def test_npc_Array_sort():
print("sort a square matrix")
a = npc.Array.from_ndarray(arr, [lc, lc.conj()])
print(lc)
p_flat, a_s = a.sort_legcharge(True, False)
npt.assert_equal(p_flat[0], [3, 0, 2, 1, 4])
arr_s = arr[np.ix_(*p_flat)] # what a_s should be
npt.assert_equal(a_s.to_ndarray(), arr_s) # sort without bunch
_, a_sb = a_s.sort_legcharge(False, True)
npt.assert_equal(a_sb.to_ndarray(), arr_s) # bunch after sort
# after re-implementation of sort_legcharge, this is automatically _qdata_sorted...
# npt.assert_equal(a_sb._qdata_sorted, False)
a_sb.isort_qdata()
npt.assert_equal(a_sb.to_ndarray(), arr_s) # sort_qdata
print("sort a for larger random array")
a = random_Array((20, 15, 10), chinfo2, sort=False)
p_flat, a_s = a.sort_legcharge(True, False)
arr_s = a.to_ndarray()[np.ix_(*p_flat)] # what a_s should be
npt.assert_equal(a_s.to_ndarray(), arr_s) # sort without bunch
_, a_sb = a_s.sort_legcharge(False, True)
npt.assert_equal(a_sb.to_ndarray(), arr_s) # bunch after sort
# npt.assert_equal(a_sb._qdata_sorted, False)
a_sb.isort_qdata()
npt.assert_equal(a_sb.to_ndarray(), arr_s) # sort_qdata
print("sort trivial charge data")
a = random_Array((10, 5), chinfoTr, sort=False)
p_flat, a_sb = a.sort_legcharge(False, True)
print("'sort' trivial charge")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
p_flat, a_s = a.sort_legcharge(True, False)
a_s.test_sanity()
npt.assert_equal(a_s.to_ndarray(), a.to_ndarray()) # p_flat should be trivial permuations...
def test_npc_Array_conversion():
print("trivial")
a = npc.Array.from_ndarray_trivial(arr)
npt.assert_equal(a.to_ndarray(), arr)
print("non-trivial charges")
a = npc.Array.from_ndarray(arr, [lc, lc.conj()])
npt.assert_equal(a._get_block_charge([0, 2]), [-2, 0])
npt.assert_equal(a.to_ndarray(), arr)
npt.assert_equal(a.qtotal, [0, 0])
print("check non-zero total charge")
a = npc.Array.from_ndarray(arr, [lc, lc_add.conj()])
npt.assert_equal(a.qtotal, [-1, 0])
npt.assert_equal(a.to_ndarray(), arr)
a = a.gauge_total_charge(1)
npt.assert_equal(a.qtotal, [0, 0])
print("check type conversion")
a_clx = a.astype(np.complex128)
assert a_clx.dtype == np.complex128
npt.assert_equal(a_clx.to_ndarray(), arr.astype(np.complex128))
print("from_func")
a = npc.Array.from_func(np.ones, [lc, lc.conj()])
a.test_sanity()
aflat = np.zeros((5, 5))
for ind in [(0, 0), (1, 1), (1, 4), (4, 1), (2, 2), (3, 3), (4, 4)]:
aflat[ind] = 1.
