






import numpy

# List of input, output pairs
UpperCamelCase							       =    (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
UpperCamelCase							       =    (((515, 22, 13), 555), ((61, 35, 49), 150))
UpperCamelCase							       =    [2, 4, 1, 5]
UpperCamelCase							       =    len(train_data)
UpperCamelCase							       =    0.009






def        lowerCAmelCase (      UpperCamelCase_:							Optional[Any]     , UpperCamelCase_:							Any="train"					)       ->							List[str]:







  '''simple docstring'''







  return calculate_hypothesis_value(UpperCamelCase_     , UpperCamelCase_					) - output(
      UpperCamelCase_     , UpperCamelCase_					)






def        lowerCAmelCase (      UpperCamelCase_:							Dict					)       ->							Optional[Any]:







  '''simple docstring'''







  _a							=	0
  for i in range(len(UpperCamelCase_					) - 1					):
    hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
  hyp_val += parameter_vector[0]
  return hyp_val






def        lowerCAmelCase (      UpperCamelCase_:							Dict     , UpperCamelCase_:							Union[str, Any]					)       ->							Optional[int]:







  '''simple docstring'''







  if data_set == "train":
    return train_data[example_no][1]
  elif data_set == "test":
    return test_data[example_no][1]
  return None






def        lowerCAmelCase (      UpperCamelCase_:							Dict     , UpperCamelCase_:							Tuple					)       ->							List[Any]:







  '''simple docstring'''







  if data_set == "train":
    return _hypothesis_value(train_data[example_no][0]					)
  elif data_set == "test":
    return _hypothesis_value(test_data[example_no][0]					)
  return None






def        lowerCAmelCase (      UpperCamelCase_:							List[Any]     , UpperCamelCase_:							Optional[int]=m					)       ->							Optional[Any]:







  '''simple docstring'''







  _a							=	0
  for i in range(UpperCamelCase_					):
    if index == -1:
      summation_value += _error(UpperCamelCase_					)
    else:
      summation_value += _error(UpperCamelCase_					) * train_data[i][0][index]
  return summation_value






def        lowerCAmelCase (      UpperCamelCase_:							Union[str, Any]					)       ->							Union[str, Any]:







  '''simple docstring'''







  _a							=	summation_of_cost_derivative(UpperCamelCase_     , UpperCamelCase_					) / m
  return cost_derivative_value






def        lowerCAmelCase (      )       ->							List[str]:







  '''simple docstring'''







  global parameter_vector
  # Tune these values to set a tolerance value for predicted output
  _a							=	0.00_0002
  _a							=	0
  _a							=	0
  while True:
    j += 1
    _a							=	[0, 0, 0, 0]
    for i in range(0     , len(UpperCamelCase_					)					):
      _a							=	get_cost_derivative(i - 1					)
      _a							=	(
          parameter_vector[i] - LEARNING_RATE * cost_derivative
      )
    if numpy.allclose(
        UpperCamelCase_     , UpperCamelCase_     , atol=UpperCamelCase_     , rtol=UpperCamelCase_     , ):
      break
    _a							=	temp_parameter_vector
  print(("Number of iterations:", j)					)






def        lowerCAmelCase (      )       ->							Any:







  '''simple docstring'''







  for i in range(len(UpperCamelCase_					)					):
    print(("Actual output value:", output(UpperCamelCase_     , "test"					))					)
    print(("Hypothesis output:", calculate_hypothesis_value(UpperCamelCase_     , "test"					))					)


if __name__ == "__main__":
     run_gradient_descent()
     print("""\nTesting gradient descent for a linear hypothesis function.\n""")
     test_gradient_descent()










"""simple docstring"""




import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class    lowercase_    (_UpperCAmelCase     ):
      A__	:		Tuple       			=				(KDPMaDiscreteScheduler,)
      A__	:		Tuple       			=				10






      def 			lowerCamelCase__    (    self     ,     **a_	)	->List[str]:







        '''simple docstring'''


        _a							=	{
            "num_train_timesteps": 1_1_0_0,
            "beta_start": 0.0_001,
            "beta_end": 0.02,
            "beta_schedule": "linear",
        }

        config.update(**a_	)
        return config






      def 			lowerCamelCase__    (    self	)	->Tuple:







        '''simple docstring'''


        for timesteps in [1_0, 5_0, 1_0_0, 1_0_0_0]:
          self.check_over_configs(num_train_timesteps=a_	)






      def 			lowerCamelCase__    (    self	)	->List[Any]:







