




"""simple docstring"""


def       UpperCAmelCase__ (snake_case__							:      list[list]					):
  """simple docstring"""

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


def       UpperCAmelCase__ (snake_case__							:      list[list]					):
  """simple docstring"""

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


if __name__ == "__main__":
     import doctest

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








"""simple docstring"""


import os
import sys
import unittest


A_      			=       os.path.abspath(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
sys.path.append(os.path.join(git_repo_path, '''utils'''))

import check_dummies  # noqa: E402
from check_dummies import create_dummy_files, create_dummy_object, find_backend, read_init  # noqa: E402


# Align TRANSFORMERS_PATH in check_dummies with the current path
A_      			=       os.path.join(git_repo_path, '''src''', '''diffusers''')






class       lowercase(  unittest.TestCase				):







 '''simple docstring'''





 def 				UpperCamelCase_     (       self:	Tuple	):




   '''simple docstring'''



   _snake_case							:	Optional[int]			=						find_backend("""    if not is_torch_available():"""	)
   self.assertEqual(a_,   """torch"""	)

   # backend_with_underscore = find_backend("    if not is_tensorflow_text_available():")
   # self.assertEqual(backend_with_underscore, "tensorflow_text")

   _snake_case							:	Any			=						find_backend("""    if not (is_torch_available() and is_transformers_available()):"""	)
   self.assertEqual(a_,   """torch_and_transformers"""	)

   # double_backend_with_underscore = find_backend(
   #    "    if not (is_sentencepiece_available() and is_tensorflow_text_available()):"
   # )
   # self.assertEqual(double_backend_with_underscore, "sentencepiece_and_tensorflow_text")

   _snake_case							:	Union[str, Any]			=						find_backend(
       """    if not (is_torch_available() and is_transformers_available() and is_onnx_available()):"""	)
   self.assertEqual(a_,   """torch_and_transformers_and_onnx"""	)


 def 				UpperCamelCase_     (       self:	List[Any]	):




   '''simple docstring'''



   _snake_case							:	Dict			=						read_init()
   # We don't assert on the exact list of keys to allow for smooth grow of backend-specific objects
   self.assertIn("""torch""",   a_	)
   self.assertIn("""torch_and_transformers""",   a_	)
   self.assertIn("""flax_and_transformers""",   a_	)
   self.assertIn("""torch_and_transformers_and_onnx""",   a_	)

   # Likewise, we can't assert on the exact content of a key
   self.assertIn("""UNet2DModel""",   objects["""torch"""]	)
   self.assertIn("""FlaxUNet2DConditionModel""",   objects["""flax"""]	)
   self.assertIn("""StableDiffusionPipeline""",   objects["""torch_and_transformers"""]	)
   self.assertIn("""FlaxStableDiffusionPipeline""",   objects["""flax_and_transformers"""]	)
   self.assertIn("""LMSDiscreteScheduler""",   objects["""torch_and_scipy"""]	)
   self.assertIn("""OnnxStableDiffusionPipeline""",   objects["""torch_and_transformers_and_onnx"""]	)


 def 				UpperCamelCase_     (       self:	List[str]	):




   '''simple docstring'''



   _snake_case							:	Optional[Any]			=						create_dummy_object("""CONSTANT""",   """'torch'"""	)
   self.assertEqual(a_,   """\nCONSTANT = None\n"""	)

   _snake_case							:	Optional[int]			=						create_dummy_object("""function""",   """'torch'"""	)
   self.assertEqual(
       a_,   """\ndef function(*args, **kwargs):\n    requires_backends(function, 'torch')\n"""	)

   _snake_case							:	List[Any]			=						"""
class FakeClass(metaclass=DummyObject):
    _backends = 'torch'

    def __init__(self, *args, **kwargs):
        requires_backends(self, 'torch')

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, 'torch')

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, 'torch')
"""
   _snake_case							:	Union[str, Any]			=						create_dummy_object("""FakeClass""",   """'torch'"""	)
   self.assertEqual(a_,   a_	)


 def 				UpperCamelCase_     (       self:	Union[str, Any]	):




   '''simple docstring'''



   _snake_case							:	Union[str, Any]			=						"""# This file is autogenerated by the command `make fix-copies`, do not edit.
from ..utils import DummyObject, requires_backends


CONSTANT = None


def function(*args, **kwargs):
    requires_backends(function, [\"torch\"])


class FakeClass(metaclass=DummyObject):
    _backends = [\"torch\"]

    def __init__(self, *args, **kwargs):
        requires_backends(self, [\"torch\"])

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, [\"torch\"])

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, [\"torch\"])
"""
   _snake_case							:	List[Any]			=						create_dummy_files({"""torch""": ["""CONSTANT""", """function""", """FakeClass"""]}	)
   self.assertEqual(dummy_files["""torch"""],   a_	)


