Inverse power method applied to a tridiagonal matrix in Python，inversetridiagonal,''' lam,x =

Inverse power method applied to a tridiagonal matrix in Python，inversetridiagonal,''' lam,x =

''' lam,x = inversePower3(d,c,s,tol=1.0e-6).    Inverse power method applied to a tridiagonal matrix    [A] = [c\d\c]. Returns the eigenvalue closest to 's'    and the corresponding eigenvector.'''from numpy import dot,zerosfrom LUdecomp3 import *from math import sqrtfrom random import randomdef inversePower3(d,c,s,tol=1.0e-6):    n = len(d)    e = c.copy()    cc = c.copy()               # Save original [c]    dStar = d - s               # Form [A*] = [A] - s[I]    LUdecomp3(cc,dStar,e)       # Decompose [A*]    x = zeros(n)    for i in range(n):          # Seed [x] with random numbers        x[i] = random()    xMag = sqrt(dot(x,x))       # Normalize [x]    x =x/xMag    flag = 0    for i in range(30):         # Begin iterations            xOld = x.copy()         # Save current [x]        LUsolve3(cc,dStar,e,x)  # Solve [A*][x] = [xOld]        xMag = sqrt(dot(x,x))   # Normalize [x]        x = x/xMag        if dot(xOld,x) < 0.0:   # Detect change in sign of [x]            sign = -1.0            x = -x        else: sign = 1.0        if sqrt(dot(xOld - x,xOld - x)) < tol:            return s + sign/xMag,x    print 'Inverse power method did not converge'