linear_algebra.src.power_iteration
==================================

.. py:module:: linear_algebra.src.power_iteration


Functions
---------

.. autoapisummary::

   linear_algebra.src.power_iteration.power_iteration
   linear_algebra.src.power_iteration.test_power_iteration


Module Contents
---------------

.. py:function:: power_iteration(input_matrix: numpy.ndarray, vector: numpy.ndarray, error_tol: float = 1e-12, max_iterations: int = 100) -> tuple[float, numpy.ndarray]

   Power Iteration.
   Find the largest eigenvalue and corresponding eigenvector
   of matrix input_matrix given a random vector in the same space.
   Will work so long as vector has component of largest eigenvector.
   input_matrix must be either real or Hermitian.

   Input
   input_matrix: input matrix whose largest eigenvalue we will find.
   Numpy array. np.shape(input_matrix) == (N,N).
   vector: random initial vector in same space as matrix.
   Numpy array. np.shape(vector) == (N,) or (N,1)

   Output
   largest_eigenvalue: largest eigenvalue of the matrix input_matrix.
   Float. Scalar.
   largest_eigenvector: eigenvector corresponding to largest_eigenvalue.
   Numpy array. np.shape(largest_eigenvector) == (N,) or (N,1).

   >>> import numpy as np
   >>> input_matrix = np.array([
   ... [41,  4, 20],
   ... [ 4, 26, 30],
   ... [20, 30, 50]
   ... ])
   >>> vector = np.array([41,4,20])
   >>> power_iteration(input_matrix,vector)
   (79.66086378788381, array([0.44472726, 0.46209842, 0.76725662]))


.. py:function:: test_power_iteration() -> None

   >>> test_power_iteration()  # self running tests