




"""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  _snake_case				(							A_       ):

				'''simple docstring'''




				UpperCamelCase__		     =42
				UpperCamelCase__		     =None



def 				a (						__snake_case     :				Tuple,    __snake_case     :				int=0.999,    __snake_case     :				List[Any]="cosine",    ):



				'''simple docstring'''





				if alpha_transform_type == "cosine":

								def alpha_bar_fn(__snake_case     :				Optional[Any]  ):
												return math.cos((t + 0.008) / 1.008 * math.pi / 2  ) ** 2

				elif alpha_transform_type == "exp":

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

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

				UpperCAmelCase_					:List[str]      			=      []
				for i in range(lowercase__  ):
								UpperCAmelCase_					:Dict      			=      i / num_diffusion_timesteps
								UpperCAmelCase_					:Dict      			=      (i + 1) / num_diffusion_timesteps
								betas.append(min(1 - alpha_bar_fn(lowercase__  ) / alpha_bar_fn(lowercase__  ),    lowercase__  )  )
				return torch.tensor(lowercase__,    dtype=torch.floataa  )





class  _snake_case				(							A_							,						A_       ):

				'''simple docstring'''




				UpperCamelCase__		     =[e.name for e in KarrasDiffusionSchedulers]
				UpperCamelCase__		     =1





				@register_to_config
				def __init__(							self      :  Dict					,							snake_case      :  int = 1_000					,							snake_case      :  Dict = 0.0_001					,							snake_case      :  Union[str, Any] = 0.02					,							snake_case      :  List[Any] = "linear"					,							snake_case      :  str = None					,							snake_case      :  int = False					,							snake_case      :  str = "epsilon"					,							snake_case      :  List[str] = "linspace"					,							snake_case      :  List[str] = 0					,							):
								if trained_betas is not None:
												UpperCAmelCase_					:str      			=      torch.tensor(snake_case					,							dtype=torch.floataa     )
								elif beta_schedule == "linear":
												UpperCAmelCase_					:Optional[Any]      			=      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.
												UpperCAmelCase_					:Optional[int]      			=      (
												    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
												UpperCAmelCase_					:Dict      			=      betas_for_alpha_bar(snake_case     )
								else:
												raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'     )

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

								UpperCAmelCase_					:Tuple      			=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
								UpperCAmelCase_					:Optional[int]      			=      np.concatenate([sigmas[::-1], [0.0]]     ).astype(np.floataa     )
								UpperCAmelCase_					:List[Any]      			=      torch.from_numpy(snake_case     )

								# setable values
								UpperCAmelCase_					:Optional[int]      			=      None
								UpperCAmelCase_					:str      			=      use_karras_sigmas
								self.set_timesteps(snake_case					,							snake_case     )
								UpperCAmelCase_					:List[str]      			=      []
								UpperCAmelCase_					:Optional[Any]      			=      False





				@property
				def 				snake_case_ (							self      :  Optional[int]     ):
								# 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      :  Dict					,							snake_case      :  Any					,							snake_case      :  Union[str, Any]     ):
								if isinstance(snake_case					,							torch.Tensor     ):
												UpperCAmelCase_					:Any      			=      timestep.to(self.timesteps.device     )
								UpperCAmelCase_					:List[str]      			=      (self.timesteps == timestep).nonzero().item()
								UpperCAmelCase_					:Union[str, Any]      			=      self.sigmas[step_index]
								UpperCAmelCase_					:Dict      			=      sample / ((sigma**2 + 1) ** 0.5)
								UpperCAmelCase_					:Optional[Any]      			=      True
								return sample





				def 				snake_case_ (							self      :  Optional[int]					,							snake_case      :  str					,							snake_case      :  Tuple					,							snake_case      :  List[str]     ):

								def lms_derivative(snake_case      :  List[str]     ):
												UpperCAmelCase_					:Dict      			=      1.0
												for k in range(snake_case     ):
																if current_order == k:
																				continue
																prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
												return prod

