
"""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_    							=					(((515, 22, 13), 555), ((61, 35, 49), 150))
A_    							=					[2, 4, 1, 5]
A_    							=					len(train_data)
A_    							=					0.009






def  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__="train"						):
			return calculate_hypothesis_value(lowerCAmelCase__	,lowerCAmelCase__						) - output(
			    lowerCAmelCase__	,lowerCAmelCase__						)






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  0
			for i in range(len(lowerCAmelCase__						) - 1						):
						hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
			hyp_val += parameter_vector[0]
			return hyp_val






def  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__						):
			if data_set == "train":
						return train_data[example_no][1]
			elif data_set == "test":
						return test_data[example_no][1]
			return None






def  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__						):
			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  lowercase						(	lowerCAmelCase__	,lowerCAmelCase__=m						):
			lowerCamelCase_					=  0
			for i in range(lowerCAmelCase__						):
						if index == -1:
									summation_value += _error(lowerCAmelCase__						)
						else:
									summation_value += _error(lowerCAmelCase__						) * train_data[i][0][index]
			return summation_value






def  lowercase						(	lowerCAmelCase__						):
			lowerCamelCase_					=  summation_of_cost_derivative(lowerCAmelCase__	,lowerCAmelCase__						) / m
			return cost_derivative_value






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






def  lowercase						(	):
			for i in range(len(lowerCAmelCase__						)						):
						print(('''Actual output value:''', output(lowerCAmelCase__	,'''test'''						))						)
						print(('''Hypothesis output:''', calculate_hypothesis_value(lowerCAmelCase__	,'''test'''						))						)


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









from __future__ import annotations

from collections.abc import MutableSequence



class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )  ->					None:




				"""simple docstring"""



				if len(SCREAMING_SNAKE_CASE      ) != degree + 1:
							raise ValueError(
							    'The number of coefficients should be equal to the degree + 1.'      )

				SCREAMING_SNAKE_CASE_								=						list(SCREAMING_SNAKE_CASE      )
				SCREAMING_SNAKE_CASE_								=						degree





	def __add__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				if self.degree > polynomial_a.degree:
							SCREAMING_SNAKE_CASE_								=						self.coefficients[:]
							for i in range(polynomial_a.degree + 1      ):
										coefficients[i] += polynomial_a.coefficients[i]
							return Polynomial(self.degree      ,     SCREAMING_SNAKE_CASE      )
				else:
							SCREAMING_SNAKE_CASE_								=						polynomial_a.coefficients[:]
							for i in range(self.degree + 1      ):
										coefficients[i] += self.coefficients[i]
							return Polynomial(polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def __sub__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				return self + polynomial_a * Polynomial(0      ,     [-1]      )





	def __neg__(							self      )  ->					Polynomial:




				"""simple docstring"""



				return Polynomial(self.degree      ,     [-c for c in self.coefficients]      )





	def __mul__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + polynomial_a.degree + 1)
				for i in range(self.degree + 1      ):
							for j in range(polynomial_a.degree + 1      ):
										coefficients[i + j] += (
										    self.coefficients[i] * polynomial_a.coefficients[j]
										)

				return Polynomial(self.degree + polynomial_a.degree      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					int | float:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						0
				for i in range(self.degree + 1      ):
							result += self.coefficients[i] * (substitution**i)
				return result





	def __str__(							self      )  ->					str:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						''
				for i in range(self.degree      ,     -1      ,     -1      ):
							if self.coefficients[i] == 0:
										continue
							elif self.coefficients[i] > 0:
										if polynomial:
													polynomial += " + "
							else:
										polynomial += " - "

							if i == 0:
										polynomial += str(abs(self.coefficients[i]      )      )
							elif i == 1:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x"
							else:
										polynomial += str(abs(self.coefficients[i]      )      ) + "x^" + str(SCREAMING_SNAKE_CASE      )

				return polynomial





	def __repr__(							self      )  ->					str:




				"""simple docstring"""



				return self.__str__()





	def 						A_(							self      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * self.degree
				for i in range(self.degree      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i + 1] * (i + 1)
				return Polynomial(self.degree - 1      ,     SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE = 0      )  ->					Polynomial:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						[0] * (self.degree + 2)
				SCREAMING_SNAKE_CASE_								=						constant
				for i in range(self.degree + 1      ):
							SCREAMING_SNAKE_CASE_								=						self.coefficients[i] / (i + 1)
				return Polynomial(self.degree + 1      ,     SCREAMING_SNAKE_CASE      )





	def __eq__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				if not isinstance(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      ):
							return False

				if self.degree != polynomial_a.degree:
							return False

				for i in range(self.degree + 1      ):
							if self.coefficients[i] != polynomial_a.coefficients[i]:
										return False

				return True





	def __ne__(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				return not self.__eq__(SCREAMING_SNAKE_CASE      )
