def _update(graph, leaves, root, n_branch, prefix='A'):
subtree, r = huffman_tree(leaves, prefix=prefix)
try:
subtree[root] = subtree.pop(r)
graph.update(subtree)
except KeyError:
pass
return
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 _update(graph, leaves, root, n_branch, prefix='A'):
def obj_new(x=0):
x += 1
return str(prefix) + str(x)
subtree, r = huffman_tree(leaves, obj_new=obj_new)
try:
subtree[root] = subtree.pop(r)
graph.update(subtree)
except KeyError:
pass
return
def test_mctdh(fname=None):
sys_leaf = Leaf(name='sys0')
ph_leaves = []
for n, (omega, g) in enumerate(ph_parameters, 1):
ph_leaf = Leaf(name='ph{}'.format(n))
ph_leaves.append(ph_leaf)
def ph_spf():
t = Tensor(axis=0)
t.name = 'spf' + str(hex(id(t)))[-4:]
return t
graph, root = huffman_tree(ph_leaves, obj_new=ph_spf, n_branch=2)
try:
graph[root].insert(0, sys_leaf)
except KeyError:
ph_leaf = root
root = Tensor()
graph[root] = [sys_leaf, ph_leaf]
finally:
root.name = 'wfn'
root.axis = None
stack = [root]
while stack:
parent = stack.pop()
for child in graph[parent]:
parent.link_to(parent.order, child, 0)
if child in graph:
stack.append(child)
# Define the detailed parameters for the ML-MCTDH tree
h_list = model.wfn_h_list(sys_leaf, ph_leaves)
solver = MultiLayer(root, h_list)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if t.name.startswith('sys'):
bond_dict[(s, i, t, j)] = 2
else:
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = max_tier
else:
bond_dict[(s, i, t, j)] = rank_wfn
solver.autocomplete(bond_dict)
# set initial root array
init_proj = np.array([[A, 0.0], [B, 0.0]]) / np.sqrt(A**2 + B**2)
root_array = Tensor.partial_product(root.array, 0, init_proj, 1)
root.set_array(root_array)
solver = MultiLayer(root, h_list)
solver.ode_method = 'RK45'
solver.cmf_steps = solver.max_ode_steps # constant mean-field
solver.ps_method = 'split'
solver.svd_err = 1.0e-14
# Define the obersevable of interest
logger = Logger(filename=prefix + fname, level='info').logger
logger2 = Logger(filename=prefix + 'en_' + fname, level='info').logger
for n, (time, r) in enumerate(
solver.propagator(
steps=count,
ode_inter=dt_unit,
split=True,
)):
if n % callback_interval == 0:
t = Quantity(time).convert_to(unit='fs').value
rho = r.partial_env(0, proper=False)
logger.info("{} {} {} {} {}".format(t, rho[0, 0], rho[0, 1],
rho[1, 0], rho[1, 1]))
en = np.trace(rho @ model.h)
logger2.info('{} {}'.format(t, en))
def ml(fname,
e,
v,
primitive_dim,
spf_dim,
ph_parameters,
steps=2000,
ode_inter=0.1):
logger = Logger(filename=fname).logger
# define parameters
sys_hamiltonian = np.array([[e, v], [v, -e]], dtype=DTYPE)
projector = np.array([[1.0, 0.0], [0.0, -1.0]],
dtype=DTYPE) # S in H_SB = S x B
primitive_dim = primitive_dim
spf_dim = spf_dim
# Define all Leaf tensors and hamiltonian we need
h_list = []
sys_leaf = Leaf(name='sys0')
h_list.append([(sys_leaf, -1.0j * sys_hamiltonian)])
ph_parameters = ph_parameters
leaves = []
for n, (omega, g) in enumerate(ph_parameters, 1):
ph = Phonon(primitive_dim, omega)
ph_leaf = Leaf(name='ph{}'.format(n))
leaves.append(ph_leaf)
# hamiltonian ph part
h_list.append([(ph_leaf, -1.0j * ph.hamiltonian)])
# e-ph part
op = ph.annihilation_operator + ph.creation_operator
h_list.append([(ph_leaf, g * op), (sys_leaf, -1.0j * projector)])
def ph_spf():
t = Tensor(axis=0, normalized=True)
t.name = str(hex(id(t)))[-4:]
return t
graph, root = huffman_tree(leaves, obj_new=ph_spf, n_branch=2)
try:
graph[root].insert(0, sys_leaf)
except KeyError:
ph_leaf = root
root = Tensor()
graph[root] = [sys_leaf, ph_leaf]
finally:
root.name = 'wfn'
root.axis = None
root.normalized = True
stack = [root]
while stack:
parent = stack.pop()
for child in graph[parent]:
parent.link_to(parent.order, child, 0)
if child in graph:
stack.append(child)
logger.info(f"graph:{graph}")
# Define the detailed parameters for the ML-MCTDH tree
solver = MultiLayer(root, h_list)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if t.name and t.name.startswith('sys'):
