source('utils.R')

##n = 6 ## tester size
n = 21 ## official problem size
A = build_tridiagonal_matrix(n, 0, 1, 1)
d = 10
A_shifted = A + diag(rep(d, n))
if(n<=10){
    print('A_shifted=')
    print(A_shifted)
}
pm = power_method(A_shifted, tol=1e-3)

exact = exact_tridiagonal_eigensystem(n, d, 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')))