"""simple docstring"""






import numpy

# List of input, output pairs
__A			   = (
    ((5, 2, 3), 1_5),
    ((6, 5, 9), 2_5),
    ((1_1, 1_2, 1_3), 4_1),
    ((1, 1, 1), 8),
    ((1_1, 1_2, 1_3), 4_1),
)
__A			   = (((5_1_5, 2_2, 1_3), 5_5_5), ((6_1, 3_5, 4_9), 1_5_0))
__A			   = [2, 4, 1, 5]
__A			   = len(train_data)
__A			   = 0.009



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase="train" )  ->  str:
   return calculate_hypothesis_value(__UpperCAmelCase       ,    __UpperCAmelCase ) - output(
       __UpperCAmelCase       ,    __UpperCAmelCase )



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  List[str]:
   lowercase__:   str					=      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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  Tuple:
   if data_set == "train":
      return train_data[example_no][1]
   elif data_set == "test":
      return test_data[example_no][1]
   return None



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  Optional[Any]:
   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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase=m )  ->  Union[str, Any]:
   lowercase__:   List[Any]					=      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 SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  str:
   lowercase__:   Tuple					=      summation_of_cost_derivative(__UpperCAmelCase       ,    __UpperCAmelCase ) / m
   return cost_derivative_value



def SCREAMING_SNAKE_CASE__			(   )  ->  List[Any]:
   global parameter_vector
   # Tune these values to set a tolerance value for predicted output
   lowercase__:   int					=      0.0_0_0_0_0_2
   lowercase__:   Optional[int]					=      0
   lowercase__:   List[str]					=      0
   while True:
      j += 1
      lowercase__:   Dict					=      [0, 0, 0, 0]
      for i in range(0       ,    len(__UpperCAmelCase ) ):
         lowercase__:   Tuple					=      get_cost_derivative(i - 1 )
         lowercase__:   str					=      (
             parameter_vector[i] - LEARNING_RATE * cost_derivative
         )
      if numpy.allclose(
          __UpperCAmelCase       ,    __UpperCAmelCase       ,    atol=__UpperCAmelCase       ,    rtol=__UpperCAmelCase       ,    ):
         break
      lowercase__:   str					=      temp_parameter_vector
   print(('''Number of iterations:''', j) )



def SCREAMING_SNAKE_CASE__			(   )  ->  List[Any]:
   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"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase )  ->  int:

   if not grid or not grid[0]:
      raise TypeError('''The grid does not contain the appropriate information''' )

   for cell_n in range(1       ,    len(grid[0] ) ):
      grid[0][cell_n] += grid[0][cell_n - 1]
   lowercase__:   Tuple					=      grid[0]

   for row_n in range(1       ,    len(__UpperCAmelCase ) ):
      lowercase__:   Tuple					=      grid[row_n]
      lowercase__:   Dict					=      fill_row(__UpperCAmelCase       ,    __UpperCAmelCase )
      lowercase__:   Union[str, Any]					=      grid[row_n]

   return grid[-1][-1]



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase )  ->  list:
   current_row[0] += row_above[0]
   for cell_n in range(1       ,    len(__UpperCAmelCase ) ):
      current_row[cell_n] += min(current_row[cell_n - 1]       ,    row_above[cell_n] )

   return current_row


if __name__ == "__main__":
       import doctest

       doctest.testmod()
