



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 						lowerCamelCase_     (			__a    ):






						'''simple docstring'''
						a__ =	42
						a__ =	None







def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase=0.9_99			,     _lowerCamelCase="cosine"			,     ):
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(_lowerCamelCase     ):
									return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2     ) ** 2

			elif alpha_transform_type == "exp":

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

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

			A				:       Optional[int]														=    []
			for i in range(_a     ):
						A				:       int														=    i / num_diffusion_timesteps
						A				:       Dict														=    (i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(_a     ) / alpha_bar_fn(_a     )			,     _a     )     )
			return torch.tensor(_a			,     dtype=torch.floataa     )






class 						lowerCamelCase_     (			__a    ,__a    ):






						'''simple docstring'''
						a__ =	[e.name for e in KarrasDiffusionSchedulers]
						a__ =	1







						@register_to_config
						def __init__(						self   :      Union[str, Any]						,						__lowerCamelCase   :      int = 10_00						,						__lowerCamelCase   :      float = 0.0001						,						__lowerCamelCase   :      float = 0.02						,						__lowerCamelCase   :      str = "linear"						,						__lowerCamelCase   :      Optional[Union[np.ndarray, List[float]]] = None						,						__lowerCamelCase   :      Optional[bool] = False						,						__lowerCamelCase   :      str = "epsilon"						,						__lowerCamelCase   :      str = "linspace"						,						__lowerCamelCase   :      int = 0						,						)   ->					Any:

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

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

									A				:       Any														=    np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
									A				:       List[Any]														=    np.concatenate([sigmas[::-1], [0.0]]			).astype(np.floataa			)
									A				:       str														=    torch.from_numpy(__lowerCamelCase			)

									# setable values
									A				:       List[str]														=    None
									A				:       List[Any]														=    use_karras_sigmas
									self.set_timesteps(__lowerCamelCase						,						__lowerCamelCase			)
									A				:       Union[str, Any]														=    []
									A				:       Dict														=    False







						@property
						def       SCREAMING_SNAKE_CASE__		(						self   :      Union[str, Any]			)   ->					List[str]:

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

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







						def       SCREAMING_SNAKE_CASE__		(						self   :      Optional[int]						,						__lowerCamelCase   :      torch.FloatTensor						,						__lowerCamelCase   :      Union[float, torch.FloatTensor]			)   ->					Dict:

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







						def       SCREAMING_SNAKE_CASE__		(						self   :      Optional[Any]						,						__lowerCamelCase   :      Optional[Any]						,						__lowerCamelCase   :      Optional[Any]						,						__lowerCamelCase   :      List[str]			)   ->					List[Any]:

									def lms_derivative(__lowerCamelCase   :      List[Any]			):
												A				:       Tuple														=    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

									A				:       Optional[Any]														=    integrate.quad(__lowerCamelCase						,						self.sigmas[t]						,						self.sigmas[t + 1]						,						epsrel=1e-4			)[0]

									return integrated_coeff







						def       SCREAMING_SNAKE_CASE__		(						self   :      Any						,						__lowerCamelCase   :      int						,						__lowerCamelCase   :      Union[str, torch.device] = None			)   ->					Optional[int]:
									A				:       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":
												A				:       Tuple														=    np.linspace(0						,						self.config.num_train_timesteps - 1						,						__lowerCamelCase						,						dtype=__lowerCamelCase			)[
												    ::-1
												].copy()
									elif self.config.timestep_spacing == "leading":
												A				:       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
												A				:       Tuple														=    (np.arange(0						,						__lowerCamelCase			) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase			)
												timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
												A				:       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
												A				:       Union[str, Any]														=    (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'."""			)

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

									if self.use_karras_sigmas:
												A				:       Union[str, Any]														=    self._convert_to_karras(in_sigmas=__lowerCamelCase			)
												A				:       Union[str, Any]														=    np.array([self._sigma_to_t(__lowerCamelCase						,						__lowerCamelCase			) for sigma in sigmas]			)

									A				:       List[Any]														=    np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)

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

									A				:       Dict														=    []







						def       SCREAMING_SNAKE_CASE__		(						self   :      int						,						__lowerCamelCase   :      List[str]						,						__lowerCamelCase   :      Union[str, Any]			)   ->					Union[str, Any]:
									A				:       Union[str, Any]														=    np.log(__lowerCamelCase			)

