


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403


def 		lowercase_	(  _UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase = "x"							,      _UpperCamelCase = 10**-10							,      _UpperCamelCase = 1							,      ):


			'''simple docstring'''







			__lowercase			       = symbols(_UpperCamelCase	)
			__lowercase			       = lambdify(_UpperCamelCase							,      _UpperCamelCase	)
			__lowercase			       = lambdify(_UpperCamelCase							,      diff(_UpperCamelCase							,      _UpperCamelCase	)	)

			__lowercase			       = starting_point

			while True:
						if diff_function(_UpperCamelCase	) != 0:
									__lowercase			       = prev_guess - multiplicity * func(_UpperCamelCase	) / diff_function(
									    _UpperCamelCase	)
						else:
									raise ZeroDivisionError('''Could not find root'''	) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess	) < precision:
									return next_guess

						__lowercase			       = next_guess


# Let's Execute
if __name__ == "__main__":
	# Find root of trigonometric function
	# Find value of pi
	print(f'''The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}''')

	# Find root of polynomial
	# Find fourth Root of 5
	print(f'''The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}''')

	# Find value of e
	print(
	    '''The root of log(y) - 1 = 0 is ''',
	    f'''{newton_raphson('log(y) - 1', 2, variable='y')}''',
	)

	# Exponential Roots
	print(
	    '''The root of exp(x) - 1 = 0 is''',
	    f'''{newton_raphson('exp(x) - 1', 10, precision=0.005)}''',
	)

	# Find root of cos(x)
	print(f'''The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}''')






from __future__ import annotations
class 						lowerCamelCase_							:



					'''simple docstring'''







					def __init__(					self			,							snake_case_    ) ->      None:







								'''simple docstring'''

								__lowercase			       = order

								# a_{0} ... a_{k}
								__lowercase			       = [1.0] + [0.0] * order
								# b_{0} ... b_{k}
								__lowercase			       = [1.0] + [0.0] * order

								# x[n-1] ... x[n-k]
								__lowercase			       = [0.0] * self.order
								# y[n-1] ... y[n-k]
								__lowercase			       = [0.0] * self.order






					def A   (					self			,							snake_case_			,							snake_case_    ) ->      None:







								'''simple docstring'''

								if len(snake_case_    ) < self.order:
											__lowercase			       = [1.0, *a_coeffs]

								if len(snake_case_    ) != self.order + 1:
											__lowercase			       = (
											    F'Expected a_coeffs to have {self.order + 1} elements '
											    F'for {self.order}-order filter, got {len(snake_case_    )}'
											)
											raise ValueError(snake_case_    )

								if len(snake_case_    ) != self.order + 1:
											__lowercase			       = (
											    F'Expected b_coeffs to have {self.order + 1} elements '
											    F'for {self.order}-order filter, got {len(snake_case_    )}'
											)
											raise ValueError(snake_case_    )

								__lowercase			       = a_coeffs
								__lowercase			       = b_coeffs






					def A   (					self			,							snake_case_    ) ->      float:







								'''simple docstring'''

								__lowercase			       = 0.0

								# Start at index 1 and do index 0 at the end.
								for i in range(1			,							self.order + 1    ):
											result += (
											    self.b_coeffs[i] * self.input_history[i - 1]
											    - self.a_coeffs[i] * self.output_history[i - 1]
											)

								__lowercase			       = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

								__lowercase			       = self.input_history[:-1]
								__lowercase			       = self.output_history[:-1]

								__lowercase			       = sample
								__lowercase			       = result

								return result