npt.assert_equal(a.to_ndarray(), aflat)
print("random array")
a = random_Array((20, 15, 10), chinfo2, sort=False)
a.test_sanity()
a = random_Array((20, 15, 10), chinfoTr, sort=False)
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()],
shape_kw='size')
a.test_sanity()
def test_npc_Array_reshape():
a = random_Array((20, 15, 10), chinfo, sort=False)
aflat = a.to_ndarray()
for comb_legs, transpose in [([[1]], [0, 1, 2]), ([[1], [2]], [0, 1, 2]),
([[0], [1], [2]], [0, 1, 2]), ([[2, 0]], [1, 2, 0]),
([[2, 0, 1]], [2, 0, 1])]:
print('combine legs', comb_legs)
with warnings.catch_warnings():
warnings.simplefilter("ignore", FutureWarning)
acomb = a.combine_legs(comb_legs) # just sorts second leg
print("=> labels: ", acomb.get_leg_labels())
acomb.test_sanity()
asplit = acomb.split_legs()
asplit.test_sanity()
npt.assert_equal(asplit.to_ndarray(), aflat.transpose(transpose))
print("test squeeze")
b = random_Array((10, 1, 5, 1), chinfo3, sort=True)
bflat = b.to_ndarray()
bs = b.squeeze()
bs.test_sanity()
npt.assert_equal(bs.to_ndarray(), np.squeeze(bflat))
bs.test_sanity()
if b.stored_blocks > 0:
# find a index with non-zero entry
idx = tuple([l.slices[qi] for l, qi in zip(b.legs, b._qdata[0])])
else:
idx = tuple([0] * b.rank)
assert b[idx[0], :, idx[2], :].squeeze() == bflat[idx]
print("test add_trivial_leg")
be = bs.copy(deep=True).add_trivial_leg(1, 'tr1', +1).add_trivial_leg(3, 'tr2', -1)
be.test_sanity()
npt.assert_equal(be.to_ndarray(), bflat)
print("test concatenate")
# create array `c` to concatenate with b along axis 2
legs = b.legs[:]
legs[1] = gen_random_legcharge(b.chinfo, 5)
c1 = npc.Array.from_func(np.random.random, legs, qtotal=b.qtotal, shape_kw='size')
c1flat = c1.to_ndarray()
legs[1] = gen_random_legcharge(b.chinfo, 3)
c2 = npc.Array.from_func(np.random.random, legs, qtotal=b.qtotal, shape_kw='size')
c2flat = c2.to_ndarray()
bc1c2 = npc.concatenate([b, c1, c2], axis=1)
bc1c2.test_sanity()
npt.assert_equal(bc1c2.to_ndarray(), np.concatenate([bflat, c1flat, c2flat], axis=1))
print("trivial charges")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
acomb = a.combine_legs([0, 1])
acomb.test_sanity()
asplit = acomb.split_legs([0])
asplit.test_sanity()
npt.assert_equal(asplit.to_ndarray(), aflat)
def test_npc_inner(tol=1.e-13):
for sort in [True, False]:
print("sort =", sort)
a = random_Array((10, 7, 5), chinfo3, sort=sort)
a.iset_leg_labels(['x', 'y', 'z'])
aflat = a.to_ndarray()
b = npc.Array.from_func(np.random.random, a.legs, qtotal=a.qtotal, shape_kw='size')
b.iset_leg_labels(['x', 'y', 'z'])
b_conj = b.conj()
b_conj_flat = b.to_ndarray()
cflat = np.tensordot(aflat, b_conj_flat, axes=[[0, 1, 2], [0, 1, 2]])
c = npc.inner(a, b_conj, axes='range') # no transpose
assert type(c) == np.dtype(float)
assert (abs(c - cflat) < tol)
c = npc.inner(a, b_conj, axes=[[0, 1, 2], [0, 1, 2]])
assert (abs(c - cflat) < tol)
c = npc.inner(a, b, axes='range', do_conj=True)
assert (abs(c - cflat) < tol)
# now transpose
b.itranspose([2, 1, 0])
b_conj.itranspose([2, 1, 0])
c = npc.inner(a, b_conj, axes=[[2, 0, 1], [0, 2, 1]]) # unordered axes!
