
"""simple docstring"""

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

import numpy as np
import torch

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


SCREAMING_SNAKE_CASE_         =  logging.get_logger(__name__)  # pylint: disable=invalid-name
@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class        _UpperCAmelCase							(						_A							):
      __SCREAMING_SNAKE_CASE				:							str							 =		4_2
      __SCREAMING_SNAKE_CASE				:							str							 =		None




def       lowercase__  (   lowerCAmelCase			:   Optional[Any]	,			lowerCAmelCase			:   List[Any]=0.999	,			lowerCAmelCase			:   Tuple="cosine"	,			)	-> int:






    """simple docstring"""




    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			:   List[str]	):
            return math.exp(t * -12.0	)

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

    UpperCAmelCase       =   []
    for i in range(A_	):
        UpperCAmelCase       =   i / num_diffusion_timesteps
        UpperCAmelCase       =   (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        _UpperCAmelCase							(						_A       ,     _A							):
      __SCREAMING_SNAKE_CASE				:							Optional[Any]							 =		[e.name for e in KarrasDiffusionSchedulers]
      __SCREAMING_SNAKE_CASE				:							Optional[int]							 =		1




      @register_to_config
      def __init__(							self				,    lowercase_ = 1_0_0_0				,    lowercase_ = 0.0_0_0_1				,    lowercase_ = 0.0_2				,    lowercase_ = "linear"				,    lowercase_ = None				,    lowercase_ = "epsilon"				,    lowercase_ = "linear"				,    lowercase_ = False				,    lowercase_ = "linspace"				,    lowercase_ = 0				,    )  ->   Optional[Any]:






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

          UpperCAmelCase       =   1.0 - self.betas
          UpperCAmelCase       =   torch.cumprod(self.alphas				,    dim=0							)

          UpperCAmelCase       =   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
          UpperCAmelCase       =   np.concatenate([sigmas[::-1], [0.0]]							).astype(np.floataa							)
          UpperCAmelCase       =   torch.from_numpy(UpperCamelCase__							)

          # setable values
          UpperCAmelCase       =   None
          UpperCAmelCase       =   np.linspace(0				,    num_train_timesteps - 1				,    UpperCamelCase__				,    dtype=UpperCamelCase__							)[::-1].copy()
          UpperCAmelCase       =   torch.from_numpy(UpperCamelCase__							)
          UpperCAmelCase       =   False
          UpperCAmelCase       =   use_karras_sigmas




      @property
      def       a_ (							self							)  ->   int:






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

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




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   torch.FloatTensor:






          if isinstance(UpperCamelCase__				,    torch.Tensor							):
              UpperCAmelCase       =   timestep.to(self.timesteps.device							)
          UpperCAmelCase       =   (self.timesteps == timestep).nonzero().item()
          UpperCAmelCase       =   self.sigmas[step_index]

          UpperCAmelCase       =   sample / ((sigma**2 + 1) ** 0.5)

          UpperCAmelCase       =   True
          return sample




      def       a_ (							self				,    lowercase_				,    lowercase_ = None							)  ->   int:
          UpperCAmelCase       =   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       =   np.linspace(0				,    self.config.num_train_timesteps - 1				,    UpperCamelCase__				,    dtype=UpperCamelCase__							)[
                  ::-1
              ].copy()
          elif self.config.timestep_spacing == "leading":
              UpperCAmelCase       =   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       =   (np.arange(0				,    UpperCamelCase__							) * step_ratio).round()[::-1].copy().astype(UpperCamelCase__							)
              timesteps += self.config.steps_offset
          elif self.config.timestep_spacing == "trailing":
              UpperCAmelCase       =   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       =   (np.arange(self.config.num_train_timesteps				,    0				,    -step_ratio							)).round().copy().astype(UpperCamelCase__							)
              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       =   np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
          UpperCAmelCase       =   np.log(UpperCamelCase__							)

          if self.config.interpolation_type == "linear":
              UpperCAmelCase       =   np.interp(UpperCamelCase__				,    np.arange(0				,    len(UpperCamelCase__							)							)				,    UpperCamelCase__							)
          elif self.config.interpolation_type == "log_linear":
              UpperCAmelCase       =   torch.linspace(np.log(sigmas[-1]							)				,    np.log(sigmas[0]							)				,    num_inference_steps + 1							).exp()
          else:
              raise ValueError(
                  F"{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either"
                  ' \'linear\' or \'log_linear\''							)

          if self.use_karras_sigmas:
              UpperCAmelCase       =   self._convert_to_karras(in_sigmas=UpperCamelCase__				,    num_inference_steps=self.num_inference_steps							)
              UpperCAmelCase       =   np.array([self._sigma_to_t(UpperCamelCase__				,    UpperCamelCase__							) for sigma in sigmas]							)

