def test_specials(self, var_one, var_two):
K1 = qu.rand_herm(2**1)
n = 10
HB = qtn.SpinHam(S=1 / 2)
if var_two == 'some':
HB += 1, K1, K1
HB[4, 5] += 1, K1, K1
HB[7, 8] += 1, K1, K1
elif var_two == 'only':
for i in range(n - 1):
HB[i, i + 1] += 1, K1, K1
else:
HB += 1, K1, K1
if var_one == 'some':
HB += 1, K1
HB[2] += 1, K1
HB[3] += 1, K1
elif var_one == 'only':
for i in range(n - 1):
HB[i] += 1, K1
elif var_one == 'only-some':
HB[1] += 1, K1
elif var_one == 'def-only':
HB += 1, K1
HB.build_nni(n)
H_mpo = HB.build_mpo(n)
H_sps = HB.build_sparse(n)
assert_allclose(H_mpo.to_dense(), H_sps.A)
def test_rand_herm_sparse(self):
a = rand_herm(3, sparse=True, density=0.3)
assert a.shape == (3, 3)
assert type(a) == sp.csr_matrix
assert isherm(a)
evals = np.linalg.eigvals(a.A)
assert_allclose(evals.imag, [0, 0, 0], atol=1e-14)
def test_thermal_state_precomp(self):
full = rand_herm(2**4)
beta = 0.624
rhoth1 = thermal_state(full, beta)
func = thermal_state(full, None, precomp_func=True)
rhoth2 = func(beta)
assert_allclose(rhoth1, rhoth2)
def test_specials(self, var_one, var_two):
K1 = qu.rand_herm(2**1)
n = 10
HB = qtn.SpinHam(S=1 / 2)
if var_two == 'some':
HB += 1, K1, K1
HB[4, 5] += 1, K1, K1
HB[7, 8] += 1, K1, K1
elif var_two == 'only':
for i in range(n - 1):
HB[i, i + 1] += 1, K1, K1
else:
HB += 1, K1, K1
if var_one == 'some':
HB += 1, K1
HB[2] += 1, K1
HB[3] += 1, K1
elif var_one == 'only':
for i in range(n - 1):
HB[i] += 1, K1
elif var_one == 'only-some':
HB[1] += 1, K1
elif var_one == 'def-only':
HB += 1, K1
HB.build_mpo(n)
HB.build_nni(n)
def test_rand_herm(self):
a = rand_herm(3)
assert a.shape == (3, 3)
assert type(a) == np.matrix
assert_allclose(a, a.H)
evals = np.linalg.eigvals(a)
assert_allclose(evals.imag, [0, 0, 0], atol=1e-14)
def test_thermal_state_tuple(self):
full = rand_herm(2**4)
l, v = eigsys(full)
for beta in (0, 0.5, 1, 10):
rhoth1 = thermal_state(full, beta)
rhoth2 = thermal_state((l, v), beta)
assert_allclose(rhoth1, rhoth2)
def test_seigsys_slepc_eigvecs(self):
h = rand_herm(100, sparse=True, density=0.2)
lks, vks = seigsys_slepc(h, k=5)
lka, vka = seigsys(h, k=5)
assert vks.shape == vka.shape
for ls, vs, la, va in zip(lks, vks.T, lka, vka.T):
assert_allclose(ls, la)
assert_allclose(expec(vs, va), 1.0)
def test_rand_herm(self, dtype):
a = qu.rand_herm(3, dtype=dtype)
assert a.shape == (3, 3)
assert type(a) == qu.qarray
assert a.dtype == dtype
assert_allclose(a, a.H)
evals = qu.eigvalsh(a)
assert_allclose(evals.imag, [0, 0, 0], atol=1e-14)
def test_internal_interior_default(self):
a = rand_herm(100, sparse=True)
alo = sp.linalg.aslinearoperator(a)
el, ev = eigs_slepc(alo, k=1, which='TR', sigma=0.0)
el_s, ev_s = sp.linalg.eigsh(a.tocsc(), k=1, which='LM', sigma=0.0)
assert_allclose(el_s, el, rtol=1e-5)
assert_allclose(np.abs(ev_s.conj().T @ ev), 1.0)
def test_rand_herm_sparse(self, dtype):
a = qu.rand_herm(3, sparse=True, density=0.3, dtype=dtype)
assert a.shape == (3, 3)
assert type(a) == sp.csr_matrix
assert qu.isherm(a)
assert a.dtype == dtype
