diff --git a/rrompy/hfengines/base/matrix_engine_base.py b/rrompy/hfengines/base/matrix_engine_base.py
index 9767fc7..d90e526 100644
--- a/rrompy/hfengines/base/matrix_engine_base.py
+++ b/rrompy/hfengines/base/matrix_engine_base.py
@@ -1,570 +1,553 @@
# 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 .
#
from abc import abstractmethod
import numpy as np
import scipy.sparse as scsp
from matplotlib import pyplot as plt
from copy import deepcopy as copy, copy as softcopy
from rrompy.utilities.base.types import (Np1D, Np2D, ScOp, strLst, Tuple, List,
DictAny, paramVal, paramList,
sampList)
-from rrompy.utilities.base import (purgeList, getNewFilename, verbosityDepth,
- multibinom)
+from rrompy.utilities.base import (purgeList, getNewFilename,
+ verbosityManager as vbMng, multibinom)
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameter, checkParameterList
from rrompy.sampling import sampleList, emptySampleList
from rrompy.solver import setupSolver, Np2DLikeEye
from rrompy.solver.scipy import tensorizeLS, detensorizeLS
__all__ = ['MatrixEngineBase']
class MatrixEngineBase:
"""
Generic solver for parametric matrix problems.
Attributes:
verbosity: Verbosity level.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product.
energyNormDualMatrix: Scipy sparse matrix representing dual inner
product.
dualityMatrix: Scipy sparse matrix representing duality.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product without duality.
"""
_solveBatchSize = 1
def __init__(self, verbosity : int = 10, timestamp : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
self.nAs, self.nbs = 1, 1
self.setSolver("SPSOLVE", {"use_umfpack" : False})
self.npar = 0
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def __dir_base__(self):
return [x for x in self.__dir__() if x[:2] != "__"]
def __deepcopy__(self, memo):
return softcopy(self)
@property
def npar(self):
"""Value of npar."""
return self._npar
@npar.setter
def npar(self, npar):
nparOld = self._npar if hasattr(self, "_npar") else -1
if npar != nparOld:
self.rescalingExp = [1.] * npar
self._npar = npar
@property
def nAs(self):
"""Value of nAs."""
return self._nAs
@nAs.setter
def nAs(self, nAs):
self._nAs = nAs
self.resetAs()
@property
def nbs(self):
"""Value of nbs."""
return self._nbs
@nbs.setter
def nbs(self, nbs):
self._nbs = nbs
self.resetbs()
@property
def nbsH(self) -> int:
return max(self.nbs, self.nAs)
def spacedim(self):
return self.As[0].shape[1]
def checkParameter(self, mu:paramList):
return checkParameter(mu, self.npar)
def checkParameterList(self, mu:paramList):
return checkParameterList(mu, self.npar)
def buildEnergyNormForm(self): # eye
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy matrix.", 20)
self.energyNormMatrix = Np2DLikeEye()
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildEnergyNormDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product.
"""
if not hasattr(self, "energyNormMatrix"):
self.buildEnergyNormForm()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy dual matrix.", 20)
self.energyNormDualMatrix = self.energyNormMatrix
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy dual matrix.", 20)
def buildDualityPairingForm(self):
"""Build sparse matrix (in CSR format) representative of duality."""
if not hasattr(self, "energyNormMatrix"):
self.buildEnergyNormForm()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling duality matrix.", 20)
self.dualityMatrix = self.energyNormMatrix
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling duality matrix.", 20)
def buildEnergyNormPartialDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product without duality.
"""
if not hasattr(self, "energyNormDualMatrix"):
self.buildEnergyNormDualForm()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy partial dual matrix.", 20)
self.energyNormPartialDualMatrix = self.energyNormDualMatrix
- if self.verbosity >= 20:
- verbosityDepth("DEL",
- "Done assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy partial dual matrix.", 20)
def innerProduct(self, u:Np2D, v:Np2D, onlyDiag : bool = False,
dual : bool = False, duality : bool = True) -> Np2D:
"""Scalar product."""
if dual:
if duality:
if not hasattr(self, "energyNormDualMatrix"):
self.buildEnergyNormDualForm()
energyMat = self.energyNormDualMatrix
else:
if not hasattr(self, "energyNormPartialDualMatrix"):
self.buildEnergyNormPartialDualForm()
energyMat = self.energyNormPartialDualMatrix
else:
if not hasattr(self, "energyNormMatrix"):
self.buildEnergyNormForm()
energyMat = self.energyNormMatrix
if not isinstance(u, (np.ndarray,)): u = u.data
if not isinstance(v, (np.ndarray,)): v = v.data
if onlyDiag:
return np.sum(energyMat.dot(u) * v.conj(), axis = 0)
return v.T.conj().dot(energyMat.dot(u))
def norm(self, u:Np2D, dual : bool = False, duality : bool = True) -> Np1D:
return np.abs(self.innerProduct(u, u, onlyDiag = True, dual = dual,
duality = duality)) ** .5
def checkAInBounds(self, derI : int = 0):
"""Check if derivative index is oob for operator of linear system."""
if derI < 0 or derI >= self.nAs:
d = self.spacedim()
return scsp.csr_matrix((np.zeros(0), np.zeros(0), np.zeros(d + 1)),
shape = (d, d), dtype = np.complex)
def checkbInBounds(self, derI : int = 0, homogeneized : bool = False):
"""Check if derivative index is oob for RHS of linear system."""
nbs = self.nbsH if homogeneized else self.nbs
if derI < 0 or derI >= nbs:
return np.zeros(self.spacedim(), dtype = np.complex)
def resetAs(self):
"""Reset (derivatives of) operator of linear system."""
self.setAs([None] * self.nAs)
if hasattr(self, "_nbs"): self.resetbsH()
def resetbs(self):
"""Reset (derivatives of) RHS of linear system."""
self.setbs([None] * self.nbs)
if hasattr(self, "_nAs"): self.resetbsH()
def resetbsH(self):
"""Reset (derivatives of) homogeneized RHS of linear system."""
self.setbsH([None] * self.nbsH)
def setAs(self, As:List[Np2D]):
"""Assign terms of operator of linear system."""
if len(As) != self.nAs:
raise RROMPyException(("Expected number {} of terms of As not "
"matching given list length {}.").format(self.nAs,
len(As)))
self.As = [copy(A) for A in As]
def setbs(self, bs:List[Np1D]):
"""Assign terms of RHS of linear system."""
if len(bs) != self.nbs:
raise RROMPyException(("Expected number {} of terms of bs not "
"matching given list length {}.").format(self.nbs,
len(bs)))
self.bs = [copy(b) for b in bs]
def setbsH(self, bsH:List[Np1D]):
"""Assign terms of homogeneized RHS of linear system."""
if len(bsH) != self.nbsH:
raise RROMPyException(("Expected number {} of terms of bsH not "
"matching given list length {}.").format(self.nbsH,
len(bsH)))
self.bsH = [copy(bH) for bH in bsH]
def _assembleA(self, mu : paramVal = [], der : List[int] = 0,
derI : int = None, muBase : paramVal = None) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if muBase is None: muBase = [0.] * self.npar
muBase = self.checkParameter(muBase)
if self.npar > 0: mu, muBase = mu[0], muBase[0]
if not hasattr(der, "__len__"): der = [der] * self.npar
if derI is None: derI = hashD(der)
Anull = self.checkAInBounds(derI)
if Anull is not None: return Anull
rExp = self.rescalingExp
A = copy(self.As[derI])
for j in range(derI + 1, self.nAs):
derIdx = hashI(j, self.npar)
diffIdx = [x - y for (x, y) in zip(derIdx, der)]
if np.all([x >= 0 for x in diffIdx]):
A = A + (np.prod((mu ** rExp - muBase ** rExp) ** diffIdx)
* multibinom(derIdx, diffIdx) * self.As[j])
return A
@abstractmethod
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""
Assemble terms of operator of linear system and return it (or its
derivative) at a given parameter.
"""
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
for j in range(derI, self.nAs):
if self.As[j] is None: self.As[j] = self.checkAInBounds(-1)
return self._assembleA(mu, der, derI)
def affineLinearSystemA(self, mu : paramVal = []) -> List[Np2D]:
"""
Assemble affine blocks of operator of linear system (just linear
blocks).
"""
As = [None] * self.nAs
for j in range(self.nAs):
As[j] = self.A(mu, hashI(j, self.npar))
return As
def affineWeightsA(self, mu : paramVal = []) -> List[str]:
"""
Assemble affine blocks of operator of linear system (just affine
weights). Stored as strings for the sake of pickling.
"""
mu = self.checkParameter(mu)
lambdasA = ["1."]
mu0Eff = mu ** self.rescalingExp
for j in range(1, self.nAs):
lambdasA += ["np.prod((mu ** ({1}) - [{0}]) ** ({2}))".format(
','.join([str(x) for x in mu0Eff[0]]),
self.rescalingExp, hashI(j, self.npar))]
return lambdasA
def affineBlocksA(self, mu : paramVal = [])\
-> Tuple[List[Np2D], List[str]]:
"""Assemble affine blocks of operator of linear system."""
return self.affineLinearSystemA(mu), self.affineWeightsA(mu)
def _assembleb(self, mu : paramVal = [], der : List[int] = 0,
derI : int = None, homogeneized : bool = False,
muBase : paramVal = None) -> ScOp:
"""Assemble (derivative of) (homogeneized) RHS of linear system."""
mu = self.checkParameter(mu)
if muBase is None: muBase = [0.] * self.npar
muBase = self.checkParameter(muBase)
if self.npar > 0: mu, muBase = mu[0], muBase[0]
if not hasattr(der, "__len__"): der = [der] * self.npar
if derI is None: derI = hashD(der)
bnull = self.checkbInBounds(derI, homogeneized)
if bnull is not None: return bnull
bs = self.bsH if homogeneized else self.bs
rExp = self.rescalingExp
b = copy(bs[derI])
for j in range(derI + 1, len(bs)):
derIdx = hashI(j, self.npar)
diffIdx = [x - y for (x, y) in zip(derIdx, der)]
if np.all([x >= 0 for x in diffIdx]):
b = b + (np.prod((mu ** rExp - muBase ** rExp) ** diffIdx)
* multibinom(derIdx, diffIdx) * bs[j])
return b
@abstractmethod
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""
Assemble terms of (homogeneized) RHS of linear system and return it (or
its derivative) at a given parameter.
"""
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if homogeneized:
for j in range(derI, self.nbsH):
if self.bsH[j] is None: self.bsH[j] = self.checkbInBounds(-1)
else:
for j in range(derI, self.nbs):
if self.bs[j] is None: self.bs[j] = self.checkbInBounds(-1)
return self._assembleb(mu, der, derI, homogeneized)
def affineLinearSystemb(self, mu : paramVal = [],
homogeneized : bool = False) -> List[Np1D]:
"""
Assemble affine blocks of RHS of linear system (just linear blocks).
"""
nbs = self.nbsH if homogeneized else self.nbs
bs = [None] * nbs
for j in range(nbs):
bs[j] = self.b(mu, hashI(j, self.npar), homogeneized)
return bs
def affineWeightsb(self, mu : paramVal = [],
homogeneized : bool = False) -> List[str]:
"""
Assemble affine blocks of RHS of linear system (just affine weights).
Stored as strings for the sake of pickling.
"""
mu = self.checkParameter(mu)
nbs = self.nbsH if homogeneized else self.nbs
lambdasb = ["1."]
mu0Eff = mu ** self.rescalingExp
for j in range(1, nbs):
lambdasb += ["np.prod((mu ** ({1}) - [{0}]) ** ({2}))".format(
','.join([str(x) for x in mu0Eff[0]]),
self.rescalingExp, hashI(j, self.npar))]
return lambdasb
def affineBlocksb(self, mu : paramVal = [], homogeneized : bool = False)\
-> Tuple[List[Np1D], List[str]]:
"""Assemble affine blocks of RHS of linear system."""
return (self.affineLinearSystemb(mu, homogeneized),
self.affineWeightsb(mu, homogeneized))
def setSolver(self, solverType:str, solverArgs : DictAny = {}):
"""Choose solver type and parameters."""
self._solver, self._solverArgs = setupSolver(solverType, solverArgs)
def solve(self, mu : paramList = [], RHS : sampList = None,
homogeneized : bool = False) -> sampList:
"""
Find solution of linear system.
Args:
mu: parameter value.
RHS: RHS of linear system. If None, defaults to that of parametric
system. Defaults to None.
"""
mu, _ = self.checkParameterList(mu)
if mu.shape[0] == 0: mu.reset((1, self.npar), mu.dtype)
sol = emptySampleList()
if len(mu) > 0:
if RHS is None:
RHS = [self.b(m, homogeneized = homogeneized) for m in mu]
RHS = sampleList(RHS)
mult = 0 if len(RHS) == 1 else 1
RROMPyAssert(mult * (len(mu) - 1) + 1, len(RHS), "Sample size")
u = self._solver(self.A(mu[0]), RHS[0], self._solverArgs)
sol.reset((len(u), len(mu)), dtype = u.dtype)
sol[0] = u
for j in range(1, len(mu), self._solveBatchSize):
if self._solveBatchSize != 1:
iRange = list(range(j, min(j + self._solveBatchSize,
len(mu))))
As = [self.A(mu[i]) for i in iRange]
bs = [RHS[mult * i] for i in iRange]
A, b = tensorizeLS(As, bs)
else:
A, b = self.A(mu[j]), RHS[mult * j]
solStack = self._solver(A, b, self._solverArgs)
if self._solveBatchSize != 1:
sol[iRange] = detensorizeLS(solStack, len(iRange))
else:
sol[j] = solStack
return sol
def residual(self, u:sampList, mu : paramList = [],
homogeneized : bool = False,
duality : bool = True) -> sampList:
"""
Find residual of linear system for given approximate solution.
Args:
u: numpy complex array with function dofs. If None, set to 0.
mu: parameter value.
"""
mu, _ = self.checkParameterList(mu)
if mu.shape[0] == 0: mu.reset((1, self.npar), mu.dtype)
if u is not None:
u = sampleList(u)
mult = 0 if len(u) == 1 else 1
RROMPyAssert(mult * (len(mu) - 1) + 1, len(u), "Sample size")
res = emptySampleList()
if duality and not hasattr(self, "dualityMatrix"):
self.buildDualityPairingForm()
for j in range(len(mu)):
b = self.b(mu[j], homogeneized = homogeneized)
if u is None:
r = b
else:
r = b - self.A(mu[j]).dot(u[mult * j])
if j == 0:
res.reset((len(r), len(mu)), dtype = r.dtype)
if duality:
r = self.dualityMatrix.dot(r)
res[j] = r
return res
def _rayleighQuotient(self, A:Np2D, v0:Np1D, M:Np2D, sigma : float = 0.,
nIterP : int = 10, nIterR : int = 10) -> float:
nIterP = min(nIterP, len(v0) // 2)
nIterR = min(nIterR, (len(v0) + 1) // 2)
v0 /= v0.T.conj().dot(M.dot(v0)) ** .5
for j in range(nIterP):
v0 = self._solver(A - sigma * M, M.dot(v0), self._solverArgs)
v0 /= v0.T.conj().dot(M.dot(v0)) ** .5
l0 = v0.T.conj().dot(A.dot(v0))
for j in range(nIterR):
v0 = self._solver(A - l0 * M, M.dot(v0), self._solverArgs)
v0 /= v0.T.conj().dot(M.dot(v0)) ** .5
l0 = v0.T.conj().dot(A.dot(v0))
if np.isnan(l0): l0 = np.finfo(float).eps
return np.abs(l0)
def stabilityFactor(self, u:sampList, mu : paramList = [],
nIterP : int = 10, nIterR : int = 10) -> sampList:
"""
Find stability factor of matrix of linear system using iterative
inverse power iteration- and Rayleigh quotient-based procedure.
Args:
u: numpy complex arrays with function dofs.
mu: parameter values.
nIterP: number of iterations of power method.
nIterR: number of iterations of Rayleigh quotient method.
"""
mu, _ = self.checkParameterList(mu)
if mu.shape[0] == 0: mu.reset((1, self.npar), mu.dtype)
u = sampleList(u)
mult = 0 if len(u) == 1 else 1
RROMPyAssert(mult * (len(mu) - 1) + 1, len(u), "Sample size")
stabFact = np.empty(len(mu), dtype = float)
if not hasattr(self, "energyNormMatrix"):
self.buildEnergyNormForm()
for j in range(len(mu)):
stabFact[j] = self._rayleighQuotient(self.A(mu[j]), u[mult * j],
self.energyNormMatrix,
0., nIterP, nIterR)
return stabFact
def plot(self, u:Np1D, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, pyplotArgs : dict = {},
**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'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
pyplotArgs(optional): Optional arguments for pyplot.
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
idxs = np.arange(self.spacedim())
plt.figure(**figspecs)
plt.jet()
if 'ABS' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.abs(u).flatten(), **pyplotArgs)
plt.title("|{0}|".format(name))
if 'PHASE' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.angle(u).flatten(), **pyplotArgs)
plt.title("phase({0})".format(name))
if 'REAL' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.real(u).flatten(), **pyplotArgs)
plt.title("Re({0})".format(name))
if 'IMAG' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.imag(u).flatten(), **pyplotArgs)
plt.title("Im({0})".format(name))
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_fig_".format(save), saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
diff --git a/rrompy/hfengines/base/problem_engine_base.py b/rrompy/hfengines/base/problem_engine_base.py
index 5a7c3fc..3c13438 100644
--- a/rrompy/hfengines/base/problem_engine_base.py
+++ b/rrompy/hfengines/base/problem_engine_base.py
@@ -1,373 +1,362 @@
# 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 .
#
from os import path, mkdir
import fenics as fen
import numpy as np
from matplotlib import pyplot as plt
from copy import deepcopy as copy
from rrompy.utilities.base.types import (Np1D, strLst, FenFunc, Tuple, List,
paramVal)
-from rrompy.utilities.base import purgeList, getNewFilename, verbosityDepth
+from rrompy.utilities.base import (purgeList, getNewFilename,
+ verbosityManager as vbMng)
from rrompy.solver import Np2DLikeEye
from rrompy.solver.fenics import L2NormMatrix, fenplot, interp_project
from .boundary_conditions import BoundaryConditions
from .matrix_engine_base import MatrixEngineBase
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['ProblemEngineBase']
class ProblemEngineBase(MatrixEngineBase):
"""
Generic solver for parametric problems.
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
"""
_dualityCompress = None
def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(verbosity = verbosity, timestamp = timestamp)
self.BCManager = BoundaryConditions("Dirichlet")
self.V = fen.FunctionSpace(fen.UnitSquareMesh(10, 10), "P", 1)
self.mu0BC = np.nan
self.degree_threshold = degree_threshold
self.npar = 0
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
self.resetAs()
self.resetbs()
if not type(V).__name__ == 'FunctionSpace':
raise RROMPyException("V type not recognized.")
self._V = V
self.u = fen.TrialFunction(V)
self.v = fen.TestFunction(V)
def spacedim(self):
return self.V.dim()
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy matrix.", 20)
self.energyNormMatrix = L2NormMatrix(self.V)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildDualityPairingForm(self):
"""Build sparse matrix (in CSR format) representative of duality."""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling duality matrix.", 20)
self.dualityMatrix = Np2DLikeEye()
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling duality matrix.", 20)
def liftDirichletData(self, mu : paramVal = []) -> Np1D:
"""Lift Dirichlet datum."""
mu = self.checkParameter(mu)
if mu != self.mu0BC:
self.mu0BC = copy(mu)
liftRe = interp_project(self.DirichletDatum[0], self.V)
liftIm = interp_project(self.DirichletDatum[1], self.V)
self.liftedDirichletDatum = (np.array(liftRe.vector())
+ 1.j * np.array(liftIm.vector()))
return self.liftedDirichletDatum
def reduceQuadratureDegree(self, fun:FenFunc, name:str):
"""Check whether to reduce compiler parameters to degree threshold."""
if not np.isinf(self.degree_threshold):
from ufl.algorithms.estimate_degrees import (
estimate_total_polynomial_degree as ETPD)
try:
deg = ETPD(fun)
except:
return False
if deg > self.degree_threshold:
- if self.verbosity >= 15:
- verbosityDepth("MAIN", ("Reducing quadrature degree from "
- "{} to {} for {}.").format(
- deg,
- self.degree_threshold,
- name),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Reducing quadrature degree from {} to {} for "
+ "{}.").format(deg, self.degree_threshold, name), 15)
return True
return False
def iterReduceQuadratureDegree(self, funsNames:List[Tuple[FenFunc, str]]):
"""
Iterate reduceQuadratureDegree over list and define reduce compiler
parameters.
"""
if funsNames is not None:
for fun, name in funsNames:
if self.reduceQuadratureDegree(fun, name):
return {"quadrature_degree" : self.degree_threshold}
return {}
def plot(self, u:Np1D, warping : List[callable] = None, name : str = "u",
save : str = None, what : strLst = 'all',
saveFormat : str = "eps", saveDPI : int = 100, show : bool = True,
fenplotArgs : dict = {}, **figspecs):
"""
Do some nice plots of the complex-valued function with given dofs.
Args:
u: numpy complex array with function dofs.
warping(optional): Domain warping functions.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
fenplotArgs(optional): Optional arguments for fenplot.
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
plt.figure(**figspecs)
plt.jet()
if 'ABS' in what:
uAb = fen.Function(self.V)
uAb.vector().set_local(np.abs(u))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fenplot(uAb, warping = warping, title = "|{0}|".format(name),
**fenplotArgs)
plt.colorbar(p)
if 'PHASE' in what:
uPh = fen.Function(self.V)
uPh.vector().set_local(np.angle(u))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fenplot(uPh, warping = warping,
title = "phase({0})".format(name), **fenplotArgs)
plt.colorbar(p)
if 'REAL' in what:
uRe = fen.Function(self.V)
uRe.vector().set_local(np.real(u))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fenplot(uRe, warping = warping, title = "Re({0})".format(name),
**fenplotArgs)
plt.colorbar(p)
if 'IMAG' in what:
uIm = fen.Function(self.V)
uIm.vector().set_local(np.imag(u))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fenplot(uIm, warping = warping, title = "Im({0})".format(name),
**fenplotArgs)
plt.colorbar(p)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_fig_".format(save), saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
def plotmesh(self, warping : List[callable] = None, name : str = "Mesh",
save : str = None, saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True,
fenplotArgs : dict = {}, **figspecs):
"""
Do a nice plot of the mesh.
Args:
u: numpy complex array with function dofs.
warping(optional): Domain warping functions.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
fenplotArgs(optional): Optional arguments for fenplot.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
plt.figure(**figspecs)
fenplot(self.V.mesh(), warping = warping, **fenplotArgs)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_msh_".format(save), saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
def outParaview(self, u:Np1D, warping : List[callable] = None,
name : str = "u", filename : str = "out",
time : float = 0., what : strLst = 'all',
forceNewFile : bool = True, folder : bool = False,
filePW = None):
"""
Output complex-valued function with given dofs to ParaView file.
Args:
u: numpy complex array with function dofs.
warping(optional): Domain warping functions.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
time(optional): Timestamp.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
folder(optional): Whether to create an additional folder layer.
filePW(optional): Fenics File entity (for time series).
"""
if isinstance(what, (str,)):
if what.upper() == 'ALL':
what = ['MESH', 'ABS', 'PHASE', 'REAL', 'IMAG']
else:
what = [what]
what = purgeList(what, ['MESH', 'ABS', 'PHASE', 'REAL', 'IMAG'],
listname = self.name() + ".what", baselevel = 1)
if len(what) == 0: return
if filePW is None:
if folder:
if not path.exists(filename + "/"):
mkdir(filename)
idxpath = filename.rfind("/")
filename += "/" + filename[idxpath + 1 :]
if forceNewFile:
filePW = fen.File(getNewFilename(filename, "pvd"))
else:
filePW = fen.File("{}.pvd".format(filename))
if warping is not None:
fen.ALE.move(self.V.mesh(),
interp_project(warping[0], self.V.mesh()))
if what == ['MESH']:
filePW << (self.V.mesh(), time)
if 'ABS' in what:
uAb = fen.Function(self.V, name = "{}_ABS".format(name))
uAb.vector().set_local(np.abs(u))
filePW << (uAb, time)
if 'PHASE' in what:
uPh = fen.Function(self.V, name = "{}_PHASE".format(name))
uPh.vector().set_local(np.angle(u))
filePW << (uPh, time)
if 'REAL' in what:
uRe = fen.Function(self.V, name = "{}_REAL".format(name))
uRe.vector().set_local(np.real(u))
filePW << (uRe, time)
if 'IMAG' in what:
uIm = fen.Function(self.V, name = "{}_IMAG".format(name))
uIm.vector().set_local(np.imag(u))
filePW << (uIm, time)
if warping is not None:
fen.ALE.move(self.V.mesh(),
interp_project(warping[1], self.V.mesh()))
return filePW
def outParaviewTimeDomain(self, u:Np1D, omega:float,
warping : List[callable] = None,
timeFinal : float = None,
periodResolution : int = 20, name : str = "u",
filename : str = "out",
forceNewFile : bool = True,
folder : bool = False):
"""
Output complex-valued function with given dofs to ParaView file,
converted to time domain.
Args:
u: numpy complex array with function dofs.
omega: frequency.
warping(optional): Domain warping functions.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
folder(optional): Whether to create an additional folder layer.
"""
if folder:
if not path.exists(filename + "/"):
mkdir(filename)
idxpath = filename.rfind("/")
filename += "/" + filename[idxpath + 1 :]
if forceNewFile:
filePW = fen.File(getNewFilename(filename, "pvd"))
else:
filePW = fen.File("{}.pvd".format(filename))
omega = np.abs(omega)
t = 0.
dt = 2. * np.pi / omega / periodResolution
if timeFinal is None: timeFinal = 2. * np.pi / omega - dt
if warping is not None:
fen.ALE.move(self.V.mesh(),
interp_project(warping[0], self.V.mesh()))
for j in range(int(np.ceil(timeFinal / dt)) + 1):
ut = fen.Function(self.V, name = name)
ut.vector().set_local(np.real(u) * np.cos(omega * t)
+ np.imag(u) * np.sin(omega * t))
filePW << (ut, t)
t += dt
if warping is not None:
fen.ALE.move(self.V.mesh(),
interp_project(warping[1], self.V.mesh()))
return filePW
diff --git a/rrompy/hfengines/linear_problem/bidimensional/cookie_engine_single.py b/rrompy/hfengines/linear_problem/bidimensional/cookie_engine_single.py
index 49e4acd..d24e1ca 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/cookie_engine_single.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/cookie_engine_single.py
@@ -1,137 +1,125 @@
# 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 .
#
import numpy as np
import fenics as fen
import ufl
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenONE, fenZERO
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['CookieEngineSingle']
class CookieEngineSingle(HelmholtzProblemEngine):
def __init__(self, kappa:float, theta:float, n:int, R : int = 1.,
L : int = 2., nX : int = 1, nY : int = 1,
mu0 : paramVal = [12. ** .5, 1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 5
self.npar = 2
self.rescalingExp = [2., 2.]
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(L * nX, L * nY),
n * nX, n * nY)
self.V = fen.FunctionSpace(mesh, "P", 1)
x, y = fen.SpatialCoordinate(mesh)[:]
cxs = np.linspace(0, L * nX, 2 * nX + 1)[1::2]
cys = np.linspace(0, L * nY, 2 * nY + 1)[1::2]
self.cookieIn = fenZERO
for cx in cxs:
for cy in cys:
self.cookieIn += ufl.conditional(
ufl.le((x-cx)**2. + (y-cy)**2., R**2.),
fenONE, fenZERO)
self.cookieOut = fenONE - self.cookieIn
c, s = np.cos(theta), np.sin(theta)
self.forcingTerm = [fen.cos(kappa * (c * x + s * y)),
fen.sin(kappa * (c * x + s * y))]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * self.cookieOut * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * self.cookieOut * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
self.As[2] = self.checkAInBounds(-1)
if derI <= 3 and self.As[3] is None:
self.As[3] = self.checkAInBounds(-1)
if derI <= 4 and self.As[4] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A4.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A4.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a4Re = - n2Re * self.cookieIn * fen.dot(self.u, self.v) * fen.dx
a4Im = - n2Im * self.cookieIn * fen.dot(self.u, self.v) * fen.dx
self.As[4] = (fenics2Sparse(a4Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a4Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py
index cf05c29..5bcd29e 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_domain_problem_engine.py
@@ -1,203 +1,184 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import (ScOp, List, Tuple, paramVal, Np1D,
FenExpr)
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['HelmholtzSquareDomainProblemEngine']
class HelmholtzSquareDomainProblemEngine(HelmholtzProblemEngine):
"""
Solver for square Helmholtz problems with parametric laplacian.
