def test_mt_vectorize():
from representability.tensor import index_tuple_basis
from representability.tensor import Bijection
a = np.arange(16).reshape((4, 4), order='C')
print(a)
basis = [(0, 0), (0, 1), (1, 0), (1, 1)]
basis = index_tuple_basis(basis)
ta = Tensor(a, basis=basis, name='a')
assert np.allclose(ta.data, a)
assert ta.size == 16
assert isinstance(ta.basis, Bijection)
b = np.arange(16, 16 + 36).reshape((6, 6), order='C')
print(b)
basis = [(0, 0), (0, 1), (0, 2), (0, 3), (1, 2), (2, 3)]
basis = index_tuple_basis(basis)
tb = Tensor(b, basis=basis, name='b')
mt = MultiTensor([ta, tb])
dbe = DualBasisElement()
dbe.add_element('a', (0, 0, 0, 1), 1.0) # 1
dbe.add_element('b', (0, 1, 0, 2), 1.0) # 24
assert mt.off_set_map == {'a': 0, 'b': 16}
mt_vec_idx, _ = mt.synthesize_element(dbe)
assert mt_vec_idx[0] == 1
assert mt_vec_idx[1] == 24
def test_tensor_index():
"""
Testing the index_vectorized which is mapped through the basis
:return:
"""
a = np.arange(16).reshape((4, 4), order='C')
print(a)
basis = [(0, 0), (0, 1), (1, 0), (1, 1)]
basis = index_tuple_basis(basis)
tt = Tensor(a, basis=basis)
assert np.allclose(tt.data, a)
assert tt.size == 16
assert isinstance(tt.basis, Bijection)
assert np.isclose(tt.index_vectorized(0, 0, 0, 0), 0)
assert np.isclose(tt.index_vectorized(0, 0, 0, 1), 1)
assert np.isclose(tt.index_vectorized(0, 0, 1, 0), 2)
assert np.isclose(tt.index_vectorized(0, 0, 1, 1), 3)
assert np.isclose(tt.index_vectorized(0, 1, 0, 0), 4)
assert np.isclose(tt.index_vectorized(0, 1, 0, 1), 5)
assert np.isclose(tt.index_vectorized(0, 1, 1, 0), 6)
assert np.isclose(tt.index_vectorized(0, 1, 1, 1), 7)
assert np.isclose(tt.index_vectorized(1, 0, 0, 0), 8)
assert np.isclose(tt.index_vectorized(1, 0, 0, 1), 9)
assert np.isclose(tt.index_vectorized(1, 0, 1, 0), 10)
assert np.isclose(tt.index_vectorized(1, 0, 1, 1), 11)
assert np.isclose(tt.index_vectorized(1, 1, 0, 0), 12)
assert np.isclose(tt.index_vectorized(1, 1, 0, 1), 13)
assert np.isclose(tt.index_vectorized(1, 1, 1, 0), 14)
assert np.isclose(tt.index_vectorized(1, 1, 1, 1), 15)
# etc...
a = np.arange(16).reshape((4, 4), order='C')
tt = Tensor(a) # the canonical basis
assert np.isclose(tt.index_vectorized(0, 0), 0)
assert np.isclose(tt.index_vectorized(0, 1), 1)
assert np.isclose(tt.index_vectorized(0, 2), 2)
assert np.isclose(tt.index_vectorized(0, 3), 3)
assert np.isclose(tt.index_vectorized(1, 0), 4)
assert np.isclose(tt.index_vectorized(1, 1), 5)
assert np.isclose(tt.index_vectorized(1, 2), 6)
assert np.isclose(tt.index_vectorized(1, 3), 7)
b = np.arange(16, 16 + 36).reshape((6, 6), order='C')
print(b)
basis = [(0, 0), (0, 1), (0, 2), (0, 3), (1, 2), (2, 3)]
basis = index_tuple_basis(basis)
tb = Tensor(b, basis=basis)
def test_geminal_basis():
gems = list(product(range(5), repeat=2))
b = index_tuple_basis(gems)
assert b.fwd(4) == (0, 4)
assert b.rev((0, 4)) == 4
assert b.rev(b.fwd(4)) == 4
assert b.domain_element_sizes() == (1, 2)
def geminal_spin_basis(m_dim):
"""
Construct the geminal basis blocked by Sz
D2 and Q2 have the same aa, bb, ab basis structure.