evals = qu.eigvalsh(a.A)
assert_allclose(evals.imag, [0, 0, 0], atol=1e-14)
def test_construct_lanczos_tridiag_beta_breakdown(self, bsz):
a = rand_herm(8)
alpha, beta, scaling = last(construct_lanczos_tridiag(a, bsz=bsz, K=9))
assert alpha.shape == (8,)
assert beta.shape == (8,)
el, ev = lanczos_tridiag_eig(alpha, beta)
assert el.shape == (8,)
assert el.dtype == float
assert ev.shape == (8, 8)
assert ev.dtype == float
def test_exp_sparse(self):
a = rand_herm(100, sparse=True, density=0.1)
k = rand_ket(100)
out = mfn_multiply_slepc(a, k)
al, av = eigh(a.A)
expected = av @ np.diag(np.exp(al)) @ av.conj().T @ k
assert_allclose(out, expected)
def test_eigs_slepc_eigvecs(self, dtype):
h = rand_herm(32, sparse=True, density=0.5)
if dtype == 'real':
h = h.real
lks, vks = eigs_slepc(h, k=5)
lka, vka = eigh(h, k=5, backend='scipy')
assert vks.shape == vka.shape
assert h.dtype == vks.dtype
assert_allclose(lks, lka)
assert_allclose(abs(vka.H @ vks), np.eye(5), atol=1e-8)
def srho_dot_ls():
rho = rand_rho(3)
ham = rand_herm(3, sparse=True, density=0.5)
gamma = 0.7
ls = [rand_matrix(3, sparse=True, density=0.5) for _ in range(3)]
rhodl = -1.0j * (ham @ rho - rho @ ham)
for l in ls:
rhodl += gamma * (l @ rho @ l.H)
rhodl -= gamma * 0.5 * (rho @ l.H @ l)
rhodl -= gamma * 0.5 * (l.H @ l @ rho)
return rho, ham, gamma, ls, rhodl
def test_construct_lanczos_tridiag(self, bsz):
a = rand_herm(2**5)
alpha, beta, scaling = last(
construct_lanczos_tridiag(a, bsz=bsz, K=20))
assert alpha.shape == (20,)
assert beta.shape == (20,)
el, ev = lanczos_tridiag_eig(alpha, beta)
assert el.shape == (20,)
assert el.dtype == float
assert ev.shape == (20, 20)
assert ev.dtype == float
def rho_dot_ls():
np.random.seed(1)
rho = rand_rho(3)
ham = rand_herm(3)
gamma = 0.7
ls = [rand_matrix(3) for _ in range(3)]
rhodl = -1.0j * (ham @ rho - rho @ ham)
for l in ls:
rhodl += gamma * (l @ rho @ l.H)
rhodl -= gamma * 0.5 * (rho @ l.H @ l)
rhodl -= gamma * 0.5 * (l.H @ l @ rho)
return rho, ham, gamma, ls, rhodl
def test_1(self):
a = rand_herm(100, sparse=True)
el, ev = eigh(a.A)
which = abs(el) < 0.2
el, ev = el[which], ev[:, which]
offset = norm(a, 'fro')
a = a + offset * sp.eye(a.shape[0])
sl, sv = eigs_slepc(a, k=6, l_win=(-0.2 + offset, 0.2 + offset))
sl -= offset
assert_allclose(el, sl)
assert_allclose(np.abs(sv.H @ ev), np.eye(el.size), atol=1e-11)
def test_extermal_eigen(self):
a = rand_herm(100, sparse=True)
alo = sp.linalg.aslinearoperator(a)
el_us, ev_us = sp.linalg.eigsh(alo, k=1, which='LA')
el_u, ev_u = eigs_slepc(alo, k=1, which='LA')
assert_allclose(el_us, el_u)
assert_allclose(np.abs(ev_us.conj().T @ ev_u), 1.0)
el_ls, ev_ls = sp.linalg.eigsh(alo, k=1, which='SA')
el_l, ev_l = eigs_slepc(alo, k=1, which='SA')
assert_allclose(el_ls, el_l)
assert_allclose(np.abs(ev_ls.conj().T @ ev_l), 1.0)
def test_expm_krylov_expokit(self):
ham = rand_herm(100, sparse=True, density=0.8)
psi = rand_ket(100)
evo_exact = QuEvo(psi, ham, method='solve')
evo_krylov = QuEvo(psi,
ham,
method='expm',