- \dxx u - mu_2**2 \dyy u - mu_1**2 * u = f(mu_2) in \Omega = [0,\pi]^2
u = 0 on \partial\Omega
"""
def __init__(self, kappa:float, theta:float, n:int,
mu0 : paramVal = [12. ** .5, 1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs, self.nbs = 6, 11 * 12 // 2
self.npar = 2
self.rescalingExp = [2., 1.]
pi = np.pi
mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
3 * n, 3 * n)
self.V = fen.FunctionSpace(mesh, "P", 1)
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
self.forcingTerm = [fen.cos(kappa * (c * x + s / self.mu0(0, 1) * y)),
fen.sin(kappa * (c * x + s / self.mu0(0, 1) * y))]
self.forcingTermDer = kappa * s * y
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
mu = self.checkParameter(mu)
def getPowMinusj(x, power):
powR = x ** power
powI = fenZERO
if power % 2 == 1:
powR, powI = powI, powR
if power % 4 > 1:
powR, powI = - powR, - powI
return powR, powI
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling auxiliary expression for "
- "forcing term derivative."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Assembling auxiliary expression for forcing term derivative.",
+ 25)
if derI == 0: return fenONE, fenZERO
coeffs = np.zeros(derI + 1)
coeffs[1] = - 2.
for j in range(2, derI + 1):
coeffs[1 :] = (-2. / j * coeffs[1 :]
- (3 - (1 + 2 * np.arange(derI)) / j) * coeffs[: -1])
for j in range(derI):
powR, powI = getPowMinusj(self.forcingTermDer, derI - j)
mupBase = coeffs[j + 1] * mu(0, 1) ** (- 3 * derI + 2 * j)
mupR, mupI = np.real(mupBase), np.imag(mupBase)
if j == 0:
exprR = mupR * powR - mupI * powI
exprI = mupI * powR + mupR * powI
else:
exprR += mupR * powR - mupI * powI
exprI += mupI * powR + mupR * powI
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling auxiliary expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling auxiliary expression.", 25)
return exprR, exprI
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
for j in range(2, 5):
if derI <= j and self.As[j] is None:
self.As[j] = self.checkAInBounds(-1)
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 5 and self.As[5] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A5.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A5.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a5Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
self.As[5] = fenics2Sparse(a5Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
derH = hashI(j, self.npar)
if bs[j] is None:
if np.sum(derH) != derH[-1]:
if homogeneized:
self.bsH[j] = self.checkbInBounds(-1)
else:
self.bs[j] = self.checkbInBounds(-1)
continue
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
if j == 0:
u0Re, u0Im = self.DirichletDatum
else:
u0Re, u0Im = fenZERO, fenZERO
if j < self.nbs:
fRe, fIm = self.forcingTerm
cRe, cIm = self.getExtraFactorB(self.mu0, derH[-1])
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
if homogeneized:
Ader = self.A(self.mu0, derH)
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
index 68a0f00..b99b9e4 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/helmholtz_square_simplified_domain_problem_engine.py
@@ -1,106 +1,94 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenZERO
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['HelmholtzSquareSimplifiedDomainProblemEngine']
class HelmholtzSquareSimplifiedDomainProblemEngine(HelmholtzProblemEngine):
"""
Solver for square Helmholtz problems with parametric laplacian.
- \dxx u - mu_2**2 \dyy u - mu_1**2 * u = f in \Omega_mu = [0,\pi]^2
u = 0 on \partial\Omega
"""
def __init__(self, kappa:float, theta:float, n:int,
mu0 : paramVal = [12. ** .5, 1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 3
self.npar = 2
self.rescalingExp = [2., 2.]
pi = np.pi
mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi),
3 * n, 3 * n)
self.V = fen.FunctionSpace(mesh, "P", 1)
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
self.forcingTerm = [fen.cos(kappa * (c * x + s * y)),
fen.sin(kappa * (c * x + s * y))]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a2Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
self.As[2] = fenics2Sparse(a2Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py b/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
index cd3ec26..713e066 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/laplace_disk_gaussian_2.py
@@ -1,123 +1,115 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import Np1D, Tuple, List, FenExpr, paramVal
from rrompy.hfengines.linear_problem.laplace_disk_gaussian import (
LaplaceDiskGaussian)
from rrompy.solver.fenics import fenZERO, fenONE
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import RROMPyException
from rrompy.solver.fenics import fenics2Vector
__all__ = ['LaplaceDiskGaussian2']
class LaplaceDiskGaussian2(LaplaceDiskGaussian):
"""
Solver for disk Laplace problems with parametric forcing term center.
- \Delta u = C exp(-.5 * ||\cdot - (mu1, mu2)||^2) in \Omega = B(0, 5)
u = 0 on \partial\Omega.
"""
def __init__(self, n:int, mu0 : paramVal = [0., 0.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(n = n, mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nbs = 1
self.npar = 2
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling base expression for "
- "forcing term."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling base expression for forcing term.",
+ 25)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
C = np.exp(-.5 * (mu(0, 0) ** 2. + mu(0, 1) ** 2.))
CR, CI = np.real(C), np.imag(C)
f0 = (2 * np.pi) ** -.5 * fen.exp(-.5 * (x ** 2. + y ** 2.))
muxR, muxI = np.real(mu(0, 0)), np.imag(mu(0, 0))
muyR, muyI = np.real(mu(0, 1)), np.imag(mu(0, 1))
f1R = fen.exp(muxR * x + muyR * y) * fen.cos(muxI * x + muyI * y)
f1I = fen.exp(muxR * x + muyR * y) * fen.sin(muxI * x + muyI * y)
self.forcingTerm = [f0 * (CR * f1R - CI * f1I),
f0 * (CR * f1I + CI * f1R)]
self.forcingTermMu = mu
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling base expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling base expression.", 25)
return self.forcingTerm
def computebsFactors(self):
pass
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
if derI == 0: return [fenONE, fenZERO]
raise RROMPyException("Not implemented.")
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(mu)
cRe, cIm = self.getExtraFactorB(mu, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DirichletBC0, 1))
if homogeneized:
Ader = self.A(self.mu0, hashI(j, self.npar))
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py b/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
index 98c1119..dd131a4 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/membrane_fracture_engine.py
@@ -1,188 +1,156 @@
# 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 .
#
import numpy as np
import fenics as fen
import mshr, ufl
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['MembraneFractureEngine']
class MembraneFractureEngine(HelmholtzProblemEngine):
def __init__(self, mu0 : paramVal = [20. ** .5, .6], H : float = 1.,
L : float = .75, delta : float = .05, n : int = 50,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 20
self.npar = 2
self.H = H
self.rescalingExp = [2., 1.]
domain = (mshr.Rectangle(fen.Point(0., - H / 2.),
fen.Point(2. * L + delta, H / 2.))
- mshr.Rectangle(fen.Point(L, 0.),
fen.Point(L + delta, H / 2.)))
mesh = mshr.generate_mesh(domain, n)
self.V = fen.FunctionSpace(mesh, "P", 1)
self.NeumannBoundary = lambda x, on_b: (on_b and x[1] >= - H / 4.
and x[0] >= L
and x[0] <= L + delta)
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
self._belowIndicator = ufl.conditional(ufl.le(y, 0.), fenONE, fenZERO)
self._aboveIndicator = fenONE - self._belowIndicator
self.DirichletDatum = [fen.exp(- 10. * (H / 2. + y) / H
- .5 * ((x - .6 * L) / (.1 * L)) ** 2.
) * self._belowIndicator, fenZERO]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
for j in [1, 3, 4, 6, 7, 10, 11, 12, 15, 16, 17, 18]:
if derI <= j and self.As[j] is None:
self.As[j] = self.checkAInBounds(-1)
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = (self.H ** 4 / 4. * self._aboveIndicator
* fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx)
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a2Re = (- self.H ** 3 / 2. * self._aboveIndicator
* fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx)
self.As[2] = fenics2Sparse(a2Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 5 and self.As[5] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A6.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A6.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a5Re = self.H ** 2 * (fen.dot(self.u.dx(0), self.v.dx(0))
+ .25 * fen.dot(self.u.dx(1), self.v.dx(1))) * fen.dx
self.As[5] = fenics2Sparse(a5Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 8 and self.As[8] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A8.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A8.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a8Re = - self.H ** 2. * n2Re * fen.dot(self.u, self.v) * fen.dx
a8Im = - self.H ** 2. * n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[8] = (fenics2Sparse(a8Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a8Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 9 and self.As[9] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A9.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A9.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a9Re = - 2. * self.H * fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
self.As[9] = fenics2Sparse(a9Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 13 and self.As[13] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A13.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A13.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a13Re = 2. * self.H * n2Re * fen.dot(self.u, self.v) * fen.dx
a13Im = 2. * self.H * n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[13] = (fenics2Sparse(a13Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a13Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 14 and self.As[14] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A14.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A14.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a14Re = fen.dot(self.u.dx(0), self.v.dx(0)) * fen.dx
self.As[14] = fenics2Sparse(a14Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 19 and self.As[19] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A19.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A19.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a19Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a19Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[19] = (fenics2Sparse(a19Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a19Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/bidimensional/synthetic_bivariate_engine.py b/rrompy/hfengines/linear_problem/bidimensional/synthetic_bivariate_engine.py
index 2fb7ca5..c7315a7 100644
--- a/rrompy/hfengines/linear_problem/bidimensional/synthetic_bivariate_engine.py
+++ b/rrompy/hfengines/linear_problem/bidimensional/synthetic_bivariate_engine.py
@@ -1,123 +1,111 @@
# 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 .
#
import numpy as np
import fenics as fen
import ufl
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenONE, fenZERO
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['SyntheticBivariateEngine']
class SyntheticBivariateEngine(HelmholtzProblemEngine):
def __init__(self, kappa:float, theta:float, n:int, L : int = 2.,
mu0 : paramVal = [12. ** .5, 15. ** .5],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 3
self.npar = 2
self.rescalingExp = [2., 2.]
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(L, L), n, n)
self.V = fen.FunctionSpace(mesh, "P", 1)
x, y = fen.SpatialCoordinate(mesh)[:]
self._above = ufl.conditional(ufl.ge(y, .5 * L), fenONE, fenZERO)
self._below = fenONE - self._above
c, s = np.cos(theta), np.sin(theta)
self.forcingTerm = [fen.cos(kappa * (c * x + s * y)),
fen.sin(kappa * (c * x + s * y))]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * self._above * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * self._above * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a2Re = - n2Re * self._below * fen.dot(self.u, self.v) * fen.dx
a2Im = - n2Im * self._below * fen.dot(self.u, self.v) * fen.dx
self.As[2] = (fenics2Sparse(a2Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a2Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
index e65c100..ad74541 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
@@ -1,145 +1,137 @@
# 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 .
#
import numpy as np
import fenics as fen
from .laplace_base_problem_engine import LaplaceBaseProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenONE
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['HelmholtzProblemEngine']
class HelmholtzProblemEngine(LaplaceBaseProblemEngine):
"""
Solver for generic Helmholtz problems with parametric wavenumber.
- \nabla \cdot (a \nabla u) - omega^2 * n**2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
diffusivity: Value of a.
refractionIndex: Value of n.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 2
self.rescalingExp = [2.]
self.refractionIndex = fenONE
@property
def refractionIndex(self):
"""Value of n."""
return self._refractionIndex
@refractionIndex.setter
def refractionIndex(self, refractionIndex):
self.resetAs()
if not isinstance(refractionIndex, (list, tuple,)):
refractionIndex = [refractionIndex, fenZERO]
self._refractionIndex = refractionIndex
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
index 7106dae..3c0da78 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_domain_problem_engine.py
@@ -1,214 +1,195 @@
# 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 .
#
import numpy as np
import scipy.sparse as scsp
import fenics as fen
from rrompy.utilities.base.types import (Np1D, ScOp, Tuple, List, FenExpr,
paramVal)
from rrompy.solver.fenics import fenZERO
from .helmholtz_problem_engine import HelmholtzProblemEngine
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['HelmholtzSquareBubbleDomainProblemEngine']
class HelmholtzSquareBubbleDomainProblemEngine(HelmholtzProblemEngine):
"""
Solver for square bubble Helmholtz problems with parametric domain heigth.
- \Delta u - kappa^2 * u = f in \Omega_mu = [0,\pi] x [0,\mu\pi]
u = 0 on \Gamma_mu = \partial\Omega_mu
with exact solution square bubble times plane wave.
"""
def __init__(self, kappa:float, theta:float, n:int, mu0 : paramVal = [1.],
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs, self.nbs = 3, 20
self.kappa = kappa
self.theta = theta
self.forcingTermMu = np.nan
mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(np.pi, np.pi),
3 * n, 3 * n)
self.V = fen.FunctionSpace(mesh, "P", 1)
self.rescalingExp = [1.]
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling base expression for "
- "forcing term."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling base expression for forcing term.",
+ 25)
pi = np.pi
c, s = np.cos(self.theta), np.sin(self.theta)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
mu2R, mu2I = np.real(mu(0, 0) ** 2.), np.imag(mu(0, 0) ** 2.)
C = 16. / pi ** 4.
bR = C * (2 * (x * (pi - x) + y * (pi - y))
+ (self.kappa * s) ** 2. * (mu2R - 1.)
* x * (pi - x) * y * (pi - y))
bI = C * (2 * self.kappa * (c * (pi - 2 * x) * y * (pi - y)
+ s * x * (pi - x) * (pi - 2 * y))
+ (self.kappa * s) ** 2. * mu2I
* x * (pi - x) * y * (pi - y))
wR = (fen.cos(self.kappa * (c * x + s * muR * y))
* fen.exp(self.kappa * s * muI * y))
wI = (fen.sin(self.kappa * (c * x + s * muR * y))
* fen.exp(self.kappa * s * muI * y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
self.forcingTermMu = mu
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling base expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling base expression.", 25)
return self.forcingTerm
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
mu = self.checkParameter(mu)
def getPowMinusj(x, power):
powR = x ** power
powI = fenZERO
if power % 2 == 1:
powR, powI = powI, powR
if (power + 3) % 4 < 2:
powR, powI = - powR, - powI
return powR, powI
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling auxiliary expression for "
- "forcing term derivative."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Assembling auxiliary expression for forcing term derivative.",
+ 25)
from scipy.special import factorial as fact
y = fen.SpatialCoordinate(self.V.mesh())[1]
powR, powI = [(self.kappa * np.sin(self.theta)) ** derI * k\
for k in getPowMinusj(y, derI)]
mu2R, mu2I = np.real(mu(0, 0) ** 2.), np.imag(mu(0, 0) ** 2.)
exprR = mu2R * powR - mu2I * powI
exprI = mu2I * powR + mu2R * powI
if derI >= 1:
muR, muI = np.real(2. * mu(0, 0)), np.imag(2. * mu(0, 0))
powR, powI = [(self.kappa * np.sin(self.theta)) ** (derI - 1) * k\
* derI for k in getPowMinusj(y, derI - 1)]
exprR += muR * powR - muI * powI
exprI += muI * powR + muR * powI
if derI >= 2:
powR, powI = [(self.kappa * np.sin(self.theta)) ** (derI - 2) * k\
* derI * (derI - 1) for k in getPowMinusj(y, derI - 2)]
exprR += powR
exprI += powI
fac = fact(derI)
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling auxiliary expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling auxiliary expression.", 25)
return [exprR / fac, exprI / fac]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
self.As[1] = self.checkAInBounds(-1)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
k2Re, k2Im = np.real(self.omega ** 2), np.imag(self.omega ** 2)
k2n2Re = k2Re * n2Re - k2Im * n2Im
k2n2Im = k2Re * n2Im + k2Im * n2Re
parsRe = self.iterReduceQuadratureDegree(zip([k2n2Re],
["kappaSquaredRefractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([k2n2Im],
["kappaSquaredRefractionIndexSquaredImag"]))
a2Re = (fen.dot(self.u.dx(0), self.v.dx(0))
- k2n2Re * fen.dot(self.u, self.v)) * fen.dx
a2Im = - k2n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[2] = (fenics2Sparse(a2Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a2Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(self.mu0)
cRe, cIm = self.getExtraFactorB(self.mu0, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DirichletBC0, 1))
if homogeneized:
Ader = self.A(self.mu0, hashI(j, self.npar))
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
index eecea62..676d76f 100644
--- a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
@@ -1,366 +1,337 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.hfengines.base.problem_engine_base import ProblemEngineBase
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.solver.fenics import (fenZERO, fenONE, L2InverseNormMatrix,
H1NormMatrix, Hminus1NormMatrix)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.parameter import checkParameter
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['LaplaceBaseProblemEngine']
class LaplaceBaseProblemEngine(ProblemEngineBase):
"""
Solver for generic Laplace problems.
- \nabla \cdot (a \nabla u) = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
diffusivity: Value of a.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
_energyDualNormCompress = None
def __init__(self, mu0 : paramVal = [], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.mu0 = checkParameter(mu0)
self.npar = self.mu0.shape[1]
self.omega = np.abs(self.mu0(0, 0)) if self.npar > 0 else 0.
self.diffusivity = fenONE
self.forcingTerm = fenZERO
self.DirichletDatum = fenZERO
self.NeumannDatum = fenZERO
self.RobinDatumG = fenZERO
self.RobinDatumH = fenZERO
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
ProblemEngineBase.V.fset(self, V)
self.dsToBeSet = True
@property
def diffusivity(self):
"""Value of a."""
return self._diffusivity
@diffusivity.setter
def diffusivity(self, diffusivity):
self.resetAs()
if not isinstance(diffusivity, (list, tuple,)):
diffusivity = [diffusivity, fenZERO]
self._diffusivity = diffusivity
@property
def forcingTerm(self):
"""Value of f."""
return self._forcingTerm
@forcingTerm.setter
def forcingTerm(self, forcingTerm):
self.resetbs()
if not isinstance(forcingTerm, (list, tuple,)):
forcingTerm = [forcingTerm, fenZERO]
self._forcingTerm = forcingTerm
@property
def DirichletDatum(self):
"""Value of u0."""
return self._DirichletDatum
@DirichletDatum.setter
def DirichletDatum(self, DirichletDatum):
self.resetbs()
if not isinstance(DirichletDatum, (list, tuple,)):
DirichletDatum = [DirichletDatum, fenZERO]
self._DirichletDatum = DirichletDatum
@property
def NeumannDatum(self):
"""Value of g1."""
return self._NeumannDatum
@NeumannDatum.setter
def NeumannDatum(self, NeumannDatum):
self.resetbs()
if not isinstance(NeumannDatum, (list, tuple,)):
NeumannDatum = [NeumannDatum, fenZERO]
self._NeumannDatum = NeumannDatum
@property
def RobinDatumG(self):
"""Value of g2."""
return self._RobinDatumG
@RobinDatumG.setter
def RobinDatumG(self, RobinDatumG):
self.resetbs()
if not isinstance(RobinDatumG, (list, tuple,)):
RobinDatumG = [RobinDatumG, fenZERO]
self._RobinDatumG = RobinDatumG
@property
def RobinDatumH(self):
"""Value of h."""
return self._RobinDatumH
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
self.resetAs()
if not isinstance(RobinDatumH, (list, tuple,)):
RobinDatumH = [RobinDatumH, fenZERO]
self._RobinDatumH = RobinDatumH
@property
def DirichletBoundary(self):
"""Function handle to DirichletBoundary."""
return self.BCManager.DirichletBoundary
@DirichletBoundary.setter
def DirichletBoundary(self, DirichletBoundary):
self.resetAs()
self.resetbs()
self.BCManager.DirichletBoundary = DirichletBoundary
@property
def NeumannBoundary(self):
"""Function handle to NeumannBoundary."""
return self.BCManager.NeumannBoundary
@NeumannBoundary.setter
def NeumannBoundary(self, NeumannBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.NeumannBoundary = NeumannBoundary
@property
def RobinBoundary(self):
"""Function handle to RobinBoundary."""
return self.BCManager.RobinBoundary
@RobinBoundary.setter
def RobinBoundary(self, RobinBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.RobinBoundary = RobinBoundary
def autoSetDS(self):
"""Set FEniCS boundary measure based on boundary function handles."""
if self.dsToBeSet:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Initializing boundary measures.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Initializing boundary measures.", 20)
mesh = self.V.mesh()
NB = self.NeumannBoundary
RB = self.RobinBoundary
boundary_markers = fen.MeshFunction("size_t", mesh,
mesh.topology().dim() - 1)
NB.mark(boundary_markers, 0)
RB.mark(boundary_markers, 1)
self.ds = fen.Measure("ds", domain = mesh,
subdomain_data = boundary_markers)
self.dsToBeSet = False
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done initializing boundary measures.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling boundary measures.", 20)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy matrix.", 20)
self.energyNormMatrix = H1NormMatrix(self.V, np.abs(self.omega)**2)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildEnergyNormDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy dual matrix.", 20)
self.energyNormDualMatrix = Hminus1NormMatrix(
self.V, np.abs(self.omega)**2,
compressRank = self._energyDualNormCompress)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy dual matrix.", 20)
def buildDualityPairingForm(self):
"""Build sparse matrix (in CSR format) representative of duality."""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling duality matrix.", 20)
self.dualityMatrix = L2InverseNormMatrix(
self.V, solverType = self._solver,
solverArgs = self._solverArgs,
compressRank = self._dualityCompress)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling duality matrix.", 20)
def buildEnergyNormPartialDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product without duality.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy partial dual matrix.", 20)
self.energyNormPartialDualMatrix = Hminus1NormMatrix(
self.V, np.abs(self.omega)**2,
compressRank = self._energyDualNormCompress,
duality = False)
- if self.verbosity >= 20:
- verbosityDepth("DEL",
- "Done assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy partial dual matrix.", 20)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
hRe, hIm = self.RobinDatumH
termNames = ["diffusivity", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip([aRe, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip([aIm, hIm],
[x + "Imag" for x in termNames]))
a0Re = (aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hRe * fen.dot(self.u, self.v) * self.ds(1))
a0Im = (aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
+ hIm * fen.dot(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
termNames, terms = [], []
if j == 0:
u0Re, u0Im = self.DirichletDatum
fRe, fIm = self.forcingTerm
g1Re, g1Im = self.NeumannDatum
g2Re, g2Im = self.RobinDatumG
termNames += ["forcingTerm", "NeumannDatum", "RobinDatumG"]
terms += [[fRe, fIm], [g1Re, g1Im], [g2Re, g2Im]]
else:
u0Re, u0Im = fenZERO, fenZERO
fRe, fIm = fenZERO, fenZERO
g1Re, g1Im = fenZERO, fenZERO
g2Re, g2Im = fenZERO, fenZERO
if len(termNames) > 0:
parsRe = self.iterReduceQuadratureDegree(zip(
[term[0] for term in terms],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[term[1] for term in terms],
[x + "Imag" for x in termNames]))
else:
parsRe, parsIm = {}, {}
L0Re = (fen.dot(fRe, self.v) * fen.dx
+ fen.dot(g1Re, self.v) * self.ds(0)
+ fen.dot(g2Re, self.v) * self.ds(1))
L0Im = (fen.dot(fIm, self.v) * fen.dx
+ fen.dot(g1Im, self.v) * self.ds(0)
+ fen.dot(g2Im, self.v) * self.ds(1))
DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
if homogeneized:
Ader = self.A(self.mu0, hashI(j, self.npar))
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
index 227c446..6f66640 100644
--- a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
+++ b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
@@ -1,158 +1,147 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.utilities.base.types import Np1D, Tuple, FenExpr, paramVal
from .laplace_base_problem_engine import LaplaceBaseProblemEngine
from rrompy.solver.fenics import fenZERO, fenONE
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.solver.fenics import fenics2Vector
__all__ = ['LaplaceDiskGaussian']
class LaplaceDiskGaussian(LaplaceBaseProblemEngine):
"""
Solver for disk Laplace problems with parametric forcing term center.
- \Delta u = C exp(-.5 * ||\cdot - (mu, 0)||^2) in \Omega = B(0, 5)
u = 0 on \partial\Omega.
"""
def __init__(self, n:int, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nbs = 20
self.computebsFactors()
self.forcingTermMu = np.nan
import mshr
mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0., 0.), 5.), 3 * n)
self.V = fen.FunctionSpace(mesh, "P", 1)
def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling base expression for "
- "forcing term."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling base expression for forcing term.",
+ 25)
x, y = fen.SpatialCoordinate(self.V.mesh())[:]
C = np.exp(-.5 * mu(0, 0) ** 2.)
CR, CI = np.real(C), np.imag(C)
f0 = (2 * np.pi) ** -.5 * fen.exp(-.5 * (x ** 2. + y ** 2.))
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
f1R = fen.exp(muR * x) * fen.cos(muI * x)
f1I = fen.exp(muR * x) * fen.sin(muI * x)
self.forcingTerm = [f0 * (CR * f1R - CI * f1I),
f0 * (CR * f1I + CI * f1R)]
self.forcingTermMu = mu
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling base expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling base expression.", 25)
return self.forcingTerm
def computebsFactors(self):
self.bsFactors = np.zeros((self.nbs, self.nbs), dtype = float)
self.bsFactors[0, 0] = 1.
self.bsFactors[1, 1] = 1.
for j in range(2, self.nbs):
l = (j + 1) % 2 + 1
J = np.arange(l, j + 1, 2)
self.bsFactors[j, J] = self.bsFactors[j - 1, J - 1]
if l == 2:
l = 0
J = np.arange(l, j, 2)
self.bsFactors[j, J] += np.multiply(- 1 - J,
self.bsFactors[j - 1, J + 1])
self.bsFactors[j, l : j + 2 : 2] /= j
def getExtraFactorB(self, mu : paramVal = [],
derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
mu = self.checkParameter(mu)
- if self.verbosity >= 25:
- verbosityDepth("INIT", ("Assembling auxiliary expression for "
- "forcing term derivative."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Assembling auxiliary expression for forcing term derivative.",
+ 25)
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
x = fen.SpatialCoordinate(self.V.mesh())[0]
l = derI % 2
if l == 0:
powR, powI = fenONE, fenZERO
else:
powR, powI = x - muR, fen.Constant(muI)
exprR, exprI = [self.bsFactors[derI, l] * k for k in [powR, powI]]
for j in range(l + 2, derI + 1, 2):
for _ in range(2):
powR, powI = (powR * (x - muR) - powI * muI,
powR * muI + powI * (x - muR))
exprR += self.bsFactors[derI, j] * powR
exprI += self.bsFactors[derI, j] * powI
- if self.verbosity >= 25:
- verbosityDepth("DEL", "Done assembling auxiliary expression.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling auxiliary expression.", 25)
return[exprR, exprI]
def b(self, mu : paramVal = [], der : int = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu0 != self.mu0BC:
self.liftDirichletData(self.mu0)
for j in range(derI, nbsTot):
if bs[j] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
if j < self.nbs:
fRe, fIm = self.getForcingTerm(self.mu0)
cRe, cIm = self.getExtraFactorB(self.mu0, j)
cfRe, cfIm = cRe * fRe - cIm * fIm, cRe * fIm + cIm * fRe
else:
cfRe, cfIm = fenZERO, fenZERO
parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
["forcingTermDer{}Real".format(j)]))
parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
["forcingTermDer{}Imag".format(j)]))
L0Re = fen.dot(cfRe, self.v) * fen.dx
L0Im = fen.dot(cfIm, self.v) * fen.dx
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DirichletBC0, 1))
if homogeneized:
Ader = self.A(self.mu0, hashI(j, self.npar))
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py b/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
index a7ad7bb..90bcde2 100644
--- a/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
+++ b/rrompy/hfengines/linear_problem/membrane_fracture_engine_nodomain.py
@@ -1,104 +1,96 @@
# 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 .
#
import numpy as np
import fenics as fen
import mshr, ufl
from rrompy.utilities.base.types import ScOp, List, paramVal
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
HelmholtzProblemEngine)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['MembraneFractureEngineNoDomain']
class MembraneFractureEngineNoDomain(HelmholtzProblemEngine):
def __init__(self, mu0 : paramVal = [20. ** .5, .6], H : float = 1.,
L : float = .75, delta : float = .05, n : int = 50,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(mu0 = mu0[0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.npar = 1
self.lFrac = mu0[1]
self.H = H
self.rescalingExp = [2.]
domain = (mshr.Rectangle(fen.Point(0., - H / 2.),
fen.Point(2. * L + delta, H / 2.))
