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#!/usr/bin/env python
"""Tests for the linalg.isolve.lgmres module
"""
from numpy.testing import TestCase, assert_
from numpy import zeros, array, allclose
from scipy.linalg import norm
from scipy.sparse import csr_matrix
from scipy.sparse.linalg.interface import LinearOperator
from scipy.sparse.linalg import splu
from scipy.sparse.linalg.isolve import lgmres
Am = csr_matrix(array([[-2,1,0,0,0,9],
[1,-2,1,0,5,0],
[0,1,-2,1,0,0],
[0,0,1,-2,1,0],
[0,3,0,1,-2,1],
[1,0,0,0,1,-2]]))
b = array([1,2,3,4,5,6])
count = [0]
def matvec(v):
count[0] += 1
return Am*v
A = LinearOperator(matvec=matvec, shape=Am.shape, dtype=Am.dtype)
def do_solve(**kw):
count[0] = 0
x0, flag = lgmres(A, b, x0=zeros(A.shape[0]), inner_m=6, tol=1e-14, **kw)
count_0 = count[0]
assert_(allclose(A*x0, b, rtol=1e-12, atol=1e-12), norm(A*x0-b))
return x0, count_0
class TestLGMRES(TestCase):
def test_preconditioner(self):
# Check that preconditioning works
pc = splu(Am.tocsc())
M = LinearOperator(matvec=pc.solve, shape=A.shape, dtype=A.dtype)
x0, count_0 = do_solve()
x1, count_1 = do_solve(M=M)
assert_(count_1 == 3)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
def test_outer_v(self):
# Check that the augmentation vectors behave as expected
outer_v = []
x0, count_0 = do_solve(outer_k=6, outer_v=outer_v)
assert_(len(outer_v) > 0)
assert_(len(outer_v) <= 6)
x1, count_1 = do_solve(outer_k=6, outer_v=outer_v)
assert_(count_1 == 2, count_1)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
# ---
outer_v = []
x0, count_0 = do_solve(outer_k=6, outer_v=outer_v, store_outer_Av=False)
assert_(array([v[1] is None for v in outer_v]).all())
assert_(len(outer_v) > 0)
assert_(len(outer_v) <= 6)
x1, count_1 = do_solve(outer_k=6, outer_v=outer_v)
assert_(count_1 == 3, count_1)
assert_(count_1 < count_0/2)
assert_(allclose(x1, x0, rtol=1e-14))
if __name__ == "__main__":
import nose
nose.run(argv=['', __file__])
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