def test_2(self):
n = 4
# build matrix with specified first generalized eigenvector
A, B = build_lowrank(n, [1, 2, 0.001, 3], seed=0)
w, V = eigh(A, B)
v0 = speigh(A, B, rho=0)[1][2]
vm4 = speigh(A, B, rho=1e-4)[1][2]
vm2 = speigh(A, B, rho=0.01)[1][2]
# using a low value for `rho`, we should recover the small element
# but when rho is higher, it should be truncated to zero.
np.testing.assert_almost_equal(np.abs(v0), 0.001)
np.testing.assert_almost_equal(np.abs(vm4), 0.001)
np.testing.assert_almost_equal(vm2, 0)
def test_1(self):
# test with indefinite A matrix, identity B
n = 4
x = np.array([1.0, 2.0, 3.0, 0])
A = np.outer(x, x)
B = np.eye(n)
w, V = eigh(A, B)
w0, v0, v0f = speigh(A, B, rho=0.0001, return_x_f=True)
self.assert_close(w0, v0, v0f, A, B)
def test_4(self):
# test with positive semidefinite A matrix, and general
# matrix B
n = 4
A = rand_pos_semidef(n)
B = rand_pos_semidef(n) + np.eye(n)
w, V = eigh(A, B)
v_init = V[:, 0] + 0.1*np.random.randn(n)
w0, v0, v0f = speigh(A, B, rho=0, return_x_f=True)
self.assert_close(w0, v0, v0f, A, B)
def test_3(self):
# test with positive semidefinite A matrix, and diagonal
# matrix B
n = 4
A = rand_pos_semidef(n)
B = np.diag(np.random.randn(n)**2)
w, V = eigh(A, B)
w0, v0, v0f = speigh(A, B, rho=0, return_x_f=True)
self.assert_close(w0, v0, v0f, A, B)
