


"""simple docstring"""





def        _lowerCAmelCase      (						UpperCAmelCase     :							list[list[int]]				):


					'''simple docstring'''






					UpperCamelCase__		:    Dict         =[list(UpperCAmelCase				) for row in matrix]
					if matrix and isinstance(UpperCAmelCase      ,							UpperCAmelCase				):
										if isinstance(matrix[0]      ,							UpperCAmelCase				):
															UpperCamelCase__		:    List[Any]         =0
															for row in matrix:
																				if prev_len == 0:
																									UpperCamelCase__		:    Optional[Any]         =len(UpperCAmelCase				)
																									UpperCamelCase__		:    Optional[int]         =True
																				else:
																									UpperCamelCase__		:    List[str]         =prev_len == len(UpperCAmelCase				)
										else:
															UpperCamelCase__		:    Tuple         =True
					else:
										UpperCamelCase__		:    Optional[Any]         =False

					return result



def        _lowerCAmelCase      (						UpperCAmelCase     :							list[list[int]]				):


					'''simple docstring'''






					if check_matrix(UpperCAmelCase				) and len(UpperCAmelCase				) > 0:
										UpperCamelCase__		:    Optional[int]         =[list(UpperCAmelCase				) for row in a]
										UpperCamelCase__		:    Any         =len(UpperCAmelCase				)
										if isinstance(a[0]      ,							UpperCAmelCase				):
															UpperCamelCase__		:    Tuple         =len(a[0]				)
										else:
															for dat in a:
																				print(UpperCAmelCase				)
															return

										# horizotal printing increasing
										for i in range(0      ,							UpperCAmelCase				):
															print(a[0][i]				)
										# vertical printing down
										for i in range(1      ,							UpperCAmelCase				):
															print(a[i][mat_col - 1]				)
										# horizotal printing decreasing
										if mat_row > 1:
															for i in range(mat_col - 2      ,							-1      ,							-1				):
																				print(a[mat_row - 1][i]				)
        # vertical printing up
										for i in range(mat_row - 2      ,							0      ,							-1				):
															print(a[i][0]				)
										UpperCamelCase__		:    Tuple         =[row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
										if len(UpperCAmelCase				) > 0:
															spiral_print_clockwise(UpperCAmelCase				)
										else:
															return
					else:
										print('''Not a valid matrix'''				)
										return



def        _lowerCAmelCase      (						UpperCAmelCase     :							list[list]				):


					'''simple docstring'''






					if matrix:
										return list(matrix.pop(0				)				) + spiral_traversal(list(zip(*UpperCAmelCase				)				)[::-1]				)
					else:
										return []


# driver code
if __name__ == "__main__":
				import doctest

				doctest.testmod()

				_SCREAMING_SNAKE_CASE       :  int        = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 1_0, 1_1, 1_2]]
				spiral_print_clockwise(a)





"""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}}}''')


