
from typing import Any

import numpy as np

def 		UpperCamelCase						(   lowercase_ )		->						Dict:


  '''simple docstring'''






  return np.array_equal(_SCREAMING_SNAKE_CASE			,			matrix.conjugate().T )

def 		UpperCamelCase						(   lowercase_			,			lowercase_ )		->						str:


  '''simple docstring'''






  lowercase__	: Tuple     		=   v.conjugate().T
  lowercase__	: Dict     		=   v_star.dot(_SCREAMING_SNAKE_CASE )
  assert isinstance(_SCREAMING_SNAKE_CASE			,			np.ndarray )
  return (v_star_dot.dot(_SCREAMING_SNAKE_CASE )) / (v_star.dot(_SCREAMING_SNAKE_CASE ))

def 		UpperCamelCase						(   )		->						str:


  '''simple docstring'''






  lowercase__	: List[Any]     		=   np.array([[2, 2 + 1J, 4], [2 - 1J, 3, 1J], [4, -1J, 1]] )
  lowercase__	: str     		=   np.array([[1], [2], [3]] )
  assert is_hermitian(_SCREAMING_SNAKE_CASE ), F'{a} is not hermitian.'
  print(rayleigh_quotient(_SCREAMING_SNAKE_CASE			,			_SCREAMING_SNAKE_CASE ) )

  lowercase__	: List[Any]     		=   np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]] )
  assert is_hermitian(_SCREAMING_SNAKE_CASE ), F'{a} is not hermitian.'
  assert rayleigh_quotient(_SCREAMING_SNAKE_CASE			,			_SCREAMING_SNAKE_CASE ) == float(3 )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     tests()







from __future__ import annotations

SCREAMING_SNAKE_CASE		:     Tuple         =	1.6_021E-19  # units = C






def     lowerCAmelCase_			(   _SCREAMING_SNAKE_CASE     :				float		, _SCREAMING_SNAKE_CASE     :				float		, _SCREAMING_SNAKE_CASE     :				float		, ):
						if (conductivity, electron_conc, mobility).count(0			) != 1:
												raise ValueError("""You cannot supply more or less than 2 values"""			)
						elif conductivity < 0:
												raise ValueError("""Conductivity cannot be negative"""			)
						elif electron_conc < 0:
												raise ValueError("""Electron concentration cannot be negative"""			)
						elif mobility < 0:
												raise ValueError("""mobility cannot be negative"""			)
						elif conductivity == 0:
												return (
												    "conductivity",
												    mobility * electron_conc * ELECTRON_CHARGE,
												)
						elif electron_conc == 0:
												return (
												    "electron_conc",
												    conductivity / (mobility * ELECTRON_CHARGE),
												)
						else:
												return (
												    "mobility",
												    conductivity / (electron_conc * ELECTRON_CHARGE),
												)


if __name__ == "__main__":
	import doctest

	doctest.testmod()