bond_dict[(s, i, t, j)] = 2
else:
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = primitive_dim
else:
bond_dict[(s, i, t, j)] = spf_dim
solver.autocomplete(bond_dict)
logger.info(f"bond_dict:{bond_dict}")
# set initial root array
a, b = 1.0, 0
init_proj = np.array([[a, 0.0], [b, 0.0]]) / np.sqrt(a**2 + b**2)
root_array = Tensor.partial_product(root.array, 0, init_proj, 1)
root.set_array(root_array)
# Define the computation details
solver.ode_method = 'RK45'
solver.snd_order = False
solver.cmf_steps = 100
# Define the obersevable of interest
logger.info('''# time rho00 rho01 rho10 rho11''')
for time, _ in solver.propagator(
steps=steps,
ode_inter=ode_inter,
split=True,
):
t = time
for tensor in root.visitor(axis=None):
tensor.reset()
tensor.normalize(forced=True)
rho = root.partial_env(0, proper=False)
for tensor in root.visitor(axis=None):
tensor.reset()
flat_data = [t] + list(np.reshape(rho, -1))
logger.info('{} {} {} {} {}'.format(*flat_data))
def ml(dof, e, v, eta, cutoff, scale=5, loc=None, steps=2000, ode_inter=0.1):
f_ = 'dof{}-eta{}.log'.format(dof, eta)
logger = Logger(filename=f_).logger
# define parameters
e = Quantity(e, 'cm-1').value_in_au
v = Quantity(v, 'cm-1').value_in_au
eta = Quantity(eta, 'cm-1').value_in_au
omega0 = Quantity(cutoff, 'cm-1').value_in_au
sys_hamiltonian = np.array([[-e / 2.0, v], [v, e / 2.0]], dtype=DTYPE)
projector = np.array([[0.0, 0.0], [0.0, 1.0]],
dtype=DTYPE) # S in H_SB = S x B
primitive_dim = 100
spf_dim = 20
# Spectrum function
def spec_func(omega):
if 0 < omega < omega0:
return eta
else:
return 0.0
# Define all Leaf tensors and hamiltonian we need
h_list = []
sys_leaf = Leaf(name='sys0')
h_list.append([(sys_leaf, -1.0j * sys_hamiltonian)])
ph_parameters = linear_discretization(spec_func, omega0, dof)
if loc is not None:
adj_pair = (ph_parameters[loc][0], ph_parameters[loc][1] * scale)
ph_parameters[loc] = adj_pair
leaves = []
for n, (omega, g) in enumerate(ph_parameters, 1):
ph = Phonon(primitive_dim, omega)
ph_leaf = Leaf(name='ph{}'.format(n))
leaves.append(ph_leaf)
# hamiltonian ph part
h_list.append([(ph_leaf, -1.0j * ph.hamiltonian)])
# e-ph part
op = ph.annihilation_operator + ph.creation_operator
h_list.append([(ph_leaf, g * op), (sys_leaf, -1.0j * projector)])
def ph_spf(n=0):
n += 1
return Tensor(name='spf{}'.format(n), axis=0)
graph, root = huffman_tree(leaves, obj_new=ph_spf, n_branch=2)
try:
graph[root].insert(0, sys_leaf)
except KeyError:
ph_leaf = root
root = Tensor()
graph[root] = [sys_leaf, ph_leaf]
finally:
root.name = 'wfn'
root.axis = None
print(graph)
stack = [root]
while stack:
parent = stack.pop()
for child in graph[parent]:
parent.link_to(parent.order, child, 0)
if child in graph:
stack.append(child)
# Define the detailed parameters for the ML-MCTDH tree
solver = MultiLayer(root, h_list)
bond_dict = {}
# Leaves
for s, i, t, j in root.linkage_visitor():
if t.name.startswith('sys'):
bond_dict[(s, i, t, j)] = 2
else:
if isinstance(t, Leaf):
bond_dict[(s, i, t, j)] = primitive_dim
else:
bond_dict[(s, i, t, j)] = spf_dim
solver.autocomplete(bond_dict)
# set initial root array
a, b = 1.0, 1.0
init_proj = np.array([[a, 0.0], [b, 0.0]]) / np.sqrt(a**2 + b**2)
root_array = Tensor.partial_product(root.array, 0, init_proj, 1)
root.set_array(root_array)
# Define the computation details
solver.ode_method = 'RK45'
solver.snd_order = True
solver.cmf_steps = 1
root.is_normalized = True
# Define the obersevable of interest
logger.info('''# time/fs rho00 rho01 rho10 rho11''')
for time, _ in solver.propagator(
steps=steps,
ode_inter=Quantity(ode_inter, 'fs').value_in_au,
split=True,
):
t = Quantity(time).convert_to(unit='fs').value
for tensor in root.visitor(axis=None):
tensor.reset()
rho = root.partial_env(0, proper=False)
for tensor in root.visitor(axis=None):
tensor.reset()
flat_data = [t] + list(np.reshape(rho, -1))
logger.info('{} {} {} {} {}'.format(*flat_data))