


'''simple docstring'''

import numpy as np





def __snake_case					(      UpperCAmelCase_						:						np.ndarray					,				UpperCAmelCase_						:						np.ndarray					,				UpperCAmelCase_						:						float = 1E-1_2					,				UpperCAmelCase_						:						int = 100					,				):
 assert np.shape(UpperCAmelCase_		)[0] == np.shape(UpperCAmelCase_		)[1]
 # Ensure proper dimensionality.
 assert np.shape(UpperCAmelCase_		)[0] == np.shape(UpperCAmelCase_		)[0]
 # Ensure inputs are either both complex or both real
 assert np.iscomplexobj(UpperCAmelCase_		) == np.iscomplexobj(UpperCAmelCase_		)
 lowerCamelCase_      =  np.iscomplexobj(UpperCAmelCase_		)
 if is_complex:
  # Ensure complex input_matrix is Hermitian
  assert np.array_equal(UpperCAmelCase_					,				input_matrix.conj().T		)

 # Set convergence to False. Will define convergence when we exceed max_iterations
 # or when we have small changes from one iteration to next.

 lowerCamelCase_      =  False
 lowerCamelCase_      =  0
 lowerCamelCase_      =  0
 lowerCamelCase_      =  1E1_2

 while not convergence:
  # Multiple matrix by the vector.
  lowerCamelCase_      =  np.dot(UpperCAmelCase_					,				UpperCAmelCase_		)
  # Normalize the resulting output vector.
  lowerCamelCase_      =  w / np.linalg.norm(UpperCAmelCase_		)
  # Find rayleigh quotient
  # (faster than usual b/c we know vector is normalized already)
  lowerCamelCase_      =  vector.conj().T if is_complex else vector.T
  lowerCamelCase_      =  np.dot(UpperCAmelCase_					,				np.dot(UpperCAmelCase_					,				UpperCAmelCase_		)		)

  # Check convergence.
  lowerCamelCase_      =  np.abs(lambda_ - lambda_previous		) / lambda_
  iterations += 1

  if error <= error_tol or iterations >= max_iterations:
   lowerCamelCase_      =  True

  lowerCamelCase_      =  lambda_

 if is_complex:
  lowerCamelCase_      =  np.real(lambda_		)

 return lambda_, vector





def __snake_case					(      ):
 lowerCamelCase_      =  np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]		)
 lowerCamelCase_      =  np.array([41, 4, 20]		)
 lowerCamelCase_      =  real_input_matrix.astype(np.complexaaa		)
 lowerCamelCase_      =  np.triu(1J * complex_input_matrix					,				1		)
 complex_input_matrix += imag_matrix
 complex_input_matrix += -1 * imag_matrix.T
 lowerCamelCase_      =  np.array([41, 4, 20]		).astype(np.complexaaa		)

 for problem_type in ["real", "complex"]:
  if problem_type == "real":
   lowerCamelCase_      =  real_input_matrix
   lowerCamelCase_      =  real_vector
  elif problem_type == "complex":
   lowerCamelCase_      =  complex_input_matrix
   lowerCamelCase_      =  complex_vector

  # Our implementation.
  lowerCamelCase_ ,lowerCamelCase_      =  power_iteration(UpperCAmelCase_					,				UpperCAmelCase_		)

  # Numpy implementation.

  # Get eigenvalues and eigenvectors using built-in numpy
  # eigh (eigh used for symmetric or hermetian matrices).
  lowerCamelCase_ ,lowerCamelCase_      =  np.linalg.eigh(UpperCAmelCase_		)
  # Last eigenvalue is the maximum one.
  lowerCamelCase_      =  eigen_values[-1]
  # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
  lowerCamelCase_      =  eigen_vectors[:, -1]

  # Check our implementation and numpy gives close answers.
  assert np.abs(eigen_value - eigen_value_max		) <= 1E-6
  # Take absolute values element wise of each eigenvector.
  # as they are only unique to a minus sign.
  assert np.linalg.norm(np.abs(UpperCAmelCase_		) - np.abs(UpperCAmelCase_		)		) <= 1E-6


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     test_power_iteration()






from __future__ import annotations

from math import pi, sqrt


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__       ):

						if inductance <= 0:
												raise ValueError('''Inductance cannot be 0 or negative'''       )

						elif capacitance <= 0:
												raise ValueError('''Capacitance cannot be 0 or negative'''       )

						else:
												return (
												    "Resonant frequency",
												    float(1 / (2 * pi * (sqrt(inductance * capacitance       )))       ),
												)


if __name__ == "__main__":
					import doctest

					doctest.testmod()