expm_backend='slepc-krylov')
evo_expokit = QuEvo(psi,
ham,
method='expm',
expm_backend='slepc-expokit')
ts = np.linspace(0, 100, 21)
for p1, p2, p3 in zip(evo_exact.at_times(ts), evo_krylov.at_times(ts),
evo_expokit.at_times(ts)):
assert abs(expec(p1, p2) - 1) < 1e-9
assert abs(expec(p1, p3) - 1) < 1e-9
def test_multisubsystem(self):
qu.seed_rand(42)
dims = [2, 2, 2]
IIX = qu.ikron(qu.rand_herm(2), dims, 2)
dcmp = qu.pauli_decomp(IIX, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert (p[0] != 'I') or (p[1] != 'I')
else:
assert p[0] == p[1] == 'I'
K = qu.rand_iso(3 * 4, 4).reshape(3, 4, 4)
KIIXK = qu.kraus_op(IIX, K, dims=dims, where=[0, 2])
dcmp = qu.pauli_decomp(KIIXK, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert p[1] != 'I'
else:
assert p[1] == 'I'
def test_internal_shift_invert_precond_jd(self):
a = rand_herm(20, sparse=True, seed=42)
alo = sp.linalg.aslinearoperator(a)
st_opts = {
'STType': 'precond',
'KSPType': 'bcgs', # / 'gmres'
'PCType': 'none',
}
el, ev = eigs_slepc(alo,
k=1,
which='TR',
sigma=0.0,
st_opts=st_opts,
EPSType='jd')
el_s, ev_s = sp.linalg.eigsh(a.tocsc(), k=1, which='LM', sigma=0.0)
assert_allclose(el_s, el, rtol=1e-6)
assert_allclose(np.abs(ev_s.conj().T @ ev), 1.0)
def test_internal_shift_invert_linear_solver(self):
a = rand_herm(100, sparse=True)
alo = sp.linalg.aslinearoperator(a)
st_opts = {
'STType': 'sinvert',
'KSPType': 'bcgs', # / 'gmres'
'PCType': 'none',
}
el, ev = seigsys_slepc(alo,
k=1,
which='TR',
sigma=0.0,
st_opts=st_opts,
EPSType='krylovschur')
el_s, ev_s = sp.linalg.eigsh(a.tocsc(), k=1, which='LM', sigma=0.0)
assert_allclose(el_s, el, rtol=1e-5)
assert_allclose(np.abs(ev_s.conj().T @ ev), 1.0)
def test_against_arpack(self):
A = qu.rand_herm(32, dtype=float)
lk, vk = qu.eigh(A, k=6, backend='lobpcg')
slk, svk = qu.eigh(A, k=6, backend='scipy')
assert_allclose(lk, slk)
assert_allclose(np.eye(6), abs(vk.H @ svk), atol=1e-9, rtol=1e-9)
def test_sparse(self):
a = qu.rand_herm(10, sparse=True, density=0.9)
vt = qu.eigvecsh(a, sigma=0, k=1)
assert qu.is_eigenvector(vt, a)
vf = qu.rand_ket(10)
assert not qu.is_eigenvector(vf, a)
def test_dense_false(self):
a = qu.rand_herm(10)
v = qu.rand_ket(10)
assert not qu.is_eigenvector(v, a)
def test_dense_true(self):
a = qu.rand_herm(10)
v = qu.eigvecsh(a)
for i in range(10):
assert qu.is_eigenvector(v[:, [i]], a)
def test_simple_dense(self):
a = rand_herm(2**4, sparse=True)
y = rand_ket(2**4)
x = ssolve_slepc(a, y)
assert_allclose(a @ x, y, atol=1e-12, rtol=1e-6)
def test_thermal_state_hot(self):
full = rand_herm(2**4)
rhoth = chop(thermal_state(full, 0.0))
assert_allclose(rhoth, eye(2**4) / 2**4)
def test_norm_fro_approx(self, bsz):
A = rand_herm(2**5)
actual_norm_fro = norm_fro(A)
approx_norm_fro = norm_fro_approx(A, tol=1e-2, bsz=bsz)
assert_allclose(actual_norm_fro, approx_norm_fro, rtol=1e-1)
def test_thermal_state_normalization(self):
full = rand_herm(2**4)
for beta in (0, 0.5, 1, 10):
rhoth = thermal_state(full, beta)
assert_allclose(tr(rhoth), 1)
