





from unittest import TestCase

from datasets import Sequence, Value
from datasets.arrow_dataset import Dataset


class 						lowerCamelCase       (__lowerCamelCase      ):







							"""simple docstring"""




							def  A_     ( self     :					Optional[int]						)				->			str:





														"""simple docstring"""
														return [
														    {"col_1": 3, "col_2": "a"},
														    {"col_1": 2, "col_2": "b"},
														    {"col_1": 1, "col_2": "c"},
														    {"col_1": 0, "col_2": "d"},
														]






							def  A_     ( self     :					int						)				->			Dict:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Dict     =						{"col_1": [3, 2, 1, 0], "col_2": ["a", "b", "c", "d"]}
														return Dataset.from_dict(_UpperCAmelCase						)






							def  A_     ( self     :					Dict						)				->			Union[str, Any]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      List[str]     =						self._create_example_records()
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						Dataset.from_list(_UpperCAmelCase						)
														self.assertListEqual(dset.column_names,			["col_1", "col_2"]						)
														for i, r in enumerate(_UpperCAmelCase						):
																					self.assertDictEqual(_UpperCAmelCase,			example_records[i]						)






							def  A_     ( self     :					Tuple						)				->			List[str]:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Dict     =						self._create_example_records()
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						Dataset.from_list(_UpperCAmelCase						)
														SCREAMING_SNAKE_CASE__       :      int     =						Dataset.from_dict({k: [r[k] for r in example_records] for k in example_records[0]}						)
														self.assertEqual(dset.info,			dset_from_dict.info						)






							def  A_     ( self     :					str						)				->			Any:  # checks what happens with missing columns





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      List[Any]     =						[{"col_1": 1}, {"col_2": "x"}]
														SCREAMING_SNAKE_CASE__       :      List[str]     =						Dataset.from_list(_UpperCAmelCase						)
														self.assertDictEqual(dset[0],			{"col_1": 1}						)
														self.assertDictEqual(dset[1],			{"col_1": None}						)  # NB: first record is used for columns






							def  A_     ( self     :					Dict						)				->			Optional[Any]:  # checks if the type can be inferred from the second record





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Tuple     =						[{"col_1": []}, {"col_1": [1, 2]}]
														SCREAMING_SNAKE_CASE__       :      List[Any]     =						Dataset.from_list(_UpperCAmelCase						)
														self.assertEqual(dset.info.features["col_1"],			Sequence(Value("int64"						)						)						)






							def  A_     ( self     :					Dict						)				->			str:





														"""simple docstring"""
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						Dataset.from_list([]						)
														self.assertEqual(len(_UpperCAmelCase						),			0						)
														self.assertListEqual(dset.column_names,			[]						)













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




def _a (  SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  complex			,				SCREAMING_SNAKE_CASE__      :  str = "x"			,				SCREAMING_SNAKE_CASE__      :  float = 10**-10			,				SCREAMING_SNAKE_CASE__      :  int = 1			,				)	->    complex:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						symbols(SCREAMING_SNAKE_CASE__       )
							SCREAMING_SNAKE_CASE__       :      str     =						lambdify(SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__       )
							SCREAMING_SNAKE_CASE__       :      int     =						lambdify(SCREAMING_SNAKE_CASE__			,				diff(SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__       )       )

							SCREAMING_SNAKE_CASE__       :      Any     =						starting_point

							while True:
														if diff_function(SCREAMING_SNAKE_CASE__       ) != 0:
																					SCREAMING_SNAKE_CASE__       :      Any     =						prev_guess - multiplicity * func(SCREAMING_SNAKE_CASE__       ) / diff_function(
																					    SCREAMING_SNAKE_CASE__       )
														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

														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						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', 1_0, precision=0.005)}",
		)

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






