def 		__lowerCamelCase							(UpperCAmelCase__       :							list[list]					):
					SCREAMING_SNAKE_CASE           =    current_set.copy()
					for row_index, row in enumerate(UpperCAmelCase__					):
										SCREAMING_SNAKE_CASE           =    row[0]
										for column_index, column in enumerate(UpperCAmelCase__					):
															if magnitude == 0:
																				SCREAMING_SNAKE_CASE           =    column
																				continue
															SCREAMING_SNAKE_CASE           =    column / magnitude
    # Subtract to cancel term
					SCREAMING_SNAKE_CASE           =    current_set[0]
					SCREAMING_SNAKE_CASE           =    [first_row]
					SCREAMING_SNAKE_CASE           =    current_set[1::]
					for row in current_set:
										SCREAMING_SNAKE_CASE           =    []
										# If first term is 0, it is already in form we want, so we preserve it
										if row[0] == 0:
															final_set.append(UpperCAmelCase__					)
															continue
										for column_index in range(len(UpperCAmelCase__					)					):
															temp_row.append(first_row[column_index] - row[column_index]					)
										final_set.append(UpperCAmelCase__					)
					# Create next recursion iteration set
					if len(final_set[0]					) != 3:
										SCREAMING_SNAKE_CASE           =    final_set[0]
										SCREAMING_SNAKE_CASE           =    []
										SCREAMING_SNAKE_CASE           =    []
										for row in final_set[1::]:
															current_first_column.append(row[0]					)
															next_iteration.append(row[1::]					)
										SCREAMING_SNAKE_CASE           =    simplify(UpperCAmelCase__					)
										for i in range(len(UpperCAmelCase__					)					):
															resultant[i].insert(0 ,	current_first_column[i]					)
										resultant.insert(0 ,	UpperCAmelCase__					)
										SCREAMING_SNAKE_CASE           =    resultant
					return final_set





def 		__lowerCamelCase							(UpperCAmelCase__       :							list[list]					):
					if len(UpperCAmelCase__					) == 0:
										raise IndexError("solve_simultaneous() requires n lists of length n+1"					)
					SCREAMING_SNAKE_CASE           =    len(UpperCAmelCase__					) + 1
					if any(len(UpperCAmelCase__					) != _length for item in equations					):
										raise IndexError("solve_simultaneous() requires n lists of length n+1"					)
					for row in equations:
										if any(not isinstance(UpperCAmelCase__ ,	(int, float)					) for column in row					):
															raise ValueError("solve_simultaneous() requires lists of integers"					)
					if len(UpperCAmelCase__					) == 1:
										return [equations[0][-1] / equations[0][0]]
					SCREAMING_SNAKE_CASE           =    equations.copy()
					if any(0 in row for row in data_set					):
										SCREAMING_SNAKE_CASE           =    data_set.copy()
										SCREAMING_SNAKE_CASE           =    []
										for row_index, row in enumerate(UpperCAmelCase__					):
															if 0 not in row:
																				SCREAMING_SNAKE_CASE           =    data_set.pop(UpperCAmelCase__					)
																				break
										if not full_row:
															raise ValueError("solve_simultaneous() requires at least 1 full equation"					)
										data_set.insert(0 ,	UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    data_set.copy()
					SCREAMING_SNAKE_CASE           =    simplify(UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    simplified[::-1]
					SCREAMING_SNAKE_CASE           =    []
					for row in simplified:
										SCREAMING_SNAKE_CASE           =    row[-1]
										if not solutions:
															if row[-2] == 0:
																				solutions.append(0					)
																				continue
															solutions.append(current_solution / row[-2]					)
															continue
										SCREAMING_SNAKE_CASE           =    row.copy()[: len(UpperCAmelCase__					) - 1 :]
										while temp_row[0] == 0:
															temp_row.pop(0					)
										if len(UpperCAmelCase__					) == 0:
															solutions.append(0					)
															continue
										SCREAMING_SNAKE_CASE           =    temp_row[1::]
										SCREAMING_SNAKE_CASE           =    temp_row[::-1]
										for column_index, column in enumerate(UpperCAmelCase__					):
															current_solution -= column * solutions[column_index]
										solutions.append(UpperCAmelCase__					)
					SCREAMING_SNAKE_CASE           =    []
					for item in solutions:
										final.append(float(round(UpperCAmelCase__ ,	5					)					)					)
					return final[::-1]