          UpperCAmelCase       =   np.concatenate([sigmas, [0.0]]							).astype(np.floataa							)
          UpperCAmelCase       =   torch.from_numpy(UpperCamelCase__							).to(device=UpperCamelCase__							)
          if str(UpperCamelCase__							).startswith('mps'							):
              # mps does not support float64
              UpperCAmelCase       =   torch.from_numpy(UpperCamelCase__							).to(UpperCamelCase__				,    dtype=torch.floataa							)
          else:
              UpperCAmelCase       =   torch.from_numpy(UpperCamelCase__							).to(device=UpperCamelCase__							)




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   List[str]:
          UpperCAmelCase       =   np.log(UpperCamelCase__							)

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

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

          UpperCAmelCase       =   log_sigmas[low_idx]
          UpperCAmelCase       =   log_sigmas[high_idx]

          # interpolate sigmas
          UpperCAmelCase       =   (low - log_sigma) / (low - high)
          UpperCAmelCase       =   np.clip(UpperCamelCase__				,    0				,    1							)

          # transform interpolation to time range
          UpperCAmelCase       =   (1 - w) * low_idx + w * high_idx
          UpperCAmelCase       =   t.reshape(sigma.shape							)
          return t




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   torch.FloatTensor:
          UpperCAmelCase       =   in_sigmas[-1].item()
          UpperCAmelCase       =   in_sigmas[0].item()

          UpperCAmelCase       =   7.0  # 7.0 is the value used in the paper
          UpperCAmelCase       =   np.linspace(0				,    1				,    UpperCamelCase__							)
          UpperCAmelCase       =   sigma_min ** (1 / rho)
          UpperCAmelCase       =   sigma_max ** (1 / rho)
          UpperCAmelCase       =   (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
          return sigmas




      def       a_ (							self				,    lowercase_				,    lowercase_				,    lowercase_				,    lowercase_ = 0.0				,    lowercase_ = 0.0				,    lowercase_ = float('inf'							)				,    lowercase_ = 1.0				,    lowercase_ = None				,    lowercase_ = True				,    )  ->   Union[EulerDiscreteSchedulerOutput, Tuple]:






          if (
              isinstance(UpperCamelCase__				,    UpperCamelCase__							)
              or isinstance(UpperCamelCase__				,    torch.IntTensor							)
              or isinstance(UpperCamelCase__				,    torch.LongTensor							)
          ):
              raise ValueError(
                  (
                      'Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'
                      ' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'
                      ' one of the `scheduler.timesteps` as a timestep.'
                  )				,    )

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

          if isinstance(UpperCamelCase__				,    torch.Tensor							):
              UpperCAmelCase       =   timestep.to(self.timesteps.device							)

          UpperCAmelCase       =   (self.timesteps == timestep).nonzero().item()
          UpperCAmelCase       =   self.sigmas[step_index]

          UpperCAmelCase       =   min(s_churn / (len(self.sigmas							) - 1)				,    2**0.5 - 1							) if s_tmin <= sigma <= s_tmax else 0.0

          UpperCAmelCase       =   randn_tensor(
              model_output.shape				,    dtype=model_output.dtype				,    device=model_output.device				,    generator=UpperCamelCase__							)

          UpperCAmelCase       =   noise * s_noise
          UpperCAmelCase       =   sigma * (gamma + 1)

          if gamma > 0:
              UpperCAmelCase       =   sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

          # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
          # NOTE: "original_sample" should not be an expected prediction_type but is left in for
          # backwards compatibility
          if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
              UpperCAmelCase       =   model_output
          elif self.config.prediction_type == "epsilon":
              UpperCAmelCase       =   sample - sigma_hat * model_output
          elif self.config.prediction_type == "v_prediction":
              # * c_out + input * c_skip
              UpperCAmelCase       =   model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
          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       =   (sample - pred_original_sample) / sigma_hat

