lowerCAmelCase    :					Any							=   sample + sum(
									    coeff * derivative for coeff, derivative in zip(lowerCAmelCase__				,				reversed(self.derivatives					)					)					)

									if not return_dict:
											return (prev_sample,)

									return LMSDiscreteSchedulerOutput(prev_sample=lowerCAmelCase__				,				pred_original_sample=lowerCAmelCase__					)




							def 							__UpperCamelCase    (       self				,				snake_case_				,				snake_case_				,				snake_case_				,				):
									_lowerCAmelCase    :					List[Any]							=   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
											_lowerCAmelCase    :					Dict							=   self.timesteps.to(original_samples.device				,				dtype=torch.floataa					)
											_lowerCAmelCase    :					Tuple							=   timesteps.to(original_samples.device				,				dtype=torch.floataa					)
									else:
											_lowerCAmelCase    :					Tuple							=   self.timesteps.to(original_samples.device					)
											_lowerCAmelCase    :					Union[str, Any]							=   timesteps.to(original_samples.device					)

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

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

									_lowerCAmelCase    :					str							=   original_samples + noise * sigma
									return noisy_samples







							def __len__(       self					):
									return self.config.num_train_timesteps




'''simple docstring'''

def 		_UpperCAmelCase			(					_lowerCamelCase  :    list[list[int]]					, _lowerCamelCase  :    list[list[int]]						)      ->  list[list[int]]:
  _lowerCAmelCase    :					int							=   []
  _lowerCAmelCase    :					Union[str, Any]							=   len(_lowerCamelCase						)
  for i in range(_lowerCamelCase						):
    _lowerCAmelCase    :					List[str]							=   []
    for j in range(_lowerCamelCase						):
      _lowerCAmelCase    :					Union[str, Any]							=   0
      for k in range(_lowerCamelCase						):
        _lowerCAmelCase    :					Any							=   val + matrix_a[i][k] * matrix_b[k][j]
      list_a.append(_lowerCamelCase						)
    matrix_c.append(_lowerCamelCase						)
  return matrix_c


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  list[list[int]]:
  return [[int(row == column						) for column in range(_lowerCamelCase						)] for row in range(_lowerCamelCase						)]


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  int:
  if n <= 1:
    return n
  _lowerCAmelCase    :					Tuple							=   identity(2						)
  _lowerCAmelCase    :					Union[str, Any]							=   [[1, 1], [1, 0]]
  _lowerCAmelCase    :					Optional[int]							=   n - 1
  while n > 0:
    if n % 2 == 1:
      _lowerCAmelCase    :					str							=   multiply(_lowerCamelCase					, _lowerCamelCase						)
    _lowerCAmelCase    :					Tuple							=   multiply(_lowerCamelCase					, _lowerCamelCase						)
    _lowerCAmelCase    :					Dict							=   int(n / 2						)
  return res_matrix[0][0]


def 		_UpperCAmelCase			(					_lowerCamelCase  :    int						)      ->  int:
  if n <= 1:
    return n
  _lowerCAmelCase    :					Any							=   0
  _lowerCAmelCase    :					Dict							=   1
  for _ in range(2					, n + 1						):
    _lowerCAmelCase			,   _lowerCAmelCase    :					int							=   fiba, fiba + fiba
  return fiba


def 		_UpperCAmelCase			(					)      ->  None:
  for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
    _lowerCAmelCase    :					Union[str, Any]							=   int("""""".join(c for c in ordinal if c in """0123456789"""						)						)  # 1000th --> 1000
    print(
        f'{ordinal} fibonacci number using matrix exponentiation is '
        f'{nth_fibonacci_matrix(_lowerCamelCase						)} and using bruteforce is '
        f'{nth_fibonacci_bruteforce(_lowerCamelCase						)}\n'						)
  # from timeit import timeit
  # print(timeit("nth_fibonacci_matrix(1000000)",
  #              "from main import nth_fibonacci_matrix", number=5))
  # print(timeit("nth_fibonacci_bruteforce(1000000)",
  #              "from main import nth_fibonacci_bruteforce", number=5))
  # 2.3342058970001744
  # 57.256506615000035


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()