assert (abs(c - cflat) < tol)
c = npc.inner(a, b_conj, axes='labels')
assert (abs(c - cflat) < tol)
c = npc.inner(a, b, axes='labels', do_conj=True)
assert (abs(c - cflat) < tol)
print("for trivial charge")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
b = npc.tensordot(a, a, axes=2)
bflat = np.tensordot(aflat, aflat, axes=2)
npt.assert_array_almost_equal_nulp(b, bflat, sum(a.shape))
def test_qr():
for shape in [(4, 4), (6, 8), (8, 6)]:
tol = shape[0] * shape[1] * 100
for qtotal_A in [None, [1]]:
A = random_Array(shape, chinfo3, qtotal=qtotal_A, sort=False)
A_flat = A.to_ndarray()
for qtotal_Q in [None, [1]]:
for mode in ['reduced', 'complete']:
for qconj in [+1, -1]:
for pos in [False, True]:
print(
f"shape={shape!s} qtot_A={qtotal_A!s} qtot_Q={qtotal_Q!s}"
f"mode={mode!s} pos_diag_R={pos!s} inner_qconj={qconj:+d}"
)
Q, R = npc.qr(A,
mode=mode,
pos_diag_R=pos,
qtotal_Q=qtotal_Q,
inner_qconj=qconj)
# print(q._qdata)
Q.test_sanity()
R.test_sanity()
assert np.all(
Q.qtotal) == A.chinfo.make_valid(qtotal_Q)
assert R.legs[0].qconj == qconj
QR = npc.tensordot(Q, R, axes=1)
npt.assert_array_almost_equal_nulp(
A_flat, QR.to_ndarray(), tol)
QdaggerQ = npc.tensordot(Q.conj(), Q, axes=[0, 0])
assert npc.norm(QdaggerQ -
npc.eye_like(QdaggerQ)) < 1.e-10
def test_drop_add_change_charge():
chinfo14 = npc.ChargeInfo([1, 4], ['U1', 'Z4'])
chinfo41 = npc.ChargeInfo([4, 1], ['Z4', 'U1'])
chinfo1 = npc.ChargeInfo([1], ['U1'])
chinfo4 = npc.ChargeInfo([4], ['Z4'])
chinfo12 = npc.ChargeInfo([1, 2], ['U1', 'Z2'])
for shape in [(50, ), (10, 4), (1, 1, 2)]:
A14 = random_Array(shape, chinfo14)
A14_flat = A14.to_ndarray()
A = A14.drop_charge()
A.test_sanity()
npt.assert_equal(A.to_ndarray(), A14_flat)
assert A.chinfo == chinfoTr
A1 = A14.drop_charge(1)
A1.test_sanity()
npt.assert_equal(A1.to_ndarray(), A14_flat)
assert A1.chinfo == chinfo1
A4 = A14.drop_charge('U1', chinfo4)
npt.assert_equal(A4.to_ndarray(), A14_flat)
assert A4.chinfo is chinfo4
A12 = A14.change_charge('Z4', 2, 'Z2', chinfo12)
A12.test_sanity()
npt.assert_equal(A4.to_ndarray(), A14_flat)
assert A12.chinfo is chinfo12
A14_new = A1.add_charge(A4.legs, qtotal=A4.qtotal)
A14_new.test_sanity()
npt.assert_equal(A14_new.to_ndarray(), A14_flat)
assert A14_new.chinfo == chinfo14
A41_new = A4.add_charge(A1.legs, chinfo41, qtotal=A1.qtotal)
A41_new.test_sanity()
npt.assert_equal(A41_new.to_ndarray(), A14_flat)
assert A41_new.chinfo is chinfo41
def test_npc_Array_ops():
a = random_Array((15, 10), chinfo3, sort=True)
b = npc.Array.from_func(np.random.random,
a.legs,
qtotal=a.qtotal,
shape_kw='size')
s = 3.12
aflat = a.to_ndarray()
bflat = b.to_ndarray()
import operator as Op
# addition / subtraction
for op in [Op.add, Op.sub, Op.iadd, Op.isub]:
print(op.__name__)
a2 = op(a, b)
a.test_sanity()
b.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, bflat)
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
npt.assert_equal(b.to_ndarray(), bflat) # should not have been modified...