          UpperCAmelCase       =   self.sigmas[step_index + 1] - sigma_hat

          UpperCAmelCase       =   sample + derivative * dt

          if not return_dict:
              return (prev_sample,)

          return EulerDiscreteSchedulerOutput(prev_sample=UpperCamelCase__				,    pred_original_sample=UpperCamelCase__							)




      def       a_ (							self				,    lowercase_				,    lowercase_				,    lowercase_				,    )  ->   torch.FloatTensor:
          UpperCAmelCase       =   self.sigmas.to(device=original_samples.device				,    dtype=original_samples.dtype							)
          if original_samples.device.type == "mps" and torch.is_floating_point(UpperCamelCase__							):
              # mps does not support float64
              UpperCAmelCase       =   self.timesteps.to(original_samples.device				,    dtype=torch.floataa							)
              UpperCAmelCase       =   timesteps.to(original_samples.device				,    dtype=torch.floataa							)
          else:
              UpperCAmelCase       =   self.timesteps.to(original_samples.device							)
              UpperCAmelCase       =   timesteps.to(original_samples.device							)

          UpperCAmelCase       =   [(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

          UpperCAmelCase       =   original_samples + noise * sigma
          return noisy_samples




      def __len__(							self							)  ->   Union[str, Any]:
          return self.config.num_train_timesteps




"""simple docstring"""

import math
import sys
class        _UpperCAmelCase							:




      def __init__(							self							)  ->   List[str]:
          UpperCAmelCase       =   0
          UpperCAmelCase       =   []
          UpperCAmelCase       =   {}  # To store the pos of node in array




      def       a_ (							self							)  ->   Dict:
          return self.cur_size == 0




      def       a_ (							self				,    lowercase_							)  ->   List[str]:
          UpperCAmelCase       =   self.left(lowercase_							)
          UpperCAmelCase       =   self.right(lowercase_							)
          if lc < self.cur_size and self.array(lowercase_							)[0] < self.array(lowercase_							)[0]:
              UpperCAmelCase       =   lc
          else:
              UpperCAmelCase       =   idx
          if rc < self.cur_size and self.array(lowercase_							)[0] < self.array(lowercase_							)[0]:
              UpperCAmelCase       =   rc
          if smallest != idx:
              self.swap(lowercase_				,    lowercase_							)
              self.min_heapify(lowercase_							)




      def       a_ (							self				,    lowercase_							)  ->   List[str]:
          # Inserts a node into the Priority Queue
          UpperCAmelCase       =   self.cur_size
          self.cur_size += 1
          self.array.append((sys.maxsize, tup[1])							)
          self.decrease_key((sys.maxsize, tup[1])				,    tup[0]							)




      def       a_ (							self							)  ->   int:
          # Removes and returns the min element at top of priority queue
          UpperCAmelCase       =   self.array[0][1]
          UpperCAmelCase       =   self.array[self.cur_size - 1]
          self.cur_size -= 1
          self.min_heapify(1							)
          del self.pos[min_node]
          return min_node




      def       a_ (							self				,    lowercase_							)  ->   Optional[int]:
          # returns the index of left child
          return 2 * i + 1




      def       a_ (							self				,    lowercase_							)  ->   List[Any]:
          # returns the index of right child
          return 2 * i + 2




      def       a_ (							self				,    lowercase_							)  ->   List[Any]:
          # returns the index of parent
          return math.floor(i / 2							)




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   List[Any]:
          # swaps array elements at indices i and j
          # update the pos{}
          UpperCAmelCase       =   j
          UpperCAmelCase       =   i
          UpperCAmelCase       =   self.array[i]
          UpperCAmelCase       =   self.array[j]
          UpperCAmelCase       =   temp