- mshr.Rectangle(fen.Point(L, 0.),
fen.Point(L + delta, H / 2.)))
mesh = mshr.generate_mesh(domain, n)
self.V = fen.FunctionSpace(mesh, "P", 1)
self.NeumannBoundary = lambda x, on_b: (on_b and x[1] >= - H / 4.
and x[0] >= L
and x[0] <= L + delta)
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
self._belowIndicator = ufl.conditional(ufl.le(y, 0.), fenONE, fenZERO)
self._aboveIndicator = fenONE - self._belowIndicator
self.DirichletDatum = [fen.exp(- 10. * (H / 2. + y) / H
- .5 * ((x - .6 * L) / (.1 * L)) ** 2.
) * self._belowIndicator, fenZERO]
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = (fen.dot(self.u.dx(0), self.v.dx(0))
+ self.H ** 4 / 4. * (self.lFrac ** -2. * self._aboveIndicator
+ (self.H - self.lFrac) ** -2. * self._belowIndicator)
* fen.dot(self.u.dx(1), self.v.dx(1))
) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a1Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a1Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/scattering_problem_engine.py b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
index 2bd8229..8f0fdfd 100644
--- a/rrompy/hfengines/linear_problem/scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
@@ -1,155 +1,143 @@
# 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 .
#
from numpy import inf
import fenics as fen
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from .helmholtz_problem_engine import HelmholtzProblemEngine
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['ScatteringProblemEngine']
class ScatteringProblemEngine(HelmholtzProblemEngine):
"""
Solver for scattering problems with parametric wavenumber.
- \nabla \cdot (a \nabla u) - omega^2 * n**2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu +- i omega u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
bsH: Numpy array representation of homogeneized bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
signR: Sign in ABC.
omega: Value of omega.
diffusivity: Value of a.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
A2: Scipy sparse array representation (in CSC format) of A2.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
signR = - 1.
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = inf,
verbosity : int = 10, timestamp : bool = True):
self.silenceWarnings = True
super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
del self.silenceWarnings
self.nAs = 3
self.rescalingExp = [1.]
@property
def RobinDatumH(self):
"""Value of h."""
return self.signR * self.omega
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
if not hasattr(self, "silenceWarnings"):
RROMPyWarning(("Scattering problems do not allow changes of h. "
"Ignoring assignment."))
return
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
parsRe = self.iterReduceQuadratureDegree(zip([aRe],
["diffusivityReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([aIm],
["diffusivityImag"]))
a0Re = aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
a0Im = aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a1 = fen.dot(self.u, self.v) * self.ds(1)
self.As[1] = (self.signR * 1.j
* fenics2Sparse(a1, {}, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
parsRe = self.iterReduceQuadratureDegree(zip([n2Re],
["refractionIndexSquaredReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([n2Im],
["refractionIndexSquaredImag"]))
a2Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a2Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
self.As[2] = (fenics2Sparse(a2Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a2Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/linear_problem/tridimensional/__init__.py b/rrompy/hfengines/linear_problem/tridimensional/__init__.py
new file mode 100644
index 0000000..87dcc3f
--- /dev/null
+++ b/rrompy/hfengines/linear_problem/tridimensional/__init__.py
@@ -0,0 +1,26 @@
+# 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 .
+#
+
+from .membrane_fracture_engine3 import MembraneFractureEngine3
+
+__all__ = [
+ 'MembraneFractureEngine3'
+ ]
+
+
+
diff --git a/rrompy/hfengines/linear_problem/tridimensional/membrane_fracture_engine3.py b/rrompy/hfengines/linear_problem/tridimensional/membrane_fracture_engine3.py
new file mode 100644
index 0000000..dea60df
--- /dev/null
+++ b/rrompy/hfengines/linear_problem/tridimensional/membrane_fracture_engine3.py
@@ -0,0 +1,331 @@
+# 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 .
+#
+
+import numpy as np
+import fenics as fen
+import ufl
+from rrompy.utilities.base.types import ScOp, List, paramVal
+from rrompy.solver.fenics import fenZERO, fenONE
+from rrompy.hfengines.linear_problem.helmholtz_problem_engine import (
+ HelmholtzProblemEngine)
+from rrompy.utilities.base import verbosityManager as vbMng
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
+from rrompy.solver.fenics import fenics2Sparse
+
+__all__ = ['MembraneFractureEngine3']
+
+def gen_mesh_fracture(W, delta, H, n):
+ n = 2 * (n // 2) + 1
+ xL = np.linspace(-.5 * W, - .5 * delta, n // 2 + 1)
+ xR = - xL[::-1]
+ nEff = int(np.ceil(delta / (xL[1] - xL[0])))
+ xC = np.linspace(-.5 * delta, .5 * delta, nEff + 1)[1:-1]
+ yA = np.linspace(-.5 * H, .5 * H, n)
+ yL = np.linspace(-.5 * H, 0., n // 2 + 1)
+ editor = fen.MeshEditor()
+ mesh = fen.Mesh()
+ editor.open(mesh, "triangle", 2, 2)
+ editor.init_vertices((2 * n + nEff - 1) * (n // 2 + 1))
+ editor.init_cells(2 * (2 * n - 2 + nEff) * (n // 2))
+ for j, y in enumerate(yA):
+ for i, x in enumerate(xL):
+ editor.add_vertex(i + j * (n // 2 + 1), np.array([x, y]))
+ for j in range(n - 1):
+ for i in range(n // 2):
+ editor.add_cell(2 * (i + j * (n // 2)),
+ np.array([i + j * (n // 2 + 1), i + 1 + j * (n // 2 + 1),
+ i + (j + 1) * (n // 2 + 1)], dtype=np.uintp))
+ editor.add_cell(2 * (i + j * (n // 2)) + 1,
+ np.array([i + 1 + j * (n // 2 + 1), i + 1 + (j + 1) * (n // 2 + 1),
+ i + (j + 1) * (n // 2 + 1)], dtype=np.uintp))
+ vBase1, cBase1 = n * (n // 2 + 1), 2 * (n - 1) * (n // 2)
+ for j, y in enumerate(yA):
+ for i, x in enumerate(xR):
+ editor.add_vertex(vBase1 + i + j * (n // 2 + 1), np.array([x, y]))
+ for j in range(n - 1):
+ for i in range(n // 2):
+ editor.add_cell(cBase1 + 2 * (i + j * (n // 2)),
+ np.array([vBase1 + i + j * (n // 2 + 1), vBase1 + i + 1 + j * (n // 2 + 1),
+ vBase1 + i + (j + 1) * (n // 2 + 1)], dtype=np.uintp))
+ editor.add_cell(cBase1 + 2 * (i + j * (n // 2)) + 1,
+ np.array([vBase1 + i + 1 + j * (n // 2 + 1),
+ vBase1 + i + 1 + (j + 1) * (n // 2 + 1),
+ vBase1 + i + (j + 1) * (n // 2 + 1)], dtype=np.uintp))
+ vBase2, cBase2 = 2 * n * (n // 2 + 1), 4 * (n - 1) * (n // 2)
+ for j, y in enumerate(yL):
+ for i, x in enumerate(xC):
+ editor.add_vertex(vBase2 + i + j * (nEff - 1), np.array([x, y]))
+ for j in range(n // 2):
+ for i in range(nEff - 2):
+ editor.add_cell(cBase2 + 2 * (i + j * (nEff - 2)),
+ np.array([vBase2 + i + j * (nEff - 1), vBase2 + i + 1 + j * (nEff - 1),
+ vBase2 + i + (j + 1) * (nEff - 1)], dtype=np.uintp))
+ editor.add_cell(cBase2 + 2 * (i + j * (nEff - 2)) + 1,
+ np.array([vBase2 + i + 1 + j * (nEff - 1),
+ vBase2 + i + 1 + (j + 1) * (nEff - 1),
+ vBase2 + i + (j + 1) * (nEff - 1)], dtype=np.uintp))
+ if nEff == 1:
+ for j in range(n // 2):
+ editor.add_cell(cBase2 + 2 * j,
+ np.array([(j + 1) * (n // 2 + 1) - 1, vBase1 + j * (n // 2 + 1),
+ (j + 2) * (n // 2 + 1) - 1], dtype=np.uintp))
+ editor.add_cell(cBase2 + 2 * j + 1,
+ np.array([vBase1 + j * (n // 2 + 1), vBase1 + (j + 1) * (n // 2 + 1),
+ (j + 2) * (n // 2 + 1) - 1], dtype=np.uintp))
+ else:
+ cBase3 = 2 * (2 * n + nEff - 4) * (n // 2)
+ for j in range(n // 2):
+ editor.add_cell(cBase3 + 2 * j,
+ np.array([(j + 1) * (n // 2 + 1) - 1, vBase2 + j * (nEff - 1),
+ (j + 2) * (n // 2 + 1) - 1], dtype=np.uintp))
+ editor.add_cell(cBase3 + 2 * j + 1,
+ np.array([vBase2 + j * (nEff - 1), vBase2 + (j + 1) * (nEff - 1),
+ (j + 2) * (n // 2 + 1) - 1], dtype=np.uintp))
+ cBase4 = 2 * (2 * n + nEff - 3) * (n // 2)
+ for j in range(n // 2):
+ editor.add_cell(cBase4 + 2 * j,
+ np.array([vBase2 + (j + 1) * (nEff - 1) - 1, vBase1 + j * (n // 2 + 1),
+ vBase2 + (j + 2) * (nEff - 1) - 1], dtype=np.uintp))
+ editor.add_cell(cBase4 + 2 * j + 1,
+ np.array([vBase1 + j * (n // 2 + 1), vBase1 + (j + 1) * (n // 2 + 1),
+ vBase2 + (j + 2) * (nEff - 1) - 1], dtype=np.uintp))
+ editor.close()
+ return mesh
+
+class MembraneFractureEngine3(HelmholtzProblemEngine):
+
+ def __init__(self, mu0 : paramVal = [20. ** .5, .6, .08], H : float = 1.,
+ L : float = .75, delta : float = .05, n : int = 50,
+ degree_threshold : int = np.inf, verbosity : int = 10,
+ timestamp : bool = True):
+ super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
+ verbosity = verbosity, timestamp = timestamp)
+ self.nAs = 206
+ self.npar = 3
+ self._H = H
+ self._delta = delta
+ self._L = L
+ self._W = 2 * L + delta
+ self.rescalingExp = [2., 1., 1.]
+ mesh = gen_mesh_fracture(self._W, delta, H, n)
+ self.V = fen.FunctionSpace(mesh, "P", 1)
+ self.NeumannBoundary = lambda x, on_b: (on_b and x[1] >= - H / 4.
+ and x[0] >= - .5 * delta and x[0] <= .5 * delta)
+ self.DirichletBoundary = "REST"
+
+ x, y = fen.SpatialCoordinate(mesh)[:]
+ self._aboveIndicator = ufl.conditional(ufl.gt(y, 0.), fenONE, fenZERO)
+ self._belowCenterIndicator = ufl.conditional(
+ ufl.And(ufl.ge(x, - .5 * delta),
+ ufl.le(x, .5 * delta)),
+ fenONE, fenZERO)
+ self._belowSidesIndicator = (fenONE - self._aboveIndicator
+ - self._belowCenterIndicator)
+ self.DirichletDatum = [fen.exp(- 10. * (H / 2. + y) / H
+ - .5 * ((x + .4 * L + .5 * delta) / (.1 * L)) ** 2.
+ ) * self._belowSidesIndicator, fenZERO]
+
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
+ """Assemble (derivative of) operator of linear system."""
+ mu = self.checkParameter(mu)
+ if not hasattr(der, "__len__"): der = [der] * self.npar
+ derI = hashD(der)
+ self.autoSetDS()
+
+ spKx, spKy = [None] * 2, [None] * 2
+ spM = None
+ def getstiffnessblockj(direc:int, j:int):
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ if direc == 0:
+ if j == 0:
+ fact = 16. * self._L ** 2.
+ else:
+ fact = 4. * self._delta ** 2.
+ else:
+ fact = self._H ** 2.
+ if direc == 0:
+ if j == 0:
+ fact *= (self._aboveIndicator + self._belowSidesIndicator)
+ else:
+ fact *= self._belowCenterIndicator
+ else:
+ if j == 0:
+ fact *= self._aboveIndicator
+ else:
+ fact *= (self._belowSidesIndicator
+ + self._belowCenterIndicator)
+ ajRe = fact * self.u.dx(direc) * self.v.dx(direc) * fen.dx
+ return fenics2Sparse(ajRe, {}, DirichletBC0, 0)
+ def getmass():
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ ajRe = - 4. * self.u * self.v * fen.dx
+ return fenics2Sparse(ajRe, {}, DirichletBC0, 0)
+
+ if derI <= 0 and self.As[0] is None:
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ a0Re = fenZERO * fen.dot(self.u, self.v) * fen.dx
+ self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 7 and self.As[7] is None:
+ vbMng(self, "INIT", "Assembling operator term A7.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[7] = self._W ** 2. * self._H ** 2. * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 9 and self.As[9] is None:
+ vbMng(self, "INIT", "Assembling operator term A9.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[9] = self._W ** 2. * self._H ** 2. * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 16 and self.As[16] is None:
+ vbMng(self, "INIT", "Assembling operator term A16.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[16] = - 2. * self._W ** 2. * self._H * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 17 and self.As[17] is None:
+ vbMng(self, "INIT", "Assembling operator term A17.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[17] = - 2. * self._W * self._H ** 2. * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 18 and self.As[18] is None:
+ vbMng(self, "INIT", "Assembling operator term A18.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[18] = - 2. * self._W ** 2. * self._H * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 19 and self.As[19] is None:
+ vbMng(self, "INIT", "Assembling operator term A19.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[19] = - 2. * self._W * self._H ** 2. * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 30 and self.As[30] is None:
+ vbMng(self, "INIT", "Assembling operator term A30.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[30] = self._W ** 2. * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 31 and self.As[31] is None:
+ vbMng(self, "INIT", "Assembling operator term A31.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[31] = 4. * self._W * self._H * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 32 and self.As[32] is None:
+ vbMng(self, "INIT", "Assembling operator term A32.", 20)
+ if spKx[0] is None: spKx[0] = getstiffnessblockj(0, 0)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ if spKy[1] is None: spKy[1] = getstiffnessblockj(1, 1)
+ self.As[32] = (self._H ** 2. * (spKx[0] + spKx[1])
+ + self._W ** 2. * (spKy[0] + spKy[1]))
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 33 and self.As[33] is None:
+ vbMng(self, "INIT", "Assembling operator term A33.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[33] = 4. * self._W * self._H * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 34 and self.As[34] is None:
+ vbMng(self, "INIT", "Assembling operator term A34.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[34] = self._H ** 2. * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 47 and self.As[47] is None:
+ vbMng(self, "INIT", "Assembling operator term A47.", 20)
+ if spM is None: spM = getmass()
+ self.As[47] = self._W ** 2. * self._H ** 2. * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 51 and self.As[51] is None:
+ vbMng(self, "INIT", "Assembling operator term A51.", 20)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[51] = - 2. * self._W * spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 52 and self.As[52] is None:
+ vbMng(self, "INIT", "Assembling operator term A52.", 20)
+ if spKx[0] is None: spKx[0] = getstiffnessblockj(0, 0)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[52] = - 2. * self._H * (spKx[0] + spKx[1])
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 53 and self.As[53] is None:
+ vbMng(self, "INIT", "Assembling operator term A53.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ if spKy[1] is None: spKy[1] = getstiffnessblockj(1, 1)
+ self.As[53] = - 2. * self._W * (spKy[0] + spKy[1])
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 54 and self.As[54] is None:
+ vbMng(self, "INIT", "Assembling operator term A54.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ self.As[54] = - 2. * self._H * spKy[0]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 73 and self.As[73] is None:
+ vbMng(self, "INIT", "Assembling operator term A73.", 20)
+ if spM is None: spM = getmass()
+ self.As[73] = - 2. * self._W ** 2. * self._H * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 74 and self.As[74] is None:
+ vbMng(self, "INIT", "Assembling operator term A74.", 20)
+ if spM is None: spM = getmass()
+ self.As[74] = - 2. * self._W * self._H ** 2. * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 79 and self.As[79] is None:
+ vbMng(self, "INIT", "Assembling operator term A79.", 20)
+ if spKx[0] is None: spKx[0] = getstiffnessblockj(0, 0)
+ if spKx[1] is None: spKx[1] = getstiffnessblockj(0, 1)
+ self.As[79] = spKx[0] + spKx[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 81 and self.As[81] is None:
+ vbMng(self, "INIT", "Assembling operator term A81.", 20)
+ if spKy[0] is None: spKy[0] = getstiffnessblockj(1, 0)
+ if spKy[1] is None: spKy[1] = getstiffnessblockj(1, 1)
+ self.As[81] = spKy[0] + spKy[1]
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 107 and self.As[107] is None:
+ vbMng(self, "INIT", "Assembling operator term A107.", 20)
+ if spM is None: spM = getmass()
+ self.As[107] = self._W ** 2. * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 108 and self.As[108] is None:
+ vbMng(self, "INIT", "Assembling operator term A108.", 20)
+ if spM is None: spM = getmass()
+ self.As[108] = 4. * self._W * self._H * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 109 and self.As[109] is None:
+ vbMng(self, "INIT", "Assembling operator term A109.", 20)
+ if spM is None: spM = getmass()
+ self.As[109] = self._H ** 2. * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 151 and self.As[151] is None:
+ vbMng(self, "INIT", "Assembling operator term A151.", 20)
+ if spM is None: spM = getmass()
+ self.As[151] = - 2. * self._W * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 152 and self.As[152] is None:
+ vbMng(self, "INIT", "Assembling operator term A152.", 20)
+ if spM is None: spM = getmass()
+ self.As[152] = - 2. * self._H * spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ if derI <= 205 and self.As[205] is None:
+ vbMng(self, "INIT", "Assembling operator term A205.", 20)
+ if spM is None: spM = getmass()
+ self.As[205] = spM
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
+ for j in range(derI, self.nAs):
+ if self.As[j] is None:
+ self.As[j] = self.checkAInBounds(-1)
+ return self._assembleA(mu, der, derI)
+
diff --git a/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py b/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
index 80c1a2b..d78b291 100644
--- a/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
+++ b/rrompy/hfengines/vector_linear_problem/bidimensional/linear_elasticity_beam_elasticity_constants.py
@@ -1,157 +1,135 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.hfengines.vector_linear_problem.\
linear_elasticity_beam_poisson_ratio import LinearElasticityBeamPoissonRatio
from rrompy.solver.fenics import fenZEROS
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['LinearElasticityBeamElasticityConstants']
class LinearElasticityBeamElasticityConstants(
LinearElasticityBeamPoissonRatio):
"""
Solver for linear elasticity problem of a beam subject to its own weight,
with parametric Joung modulus and Poisson's ratio.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = rho_ * g in \Omega
u = 0 on \Gamma_D
\partial_nu = 0 on \Gamma_N
"""
def __init__(self, n:int, rho_:float, g:float, E0:float, nu0:float,
length:float, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [nu0, E0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs, self.nbs = 5, 4
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(length, 1),
n, max(int(n / length), 1))
self.V = fen.VectorFunctionSpace(mesh, "P", 1)
self.forcingTerm = [fen.Constant((0., - rho_ * g)), fenZEROS(2)]
self.DirichletBoundary = lambda x, on_b: on_b and fen.near(x[0], 0.)
self.NeumannBoundary = "REST"
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
for j in [1, 3]:
if derI <= j and self.As[j] is None:
self.As[j] = self.checkAInBounds(-1)
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
a0Re = fen.inner(fenZEROS(2), self.v) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 4 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
a2Re = 2. * fen.inner(epsilon(self.u), epsilon(self.v)) * fen.dx
self.As[2] = fenics2Sparse(a2Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 4 and self.As[4] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A4.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A4.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
a4Re = fen.div(self.u) * fen.div(self.v) * fen.dx
self.As[4] = (fenics2Sparse(a4Re, {}, DirichletBC0, 0)
- 2. * self.As[2])
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
RROMPyAssert(homogeneized, False, "Homogeneized")
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.bs[0] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b0.", 20)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L0Re = fen.inner(fRe, self.v) * fen.dx
L0Im = fen.inner(fIm, self.v) * fen.dx
DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
self.DirichletBoundary)
self.bs[0] = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
if derI <= 3 and self.bs[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b1.", 20)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L1Re = - fen.inner(fRe, self.v) * fen.dx
L1Im = - fen.inner(fIm, self.v) * fen.dx
DBC0 = fen.DirichletBC(self.V, fenZEROS(2), self.DirichletBoundary)
self.bs[1] = (fenics2Vector(L1Re, parsRe, DBC0, 1)
+ 1.j * fenics2Vector(L1Im, parsIm, DBC0, 1))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
if derI <= 2 and self.bs[2] is None:
self.bs[2] = self.checkbInBounds(-1)
if derI <= 3 and self.bs[3] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b3.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b3.", 20)
self.bs[3] = 2. * self.bs[1]
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
index 096c4ce..03a50a8 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_poisson_ratio.py
@@ -1,145 +1,127 @@
# 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 .
#
import numpy as np
import fenics as fen
from .linear_elasticity_problem_engine import LinearElasticityProblemEngine
from rrompy.solver.fenics import fenZEROS
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['LinearElasticityBeamPoissonRatio']
class LinearElasticityBeamPoissonRatio(LinearElasticityProblemEngine):
"""
Solver for linear elasticity problem of a beam subject to its own weight,
with parametric Poisson's ratio.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = rho_ * g in \Omega
u = 0 on \Gamma_D
\partial_nu = 0 on \Gamma_N
"""
def __init__(self, n:int, rho_:float, g:float, E:float, nu0:float,
length:float, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [nu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs, self.nbs = 2, 3
self.E_ = E
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(length, 1),
n, max(int(n / length), 1))
self.V = fen.VectorFunctionSpace(mesh, "P", 1)
self.forcingTerm = [fen.Constant((0., - rho_ * g / E)), fenZEROS(2)]
self.DirichletBoundary = lambda x, on_b: on_b and fen.near(x[0], 0.)
self.NeumannBoundary = "REST"
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
a0Re = 2. * self.E_ * fen.inner(epsilon(self.u),
epsilon(self.v)) * fen.dx
self.As[0] = fenics2Sparse(a0Re, {}, DirichletBC0, 1)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
a1Re = self.E_ * (fen.div(self.u) * fen.div(self.v)
- 4. * fen.inner(epsilon(self.u),
epsilon(self.v))) * fen.dx
self.As[1] = fenics2Sparse(a1Re, {}, DirichletBC0, 0)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
RROMPyAssert(homogeneized, False, "Homogeneized")
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
if derI <= 0 and self.bs[0] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b0.", 20)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L0Re = fen.inner(fRe, self.v) * fen.dx
L0Im = fen.inner(fIm, self.v) * fen.dx
DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
self.DirichletBoundary)
self.bs[0] = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
if derI <= 2 and self.bs[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b1.", 20)
fRe, fIm = self.forcingTerm
parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
L1Re = - fen.inner(fRe, self.v) * fen.dx
L1Im = - fen.inner(fIm, self.v) * fen.dx
DBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
self.bs[1] = (fenics2Vector(L1Re, parsRe, DBC0, 1)
+ 1.j * fenics2Vector(L1Im, parsIm, DBC0, 1))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
if derI <= 2 and self.bs[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b2.", 20)
self.bs[2] = 2. * self.bs[1]
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
index 8f68161..d8b192a 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine.py
@@ -1,204 +1,183 @@
# 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 .
#
import numpy as np
import fenics as fen
from .linear_elasticity_problem_engine import LinearElasticityProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import (fenZERO, fenZEROS, fenONE, L2NormMatrix,
elasticNormMatrix, elasticDualNormMatrix)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['LinearElasticityHelmholtzProblemEngine']
class LinearElasticityHelmholtzProblemEngine(LinearElasticityProblemEngine):
"""
Solver for generic linear elasticity Helmholtz problems with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * mu^2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
lambda_: Value of lambda_.
mu_: Value of mu_.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [mu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 2
self.omega = np.abs(self.mu0(0, 0))
self.rho_ = fenONE
self.rescalingExp = [2.]
@property
def rho_(self):
"""Value of rho_."""
return self._rho_
@rho_.setter
def rho_(self, rho_):
self.resetAs()
if not isinstance(rho_, (list, tuple,)):
rho_ = [rho_, fenZERO]
self._rho_ = rho_
def buildEnergyNormForm(self): # energy + omega norm
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy matrix.", 20)
self.energyNormMatrix = elasticNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
np.abs(self.omega)**2 * self.rho_[0])
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildEnergyNormDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy dual matrix.", 20)
self.energyNormDualMatrix = elasticDualNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
np.abs(self.omega)**2 * self.rho_[0],
compressRank = self._energyDualNormCompress)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy dual matrix.", 20)
def buildEnergyNormPartialDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product without duality.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy partial dual matrix.", 20)
self.energyNormPartialDualMatrix = elasticDualNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
np.abs(self.omega)**2 * self.rho_[0],
compressRank = self._energyDualNormCompress,
duality = False)
- if self.verbosity >= 20:
- verbosityDepth("DEL",
- "Done assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy partial dual matrix.", 20)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re],
["rho_Real"]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im],
["rho_Imag"]))
a1Re = - rho_Re * fen.inner(self.u, self.v) * fen.dx
a1Im = - rho_Im * fen.inner(self.u, self.v) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
index 2642941..9902192 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_problem_engine_damped.py
@@ -1,180 +1,168 @@
# 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 .
#
import numpy as np
import fenics as fen
from .linear_elasticity_helmholtz_problem_engine import \
LinearElasticityHelmholtzProblemEngine
from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD)
from rrompy.solver.fenics import fenics2Sparse
__all__ = ['LinearElasticityHelmholtzProblemEngineDamped']
class LinearElasticityHelmholtzProblemEngineDamped(
LinearElasticityHelmholtzProblemEngine):
"""
Solver for generic linear elasticity Helmholtz problems with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * (mu^2 - i * eta * mu) * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
lambda_: Value of lambda_.
mu_: Value of mu_.
eta: Value of eta.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(mu0 = [mu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.nAs = 3
self.eta = fenZERO
self.rescalingExp = [1.]
