

from __future__ import annotations

from typing import TypedDict




class  _lowerCAmelCase  (     lowercase       ):







 """simple docstring"""







 __UpperCAmelCase     : str
 __UpperCAmelCase     : int







def   _A  (  UpperCamelCase_					:	str)     ->						list[str]:
   '''simple docstring'''


   if not isinstance(UpperCamelCase_,      UpperCamelCase_):
      raise TypeError("The parameter s type must be str.")

   return [s[i:] + s[:i] for i in range(len(UpperCamelCase_))]




def   _A  (  UpperCamelCase_					:	str)     ->						BWTTransformDict:
   '''simple docstring'''


   if not isinstance(UpperCamelCase_,      UpperCamelCase_):
      raise TypeError("The parameter s type must be str.")
   if not s:
      raise ValueError("The parameter s must not be empty.")

   __lowercase								=						all_rotations(UpperCamelCase_)
   rotations.sort()  # sort the list of rotations in alphabetically order
   # make a string composed of the last char of each rotation
   __lowercase								=						{
       "bwt_string": "".join([word[-1] for word in rotations]),
       "idx_original_string": rotations.index(UpperCamelCase_),
   }
   return response




def   _A  (  UpperCamelCase_					:	str,      UpperCamelCase_					:	int)     ->						str:
   '''simple docstring'''


   if not isinstance(UpperCamelCase_,      UpperCamelCase_):
      raise TypeError("The parameter bwt_string type must be str.")
   if not bwt_string:
      raise ValueError("The parameter bwt_string must not be empty.")
   try:
      __lowercase								=						int(UpperCamelCase_)
   except ValueError:
      raise TypeError(
          "The parameter idx_original_string type must be int or passive"
          " of cast to int.")
   if idx_original_string < 0:
      raise ValueError("The parameter idx_original_string must not be lower than 0.")
   if idx_original_string >= len(UpperCamelCase_):
      raise ValueError(
          "The parameter idx_original_string must be lower than" " len(bwt_string).")

   __lowercase								=						[""] * len(UpperCamelCase_)
   for _ in range(len(UpperCamelCase_)):
      for i in range(len(UpperCamelCase_)):
         __lowercase								=						bwt_string[i] + ordered_rotations[i]
      ordered_rotations.sort()
   return ordered_rotations[idx_original_string]


if __name__ == "__main__":
   _a							=							'Provide a string that I will generate its BWT transform: '
   _a							=							input(entry_msg).strip()
   _a							=							bwt_transform(s)
   print(
       F"Burrows Wheeler transform for string '{s}' results "
       F"in '{result['bwt_string']}'"
   )
   _a							=							reverse_bwt(result['bwt_string'], result['idx_original_string'])
   print(
       F"Reversing Burrows Wheeler transform for entry '{result['bwt_string']}' "
       F"we get original string '{original_string}'"
   )







"""simple docstring"""





import numpy

# List of input, output pairs
_a							=							(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
_a							=							(((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
_a							=							[2, 4, 1, 5]
_a							=							len(train_data)
_a							=							0.009




def   _A  (  UpperCamelCase_					:	str,      UpperCamelCase_					:	List[Any]="train")     ->						Optional[Any]:
   '''simple docstring'''


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




def   _A  (  UpperCamelCase_					:	List[Any])     ->						Union[str, Any]:
   '''simple docstring'''


   __lowercase								=						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   _A  (  UpperCamelCase_					:	Dict,      UpperCamelCase_					:	Optional[int])     ->						Dict:
   '''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   _A  (  UpperCamelCase_					:	Dict,      UpperCamelCase_					:	List[str])     ->						int:
   '''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   _A  (  UpperCamelCase_					:	Any,      UpperCamelCase_					:	Tuple=m)     ->						int:
   '''simple docstring'''


   __lowercase								=						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   _A  (  UpperCamelCase_					:	str)     ->						str:
   '''simple docstring'''


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




def   _A  (  )     ->						List[str]:
   '''simple docstring'''


   global parameter_vector
   # Tune these values to set a tolerance value for predicted output
   __lowercase								=						0.000_002
   __lowercase								=						0
   __lowercase								=						0
   while True:
      j += 1
      __lowercase								=						[0, 0, 0, 0]
      for i in range(0,      len(UpperCamelCase_)):
         __lowercase								=						get_cost_derivative(i - 1)
         __lowercase								=						(
             parameter_vector[i] - LEARNING_RATE * cost_derivative
         )
      if numpy.allclose(
          UpperCamelCase_,      UpperCamelCase_,      atol=UpperCamelCase_,      rtol=UpperCamelCase_,      ):
         break
      __lowercase								=						temp_parameter_vector
   print(("Number of iterations:", j))




def   _A  (  )     ->						int:
   '''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()