									# get distribution
									A				:       Optional[int]														=    log_sigma - log_sigmas[:, np.newaxis]

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

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

									# interpolate sigmas
									A				:       List[Any]														=    (low - log_sigma) / (low - high)
									A				:       List[Any]														=    np.clip(__lowerCamelCase						,						0						,						1			)

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







						def       SCREAMING_SNAKE_CASE__		(						self   :      Any						,						__lowerCamelCase   :      torch.FloatTensor			)   ->					Dict:
									A				:       Any														=    in_sigmas[-1].item()
									A				:       List[str]														=    in_sigmas[0].item()

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







						def       SCREAMING_SNAKE_CASE__		(						self   :      Union[str, Any]						,						__lowerCamelCase   :      torch.FloatTensor						,						__lowerCamelCase   :      Union[float, torch.FloatTensor]						,						__lowerCamelCase   :      torch.FloatTensor						,						__lowerCamelCase   :      int = 4						,						__lowerCamelCase   :      bool = True						,						)   ->					Optional[Any]:

									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			):
												A				:       Dict														=    timestep.to(self.timesteps.device			)
									A				:       List[Any]														=    (self.timesteps == timestep).nonzero().item()
									A				:       List[Any]														=    self.sigmas[step_index]

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

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

									# 4. Compute previous sample based on the derivatives path
									A				:       Optional[int]														=    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       SCREAMING_SNAKE_CASE__		(						self   :      Optional[Any]						,						__lowerCamelCase   :      torch.FloatTensor						,						__lowerCamelCase   :      torch.FloatTensor						,						__lowerCamelCase   :      torch.FloatTensor						,						)   ->					List[str]:
									A				:       Union[str, 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
												A				:       Union[str, Any]														=    self.timesteps.to(original_samples.device						,						dtype=torch.floataa			)
												A				:       Optional[int]														=    timesteps.to(original_samples.device						,						dtype=torch.floataa			)
									else:
												A				:       List[Any]														=    self.timesteps.to(original_samples.device			)
												A				:       Dict														=    timesteps.to(original_samples.device			)

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

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

									A				:       int														=    original_samples + noise * sigma
									return noisy_samples







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





'''simple docstring'''







A					       =[[0, 1, 1], [0, 0, 1], [1, 0, 0]]


class      _a    :
       def __init__(      self		:      Optional[int]  ,							lowercase		:      str							):



           '''simple docstring'''

           UpperCAmelCase     			=						name
           UpperCAmelCase     			=						[]
           UpperCAmelCase     			=						[]
       def        A (      self		:      Union[str, Any]  ,							lowercase		:      int							):



           '''simple docstring'''

           self.inbound.append(lowercase							)
       def        A (      self		:      List[str]  ,							lowercase		:      Optional[Any]							):



           '''simple docstring'''

           self.outbound.append(lowercase							)







       def __repr__(      self		:      Any							):



           '''simple docstring'''

           return f"<node={self.name} inbound={self.inbound} outbound={self.outbound}>"






def 		snake_case_				(_a      :				str       ,  _a      :				str=3       ,  _a      :				Any=0.85	):
    UpperCAmelCase     			=						{}
    for node in nodes:
        UpperCAmelCase     			=						1

    UpperCAmelCase     			=						{}
    for node in nodes:
        UpperCAmelCase     			=						len(node.outbound	)

    for i in range(_a	):
        print(F"======= Iteration {i + 1} ======="	)
        for _, node in enumerate(_a	):
            UpperCAmelCase     			=						(1 - d) + d * sum(
                ranks[ib] / outbounds[ib] for ib in node.inbound	)
        print(_a	)





def 		snake_case_				():
    UpperCAmelCase     			=						list(input('''Enter Names of the Nodes: '''	).split()	)

    UpperCAmelCase     			=						[Node(_a	) for name in names]

    for ri, row in enumerate(_a	):
        for ci, col in enumerate(_a	):
            if col == 1:
                nodes[ci].add_inbound(names[ri]	)
                nodes[ri].add_outbound(names[ci]	)

    print('''======= Nodes ======='''	)
    for node in nodes:
        print(_a	)

    page_rank(_a	)


if __name__ == "__main__":
   main()