@property
def eta(self):
"""Value of eta."""
return self._eta
@eta.setter
def eta(self, eta):
self.resetAs()
if not isinstance(eta, (list, tuple,)):
eta = [eta, fenZERO]
self._eta = eta
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 1 and self.As[1] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A1.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A1.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
eta_Re, eta_Im = self.eta
termNames = ["rho_", "eta"]
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re, eta_Re],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im, eta_Im],
[x + "Imag" for x in termNames]))
a1Re = - ((eta_Re * rho_Im + eta_Im * rho_Re)
* fen.inner(self.u, self.v)) * fen.dx
a1Im = ((eta_Re * rho_Re - eta_Im * rho_Im)
* fen.inner(self.u, self.v)) * fen.dx
self.As[1] = (fenics2Sparse(a1Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a1Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
if derI <= 2 and self.As[2] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A2.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A2.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
rho_Re, rho_Im = self.rho_
parsRe = self.iterReduceQuadratureDegree(zip([rho_Re],
["rho_Real"]))
parsIm = self.iterReduceQuadratureDegree(zip([rho_Im],
["rho_Imag"]))
a2Re = - rho_Re * fen.inner(self.u, self.v) * fen.dx
a2Im = - rho_Im * fen.inner(self.u, self.v) * fen.dx
self.As[2] = (fenics2Sparse(a2Re, parsRe, DirichletBC0, 0)
+ 1.j * fenics2Sparse(a2Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
index 28c8886..cde25bb 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
@@ -1,392 +1,363 @@
# 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 .
#
import numpy as np
import fenics as fen
from rrompy.hfengines.base.vector_problem_engine_base import \
VectorProblemEngineBase
from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.solver.fenics import (fenZERO, fenZEROS, fenONE,
L2InverseNormMatrix, elasticNormMatrix,
elasticDualNormMatrix)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (
hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.parameter import checkParameter
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['LinearElasticityProblemEngine']
class LinearElasticityProblemEngine(VectorProblemEngineBase):
"""
Solver for generic linear elasticity problems.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u)) = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
lambda_: Value of lambda_.
mu_: Value of mu_.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
_energyDualNormCompress = None
def __init__(self, mu0 : paramVal = [], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.lambda_ = fenONE
self.mu_ = fenONE
self.mu0 = checkParameter(mu0)
self.npar = self.mu0.shape[1]
self.forcingTerm = fenZEROS(self.V.mesh().topology().dim())
self.DirichletDatum = fenZEROS(self.V.mesh().topology().dim())
self.NeumannDatum = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumG = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumH = fenZERO
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
VectorProblemEngineBase.V.fset(self, V)
self.forcingTerm = fenZEROS(self.V.mesh().topology().dim())
self.DirichletDatum = fenZEROS(self.V.mesh().topology().dim())
self.NeumannDatum = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumG = fenZEROS(self.V.mesh().topology().dim())
self.dsToBeSet = True
@property
def lambda_(self):
"""Value of lambda_."""
return self._lambda_
@lambda_.setter
def lambda_(self, lambda_):
self.resetAs()
if not isinstance(lambda_, (list, tuple,)):
lambda_ = [lambda_, fenZERO]
self._lambda_ = lambda_
@property
def mu_(self):
"""Value of mu_."""
return self._mu_
@mu_.setter
def mu_(self, mu_):
self.resetAs()
if not isinstance(mu_, (list, tuple,)):
mu_ = [mu_, fenZERO]
self._mu_ = mu_
@property
def forcingTerm(self):
"""Value of f."""
return self._forcingTerm
@forcingTerm.setter
def forcingTerm(self, forcingTerm):
self.resetbs()
if not isinstance(forcingTerm, (list, tuple,)):
forcingTerm = [forcingTerm,
fenZEROS(self.V.mesh().topology().dim())]
self._forcingTerm = forcingTerm
@property
def DirichletDatum(self):
"""Value of u0."""
return self._DirichletDatum
@DirichletDatum.setter
def DirichletDatum(self, DirichletDatum):
self.resetbs()
if not isinstance(DirichletDatum, (list, tuple,)):
DirichletDatum = [DirichletDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._DirichletDatum = DirichletDatum
@property
def NeumannDatum(self):
"""Value of g1."""
return self._NeumannDatum
@NeumannDatum.setter
def NeumannDatum(self, NeumannDatum):
self.resetbs()
if not isinstance(NeumannDatum, (list, tuple,)):
NeumannDatum = [NeumannDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._NeumannDatum = NeumannDatum
@property
def RobinDatumG(self):
"""Value of g2."""
return self._RobinDatumG
@RobinDatumG.setter
def RobinDatumG(self, RobinDatumG):
self.resetbs()
if not isinstance(RobinDatumG, (list, tuple,)):
RobinDatumG = [RobinDatumG,
fenZEROS(self.V.mesh().topology().dim())]
self._RobinDatumG = RobinDatumG
@property
def RobinDatumH(self):
"""Value of h."""
return self._RobinDatumH
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
self.resetAs()
if not isinstance(RobinDatumH, (list, tuple,)):
RobinDatumH = [RobinDatumH, fenZERO]
self._RobinDatumH = RobinDatumH
@property
def DirichletBoundary(self):
"""Function handle to DirichletBoundary."""
return self.BCManager.DirichletBoundary
@DirichletBoundary.setter
def DirichletBoundary(self, DirichletBoundary):
self.resetAs()
self.resetbs()
self.BCManager.DirichletBoundary = DirichletBoundary
@property
def NeumannBoundary(self):
"""Function handle to NeumannBoundary."""
return self.BCManager.NeumannBoundary
@NeumannBoundary.setter
def NeumannBoundary(self, NeumannBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.NeumannBoundary = NeumannBoundary
@property
def RobinBoundary(self):
"""Function handle to RobinBoundary."""
return self.BCManager.RobinBoundary
@RobinBoundary.setter
def RobinBoundary(self, RobinBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.RobinBoundary = RobinBoundary
def autoSetDS(self):
"""Set FEniCS boundary measure based on boundary function handles."""
if self.dsToBeSet:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Initializing boundary measures.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Initializing boundary measures.", 20)
NB = self.NeumannBoundary
RB = self.RobinBoundary
boundary_markers = fen.MeshFunction("size_t", self.V.mesh(),
self.V.mesh().topology().dim() - 1)
NB.mark(boundary_markers, 0)
RB.mark(boundary_markers, 1)
self.ds = fen.Measure("ds", domain = self.V.mesh(),
subdomain_data = boundary_markers)
self.dsToBeSet = False
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done initializing boundary measures.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done initializing boundary measures.", 20)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy matrix.", 20)
self.energyNormMatrix = elasticNormMatrix(self.V, self.lambda_[0],
self.mu_[0])
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildEnergyNormDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy dual matrix.", 20)
self.energyNormDualMatrix = elasticDualNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
compressRank = self._energyDualNormCompress)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling energy dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy dual matrix.", 20)
def buildDualityPairingForm(self):
"""Build sparse matrix (in CSR format) representative of duality."""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling duality matrix.", 20)
self.dualityMatrix = L2InverseNormMatrix(
self.V, solverType = self._solver,
solverArgs = self._solverArgs,
compressRank = self._dualityCompress)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling duality matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling duality matrix.", 20)
def buildEnergyNormPartialDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product without duality.
"""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling energy partial dual matrix.", 20)
self.energyNormPartialDualMatrix = elasticDualNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
compressRank = self._energyDualNormCompress,
duality = False)
- if self.verbosity >= 20:
- verbosityDepth("DEL",
- "Done assembling energy partial dual matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling energy partial dual matrix.", 20)
def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
self.autoSetDS()
if derI <= 0 and self.As[0] is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling operator term A0.", 20)
DirichletBC0 = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
lambda_Re, lambda_Im = self.lambda_
mu_Re, mu_Im = self.mu_
hRe, hIm = self.RobinDatumH
termNames = ["lambda_", "mu_", "RobinDatumH"]
parsRe = self.iterReduceQuadratureDegree(zip(
[lambda_Re, mu_Re, hRe],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[lambda_Im, mu_Re, hIm],
[x + "Imag" for x in termNames]))
epsilon = lambda u: 0.5 * (fen.grad(u) + fen.nabla_grad(u))
sigma = lambda u, l_, m_: (
l_ * fen.div(u) * fen.Identity(u.geometric_dimension())
+ 2. * m_ * epsilon(u))
a0Re = (fen.inner(sigma(self.u, lambda_Re, mu_Re),
epsilon(self.v)) * fen.dx
+ hRe * fen.inner(self.u, self.v) * self.ds(1))
a0Im = (fen.inner(sigma(self.u, lambda_Im, mu_Im),
epsilon(self.v)) * fen.dx
+ hIm * fen.inner(self.u, self.v) * self.ds(1))
self.As[0] = (fenics2Sparse(a0Re, parsRe, DirichletBC0, 1)
+ 1.j * fenics2Sparse(a0Im, parsIm, DirichletBC0, 0))
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling operator term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling operator term.", 20)
return self._assembleA(mu, der, derI)
def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
if not hasattr(der, "__len__"): der = [der] * self.npar
derI = hashD(der)
nbsTot = self.nbsH if homogeneized else self.nbs
bs = self.bsH if homogeneized else self.bs
if homogeneized and self.mu != self.mu0BC:
self.liftDirichletData(self.mu)
fenZEROSEff = fenZEROS(self.V.mesh().topology().dim())
for j in range(derI, nbsTot):
if bs[j] is None:
self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(j),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Assembling forcing term b{}.".format(j),
+ 20)
if j == 0:
u0Re, u0Im = self.DirichletDatum
fRe, fIm = self.forcingTerm
g1Re, g1Im = self.NeumannDatum
g2Re, g2Im = self.RobinDatumG
else:
u0Re, u0Im = fenZEROSEff, fenZEROSEff
fRe, fIm = fenZEROSEff, fenZEROSEff
g1Re, g1Im = fenZEROSEff, fenZEROSEff
g2Re, g2Im = fenZEROSEff, fenZEROSEff
termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
parsRe = self.iterReduceQuadratureDegree(zip(
[fRe, g1Re, g2Re],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip(
[fIm, g1Im, g2Im],
[x + "Imag" for x in termNames]))
L0Re = (fen.inner(fRe, self.v) * fen.dx
+ fen.inner(g1Re, self.v) * self.ds(0)
+ fen.inner(g2Re, self.v) * self.ds(1))
L0Im = (fen.inner(fIm, self.v) * fen.dx
+ fen.inner(g1Im, self.v) * self.ds(0)
+ fen.inner(g2Im, self.v) * self.ds(1))
DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
b = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
if homogeneized:
Ader = self.A(self.mu0, hashI(j, self.npar))
b -= Ader.dot(self.liftedDirichletDatum)
if homogeneized:
self.bsH[j] = b
else:
self.bs[j] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling forcing term.", 20)
return self._assembleb(mu, der, derI, homogeneized, self.mu0)
diff --git a/rrompy/reduction_methods/base/generic_approximant.py b/rrompy/reduction_methods/base/generic_approximant.py
index 44d571a..478ee33 100644
--- a/rrompy/reduction_methods/base/generic_approximant.py
+++ b/rrompy/reduction_methods/base/generic_approximant.py
@@ -1,886 +1,867 @@
# 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 .
#
from abc import abstractmethod
import numpy as np
from itertools import product as iterprod
from copy import deepcopy as copy
from os import remove as osrm
from rrompy.sampling.linear_problem import (SamplingEngineLinear,
SamplingEngineLinearPOD)
from rrompy.utilities.base.types import (Np1D, DictAny, HFEng, List, Tuple,
ListAny, strLst, paramVal, paramList,
sampList)
-from rrompy.utilities.base import purgeDict, verbosityDepth, getNewFilename
+from rrompy.utilities.base import (purgeDict, verbosityManager as vbMng,
+ getNewFilename)
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPy_READY, RROMPy_FRAGILE)
from rrompy.utilities.base import pickleDump, pickleLoad
from rrompy.parameter import (emptyParameterList, checkParameter,
checkParameterList)
from rrompy.sampling import sampleList, emptySampleList
__all__ = ['GenericApproximant']
def addNormFieldToClass(self, fieldName):
def objFunc(self, mu:paramList, homogeneized : bool = False) -> Np1D:
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
val = self.HFEngine.norm(uV)
return val
setattr(self.__class__, "norm" + fieldName, objFunc)
def addPlotFieldToClass(self, fieldName):
def objFunc(self, mu:paramList, *args, homogeneized : bool = False,
**kwargs):
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.plot(u, *args, **kwargs)
setattr(self.__class__, "plot" + fieldName, objFunc)
def addOutParaviewFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, *args, homogeneized : bool = False,
**kwargs):
if not hasattr(self.HFEngine, "outParaview"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.outParaview(u, *args, **kwargsCopy)
setattr(self.__class__, "outParaview" + fieldName, objFunc)
def addOutParaviewTimeDomainFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, *args,
homogeneized : bool = False, **kwargs):
if not hasattr(self.HFEngine, "outParaviewTimeDomain"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
omega = args.pop(0) if len(args) > 0 else np.real(mu)
kwargsCopy = copy(kwargs)
for j, u in enumerate(uV):
if "name" in kwargs.keys():
kwargsCopy["name"] = kwargs["name"] + str(j)
self.HFEngine.outParaviewTimeDomain(u, omega, *args,
**kwargsCopy)
setattr(self.__class__, "outParaviewTimeDomain" + fieldName, objFunc)
class GenericApproximant:
"""
ABSTRACT
ROM approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
trainedModel: Trained model evaluator.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList{Soft,Critical}.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
"""
__all__ += [ftype + dtype for ftype, dtype in iterprod(
["norm", "plot", "outParaview", "outParaviewTimeDomain"],
["HF", "RHS", "Approx", "Res", "Err"])]
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._mode = RROMPy_READY
self.verbosity = verbosity
self.timestamp = timestamp
- if self.verbosity >= 10:
- verbosityDepth("INIT", ("Initializing approximant engine of "
- "type {}.").format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Initializing engine of type {}.".format(self.name()), 10)
self._HFEngine = HFEngine
self.trainedModel = None
self.lastSolvedHF = emptyParameterList()
self.uHF = emptySampleList()
self._addParametersToList(["POD"], [True], ["S"], [[1]])
if mu0 is None:
if hasattr(self.HFEngine, "mu0"):
self.mu0 = checkParameter(self.HFEngine.mu0)
else:
raise RROMPyException(("Center of approximation cannot be "
"inferred from HF engine. Parameter "
"required"))
else:
self.mu0 = checkParameter(mu0, self.HFEngine.npar)
self.resetSamples()
self.homogeneized = homogeneized
self.approxParameters = approxParameters
self._postInit()
### add norm{HF,RHS,Approx,Res,Err} methods
"""
Compute norm of * at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of *.
"""
for objName in ["HF", "RHS", "Err"]:
addNormFieldToClass(self, objName)
def objFunc(self, mu:paramList, homogeneized : bool = False) -> Np1D:
# uV = getattr(self.__class__, "getRes")(self, mu, homogeneized,
# duality = False)
uV = self.getRes(mu, homogeneized, duality = False)
val = self.HFEngine.norm(uV, dual = True, duality = False)
return val
setattr(self.__class__, "normRes", objFunc)
if not hasattr(self, "normApprox"):
addNormFieldToClass(self, "Approx")
### add plot{HF,RHS,Approx,Res,Err} methods
"""
Do some nice plots of * at arbitrary parameter.
Args:
mu: Target parameter.
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): Where to save plot(s). Defaults to None, i.e. no
saving.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addPlotFieldToClass(self, objName)
### add outParaview{HF,RHS,Approx,Res,Err} methods
"""
Output * to ParaView file.
Args:
mu: Target parameter.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
time(optional): Timestamp.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
filePW(optional): Fenics File entity (for time series).
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addOutParaviewFieldToClass(self, objName)
### add outParaviewTimeDomain{HF,RHS,Approx,Res,Err} methods
"""
Output * to ParaView file, converted to time domain.
Args:
mu: Target parameter.
omega(optional): frequency.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
"""
for objName in ["HF", "RHS", "Approx", "Res", "Err"]:
addOutParaviewTimeDomainFieldToClass(self, objName)
def _preInit(self):
if not hasattr(self, "depth"): self.depth = 0
else: self.depth += 1
@property
def parameterList(self):
"""Value of parameterListSoft + parameterListCritical."""
return self.parameterListSoft + self.parameterListCritical
def _addParametersToList(self, whatSoft:strLst, defaultSoft:ListAny,
whatCritical : strLst = [],
defaultCritical : ListAny = [],
toBeExcluded : strLst = []):
if not hasattr(self, "parameterToBeExcluded"):
self.parameterToBeExcluded = []
self.parameterToBeExcluded += toBeExcluded
if not hasattr(self, "parameterListSoft"):
self.parameterListSoft = []
if not hasattr(self, "parameterDefaultSoft"):
self.parameterDefaultSoft = {}
if not hasattr(self, "parameterListCritical"):
self.parameterListCritical = []
if not hasattr(self, "parameterDefaultCritical"):
self.parameterDefaultCritical = {}
for j, what in enumerate(whatSoft):
if what not in self.parameterToBeExcluded:
self.parameterListSoft += [what]
self.parameterDefaultSoft[what] = defaultSoft[j]
for j, what in enumerate(whatCritical):
if what not in self.parameterToBeExcluded:
self.parameterListCritical += [what]
self.parameterDefaultCritical[what] = defaultCritical[j]
def _postInit(self):
if self.depth == 0:
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done initializing.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done initializing.", 10)
del self.depth
else: self.depth -= 1
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def setupSampling(self):
"""Setup sampling engine."""
RROMPyAssert(self._mode, message = "Cannot setup sampling engine.")
if not hasattr(self, "_POD") or self._POD is None: return
if self.POD:
SamplingEngine = SamplingEngineLinearPOD
else:
SamplingEngine = SamplingEngineLinear
self.samplingEngine = SamplingEngine(self.HFEngine,
verbosity = self.verbosity,
allowRepeatedSamples = True)
@property
def HFEngine(self):
"""Value of HFEngine."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
raise RROMPyException("Cannot change HFEngine.")
@property
def mu0(self):
"""Value of mu0."""
return self._mu0
@mu0.setter
def mu0(self, mu0):
mu0 = checkParameter(mu0)
if not hasattr(self, "_mu0") or mu0 != self.mu0:
self.resetSamples()
self._mu0 = mu0
@property
def npar(self):
"""Number of parameters."""
return self.mu0.shape[1]
@property
def approxParameters(self):
"""Value of approximant parameters."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
if not hasattr(self, "approxParameters"):
self._approxParameters = {}
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
keyList = list(approxParameters.keys())
for key in self.parameterListCritical:
if key in keyList:
setattr(self, "_" + key, self.parameterDefaultCritical[key])
for key in self.parameterListSoft:
if key in keyList:
setattr(self, "_" + key, self.parameterDefaultSoft[key])
fragile = False
for key in self.parameterListCritical:
if key in keyList:
val = approxParameters[key]
else:
val = getattr(self, "_" + key, None)
if val is None:
val = self.parameterDefaultCritical[key]
getattr(self.__class__, key, None).fset(self, val)
fragile = fragile or val is None
for key in self.parameterListSoft:
if key in keyList:
val = approxParameters[key]
else:
val = getattr(self, "_" + key, None)
if val is None:
val = self.parameterDefaultSoft[key]
getattr(self.__class__, key, None).fset(self, val)
if fragile:
self._mode = RROMPy_FRAGILE
@property
def POD(self):
"""Value of POD."""
return self._POD
@POD.setter
def POD(self, POD):
if hasattr(self, "_POD"): PODold = self.POD
else: PODold = -1
self._POD = POD
self._approxParameters["POD"] = self.POD
if PODold != self.POD:
self.samplingEngine = None
self.resetSamples()
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
if not hasattr(S, "__len__"): S = [S]
if any([s <= 0 for s in S]):
raise RROMPyException("S must be positive.")
if hasattr(self, "_S") and self._S is not None: Sold = tuple(self.S)
else: Sold = -1
self._S = S
self._approxParameters["S"] = self.S
if Sold != tuple(self.S):
self.resetSamples()
@property
def homogeneized(self):
"""Value of homogeneized."""
return self._homogeneized
@homogeneized.setter
def homogeneized(self, homogeneized):
if not hasattr(self, "_homogeneized"):
self._homogeneized = None
if homogeneized != self.homogeneized:
self._homogeneized = homogeneized
self.resetSamples()
@property
def trainedModel(self):
"""Value of trainedModel."""
return self._trainedModel
@trainedModel.setter
def trainedModel(self, trainedModel):
self._trainedModel = trainedModel
if self._trainedModel is not None:
self._trainedModel.lastSolvedApproxReduced = emptyParameterList()
self._trainedModel.lastSolvedApprox = emptyParameterList()
self.lastSolvedApproxReduced = emptyParameterList()
self.lastSolvedApprox = emptyParameterList()
self.uApproxReduced = emptySampleList()
self.uApprox = emptySampleList()
def resetSamples(self):
if hasattr(self, "samplingEngine") and self.samplingEngine is not None:
self.samplingEngine.resetHistory()
else:
self.setupSampling()
self._mode = RROMPy_READY
def plotSamples(self, warping : List[callable] = None, name : str = "u",
save : str = None, what : strLst = 'all',
saveFormat : str = "eps", saveDPI : int = 100,
show : bool = True, plotArgs : dict = {}, **figspecs):
"""
Do some nice plots of the samples.
Args:
warping(optional): Domain warping functions.
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): Where to save plot(s). Defaults to None, i.e. no
saving.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
plotArgs(optional): Optional arguments for fen/pyplot.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
RROMPyAssert(self._mode, message = "Cannot plot samples.")
self.samplingEngine.plotSamples(warping, name, save, what, saveFormat,
saveDPI, show, plotArgs, **figspecs)
def outParaviewSamples(self, name : str = "u", filename : str = "out",
times : Np1D = None, what : strLst = 'all',
forceNewFile : bool = True, folders : bool = False,
filePW = None):
"""
Output samples to ParaView file.
Args:
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
times(optional): Timestamps.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
folders(optional): Whether to split output in folders.
filePW(optional): Fenics File entity (for time series).
"""
RROMPyAssert(self._mode, message = "Cannot output samples.")
self.samplingEngine.outParaviewSamples(name = name,
filename = filename,
times = times, what = what,
forceNewFile = forceNewFile,
folders = folders,
filePW = filePW)
def outParaviewTimeDomainSamples(self, omegas : Np1D = None,
timeFinal : Np1D = None,
periodResolution : int = 20,
name : str = "u",
filename : str = "out",
forceNewFile : bool = True,
folders : bool = False):
"""
Output samples to ParaView file, converted to time domain.
Args:
omegas(optional): frequencies.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
folders(optional): Whether to split output in folders.
"""
RROMPyAssert(self._mode, message = "Cannot output samples.")
self.samplingEngine.outParaviewTimeDomainSamples(omegas = omegas,
timeFinal = timeFinal,
periodResolution = periodResolution,
name = name, filename = filename,
forceNewFile = forceNewFile,
folders = folders)
def setSamples(self, samplingEngine):
"""Copy samplingEngine and samples."""
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Transfering samples.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Transfering samples.", 10)
self.samplingEngine = copy(samplingEngine)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done transfering samples.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done transfering samples.", 10)
def setTrainedModel(self, model):
"""Deepcopy approximation from trained model."""
if hasattr(model, "storeTrainedModel"):
verb = model.verbosity
model.verbosity = 0
fileOut = model.storeTrainedModel()
model.verbosity = verb
else:
try:
fileOut = getNewFilename("trained_model", "pkl")
pickleDump(model.data.__dict__, fileOut)
except:
raise RROMPyException(("Failed to store model data. Parameter "
"model must have either "
"storeTrainedModel or "
"data.__dict__ properties."))
self.loadTrainedModel(fileOut)
osrm(fileOut)
@abstractmethod
def setupApprox(self):
"""
Setup approximant. (ABSTRACT)
Any specialization should include something like
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
...
self.trainedModel = ...
self.trainedModel.data = ...
self.trainedModel.data.approxParameters = copy(
self.approxParameters)
"""
pass
def checkComputedApprox(self) -> bool:
"""
Check if setup of new approximant is not needed.
Returns:
True if new setup is not needed. False otherwise.
"""
return self._mode == RROMPy_FRAGILE or (self.trainedModel is not None
and self.trainedModel.data.approxParameters == self.approxParameters)
def _pruneBeforeEval(self, mu:paramList, field:str, append:bool,
prune:bool) -> Tuple[paramList, Np1D, Np1D, bool]:
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
muExtra = emptyParameterList()
lastSolvedMus = getattr(self, "lastSolved" + field)
if (len(mu) > 0 and len(mu) == len(lastSolvedMus)
and mu == lastSolvedMus):
idx = np.arange(len(mu), dtype = np.int)
return muExtra, jExtra, idx, True
muKeep = copy(muExtra)
for j in range(len(mu)):
jPos = lastSolvedMus.find(mu[j])
if jPos is not None:
idx[j] = jPos
muKeep.append(mu[j])
else:
jExtra[j] = True
muExtra.append(mu[j])
if len(muKeep) > 0 and not append:
lastSolvedu = getattr(self, "u" + field)
idx[~jExtra] = getattr(self.__class__, "set" + field)(self,
muKeep, lastSolvedu[idx[~jExtra]], append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
return muExtra, jExtra, idx, append
def _setObject(self, mu:paramList, field:str, object:sampList,
append:bool) -> List[int]:
newMus, _ = checkParameterList(mu, self.npar)
newObj = sampleList(object)
if append:
getattr(self, "lastSolved" + field).append(newMus)
getattr(self, "u" + field).append(newObj)
Ltot = len(getattr(self, "u" + field))
return list(range(Ltot - len(newObj), Ltot))
setattr(self, "lastSolved" + field, copy(newMus))
setattr(self, "u" + field, copy(newObj))
return list(range(len(getattr(self, "u" + field))))
def setHF(self, muHF:paramList, uHF:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
return self._setObject(muHF, "HF", uHF, append)
def evalHF(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Find high fidelity solution with original parameters and arbitrary
parameter.
Args:
mu: Target parameter.
append(optional): Whether to append new HF solutions to old ones.
prune(optional): Whether to remove duplicates of already appearing
HF solutions.
"""
muExtra, jExtra, idx, append = self._pruneBeforeEval(mu, "HF", append,
prune)
if len(muExtra) > 0:
newuHFs = self.samplingEngine.solveLS(muExtra,
homogeneized = self.homogeneized)
idx[jExtra] = self.setHF(muExtra, newuHFs, append)
return list(idx)
def setApproxReduced(self, muApproxR:paramList, uApproxR:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
return self._setObject(muApproxR, "ApproxReduced", uApproxR, append)
def evalApproxReduced(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
append(optional): Whether to append new HF solutions to old ones.
prune(optional): Whether to remove duplicates of already appearing
HF solutions.
"""
self.setupApprox()
muExtra, jExtra, idx, append = self._pruneBeforeEval(mu,
"ApproxReduced",
append, prune)
if len(muExtra) > 0:
newuApproxs = self.trainedModel.getApproxReduced(muExtra)
idx[jExtra] = self.setApproxReduced(muExtra, newuApproxs, append)
return list(idx)
def setApprox(self, muApprox:paramList, uApprox:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
return self._setObject(muApprox, "Approx", uApprox, append)
def evalApprox(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate approximant at arbitrary parameter.
Args:
mu: Target parameter.
append(optional): Whether to append new HF solutions to old ones.
prune(optional): Whether to remove duplicates of already appearing
HF solutions.
"""
self.setupApprox()
muExtra, jExtra, idx, append = self._pruneBeforeEval(mu, "Approx",
append, prune)
if len(muExtra) > 0:
newuApproxs = self.trainedModel.getApprox(muExtra)
idx[jExtra] = self.setApprox(muExtra, newuApproxs, append)
return list(idx)
def getHF(self, mu:paramList, homogeneized : bool = False,
append : bool = False, prune : bool = True) -> sampList:
"""
Get HF solution at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
HFsolution.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalHF(mu, append = append, prune = prune)
uHFs = self.uHF(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
uHFs[j] += self.HFEngine.liftDirichletData(m)
if not self.homogeneized and homogeneized:
for j, m in enumerate(mu):
uHFs[j] -= self.HFEngine.liftDirichletData(m)
return uHFs
def getRHS(self, mu:paramList, homogeneized : bool = False,
duality : bool = True) -> sampList:
"""
Get linear system RHS at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Linear system RHS.
"""
return self.HFEngine.residual(None, mu, homogeneized = homogeneized,
duality = duality)
def getApproxReduced(self, mu:paramList, append : bool = False,
prune : bool = True) -> sampList:
"""
Get approximant at arbitrary parameter.
Args:
mu: Target parameter.
Returns:
Reduced approximant.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalApproxReduced(mu, append = append, prune = prune)
uApproxRs = self.uApproxReduced(idx)
return uApproxRs
def getApprox(self, mu:paramList, homogeneized : bool = False,
append : bool = False, prune : bool = True) -> sampList:
"""
Get approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = self.evalApprox(mu, append = append, prune = prune)
uApproxs = self.uApprox(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
uApproxs[j] += self.HFEngine.liftDirichletData(m)
if not self.homogeneized and homogeneized:
for j, m in enumerate(mu):
uApproxs[j] -= self.HFEngine.liftDirichletData(m)
return uApproxs
def getRes(self, mu:paramList, homogeneized : bool = False,
duality : bool = True) -> sampList:
"""
Get residual at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant residual.
"""
return self.HFEngine.residual(self.getApprox(mu, homogeneized), mu,
homogeneized = homogeneized,
duality = duality)
def getErr(self, mu:paramList, homogeneized : bool = False,
append : bool = False, prune : bool = True) -> sampList:
"""
Get error at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Approximant error.