# multiplication
for op in [Op.mul, Op.imul]:
print(op.__name__)
a2 = op(a, s)
a.test_sanity()
b.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, s)
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
# reversed multiplication
print("rmul")
a2 = s * a
a.test_sanity()
a2.test_sanity()
aflat2 = s * aflat
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
# division
for op in [Op.truediv, Op.itruediv]:
# may differ by machine precision due to rounding errors
print(op.__name__)
a2 = op(a, s)
a.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, s)
assert (np.max(np.abs(a.to_ndarray() - aflat)) < EPS)
assert (np.max(np.abs(a.to_ndarray() - aflat)) < EPS)
# equality
assert a == a
a2 = a.copy(deep=False)
b = a.copy(deep=True)
assert b == a == a2
assert len(b._data) > 0
b._data[-1][0, -1] += 1.e-13 # change
assert not b == a # not exactly equal
assert a.__eq__(b, 1.e-12) # but to high precision
def test_npc_Array_norm():
a = random_Array((15, 10), chinfo3, sort=True)
aflat = a.to_ndarray()
for ord in [np.inf, -np.inf, 0, 1, 2, 3.]: # divides by 0 for neg. ord
print("ord = ", ord)
anorm = a.norm(ord)
aflnorm = npc.norm(aflat, ord)
print(abs(anorm - aflnorm))
assert (abs(anorm - aflnorm) < 100 * EPS)
def test_npc_pinv():
m, n = (10, 20)
A = random_Array((m, n), chinfo3)
tol_NULP = max(max(m, n)**3, 1000)
Aflat = A.to_ndarray()
P = npc.pinv(A, 1.e-13)
P.test_sanity()
Pflat = np.linalg.pinv(Aflat, 1.e-13)
assert (np.max(np.abs(P.to_ndarray() - Pflat)) < tol_NULP * EPS)
def test_npc_tensordot():
for sort in [True, False]:
print("sort =", sort)
a = random_Array((10, 12, 15), chinfo3, qtotal=[0], sort=sort)
aflat = a.to_ndarray()
legs_b = [l.conj() for l in a.legs[::-1]]
b = npc.Array.from_func(np.random.random,
legs_b,
qtotal=[1],
shape_kw='size')
b = b * (
1 + 1.j
) # make second array complex: check that different dtypes work
bflat = b.to_ndarray()
print("axes = 1") # start simple: only one axes
c = npc.tensordot(a, b, axes=1)
c.test_sanity()
a.test_sanity()
b.test_sanity()
npt.assert_array_almost_equal_nulp(a.to_ndarray(), aflat, 1)
npt.assert_array_almost_equal_nulp(b.to_ndarray(), bflat, 1)
cflat = np.tensordot(aflat, bflat, axes=1)
npt.assert_array_almost_equal_nulp(c.to_ndarray(), cflat, sum(a.shape))
print("axes = 2") # second: more than one axis
c = npc.tensordot(a, b, axes=([1, 2], [1, 0]))
a.test_sanity()
b.test_sanity()
npt.assert_array_almost_equal_nulp(a.to_ndarray(), aflat, 1)
npt.assert_array_almost_equal_nulp(b.to_ndarray(), bflat, 1)
c.test_sanity()
cflat = np.tensordot(aflat, bflat, axes=([1, 2], [1, 0]))
npt.assert_array_almost_equal_nulp(c.to_ndarray(), cflat, sum(a.shape))
for i in range(b.shape[0]):
b2 = b[i, :, :]
if b2.stored_blocks > 0:
break
b2flat = b2.to_ndarray()
print("right tensor fully contracted")
print(a.shape, b2.shape)
d = npc.tensordot(a, b2, axes=([0, 1], [1, 0]))
d.test_sanity()
dflat = np.tensordot(aflat, b2flat, axes=([0, 1], [1, 0]))