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							_lowerCamelCase   :				List[str]     			=						[
							    [2, 1, 1, 1, 1, 4],
							    [1, 2, 1, 1, 1, 5],
							    [1, 1, 2, 1, 1, 6],
							    [1, 1, 1, 2, 1, 7],
							    [1, 1, 1, 1, 2, 8],
							]
							print(solve_simultaneous(eq))
							print(solve_simultaneous([[4, 2]]))





from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
							import PIL


_lowerCamelCase   :				List[Any]     			=						logging.get_logger(__name__)


class   lowercase      (       a       ):
							lowercase__  :    List[str]									=							["""pixel_values"""]




							def __init__(  self				:   List[str]		,							_UpperCamelCase				:   bool = True		,							_UpperCamelCase				:   Dict[str, int] = None		,							_UpperCamelCase				:   float = None		,							_UpperCamelCase				:   PILImageResampling = PILImageResampling.BILINEAR		,							_UpperCamelCase				:   bool = True		,							_UpperCamelCase				:   Union[int, float] = 1 / 255		,							_UpperCamelCase				:   bool = True		,							_UpperCamelCase				:   Optional[Union[float, List[float]]] = None		,							_UpperCamelCase				:   Optional[Union[float, List[float]]] = None		,							**_UpperCamelCase				:   Dict		,							)   ->			None:



												'''simple docstring'''

												super().__init__(**_UpperCamelCase )
												SCREAMING_SNAKE_CASE           =    size if size is not None else {"shortest_edge": 384}
												SCREAMING_SNAKE_CASE           =    get_size_dict(_UpperCamelCase		,							default_to_square=_UpperCamelCase )

												SCREAMING_SNAKE_CASE           =    do_resize
												SCREAMING_SNAKE_CASE           =    size
												# Default value set here for backwards compatibility where the value in config is None
												SCREAMING_SNAKE_CASE           =    crop_pct if crop_pct is not None else 224 / 256
												SCREAMING_SNAKE_CASE           =    resample
												SCREAMING_SNAKE_CASE           =    do_rescale
												SCREAMING_SNAKE_CASE           =    rescale_factor
												SCREAMING_SNAKE_CASE           =    do_normalize
												SCREAMING_SNAKE_CASE           =    image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
												SCREAMING_SNAKE_CASE           =    image_std if image_std is not None else IMAGENET_STANDARD_STD




							def 		__snake_case(  self				:   Optional[Any]		,							_UpperCamelCase				:   np.ndarray		,							_UpperCamelCase				:   Dict[str, int]		,							_UpperCamelCase				:   float		,							_UpperCamelCase				:   PILImageResampling = PILImageResampling.BICUBIC		,							_UpperCamelCase				:   Optional[Union[str, ChannelDimension]] = None		,							**_UpperCamelCase				:   Optional[int]		,							)   ->			np.ndarray:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    get_size_dict(_UpperCamelCase		,							default_to_square=_UpperCamelCase )
												if "shortest_edge" not in size:
																	raise ValueError(F"Size dictionary must contain 'shortest_edge' key. Got {size.keys()}" )
												SCREAMING_SNAKE_CASE           =    size["shortest_edge"]

												if shortest_edge < 384:
																	# maintain same ratio, resizing shortest edge to shortest_edge/crop_pct
																	SCREAMING_SNAKE_CASE           =    int(shortest_edge / crop_pct )
																	SCREAMING_SNAKE_CASE           =    get_resize_output_image_size(_UpperCamelCase		,							size=_UpperCamelCase		,							default_to_square=_UpperCamelCase )
																	SCREAMING_SNAKE_CASE           =    resize(image=_UpperCamelCase		,							size=_UpperCamelCase		,							resample=_UpperCamelCase		,							data_format=_UpperCamelCase		,							**_UpperCamelCase )
																	# then crop to (shortest_edge, shortest_edge)
																	return center_crop(image=_UpperCamelCase		,							size=(shortest_edge, shortest_edge)		,							data_format=_UpperCamelCase		,							**_UpperCamelCase )
												else:
																	# warping (no cropping) when evaluated at 384 or larger
																	return resize(
																	    _UpperCamelCase		,							size=(shortest_edge, shortest_edge)		,							resample=_UpperCamelCase		,							data_format=_UpperCamelCase		,							**_UpperCamelCase )




							def 		__snake_case(  self				:   int		,							_UpperCamelCase				:   np.ndarray		,							_UpperCamelCase				:   Union[int, float]		,							_UpperCamelCase				:   Optional[Union[str, ChannelDimension]] = None		,							**_UpperCamelCase				:   Optional[Any]		,							)   ->			List[Any]:



