def test_spin_half_double_space(self, sz):
prj = zspin_projector(5, sz)
h = ham_heis(5)
h0 = prj @ h @ prj.H
v0s = eigvecs(h0)
for v0 in v0s.T:
vf = prj.H @ v0.T
prjv = vf @ vf.H
# Check reconstructed full eigenvectors commute with full ham
assert_allclose(prjv @ h, h @ prjv, atol=1e-13)
if sz == 0:
# Groundstate must be in most symmetric subspace
gs = groundstate(h)
gs0 = prj .H @ v0s[:, 0]
assert_allclose(expec(gs, gs0), 1.0)
assert_allclose(expec(h, gs0), expec(h, gs))
def test_eigvecs(self, mat_herm_dense, bkd):
u, a = mat_herm_dense
v = eigvecs(a, backend=bkd)
for i, j in zip([3, 0, 1, 2], range(4)):
o = u[:, i].H @ v[:, j]
assert_allclose(abs(o), 1.)
def orthog_ks():
p = rand_rho(3)
v = eigvecs(p)
return (v[:, 0], v[:, 1], v[:, 2])
def test_dense_true(self):
a = rand_herm(10)
v = eigvecs(a)
for i in range(10):
assert is_eigenvector(v[:, i], a)