npt.assert_array_almost_equal_nulp(d.to_ndarray(), dflat, sum(a.shape))
print("left tensor fully contracted")
d = npc.tensordot(b2, a, axes=([0, 1], [1, 0]))
d.test_sanity()
dflat = np.tensordot(b2flat, aflat, axes=([0, 1], [1, 0]))
npt.assert_array_almost_equal_nulp(d.to_ndarray(), dflat, sum(a.shape))
# full/no contraction is tested in test_npc_inner/test_npc_outer
print("for trivial charge")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()],
shape_kw='size')
aflat = a.to_ndarray()
b = npc.tensordot(a, a, axes=1)
bflat = np.tensordot(aflat, aflat, axes=1)
npt.assert_array_almost_equal_nulp(b.to_ndarray(), bflat, sum(a.shape))
def test_npc_Array_transpose():
a = random_Array((20, 15, 10), chinfo)
aflat = a.to_ndarray()
for tr in [None, [2, 1, 0], (1, 2, 0), (0, 2, 1)]:
atr = a.transpose(tr)
atr.test_sanity()
npt.assert_equal(atr.to_ndarray(), aflat.transpose(tr))
ax1, ax2 = -1, 0
a.iswapaxes(ax1, ax2)
npt.assert_equal(a.to_ndarray(), aflat.swapaxes(ax1, ax2))
def test_npc_Array_permute():
sh = (20, 15, 10)
a = random_Array(sh, chinfo)
aflat = a.to_ndarray().copy()
for ax in range(len(sh)):
p = np.arange(sh[ax], dtype=np.intp)
np.random.shuffle(p)
a = a.permute(p, axis=ax)
a.test_sanity()
aflat = np.take(aflat, p, axis=ax)
npt.assert_equal(a.to_ndarray(), aflat)
def test_npc_outer():
for sort in [True, False]:
print("sort =", sort)
a = random_Array((6, 7), chinfo3, sort=sort)
b = random_Array((5, 5), chinfo3, sort=sort)
aflat = a.to_ndarray()
bflat = b.to_ndarray()
c = npc.outer(a, b)
c.test_sanity()
cflat = np.tensordot(aflat, bflat, axes=0)
npt.assert_equal(c.to_ndarray(), cflat)
c = npc.tensordot(a, b, axes=0) # (should as well call npc.outer)
npt.assert_equal(c.to_ndarray(), cflat)
print("for trivial charge")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
b = npc.tensordot(a, a, axes=0)
bflat = np.tensordot(aflat, aflat, axes=0)
npt.assert_array_almost_equal_nulp(b.to_ndarray(), bflat, sum(a.shape))
def test_qr():
for shape in [(4, 4), (6, 8), (8, 6)]:
for qtotal in [None, [1]]:
print("qtotal=", qtotal, "shape =", shape)
A = random_Array(shape, chinfo3, qtotal=qtotal, sort=False)
A_flat = A.to_ndarray()
q, r = npc.qr(A, 'reduced')
print(q._qdata)
q.test_sanity()
r.test_sanity()
qr = npc.tensordot(q, r, axes=1)
npt.assert_array_almost_equal_nulp(A_flat, qr.to_ndarray(), shape[0] * shape[1] * 100)
def test_npc_Array_ops():
a = random_Array((15, 10), chinfo3, sort=True)
b = npc.Array.from_func(np.random.random,
a.legs,
qtotal=a.qtotal,
shape_kw='size')
s = 3.12
aflat = a.to_ndarray()
bflat = b.to_ndarray()
import operator as Op
# addition / subtraction
for op in [Op.add, Op.sub, Op.iadd, Op.isub]:
print(op.__name__)
a2 = op(a, b)
a.test_sanity()
b.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, bflat)
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
npt.assert_equal(b.to_ndarray(), bflat) # should not have been modified...
