# Copyright 2020, 2021 The NetKet Authors - All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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from typing import Callable, Union
from functools import partial
import jax
import jax.numpy as jnp
import netket as nk
from netket.driver.vmc_common import info
from netket.operator import AbstractOperator
from netket.optimizer import LinearOperator
from netket.optimizer.qgt import QGTAuto
from netket.vqs import VariationalState, VariationalMixedState, MCState, ExactState
from netket.experimental.dynamics import RKIntegratorConfig
from .tdvp_common import TDVPBaseDriver, odefun
class TDVP(TDVPBaseDriver):
"""
Variational time evolution based on the time-dependent variational principle which,
when used with Monte Carlo sampling via :class:`netket.vqs.MCState`, is the time-dependent VMC
(t-VMC) method.
.. note::
This TDVP Driver uses the time-integrators from the `nkx.dynamics` module, which are
automatically executed under a `jax.jit` context.
When running computations on GPU, this can lead to infinite hangs or extremely long
compilation times. In those cases, you might try setting the configuration variable
`nk.config.netket_experimental_disable_ode_jit = True` to mitigate those issues.
"""
[docs] def __init__(
self,
operator: AbstractOperator,
variational_state: VariationalState,
integrator: RKIntegratorConfig,
*,
t0: float = 0.0,
propagation_type="real",
qgt: LinearOperator = None,
linear_solver=nk.optimizer.solver.svd,
linear_solver_restart: bool = False,
error_norm: Union[str, Callable] = "euclidean",
):
r"""
Initializes the time evolution driver.
Args:
operator: The generator of the dynamics (Hamiltonian for pure states,
Lindbladian for density operators).
variational_state: The variational state.
integrator: Configuration of the algorithm used for solving the ODE.
t0: Initial time at the start of the time evolution.
propagation_type: Determines the equation of motion: "real" for the
real-time Schrödinger equation (SE), "imag" for the imaginary-time SE.
qgt: The QGT specification.
linear_solver: The solver for solving the linear system determining the time evolution.
This must be a jax-jittable function :code:`f(A,b) -> x` that accepts a Matrix-like, Linear Operator
PyTree object :math:`A` and a vector-like PyTree :math:`b` and returns the PyTree :math:`x` solving
the system :math:`Ax=b`.
Defaults to :func:`nk.optimizer.solver.svd` with the default svd threshold of 1e-10.
To change the svd threshold you can use :func:`functools.partial` as follows:
:code:`functools.partial(nk.optimizer.solver.svd, rcond=1e-4)`.
linear_solver_restart: If False (default), the last solution of the linear system
is used as initial value in subsequent steps.
error_norm: Norm function used to calculate the error with adaptive integrators.
Can be either "euclidean" for the standard L2 vector norm :math:`w^\dagger w`,
"maximum" for the maximum norm :math:`\max_i |w_i|`
or "qgt", in which case the scalar product induced by the QGT :math:`S` is used
to compute the norm :math:`\Vert w \Vert^2_S = w^\dagger S w` as suggested
in PRL 125, 100503 (2020).
Additionally, it possible to pass a custom function with signature
:code:`norm(x: PyTree) -> float`
which maps a PyTree of parameters :code:`x` to the corresponding norm.
Note that norm is used in jax.jit-compiled code.
"""
if qgt is None:
qgt = QGTAuto(solver=linear_solver)
self.propagation_type = propagation_type
if isinstance(variational_state, VariationalMixedState):
# assuming Lindblad Dynamics
# TODO: support density-matrix imaginary time evolution
if propagation_type == "real":
self._loss_grad_factor = 1.0
else:
raise ValueError(
"only real-time Lindblad evolution is supported for " "mixed states"
)
else:
if propagation_type == "real":
self._loss_grad_factor = -1.0j
elif propagation_type == "imag":
self._loss_grad_factor = -1.0
else:
raise ValueError("propagation_type must be one of 'real', 'imag'")
self.qgt = qgt
self.linear_solver = linear_solver
self.linear_solver_restart = linear_solver_restart
super().__init__(
operator, variational_state, integrator, t0=t0, error_norm=error_norm
)
[docs] def info(self, depth=0):
lines = [
"{}: {}".format(name, info(obj, depth=depth + 1))
for name, obj in [
("generator ", self._generator_repr),
("integrator ", self._integrator),
("linear solver ", self.linear_solver),
("state ", self.state),
]
]
return "\n{}".format(" " * 3 * (depth + 1)).join([str(self)] + lines)
@odefun.dispatch
def odefun_tdvp( # noqa: F811
state: Union[MCState, ExactState], driver: TDVP, t, w, *, stage=0
):
# pylint: disable=protected-access
state.parameters = w
state.reset()
op_t = driver.generator(t)
driver._loss_stats, driver._loss_forces = state.expect_and_forces(
op_t,
)
driver._loss_grad = _map_parameters(
driver._loss_forces,
state.parameters,
driver._loss_grad_factor,
driver.propagation_type,
type(state),
)
qgt = driver.qgt(driver.state)
if stage == 0: # TODO: This does not work with FSAL.
driver._last_qgt = qgt
initial_dw = None if driver.linear_solver_restart else driver._dw
driver._dw, _ = qgt.solve(driver.linear_solver, driver._loss_grad, x0=initial_dw)
# If parameters are real, then take only real part of the gradient (if it's complex)
driver._dw = jax.tree_map(
lambda x, target: (x if jnp.iscomplexobj(target) else x.real),
driver._dw,
state.parameters,
)
return driver._dw
@partial(jax.jit, static_argnums=(3, 4))
def _map_parameters(forces, parameters, loss_grad_factor, propagation_type, state_T):
forces = jax.tree_map(
lambda x, target: loss_grad_factor * x,
forces,
parameters,
)
forces = jax.tree_map(
lambda x, target: (x if jnp.iscomplexobj(target) else x.real),
forces,
parameters,
)
return forces
