block-iterates.py

import numpy
from krypy import linsys

m = 10
n = 5
A = numpy.random.rand(m, m)
A = A + A.T
B = numpy.random.rand(n, m)
Z = numpy.zeros((n, n))
tau = 1e-4
f = numpy.ones((n+m, 1))

ls1 = linsys.LinearSystem(numpy.bmat([[A, -tau*B.T], [B, Z]]), f)
sol1 = linsys.Gmres(ls1, tol=0.5)
x1 = sol1.xk

ls2 = linsys.LinearSystem(numpy.bmat([[A, B.T], [B, Z]]), f)
sol2 = linsys.Gmres(ls2, tol=0.5)
x2 = sol2.xk
x2[m:] /= -tau

print(x1 - x2)
print(len(sol1.resnorms))
print(len(sol2.resnorms))

'''The above results in
[[  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  1.76809663e-02]
 [  8.46503582e+02]
 [  8.46503582e+02]
 [  8.46503582e+02]
 [  8.46503582e+02]
 [  8.46503582e+02]]
2
2

The last lines mean that one iteration was carried out for both linear systems.
'''