





from typing import Any, Dict, List, Mapping

import numpy as np
import torch

from ...utils import is_cython_available, requires_backends


if is_cython_available():
						import pyximport

						pyximport.install(setup_args={"include_dirs": np.get_include()})
						from . import algos_graphormer  # noqa E402





def  __UpperCamelCase   (     a,  a = 512)			->Any:
					lowerCamelCase__      =							x.shape[1] if len(x.shape) > 1 else 1
					lowerCamelCase__      =							1 + np.arange(0,  feature_num * offset,  a,  dtype=np.intaa)
					lowerCamelCase__      =							x + feature_offset
					return x





def  __UpperCamelCase   (     a,  a=True)			->Union[str, Any]:
					requires_backends(a,  ["cython"])

					if keep_features and "edge_attr" in item.keys():  # edge_attr
										lowerCamelCase__      =							np.asarray(item["edge_attr"],  dtype=np.intaa)
					else:
										lowerCamelCase__      =							np.ones((len(item["edge_index"][0]), 1),  dtype=np.intaa)  # same embedding for all

					if keep_features and "node_feat" in item.keys():  # input_nodes
										lowerCamelCase__      =							np.asarray(item["node_feat"],  dtype=np.intaa)
					else:
										lowerCamelCase__      =							np.ones((item["num_nodes"], 1),  dtype=np.intaa)  # same embedding for all

					lowerCamelCase__      =							np.asarray(item["edge_index"],  dtype=np.intaa)

					lowerCamelCase__      =							convert_to_single_emb(a) + 1
					lowerCamelCase__      =							item["num_nodes"]

					if len(edge_attr.shape) == 1:
										lowerCamelCase__      =							edge_attr[:, None]
					lowerCamelCase__      =							np.zeros([num_nodes, num_nodes, edge_attr.shape[-1]],  dtype=np.intaa)
					lowerCamelCase__      =							convert_to_single_emb(a) + 1

					# node adj matrix [num_nodes, num_nodes] bool
					lowerCamelCase__      =							np.zeros([num_nodes, num_nodes],  dtype=a)
					lowerCamelCase__      =							True

					lowerCamelCase__     ,		lowerCamelCase__      =							algos_graphormer.floyd_warshall(a)
					lowerCamelCase__      =							np.amax(a)

					lowerCamelCase__      =							algos_graphormer.gen_edge_input(a,  a,  a)
					lowerCamelCase__      =							np.zeros([num_nodes + 1, num_nodes + 1],  dtype=np.single)  # with graph token

					# combine
					lowerCamelCase__      =							input_nodes + 1  # we shift all indices by one for padding
					lowerCamelCase__      =							attn_bias
					lowerCamelCase__      =							attn_edge_type
					lowerCamelCase__      =							shortest_path_result.astype(np.intaa) + 1  # we shift all indices by one for padding
					lowerCamelCase__      =							np.sum(a,  axis=1).reshape(-1) + 1  # we shift all indices by one for padding
					lowerCamelCase__      =							item["in_degree"]  # for undirected graph
					lowerCamelCase__      =							input_edges + 1  # we shift all indices by one for padding
					if "labels" not in item:
										lowerCamelCase__      =							item["y"]

					return item







class SCREAMING_SNAKE_CASE_			:





					"""simple docstring"""


					def __init__(			self						,	_lowerCAmelCase=20						,	_lowerCAmelCase=False						):
										if not is_cython_available():
															raise ImportError("Graphormer preprocessing needs Cython (pyximport)"						)

										lowerCamelCase__      =							spatial_pos_max
										lowerCamelCase__      =							on_the_fly_processing






					def __call__(			self						,	_lowerCAmelCase						):
										if self.on_the_fly_processing:
															lowerCamelCase__      =							[preprocess_item(_lowerCAmelCase						) for i in features]

										if not isinstance(features[0]						,	_lowerCAmelCase						):
															lowerCamelCase__      =							[vars(_lowerCAmelCase						) for f in features]
										lowerCamelCase__      =							{}

										lowerCamelCase__      =							max(len(i["input_nodes"]						) for i in features						)
										lowerCamelCase__      =							len(features[0]["input_nodes"][0]						)
										lowerCamelCase__      =							len(features[0]["attn_edge_type"][0][0]						)
										lowerCamelCase__      =							max(len(i["input_edges"][0][0]						) for i in features						)
										lowerCamelCase__      =							len(features[0]["input_edges"][0][0][0]						)
										lowerCamelCase__      =							len(_lowerCAmelCase						)