# multiplication
for op in [Op.mul, Op.imul]:
print(op.__name__)
a2 = op(a, s)
a.test_sanity()
b.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, s)
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
# reversed multiplication
print("rmul")
a2 = s * a
a.test_sanity()
a2.test_sanity()
aflat2 = s * aflat
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(a2.to_ndarray(), aflat2)
# division
for op in [Op.truediv, Op.itruediv]:
# may differ by machine precision due to rounding errors
print(op.__name__)
a2 = op(a, s)
a.test_sanity()
a2.test_sanity()
aflat2 = op(aflat, s)
assert (np.max(np.abs(a.to_ndarray() - aflat)) < EPS)
assert (np.max(np.abs(a.to_ndarray() - aflat)) < EPS)
def test_npc_Array_scale_axis():
a = random_Array((5, 15, 10), chinfo3, sort=True)
aflat = a.to_ndarray()
s0 = np.random.random((a.shape[0], 1, 1))
s1 = np.random.random((1, a.shape[1], 1))
s2 = np.random.random((1, 1, a.shape[2]))
b = a.scale_axis(s0.flatten(), 0)
b.test_sanity()
npt.assert_equal(b.to_ndarray(), aflat * s0)
a.iscale_axis(s1.flatten(), 1)
a.test_sanity()
aflat = aflat * s1
npt.assert_equal(a.to_ndarray(), aflat)
c = a.scale_axis(s2.flatten(), -1)
c.test_sanity()
npt.assert_equal(c.to_ndarray(), aflat * s2)
def test_npc_Array_reshape_2():
# check that combine_leg is compatible with pipe.map_incoming_flat
shape = (2, 5, 2)
a = random_Array(shape, chinfo3, sort=True)
aflat = a.to_ndarray()
acomb = a.combine_legs([[0, 1]])
acombflat = acomb.to_ndarray()
pipe = acomb.legs[0]
print(a)
print(acomb)
print(pipe.q_map)
print(pipe.slices)
# expensive: compare all entries
for i, j, k in it.product(*[list(range(s)) for s in shape]):
ij = pipe.map_incoming_flat([i, j])
print(i, j, k, ij)
assert (acombflat[ij, k] == aflat[i, j, k])
def test_orthogonal_columns():
for shape in [(8, 6), (8, 2)]:
tol = shape[0] * shape[1] * 100
for qtotal_A in [None, [1]]:
A = random_Array(shape, chinfo3, qtotal=qtotal_A, sort=False)
A_flat = A.to_ndarray()
ortho = npc.orthogonal_columns(A)
ortho.test_sanity()
ortho_flat = ortho.to_ndarray()
# check orthogonality to A_flat
assert np.linalg.norm(
A_flat.T.conj().dot(ortho_flat)) < tol * 1.e-15
# check orthonormality of columns
orthonormal = ortho_flat.T.conj().dot(ortho_flat)
npt.assert_almost_equal(orthonormal,
np.eye(orthonormal.shape[0]),
decimal=14)
def test_npc_Array_conj():
a = random_Array((15, 10), chinfo3, sort=True)
a.iset_leg_labels(['a', 'b*'])
aflat = a.to_ndarray()
b = a.conj()
b.test_sanity()
npt.assert_equal(a.to_ndarray(), aflat)
npt.assert_equal(b.to_ndarray(), aflat.conj())
a.iconj()
npt.assert_equal(a.to_ndarray(), aflat.conj())
a.test_sanity()
print(a.get_leg_labels())
assert a._conj_leg_label('(a*.(b.c*).(d*.e))') == '(a.(b*.c).(d.e*))'
print("conjugate Trivial charges")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
a.iconj()
npt.assert_equal(a.to_ndarray(), aflat.conj())
a.test_sanity()
def test_npc_inner():
for sort in [True, False]:
print("sort =", sort)
