probable bug in AMLI cycle

[bensworth]

So pairwise aggregation is typically used with an AMLI/K-cycle. I tested the pairwise method without Krylov on 100x100 Poisson and get junk with the AMLI cycle. Below code and output for reproducibility. I have not looked into the AMLI code, but its convergence on isotropic Poisson is definitely suspicious.

import numpy as np
from pyamg.gallery import poisson
from pyamg.aggregation.pairwise import pairwise_solver

A = poisson((100,), format='csr')
smooth = ('gauss_seidel',{'sweep': 'symmetric'})
ml = pairwise_solver(A, strength='classical', presmoother=smooth, postsmoother=smooth)
x = np.random.rand(A.shape[0])
b = A * np.random.rand(A.shape[0])

res = []
x_sol = ml.solve(b, x0=x, maxiter=200, tol=1e-10, cycle='AMLI', residuals=res)
amli_cf = (res[-1] / res[0]) ** (1.0 / (len(res)-1))
res = []
x_sol = ml.solve(b, x0=x, maxiter=200, tol=1e-10, cycle='V', residuals=res)
v_cf = (res[-1] / res[0]) ** (1.0 / (len(res)-1))
res = []
x_sol = ml.solve(b, x0=x, maxiter=200, tol=1e-10, cycle='W', residuals=res)
w_cf = (res[-1] / res[0]) ** (1.0 / (len(res)-1))
res = []
x_sol = ml.solve(b, x0=x, maxiter=200, tol=1e-10, cycle='F', residuals=res)
f_cf = (res[-1] / res[0]) ** (1.0 / (len(res)-1))
print([v_cf, f_cf, w_cf, amli_cf])

Output: [V-cycle, F-cycle, W-cycle, AMLI-cycle]:

[0.8243799083973229, 0.6059711859082966, 0.5148452009914897, 0.94009796522041]

If I add CG acceleration (which may or may not make sense with an AMLI cycle, but nevertheless):

[0.28781331076950806, 0.2477191250020367, 0.20878133901435386, 0.94009796522041]