										lowerCamelCase__      =							torch.zeros(_lowerCAmelCase						,	max_node_num + 1						,	max_node_num + 1						,	dtype=torch.float						)
										lowerCamelCase__      =							torch.zeros(_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	dtype=torch.long						)
										lowerCamelCase__      =							torch.zeros(_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	dtype=torch.long						)
										lowerCamelCase__      =							torch.zeros(_lowerCAmelCase						,	_lowerCAmelCase						,	dtype=torch.long						)
										lowerCamelCase__      =							torch.zeros(_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	dtype=torch.long						)
										lowerCamelCase__      =							torch.zeros(
										    _lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	_lowerCAmelCase						,	dtype=torch.long						)

										for ix, f in enumerate(_lowerCAmelCase						):
															for k in ["attn_bias", "attn_edge_type", "spatial_pos", "in_degree", "input_nodes", "input_edges"]:
																				lowerCamelCase__      =							torch.tensor(f[k]						)

															if len(f["attn_bias"][1:, 1:][f["spatial_pos"] >= self.spatial_pos_max]						) > 0:
																				lowerCamelCase__      =							float("-inf"						)

															lowerCamelCase__      =							f["attn_bias"]
															lowerCamelCase__      =							f[
															    "attn_edge_type"
															]
															lowerCamelCase__      =							f["spatial_pos"]
															lowerCamelCase__      =							f["in_degree"]
															lowerCamelCase__      =							f["input_nodes"]
															lowerCamelCase__      =							f["input_edges"]

										lowerCamelCase__      =							batch["in_degree"]

										lowerCamelCase__      =							features[0]["labels"]
										if len(_lowerCAmelCase						) == 1:  # one task
															if isinstance(sample[0]						,	_lowerCAmelCase						):  # regression
																				lowerCamelCase__      =							torch.from_numpy(np.concatenate([i["labels"] for i in features]						)						)
															else:  # binary classification
																				lowerCamelCase__      =							torch.from_numpy(np.concatenate([i["labels"] for i in features]						)						)
										else:  # multi task classification, left to float to keep the NaNs
															lowerCamelCase__      =							torch.from_numpy(np.stack([i["labels"] for i in features]						,	axis=0						)						)

										return batch








def  __UpperCamelCase   (     a)			->str:
					if len(a) == 0 or not all(len(a) == 2 for pair in coordinates):
										raise ValueError("The program cannot work out a fitting polynomial.")

					if len({tuple(a) for pair in coordinates}) != len(a):
										raise ValueError("The program cannot work out a fitting polynomial.")

					lowerCamelCase__      =							{x for x, _ in coordinates}
					if len(a) == 1:
										return f"x={coordinates[0][0]}"

					if len(a) != len(a):
										raise ValueError("The program cannot work out a fitting polynomial.")

					lowerCamelCase__      =							len(a)

					lowerCamelCase__      =							0
					lowerCamelCase__      =							[]
					# put the x and x to the power values in a matrix
					while count_of_line < x:
										lowerCamelCase__      =							0
										lowerCamelCase__      =							coordinates[count_of_line][0]
										lowerCamelCase__      =							[]
										while count_in_line < x:
															count_line.append(a ** (x - (count_in_line + 1)))
															count_in_line += 1
										matrix.append(a)
										count_of_line += 1

					lowerCamelCase__      =							0
					# put the y values into a vector
					lowerCamelCase__      =							[]
					while count_of_line < x:
										vector.append(coordinates[count_of_line][1])
										count_of_line += 1

					lowerCamelCase__      =							0

					while count < x:
										lowerCamelCase__      =							0
										while zahlen < x:
															if count == zahlen:
																				zahlen += 1
															if zahlen == x:
																				break
															lowerCamelCase__      =							matrix[zahlen][count] / matrix[count][count]
															for counting_columns, item in enumerate(matrix[count]):
																				# manipulating all the values in the matrix
																				matrix[zahlen][counting_columns] -= item * bruch
															# manipulating the values in the vector
															vector[zahlen] -= vector[count] * bruch
															zahlen += 1
										count += 1

					lowerCamelCase__      =							0
					# make solutions
					lowerCamelCase__      =							[]
					while count < x:
										solution.append(str(vector[count] / matrix[count][count]))
										count += 1

					lowerCamelCase__      =							0
					lowerCamelCase__      =							"f(x)="

					while count < x:
										lowerCamelCase__      =							solution[count].split("E")
										if len(a) > 1:
															lowerCamelCase__      =							f"{remove_e[0]}*10^{remove_e[1]}"
										solved += f"x^{x - (count + 1)}*{solution[count]}"
										if count + 1 != x:
															solved += "+"
										count += 1

					return solved


if __name__ == "__main__":
						print(points_to_polynomial([]))
						print(points_to_polynomial([[]]))
						print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
						print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
						print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
						print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))