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   int:
          UpperCAmelCase       =   self.pos[tup[1]]
          # assuming the new_d is atmost old_d
          UpperCAmelCase       =   (new_d, tup[1])
          while idx > 0 and self.array[self.par(lowercase_							)][0] > self.array[idx][0]:
              self.swap(lowercase_				,    self.par(lowercase_							)							)
              UpperCAmelCase       =   self.par(lowercase_							)

class        _UpperCAmelCase							:




      def __init__(							self				,    lowercase_							)  ->   Union[str, Any]:
          UpperCAmelCase       =   {}  # To store graph: u -> (v,w)
          UpperCAmelCase       =   num  # Number of nodes in graph
          # To store the distance from source vertex
          UpperCAmelCase       =   [0] * self.num_nodes
          UpperCAmelCase       =   [-1] * self.num_nodes  # To store the path




      def       a_ (							self				,    lowercase_				,    lowercase_				,    lowercase_							)  ->   Any:
          #  Edge going from node u to v and v to u with weight w
          # u (w)-> v, v (w) -> u
          # Check if u already in graph
          if u in self.adjList:
              self.adjList[u].append((v, w)							)
          else:
              UpperCAmelCase       =   [(v, w)]

          # Assuming undirected graph
          if v in self.adjList:
              self.adjList[v].append((u, w)							)
          else:
              UpperCAmelCase       =   [(u, w)]




      def       a_ (							self							)  ->   Optional[Any]:
          # u -> v(w)
          for u in self.adjList:
              print(lowercase_				,    '->'				,    ' -> '.join(str(F"{v}({w})"							) for v, w in self.adjList[u]							)							)




      def       a_ (							self				,    lowercase_							)  ->   int:
          # Flush old junk values in par[]
          UpperCAmelCase       =   [-1] * self.num_nodes
          # src is the source node
          UpperCAmelCase       =   0
          UpperCAmelCase       =   PriorityQueue()
          q.insert((0, src)							)  # (dist from src, node)
          for u in self.adjList:
              if u != src:
                  UpperCAmelCase       =   sys.maxsize  # Infinity
                  UpperCAmelCase       =   -1

          while not q.is_empty():
              UpperCAmelCase       =   q.extract_min()  # Returns node with the min dist from source
              # Update the distance of all the neighbours of u and
              # if their prev dist was INFINITY then push them in Q
              for v, w in self.adjList[u]:
                  UpperCAmelCase       =   self.dist[u] + w
                  if self.dist[v] > new_dist:
                      if self.dist[v] == sys.maxsize:
                          q.insert((new_dist, v)							)
                      else:
                          q.decrease_key((self.dist[v], v)				,    lowercase_							)
                      UpperCAmelCase       =   new_dist
                      UpperCAmelCase       =   u

        # Show the shortest distances from src
          self.show_distances(lowercase_							)




      def       a_ (							self				,    lowercase_							)  ->   Any:
          print(F"Distance from node: {src}"							)
          for u in range(self.num_nodes							):
              print(F"Node {u} has distance: {self.dist[u]}"							)




      def       a_ (							self				,    lowercase_				,    lowercase_							)  ->   List[Any]:
          # To show the shortest path from src to dest
          # WARNING: Use it *after* calling dijkstra
          UpperCAmelCase       =   []
          UpperCAmelCase       =   0
          UpperCAmelCase       =   dest
          # Backtracking from dest to src
          while self.par[temp] != -1:
              path.append(lowercase_							)
              if temp != src:
                  for v, w in self.adjList[temp]:
                      if v == self.par[temp]:
                          cost += w
                          break
              UpperCAmelCase       =   self.par[temp]
          path.append(lowercase_							)
          path.reverse()

          print(F"----Path to reach {dest} from {src}----"							)
          for u in path:
              print(F"{u}"				,    end=' '							)
              if u != dest:
                  print('-> '				,    end=''							)

          print('\nTotal cost of path: '				,    lowercase_							)


if __name__ == "__main__":
   SCREAMING_SNAKE_CASE_         =  Graph(9)
   graph.add_edge(0, 1, 4)
   graph.add_edge(0, 7, 8)
   graph.add_edge(1, 2, 8)
   graph.add_edge(1, 7, 11)
   graph.add_edge(2, 3, 7)
   graph.add_edge(2, 8, 2)
   graph.add_edge(2, 5, 4)
   graph.add_edge(3, 4, 9)
   graph.add_edge(3, 5, 14)
   graph.add_edge(4, 5, 10)
   graph.add_edge(5, 6, 2)
   graph.add_edge(6, 7, 1)
   graph.add_edge(6, 8, 6)
   graph.add_edge(7, 8, 7)
   graph.show_graph()
   graph.dijkstra(0)
   graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21