"""
return (self.getApprox(mu, homogeneized, append = append, prune =prune)
- self.getHF(mu, homogeneized, append = append, prune = prune))
def getPoles(self, *args, **kwargs) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
self.setupApprox()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Computing poles of model.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing poles of model.", 20)
poles = self.trainedModel.getPoles(*args, **kwargs)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done computing poles.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing poles.", 20)
return poles
def storeTrainedModel(self, filenameBase : str = "trained_model",
forceNewFile : bool = True) -> str:
"""Store trained reduced model to file."""
self.setupApprox()
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Storing trained model to file.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Storing trained model to file.", 20)
if forceNewFile:
filename = getNewFilename(filenameBase, "pkl")
else:
filename = "{}.pkl".format(filenameBase)
pickleDump(self.trainedModel.data.__dict__, filename)
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done storing trained model.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done storing trained model.", 20)
return filename
def loadTrainedModel(self, filename:str):
"""Load trained reduced model from file."""
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Loading pre-trained model from file.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Loading pre-trained model from file.", 20)
datadict = pickleLoad(filename)
name = datadict.pop("name")
if name == "TrainedModelPade":
from rrompy.reduction_methods.trained_model import \
TrainedModelPade as tModel
elif name == "TrainedModelRB":
from rrompy.reduction_methods.trained_model import \
TrainedModelRB as tModel
else:
raise RROMPyException(("Trained model name not recognized. "
"Loading failed."))
self.mu0 = datadict.pop("mu0")
from rrompy.reduction_methods.trained_model import TrainedModelData
trainedModel = tModel()
trainedModel.verbosity = self.verbosity
trainedModel.timestamp = self.timestamp
data = TrainedModelData(name, self.mu0, datadict.pop("projMat"),
datadict.pop("rescalingExp"))
if "mus" in datadict:
data.mus = datadict.pop("mus")
approxParameters = datadict.pop("approxParameters")
data.approxParameters = copy(approxParameters)
if "sampler" in approxParameters:
self._approxParameters["sampler"] = approxParameters.pop("sampler")
self.approxParameters = copy(approxParameters)
if "mus" in data.__dict__:
self.mus = copy(data.mus)
if name == "TrainedModelPade":
self.scaleFactor = datadict.pop("scaleFactor")
data.scaleFactor = self.scaleFactor
for key in datadict:
setattr(data, key, datadict[key])
trainedModel.data = data
self.trainedModel = trainedModel
self._mode = RROMPy_FRAGILE
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done loading pre-trained model.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done loading pre-trained model.", 20)
diff --git a/rrompy/reduction_methods/centered/generic_centered_approximant.py b/rrompy/reduction_methods/centered/generic_centered_approximant.py
index aea1c71..d9e5fb3 100644
--- a/rrompy/reduction_methods/centered/generic_centered_approximant.py
+++ b/rrompy/reduction_methods/centered/generic_centered_approximant.py
@@ -1,113 +1,109 @@
# 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 .
#
import numpy as np
from rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
from rrompy.utilities.base.types import paramList
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyAssert
__all__ = ['GenericCenteredApproximant']
class GenericCenteredApproximant(GenericApproximant):
"""
ROM single-point approximant computation for parametric problems
(ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
S: Number of solution snapshots over which current approximant is
based upon.
initialHFData: HF problem initial data.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
"""
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericApproximant.S.fset(self, S)
RROMPyAssert(len(self.S), 1, "Length of S")
def computeDerivatives(self):
"""Compute derivatives of solution map starting from order 0."""
RROMPyAssert(self._mode,
message = "Cannot start derivative computation.")
if self.samplingEngine.nsamples != np.prod(self.S):
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Starting computation of derivatives.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of derivatives.", 5)
self.samplingEngine.iterSample([self.mu0[0]] * np.prod(self.S),
homogeneized = self.homogeneized)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done computing derivatives.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing derivatives.", 5)
def normApprox(self, mu:paramList, homogeneized : bool = False) -> float:
"""
Compute norm of approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of approximant.
"""
if not self.POD or self.homogeneized != homogeneized:
return super().normApprox(mu, homogeneized)
return np.linalg.norm(self.getApproxReduced(mu).data, axis = 0)
diff --git a/rrompy/reduction_methods/centered/rational_pade.py b/rrompy/reduction_methods/centered/rational_pade.py
index 26bcf03..1638e71 100644
--- a/rrompy/reduction_methods/centered/rational_pade.py
+++ b/rrompy/reduction_methods/centered/rational_pade.py
@@ -1,442 +1,409 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.base import checkRobustTolerance
from rrompy.reduction_methods.trained_model import (TrainedModelData,
TrainedModelPade as tModel)
from .generic_centered_approximant import GenericCenteredApproximant
from rrompy.utilities.base.types import (Np1D, Np2D, Tuple, DictAny, HFEng,
paramVal, paramList, sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import (nextDerivativeIndices,
hashDerivativeToIdx as hashD,
hashIdxToDerivative as hashI,
homogeneizedToFull)
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
__all__ = ['RationalPade']
class RationalPade(GenericCenteredApproximant):
"""
ROM single-point fast Pade' approximant computation for parametric
problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'E': number of derivatives used to compute Pade'; defaults to 0;
- 'M': degree of Pade' approximant numerator; defaults to 0;
- 'N': degree of Pade' approximant denominator; defaults to 0;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'E': number of derivatives used to compute Pade';
- 'M': degree of Pade' approximant numerator;
- 'N': degree of Pade' approximant denominator;
- 'robustTol': tolerance for robust Pade' denominator management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
S: Number of solution snapshots over which current approximant is
based upon.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
robustTol: Tolerance for robust Pade' denominator management.
E: Complete derivative depth level of S.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
G: Square Numpy 2D vector of size (N+1) corresponding to Pade'
denominator matrix (see paper).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["E", "M", "N", "robustTol"], [-1, 0, 0, 0])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def M(self):
"""Value of M.."""
return self._M
@M.setter
def M(self, M):
if M < 0: raise RROMPyException("M must be non-negative.")
self._M = M
self._approxParameters["M"] = self.M
if hasattr(self, "_E") and self.E >= 0 and self.E < self.M:
RROMPyWarning("Prescribed E is too small. Decreasing M.")
self.M = self.E
@property
def N(self):
"""Value of N."""
return self._N
@N.setter
def N(self, N):
if N < 0: raise RROMPyException("N must be non-negative.")
self._N = N
self._approxParameters["N"] = self.N
if hasattr(self, "_E") and self.E >= 0 and self.E < self.N:
RROMPyWarning("Prescribed E is too small. Decreasing N.")
self.N = self.E
@property
def E(self):
"""Value of E."""
return self._E
@E.setter
def E(self, E):
if E < 0:
if not hasattr(self, "_S"):
raise RROMPyException(("Value of E must be positive if S is "
"not yet assigned."))
E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
self._E = E
self._approxParameters["E"] = self.E
if (hasattr(self, "_S")
and self.E >= np.sum(hashI(np.prod(self.S), self.npar))):
RROMPyWarning("Prescribed S is too small. Decreasing E.")
self.E = -1
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
@property
def robustTol(self):
"""Value of tolerance for robust Pade' denominator management."""
return self._robustTol
@robustTol.setter
def robustTol(self, robustTol):
if robustTol < 0.:
RROMPyWarning(("Overriding prescribed negative robustness "
"tolerance to 0."))
robustTol = 0.
self._robustTol = robustTol
self._approxParameters["robustTol"] = self.robustTol
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericCenteredApproximant.S.fset(self, S)
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
if hasattr(self, "_E"): self.E = self.E
def _setupDenominator(self):
"""Compute Pade' denominator."""
RROMPyAssert(self._mode, message = "Cannot setup denominator.")
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Starting computation of denominator.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of denominator.", 7)
while self.N > 0:
if self.POD:
ev, eV = self.findeveVGQR()
else:
ev, eV = self.findeveVGExplicit()
newParameters = checkRobustTolerance(ev, self.N, self.robustTol)
if not newParameters:
break
self.approxParameters = newParameters
if self.N <= 0:
eV = np.ones((1, 1))
q = homogeneizedToFull(tuple([self.N + 1] * self.npar), self.npar,
eV[:, 0])
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing denominator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing denominator.", 7)
return q
def _setupNumerator(self):
"""Compute Pade' numerator."""
RROMPyAssert(self._mode, message = "Cannot setup numerator.")
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Starting computation of numerator.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of numerator.", 7)
P = np.zeros(tuple([self.M + 1] * self.npar) + (np.prod(self.S),),
dtype = np.complex)
mEnd = hashD([self.M + 1] + [0] * (self.npar - 1))
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
mnIdxs = nextDerivativeIndices([], self.npar, max(mEnd, nEnd))
for j in range(mEnd):
mIdx = mnIdxs[j]
for n in range(nEnd):
diffIdx = [x - y for (x, y) in zip(mIdx, mnIdxs[n])]
if all([x >= 0 for x in diffIdx]):
P[tuple(mIdx) + (hashD(diffIdx),)] = (
self.trainedModel.data.Q[tuple(mnIdxs[n])])
Pr = self.rescaleByParameter(P)
if self.POD:
Pr = np.tensordot(Pr, self.samplingEngine.RPOD.T, 1)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computation numerator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computation numerator.", 7)
return Pr
def setupApprox(self):
"""
Compute Pade' approximant. SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeDerivatives()
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
None, self.HFEngine.rescalingExp)
data.polytype = "MONOMIAL"
data.polytypeP = "MONOMIAL"
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
if self.N > 0:
Q = self._setupDenominator()
else:
self.setScaleParameter()
Q = np.ones(tuple([1] * self.npar), dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.scaleFactor = self.scaleFactor
self.trainedModel.data.projMat = copy(self.samplingEngine.samples(
list(range(np.prod(self.S)))))
self.trainedModel.data.P = copy(self._setupNumerator())
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def setScaleParameter(self) -> Np2D:
"""Compute parameter for rescaling."""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
self.computeDerivatives()
self.scaleFactor = [1.] * self.npar
for d in range(self.npar):
hashesd = [0]
for n in range(1, self.E + 1):
hashesd += [hashD([0] * (d - 1) + [n]
+ [0] * (self.npar - d - 1))]
if self.POD:
Rd = self.samplingEngine.RPOD[: hashesd[-1] + 1, hashesd]
Gd = np.diag(Rd.T.conj().dot(Rd))
else:
DerEd = self.samplingEngine.samples(hashesd)
Gd = self.HFEngine.norm(DerEd)
if len(Gd) > 1:
scaleCoeffs = np.polyfit(np.arange(len(Gd)), np.log(Gd), 1)
self.scaleFactor[d] = np.exp(- scaleCoeffs[0] / 2.)
def rescaleByParameter(self, R:Np2D) -> Np2D:
"""
Rescale by scale parameter.
Args:
R: Matrix whose columns need rescaling.
Returns:
Rescaled matrix.
"""
RIdxs = nextDerivativeIndices([], self.npar, R.shape[-1])
Rscaled = copy(R)
for j, RIdx in enumerate(RIdxs):
Rscaled[..., j] *= np.prod([x ** y for (x, y) in
zip(self.scaleFactor, RIdx)])
return Rscaled
def buildG(self):
"""Assemble Pade' denominator matrix."""
RROMPyAssert(self._mode, message = "Cannot compute G matrix.")
self.computeDerivatives()
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Building gramian matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Building gramian matrix.", 10)
eStart = hashD([self.E] + [0] * (self.npar - 1))
eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
eIdxs = [hashI(e, self.npar) for e in range(eStart, eEnd)]
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
nIdxs = nextDerivativeIndices([], self.npar, nEnd)
self.setScaleParameter()
if self.POD:
RPODE = self.rescaleByParameter(self.samplingEngine.RPOD[: eEnd,
: eEnd])
else:
DerE = self.rescaleByParameter(self.samplingEngine.samples(
list(range(eEnd))).data)
self.G = np.zeros((nEnd, nEnd), dtype = np.complex)
for eIdx in eIdxs:
nLoc = []
samplesIdxs = []
for n, nIdx in enumerate(nIdxs):
diffIdx = [x - y for (x, y) in zip(eIdx, nIdx)]
if all([x >= 0 for x in diffIdx]):
nLoc += [n]
samplesIdxs += [hashD(diffIdx)]
if self.POD:
RPODELoc = RPODE[: samplesIdxs[-1] + 1, samplesIdxs]
GLoc = RPODELoc.T.conj().dot(RPODELoc)
else:
DerELoc = DerE[:, samplesIdxs]
GLoc = self.HFEngine.innerProduct(DerELoc, DerELoc)
for j in range(len(nLoc)):
self.G[nLoc[j], nLoc] = self.G[nLoc[j], nLoc] + GLoc[j]
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done building gramian.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done building gramian.", 10)
def findeveVGExplicit(self) -> Tuple[Np1D, Np2D]:
"""
Compute explicitly eigenvalues and eigenvectors of Pade' denominator
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
self.buildG()
- if self.verbosity >= 7:
- verbosityDepth("INIT",
- "Solving eigenvalue problem for gramian matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Solving eigenvalue problem for gramian matrix.",
+ 7)
ev, eV = np.linalg.eigh(self.G)
- if self.verbosity >= 5:
- try: condev = ev[-1] / ev[0]
- except: condev = np.inf
- verbosityDepth("MAIN", ("Solved eigenvalue problem of size {} "
- "with condition number {:.4e}.").format(
- self.G.shape[0],
- condev),
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done solving eigenvalue problem.",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Solved eigenvalue problem of size {} with condition number "
+ "{:.4e}.").format(self.G.shape[0], ev[-1] / ev[0]), 5)
+ vbMng(self, "DEL", "Done solving eigenvalue problem.", 7)
return ev, eV
def findeveVGQR(self) -> Tuple[Np1D, Np2D]:
"""
Compute eigenvalues and eigenvectors of Pade' denominator matrix
through SVD of R factor.
Returns:
Eigenvalues in ascending order and corresponding eigenvector
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
RROMPyAssert(self.POD, True, "POD value")
self.computeDerivatives()
eStart = hashD([self.E] + [0] * (self.npar - 1))
eEnd = hashD([self.E + 1] + [0] * (self.npar - 1))
eIdxs = [hashI(e, self.npar) for e in range(eStart, eEnd)]
nEnd = hashD([self.N + 1] + [0] * (self.npar - 1))
nIdxs = nextDerivativeIndices([], self.npar, nEnd)
self.setScaleParameter()
RPODE = self.rescaleByParameter(self.samplingEngine.RPOD[: eEnd,
: eEnd])
Rstack = np.zeros((RPODE.shape[0] * (eEnd - eStart), nEnd),
dtype = np.complex)
for k, eIdx in enumerate(eIdxs):
nLoc = []
samplesIdxs = []
for n, nIdx in enumerate(nIdxs):
diffIdx = [x - y for (x, y) in zip(eIdx, nIdx)]
if all([x >= 0 for x in diffIdx]):
nLoc += [n]
samplesIdxs += [hashD(diffIdx)]
RPODELoc = RPODE[:, samplesIdxs]
for j in range(len(nLoc)):
Rstack[k * RPODE.shape[0] : (k + 1) * RPODE.shape[0],
nLoc[j]] = RPODELoc[:, j]
- if self.verbosity >= 7:
- verbosityDepth("INIT", ("Solving svd for square root of "
- "gramian matrix."),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Solving svd for square root of gramian matrix.",
+ 7)
sizeI = Rstack.shape
_, s, V = np.linalg.svd(Rstack, full_matrices = False)
eV = V[::-1, :].T.conj()
- if self.verbosity >= 5:
- try: condev = s[0] / s[-1]
- except: condev = np.inf
- verbosityDepth("MAIN", ("Solved svd problem of size {} x {} with "
- "condition number {:.4e}.").format(*sizeI,
- condev),
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done solving eigenvalue problem.",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Solved svd problem of size {} x {} with condition number "
+ "{:.4e}.").format(*sizeI, s[0] / s[-1]), 5)
+ vbMng(self, "DEL", "Done solving eigenvalue problem.", 7)
return s[::-1], eV
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.mu0.
Returns:
Normalized parameter.
"""
return self.trainedModel.centerNormalize(mu, mu0)
def getResidues(self) -> sampList:
"""
Obtain approximant residues.
Returns:
Matrix with residues as columns.
"""
return self.trainedModel.getResidues()
diff --git a/rrompy/reduction_methods/centered/rb_centered.py b/rrompy/reduction_methods/centered/rb_centered.py
index a646478..a609c4e 100644
--- a/rrompy/reduction_methods/centered/rb_centered.py
+++ b/rrompy/reduction_methods/centered/rb_centered.py
@@ -1,222 +1,203 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from .generic_centered_approximant import GenericCenteredApproximant
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.reduction_methods.base.rb_utils import projectAffineDecomposition
from rrompy.utilities.base.types import (Np1D, Np2D, Tuple, List, DictAny,
HFEng, paramVal, sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyWarning,
RROMPyAssert)
__all__ = ['RBCentered']
class RBCentered(GenericCenteredApproximant):
"""
ROM single-point fast RB approximant computation for parametric problems
with polynomial dependence up to degree 2.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'R': rank for Galerkin projection; defaults to prod(S);
- 'PODTolerance': tolerance for snapshots POD; defaults to -1.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'R': rank for Galerkin projection;
- 'PODTolerance': tolerance for snapshots POD.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
R: Rank for Galerkin projection.
PODTolerance: Tolerance for snapshots POD.
S: Number of solution snapshots over which current approximant is
based upon.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix wrt theta(mu).
bs: List of numpy vectors representing coefficients of linear system
RHS wrt theta(mu).
thetaAs: List of callables representing coefficients of linear system
matrix wrt mu.
thetabs: List of callables representing coefficients of linear system
RHS wrt mu.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix wrt theta(mu).
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS wrt theta(mu).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["R", "PODTolerance"], [1, -1])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Computing affine blocks of system.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing affine blocks of system.", 10)
self.As = self.HFEngine.affineLinearSystemA(self.mu0)
self.bs = self.HFEngine.affineLinearSystemb(self.mu0,
self.homogeneized)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done computing affine blocks.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing affine blocks.", 10)
self._postInit()
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericCenteredApproximant.S.fset(self, S)
if not hasattr(self, "_R"): self._R = np.prod(self.S)
@property
def R(self):
"""Value of R. Its assignment may change S."""
return self._R
@R.setter
def R(self, R):
if R < 0: raise RROMPyException("R must be non-negative.")
self._R = R
self._approxParameters["R"] = self.R
if hasattr(self, "_S") and np.prod(self.S) < self.R:
RROMPyWarning("Prescribed S is too small. Decreasing R.")
self.R = np.prod(self.S)
@property
def PODTolerance(self):
"""Value of PODTolerance."""
return self._PODTolerance
@PODTolerance.setter
def PODTolerance(self, PODTolerance):
self._PODTolerance = PODTolerance
self._approxParameters["PODTolerance"] = self.PODTolerance
def setupApprox(self):
"""Setup RB system."""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeDerivatives()
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing projection matrix.", 7)
if self.POD:
U, s, _ = np.linalg.svd(self.samplingEngine.RPOD)
s = s ** 2.
else:
Gramian = self.HFEngine.innerProduct(self.samplingEngine.samples,
self.samplingEngine.samples)
U, s, _ = np.linalg.svd(Gramian)
nsamples = self.samplingEngine.nsamples
snorm = np.cumsum(s[::-1]) / np.sum(s)
nPODTrunc = min(nsamples - np.argmax(snorm > self.PODTolerance),
self.R)
pMat = self.samplingEngine.samples.dot(U[:, : nPODTrunc])
- if self.verbosity >= 5:
- verbosityDepth("MAIN", ("Assembling {}x{} projection matrix from "
- "{} samples.").format(*(pMat.shape),
- nsamples),
- timestamp = self.timestamp)
-
+ vbMng(self, "MAIN",
+ ("Assembling {}x{} projection matrix from {} "
+ "samples.").format(*(pMat.shape), nsamples), 5)
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(pMat)
ARBs, bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing projection matrix.", 7)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def assembleReducedSystem(self, pMat : sampList = None,
pMatOld : sampList = None)\
-> Tuple[List[Np2D], List[Np1D]]:
"""Build affine blocks of RB linear system through projections."""
if pMat is None:
self.setupApprox()
ARBs = self.trainedModel.data.ARBs
bRBs = self.trainedModel.data.bRBs
else:
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Projecting affine terms of HF model.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Projecting affine terms of HF model.", 10)
ARBsOld = None if pMatOld is None else self.trainedModel.data.ARBs
bRBsOld = None if pMatOld is None else self.trainedModel.data.bRBs
ARBs, bRBs = projectAffineDecomposition(self.As, self.bs, pMat,
ARBsOld, bRBsOld, pMatOld)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done projecting affine terms.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done projecting affine terms.", 10)
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
index 11c620f..a55bff3 100644
--- a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
+++ b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
@@ -1,167 +1,163 @@
# 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 .
#
import numpy as np
from copy import deepcopy as copy
from rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
from rrompy.utilities.base.types import DictAny, HFEng, paramVal, paramList
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['GenericDistributedApproximant']
class GenericDistributedApproximant(GenericApproximant):
"""
ROM interpolant computation for parametric problems (ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
self._addParametersToList([], [], ["sampler"],
[QS([[0], [1]], "UNIFORM")])
del QS
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def mus(self):
"""Value of mus. Its assignment may reset snapshots."""
return self._mus
@mus.setter
def mus(self, mus):
mus, _ = checkParameterList(mus, self.npar)
musOld = copy(self.mus) if hasattr(self, '_mus') else None
if (musOld is None or len(mus) != len(musOld) or not mus == musOld):
self.resetSamples()
self._mus = mus
@property
def muBounds(self):
"""Value of muBounds."""
return self.sampler.lims
@property
def sampler(self):
"""Value of sampler."""
return self._sampler
@sampler.setter
def sampler(self, sampler):
if 'generatePoints' not in dir(sampler):
raise RROMPyException("Sampler type not recognized.")
if hasattr(self, '_sampler') and self._sampler is not None:
samplerOld = self.sampler
self._sampler = sampler
self._approxParameters["sampler"] = self.sampler.__str__()
if not 'samplerOld' in locals() or samplerOld != self.sampler:
self.resetSamples()
def setSamples(self, samplingEngine):
"""Copy samplingEngine and samples."""
super().setSamples(samplingEngine)
self.mus = copy(self.samplingEngine.mus)
def computeSnapshots(self):
"""Compute snapshots of solution map."""
RROMPyAssert(self._mode,
message = "Cannot start snapshot computation.")
if self.samplingEngine.nsamples != np.prod(self.S):
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Starting computation of snapshots.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of snapshots.", 5)
self.mus = self.sampler.generatePoints(self.S)
self.samplingEngine.iterSample(self.mus,
homogeneized = self.homogeneized)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done computing snapshots.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing snapshots.", 5)
def normApprox(self, mu:paramList, homogeneized : bool = False) -> float:
"""
Compute norm of approximant at arbitrary parameter.
Args:
mu: Target parameter.
homogeneized(optional): Whether to remove Dirichlet BC. Defaults to
False.
Returns:
Target norm of approximant.
"""
if not self.POD or self.homogeneized != homogeneized:
return super().normApprox(mu, homogeneized)
return np.linalg.norm(self.getApproxReduced(mu).data, axis = 0)
def computeScaleFactor(self):
"""Compute parameter rescaling factor."""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
self.scaleFactor = .5 * np.abs(
self.muBounds[0] ** self.HFEngine.rescalingExp
- self.muBounds[1] ** self.HFEngine.rescalingExp)
diff --git a/rrompy/reduction_methods/distributed/rational_interpolant.py b/rrompy/reduction_methods/distributed/rational_interpolant.py
index 64846fc..3845d8e 100644
--- a/rrompy/reduction_methods/distributed/rational_interpolant.py
+++ b/rrompy/reduction_methods/distributed/rational_interpolant.py
@@ -1,611 +1,571 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.base import checkRobustTolerance
from .generic_distributed_approximant import GenericDistributedApproximant
from rrompy.utilities.poly_fitting import customFit, customPInv
from rrompy.utilities.poly_fitting.polynomial import (polybases, polyfitname,
nextDerivativeIndices,
hashDerivativeToIdx as hashD,
hashIdxToDerivative as hashI,
homogeneizedpolyvander as hpvP,
homogeneizedToFull)
from rrompy.utilities.poly_fitting.radial_basis import (rbbases,
radialFunction,
polyfitname as polyfitnameR,
homogeneizedpolyvander as hpvR)
from rrompy.reduction_methods.trained_model import TrainedModelPade as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import (Np1D, Np2D, HFEng, DictAny, Tuple,
List, paramVal, paramList, sampList)
-from rrompy.utilities.base import verbosityDepth, multifactorial
+from rrompy.utilities.base import verbosityManager as vbMng, multifactorial
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
__all__ = ['RationalInterpolant']
class RationalInterpolant(GenericDistributedApproximant):
"""
ROM rational interpolant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'polybasis': type of polynomial basis for interpolation; allowed
values include 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults
to 'MONOMIAL';
- 'E': number of derivatives used to compute interpolant; defaults
to 0;
- 'M': degree of Pade' interpolant numerator; defaults to 0;
- 'N': degree of Pade' interpolant denominator; defaults to 0;
- 'radialBasis': radial basis family for interpolant numerator;
defaults to 0, i.e. no radial basis;
- 'radialBasisWeights': radial basis weights for interpolant
numerator; defaults to 0, i.e. identity;
- 'interpRcond': tolerance for interpolation; defaults to None;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'polybasis': type of polynomial basis for interpolation;
- 'E': number of derivatives used to compute interpolant;
- 'M': degree of Pade' interpolant numerator;
- 'N': degree of Pade' interpolant denominator;
- 'radialBasis': radial basis family for interpolant numerator;
- 'radialBasisWeights': radial basis weights for interpolant
numerator;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
- 'robustTol': tolerance for robust Pade' denominator management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
polybasis: type of polynomial basis for interpolation.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
radialBasis: Radial basis family for interpolant numerator.
radialBasisWeights: Radial basis weights for interpolant numerator.
interpRcond: Tolerance for interpolation via numpy.polyfit.
robustTol: Tolerance for robust Pade' denominator management.
E: Complete derivative depth level of S.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["polybasis", "E", "M", "N", "radialBasis",
"radialBasisWeights", "interpRcond",
"robustTol"],
["MONOMIAL", -1, 0, 0, 0, 1, -1, 0])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def polybasis(self):
"""Value of polybasis."""
return self._polybasis
@polybasis.setter
def polybasis(self, polybasis):
try:
polybasis = polybasis.upper().strip().replace(" ","")
if polybasis not in polybases:
raise RROMPyException("Prescribed polybasis not recognized.")
self._polybasis = polybasis
except:
RROMPyWarning(("Prescribed polybasis not recognized. Overriding "
"to 'MONOMIAL'."))
self._polybasis = "MONOMIAL"
self._approxParameters["polybasis"] = self.polybasis
@property
def radialBasis(self):
"""Value of radialBasis."""
return self._radialBasis
@radialBasis.setter
def radialBasis(self, radialBasis):
try:
if radialBasis != 0:
radialBasis = radialBasis.upper().strip().replace(" ","")
if radialBasis not in rbbases:
raise RROMPyException(("Prescribed radialBasis not "
"recognized."))
self._radialBasis = radialBasis
except:
RROMPyWarning(("Prescribed radialBasis not recognized. Overriding "
"to 0."))
self._radialBasis = 0
self._approxParameters["radialBasis"] = self.radialBasis
@property
def polybasisP(self):
if self.radialBasis == 0:
return self._polybasis
return self._polybasis + "_" + self.radialBasis
@property
def interpRcond(self):
"""Value of interpRcond."""
return self._interpRcond
@interpRcond.setter
def interpRcond(self, interpRcond):
self._interpRcond = interpRcond
self._approxParameters["interpRcond"] = self.interpRcond
@property
def radialBasisWeights(self):
"""Value of radialBasisWeights."""
return self._radialBasisWeights
@radialBasisWeights.setter
def radialBasisWeights(self, radialBasisWeights):
self._radialBasisWeights = radialBasisWeights
self._approxParameters["radialBasisWeights"] = self.radialBasisWeights
@property
def M(self):
"""Value of M. Its assignment may change S."""
return self._M
@M.setter
def M(self, M):
if M < 0: raise RROMPyException("M must be non-negative.")
self._M = M
self._approxParameters["M"] = self.M
if hasattr(self, "_E") and self.E >= 0 and self.E < self.M:
RROMPyWarning("Prescribed S is too small. Decreasing M.")
self.M = self.E
@property
def N(self):
"""Value of N. Its assignment may change S."""
return self._N
@N.setter
def N(self, N):
if N < 0: raise RROMPyException("N must be non-negative.")
self._N = N
self._approxParameters["N"] = self.N
if hasattr(self, "_E") and self.E >= 0 and self.E < self.N:
RROMPyWarning("Prescribed S is too small. Decreasing N.")
self.N = self.E
@property
def E(self):
"""Value of E."""
return self._E
@E.setter
def E(self, E):
if E < 0:
if not hasattr(self, "_S"):
raise RROMPyException(("Value of E must be positive if S is "
"not yet assigned."))
