def tensor_train_template(init_rho, pb_index, rank=1):
"""Get rho_n from rho in a Tensor Train representation.
Parameters
----------
rho : np.ndarray
"""
n_vec = np.zeros((rank, ), dtype=DTYPE)
n_vec[0] = 1.0
root_array = np.tensordot(init_rho, n_vec, axes=0)
root = Tensor(name='root', array=root_array, axis=None)
max_terms = len(pb_index)
# +2: i and j
root[0] = (Leaf(name=max_terms), 0)
root[1] = (Leaf(name=max_terms + 1), 0)
for i in pb_index:
assert rank <= i
train = [root]
for k in range(max_terms):
if k < max_terms - 1:
array = np.eye(rank, pb_index[k] * rank)
array = np.reshape(array, (rank, -1, rank))
else:
array = np.eye(rank, pb_index[k])
spf = Tensor(name=k, array=array, axis=0)
l = Leaf(name=k)
spf[0] = (train[-1], 2)
spf[1] = (l, 0)
train.append(spf)
return root
def init_state(self):
v = 1.
for i in range(self.rank):
_, v_i = self.dvr_list[i].solve(n_state=1)
v = np.tensordot(v, v_i[0], axes=0)
v = np.reshape(v, -1)
return v
def tensor_tree_template(init_rho, pb_index, rank=1, nbranch=2):
"""Get rho_n from rho in a Tensor Tree representation.
Parameters
----------
rho : np.ndarray
"""
n_state = get_n_state(init_rho)
n_vec = np.zeros((rank, ), dtype=DTYPE)
n_vec[0] = 1.0
root_array = np.tensordot(init_rho, n_vec, axes=0)
max_terms = len(pb_index)
for i in pb_index:
assert rank <= i
# generate leaves
leaves = list(range(max_terms))
class new_spf(object):
counter = 0
prefix = 'SPF'
def __new__(cls):
name = cls.prefix + str(cls.counter)
cls.counter += 1
return name
importance = list(reversed(range(len(pb_index))))
graph, spf_root = huffman_tree(
leaves,
importances=importance,
obj_new=new_spf,
n_branch=nbranch,
)
root = 'root'
graph[root] = [str(max_terms), str(max_terms + 1), spf_root]
print(graph, root)
root = Tensor.generate(graph, root)
root.set_array(root_array)
bond_dict = {}
# Leaves
l_range = list(pb_index) + [n_state] * 2
for s, i, t, j in root.linkage_visitor():
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = l_range[int(t.name)]
else:
bond_dict[(s, i, t, j)] = rank
autocomplete(root, bond_dict)
return root
def gen_extended_rho(self, rho):
"""Get rho_n from rho with the conversion:
rho[n_0, ..., n_(k-1), i, j]
Parameters
----------
rho : np.ndarray
"""
shape = list(rho.shape)
assert len(shape) == 2 and shape[0] == shape[1]
# Let: rho_n[0, i, j] = rho and rho_n[n, i, j] = 0
ext = np.zeros((np.prod(self.n_dims), ))
ext[0] = 1
rho_n = np.reshape(np.tensordot(ext, rho, axes=0),
list(self.n_dims) + shape)
return np.array(rho_n, dtype=DTYPE)
def simple_heom(init_rho, n_indices):
"""Get rho_n from rho with the conversion:
rho[i, j, n_0, ..., n_(k-1)]
Parameters
----------
rho : np.ndarray
"""
n_state = get_n_state(init_rho)
# Let: rho_n[0, :, :] = rho and rho_n[n, :, :] = 0
ext = np.zeros((np.prod(n_indices), ))
ext[0] = 1.0
new_shape = [n_state, n_state] + list(n_indices)
rho_n = np.reshape(np.tensordot(init_rho, ext, axes=0), new_shape)
root = Tensor(name='root', array=rho_n, axis=None)
d = len(n_indices)
root[0] = (Leaf(name=d), 0)
root[1] = (Leaf(name=d + 1), 0)
for k in range(d): # +2: i and j
root[k + 2] = (Leaf(name=k), 0)
return root
beta=beta,
)
model = SBM(
sys_ham=np.array([[-0.5 * e, v], [v, 0.5 * e]], dtype=DTYPE),
sys_op=np.array([[-0.5, 0.0], [0.0, 0.5]], dtype=DTYPE),
ph_parameters=ph_parameters,
ph_dims=(dof * [max_tier]),
bath_corr=drude,
bath_dims=[max_tier],
)
# init state
A, B = 1.0, 1.0
wfn_0 = np.array([A, B]) / np.sqrt(A**2 + B**2)
rho_0 = np.tensordot(wfn_0, wfn_0, axes=0)
# Propagation
dt_unit = Quantity(0.001, 'fs').value_in_au
callback_interval = 100
count = 10_000
def test_heom(fname=None):
ph_dims = list(np.repeat(model.ph_dims, 2))
n_dims = ph_dims if model.bath_dims is None else ph_dims + model.bath_dims
print(n_dims)
root = tensor_tree_template(rho_0, n_dims, rank=rank_heom)
leaves = root.leaves()
h_list = model.heom_h_list(leaves[0], leaves[1], leaves[2:], beta=beta)
from minitn.heom.noise import Drude
from minitn.lib.units import Quantity
# System
e = Quantity(6500, 'cm-1').value_in_au
v = Quantity(500, 'cm-1').value_in_au
# Bath
lambda_0 = Quantity(2000, 'cm-1').value_in_au # reorganization energy
omega_0 = Quantity(2000, 'cm-1').value_in_au # vibrational frequency
beta = Quantity(300, 'K').value_in_au # temperature
# Superparameters
max_terms = 5 # (terms used in the expansion of the correlation function)
max_tier = 10 # (number of possble values for each n_k in the extended rho)
h = np.array([[0, v], [v, e]])
op = np.array([[0, 0], [0, 1]])
corr = Drude(lambda_0, omega_0, max_terms, beta)
heom = Hierachy([max_tier] * max_terms, h, op, corr)
phi = [1 / np.sqrt(2), 1 / np.sqrt(2)]
phi /= np.linalg.norm(phi)
rho_0 = np.tensordot(phi, phi, axes=0)
init_rho = heom.gen_extended_rho(rho_0)
print(init_rho.shape)
for n, term in enumerate(heom.diff()):
print('- Term {}:'.format(n))
for label, array in term:
print('Label: {}, shape: {}'.format(label, array.shape))
def _partial_product(array1, i, array2, j):
l1, l2 = array1.ndim, array2.ndim
ans = np.tensordot(array1, array2, axes=([i], [j]))
ans = np.moveaxis(ans, list(range(l1 - 1, l1 + l2 - 2)), list(range(i, i + l2 - 1)))
return ans