								UpperCAmelCase_					:Optional[int]      			=      integrate.quad(snake_case					,							self.sigmas[t]					,							self.sigmas[t + 1]					,							epsrel=1e-4     )[0]

								return integrated_coeff





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

								UpperCAmelCase_					:Optional[Any]      			=      np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
								UpperCAmelCase_					:int      			=      np.log(snake_case     )
								UpperCAmelCase_					:List[str]      			=      np.interp(snake_case					,							np.arange(0					,							len(snake_case     )     )					,							snake_case     )

								if self.use_karras_sigmas:
												UpperCAmelCase_					:int      			=      self._convert_to_karras(in_sigmas=snake_case     )
												UpperCAmelCase_					:Optional[int]      			=      np.array([self._sigma_to_t(snake_case					,							snake_case     ) for sigma in sigmas]     )

								UpperCAmelCase_					:Optional[Any]      			=      np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )

								UpperCAmelCase_					:Dict      			=      torch.from_numpy(snake_case     ).to(device=snake_case     )
								if str(snake_case     ).startswith('''mps'''     ):
												# mps does not support float64
												UpperCAmelCase_					:Optional[Any]      			=      torch.from_numpy(snake_case     ).to(snake_case					,							dtype=torch.floataa     )
								else:
												UpperCAmelCase_					:Union[str, Any]      			=      torch.from_numpy(snake_case     ).to(device=snake_case     )

								UpperCAmelCase_					:Tuple      			=      []





				def 				snake_case_ (							self      :  Tuple					,							snake_case      :  Union[str, Any]					,							snake_case      :  Dict     ):
								# get log sigma
								UpperCAmelCase_					:Dict      			=      np.log(snake_case     )

								# get distribution
								UpperCAmelCase_					:str      			=      log_sigma - log_sigmas[:, np.newaxis]

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

								UpperCAmelCase_					:Any      			=      log_sigmas[low_idx]
								UpperCAmelCase_					:Any      			=      log_sigmas[high_idx]

								# interpolate sigmas
								UpperCAmelCase_					:str      			=      (low - log_sigma) / (low - high)
								UpperCAmelCase_					:Tuple      			=      np.clip(snake_case					,							0					,							1     )

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





				def 				snake_case_ (							self      :  List[str]					,							snake_case      :  int     ):
								UpperCAmelCase_					:List[Any]      			=      in_sigmas[-1].item()
								UpperCAmelCase_					:List[Any]      			=      in_sigmas[0].item()

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





				def 				snake_case_ (							self      :  Union[str, Any]					,							snake_case      :  int					,							snake_case      :  str					,							snake_case      :  Tuple					,							snake_case      :  Union[str, Any] = 4					,							snake_case      :  Any = 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(snake_case					,							torch.Tensor     ):
												UpperCAmelCase_					:Tuple      			=      timestep.to(self.timesteps.device     )
								UpperCAmelCase_					:Union[str, Any]      			=      (self.timesteps == timestep).nonzero().item()
								UpperCAmelCase_					:Dict      			=      self.sigmas[step_index]

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

								# 3. Compute linear multistep coefficients
								UpperCAmelCase_					:Optional[Any]      			=      min(step_index + 1					,							snake_case     )
								UpperCAmelCase_					:str      			=      [self.get_lms_coefficient(snake_case					,							snake_case					,							snake_case     ) for curr_order in range(snake_case     )]

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

								if not return_dict:
												return (prev_sample,)

								return LMSDiscreteSchedulerOutput(prev_sample=snake_case					,							pred_original_sample=snake_case     )





				def 				snake_case_ (							self      :  Optional[Any]					,							snake_case      :  Tuple					,							snake_case      :  int					,							snake_case      :  str					,							):
								# Make sure sigmas and timesteps have the same device and dtype as original_samples
								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(snake_case     ):
												# mps does not support float64
												UpperCAmelCase_					:Dict      			=      self.timesteps.to(original_samples.device					,							dtype=torch.floataa     )
												UpperCAmelCase_					:Union[str, 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_					:Any      			=      [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