E = np.sum(hashI(np.prod(self.S), self.npar)) - 1
self._E = E
self._approxParameters["E"] = self.E
if (hasattr(self, "_S")
and self.E >= np.sum(hashI(np.prod(self.S), self.npar))):
RROMPyWarning("Prescribed S is too small. Decreasing E.")
self.E = -1
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
@property
def robustTol(self):
"""Value of tolerance for robust Pade' denominator management."""
return self._robustTol
@robustTol.setter
def robustTol(self, robustTol):
if robustTol < 0.:
RROMPyWarning(("Overriding prescribed negative robustness "
"tolerance to 0."))
robustTol = 0.
self._robustTol = robustTol
self._approxParameters["robustTol"] = self.robustTol
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericDistributedApproximant.S.fset(self, S)
if hasattr(self, "_M"): self.M = self.M
if hasattr(self, "_N"): self.N = self.N
if hasattr(self, "_E"): self.E = self.E
def resetSamples(self):
"""Reset samples."""
super().resetSamples()
self._musUniqueCN = None
self._derIdxs = None
self._reorder = None
def _setupInterpolationIndices(self):
"""Setup parameters for polyvander."""
RROMPyAssert(self._mode,
message = "Cannot setup interpolation indices.")
if self._musUniqueCN is None or len(self._reorder) != len(self.mus):
self._musUniqueCN, musIdxsTo, musIdxs, musCount = (
self.centerNormalize(self.mus).unique(return_index = True,
return_inverse = True,
return_counts = True))
self._musUnique = self.mus[musIdxsTo]
self._derIdxs = [None] * len(self._musUniqueCN)
self._reorder = np.empty(len(musIdxs), dtype = int)
filled = 0
for j, cnt in enumerate(musCount):
self._derIdxs[j] = nextDerivativeIndices([], self.mus.shape[1],
cnt)
jIdx = np.nonzero(musIdxs == j)[0]
self._reorder[jIdx] = np.arange(filled, filled + cnt)
filled += cnt
def _setupDenominator(self):
"""Compute Pade' denominator."""
RROMPyAssert(self._mode, message = "Cannot setup denominator.")
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Starting computation of denominator.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of denominator.", 7)
while self.N > 0:
invD = self._computeInterpolantInverseBlocks()
if self.POD:
ev, eV = self.findeveVGQR(self.samplingEngine.RPOD, invD)
else:
ev, eV = self.findeveVGExplicit(self.samplingEngine.samples,
invD)
newParams = checkRobustTolerance(ev, self.N, self.robustTol)
if not newParams:
break
self.approxParameters = newParams
if self.N <= 0:
self._N = 0
eV = np.ones((1, 1))
q = homogeneizedToFull(tuple([self.N + 1] * self.npar), self.npar,
eV[:, 0])
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing denominator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing denominator.", 7)
return q
def _setupNumerator(self):
"""Compute Pade' numerator."""
RROMPyAssert(self._mode, message = "Cannot setup numerator.")
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Starting computation of numerator.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of numerator.", 7)
Qevaldiag = np.zeros((len(self.mus), len(self.mus)),
dtype = np.complex)
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
self._setupInterpolationIndices()
idxGlob = 0
for j, derIdxs in enumerate(self._derIdxs):
nder = len(derIdxs)
idxLoc = np.arange(len(self.mus))[(self._reorder >= idxGlob)
* (self._reorder < idxGlob + nder)]
idxGlob += nder
Qval = [0] * nder
for der in range(nder):
derIdx = hashI(der, self.npar)
Qval[der] = (self.trainedModel.getQVal(
self._musUnique[j], derIdx,
scl = np.power(self.scaleFactor, -1.))
/ multifactorial(derIdx))
for derU, derUIdx in enumerate(derIdxs):
for derQ, derQIdx in enumerate(derIdxs):
diffIdx = [x - y for (x, y) in zip(derUIdx, derQIdx)]
if all([x >= 0 for x in diffIdx]):
diffj = hashD(diffIdx)
Qevaldiag[idxLoc[derU], idxLoc[derQ]] = Qval[diffj]
if self.POD:
Qevaldiag = Qevaldiag.dot(self.samplingEngine.RPOD.T)
self.trainedModel.verbosity = verb
while self.M >= 0:
if self.radialBasis == 0:
fitVander, _, argIdxs = hpvP(self._musUniqueCN, self.M,
self.polybasisP, self._derIdxs,
self._reorder,
scl = np.power(self.scaleFactor, -1.))
fitnameEff = polyfitname(self.polybasisP)
nsamplesPrint = "{}".format(len(fitVander))
else:
fitVander, _, argIdxs = hpvR(self._musUniqueCN, self.M,
self.polybasisP, self._derIdxs,
self._reorder, self.radialBasisWeights,
scl = np.power(self.scaleFactor, -1.))
fitnameEff = polyfitnameR(self.polybasisP)
nConstraints = len(fitVander) - len(Qevaldiag)
if nConstraints > 0:
Qevaldiag = np.pad(Qevaldiag, ((0, nConstraints), (0, 0)),
"constant")
elif nConstraints < 0:
Qevaldiag = Qevaldiag[: len(fitVander)]
fitVander = fitVander[argIdxs]
nsamplesPrint = "{}+{}".format(len(self.mus),
len(fitVander) - len(self.mus))
fitVander = fitVander[:, argIdxs]
fitOut = customFit(fitVander, Qevaldiag, full = True,
rcond = self.interpRcond)
- if self.verbosity >= 5:
- condfit = fitOut[1][2][0] / fitOut[1][2][-1]
- verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
- "through {}... Conditioning of LS "
- "system: {:.4e}.").format(
- nsamplesPrint, self.M,
- fitnameEff, condfit),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Fitting {} samples with degree {} through {}... "
+ "Conditioning of LS system: {:.4e}.").format(
+ nsamplesPrint, self.M, fitnameEff,
+ fitOut[1][2][0] / fitOut[1][2][-1]),
+ 5)
if fitOut[1][1] == fitVander.shape[1]:
P = fitOut[0]
break
RROMPyWarning("Polyfit is poorly conditioned. Reducing M by 1.")
self.M -= 1
if self.M < 0:
raise RROMPyException(("Instability in computation of numerator. "
"Aborting."))
if self.radialBasis == 0:
p = homogeneizedToFull(tuple([self.M + 1] * self.npar)
+ (P.shape[1],), self.npar, P)
else:
pGlob = homogeneizedToFull(
tuple([self.M + 1] * self.npar) + (P.shape[1],),
self.npar, P[len(self.mus) :])
p = radialFunction(self._musUniqueCN[self._reorder],
self.radialBasisWeights,
P[: len(self.mus)], pGlob)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing numerator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing numerator.", 7)
return p
def setupApprox(self):
"""
Compute Pade' interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeScaleFactor()
self.computeSnapshots()
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
self.samplingEngine.samples,
self.HFEngine.rescalingExp)
data.polytype = self.polybasis
data.polytypeP = self.polybasisP
data.scaleFactor = self.scaleFactor
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(self.samplingEngine.samples)
if self.N > 0:
Q = self._setupDenominator()
else:
Q = np.ones(tuple([1] * self.npar), dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.P = copy(self._setupNumerator())
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def _computeInterpolantInverseBlocks(self) -> List[Np2D]:
"""
Compute inverse factors for minimal interpolant target functional.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
self._setupInterpolationIndices()
while self.E >= 0:
eWidth = (hashD([self.E + 1] + [0] * (self.npar - 1))
- hashD([self.E] + [0] * (self.npar - 1)))
TE, _, argIdxs = hpvP(self._musUniqueCN, self.E, self.polybasis,
self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
fitOut = customPInv(TE[:, argIdxs], rcond = self.interpRcond,
full = True)
- if self.verbosity >= 5:
- condfit = fitOut[1][1][0] / fitOut[1][1][-1]
- verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
- "through {}... Conditioning of "
- "pseudoinverse system: {:.4e}.")\
- .format(TE.shape[0], self.E,
- polyfitname(self.polybasis),
- condfit),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Fitting {} samples with degree {} through {}... "
+ "Conditioning of pseudoinverse system: {:.4e}.").format(
+ TE.shape[0], self.E,
+ polyfitname(self.polybasis),
+ fitOut[1][1][0] / fitOut[1][1][-1]),
+ 5)
if fitOut[1][0] == len(argIdxs):
self._fitinv = fitOut[0][- eWidth : , :]
break
RROMPyWarning("Polyfit is poorly conditioned. Reducing E by 1.")
self.E -= 1
if self.E < 0:
raise RROMPyException(("Instability in computation of "
"denominator. Aborting."))
TN, _, argIdxs = hpvP(self._musUniqueCN, self.N, self.polybasis,
self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TN = TN[:, argIdxs]
invD = [None] * (eWidth)
for k in range(eWidth):
pseudoInv = np.diag(self._fitinv[k, :])
idxGlob = 0
for j, derIdxs in enumerate(self._derIdxs):
nder = len(derIdxs)
idxGlob += nder
if nder > 1:
idxLoc = np.arange(len(self.mus))[
(self._reorder >= idxGlob - nder)
* (self._reorder < idxGlob)]
invLoc = self._fitinv[k, idxLoc]
pseudoInv[np.ix_(idxLoc, idxLoc)] = 0.
for diffj, diffjIdx in enumerate(derIdxs):
for derQ, derQIdx in enumerate(derIdxs):
derUIdx = [x - y for (x, y) in
zip(diffjIdx, derQIdx)]
if all([x >= 0 for x in derUIdx]):
derU = hashD(derUIdx)
pseudoInv[idxLoc[derU], idxLoc[derQ]] = (
invLoc[diffj])
invD[k] = pseudoInv.dot(TN)
return invD
def findeveVGExplicit(self, sampleE:sampList,
invD:List[Np2D]) -> Tuple[Np1D, Np2D]:
"""
Compute explicitly eigenvalues and eigenvectors of Pade' denominator
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
nEnd = invD[0].shape[1]
eWidth = len(invD)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Building gramian matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Building gramian matrix.", 10)
gramian = self.HFEngine.innerProduct(sampleE, sampleE)
G = np.zeros((nEnd, nEnd), dtype = np.complex)
for k in range(eWidth):
G += invD[k].T.conj().dot(gramian.dot(invD[k]))
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done building gramian.",
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("INIT", ("Solving eigenvalue problem for "
- "gramian matrix."),
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done building gramian.", 10)
+ vbMng(self, "INIT", "Solving eigenvalue problem for gramian matrix.",
+ 7)
ev, eV = np.linalg.eigh(G)
- if self.verbosity >= 5:
- try: condev = ev[-1] / ev[0]
- except: condev = np.inf
- verbosityDepth("MAIN", ("Solved eigenvalue problem of "
- "size {} with condition number "
- "{:.4e}.").format(nEnd, condev),
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done solving eigenvalue problem.",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Solved eigenvalue problem of size {} with condition number "
+ "{:.4e}.").format(nEnd, ev[-1] / ev[0]), 5)
+ vbMng(self, "DEL", "Done solving eigenvalue problem.", 7)
return ev, eV
def findeveVGQR(self, RPODE:Np2D, invD:List[Np2D]) -> Tuple[Np1D, Np2D]:
"""
Compute eigenvalues and eigenvectors of Pade' denominator matrix
through SVD of R factor.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
nEnd = invD[0].shape[1]
S = RPODE.shape[0]
eWidth = len(invD)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Building half-gramian matrix stack.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Building half-gramian matrix stack.", 10)
Rstack = np.zeros((S * eWidth, nEnd), dtype = np.complex)
for k in range(eWidth):
Rstack[k * S : (k + 1) * S, :] = RPODE.dot(invD[k])
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done building half-gramian.",
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("INIT", ("Solving svd for square root of "
- "gramian matrix."),
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done building half-gramian.", 10)
+ vbMng(self, "INIT", "Solving svd for square root of gramian matrix.",
+ 7)
_, s, eV = np.linalg.svd(Rstack, full_matrices = False)
ev = s[::-1]
eV = eV[::-1, :].T.conj()
- if self.verbosity >= 5:
- try: condev = s[0] / s[-1]
- except: condev = np.inf
- verbosityDepth("MAIN", ("Solved svd problem of size {} x "
- "{} with condition number "
- "{:.4e}.").format(*Rstack.shape, condev),
- timestamp = self.timestamp)
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done solving svd.",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Solved svd problem of size {} x {} with condition number "
+ "{:.4e}.").format(*Rstack.shape, s[0] / s[-1]), 5)
+ vbMng(self, "DEL", "Done solving svd.", 7)
return ev, eV
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.mu0.
Returns:
Normalized parameter.
"""
return self.trainedModel.centerNormalize(mu, mu0)
def getResidues(self) -> Np1D:
"""
Obtain approximant residues.
Returns:
Matrix with residues as columns.
"""
return self.trainedModel.getResidues()
diff --git a/rrompy/reduction_methods/distributed/rb_distributed.py b/rrompy/reduction_methods/distributed/rb_distributed.py
index bc4a326..aa64217 100644
--- a/rrompy/reduction_methods/distributed/rb_distributed.py
+++ b/rrompy/reduction_methods/distributed/rb_distributed.py
@@ -1,229 +1,210 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from .generic_distributed_approximant import GenericDistributedApproximant
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.reduction_methods.base.rb_utils import projectAffineDecomposition
from rrompy.utilities.base.types import (Np1D, Np2D, List, Tuple, DictAny,
HFEng, paramVal, sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import (RROMPyWarning, RROMPyException,
RROMPyAssert)
__all__ = ['RBDistributed']
class RBDistributed(GenericDistributedApproximant):
"""
ROM RB approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'R': rank for Galerkin projection; defaults to prod(S);
- 'PODTolerance': tolerance for snapshots POD; defaults to -1.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxRadius: Dummy radius of approximant (i.e. distance from mu0 to
farthest sample point).
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
- 'R': rank for Galerkin projection;
- 'PODTolerance': tolerance for snapshots POD.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
POD: Whether to compute POD of snapshots.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
R: Rank for Galerkin projection.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix wrt theta(mu).
bs: List of numpy vectors representing coefficients of linear system
RHS wrt theta(mu).
thetaAs: List of callables representing coefficients of linear system
matrix wrt mu.
thetabs: List of callables representing coefficients of linear system
RHS wrt mu.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix wrt theta(mu).
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS wrt theta(mu).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["R", "PODTolerance"], [1, -1])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Computing affine blocks of system.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing affine blocks of system.", 10)
self.As = self.HFEngine.affineLinearSystemA(self.mu0)
self.bs = self.HFEngine.affineLinearSystemb(self.mu0,
self.homogeneized)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done computing affine blocks.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing affine blocks.", 10)
self._postInit()
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
GenericDistributedApproximant.S.fset(self, S)
if not hasattr(self, "_R"): self._R = np.prod(self.S)
@property
def R(self):
"""Value of R. Its assignment may change S."""
return self._R
@R.setter
def R(self, R):
if R < 0: raise RROMPyException("R must be non-negative.")
self._R = R
self._approxParameters["R"] = self.R
if hasattr(self, "_S") and np.prod(self.S) < self.R:
RROMPyWarning("Prescribed S is too small. Decreasing R.")
self.R = np.prod(self.S)
@property
def PODTolerance(self):
"""Value of PODTolerance."""
return self._PODTolerance
@PODTolerance.setter
def PODTolerance(self, PODTolerance):
self._PODTolerance = PODTolerance
self._approxParameters["PODTolerance"] = self.PODTolerance
def setupApprox(self):
"""Compute RB projection matrix."""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeSnapshots()
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing projection matrix.", 7)
if self.POD:
U, s, _ = np.linalg.svd(self.samplingEngine.RPOD)
s = s ** 2.
else:
Gramian = self.HFEngine.innerProduct(self.samplingEngine.samples,
self.samplingEngine.samples)
U, s, _ = np.linalg.svd(Gramian)
nsamples = self.samplingEngine.nsamples
snorm = np.cumsum(s[::-1]) / np.sum(s)
nPODTrunc = min(nsamples - np.argmax(snorm > self.PODTolerance),
self.R)
pMat = self.samplingEngine.samples.dot(U[:, : nPODTrunc])
- if self.verbosity >= 5:
- verbosityDepth("MAIN", ("Assembling {}x{} projection matrix from "
- "{} samples.").format(*(pMat.shape),
- nsamples),
- timestamp = self.timestamp)
-
+ vbMng(self, "MAIN",
+ ("Assembling {}x{} projection matrix from {} "
+ "samples.").format(*(pMat.shape), nsamples), 5)
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(pMat)
ARBs, bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing projection matrix.", 7)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def assembleReducedSystem(self, pMat : sampList = None,
pMatOld : sampList = None)\
-> Tuple[List[Np2D], List[Np1D]]:
"""Build affine blocks of RB linear system through projections."""
if pMat is None:
self.setupApprox()
ARBs = self.trainedModel.data.ARBs
bRBs = self.trainedModel.data.bRBs
else:
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Projecting affine terms of HF model.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Projecting affine terms of HF model.", 10)
ARBsOld = None if pMatOld is None else self.trainedModel.data.ARBs
bRBsOld = None if pMatOld is None else self.trainedModel.data.bRBs
ARBs, bRBs = projectAffineDecomposition(self.As, self.bs, pMat,
ARBsOld, bRBsOld, pMatOld)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done projecting affine terms.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done projecting affine terms.", 10)
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
index 9817e7c..f0ea714 100644
--- a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
+++ b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
@@ -1,597 +1,580 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.reduction_methods.distributed.generic_distributed_approximant \
import GenericDistributedApproximant
from rrompy.utilities.base.types import (Np1D, Np2D, DictAny, HFEng, Tuple,
List, normEng, paramVal, paramList,
sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.solver import normEngine
from rrompy.utilities.exception_manager import (RROMPyException, RROMPyAssert,
RROMPyWarning)
from rrompy.parameter import checkParameterList, emptyParameterList
__all__ = ['GenericDistributedGreedyApproximant']
def pruneSamples(mus:paramList, badmus:paramList,
tol : float = 1e-8) -> paramList:
"""Remove from mus all the elements which are too close to badmus."""
if len(badmus) == 0: return mus
musNp = np.array(mus(0))
badmus = np.array(badmus(0))
proximity = np.min(np.abs(musNp.reshape(-1, 1)
- np.tile(badmus.reshape(1, -1), [len(mus), 1])),
axis = 1).flatten()
idxPop = np.arange(len(mus))[proximity <= tol]
for i, j in enumerate(idxPop):
mus.pop(j - i)
return mus
class GenericDistributedGreedyApproximant(GenericDistributedApproximant):
"""
ROM greedy interpolant computation for parametric problems
(ABSTRACT).
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': number of starting training points;
- 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'interactive': whether to interactively terminate greedy
algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement; defaults to 0.2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'interactive': whether to interactively terminate greedy
algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement;
- 'nTestPoints': number of test points.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'trainSetGenerator': training sample points generator.
POD: whether to compute POD of snapshots.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
"""
TOL_INSTABILITY = 1e-6
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
self._addParametersToList(["greedyTol", "interactive", "maxIter",
"refinementRatio", "nTestPoints"],
[1e-2, False, 1e2, .2, 5e2],
["trainSetGenerator"],
[QS([[0], [1]], "UNIFORM")])
del QS
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized, verbosity = verbosity,
timestamp = timestamp)
RROMPyAssert(self.HFEngine.npar, 1, "Parameter dimension")
self._postInit()
@property
def greedyTol(self):
"""Value of greedyTol."""
return self._greedyTol
@greedyTol.setter
def greedyTol(self, greedyTol):
if greedyTol < 0:
raise RROMPyException("greedyTol must be non-negative.")
if hasattr(self, "_greedyTol") and self.greedyTol is not None:
greedyTolold = self.greedyTol
else:
greedyTolold = -1
self._greedyTol = greedyTol
self._approxParameters["greedyTol"] = self.greedyTol
if greedyTolold != self.greedyTol:
self.resetSamples()
@property
def interactive(self):
"""Value of interactive."""
return self._interactive
@interactive.setter
def interactive(self, interactive):
self._interactive = interactive
@property
def maxIter(self):
"""Value of maxIter."""
return self._maxIter
@maxIter.setter
def maxIter(self, maxIter):
if maxIter <= 0: raise RROMPyException("maxIter must be positive.")
if hasattr(self, "_maxIter") and self.maxIter is not None:
maxIterold = self.maxIter
else:
maxIterold = -1
self._maxIter = maxIter
self._approxParameters["maxIter"] = self.maxIter
if maxIterold != self.maxIter:
self.resetSamples()
@property
def refinementRatio(self):
"""Value of refinementRatio."""
return self._refinementRatio
@refinementRatio.setter
def refinementRatio(self, refinementRatio):
if refinementRatio <= 0. or refinementRatio > 1.:
raise RROMPyException(("refinementRatio must be between 0 "
"(excluded) and 1."))
if (hasattr(self, "_refinementRatio")
and self.refinementRatio is not None):
refinementRatioold = self.refinementRatio
else:
refinementRatioold = -1
self._refinementRatio = refinementRatio
self._approxParameters["refinementRatio"] = self.refinementRatio
if refinementRatioold != self.refinementRatio:
self.resetSamples()
@property
def nTestPoints(self):
"""Value of nTestPoints."""
return self._nTestPoints
@nTestPoints.setter
def nTestPoints(self, nTestPoints):
if nTestPoints <= 0:
raise RROMPyException("nTestPoints must be positive.")
if not np.isclose(nTestPoints, np.int(nTestPoints)):
raise RROMPyException("nTestPoints must be an integer.")
nTestPoints = np.int(nTestPoints)
if hasattr(self, "_nTestPoints") and self.nTestPoints is not None:
nTestPointsold = self.nTestPoints
else:
nTestPointsold = -1
self._nTestPoints = nTestPoints
self._approxParameters["nTestPoints"] = self.nTestPoints
if nTestPointsold != self.nTestPoints:
self.resetSamples()
@property
def trainSetGenerator(self):
"""Value of trainSetGenerator."""
return self._trainSetGenerator
@trainSetGenerator.setter
def trainSetGenerator(self, trainSetGenerator):
if 'generatePoints' not in dir(trainSetGenerator):
raise RROMPyException("trainSetGenerator type not recognized.")
if (hasattr(self, '_trainSetGenerator')
and self.trainSetGenerator is not None):
trainSetGeneratorOld = self.trainSetGenerator
self._trainSetGenerator = trainSetGenerator
self._approxParameters["trainSetGenerator"] = self.trainSetGenerator
if (not 'trainSetGeneratorOld' in locals()
or trainSetGeneratorOld != self.trainSetGenerator):
self.resetSamples()
def resetSamples(self):
"""Reset samples."""
super().resetSamples()
self._mus = emptyParameterList()
def initEstimatorNormEngine(self, normEngn : normEng = None):
"""Initialize estimator norm engine."""
if (normEngn is not None or not hasattr(self, "estimatorNormEngine")
or self.estimatorNormEngine is None):
if normEngn is None:
if not hasattr(self.HFEngine, "energyNormPartialDualMatrix"):
self.HFEngine.buildEnergyNormPartialDualForm()
estimatorEnergyMatrix = (
self.HFEngine.energyNormPartialDualMatrix)
else:
if hasattr(normEngn, "buildEnergyNormPartialDualForm"):
if not hasattr(normEngn, "energyNormPartialDualMatrix"):
normEngn.buildEnergyNormPartialDualForm()
estimatorEnergyMatrix = (
normEngn.energyNormPartialDualMatrix)
else:
estimatorEnergyMatrix = normEngn
self.estimatorNormEngine = normEngine(estimatorEnergyMatrix)
def errorEstimator(self, mus:paramList) -> List[complex]:
"""
Standard residual-based error estimator with explicit residual
computation.
"""
self.setupApprox()
if self.HFEngine.nbs == 1:
RHS = self.getRHS(mus[0], homogeneized = self.homogeneized,
duality = False)
RHSNorm = self.estimatorNormEngine.norm(RHS)
res = self.getRes(mus, homogeneized = self.homogeneized,
duality = False)
err = self.estimatorNormEngine.norm(res) / RHSNorm
else:
res = self.getRes(mus, homogeneized = self.homogeneized,
duality = False)
RHS = self.getRHS(mus, homogeneized = self.homogeneized,
duality = False)
err = (self.estimatorNormEngine.norm(res)
/ self.estimatorNormEngine.norm(RHS))
return np.abs(err)
def getMaxErrorEstimator(self, mus:paramList,
plot : bool = False) -> Tuple[Np1D, int, float]:
"""
Compute maximum of (and index of maximum of) error estimator over given
parameters.
"""
errorEstTest = self.errorEstimator(mus)
idxMaxEst = np.argmax(errorEstTest)
maxEst = errorEstTest[idxMaxEst]
if plot and not np.all(np.isinf(errorEstTest)):
musre = mus.re(0)
from matplotlib import pyplot as plt
plt.figure()
plt.semilogy(musre, errorEstTest, 'k')
plt.semilogy([musre[0], musre[-1]], [self.greedyTol] * 2, 'r--')
plt.semilogy(self.mus.re(0),
2. * self.greedyTol * np.ones(len(self.mus)), '*m')
plt.semilogy(musre[idxMaxEst], maxEst, 'xr')
plt.grid()
plt.show()
plt.close()
return errorEstTest, idxMaxEst, maxEst
def greedyNextSample(self, muidx:int, plotEst : bool = False)\
-> Tuple[Np1D, int, float, paramVal]:
"""Compute next greedy snapshot of solution map."""
RROMPyAssert(self._mode, message = "Cannot add greedy sample.")
mu = copy(self.muTest[muidx])
self.muTest.pop(muidx)
- if self.verbosity >= 2:
- verbosityDepth("MAIN", ("Adding {}-th sample point at {} to "
- "training set.").format(
- self.samplingEngine.nsamples + 1, mu),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Adding {}-th sample point at {} to training "
+ "set.").format(self.samplingEngine.nsamples + 1, mu), 2)
self.mus.append(mu)
self.samplingEngine.nextSample(mu, homogeneized = self.homogeneized)
errorEstTest, muidx, maxErrorEst = self.getMaxErrorEstimator(
self.muTest, plotEst)
return errorEstTest, muidx, maxErrorEst, self.muTest[muidx]
def _preliminaryTraining(self):
"""Initialize starting snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
self.computeScaleFactor()
if self.samplingEngine.nsamples > 0:
return
- if self.verbosity >= 2:
- verbosityDepth("INIT", "Starting computation of snapshots.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting computation of snapshots.", 2)
self.resetSamples()
self.mus = self.trainSetGenerator.generatePoints(self.S)
muLast = copy(self.mus[-1])
self.mus.pop()
muTestBase = self.sampler.generatePoints(self.nTestPoints)
if len(self.mus) > 0:
- if self.verbosity >= 2:
- verbosityDepth("MAIN",
- ("Adding first {} samples point at {} to "
- "training set.").format(np.prod(self.S) - 1,
- self.mus),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ ("Adding first {} samples point at {} to training "
+ "set.").format(np.prod(self.S) - 1, self.mus), 2)
self.samplingEngine.iterSample(self.mus,
homogeneized = self.homogeneized)
muTestBase = pruneSamples(muTestBase, self.mus,
1e-10 * self.scaleFactor[0]).sort()
self.muTest = emptyParameterList()
self.muTest.reset((len(muTestBase) + 1, self.mus.shape[1]))
self.muTest[: -1] = muTestBase
self.muTest[-1] = muLast
def _enrichTestSet(self, nTest:int):
"""Add extra elements to test set."""
