# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program 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 this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or initial
# documentation
# :author: Syver Doving Agdestein
# OTHER AUTHORS - MACROSCOPIC CHANGES
r"""
Burgers dataset
===============
This :class:`.Dataset` contains solutions to the Burgers' equation with
periodic boundary conditions on the interval :math:`[0, 2\pi]` for different
time steps:
.. math::
u_t + u u_x = \nu u_{xx},
An analytical expression can be obtained for the solution, using the Cole-Hopf
transform:
.. math::
u(t, x) = - 2 \nu \frac{\phi'}{\phi},
where :math:`\phi` is solution to the heat equation
:math:`\phi_t = \nu \phi_{xx}`.
This :class:`.Dataset` is based on a full-factorial
design of experiments. Each sample corresponds to a given time step :math:`t`,
while each feature corresponds to a given spatial point :math:`x`.
`More information about Burgers' equation
<https://en.wikipedia.org/wiki/Burgers%27_equation>`_
"""
from __future__ import absolute_import, division, unicode_literals
from future import standard_library
from numpy import exp, hstack, linspace, pi, square
from gemseo.core.dataset import Dataset
standard_library.install_aliases()
[docs]class BurgersDataset(Dataset):
""" Burgers dataset parametrization. """
def __init__(
self,
name="Burgers",
by_group=True,
n_samples=30,
n_x=501,
fluid_viscosity=0.1,
categorize=True,
):
"""Constructor.
:param str name: name of the dataset.
:param bool by_group: if True, store the data by group. Otherwise,
store them by variables. Default: True.
:param int n_samples: number of samples. Default: 30.
:param int n_x: number of spatial points. Default: 501.
:param float fluid_viscosity: fluid viscosity. Default: 0.1.
:param bool categorize: distinguish between the different groups of
variables. Default: True.
:parma bool opt_naming: use an optimization naming. Default: True.
"""
super(BurgersDataset, self).__init__(name, by_group)
time = linspace(0, 2, n_samples)[:, None]
space = linspace(0, 2 * pi, n_x)[None, :]
visc = fluid_viscosity
alpha = space - 4 * time
alpha_2 = square(alpha)
beta = 4 * visc * (time + 1)
gamma = space - 4 * time - 2 * pi
gamma_2 = square(gamma)
phi = exp(-alpha_2 / beta) + exp(-gamma_2 / beta)
phi_deriv = -2 * alpha / beta * exp(-alpha_2 / beta)
phi_deriv -= 2 * gamma / beta * exp(-gamma_2 / (beta))
u_t = -2 * visc / phi * phi_deriv
if categorize:
groups = {"t": Dataset.INPUT_GROUP, "u_t": Dataset.OUTPUT_GROUP}
else:
groups = None
data = hstack([time, u_t])
self.set_from_array(data, ["t", "u_t"], {"t": 1, "u_t": n_x}, groups=groups)
self.set_metadata("x", [[node] for node in space[0]])
self.set_metadata("nu", visc)