def solve(A, b, iters, verbose):
print("Solving system...")
x = np.zeros(A.shape[1])
d = np.diag(A)
R = A - np.diag(d)
for i in range(iters):
x = (b - np.dot(R, x)) / d
return x
def generate_2D(N, corners):
if corners:
print("Generating %dx%d 2-D adjacency system with corners..." %
(N**2, N**2))
A = np.zeros((N**2, N**2)) + 8 * np.eye(N**2)
else:
print("Generating %dx%d 2-D adjacency system without corners..." %
(N**2, N**2))
A = np.zeros((N**2, N**2)) + 4 * np.eye(N**2)
# These are the same for both cases
off_one = np.full(N**2 - 1, -1, dtype=np.float64)
A += np.diag(off_one, k=1)
A += np.diag(off_one, k=-1)
off_N = np.full(N * (N - 1), -1, dtype=np.float64)
A += np.diag(off_N, k=N)
A += np.diag(off_N, k=-N)
# If we have corners then we have four more cases
if corners:
off_N_plus = np.full(N * (N - 1) - 1, -1, dtype=np.float64)
A += np.diag(off_N_plus, k=N + 1)
A += np.diag(off_N_plus, k=-(N + 1))
off_N_minus = np.full(N * (N - 1) + 1, -1, dtype=np.float64)
A += np.diag(off_N_minus, k=N - 1)
A += np.diag(off_N_minus, k=-(N - 1))
# Then we can generate a random b matrix
b = np.random.rand(N**2)
return A, b
def precondition(A, N, corners):
if corners:
d = 8 * (N**2)
else:
d = 4 * (N**2)
M = np.diag(np.full(N**2, 1.0 / d))
return M
def test():
a = lg.array([
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
[17, 18, 19, 20],
])
an = np.array([
[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16],
[17, 18, 19, 20],
])
b = lg.diag(a)
bn = np.diag(an)
assert np.array_equal(b, bn)
c = lg.diag(b)
cn = np.diag(bn)
assert np.array_equal(c, cn)
d = lg.array([
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
])
dn = np.array([
[1, 2, 3, 4, 5],
[6, 7, 8, 9, 10],
[11, 12, 13, 14, 15],
[16, 17, 18, 19, 20],
])
e = lg.diag(d)
en = np.diag(dn)
assert np.array_equal(e, en)
f = lg.diag(e)
fn = np.diag(en)
assert np.array_equal(f, fn)
return