RROMPyAssert(self._mode, message = "Cannot enrich test set.")
muTestExtra = self.sampler.generatePoints(2 * nTest)
muTotal = copy(self.mus)
muTotal.append(self.muTest)
muTestExtra = pruneSamples(muTestExtra, muTotal,
1e-10 * self.scaleFactor[0])
muTestNew = np.empty(len(self.muTest) + len(muTestExtra),
dtype = np.complex)
muTestNew[: len(self.muTest)] = self.muTest(0)
muTestNew[len(self.muTest) :] = muTestExtra(0)
self.muTest = checkParameterList(muTestNew.sort(), self.npar)
- if self.verbosity >= 5:
- verbosityDepth("MAIN", "Enriching test set by {} elements.".format(
- len(muTestExtra)),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ "Enriching test set by {} elements.".format(len(muTestExtra)), 5)
def greedy(self, plotEst : bool = False):
"""Compute greedy snapshots of solution map."""
RROMPyAssert(self._mode, message = "Cannot start greedy algorithm.")
if self.samplingEngine.nsamples > 0:
return
self._preliminaryTraining()
nTest = self.nTestPoints
errorEstTest, muidx, maxErrorEst, mu = self.greedyNextSample(-1,
plotEst)
- if self.verbosity >= 2:
- verbosityDepth("MAIN", ("Uniform testing error estimate "
- "{:.4e}.").format(maxErrorEst),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ "Uniform testing error estimate {:.4e}.".format(maxErrorEst), 2)
trainedModelOld = copy(self.trainedModel)
while (self.samplingEngine.nsamples < self.maxIter
and maxErrorEst > self.greedyTol):
if (1. - self.refinementRatio) * nTest > len(self.muTest):
self._enrichTestSet(nTest)
nTest = len(self.muTest)
muTestOld, maxErrorEstOld = self.muTest, maxErrorEst
errorEstTest, muidx, maxErrorEst, mu = self.greedyNextSample(
muidx, plotEst)
- if self.verbosity >= 2:
- verbosityDepth("MAIN", ("Uniform testing error estimate "
- "{:.4e}.").format(maxErrorEst),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ "Uniform testing error estimate {:.4e}.".format(maxErrorEst),
+ 2)
if (np.isnan(maxErrorEst) or np.isinf(maxErrorEst)
or maxErrorEstOld < maxErrorEst * self.TOL_INSTABILITY):
RROMPyWarning(("Instability in a posteriori estimator. "
"Starting preemptive greedy loop termination."))
maxErrorEst = maxErrorEstOld
self.muTest = muTestOld
self.mus = self.mus[:-1]
self.samplingEngine.popSample()
self.trainedModel.data = copy(trainedModelOld.data)
break
trainedModelOld.data = copy(self.trainedModel.data)
if (self.interactive and maxErrorEst <= self.greedyTol):
- verbosityDepth("MAIN", ("Required tolerance {} achieved. Want "
- "to decrease greedyTol and continue? "
- "Y/N").format(self.greedyTol),
- timestamp = self.timestamp, end = "")
+ vbMng(self, "MAIN",
+ ("Required tolerance {} achieved. Want to decrease "
+ "greedyTol and continue? Y/N").format(self.greedyTol),
+ 0, end = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
- verbosityDepth("MAIN", "Reducing value of greedyTol...",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN", "Reducing value of greedyTol...", 0)
while maxErrorEst <= self._greedyTol:
self._greedyTol *= .5
if (self.interactive
and self.samplingEngine.nsamples >= self.maxIter):
- verbosityDepth("MAIN", ("Maximum number of iterations {} "
- "reached. Want to increase maxIter "
- "and continue? Y/N").format(
- self.maxIter),
- timestamp = self.timestamp, end = "")
+ vbMng(self, "MAIN",
+ ("Maximum number of iterations {} reached. Want to "
+ "increase maxIter and continue? "
+ "Y/N").format(self.maxIter), 0, end = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
- verbosityDepth("MAIN", "Doubling value of maxIter...",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN", "Doubling value of maxIter...", 0)
self._maxIter *= 2
- if self.verbosity >= 2:
- verbosityDepth("DEL", ("Done computing snapshots (final snapshot "
- "count: {}).").format(
- self.samplingEngine.nsamples),
- timestamp = self.timestamp)
+ vbMng(self, "DEL",
+ ("Done computing snapshots (final snapshot count: "
+ "{}).").format(self.samplingEngine.nsamples), 2)
def checkComputedApprox(self) -> bool:
"""
Check if setup of new approximant is not needed.
Returns:
True if new setup is not needed. False otherwise.
"""
return (super().checkComputedApprox()
and len(self.mus) == self.trainedModel.data.projMat.shape[1])
def assembleReducedResidualGramian(self, pMat:sampList):
"""
Build residual gramian of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
if (not hasattr(self.trainedModel.data, "gramian")
or self.trainedModel.data.gramian is None):
gramian = self.estimatorNormEngine.innerProduct(pMat, pMat)
else:
Sold = self.trainedModel.data.gramian.shape[0]
S = len(self.mus)
if Sold > S:
gramian = self.trainedModel.data.gramian[: S, : S]
else:
idxOld = list(range(Sold))
idxNew = list(range(Sold, S))
gramian = np.empty((S, S), dtype = np.complex)
gramian[: Sold, : Sold] = self.trainedModel.data.gramian
gramian[: Sold, Sold :] = (
self.estimatorNormEngine.innerProduct(pMat(idxNew),
pMat(idxOld)))
gramian[Sold :, : Sold] = gramian[: Sold, Sold :].T.conj()
gramian[Sold :, Sold :] = (
self.estimatorNormEngine.innerProduct(pMat(idxNew),
pMat(idxNew)))
self.trainedModel.data.gramian = gramian
def assembleReducedResidualBlocksbb(self, bs:List[Np1D],
scaling : float = 1.):
"""
Build blocks (of type bb) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nbs = len(bs)
if (not hasattr(self.trainedModel.data, "resbb")
or self.trainedModel.data.resbb is None):
resbb = np.empty((nbs, nbs), dtype = np.complex)
for i in range(nbs):
Mbi = scaling ** i * bs[i]
resbb[i, i] = self.estimatorNormEngine.innerProduct(Mbi, Mbi)
for j in range(i):
Mbj = scaling ** j * bs[j]
resbb[i, j] = self.estimatorNormEngine.innerProduct(Mbj,
Mbi)
for i in range(nbs):
for j in range(i + 1, nbs):
resbb[i, j] = resbb[j, i].conj()
self.trainedModel.data.resbb = resbb
def assembleReducedResidualBlocksAb(self, As:List[Np2D], bs:List[Np1D],
pMat:sampList, scaling : float = 1.):
"""
Build blocks (of type Ab) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nAs = len(As)
nbs = len(bs)
S = len(self.mus)
if (not hasattr(self.trainedModel.data, "resAb")
or self.trainedModel.data.resAb is None):
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAb = np.empty((nbs, S, nAs), dtype = np.complex)
for j in range(nAs):
MAj = scaling ** (j + 1) * As[j].dot(pMat)
for i in range(nbs):
Mbi = scaling ** (i + 1) * bs[i]
resAb[i, :, j] = self.estimatorNormEngine.innerProduct(MAj,
Mbi)
else:
Sold = self.trainedModel.data.resAb.shape[1]
if Sold == S: return
if Sold > S:
resAb = self.trainedModel.data.resAb[:, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAb = np.empty((nbs, S, nAs), dtype = np.complex)
resAb[:, : Sold, :] = self.trainedModel.data.resAb
for j in range(nAs):
MAj = scaling ** (j + 1) * As[j].dot(pMat[:, Sold :])
for i in range(nbs):
Mbi = scaling ** (i + 1) * bs[i]
resAb[i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj, Mbi))
self.trainedModel.data.resAb = resAb
def assembleReducedResidualBlocksAA(self, As:List[Np2D], pMat:sampList,
scaling : float = 1.):
"""
Build blocks (of type AA) of reduced linear system through projections.
"""
self.initEstimatorNormEngine()
nAs = len(As)
S = len(self.mus)
if (not hasattr(self.trainedModel.data, "resAA")
or self.trainedModel.data.resAA is None):
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
for i in range(nAs):
MAi = scaling ** (i + 1) * As[i].dot(pMat)
resAA[:, i, :, i] = (
self.estimatorNormEngine.innerProduct(MAi, MAi))
for j in range(i):
MAj = scaling ** (j + 1) * As[j].dot(pMat)
resAA[:, i, :, j] = (
self.estimatorNormEngine.innerProduct(MAj, MAi))
for i in range(nAs):
for j in range(i + 1, nAs):
resAA[:, i, :, j] = resAA[:, j, :, i].T.conj()
else:
Sold = self.trainedModel.data.resAA.shape[0]
if Sold == S: return
if Sold > S:
resAA = self.trainedModel.data.resAA[: S, :, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
resAA = np.empty((S, nAs, S, nAs), dtype = np.complex)
resAA[: Sold, :, : Sold, :] = self.trainedModel.data.resAA
for i in range(nAs):
MAi = scaling ** (i + 1) * As[i].dot(pMat)
resAA[: Sold, i, Sold :, i] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, : Sold]))
resAA[Sold :, i, : Sold, i] = resAA[: Sold, i,
Sold :, i].T.conj()
resAA[Sold :, i, Sold :, i] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, Sold :]))
for j in range(i):
MAj = scaling ** (j + 1) * As[j].dot(pMat)
resAA[: Sold, i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, Sold :],
MAi[:, : Sold]))
resAA[Sold :, i, : Sold, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, : Sold],
MAi[:, Sold :]))
resAA[Sold :, i, Sold :, j] = (
self.estimatorNormEngine.innerProduct(MAj[:, Sold :],
MAi[:, Sold :]))
for i in range(nAs):
for j in range(i + 1, nAs):
resAA[: Sold, i, Sold :, j] = (
resAA[Sold :, j, : Sold, i].T.conj())
resAA[Sold :, i, : Sold, j] = (
resAA[: Sold, j, Sold :, i].T.conj())
resAA[Sold :, i, Sold :, j] = (
resAA[Sold :, j, Sold :, i].T.conj())
self.trainedModel.data.resAA = resAA
diff --git a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
index 6a697a6..b777bb0 100644
--- a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
@@ -1,426 +1,414 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from .generic_distributed_greedy_approximant import \
GenericDistributedGreedyApproximant
from rrompy.utilities.poly_fitting.polynomial import polybases, polydomcoeff
from rrompy.reduction_methods.distributed import RationalInterpolant
from rrompy.reduction_methods.trained_model import TrainedModelPade as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import Np1D, Np2D, DictAny, HFEng, paramVal
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
__all__ = ['RationalInterpolantGreedy']
class RationalInterpolantGreedy(GenericDistributedGreedyApproximant,
RationalInterpolant):
"""
ROM greedy rational interpolant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': number of starting training points;
- 'sampler': sample point generator;
- 'radialBasis': radial basis family for interpolant numerator;
defaults to 0, i.e. no radial basis;
- 'radialBasisWeights': radial basis weights for interpolant
numerator; defaults to 0, i.e. identity;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'interactive': whether to interactively terminate greedy
algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of training points to be exhausted
before training set refinement; defaults to 0.2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to Chebyshev sampler within muBounds;
- 'polybasis': type of basis for interpolation; allowed values
include 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults to
'MONOMIAL';
- 'Delta': difference between M and N in rational approximant;
defaults to 0;
- 'errorEstimatorKind': kind of error estimator; available values
include 'EXACT', 'BASIC', and 'BARE'; defaults to 'EXACT';
- 'interpRcond': tolerance for interpolation; defaults to None;
- 'robustTol': tolerance for robust Pade' denominator management;
defaults to 0.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
- 'radialBasis': radial basis family for interpolant numerator;
defaults to 0, i.e. no radial basis;
- 'radialBasisWeights': radial basis weights for interpolant
numerator; defaults to 0, i.e. identity;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'interactive': whether to interactively terminate greedy
algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- 'Delta': difference between M and N in rational approximant;
- 'errorEstimatorKind': kind of error estimator;
- 'interpRcond': tolerance for interpolation;
- 'robustTol': tolerance for robust Pade' denominator management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: whether to compute POD of snapshots.
S: number of test points.
sampler: Sample point generator.
radialBasis: Radial basis family for interpolant numerator.
radialBasisWeights: Radial basis weights for interpolant numerator.
greedyTol: uniform error tolerance for greedy algorithm.
interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
robustTol: tolerance for robust Pade' denominator management.
Delta: difference between M and N in rational approximant.
errorEstimatorKind: kind of error estimator.
interpRcond: tolerance for interpolation.
robustTol: tolerance for robust Pade' denominator management.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
"""
_allowedEstimatorKinds = ["EXACT", "BASIC", "BARE"]
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["Delta", "polybasis", "errorEstimatorKind",
"interpRcond", "robustTol"],
[0, "MONOMIAL", "EXACT", -1, 0],
toBeExcluded = ["E"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Computing Taylor blocks of system.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing Taylor blocks of system.", 7)
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs, (nAs + 1) * self.homogeneized)
self.As = [self.HFEngine.A(self.mu0, j + 1) for j in range(nAs)]
self.bs = [self.HFEngine.b(self.mu0, j, self.homogeneized)
for j in range(nbs)]
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing Taylor blocks.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing Taylor blocks.", 7)
self._postInit()
@property
def polybasis(self):
"""Value of polybasis."""
return self._polybasis
@polybasis.setter
def polybasis(self, polybasis):
try:
polybasis = polybasis.upper().strip().replace(" ","")
if polybasis not in polybases:
raise RROMPyException("Sample type not recognized.")
self._polybasis = polybasis
except:
RROMPyWarning(("Prescribed polybasis not recognized. Overriding "
"to 'MONOMIAL'."))
self._polybasis = "MONOMIAL"
self._approxParameters["polybasis"] = self.polybasis
@property
def Delta(self):
"""Value of Delta."""
return self._Delta
@Delta.setter
def Delta(self, Delta):
if not np.isclose(Delta, np.floor(Delta)):
raise RROMPyException("Delta must be an integer.")
if Delta < 0:
RROMPyWarning(("Error estimator unreliable for Delta < 0. "
"Overloading of errorEstimator is suggested."))
else:
Deltamin = (max(self.HFEngine.nbs,
self.HFEngine.nAs * self.homogeneized)
- 1 - 1 * (self.HFEngine.nAs > 1))
if Delta < Deltamin:
RROMPyWarning(("Method may be unreliable for selected Delta. "
"Suggested minimal value of Delta: {}.").format(
Deltamin))
self._Delta = Delta
self._approxParameters["Delta"] = self.Delta
@property
def errorEstimatorKind(self):
"""Value of errorEstimatorKind."""
return self._errorEstimatorKind
@errorEstimatorKind.setter
def errorEstimatorKind(self, errorEstimatorKind):
errorEstimatorKind = errorEstimatorKind.upper()
if errorEstimatorKind not in self._allowedEstimatorKinds:
RROMPyWarning(("Error estimator kind not recognized. Overriding "
"to 'EXACT'."))
errorEstimatorKind = "EXACT"
self._errorEstimatorKind = errorEstimatorKind
self._approxParameters["errorEstimatorKind"] = self.errorEstimatorKind
@property
def nTestPoints(self):
"""Value of nTestPoints."""
return self._nTestPoints
@nTestPoints.setter
def nTestPoints(self, nTestPoints):
if nTestPoints <= np.abs(self.Delta):
RROMPyWarning(("nTestPoints must be at least abs(Delta) + 1. "
"Increasing value to abs(Delta) + 1."))
nTestPoints = np.abs(self.Delta) + 1
if not np.isclose(nTestPoints, np.int(nTestPoints)):
raise RROMPyException("nTestPoints must be an integer.")
nTestPoints = np.int(nTestPoints)
if hasattr(self, "_nTestPoints") and self.nTestPoints is not None:
nTestPointsold = self.nTestPoints
else: nTestPointsold = -1
self._nTestPoints = nTestPoints
self._approxParameters["nTestPoints"] = self.nTestPoints
if nTestPointsold != self.nTestPoints:
self.resetSamples()
def _errorSamplingRatio(self, mus:Np1D, muRTest:Np1D,
muRTrain:Np1D) -> Np1D:
"""Scalar ratio in explicit error estimator."""
self.setupApprox()
testTile = np.tile(np.reshape(muRTest, (-1, 1)), [1, len(muRTrain)])
nodalVals = np.prod(testTile - np.reshape(muRTrain, (1, -1)), axis = 1)
denVals = self.trainedModel.getQVal(mus)
return np.abs(nodalVals / denVals)
def _RHSNorms(self, radiusb0:Np2D) -> Np1D:
"""High fidelity system RHS norms."""
self.assembleReducedResidualBlocks(full = False)
# 'ij,jk,ik->k', resbb, radiusb0, radiusb0.conj()
b0resb0 = np.sum(self.trainedModel.data.resbb.dot(radiusb0)
* radiusb0.conj(), axis = 0)
RHSnorms = np.power(np.abs(b0resb0), .5)
return RHSnorms
def _errorEstimatorBare(self) -> Np1D:
"""Bare residual-based error estimator."""
self.setupApprox()
self.assembleReducedResidualGramian(self.trainedModel.data.projMat)
pDom = self.trainedModel.data.P[-1, :]
LL = pDom.conj().dot(self.trainedModel.data.gramian.dot(pDom))
Adiag = self.As[0].diagonal()
LL = ((self.scaleFactor[0] * np.linalg.norm(Adiag)) ** 2. * LL
/ np.size(Adiag))
scalingDom = polydomcoeff(len(self.mus) - 1, self.polybasis)
return scalingDom * np.power(np.abs(LL), .5)
def _errorEstimatorBasic(self, muTest:paramVal, ratioTest:complex) -> Np1D:
"""Basic residual-based error estimator."""
resmu = self.HFEngine.residual(self.trainedModel.getApprox(muTest),
muTest, self.homogeneized,
duality = False)[0]
return np.abs(self.estimatorNormEngine.norm(resmu) / ratioTest)
def _errorEstimatorExact(self, muRTrain:Np1D, vanderBase:Np2D) -> Np1D:
"""Exact residual-based error estimator."""
self.setupApprox()
self.assembleReducedResidualBlocks(full = True)
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs - 1, nAs * self.homogeneized)
delta = len(self.mus) - len(self.trainedModel.data.Q)
nbsEff = max(0, nbs - delta)
momentQ = np.zeros(nbsEff, dtype = np.complex)
momentQu = np.zeros((len(self.mus), nAs), dtype = np.complex)
radiusbTen = np.zeros((nbsEff, nbsEff, vanderBase.shape[1]),
dtype = np.complex)
radiusATen = np.zeros((nAs, nAs, vanderBase.shape[1]),
dtype = np.complex)
if nbsEff > 0:
momentQ[0] = self.trainedModel.data.Q[-1]
radiusbTen[0, :, :] = vanderBase[: nbsEff, :]
momentQu[:, 0] = self.trainedModel.data.P[-1, :]
radiusATen[0, :, :] = vanderBase[: nAs, :]
Qvals = self.trainedModel.getQVal(self.mus)
for k in range(1, max(nAs, nbs * (nbsEff > 0))):
Qvals = Qvals * muRTrain
if k > delta and k < nbs:
momentQ[k - delta] = self._fitinv.dot(Qvals)
radiusbTen[k - delta, k :, :] = (
radiusbTen[0, : delta - k, :])
if k < nAs:
momentQu[:, k] = Qvals * self._fitinv
radiusATen[k, k :, :] = radiusATen[0, : - k, :]
if self.POD and nAs > 1:
momentQu[:, 1 :] = self.samplingEngine.RPOD.dot(
momentQu[:, 1 :])
radiusA = np.tensordot(momentQu, radiusATen, 1)
if nbsEff > 0:
radiusb = np.tensordot(momentQ, radiusbTen, 1)
# 'ij,jk,ik->k', resbb, radiusb, radiusb.conj()
ff = np.sum(self.trainedModel.data.resbb[delta + 1 :, delta + 1 :]\
.dot(radiusb) * radiusb.conj(), axis = 0)
# 'ijk,jkl,il->l', resAb, radiusA, radiusb.conj()
Lf = np.sum(np.tensordot(
self.trainedModel.data.resAb[delta :, :, :], radiusA, 2)
* radiusb.conj(), axis = 0)
else:
ff, Lf = 0., 0.
# 'ijkl,klt,ijt->t', resAA, radiusA, radiusA.conj()
LL = np.sum(np.tensordot(self.trainedModel.data.resAA, radiusA, 2)
* radiusA.conj(), axis = (0, 1))
scalingDom = polydomcoeff(len(self.mus) - 1, self.polybasis)
return scalingDom * np.power(np.abs(ff - 2. * np.real(Lf) + LL), .5)
def errorEstimator(self, mus:Np1D) -> Np1D:
"""Standard residual-based error estimator."""
self.setupApprox()
if (np.any(np.isnan(self.trainedModel.data.P[-1, :]))
or np.any(np.isinf(self.trainedModel.data.P[-1, :]))):
err = np.empty(len(mus))
err[:] = np.inf
return err
nAs = self.HFEngine.nAs - 1
nbs = max(self.HFEngine.nbs - 1, nAs * self.homogeneized)
muRTest = self.centerNormalize(mus)(0)
muRTrain = self.centerNormalize(self.mus)(0)
samplingRatio = self._errorSamplingRatio(mus, muRTest, muRTrain)
vanderBase = np.polynomial.polynomial.polyvander(muRTest,
max(nAs, nbs)).T
RHSnorms = self._RHSNorms(vanderBase[: nbs + 1, :])
if self.errorEstimatorKind == "BARE":
jOpt = self._errorEstimatorBare()
elif self.errorEstimatorKind == "BASIC":
idx_muTestSample = np.argmax(samplingRatio)
jOpt = self._errorEstimatorBasic(mus[idx_muTestSample],
samplingRatio[idx_muTestSample])
else: #if self.errorEstimatorKind == "EXACT":
jOpt = self._errorEstimatorExact(muRTrain, vanderBase[: -1, :])
return jOpt * samplingRatio / RHSnorms
def setupApprox(self, plotEst : bool = False):
"""
Compute Pade' interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.computeScaleFactor()
self.greedy(plotEst)
self._S = len(self.mus)
self._N, self._M, self._E = [self._S - 1] * 3
if self.Delta < 0:
self._M += self.Delta
else:
self._N -= self.Delta
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
self.samplingEngine.samples,
self.HFEngine.rescalingExp)
data.polytype = self.polybasis
data.polytypeP = self.polybasisP
data.scaleFactor = self.scaleFactor
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
self.trainedModel.data.projMat = copy(self.samplingEngine.samples)
self.trainedModel.data.mus = copy(self.mus)
if min(self.M, self.N) < 0:
- if self.verbosity >= 5:
- verbosityDepth("MAIN", "Minimal sample size not achieved.",
- timestamp = self.timestamp)
+ vbMng(self, "MAIN", "Minimal sample size not achieved.", 5)
Q = np.empty(tuple([max(self.N, 0) + 1] * self.npar),
dtype = np.complex)
P = np.empty(tuple([max(self.M, 0) + 1] * self.npar)
+ (len(self.mus),), dtype = np.complex)
Q[:] = np.nan
P[:] = np.nan
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(
self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Aborting computation of approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Aborting computation of approximant.", 5)
return
if self.N > 0:
Q = self._setupDenominator()
else:
Q = np.ones(tuple([1] * self.npar), dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
self.trainedModel.data.P = copy(self._setupNumerator())
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def assembleReducedResidualBlocks(self, full : bool = False):
"""Build affine blocks of reduced linear system through projections."""
scaling = self.trainedModel.data.scaleFactor[0]
self.assembleReducedResidualBlocksbb(self.bs, scaling)
if full:
pMat = self.trainedModel.data.projMat
self.assembleReducedResidualBlocksAb(self.As, self.bs[1 :],
pMat, scaling)
self.assembleReducedResidualBlocksAA(self.As, pMat, scaling)
diff --git a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
index d7bab29..d66f987 100644
--- a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
@@ -1,255 +1,241 @@
# 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 .
#
import numpy as np
from copy import deepcopy as copy
from .generic_distributed_greedy_approximant import \
GenericDistributedGreedyApproximant
from rrompy.reduction_methods.distributed import RBDistributed
from rrompy.reduction_methods.trained_model import TrainedModelRB as tModel
from rrompy.reduction_methods.trained_model import TrainedModelData
from rrompy.utilities.base.types import Np1D, DictAny, HFEng, paramVal
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['RBDistributedGreedy']
class RBDistributedGreedy(GenericDistributedGreedyApproximant, RBDistributed):
"""
ROM greedy RB approximant computation for parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'S': number of starting training points;
- 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'interactive': whether to interactively terminate greedy
algorithm; defaults to False;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement; defaults to 0.2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to Chebyshev sampler within muBounds.
Defaults to empty dict.
homogeneized(optional): Whether to homogeneize Dirichlet BCs. Defaults
to False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
mus: Array of snapshot parameters.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'interactive': whether to interactively terminate greedy
algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of test points to be exhausted before
test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
POD: whether to compute POD of snapshots.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
interactive: whether to interactively terminate greedy algorithm.
maxIter: maximum number of greedy steps.
refinementRatio: ratio of training points to be exhausted before
training set refinement.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
muBounds: list of bounds for parameter values.
samplingEngine: Sampling engine.
estimatorNormEngine: Engine for estimator norm computation.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
As: List of sparse matrices (in CSC format) representing coefficients
of linear system matrix wrt theta(mu).
bs: List of numpy vectors representing coefficients of linear system
RHS wrt theta(mu).
thetaAs: List of callables representing coefficients of linear system
matrix wrt mu.
thetabs: List of callables representing coefficients of linear system
RHS wrt mu.
ARBs: List of sparse matrices (in CSC format) representing coefficients
of compressed linear system matrix wrt theta(mu).
bRBs: List of numpy vectors representing coefficients of compressed
linear system RHS wrt theta(mu).
"""
def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Computing affine blocks of system.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing affine blocks of system.", 10)
self.As = self.HFEngine.affineLinearSystemA(self.mu0)
self.bs = self.HFEngine.affineLinearSystemb(self.mu0,
self.homogeneized)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done computing affine blocks.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing affine blocks.", 10)
self._postInit()
@property
def R(self):
"""Value of R."""
self._R = np.prod(self._S)
return self._R
@R.setter
def R(self, R):
RROMPyWarning(("R is used just to simplify inheritance, and its value "
"cannot be changed from that of prod(S)."))
@property
def PODTolerance(self):
"""Value of PODTolerance."""
self._PODTolerance = -1
return self._PODTolerance
@PODTolerance.setter
def PODTolerance(self, PODTolerance):
RROMPyWarning(("PODTolerance is used just to simplify inheritance, "
"and its value cannot be changed from -1."))
def errorEstimator(self, mus:Np1D) -> Np1D:
"""
Standard residual-based error estimator. Unreliable for unstable
problems (inf-sup constant is missing).
"""
self.setupApprox()
self.assembleReducedResidualBlocks(full = True)
nmus = len(mus)
nAs = self.trainedModel.data.resAA.shape[1]
nbs = self.trainedModel.data.resbb.shape[0]
thetaAs = self.trainedModel.data.thetaAs
thetabs = self.trainedModel.data.thetabs
radiusA = np.empty((len(self.mus), nAs, nmus), dtype = np.complex)
radiusb = np.empty((nbs, nmus), dtype = np.complex)
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
if verb >= 5:
mustr = mus
if nmus > 2:
mustr = "[{} ..({}).. {}]".format(mus[0], nmus - 2, mus[-1])
- verbosityDepth("INIT", ("Computing RB solution at mu = "
- "{}.").format(mustr),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Computing RB solution at mu = {}.".format(mustr), 0)
parmus, _ = checkParameterList(mus, self.npar)
uApproxRs = self.getApproxReduced(parmus)
for j, muPL in enumerate(parmus):
mu = muPL[0]
uApproxR = uApproxRs[j]
for i in range(nAs):
radiusA[:, i, j] = eval(thetaAs[i]) * uApproxR
for i in range(nbs):
radiusb[i, j] = eval(thetabs[i])
- if verb >= 5:
- verbosityDepth("DEL", "Done computing RB solution.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing RB solution.", 5)
self.trainedModel.verbosity = verb
# 'ij,jk,ik->k', resbb, radiusb, radiusb.conj()
ff = np.sum(self.trainedModel.data.resbb.dot(radiusb) * radiusb.conj(),
axis = 0)
# 'ijk,jkl,il->l', resAb, radiusA, radiusb.conj()
Lf = np.sum(np.tensordot(self.trainedModel.data.resAb, radiusA, 2)
* radiusb.conj(), axis = 0)
# 'ijkl,klt,ijt->t', resAA, radiusA, radiusA.conj()
LL = np.sum(np.tensordot(self.trainedModel.data.resAA, radiusA, 2)
* radiusA.conj(), axis = (0, 1))
return np.abs((LL - 2. * np.real(Lf) + ff) / ff) ** .5
def setupApprox(self, plotEst : bool = False):
"""Compute RB projection matrix."""
if self.checkComputedApprox():
return
RROMPyAssert(self._mode, message = "Cannot setup approximant.")
