def test_delta(fname=None):
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
# Define the obersevable of interest
logger = Logger(filename=fname, level='info').logger
for n, (time, r) in enumerate(
solver.propagator(
steps=count,
ode_inter=dt_unit,
#split=False,
)):
if n % callback_interval == 0:
rho = np.reshape(r.array, (-1, 4))
logger.info("{} {} {} {} {}".format(time, rho[0, 0], rho[0, 1],
rho[0, 2], rho[0, 3]))
return
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)
solver = MultiLayer(root, h_list)
solver.ode_method = 'RK45'
solver.cmf_steps = solver.max_ode_steps # use constant mean-field
solver.ps_method = 'split'
#solver.svd_err = 1.0e-10
# 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,
)):
# renormalized by the trace of rho
norm = np.trace(np.reshape(np.reshape(r.array, (4, -1))[:, 0], (2, 2)))
r.set_array(r.array / norm)
if n % callback_interval == 0:
t = Quantity(time).convert_to(unit='fs').value
rho = np.reshape(r.array, (4, -1))[:, 0]
logger.info("{} {} {} {} {}".format(t, rho[0], rho[1], rho[2],
rho[3]))
en = np.trace(np.reshape(rho, (2, 2)) @ model.h)
logger2.info('{} {}'.format(t, en))
return
def test_simple(fname=None):
# Type settings
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
#solver = ProjectorSplitting(root, all_terms)
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
# Define the obersevable of interest
logger = Logger(filename=fname, level='info').logger
for n, (time, r) in enumerate(solver.propagator(
steps=count,
ode_inter=dt_unit,
)):
try:
if n % callback_interval == 0:
rho = np.reshape(r.array, (-1, 4))[0]
logger.info("{} {} {} {} {}".format(time, rho[0], rho[1], rho[2], rho[3]))
except:
break
return
def test_train(fname=None):
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt TT
tensor_train = tensor_train_template(rho_0, n_dims)
root = tensor_train[0]
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
#solver = ProjectorSplitting(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
solver.ps_method = 'split-unite'
projector = np.zeros((max_tier, 1))
projector[0] = 1.0
logger = Logger(filename=fname, level='info').logger
for n, (time, _) in enumerate(
solver.propagator(steps=count, ode_inter=dt_unit, split=False)):
if n % callback_interval == 0:
head = root.array
for t in tensor_train[1:]:
spf = Tensor.partial_product(t.array, 1, projector, 0)
head = Tensor.partial_product(head, head.ndim - 1, spf, 0)
rho = np.reshape(head, (4, -1))[:, 0]
logger.info("{} {} {} {} {}".format(time, rho[0], rho[1], rho[2],
rho[3]))
return
def test_train(fname=None):
# HEOM metas
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# 2-site TT
tensor_train = tensor_train_template(rho_0, n_dims, rank=1)
root = tensor_train[0]
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = MultiLayer(root, all_terms)
solver.ode_method = 'RK45'
solver.snd_order = False
solver.svd_err = 1.e-8
solver.svd_rank = max_tier
solver.ps_method = 'unite'
projector = np.zeros((max_tier, 1))
projector[0] = 1.0
logger = Logger(filename=fname, level='info').logger
logger2 = Logger(filename=fname + '_norm', level='info').logger
for n, (time, _) in enumerate(solver.propagator(steps=count, ode_inter=dt_unit, split=True)):
#print('n = {}: '.format(n))
#for t in tensor_train:
# print('{}: {}'.format(t, t.shape))
if n % callback_interval == 0:
head = root.array
for t in tensor_train[1:]:
spf = Tensor.partial_product(t.array, 1, projector, 0)
head = Tensor.partial_product(head, head.ndim - 1, spf, 0)
rho = np.reshape(head, (4, -1))[:, 0]
logger2.warning("{} {}".format(time, rho[0] + rho[3]))
logger.info("{} {} {} {} {}".format(time, rho[0], rho[1], rho[2], rho[3]))
return
def test_drude(fname=None):
# Type settings
corr = Correlation(k_max=max_terms)
corr.symm_coeff = np.diag(corr_dict['s'].toarray())
corr.asymm_coeff = np.diag(corr_dict['a'].toarray())
corr.exp_coeff = np.diag(corr_dict['gamma'].toarray())
corr.delta_coeff = 0.0 # delta_coeff
corr.print()
n_dims = [max_tier] * max_terms
heom = Hierachy(n_dims, H, V, corr)
# Adopt MCTDH
root = simple_heom(rho_0, n_dims)
leaves_dict = {leaf.name: leaf for leaf in root.leaves()}
all_terms = []
for term in heom.diff():
all_terms.append([(leaves_dict[str(fst)], snd) for fst, snd in term])
solver = ProjectorSplitting(root, all_terms)
solver.ode_method = 'DOP853'
solver.snd_order = False
solver.atol = 1.e-7
solver.rtol = 1.e-7
# Define the obersevable of interest
logger = Logger(filename=fname, level='info').logger
for n, (time, r) in enumerate(solver.propagator(
steps=count,
ode_inter=dt_unit,
)):
if n % callback_interval == 0:
rho = np.reshape(r.array, (-1, 4))
logger.info("{} {} {} {} {}".format(time, rho[0, 0], rho[0, 1], rho[0, 2], rho[0, 3]))
print("Time: {}; Tr rho_0: {}".format(time, rho[0, 0] + rho[0, -1]))
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))