Use invpowershift.py to evaluate all eigenvalues and all eigenvectors for:

$([3,1,2],[1,4,3],[2,3,1])$ in python.

invpowershift.py:

from triang import forsub, backsub, testcreate

from ludec import ludec

from jacobi import termcrit

from power import mag, testeigone

import numpy as np

def invpowershift $($A$,$ shift $=20,$kmax$=200,$ tol $=1.$e$-8)$:

$n=A.$ shape $0$

znews $=$ np$.$ones $($n$)$

qnews $=$ znews $\frac{?}{\text{m}\text{a}\text{g}}($znews$)$

Astar $=$ A $-$ np$.$identity$($n$)*$shift

L$,U=$ ludec $($Astar$)$

for $k$ in range $(1,$kmax$)$ :

$qs=np.$ copy $($qnews$)$

ys $=$ forsub$($L$,$ qs$)$

znews $=$ backsub$($U$,$ys$)$

qnews $=$ znews $\frac{?}{?}$ mag $($znews$)$

if qs@qnews $<mn\; id="EditorElement\_805736">0</mn>$ :

qnews $=-$ qnews

err $=$ termcrit$($qs$,$ qnews$)$

print $($k$,$ qnews, err$)$

if err $$ tol:

lam $=$ qnews@A@qnews

break

else:

lam $=$ qnews $=$ None

return lam, qnews

if $\_==\text{'}-\text{'}$:

A$,$ bs $=$ testcreate $(4,21)$

testeigone$($invpowershift$,$A$)$