:param Int m_dim: rank of the single particle position space basis (NOT SPIN ORBITAL RANK)
:return: Basis Bijections
:rtype: representability.tensor.Bijection
"""
# basis construction for canonical matrices
gem_aa_bas = []
gem_ab_bas = []
for i in range(m_dim):
for j in range(m_dim):
if i < j:
gem_aa_bas.append((i, j))
gem_ab_bas.append((i, j))
return index_tuple_basis(gem_aa_bas), index_tuple_basis(gem_ab_bas)
def triples_spin_orbital_antisymm_basis(m_dim):
"""
Construct the triples spin basis
:param Int m_dim:
:return: representbaility.tensor.Bijection
"""
bas = []
for p, q, r in product(range(m_dim), repeat=3):
if p < q < r:
bas.append((p, q, r))
return index_tuple_basis(bas)
def test_tensor_basis():
"""
make a matrix that has a different basis than indexing
"""
n = 4
dim = int(n * (n - 1) / 2)
geminals = []
bas = {}
cnt = 0
for i in range(4):
for j in range(i + 1, 4):
bas[cnt] = (i, j)
geminals.append((i, j))
cnt += 1
rev_bas = dict(zip(bas.values(), bas.keys()))
rand_mat = np.random.random((dim, dim))
basis_bijection = index_tuple_basis(geminals)
test_tensor = Tensor(rand_mat, basis=basis_bijection)
assert test_tensor.basis.fwd(0) == (0, 1)
assert test_tensor.basis.fwd(2) == (0, 3)
assert test_tensor.basis.rev(test_tensor.basis.fwd(5)) == 5
assert test_tensor.ndim == 2
assert test_tensor.dim == dim
# index into data directly
assert test_tensor[2, 3] == rand_mat[2, 3]
# index into data via basis indexing
assert test_tensor(0, 1, 0, 1) == rand_mat[0, 0]
assert test_tensor(1, 2, 0, 1) == rand_mat[rev_bas[(1, 2)],
rev_bas[(0, 1)]]
assert test_tensor.index_vectorized(1, 2, 0, 1) == rev_bas[(1, 2)] * dim + \
rev_bas[(0, 1)]
# testing iteration over the upper triangle
for iter_vals in test_tensor.utri_iterator():
val, [i, j] = iter_vals
assert val == rand_mat[test_tensor.basis.rev(i),
test_tensor.basis.rev(j)]
def d2_q2_mapping(dim):
"""
Map each d2 block to the q2 block
:param dim: rank of spatial single-particle basis
:return:
"""
krond = np.eye(dim)
def d2q2element(p, q, r, s, factor, tname_d1_1, tname_d2,
tname_q2): # , spin_string):
"""
# ( 1.00000) cre(r) cre(s) des(q) des(p)
# ( 1.00000) kdelta(p,s) cre(r) des(q)
# ( -1.00000) kdelta(p,r) cre(s) des(q)
# ( -1.00000) kdelta(q,s) cre(r) des(p)
# ( 1.00000) kdelta(q,r) cre(s) des(p)
# ( -1.00000) kdelta(p,s) kdelta(q,r)
# ( 1.00000) kdelta(p,r) kdelta(q,s)
"""
dbe = DualBasisElement()
dbe.add_element(tname_q2, (p, q, r, s), -factor)
dbe.add_element(tname_d2, (r, s, p, q), factor)
if p == s:
dbe.add_element(tname_d1_1, (r, q), factor)
if p == r:
dbe.add_element(tname_d1_1, (s, q), -factor)
if q == s:
dbe.add_element(tname_d1_1, (r, p), -factor)