a = random_Array((10, 7, 5), chinfo3, sort=sort)
aflat = a.to_ndarray()
legs_b = [l.conj() for l in a.legs[::-1]]
b = npc.Array.from_func(np.random.random, legs_b, qtotal=-a.qtotal, shape_kw='size')
bflat = b.to_ndarray()
c = npc.inner(a, b, axes=[[2, 0, 1], [0, 2, 1]])
assert type(c) == np.dtype(float)
cflat = np.tensordot(aflat, bflat, axes=[[2, 0, 1], [0, 2, 1]])
npt.assert_array_almost_equal_nulp(c, cflat, max(a.size, b.size))
print("for trivial charge")
a = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()], shape_kw='size')
aflat = a.to_ndarray()
b = npc.tensordot(a, a, axes=2)
bflat = np.tensordot(aflat, aflat, axes=2)
npt.assert_array_almost_equal_nulp(b, bflat, sum(a.shape))
def test_npc_svd():
for m, n in [(1, 1), (1, 10), (10, 1), (10, 10), (10, 20)]:
print("m, n = ", m, n)
tol_NULP = max(20 * max(m, n)**3, 1000)
for i in range(1000):
A = random_Array((m, n), chinfo3, sort=True)
if A.stored_blocks > 0:
break
Aflat = A.to_ndarray()
Sonly = npc.svd(A, compute_uv=False)
U, S, VH = npc.svd(A, full_matrices=False, compute_uv=True)
assert (U.shape[1] == S.shape[0] == VH.shape[0])
U.test_sanity()
VH.test_sanity()
npt.assert_array_almost_equal_nulp(Sonly, S, tol_NULP)
recalc = npc.tensordot(U.scale_axis(S, axis=-1), VH, axes=1)
npt.assert_array_almost_equal_nulp(recalc.to_ndarray(), Aflat,
tol_NULP)
# compare with flat SVD
Uflat, Sflat, VHflat = np.linalg.svd(Aflat, False, True)
perm = np.argsort(-S) # sort descending
print(S[perm])
iperm = inverse_permutation(perm)
for i in range(len(Sflat)):
if i not in iperm: # dopped it in npc.svd()
assert (Sflat[i] < EPS * 10)
Sflat = Sflat[iperm]
npt.assert_array_almost_equal_nulp(Sonly, Sflat, tol_NULP)
# comparing U and Uflat is hard: U columns can change by a phase...
print("with full_matrices")
Ufull, Sfull, VHfull = npc.svd(A, full_matrices=True, compute_uv=True)
Ufull.test_sanity()
VHfull.test_sanity()
npt.assert_array_almost_equal_nulp(Sfull, S, tol_NULP)
print("for trivial charges")
A = npc.Array.from_func(np.random.random, [lcTr, lcTr.conj()],
shape_kw='size')
Aflat = A.to_ndarray()
U, S, VH = npc.svd(A)
recalc = npc.tensordot(U.scale_axis(S, axis=-1), VH, axes=1)
tol_NULP = max(20 * max(A.shape)**3, 1000)
npt.assert_array_almost_equal_nulp(recalc.to_ndarray(), Aflat, tol_NULP)
def test_pickle():
import pickle
a = npc.Array.from_ndarray(arr, [lc, lc_add.conj()])
b = random_Array((20, 15, 10), chinfo2, sort=False)
a.test_sanity()
b.test_sanity()
aflat = a.to_ndarray()
bflat = b.to_ndarray()
data = {'a': a, 'b': b}
stream = pickle.dumps(data)
data2 = pickle.loads(stream)
a2 = data2['a']
b2 = data2['b']
a.test_sanity()
b.test_sanity()
a2.test_sanity()
b2.test_sanity()
a2flat = a2.to_ndarray()
b2flat = b2.to_ndarray()
npt.assert_array_equal(aflat, a2flat)
npt.assert_array_equal(bflat, b2flat)
def test_charge_detection():
chinfo = chinfo3
for qtotal in [[0], [1], None]:
print("qtotal=", qtotal)
shape = (8, 6, 5)
