source('utils.R')

n = 6 ## tester size
##n = 20 ## official problem size
A = build_tridiagonal_matrix(n, 4, -1, -1)
if(n <= 10){
    print('A=')
    print(A)
}

pm = power_method(A, tol=1e-6)

exact = exact_tridiagonal_eigensystem(n, 4, -1)

## Compare our results with the exact results:
##
print(sprintf('my eigenvalue= %f; exact eigenvalue= %f; error= %f', pm$max_eigenvalue, exact$lambda[n], exact$lambda[n]-pm$max_eigenvalue) )
print('my eigenvector=')
print(pm$max_eigenvector)
print('exact eigenvector=')
ee = exact$U[, n]; dim(ee) = c(n, 1)
ee = ee/norm(ee, '2') ## normalize to the same norm as the outputs from the power_method
print(ee)
print(sprintf('norm of the difference= %f', norm(pm$max_eigenvector-ee,'2')))