




def  SCREAMING_SNAKE_CASE     (	__UpperCamelCase      :						list[list]				)  ->							list[list]:
    UpperCAmelCase_										=					current_set.copy()
    for row_index, row in enumerate(__UpperCamelCase				):
        UpperCAmelCase_										=					row[0]
        for column_index, column in enumerate(__UpperCamelCase				):
            if magnitude == 0:
                UpperCAmelCase_										=					column
                continue
            UpperCAmelCase_										=					column / magnitude
    # Subtract to cancel term
    UpperCAmelCase_										=					current_set[0]
    UpperCAmelCase_										=					[first_row]
    UpperCAmelCase_										=					current_set[1::]
    for row in current_set:
        UpperCAmelCase_										=					[]
        # 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:
        UpperCAmelCase_										=					final_set[0]
        UpperCAmelCase_										=					[]
        UpperCAmelCase_										=					[]
        for row in final_set[1::]:
            current_first_column.append(row[0]				)
            next_iteration.append(row[1::]				)
        UpperCAmelCase_										=					simplify(__UpperCamelCase				)
        for i in range(len(__UpperCamelCase				)				):
            resultant[i].insert(0	,					current_first_column[i]				)
        resultant.insert(0	,					__UpperCamelCase				)
        UpperCAmelCase_										=					resultant
    return final_set




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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 _lowerCamelCase      			=						[
     [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]]))











import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
 import torch

if is_vision_available():
 from PIL import Image

 from transformers import MobileNetVaImageProcessor



class       a					(       unittest.TestCase      ):

     '''simple docstring'''





     def __init__(     self       :      Tuple ,   __snake_case       :      int ,   __snake_case       :      List[Any]=7 ,   __snake_case       :      Any=3 ,   __snake_case       :      Any=18 ,   __snake_case       :      str=30 ,   __snake_case       :      Any=4_00 ,   __snake_case       :      Optional[int]=True ,   __snake_case       :      str=None ,   __snake_case       :      Any=True ,   __snake_case       :      List[Any]=None ,   ):
         UpperCAmelCase_										=					size if size is not None else {'''shortest_edge''': 20}
         UpperCAmelCase_										=					crop_size if crop_size is not None else {'''height''': 18, '''width''': 18}
         UpperCAmelCase_										=					parent
         UpperCAmelCase_										=					batch_size
         UpperCAmelCase_										=					num_channels
         UpperCAmelCase_										=					image_size
         UpperCAmelCase_										=					min_resolution
         UpperCAmelCase_										=					max_resolution
         UpperCAmelCase_										=					do_resize
         UpperCAmelCase_										=					size
         UpperCAmelCase_										=					do_center_crop
         UpperCAmelCase_										=					crop_size




     def   lowerCamelCase_       (     self       :      Any    ):
         return {
             "do_resize": self.do_resize,
             "size": self.size,
             "do_center_crop": self.do_center_crop,
             "crop_size": self.crop_size,
         }



@require_torch
@require_vision
class       a					(       _A     ,       unittest.TestCase      ):

     '''simple docstring'''





     lowerCAmelCase    :	Union[str, Any]       		=  MobileNetVaImageProcessor if is_vision_available() else None
     def   lowerCamelCase_       (     self       :      Any    ):
         UpperCAmelCase_										=					MobileNetVaImageProcessingTester(self    )
     @property
     def   lowerCamelCase_       (     self       :      List[str]    ):
         return self.image_processor_tester.prepare_image_processor_dict()
     def   lowerCamelCase_       (     self       :      Optional[int]    ):
         UpperCAmelCase_										=					self.image_processing_class(**self.image_processor_dict    )
         self.assertTrue(hasattr(__snake_case ,   '''do_resize'''    )    )
         self.assertTrue(hasattr(__snake_case ,   '''size'''    )    )
         self.assertTrue(hasattr(__snake_case ,   '''do_center_crop'''    )    )
         self.assertTrue(hasattr(__snake_case ,   '''crop_size'''    )    )
     def   lowerCamelCase_       (     self       :      Dict    ):
         UpperCAmelCase_										=					self.image_processing_class.from_dict(self.image_processor_dict    )
         self.assertEqual(image_processor.size ,   {'''shortest_edge''': 20}    )
         self.assertEqual(image_processor.crop_size ,   {'''height''': 18, '''width''': 18}    )

         UpperCAmelCase_										=					self.image_processing_class.from_dict(self.image_processor_dict ,   size=42 ,   crop_size=84    )
         self.assertEqual(image_processor.size ,   {'''shortest_edge''': 42}    )
         self.assertEqual(image_processor.crop_size ,   {'''height''': 84, '''width''': 84}    )
     def   lowerCamelCase_       (     self       :      Optional[int]    ):
         pass
     def   lowerCamelCase_       (     self       :      Tuple    ):
         # Initialize image_processing
         UpperCAmelCase_										=					self.image_processing_class(**self.image_processor_dict    )
         # create random PIL images
         UpperCAmelCase_										=					prepare_image_inputs(self.image_processor_tester ,   equal_resolution=__snake_case    )
         for image in image_inputs:
             self.assertIsInstance(__snake_case ,   Image.Image    )

         # Test not batched input
         UpperCAmelCase_										=					image_processing(image_inputs[0] ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )

         # Test batched
         UpperCAmelCase_										=					image_processing(__snake_case ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )
     def   lowerCamelCase_       (     self       :      str    ):
         # Initialize image_processing
         UpperCAmelCase_										=					self.image_processing_class(**self.image_processor_dict    )
         # create random numpy tensors
         UpperCAmelCase_										=					prepare_image_inputs(self.image_processor_tester ,   equal_resolution=__snake_case ,   numpify=__snake_case    )
         for image in image_inputs:
             self.assertIsInstance(__snake_case ,   np.ndarray    )

         # Test not batched input
         UpperCAmelCase_										=					image_processing(image_inputs[0] ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )

         # Test batched
         UpperCAmelCase_										=					image_processing(__snake_case ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )




     def   lowerCamelCase_       (     self       :      int    ):
         # Initialize image_processing
         UpperCAmelCase_										=					self.image_processing_class(**self.image_processor_dict    )
         # create random PyTorch tensors
         UpperCAmelCase_										=					prepare_image_inputs(self.image_processor_tester ,   equal_resolution=__snake_case ,   torchify=__snake_case    )
         for image in image_inputs:
             self.assertIsInstance(__snake_case ,   torch.Tensor    )

         # Test not batched input
         UpperCAmelCase_										=					image_processing(image_inputs[0] ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )

         # Test batched
         UpperCAmelCase_										=					image_processing(__snake_case ,   return_tensors='''pt'''    ).pixel_values
         self.assertEqual(
             encoded_images.shape ,   (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.crop_size['''height'''],
                 self.image_processor_tester.crop_size['''width'''],
             ) ,   )