A = random_Array(shape, chinfo3, qtotal=qtotal)
Aflat = A.to_ndarray()
legs = A.legs[:]
print(A)
if not np.any(Aflat > 1.e-8):
print("skip test: no non-zero entry")
continue
qt = npc.detect_qtotal(Aflat, legs)
npt.assert_equal(qt, chinfo.make_valid(qtotal))
for i in range(len(shape)):
correct_leg = legs[i]
legs[i] = None
legs = npc.detect_legcharge(Aflat, chinfo, legs, A.qtotal, correct_leg.qconj)
res_leg = legs[i]
assert res_leg.qconj == correct_leg.qconj
legs[i].bunch()[1].test_equal(correct_leg.bunch()[1])
def test_npc_Array_itemacces():
a = npc.Array.from_ndarray(arr, [lc, lc.conj()])
aflat = a.to_ndarray().copy()
for i, j in it.product(range(5), range(5)): # access all elements
assert a[i, j] == aflat[i, j]
for i, j in [(0, 0), (2, 2), (1, 4), (4, 1), (3, 3),
(4, 4)]: # sets also emtpy blocks
val = np.random.rand()
aflat[i, j] = val
a[i, j] = val
npt.assert_equal(a.to_ndarray(), aflat)
# again for array with larger blocks
a = random_Array((10, 10), chinfo3)
aflat = a.to_ndarray().copy()
for i, j in it.product(range(10), range(10)): # access all elements
assert a[i, j] == aflat[i, j]
# take_slice and add_leg
a = random_Array((20, 10, 5), chinfo3)
aflat = a.to_ndarray().copy()
for idx, axes in [(0, 0), (4, 1), ([3, -2], [-1, 0])]:
a_sl = a.take_slice(idx, axes)
a_sl.test_sanity()
sl = [slice(None)] * a.rank
try:
for i, ax in zip(idx, axes):
sl[ax] = i
except:
sl[axes] = idx
sl = tuple(sl)
npt.assert_equal(a_sl.to_ndarray(), aflat[sl])
npt.assert_equal(a[sl].to_ndarray(), aflat[sl])
# NOTE: interally uses advanced indexing notation, but only with slices.
if type(axes) == int:
a_ext = a_sl.add_leg(a.legs[axes], idx, axes)
npt.assert_equal(a.qtotal, a_ext.qtotal)
npt.assert_equal(a_ext.to_ndarray()[sl], aflat[sl])
# advanced indexing with slices and projection/mask
# NOTE: for bflat[idx] = aflat[idx] to work, non-slices may not be separated by slices.
check_idx = [(2, Ellipsis, 1),
(slice(None), 3, np.array([True, True, False, True, False])),
(slice(3, 4), np.array([2, 4, 5]), slice(1, 4, 2)),
(slice(4, 2, -1), 2, np.array([3, 1, 4, 2]))] # yapf: disable
for idx in check_idx:
print("take slice for ", idx)
b = a[idx]
b.test_sanity()
bflat = aflat[
idx] # idx may only contain a single array for this to work
npt.assert_equal(b.to_ndarray(), bflat)
# create another random array to check copying with c[inds] = a[inds]
b = npc.Array.from_func(np.random.random,
a.legs,
a.dtype,
a.qtotal,
shape_kw='size')
# remove half of the blocks to check copying to empty sites as well
keep = (np.arange(b.stored_blocks) % 2 == 0)
try:
b._data = [d for d, k in zip(b._data, keep) if k]
b._qdata = b._qdata[keep]
except AttributeError:
pass # for cython version, we can't write _data and _qdata...
bflat = b.to_ndarray().copy()
aflat = a.to_ndarray().copy()
for idx in check_idx:
print("copy slice for ", idx)
b[idx] = a[idx]
b.test_sanity()
bflat[idx] = aflat[idx] # idx may only contain a single array
npt.assert_equal(b.to_ndarray(), bflat)