#
# This file is part of TransportMaps.
#
# TransportMaps is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# TransportMaps is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with TransportMaps. If not, see <http://www.gnu.org/licenses/>.
#
# Transport Maps Library
# Copyright (C) 2015-2018 Massachusetts Institute of Technology
# Uncertainty Quantification group
# Department of Aeronautics and Astronautics
#
# Authors: Transport Map Team
# Website: transportmaps.mit.edu
# Support: transportmaps.mit.edu/qa/
#
import numpy as np
from TransportMaps.Maps import Map
from TransportMaps.Misc import counted
__all__ = [
'DiscretizedAutonomousODEsMap',
'AutonomousForwardEulerMap',
]
[docs]class DiscretizedAutonomousODEsMap( Map ):
r""" Defines the map of discretized system of autonomous ODEs.
Evaluates the map
.. math::
{\bf u}_n \mapsto {\bf u}_{n+1}
that takes the state :math:`{\bf u}_n` at time :math:`t`
into the state :math:`{\bf u}_{n+1}` at time :math:`t+\Delta t`,
thorugh the discretization of the ODE
.. math::
\dot{\bf u} = f({\bf u}) \;.
.. document private functions
.. automethod:: __init__
"""
[docs] def __init__(
self,
dt,
rhs,
):
r"""
Args:
dt (float): time step :math:`\Delta t`
rhs (:class:`Map<TransportMaps.Maps.Map>`): the
:math:`d` dimensional map :math:`f`.
"""
self._dt = dt
self._rhs = rhs
super(DiscretizedAutonomousODEsMap, self).__init__(
dim_in = self._rhs.dim,
dim_out = self._rhs.dim)
@property
[docs] def dt(self):
return self._dt
@property
[docs] def rhs(self):
return self._rhs
@counted
[docs] def evaluate(
self,
u,
*args,
**kwargs
):
raise NotImplementedError("To be implemented in sub-classes.")
@counted
[docs] def grad_x(
self,
u,
*args,
**kwargs
):
raise NotImplementedError("To be implemented in sub-classes.")
@counted
[docs] def tuple_grad_x(
self,
u,
*args,
**kwargs
):
raise NotImplementedError("To be implemented in sub-classes.")
@counted
[docs] def hess_x(
self,
u,
*args,
**kwargs
):
raise NotImplementedError("To be implemented in sub-classes.")
@counted
[docs] def action_hess_x(
self,
u,
du,
*args,
**kwargs
):
raise NotImplementedError("To be implemented in sub-classes.")
[docs]class AutonomousForwardEulerMap( DiscretizedAutonomousODEsMap ):
r""" Defines the map of a forward Euler discretized system of autonomous ODEs.
Evaluates the Euler step:
.. math::
{\bf u}_{n+1} = {\bf u}_n + \Delta t \cdot f({\bf u}_n)
where :math:`f:\mathbb{R}^d \rightarrow \mathbb{R}^d`
is the right hand side of the ODE system.
.. document private functions
.. automethod:: __init__
"""
[docs] def __init__(
self,
dt,
rhs,
):
r"""
Args:
dt (float): time step :math:`\Delta t`
rhs (:class:`Map<TransportMaps.Maps.Map>`): the
:math:`d` dimensional map :math:`f`.
"""
super(AutonomousForwardEulerMap, self).__init__(dt, rhs)
@counted
[docs] def evaluate(
self,
u,
*args,
**kwargs
):
return u + self._dt * self._rhs.evaluate(u, *args, **kwargs)
@counted
[docs] def grad_x(
self,
u,
*args,
**kwargs
):
m = u.shape[0]
out = np.zeros( (m, self.dim, self.dim) )
out_diag = np.einsum('...ii->...i', out)
out_diag[:,:] = 1.
return out + self._dt * self._rhs.grad_x(u, *args, **kwargs)
@counted
[docs] def tuple_grad_x(
self,
u,
*args,
**kwargs
):
m = u.shape[0]
(rhs, gx_rhs) = self._rhs.tuple_grad_x(u, *args, **kwargs)
f = u + self._dt * rhs
gx = np.zeros( (m, self.dim, self.dim) )
gx_diag = np.einsum('...ii->...i', gx)
gx_diag[:,:] = 1.
gx += self._dt * gx_rhs
return (f, gx)
@counted
[docs] def hess_x(
self,
u,
*args,
**kwargs
):
return self._dt * self._rhs.hess_x( u, *args, **kwargs )
@counted
[docs] def action_hess_x(
self,
u,
du,
*args,
**kwargs
):
return self._dt * self._rhs.action_hess_x( u, du, *args, **kwargs )