if q == r:
dbe.add_element(tname_d1_1, (s, p), factor)
# remember the negative sign because AX = b
dbe.dual_scalar = -factor * (krond[p, r] * krond[q, s] -
krond[p, s] * krond[q, r])
# dbe.add_element('kkcc_' + spin_string + spin_string, (r, s, p, q), factor)
# if q == s:
# dbe.add_element('ck_' + spin_string, (p, r), factor)
# if p == s:
# dbe.add_element('ck_' + spin_string, (q, r), -factor)
# if q == r:
# dbe.add_element('kc_' + spin_string, (s, p), factor)
# if p == r:
# dbe.add_element('kc_' + spin_string, (s, q), -factor)
# dbe.add_element('cckk_' + spin_string + spin_string, (p, q, r, s), -factor)
# dbe.dual_scalar = 0
return dbe
def d2q2element_ab(p, q, r, s, factor):
dbe = DualBasisElement()
if q == s:
dbe.add_element('ck_a', (p, r), factor)
if p == r:
dbe.add_element('kc_b', (s, q), -factor)
dbe.add_element('kkcc_ab', (r, s, p, q), factor)
dbe.add_element('cckk_ab', (p, q, r, s), -factor)
# dbe.dual_scalar = -krond[q, s]*krond[p, r] * factor
dbe.dual_scalar = 0
return dbe
dual_basis_list = []
# for p, q, r, s in product(range(dim), repeat=4):
from representability.tensor import index_tuple_basis
gem_aa = []
gem_ab = []
for p, q in product(range(dim), repeat=2):
if p < q:
gem_aa.append((p, q))
gem_ab.append((p, q))
bas_aa = index_tuple_basis(gem_aa)
bas_ab = index_tuple_basis(gem_ab)
for i, j in product(range(dim * (dim - 1) // 2), repeat=2):
if i >= j:
p, q = bas_aa.fwd(i)
r, s = bas_aa.fwd(j)
# if p < q and r < s and p * dim + q < r * dim + s:
dbe1 = d2q2element(p, q, r, s, 0.5, 'ck_a', 'cckk_aa', 'kkcc_aa')
dbe2 = d2q2element(r, s, p, q, 0.5, 'ck_a', 'cckk_aa', 'kkcc_aa')
# dbe1 = d2q2element(p, q, r, s, 0.5, 'a')
# dbe2 = d2q2element(r, s, p, q, 0.5, 'a')
dual_basis_list.append(dbe1.join_elements(dbe2))
# dbe1 = d2q2element(p, q, r, s, 0.5, 'b')
# dbe2 = d2q2element(r, s, p, q, 0.5, 'b')
dbe1 = d2q2element(p, q, r, s, 0.5, 'ck_b', 'cckk_bb', 'kkcc_bb')
dbe2 = d2q2element(r, s, p, q, 0.5, 'ck_b', 'cckk_bb', 'kkcc_bb')
dual_basis_list.append(dbe1.join_elements(dbe2))
# # if p < q and r < s and p == r and q == s:
# # dbe1 = d2q2element(p, q, r, s, 1., 'a')
# dbe = d2q2element(p, q, r, s, 1., 'ck_a', 'cckk_aa', 'kkcc_aa')
# dual_basis_list.append(dbe)
# # # dbe1 = d2q2element(p, q, r, s, 1., 'b')
# dbe = d2q2element(p, q, r, s, 1., 'ck_b', 'cckk_bb', 'kkcc_bb')
# dual_basis_list.append(dbe)
for i, j in product(range(dim * dim), repeat=2):
if i >= j:
p, q = bas_ab.fwd(i)
r, s = bas_ab.fwd(j)
# if p * dim + q <= r * dim + s:
dbe1 = d2q2element_ab(p, q, r, s, 0.5)
dbe2 = d2q2element_ab(r, s, p, q, 0.5)
dual_basis_list.append(dbe1.join_elements(dbe2))
return DualBasis(elements=dual_basis_list)