

"""simple docstring"""




def    __SCREAMING_SNAKE_CASE						(						lowercase__      ):
					"""simple docstring"""
					if len(_UpperCamelCase      ) == 0 or not all(len(_UpperCamelCase      ) == 2 for pair in coordinates      ):
										raise ValueError("The program cannot work out a fitting polynomial."      )

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

					A			=					{x for x, _ in coordinates}
					if len(_UpperCamelCase      ) == 1:
										return F"""x={coordinates[0][0]}"""

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

					A			=					len(_UpperCamelCase      )

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

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

					A			=					0

					while count < x:
										A			=					0
										while zahlen < x:
															if count == zahlen:
																				zahlen += 1
															if zahlen == x:
																				break
															A			=					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

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

					A			=					0
					A			=					"f(x)="

					while count < x:
										A			=					solution[count].split("E"      )
										if len(_UpperCamelCase      ) > 1:
															A			=					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, 11]]))
	print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))






'''simple docstring'''




import tempfile
import unittest

from diffusers import (
    DDIMScheduler,
    DDPMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    PNDMScheduler,
    logging,
)
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.utils.testing_utils import CaptureLogger




class 	__UpperCAmelCase				(				_UpperCamelCase     ):





       '''simple docstring'''



       __lowercase					:					str    =				'config.json'

       @register_to_config
       def __init__(      self    ,     _SCREAMING_SNAKE_CASE=2    ,     _SCREAMING_SNAKE_CASE=5    ,     _SCREAMING_SNAKE_CASE=(2, 5)    ,     _SCREAMING_SNAKE_CASE="for diffusion"    ,     _SCREAMING_SNAKE_CASE=[1, 3]    ,     )		->     Union[str, Any]:
           pass




class 	__UpperCAmelCase				(				_UpperCamelCase     ):





       '''simple docstring'''



       __lowercase					:					Tuple    =				'config.json'

       @register_to_config
       def __init__(      self    ,     _SCREAMING_SNAKE_CASE=2    ,     _SCREAMING_SNAKE_CASE=5    ,     _SCREAMING_SNAKE_CASE=(2, 5)    ,     _SCREAMING_SNAKE_CASE="for diffusion"    ,     _SCREAMING_SNAKE_CASE=[1, 3]    ,     )		->     Union[str, Any]:
           pass




class 	__UpperCAmelCase				(				_UpperCamelCase     ):





       '''simple docstring'''



       __lowercase					:					Optional[Any]    =				'config.json'

       @register_to_config
       def __init__(      self    ,     _SCREAMING_SNAKE_CASE=2    ,     _SCREAMING_SNAKE_CASE=5    ,     _SCREAMING_SNAKE_CASE=(2, 5)    ,     _SCREAMING_SNAKE_CASE="for diffusion"    ,     _SCREAMING_SNAKE_CASE=[1, 3]    ,     _SCREAMING_SNAKE_CASE=[1, 3]    ,     )		->     Dict:
           pass




class 	__UpperCAmelCase				(				_UpperCamelCase     ):





       '''simple docstring'''



       __lowercase					:					Optional[Any]    =				'config.json'

       @register_to_config
       def __init__(      self    ,     _SCREAMING_SNAKE_CASE=2    ,     _SCREAMING_SNAKE_CASE=5    ,     _SCREAMING_SNAKE_CASE=(2, 5)    ,     _SCREAMING_SNAKE_CASE="for diffusion"    ,     _SCREAMING_SNAKE_CASE=[1, 5]    ,     _SCREAMING_SNAKE_CASE=[5, 4]    ,     )		->     List[str]:
           pass




class 	__UpperCAmelCase				(				unittest.TestCase     ):





       '''simple docstring'''



       def 					__A       (      self )		->     Optional[int]:
           with self.assertRaises(_SCREAMING_SNAKE_CASE ):
               ConfigMixin.load_config('''dummy_path''' )

       def 					__A       (      self )		->     Union[str, Any]:
           A_     =   SampleObject()
           A_     =   obj.config
           assert config["a"] == 2
           assert config["b"] == 5
           assert config["c"] == (2, 5)
           assert config["d"] == "for diffusion"
           assert config["e"] == [1, 3]

           # init ignore private arguments
           A_     =   SampleObject(_name_or_path='''lalala''' )
           A_     =   obj.config
           assert config["a"] == 2
           assert config["b"] == 5
           assert config["c"] == (2, 5)
           assert config["d"] == "for diffusion"
           assert config["e"] == [1, 3]

           # can override default
           A_     =   SampleObject(c=6 )
           A_     =   obj.config
           assert config["a"] == 2
           assert config["b"] == 5
           assert config["c"] == 6
           assert config["d"] == "for diffusion"
           assert config["e"] == [1, 3]

