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RROMPy/main/FenicsHSEngine.py
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FenicsHSEngine.py
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#!/usr/bin/python
import numpy as np
from matplotlib import pyplot as plt
import fenics as fen
class FenicsHSEngine:
"""
Fenics-based Hilbert space engine.
"""
def __init__(self, V:"Fenics FE space"):
self.V = V
def name(self) -> str:
"""Class label."""
return self.__class__.__name__
def norm(self, u:"numpy 1D array",
normType : "numpy 2D array, number or str" = "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 (FenicsHSEngine.norm(self, u, "H10")**2
+ (normType * FenicsHSEngine.norm(self, u, "L2"))**2)**.5
uRe = fen.Function(self.V)
uIm = fen.Function(self.V)
uRe.vector()[:] = np.array(np.real(u), dtype = float)
uIm.vector()[:] = np.array(np.imag(u), dtype = float)
return (fen.norm(uRe, normType)**2 + fen.norm(uIm, normType)**2)**.5
def plot(self, u:"numpy 1D array", name : str = "u", **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'.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
if 'figsize' not in figspecs.keys(): figspecs['figsize'] = (13, 3)
uRe = fen.Function(self.V)
uIm = fen.Function(self.V)
uRe.vector()[:] = np.array(np.real(u), dtype = float)
uIm.vector()[:] = np.array(np.imag(u), dtype = float)
uAbs = fen.project(np.power(np.power(uRe, 2) + np.power(uIm, 2),
.5), self.V)
uPhase = fen.project(fen.atan(np.divide(uIm, uRe)), self.V)
combined_data_ReIm = np.concatenate([np.real(u), np.imag(u)])
_min, _max = np.amin(combined_data_ReIm), np.amax(combined_data_ReIm)
plt.figure(**figspecs)
plt.jet()
plt.subplot(141)
p = fen.plot(uAbs, title = "|{0}|".format(name))
plt.colorbar(p)
plt.subplot(142)
p = fen.plot(uPhase, title = "phase({0})".format(name))
plt.colorbar(p)
plt.subplot(143)
p = fen.plot(uRe, title = "Re({0})".format(name),
vmin = _min, vmax = _max)
plt.colorbar(p)
plt.subplot(144)
p = fen.plot(uIm, title = "Im({0})".format(name),
vmin = _min, vmax = _max)
plt.colorbar(p)
plt.tight_layout()
plt.show()
class FenicsHSAugmentedEngine(FenicsHSEngine):
"""
Fenics-based Hilbert space engine for augmented spaces.
"""
def __init__(self, V:"Fenics FE space", d : int = 1):
self.d = d
FenicsHSEngine.__init__(self, V)
def getActualSize(self, u:"numpy 1D array"):
"""
Compute size of unaugmented vector batches.
Args:
u: numpy complex array with function dofs.
Returns:
Batch size.
"""
N = int(len(u) / self.d)
if not np.isclose(len(u), self.d * N):
raise Exception(("Input vector lenght must be multiple of"
"augmentation dimension d."))
return N
def norm(self, u:"numpy 1D array",
normType : "numpy 2D array, number or str" = "H10")\
-> "numpy 1D array":
"""
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:
Norms of the function (non-negative).
"""
N = self.getActualSize(u)
if isinstance(normType, (int, float)):
norms = [None] * self.d
for j in range(self.d):
uj = u[j * N : (j + 1) * N]
norms[j] = FenicsHSEngine.norm(self, uj, normType)
return norms
else:
if (type(normType).__name__[-6:] == "matrix"
and normType.shape[0] % N == 0):
N = normType.shape[0]
else:
raise Exception("Energy matrix dimension mismatch.")
return FenicsHSEngine.norm(self, u[: N], normType)
def plot(self, u:"numpy 1D array", name : str = "u", **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'.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
if 'figsize' not in figspecs.keys(): figspecs['figsize'] = (13, 3)
N = self.getActualSize(u)
for j in range(self.d):
uj = u[j * N : (j + 1) * N]
uRe = fen.Function(self.V)
uIm = fen.Function(self.V)
uRe.vector()[:] = np.array(np.real(uj), dtype = float)
uIm.vector()[:] = np.array(np.imag(uj), dtype = float)
uAbs = fen.project(np.power(np.power(uRe, 2) + np.power(uIm, 2),
.5), self.V)
uPhase = fen.project(fen.atan(np.divide(uIm, uRe)), self.V)
combined_data_ReIm = np.concatenate([np.real(uj), np.imag(uj)])
_min = np.amin(combined_data_ReIm)
_max = np.amax(combined_data_ReIm)
plt.figure(**figspecs)
plt.jet()
plt.subplot(141)
p = fen.plot(uAbs, title = "|{0}|, comp. {1}".format(name, j))
plt.colorbar(p)
plt.subplot(142)
p = fen.plot(uPhase,
title = "phase({0}, comp. {1})".format(name, j))
plt.colorbar(p)
plt.subplot(143)
p = fen.plot(uRe, title = "Re({0}, comp. {1})".format(name, j),
vmin = _min, vmax = _max)
plt.colorbar(p)
plt.subplot(144)
p = fen.plot(uIm, title = "Im({0}, comp. {1})".format(name, j),
vmin = _min, vmax = _max)
plt.colorbar(p)
plt.tight_layout()
plt.show()
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