												'''simple docstring'''

												return rescale(_UpperCamelCase		,							scale=_UpperCamelCase		,							data_format=_UpperCamelCase		,							**_UpperCamelCase )




							def 		__snake_case(  self				:   Tuple		,							_UpperCamelCase				:   np.ndarray		,							_UpperCamelCase				:   Union[float, List[float]]		,							_UpperCamelCase				:   Union[float, List[float]]		,							_UpperCamelCase				:   Optional[Union[str, ChannelDimension]] = None		,							**_UpperCamelCase				:   List[Any]		,							)   ->			np.ndarray:



												'''simple docstring'''

												return normalize(_UpperCamelCase		,							mean=_UpperCamelCase		,							std=_UpperCamelCase		,							data_format=_UpperCamelCase		,							**_UpperCamelCase )





							def 		__snake_case(  self				:   List[str]		,							_UpperCamelCase				:   ImageInput		,							_UpperCamelCase				:   bool = None		,							_UpperCamelCase				:   Dict[str, int] = None		,							_UpperCamelCase				:   float = None		,							_UpperCamelCase				:   PILImageResampling = None		,							_UpperCamelCase				:   bool = None		,							_UpperCamelCase				:   float = None		,							_UpperCamelCase				:   bool = None		,							_UpperCamelCase				:   Optional[Union[float, List[float]]] = None		,							_UpperCamelCase				:   Optional[Union[float, List[float]]] = None		,							_UpperCamelCase				:   Optional[Union[str, TensorType]] = None		,							_UpperCamelCase				:   ChannelDimension = ChannelDimension.FIRST		,							**_UpperCamelCase				:   Any		,							)   ->			PIL.Image.Image:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    do_resize if do_resize is not None else self.do_resize
												SCREAMING_SNAKE_CASE           =    crop_pct if crop_pct is not None else self.crop_pct
												SCREAMING_SNAKE_CASE           =    resample if resample is not None else self.resample
												SCREAMING_SNAKE_CASE           =    do_rescale if do_rescale is not None else self.do_rescale
												SCREAMING_SNAKE_CASE           =    rescale_factor if rescale_factor is not None else self.rescale_factor
												SCREAMING_SNAKE_CASE           =    do_normalize if do_normalize is not None else self.do_normalize
												SCREAMING_SNAKE_CASE           =    image_mean if image_mean is not None else self.image_mean
												SCREAMING_SNAKE_CASE           =    image_std if image_std is not None else self.image_std

												SCREAMING_SNAKE_CASE           =    size if size is not None else self.size
												SCREAMING_SNAKE_CASE           =    get_size_dict(_UpperCamelCase		,							default_to_square=_UpperCamelCase )

												SCREAMING_SNAKE_CASE           =    make_list_of_images(_UpperCamelCase )

												if not valid_images(_UpperCamelCase ):
																	raise ValueError(
																	    "Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, "
																	    "torch.Tensor, tf.Tensor or jax.ndarray." )

												if do_resize and size is None or resample is None:
																	raise ValueError("Size and resample must be specified if do_resize is True." )

												if do_resize and size["shortest_edge"] < 384 and crop_pct is None:
																	raise ValueError("crop_pct must be specified if size < 384." )

												if do_rescale and rescale_factor is None:
																	raise ValueError("Rescale factor must be specified if do_rescale is True." )

												if do_normalize and (image_mean is None or image_std is None):
																	raise ValueError("Image mean and std must be specified if do_normalize is True." )

												# All transformations expect numpy arrays.
												SCREAMING_SNAKE_CASE           =    [to_numpy_array(_UpperCamelCase ) for image in images]

												if do_resize:
																	SCREAMING_SNAKE_CASE           =    [self.resize(image=_UpperCamelCase		,							size=_UpperCamelCase		,							crop_pct=_UpperCamelCase		,							resample=_UpperCamelCase ) for image in images]

												if do_rescale:
																	SCREAMING_SNAKE_CASE           =    [self.rescale(image=_UpperCamelCase		,							scale=_UpperCamelCase ) for image in images]

												if do_normalize:
																	SCREAMING_SNAKE_CASE           =    [self.normalize(image=_UpperCamelCase		,							mean=_UpperCamelCase		,							std=_UpperCamelCase ) for image in images]

												SCREAMING_SNAKE_CASE           =    [to_channel_dimension_format(_UpperCamelCase		,							_UpperCamelCase ) for image in images]

												SCREAMING_SNAKE_CASE           =    {"pixel_values": images}
												return BatchFeature(data=_UpperCamelCase		,							tensor_type=_UpperCamelCase )