        '''simple docstring'''


        for beta_start, beta_end in zip([0.00_001, 0.0_001, 0.001]     ,     [0.0_002, 0.002, 0.02]	):
          self.check_over_configs(beta_start=a_     ,     beta_end=a_	)






      def 			lowerCamelCase__    (    self	)	->Any:







        '''simple docstring'''


        for schedule in ["linear", "scaled_linear"]:
          self.check_over_configs(beta_schedule=a_	)






      def 			lowerCamelCase__    (    self	)	->int:







        '''simple docstring'''


        for prediction_type in ["epsilon", "v_prediction"]:
          self.check_over_configs(prediction_type=a_	)






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







        '''simple docstring'''


        _a							=	self.scheduler_classes[0]
        _a							=	self.get_scheduler_config(prediction_type="v_prediction"	)
        _a							=	scheduler_class(**a_	)

        scheduler.set_timesteps(self.num_inference_steps	)

        _a							=	self.dummy_model()
        _a							=	self.dummy_sample_deter * scheduler.init_noise_sigma
        _a							=	sample.to(a_	)

        for i, t in enumerate(scheduler.timesteps	):
          _a							=	scheduler.scale_model_input(a_     ,     a_	)

          _a							=	model(a_     ,     a_	)

          _a							=	scheduler.step(a_     ,     a_     ,     a_	)
          _a							=	output.prev_sample

        _a							=	torch.sum(torch.abs(a_	)	)
        _a							=	torch.mean(torch.abs(a_	)	)

        if torch_device in ["cpu", "mps"]:
          assert abs(result_sum.item() - 4.6_934E-07	) < 1E-2
          assert abs(result_mean.item() - 6.1_112E-10	) < 1E-3
        else:
          # CUDA
          assert abs(result_sum.item() - 4.693_428_650_170_972E-07	) < 1E-2
          assert abs(result_mean.item() - 0.0_002	) < 1E-3






      def 			lowerCamelCase__    (    self	)	->Any:







        '''simple docstring'''


        if torch_device == "mps":
          return
        _a							=	self.scheduler_classes[0]
        _a							=	self.get_scheduler_config()
        _a							=	scheduler_class(**a_	)

        scheduler.set_timesteps(self.num_inference_steps	)

        _a							=	self.dummy_model()
        _a							=	self.dummy_sample_deter * scheduler.init_noise_sigma
        _a							=	sample.to(a_	)

        for i, t in enumerate(scheduler.timesteps	):
          _a							=	scheduler.scale_model_input(a_     ,     a_	)

          _a							=	model(a_     ,     a_	)

          _a							=	scheduler.step(a_     ,     a_     ,     a_	)
          _a							=	output.prev_sample

        _a							=	torch.sum(torch.abs(a_	)	)
        _a							=	torch.mean(torch.abs(a_	)	)

        if torch_device in ["cpu", "mps"]:
          assert abs(result_sum.item() - 20.4_125	) < 1E-2
          assert abs(result_mean.item() - 0.0_266	) < 1E-3
        else:
          # CUDA
          assert abs(result_sum.item() - 20.4_125	) < 1E-2
          assert abs(result_mean.item() - 0.0_266	) < 1E-3






      def 			lowerCamelCase__    (    self	)	->int:







        '''simple docstring'''


        if torch_device == "mps":
          return
        _a							=	self.scheduler_classes[0]
        _a							=	self.get_scheduler_config()
        _a							=	scheduler_class(**a_	)

        scheduler.set_timesteps(self.num_inference_steps     ,     device=a_	)

        _a							=	self.dummy_model()
        _a							=	self.dummy_sample_deter.to(a_	) * scheduler.init_noise_sigma

        for t in scheduler.timesteps:
          _a							=	scheduler.scale_model_input(a_     ,     a_	)

          _a							=	model(a_     ,     a_	)

          _a							=	scheduler.step(a_     ,     a_     ,     a_	)
          _a							=	output.prev_sample

        _a							=	torch.sum(torch.abs(a_	)	)
        _a							=	torch.mean(torch.abs(a_	)	)

        if str(a_	).startswith("cpu"	):
          # The following sum varies between 148 and 156 on mps. Why?
          assert abs(result_sum.item() - 20.4_125	) < 1E-2
          assert abs(result_mean.item() - 0.0_266	) < 1E-3
        else:
          # CUDA
          assert abs(result_sum.item() - 20.4_125	) < 1E-2
          assert abs(result_mean.item() - 0.0_266	) < 1E-3


