def test_lin_solve_without_last_entry(self, normal_example):
n, r, D, U, H, A, b = normal_example
D_hat, G = core.ldl_fast(D, U, H)
x = core.lin_solve(D_hat, G, U, b)
G[-1, :] = 0
x_hat = core.lin_solve(D_hat, G, U, b)
print np.linalg.norm(x - x_hat)
def test_evec_with_eval(self, normal_example):
n, r, D, U, H, A, b = normal_example
evals, evecs = np.linalg.eig(A)
index = np.random.randint(n)
D_hat = D - evals[index]
A_hat = A - np.eye(n) * evals[index]
D_hat, G, status = core.ldl_fast(D_hat, U, H)
assert status is True
b = np.zeros(n)
x = core.lin_solve(D_hat, G, U, b)
assert np.allclose(np.dot(A_hat, x), evals[index] * x)
def compute_inertia(D, U, H):
# Return the inertia of the matrix
try:
result = core.ldl_fast(D, U, H)
if len(result) == 1:
inertia = utils.inertia_ldl(result)
else:
D_hat, G = result
inertia = utils.inertia_ldl(D_hat)
except ValueError as e:
print("Turning to stable method.")
x, ratio, D_hat = core.SSQR_inertia(D, U, H, np.random.randn(len(D)))
inertia = utils.inertia_qr(ratio, D_hat)
return inertia
def test_rqi_converge(self, normal_example):
n, r, D, U, H, A, b = normal_example
b = b / np.linalg.norm(b)
mu = np.dot(b.T, np.dot(A, b))
for i in range(10):
mu, b, error, n_mid = alg.RQI_step(D, U, H, mu, b)
print error
if error < 1e-10:
print("Converged in %d iterations." % (i+1))
break
D_hat = core.ldl_fast(D-mu, U, H)
inertia = utils.inertia_ldl(D_hat)
print inertia
assert np.allclose(np.dot(A, b), mu*b)
def test_rqi_fast_converge(self, normal_example):
# RQI_fast has a problem where the eigen vector has not converged
n, r, D, U, H, A, b = normal_example
b = b / np.linalg.norm(b)
mu = np.dot(b.T, np.dot(A, b))
old_mu = mu
for i in range(20):
mu, b, error, n_mid = alg.RQI_fast(D, U, H, mu, b)
ratio = abs(old_mu - mu) / abs(old_mu)
print "Relative error between guesses: %e, error = %e" % (ratio, error)
old_mu = mu
if ratio < 1e-8:
print("Converged in %d iterations." %(i+1))
break
D_hat = core.ldl_fast(D-mu, U, H)
inertia = utils.inertia_ldl(D_hat)
print inertia