
from __future__ import annotations

from collections.abc import Callable

_lowercase											=    list[list[float | int]]
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     Optional[Any]			,							UpperCAmelCase_	:     str				)			->						int:
       SCREAMING_SNAKE_CASE_							:				Optional[Any]		=len(A__				)
       SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[[0 for _ in range(size + 1				)] for _ in range(A__				)]
       SCREAMING_SNAKE_CASE_							:				int		=4_2
       SCREAMING_SNAKE_CASE_							:				Optional[Any]		=4_2
       SCREAMING_SNAKE_CASE_							:				Tuple		=4_2
       SCREAMING_SNAKE_CASE_							:				Any		=4_2
       SCREAMING_SNAKE_CASE_							:				int		=4_2
       SCREAMING_SNAKE_CASE_							:				str		=4_2

       for row in range(A__				):
              for col in range(A__				):
                     SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=matrix[row][col]

              SCREAMING_SNAKE_CASE_							:				int		=vector[row][0]

       SCREAMING_SNAKE_CASE_							:				int		=0
       SCREAMING_SNAKE_CASE_							:				Dict		=0
       while row < size and col < size:
              # pivoting
              SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=max((abs(augmented[rowa][col]				), rowa) for rowa in range(A__			,							A__				)				)[
                  1
              ]
              if augmented[pivot_row][col] == 0:
                     col += 1
                     continue
              else:
                     SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_							:				List[Any]		=augmented[pivot_row], augmented[row]

              for rowa in range(row + 1			,							A__				):
                     SCREAMING_SNAKE_CASE_							:				Any		=augmented[rowa][col] / augmented[row][col]
                     SCREAMING_SNAKE_CASE_							:				Any		=0
                     for cola in range(col + 1			,							size + 1				):
                            augmented[rowa][cola] -= augmented[row][cola] * ratio

              row += 1
              col += 1

       # back substitution
       for col in range(1			,							A__				):
              for row in range(A__				):
                     SCREAMING_SNAKE_CASE_							:				Optional[Any]		=augmented[row][col] / augmented[col][col]
                     for cola in range(A__			,							size + 1				):
                            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
       return [
           [round(augmented[row][size] / augmented[row][row]			,							1_0				)] for row in range(A__				)
       ]
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     Tuple				)			->						Tuple:
       SCREAMING_SNAKE_CASE_							:				Optional[int]		=len(A__				)
       SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[[0 for _ in range(A__				)] for _ in range(A__				)]
       SCREAMING_SNAKE_CASE_							:				Tuple		=[[0] for _ in range(A__				)]
       SCREAMING_SNAKE_CASE_							:				str		=4_2
       SCREAMING_SNAKE_CASE_							:				int		=4_2
       SCREAMING_SNAKE_CASE_							:				List[Any]		=4_2
       SCREAMING_SNAKE_CASE_							:				Any		=4_2

       for x_val, y_val in enumerate(A__				):
              for col in range(A__				):
                     SCREAMING_SNAKE_CASE_							:				Optional[int]		=(x_val + 1) ** (size - col - 1)
              SCREAMING_SNAKE_CASE_							:				List[str]		=y_val

       SCREAMING_SNAKE_CASE_							:				List[Any]		=solve(A__			,							A__				)

       def interpolated_func(UpperCAmelCase_	:     Dict				) -> int:
              return sum(
                  round(coeffs[x_val][0]				) * (var ** (size - x_val - 1))
                  for x_val in range(A__				)				)

       return interpolated_func
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     List[Any]				)			->						List[str]:
       return (
           1
           - variable
           + variable**2
           - variable**3
           + variable**4
           - variable**5
           + variable**6
           - variable**7
           + variable**8
           - variable**9
           + variable**1_0
       )
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     Tuple = question_function			,							UpperCAmelCase_	:     List[str] = 1_0				)			->						List[str]:
       SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[func(A__				) for x_val in range(1			,							order + 1				)]

       SCREAMING_SNAKE_CASE_							:				Optional[int]		=[
           interpolate(data_points[:max_coeff]				) for max_coeff in range(1			,							order + 1				)
       ]

       SCREAMING_SNAKE_CASE_							:				Dict		=0
       SCREAMING_SNAKE_CASE_							:				List[str]		=4_2
       SCREAMING_SNAKE_CASE_							:				Tuple		=4_2

       for poly in polynomials:
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=1
              while func(A__				) == poly(A__				):
                     x_val += 1

              ret += poly(A__				)

       return ret


if __name__ == "__main__":
 print(F"{solution() = }")





import random
import unittest

import torch

from diffusers import IFImgaImgSuperResolutionPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS, TEXT_GUIDED_IMAGE_VARIATION_PARAMS
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin



@skip_mps
class    UpperCAmelCase__(				lowerCamelCase  ,				lowerCamelCase  ,				unittest.TestCase						):

   '''simple docstring'''




   A     :	str												=     IFImgaImgSuperResolutionPipeline
   A     :	Dict												=     TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {"width", "height"}
   A     :	Any												=     TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS.union({"original_image"}						)
   A     :	str												=     PipelineTesterMixin.required_optional_params - {"latents"}


   def       UpperCAmelCase		(    self	:      Dict)						->					Dict:




         """simple docstring"""

         return self._get_superresolution_dummy_components()


   def       UpperCAmelCase		(    self	:      Optional[Any]      ,					lowerCAmelCase	:      Tuple      ,					lowerCAmelCase	:      Union[str, Any]=0)						->					str:




         """simple docstring"""

         if str(lowerCAmelCase).startswith('mps'):
               lowercase__  =	torch.manual_seed(lowerCAmelCase)
         else:
               lowercase__  =	torch.Generator(device=lowerCAmelCase).manual_seed(lowerCAmelCase)

         lowercase__  =	floats_tensor((1, 3, 32, 32)      ,					rng=random.Random(lowerCAmelCase)).to(lowerCAmelCase)
         lowercase__  =	floats_tensor((1, 3, 16, 16)      ,					rng=random.Random(lowerCAmelCase)).to(lowerCAmelCase)

         lowercase__  =	{
             'prompt': 'A painting of a squirrel eating a burger',
             'image': image,
             'original_image': original_image,
             'generator': generator,
             'num_inference_steps': 2,
             'output_type': 'numpy',
         }

         return inputs


   @unittest.skipIf(
       torch_device != 'cuda' or not is_xformers_available()      ,					reason='XFormers attention is only available with CUDA and `xformers` installed'      ,					)
   def       UpperCAmelCase		(    self	:      str)						->					Dict:




         """simple docstring"""

         self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3)


   def       UpperCAmelCase		(    self	:      List[Any])						->					Dict:




         """simple docstring"""

         self._test_save_load_optional_components()


   @unittest.skipIf(torch_device != 'cuda'      ,					reason='float16 requires CUDA')
   def       UpperCAmelCase		(    self	:      Optional[Any])						->					List[Any]:




         """simple docstring"""

         super().test_save_load_floataa(expected_max_diff=1E-1)


   def       UpperCAmelCase		(    self	:      str)						->					Union[str, Any]:




         """simple docstring"""

         self._test_attention_slicing_forward_pass(expected_max_diff=1E-2)


   def       UpperCAmelCase		(    self	:      Tuple)						->					Tuple:




         """simple docstring"""

         self._test_save_load_local()



   def       UpperCAmelCase		(    self	:      List[str])						->					Tuple:




         """simple docstring"""

         self._test_inference_batch_single_identical(
             expected_max_diff=1E-2      ,					)
