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RROMPy/rrompy/hsengines/fenics/hsengine.py
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hsengine.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy 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.
#
# RROMPy 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 RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import numpy as np
from matplotlib import pyplot as plt
import fenics as fen
from rrompy.utilities.base.types import Np1D, strLst, FenSpace, N2FSExpr
from rrompy.utilities.base import purgeList, getNewFilename
__all__ = ['HSEngine']
class HSEngine:
"""
Fenics-based Hilbert space engine.
"""
def __init__(self, V:FenSpace):
self.V = V
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def norm(self, u:Np1D, normType : N2FSExpr = "H10") -> float:
"""
Compute general norm of complex-valued function with given dofs.
Args:
u: numpy complex array with function dofs.
normType(optional): Target norm identifier. If matrix, target norm
is one induced by normType. If number, target norm is weighted
H^1 norm with given weight. If string, must be recognizable by
Fenics norm command. Defaults to 'H10'.
Returns:
Norm of the function (non-negative).
"""
if type(normType).__name__[-6:] == "matrix":
return np.abs(u.dot(normType.dot(u).conj())) ** .5
if isinstance(normType, (int, float)):
return ( HSEngine.norm(self, u, "H10")**2
+ (normType * HSEngine.norm(self, u, "L2"))**2)**.5
uAbs = fen.Function(self.V)
uAbs.vector()[:] = np.array(np.abs(u), dtype = float)
return fen.norm(uAbs, normType)
def plot(self, u:Np1D, name : str = "u", save : bool = False,
what : strLst = 'all', **figspecs):
"""
Do some nice plots of the complex-valued function with given dofs.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
save(optional): Whether to save plot(s). Defaults to False.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
if isinstance(what, (str,)):
if what.upper() == 'ALL':
what = ['ABS', 'PHASE', 'REAL', 'IMAG']
else:
what = [what]
what = purgeList(what, ['ABS', 'PHASE', 'REAL', 'IMAG'],
listname = self.name() + ".what", baselevel = 1)
if len(what) == 0: return
if 'figsize' not in figspecs.keys():
figspecs['figsize'] = (13. * len(what) / 4, 3)
subplotcode = 100 + len(what) * 10
if 'REAL' in what and 'IMAG' in what:
combined_data_ReIm = np.concatenate([np.real(u), np.imag(u)])
_min = np.amin(combined_data_ReIm)
_max = np.amax(combined_data_ReIm)
pars = {'vmin' : _min, 'vmax' : _max}
else:
pars = {}
plt.figure(**figspecs)
plt.jet()
if 'ABS' in what:
uAb = fen.Function(self.V)
uAb.vector()[:] = np.array(np.abs(u), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uAb, title = "|{0}|".format(name))
plt.colorbar(p)
if 'PHASE' in what:
uPh = fen.Function(self.V)
uPh.vector()[:] = np.array(np.angle(u), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uPh, title = "phase({0})".format(name))
plt.colorbar(p)
if 'REAL' in what:
uRe = fen.Function(self.V)
uRe.vector()[:] = np.array(np.real(u), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uRe, title = "Re({0})".format(name), **pars)
plt.colorbar(p)
if 'IMAG' in what:
uIm = fen.Function(self.V)
uIm.vector()[:] = np.array(np.imag(u), dtype = float)
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uIm, title = "Im({0})".format(name), **pars)
plt.colorbar(p)
if save:
plt.savefig(getNewFilename("fig", "eps"), format='eps', dpi=1000)
plt.show()
plt.close()
def plotmesh(self, name : str = "Mesh", save : bool = False, **figspecs):
"""
Do a nice plot of the mesh.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Whether to save plot(s). Defaults to False.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
plt.figure(**figspecs)
fen.plot(self.V.mesh())
if save:
plt.savefig(getNewFilename("msh", "eps"), format='eps', dpi=1000)
plt.show()
plt.close()
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