           # can use positional arguments.
           A_     =   SampleObject(1    ,     c=6 )
           A_     =   obj.config
           assert config["a"] == 1
           assert config["b"] == 5
           assert config["c"] == 6
           assert config["d"] == "for diffusion"
           assert config["e"] == [1, 3]

       def 					__A       (      self )		->     int:
           A_     =   SampleObject()
           A_     =   obj.config

           assert config["a"] == 2
           assert config["b"] == 5
           assert config["c"] == (2, 5)
           assert config["d"] == "for diffusion"
           assert config["e"] == [1, 3]

           with tempfile.TemporaryDirectory() as tmpdirname:
               obj.save_config(_SCREAMING_SNAKE_CASE )
               A_     =   SampleObject.from_config(SampleObject.load_config(_SCREAMING_SNAKE_CASE ) )
               A_     =   new_obj.config

           # unfreeze configs
           A_     =   dict(_SCREAMING_SNAKE_CASE )
           A_     =   dict(_SCREAMING_SNAKE_CASE )

           assert config.pop('''c''' ) == (2, 5)  # instantiated as tuple
           assert new_config.pop('''c''' ) == [2, 5]  # saved & loaded as list because of json
           config.pop('''_use_default_values''' )
           assert config == new_config

       def 					__A       (      self )		->     List[Any]:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   DDIMScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler''' )

           assert ddim.__class__ == DDIMScheduler
           # no warning should be thrown
           assert cap_logger.out == ""

       def 					__A       (      self )		->     List[str]:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   EulerDiscreteScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler''' )

           assert euler.__class__ == EulerDiscreteScheduler
           # no warning should be thrown
           assert cap_logger.out == ""

       def 					__A       (      self )		->     Optional[Any]:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   EulerAncestralDiscreteScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler''' )

           assert euler.__class__ == EulerAncestralDiscreteScheduler
           # no warning should be thrown
           assert cap_logger.out == ""

       def 					__A       (      self )		->     Optional[int]:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   PNDMScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler''' )

           assert pndm.__class__ == PNDMScheduler
           # no warning should be thrown
           assert cap_logger.out == ""

       def 					__A       (      self )		->     Tuple:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   DDPMScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler'''    ,     prediction_type='''sample'''    ,     beta_end=8    ,     )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger_a:
               A_     =   DDPMScheduler.from_pretrained('''google/ddpm-celebahq-256'''    ,     beta_start=88 )

           assert ddpm.__class__ == DDPMScheduler
           assert ddpm.config.prediction_type == "sample"
           assert ddpm.config.beta_end == 8
           assert ddpm_a.config.beta_start == 88

           # no warning should be thrown
           assert cap_logger.out == ""
           assert cap_logger_a.out == ""

       def 					__A       (      self )		->     List[Any]:
           A_     =   logging.get_logger('''diffusers.configuration_utils''' )
           # 30 for warning
           logger.setLevel(30 )

           with CaptureLogger(_SCREAMING_SNAKE_CASE ) as cap_logger:
               A_     =   DPMSolverMultistepScheduler.from_pretrained(
                   '''hf-internal-testing/tiny-stable-diffusion-torch'''    ,     subfolder='''scheduler''' )

           assert dpm.__class__ == DPMSolverMultistepScheduler
           # no warning should be thrown
           assert cap_logger.out == ""

       def 					__A       (      self )		->     Optional[int]:
           # let's first save a config that should be in the form
           #    a=2,
           #    b=5,
           #    c=(2, 5),
           #    d="for diffusion",
           #    e=[1, 3],

           A_     =   SampleObject()

           A_     =   {k: v for k, v in config.config.items() if not k.startswith('''_''' )}

           # make sure that default config has all keys in `_use_default_values`
           assert set(config_dict.keys() ) == set(config.config._use_default_values )

           with tempfile.TemporaryDirectory() as tmpdirname:
               config.save_config(_SCREAMING_SNAKE_CASE )

               # now loading it with SampleObject2 should put f into `_use_default_values`
               A_     =   SampleObjecta.from_config(_SCREAMING_SNAKE_CASE )

               assert "f" in config._use_default_values
               assert config.f == [1, 3]

           # now loading the config, should **NOT** use [1, 3] for `f`, but the default [1, 4] value
           # **BECAUSE** it is part of `config._use_default_values`
           A_     =   SampleObjecta.from_config(config.config )
           assert new_config.f == [5, 4]

           config.config._use_default_values.pop()
           A_     =   SampleObjecta.from_config(config.config )
           assert new_config_a.f == [1, 3]

           # Nevertheless "e" should still be correctly loaded to [1, 3] from SampleObject2 instead of defaulting to [1, 5]
           assert new_config_a.e == [1, 3]






