def mean_norm(self, ntype='fro'):
"""Computes the average frobenius norm of local terms. Also generates
all terms if not already cached.
"""
if self.n is None:
return qu.norm(self(), ntype)
nterms = self.n - int(not self.cyclic)
return sum(qu.norm(self((i, i + 1)), ntype)
for i in range(nterms)) / nterms
def test_eigh(self):
H = qu.ham_mbl(6, dh=2.5)
a_el, a_ev = qu.eigh(H, autoblock=False)
el, ev = qu.eigh(H, autoblock=True)
assert qu.norm(ev @ qu.ldmul(el, ev.H) - H, 'fro') < 1e-12
assert_allclose(a_el, el)
assert_allclose(ev.H @ ev, np.eye(H.shape[0]), atol=1e-12)
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_rsvd(self, dtype, shape, sparse, q, p):
X = rand_rect(*shape, dtype=dtype, sparse=sparse)
k = 15
U, s, V = qu.rsvd(X, k, q=q, p=p)
assert U.shape == (shape[0], k)
assert s.shape == (k, )
assert V.shape == (k, shape[1])
assert U.dtype == dtype
assert V.dtype == dtype
assert_allclose(U.conj().T @ U, np.eye(k), rtol=1e-5, atol=1e-5)
assert_allclose(V @ V.conj().T, np.eye(k), rtol=1e-5, atol=1e-5)
Ue, se, Ve = qu.svds(X, k)
opt_err = qu.norm(X.A - usv2dense(Ue, se, Ve), 'fro')
act_err = qu.norm(X.A - usv2dense(U, s, V), 'fro')
assert act_err < 1.2 * opt_err
assert_allclose(s[:k // 2], se[:k // 2], rtol=0.05)
def test_rsvd_adaptive(self, dtype, shape, q, p):
X = rand_rank(*shape, 10, dtype=dtype)
U, s, V = qu.rsvd(X, 1e-5, q=q, p=p, k_start=10)
k = s.size
assert 10 <= k <= 20
assert U.dtype == dtype
assert V.dtype == dtype
assert_allclose(U.conj().T @ U, np.eye(k), rtol=1e-6, atol=1e-6)
assert_allclose(V @ V.conj().T, np.eye(k), rtol=1e-6, atol=1e-6)
Ue, se, Ve = qu.svds(X, k)
act_err = qu.norm(X - usv2dense(U, s, V), 'fro')
assert act_err < 1e-4
assert_allclose(s[:k // 2], se[:k // 2], rtol=0.1)
def test_norm_trace_dense(self):
a = qu.qarray(np.diag([-3, 1, 7]))
assert qu.norm(a, "trace") == 11
a = qu.rand_product_state(1, qtype="dop")
assert_allclose(qu.norm(a, "nuc"), 1)
def test_norm_spectral_sparse(self, mat_nherm_sparse, backend):
_, _, a = mat_nherm_sparse
assert_allclose(qu.norm(a, "spectral", backend=backend), 4.)
def test_norm_fro_sparse(self):
a = qu.sparse([[3, 0], [4j, 0]])
assert qu.norm(a, "fro") == (9 + 16)**0.5
def test_norm_fro_dense(self):
a = qu.quimbify([[1, 2], [3j, 4j]])
assert qu.norm(a, "fro") == (1 + 4 + 9 + 16)**0.5
def test_norm_trace_dense(self):
a = np.asmatrix(np.diag([-3, 1, 7]))
assert norm(a, "trace") == 11
a = rand_product_state(1, qtype="dop")
assert_allclose(norm(a, "nuc"), 1)
def test_norm_fro_sparse(self):
a = qu([[3, 0], [4j, 0]], sparse=True)
assert norm(a, "fro") == (9 + 16)**0.5