								UpperCAmelCase_					:str      			=      original_samples + noise * sigma
								return noisy_samples





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








"""simple docstring"""

# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint



class  _snake_case				:

				'''simple docstring'''




				def __init__(							self      :  str					,							snake_case      :  Optional[Any]					,							snake_case      :  str     ):
								UpperCAmelCase_					:Union[str, Any]      			=      key
								UpperCAmelCase_					:str      			=      freq





				def __str__(							self      :  Optional[Any]     ):
								return f'Node(key={self.key}, freq={self.freq})'



def 				a (						__snake_case     :				int,    __snake_case     :				Optional[int],    __snake_case     :				Tuple,    __snake_case     :				Any,    __snake_case     :				Dict,    __snake_case     :				List[str]  ):



				'''simple docstring'''





				if i > j or i < 0 or j > len(__snake_case  ) - 1:
								return

				UpperCAmelCase_					:List[str]      			=      root[i][j]
				if parent == -1:  # root does not have a parent
								print(f'{key[node]} is the root of the binary search tree.'  )
				elif is_left:
								print(f'{key[node]} is the left child of key {parent}.'  )
				else:
								print(f'{key[node]} is the right child of key {parent}.'  )

				print_binary_search_tree(__snake_case,    __snake_case,    __snake_case,    node - 1,    key[node],    __snake_case  )
				print_binary_search_tree(__snake_case,    __snake_case,    node + 1,    __snake_case,    key[node],    __snake_case  )



def 				a (						__snake_case     :				Optional[Any]  ):



				'''simple docstring'''





				nodes.sort(key=lambda __snake_case  : node.key  )

				UpperCAmelCase_					:List[str]      			=      len(__snake_case  )

				UpperCAmelCase_					:Any      			=      [nodes[i].key for i in range(__snake_case  )]
				UpperCAmelCase_					:int      			=      [nodes[i].freq for i in range(__snake_case  )]

				# This 2D array stores the overall tree cost (which's as minimized as possible);
				# for a single key, cost is equal to frequency of the key.
				UpperCAmelCase_					:Dict      			=      [[freqs[i] if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]
				# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
				# array
				UpperCAmelCase_					:Optional[Any]      			=      [[freqs[i] if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]
				# stores tree roots that will be used later for constructing binary search tree
				UpperCAmelCase_					:int      			=      [[i if i == j else 0 for j in range(__snake_case  )] for i in range(__snake_case  )]

				for interval_length in range(2,    n + 1  ):
								for i in range(n - interval_length + 1  ):
												UpperCAmelCase_					:Union[str, Any]      			=      i + interval_length - 1

												UpperCAmelCase_					:Optional[int]      			=      sys.maxsize  # set the value to "infinity"
												UpperCAmelCase_					:List[Any]      			=      total[i][j - 1] + freqs[j]

												# Apply Knuth's optimization
												# Loop without optimization: for r in range(i, j + 1):
												for r in range(root[i][j - 1],    root[i + 1][j] + 1  ):  # r is a temporal root
																UpperCAmelCase_					:Any      			=      dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
																UpperCAmelCase_					:Optional[int]      			=      dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
																UpperCAmelCase_					:Union[str, Any]      			=      left + total[i][j] + right

																if dp[i][j] > cost:
																				UpperCAmelCase_					:Optional[Any]      			=      cost
																				UpperCAmelCase_					:Optional[int]      			=      r

				print('''Binary search tree nodes:'''  )
				for node in nodes:
								print(__snake_case  )

				print(f'\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'  )
				print_binary_search_tree(__snake_case,    __snake_case,    0,    n - 1,    -1,    __snake_case  )



def 				a (						):



				'''simple docstring'''





				UpperCAmelCase_					:Union[str, Any]      			=      [Node(__snake_case,    randint(1,    50  )  ) for i in range(10,    0,    -1  )]
				find_optimal_binary_search_tree(__snake_case  )


if __name__ == "__main__":
						main()


