

"""simple docstring"""





def        _lowerCAmelCase      (						UpperCAmelCase     :							list				):


					'''simple docstring'''






					for insert_index, insert_value in enumerate(collection[1:]				):
										UpperCamelCase__		:    List[Any]         =insert_index
										while insert_index >= 0 and insert_value < collection[insert_index]:
															UpperCamelCase__		:    Dict         =collection[insert_index]
															insert_index -= 1
										if insert_index != temp_index:
															UpperCamelCase__		:    Optional[Any]         =insert_value
					return collection


if __name__ == "__main__":
				from doctest import testmod

				testmod()

				_SCREAMING_SNAKE_CASE       :  Optional[int]        = input("""Enter numbers separated by a comma:\n""").strip()
				_SCREAMING_SNAKE_CASE       :  List[Any]        = [int(item) for item in user_input.split(""",""")]
				print(F'''{insertion_sort(unsorted) = }''')





"""simple docstring"""





import math as m



def        _lowerCAmelCase      (						UpperCAmelCase     :							Optional[int]      ,							UpperCAmelCase     :							Optional[Any]      ,							UpperCAmelCase     :							Optional[Any]=0.001				):


					'''simple docstring'''






					return (f(a + h				) - f(a - h				)) / (2 * h)



def        _lowerCAmelCase      (						UpperCAmelCase     :							List[str]      ,							UpperCAmelCase     :							Optional[Any]=0      ,							UpperCAmelCase     :							Optional[int]=100      ,							UpperCAmelCase     :							Union[str, Any]=0.0001      ,							UpperCAmelCase     :							Dict=1E-6      ,							UpperCAmelCase     :							Any=False				):


					'''simple docstring'''






					UpperCamelCase__		:    Optional[Any]         =xa  # set the initial guess
					UpperCamelCase__		:    List[Any]         =[a]
					UpperCamelCase__		:    Optional[Any]         =abs(f(UpperCAmelCase				)				)
					UpperCamelCase__		:    List[str]         =lambda UpperCAmelCase				: calc_derivative(UpperCAmelCase      ,							UpperCAmelCase      ,							h=UpperCAmelCase				)  # noqa: E731  Derivative of f(x)
					for _ in range(UpperCAmelCase				):
										if fa(UpperCAmelCase				) == 0:
															raise ValueError('''No converging solution found'''				)
										UpperCamelCase__		:    Any         =a - f(UpperCAmelCase				) / fa(UpperCAmelCase				)  # Calculate the next estimate
										if logsteps:
															steps.append(UpperCAmelCase				)
										if error < maxerror:
															break
					else:
										raise ValueError('''Iteration limit reached, no converging solution found'''				)
					if logsteps:
										# If logstep is true, then log intermediate steps
										return a, error, steps
					return a, error


if __name__ == "__main__":
				from matplotlib import pyplot as plt

				_SCREAMING_SNAKE_CASE       :  str        = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				_SCREAMING_SNAKE_CASE       ,       _SCREAMING_SNAKE_CASE       ,       _SCREAMING_SNAKE_CASE       :  Any        = newton_raphson(
				    f, xa=1_0, maxiter=1_0_0_0, step=1e-6, logsteps=True
				)
				plt.plot([abs(f(x)) for x in steps])
				plt.xlabel("""step""")
				plt.ylabel("""error""")
				plt.show()
				print(F'''solution = {{{solution:f}}}, error = {{{error:f}}}''')