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Setting up {}.". format(self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Setting up {}.". format(self.name()), 5)
self.greedy(plotEst)
- if self.verbosity >= 7:
- verbosityDepth("INIT", "Computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Computing projection matrix.", 7)
pMat = self.samplingEngine.samples
if self.trainedModel is None:
self.trainedModel = tModel()
self.trainedModel.verbosity = self.verbosity
self.trainedModel.timestamp = self.timestamp
data = TrainedModelData(self.trainedModel.name(), self.mu0,
pMat, self.HFEngine.rescalingExp)
data.thetaAs = self.HFEngine.affineWeightsA(self.mu0)
data.thetabs = self.HFEngine.affineWeightsb(self.mu0,
self.homogeneized)
ARBs, bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
pMatOld = self.trainedModel.data.projMat
Sold = pMatOld.shape[1]
idxNew = list(range(Sold, pMat.shape[1]))
ARBs, bRBs = self.assembleReducedSystem(pMat(idxNew), pMatOld)
self.trainedModel.data.projMat = copy(pMat)
self.trainedModel.data.mus = copy(self.mus)
self.trainedModel.data.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
- if self.verbosity >= 7:
- verbosityDepth("DEL", "Done computing projection matrix.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done computing projection matrix.", 7)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Done setting up approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done setting up approximant.", 5)
def assembleReducedResidualBlocks(self, full : bool = False):
"""Build affine blocks of RB linear system through projections."""
self.assembleReducedResidualBlocksbb(self.bs)
if full:
pMat = self.trainedModel.data.projMat
self.assembleReducedResidualBlocksAb(self.As, self.bs, pMat)
self.assembleReducedResidualBlocksAA(self.As, pMat)
+
diff --git a/rrompy/reduction_methods/trained_model/trained_model_pade.py b/rrompy/reduction_methods/trained_model/trained_model_pade.py
index 1a4abb9..6e4b392 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_pade.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_pade.py
@@ -1,172 +1,159 @@
# 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 .
#
import numpy as np
from . import TrainedModel
from rrompy.utilities.base.types import (Np1D, List, paramVal, paramList,
sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.poly_fitting.polynomial import polyval, polyroots
from rrompy.utilities.poly_fitting.radial_basis import polyval as polyvalR
from rrompy.utilities.exception_manager import RROMPyAssert, RROMPyException
from rrompy.parameter import checkParameter, checkParameterList
from rrompy.sampling import sampleList
__all__ = ['TrainedModelPade']
class TrainedModelPade(TrainedModel):
"""
ROM approximant evaluation for Pade' approximant.
Attributes:
Data: dictionary with all that can be pickled.
"""
def centerNormalize(self, mu : paramList = [],
mu0 : paramVal = None) -> paramList:
"""
Compute normalized parameter to be plugged into approximant.
Args:
mu: Parameter(s) 1.
mu0: Parameter(s) 2. If None, set to self.data.mu0.
Returns:
Normalized parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
if mu0 is None: mu0 = self.data.mu0
rad = ((mu ** self.data.rescalingExp - mu0 ** self.data.rescalingExp)
/ self.data.scaleFactor)
return rad
def getPVal(self, mu : paramList = [], der : List[int] = None) -> sampList:
"""
Evaluate Pade' numerator at arbitrary parameter.
Args:
mu: Target parameter.
der(optional): Derivatives to take before evaluation.
"""
mu, _ = checkParameterList(mu, self.data.npar)
- if self.verbosity >= 17:
- verbosityDepth("INIT", ("Evaluating numerator at mu = "
- "{}.").format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Evaluating numerator at mu = {}.".format(mu), 17)
muCenter = self.centerNormalize(mu)
if "_" in self.data.polytypeP:
p = sampleList(polyvalR(muCenter, self.data.P,
self.data.polytypeP, der))
else:
p = sampleList(polyval(muCenter, self.data.P,
self.data.polytypeP, der))
- if self.verbosity >= 17:
- verbosityDepth("DEL", "Done evaluating numerator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done evaluating numerator.", 17)
return p
def getQVal(self, mu:Np1D, der : List[int] = None,
scl : Np1D = None) -> Np1D:
"""
Evaluate Pade' denominator at arbitrary parameter.
Args:
mu: Target parameter.
der(optional): Derivatives to take before evaluation.
"""
mu, _ = checkParameterList(mu, self.data.npar)
- if self.verbosity >= 17:
- verbosityDepth("INIT", ("Evaluating denominator at mu = "
- "{}.").format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Evaluating denominator at mu = {}.".format(mu),
+ 17)
muCenter = self.centerNormalize(mu)
q = polyval(muCenter, self.data.Q, self.data.polytype, der, scl)
- if self.verbosity >= 17:
- verbosityDepth("DEL", "Done evaluating denominator.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done evaluating denominator.", 17)
return q
def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
if (not hasattr(self, "lastSolvedApproxReduced")
or self.lastSolvedApproxReduced != mu):
- if self.verbosity >= 12:
- verbosityDepth("INIT", ("Evaluating approximant at mu = "
- "{}.").format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Evaluating approximant at mu = {}.".format(mu), 12)
self.uApproxReduced = self.getPVal(mu) / self.getQVal(mu)
- if self.verbosity >= 12:
- verbosityDepth("DEL", "Done evaluating approximant.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done evaluating approximant.", 12)
self.lastSolvedApproxReduced = mu
return self.uApproxReduced
def getPoles(self, *args, **kwargs) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
if len(args) + len(kwargs) > 1:
raise RROMPyException(("Wrong number of parameters passed. "
"Only 1 available."))
elif len(args) + len(kwargs) == 1:
if len(args) == 1:
mVals = args[0]
else:
mVals = kwargs["marginalVals"]
if not hasattr(mVals, "__len__"): mVals = [mVals]
mVals = list(mVals)
else:
mVals = [None]
try:
rDim = mVals.index(None)
if rDim < len(mVals) - 1 and None in mVals[rDim + 1 :]:
raise
except:
raise RROMPyException(("Exactly 1 'None' entry in "
"marginalVals must be provided."))
mVals[rDim] = self.data.mu0(rDim)
mVals = self.centerNormalize(checkParameter(mVals, len(mVals)))
mVals = list(mVals.data.flatten())
mVals[rDim] = None
return np.power(self.data.mu0(rDim) ** self.data.rescalingExp[rDim]
+ self.data.scaleFactor[rDim]
* polyroots(self.data.Q, self.data.polytype, mVals),
1. / self.data.rescalingExp[rDim])
def getResidues(self) -> Np1D:
"""
Obtain approximant residues.
Returns:
Numpy matrix with residues as columns.
"""
pls = self.getPoles()
poles, _ = checkParameterList(pls, 1)
res = (self.data.projMat.dot(self.getPVal(poles).data)
/ self.getQVal(poles, 1))
return pls, res
diff --git a/rrompy/reduction_methods/trained_model/trained_model_rb.py b/rrompy/reduction_methods/trained_model/trained_model_rb.py
index 9e82f57..607f9a8 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_rb.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_rb.py
@@ -1,113 +1,101 @@
# 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 .
#
import numpy as np
from scipy.linalg import eigvals
from .trained_model import TrainedModel
from rrompy.utilities.base.types import Np1D, paramList, sampList
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
from rrompy.parameter import checkParameterList
from rrompy.sampling import emptySampleList
__all__ = ['TrainedModelRB']
class TrainedModelRB(TrainedModel):
"""
ROM approximant evaluation for RB approximant.
Attributes:
Data: dictionary with all that can be pickled.
"""
def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mus, _ = checkParameterList(mu, self.data.npar)
if (not hasattr(self, "lastSolvedApproxReduced")
or self.lastSolvedApproxReduced != mus):
- if self.verbosity >= 12:
- verbosityDepth("INIT", ("Computing RB solution at mu = "
- "{}.").format(mus),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Computing RB solution at mu = {}.".format(mus), 12)
thetaAs, thetabs = self.data.thetaAs, self.data.thetabs
ARBs, bRBs = self.data.ARBs, self.data.bRBs
self.uApproxReduced = emptySampleList()
self.uApproxReduced.reset((ARBs[0].shape[0], len(mu)),
self.data.projMat.dtype)
for i, muPL in enumerate(mus):
mu = muPL[0]
- if self.verbosity >= 17:
- verbosityDepth("INIT", ("Assembling reduced model for mu "
- "= {}.").format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Assembling reduced model for mu = {}.".format(mu), 17)
ARBmu = eval(thetaAs[0]) * ARBs[0]
bRBmu = eval(thetabs[0]) * bRBs[0]
for j in range(1, len(ARBs)):
ARBmu += eval(thetaAs[j]) * ARBs[j]
for j in range(1, len(bRBs)):
bRBmu += eval(thetabs[j]) * bRBs[j]
- if self.verbosity >= 17:
- verbosityDepth("DEL", "Done assembling reduced model.",
- timestamp = self.timestamp)
- if self.verbosity >= 15:
- verbosityDepth("INIT", ("Solving reduced model for mu = "
- "{}.").format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done assembling reduced model.", 17)
+ vbMng(self, "INIT",
+ "Solving reduced model for mu = {}.".format(mu), 15)
self.uApproxReduced[i] = np.linalg.solve(ARBmu, bRBmu)
- if self.verbosity >= 15:
- verbosityDepth("DEL", "Done solving reduced model.",
- timestamp = self.timestamp)
- if self.verbosity >= 12:
- verbosityDepth("DEL", "Done computing RB solution.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done solving reduced model.", 15)
+ vbMng(self, "DEL", "Done computing RB solution.", 12)
self.lastSolvedApproxReduced = mus
return self.uApproxReduced
def getPoles(self, *args, **kwargs) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
RROMPyAssert(self.data.npar, 1, "Number of parameters")
RROMPyWarning(("Impossible to compute poles in general affine "
"parameter dependence. Results subject to "
"interpretation/rescaling, or possibly completely "
"wrong."))
ARBs = self.data.ARBs
R = ARBs[0].shape[0]
if len(ARBs) < 2:
return
A = np.eye(R * (len(ARBs) - 1), dtype = np.complex)
B = np.zeros_like(A)
A[: R, : R] = - ARBs[0]
for j in range(len(ARBs) - 1):
Aj = ARBs[j + 1]
B[: R, j * R : (j + 1) * R] = Aj
II = np.arange(R, R * (len(ARBs) - 1))
B[II, II - R] = 1.
return np.power(eigvals(A, B, *args, **kwargs)
+ self.data.mu0(0, 0) ** self.data.rescalingExp[0],
1. / self.data.rescalingExp[0])
diff --git a/rrompy/sampling/base/sampling_engine_base.py b/rrompy/sampling/base/sampling_engine_base.py
index 57326a8..f0ab1f3 100644
--- a/rrompy/sampling/base/sampling_engine_base.py
+++ b/rrompy/sampling/base/sampling_engine_base.py
@@ -1,197 +1,189 @@
# 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 .
#
import numpy as np
from rrompy.utilities.base.types import (Np1D, HFEng, List, strLst, paramVal,
paramList, sampList)
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.parameter import (emptyParameterList, checkParameter,
checkParameterList)
from rrompy.sampling import emptySampleList
__all__ = ['SamplingEngineBase']
class SamplingEngineBase:
"""HERE"""
def __init__(self, HFEngine:HFEng, verbosity : int = 10,
timestamp : bool = True, allowRepeatedSamples : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
self.allowRepeatedSamples = allowRepeatedSamples
- if self.verbosity >= 10:
- verbosityDepth("INIT",
- "Initializing sampling engine of type {}.".format(
- self.name()),
- timestamp = self.timestamp)
+ vbMng(self, "INIT",
+ "Initializing sampling engine of type {}.".format(self.name()),
+ 10)
self.HFEngine = HFEngine
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done initializing sampling engine.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done initializing sampling engine.", 10)
def name(self) -> str:
return self.__class__.__name__
def __str__(self) -> str:
return self.name()
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def resetHistory(self):
self.samples = emptySampleList()
self.nsamples = 0
self.mus = emptyParameterList()
self._derIdxs = []
def popSample(self):
if hasattr(self, "nsamples") and self.nsamples > 1:
if self.samples.shape[1] > self.nsamples:
RROMPyWarning(("More than 'nsamples' memory allocated for "
"samples. Popping empty sample column."))
self.nsamples += 1
self.nsamples -= 1
self.samples.pop()
self.mus.pop()
else:
self.resetHistory()
def preallocateSamples(self, u:sampList, mu:paramVal, n:int):
self.samples.reset((u.shape[0], n), u.dtype)
self.samples[0] = u
mu = checkParameter(mu, self.HFEngine.npar)
self.mus.reset((n, self.HFEngine.npar))
self.mus[0] = mu[0]
@property
def HFEngine(self):
"""Value of HFEngine. Its assignment resets history."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
self._HFEngine = HFEngine
self.resetHistory()
def solveLS(self, mu : paramList = [], RHS : sampList = None,
homogeneized : bool = False) -> sampList:
"""
Solve linear system.
Args:
mu: Parameter value.
Returns:
Solution of system.
"""
mu, _ = checkParameterList(mu, self.HFEngine.npar)
- if self.verbosity >= 15:
- verbosityDepth("INIT", "Solving HF model for mu = {}.".format(mu),
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Solving HF model for mu = {}.".format(mu), 15)
u = self.HFEngine.solve(mu, RHS, homogeneized)
- if self.verbosity >= 15:
- verbosityDepth("DEL", "Done solving HF model.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done solving HF model.", 15)
return u
def plotSamples(self, warping : List[callable] = None, name : str = "u",
save : str = None, what : strLst = 'all',
saveFormat : str = "eps", saveDPI : int = 100,
show : bool = True, plotArgs : dict = {}, **figspecs):
"""
Do some nice plots of the samples.
Args:
warping(optional): Domain warping functions.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): Where to save plot(s). Defaults to None, i.e. no
saving.
what(optional): Which plots to do. If list, can contain 'ABS',
'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard 'ALL'.
Defaults to 'ALL'.
saveFormat(optional): Format for saved plot(s). Defaults to "eps".
saveDPI(optional): DPI for saved plot(s). Defaults to 100.
show(optional): Whether to show figure. Defaults to True.
plotArgs(optional): Optional arguments for fen/pyplot.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
for j in range(self.nsamples):
self.HFEngine.plot(self.samples[j], warping,
"{}_{}".format(name, j), save, what, saveFormat,
saveDPI, show, plotArgs, **figspecs)
def outParaviewSamples(self, name : str = "u", folders : bool = True,
filename : str = "out", times : Np1D = None,
what : strLst = 'all', forceNewFile : bool = True,
filePW = None):
"""
Output samples to ParaView file.
Args:
name(optional): Base name to be used for data output.
folders(optional): Whether to split output in folders.
filename(optional): Name of output file.
times(optional): Timestamps.
what(optional): Which plots to do. If list, can contain 'MESH',
'ABS', 'PHASE', 'REAL', 'IMAG'. If str, same plus wildcard
'ALL'. Defaults to 'ALL'.
forceNewFile(optional): Whether to create new output file.
filePW(optional): Fenics File entity (for time series).
"""
if times is None: times = [0.] * self.nsamples
for j in range(self.nsamples):
self.HFEngine.outParaview(self.samples[j],
name = "{}_{}".format(name, j),
filename = "{}_{}".format(filename, j),
time = times[j], what = what,
forceNewFile = forceNewFile,
folder = folders, filePW = filePW)
def outParaviewTimeDomainSamples(self, omegas : Np1D = None,
timeFinal : Np1D = None,
periodResolution : int = 20,
name : str = "u", folders : bool = True,
filename : str = "out",
forceNewFile : bool = True):
"""
Output samples to ParaView file, converted to time domain.
Args:
omegas(optional): frequencies.
timeFinal(optional): final time of simulation.
periodResolution(optional): number of time steps per period.
name(optional): Base name to be used for data output.
folders(optional): Whether to split output in folders.
filename(optional): Name of output file.
forceNewFile(optional): Whether to create new output file.
"""
if omegas is None: omegas = np.real(self.mus)
if not isinstance(timeFinal, (list, tuple,)):
timeFinal = [timeFinal] * self.nsamples
for j in range(self.nsamples):
self.HFEngine.outParaviewTimeDomain(self.samples[j],
omega = omegas[j],
timeFinal = timeFinal[j],
periodResolution = periodResolution,
name = "{}_{}".format(name, j),
filename = "{}_{}".format(filename, j),
forceNewFile = forceNewFile,
folder = folders)
diff --git a/rrompy/sampling/linear_problem/sampling_engine_linear.py b/rrompy/sampling/linear_problem/sampling_engine_linear.py
index cdd7246..f746710 100644
--- a/rrompy/sampling/linear_problem/sampling_engine_linear.py
+++ b/rrompy/sampling/linear_problem/sampling_engine_linear.py
@@ -1,118 +1,112 @@
# 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 .
#
from copy import deepcopy as copy
import numpy as np
from rrompy.sampling.base.sampling_engine_base import SamplingEngineBase
from rrompy.utilities.base.types import Np1D, paramVal, paramList, sampList
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.utilities.exception_manager import RROMPyException
from rrompy.utilities.poly_fitting.polynomial import nextDerivativeIndices
from rrompy.parameter import checkParameter, checkParameterList
from rrompy.sampling import sampleList
__all__ = ['SamplingEngineLinear']
class SamplingEngineLinear(SamplingEngineBase):
"""HERE"""
def preprocesssamples(self, idxs:Np1D) -> sampList:
if self.samples is None or len(self.samples) == 0: return
return self.samples(idxs)
def postprocessu(self, u:sampList, overwrite : bool = False) -> Np1D:
return copy(u)
def postprocessuBulk(self, u:sampList) -> sampList:
return copy(u)
def lastSampleManagement(self):
pass
def _getSampleConcurrence(self, mu:paramVal, previous:Np1D,
homogeneized : bool = False) -> sampList:
if len(previous) >= len(self._derIdxs):
self._derIdxs += nextDerivativeIndices(self._derIdxs,
self.HFEngine.npar,
len(previous) + 1 - len(self._derIdxs))
derIdx = self._derIdxs[len(previous)]
mu = checkParameter(mu, self.HFEngine.npar)
samplesOld = self.preprocesssamples(previous)
RHS = self.HFEngine.b(mu, derIdx, homogeneized = homogeneized)
for j, derP in enumerate(self._derIdxs[: len(previous)]):
diffP = [x - y for (x, y) in zip(derIdx, derP)]
if np.all([x >= 0 for x in diffP]):
RHS -= self.HFEngine.A(mu, diffP).dot(samplesOld[j])
return self.solveLS(mu, RHS = RHS, homogeneized = homogeneized)
def nextSample(self, mu : paramVal = [], overwrite : bool = False,
homogeneized : bool = False,
lastSample : bool = True) -> Np1D:
mu = checkParameter(mu, self.HFEngine.npar)
ns = self.nsamples
muidxs = self.mus.findall(mu[0])
if len(muidxs) > 0:
u = self._getSampleConcurrence(mu, np.sort(muidxs), homogeneized)
else:
u = self.solveLS(mu, homogeneized = homogeneized)
u = self.postprocessu(u, overwrite = overwrite)
if overwrite:
self.samples[ns] = u
self.mus[ns] = mu[0]
else:
if ns == 0:
self.samples = sampleList(u)
else:
self.samples.append(u)
self.mus.append(mu)
self.nsamples += 1
if lastSample: self.lastSampleManagement()
return u
def iterSample(self, mus:paramList,
homogeneized : bool = False) -> sampList:
mus, _ = checkParameterList(mus, self.HFEngine.npar)
- if self.verbosity >= 5:
- verbosityDepth("INIT", "Starting sampling iterations.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting sampling iterations.", 5)
n = len(mus)
if n <= 0:
raise RROMPyException(("Number of samples must be positive."))
self.resetHistory()
if self.allowRepeatedSamples:
for j in range(n):
- if self.verbosity >= 7:
- verbosityDepth("MAIN", ("Computing sample "
- "{} / {}.").format(j + 1, n),
- timestamp = self.timestamp)
+ vbMng(self, "MAIN",
+ "Computing sample {} / {}.".format(j + 1, n), 7)
self.nextSample(mus[j], overwrite = (j > 0),
homogeneized = homogeneized,
lastSample = (n == j + 1))
if j == 0:
self.preallocateSamples(self.samples[0], mus[0], n)
else:
self.samples = self.postprocessuBulk(self.solveLS(mus,
homogeneized = homogeneized))
self.mus = copy(mus)
self.nsamples = n
- if self.verbosity >= 5:
- verbosityDepth("DEL", "Finished sampling iterations.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Finished sampling iterations.", 5)
return self.samples
diff --git a/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py b/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
index bcfea23..b9d283b 100644
--- a/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
+++ b/rrompy/sampling/linear_problem/sampling_engine_linear_pod.py
@@ -1,84 +1,80 @@
# 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 .
#
from copy import deepcopy as copy
from rrompy.sampling.base.pod_engine import PODEngine
from .sampling_engine_linear import SamplingEngineLinear
from rrompy.utilities.base.types import Np1D, paramVal, sampList
-from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.sampling import sampleList
__all__ = ['SamplingEngineLinearPOD']
class SamplingEngineLinearPOD(SamplingEngineLinear):
"""HERE"""
def resetHistory(self):
super().resetHistory()
self.samples_full = None
self.RPOD = None
def popSample(self):
if hasattr(self, "nsamples") and self.nsamples > 1:
self.RPOD = self.RPOD[: -1, : -1]
self.samples_full.pop()
super().popSample()
@property
def HFEngine(self):
"""Value of HFEngine. Its assignment resets history."""
return self._HFEngine
@HFEngine.setter
def HFEngine(self, HFEngine):
self._HFEngine = HFEngine
self.resetHistory()
self.PODEngine = PODEngine(self._HFEngine)
def preprocesssamples(self, idxs:Np1D) -> sampList:
if self.samples_full is None or len(self.samples_full) == 0: return
return self.samples_full(idxs)
def postprocessu(self, u:sampList, overwrite : bool = False) -> Np1D:
ns = self.nsamples
if overwrite:
self.samples_full[ns] = copy(u)
else:
if ns == 0:
self.samples_full = sampleList(u)
else:
self.samples_full.append(u)
return u
def postprocessuBulk(self, u:sampList) -> sampList:
self.samples_full = copy(u)
- if self.verbosity >= 10:
- verbosityDepth("INIT", "Starting orthogonalization.",
- timestamp = self.timestamp)
+ vbMng(self, "INIT", "Starting orthogonalization.", 10)
u, self.RPOD = self.PODEngine.generalizedQR(self.samples_full)
- if self.verbosity >= 10:
- verbosityDepth("DEL", "Done orthogonalizing.",
- timestamp = self.timestamp)
+ vbMng(self, "DEL", "Done orthogonalizing.", 10)
return u
def lastSampleManagement(self):
self.samples = self.postprocessuBulk(self.samples_full)
def preallocateSamples(self, u:Np1D, mu:paramVal, n:int):
super().preallocateSamples(u, mu, n)
self.samples_full.reset((u.shape[0], n), u.dtype)
self.samples_full[0] = u
diff --git a/rrompy/utilities/base/__init__.py b/rrompy/utilities/base/__init__.py
index 6bcf126..2ccb545 100644
--- a/rrompy/utilities/base/__init__.py
+++ b/rrompy/utilities/base/__init__.py
@@ -1,55 +1,56 @@
# 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 .
#
from .find_dict_str_key import findDictStrKey
from .get_new_filename import getNewFilename
from .kroneckerer import kroneckerer
from .factorials import multibinom, multifactorial
from .pickle_utilities import pickleDump, pickleLoad
from .purge_dict import purgeDict
from .purge_list import purgeList
from .number_theory import (squareResonances, primeFactorize,
getLowestPrimeFactor)
from .halton import haltonGenerate
from .sobol import sobolGenerate
from .low_discrepancy import vanderCorput, lowDiscrepancy
from . import types as Types
-from .verbosity_depth import verbosityDepth
+from .verbosity_depth import verbosityDepth, verbosityManager
__all__ = [
'findDictStrKey',
'getNewFilename',
'kroneckerer',
'multibinom',
'multifactorial',
'pickleDump',
'pickleLoad',
'purgeDict',
'purgeList',
'squareResonances',
'primeFactorize',
'getLowestPrimeFactor',
'haltonGenerate',
'sobolGenerate',
'vanderCorput',
'lowDiscrepancy',
'Types',
- 'verbosityDepth'
+ 'verbosityDepth',
+ 'verbosityManager'
]
diff --git a/rrompy/utilities/base/verbosity_depth.py b/rrompy/utilities/base/verbosity_depth.py
index 10626e6..483b2dc 100644
--- a/rrompy/utilities/base/verbosity_depth.py
+++ b/rrompy/utilities/base/verbosity_depth.py
@@ -1,53 +1,59 @@
# 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 .
#
from rrompy.utilities.exception_manager import RROMPyException
-__all__ = ["verbosityDepth"]
+__all__ = ["verbosityDepth", "verbosityManager"]
from datetime import datetime
def getTimestamp() -> str:
return "\x1b[42m{}\x1b[0m".format(datetime.now().strftime("%H:%M:%S.%f"))
def verbosityDepth(vdtype:str, message:str, end : str = "\n",
timestamp : bool = True):
global RROMPy_verbosity_depth
assert isinstance(vdtype, str)
if vdtype.upper() not in ["INIT", "MAIN", "DEL"]:
raise RROMPyException("Verbosity depth type not recognized.")
out = "{} ".format(getTimestamp()) if timestamp else ""
if vdtype == "INIT":
if "RROMPy_verbosity_depth" not in globals():
RROMPy_verbosity_depth = 0
RROMPy_verbosity_depth += 1
out += "│" * (RROMPy_verbosity_depth - 1)
out += "┌"
else:
assert "RROMPy_verbosity_depth" in globals()
if vdtype == "MAIN":
out += "│" * (RROMPy_verbosity_depth - 1)
out += "├"
elif vdtype == "DEL":
RROMPy_verbosity_depth -= 1
out += "│" * RROMPy_verbosity_depth
out += "└"
if RROMPy_verbosity_depth <= 0: del RROMPy_verbosity_depth
if message != "":
print("{}{}".format(out, message), end = end)
return
+
+def verbosityManager(object, vdtype:str, message:str, vlvl : int = 0,
+ end : str = "\n"):
+ if object.verbosity >= vlvl:
+ return verbosityDepth(vdtype, message, end, object.timestamp)
+
diff --git a/rrompy/utilities/poly_fitting/polynomial/vander.py b/rrompy/utilities/poly_fitting/polynomial/vander.py
index 5a44487..dd28126 100644
--- a/rrompy/utilities/poly_fitting/polynomial/vander.py
+++ b/rrompy/utilities/poly_fitting/polynomial/vander.py
@@ -1,112 +1,114 @@
# 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 .
#
import numpy as np
from rrompy.utilities.poly_fitting.polynomial import polyder
from rrompy.utilities.base.types import Np1D, Np2D, List, paramList
from rrompy.parameter import checkParameterList
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
__all__ = ['polyvander']
def firstDerTransition(dim:int, TDirac:List[Np2D], basis:str,
scl : Np1D = None) -> Np2D:
C_m = np.zeros((dim, len(TDirac), len(TDirac)), dtype = float)
for j, Tj in enumerate(TDirac):
m, om = [0] * dim, [(0, 0)] * dim
for idx in range(dim):
m[idx], om[idx] = 1, (0, 1)
J_der = polyder(Tj, basis, m, scl)
C_m[idx, :, j] = np.ravel(np.pad(J_der, mode = "constant",
pad_width = om))
m[idx], om[idx] = 0, (0, 0)
return C_m
def countDerDirections(n:int, base:int, digits:int, idx:int):
if digits == 0: return []
dig = n % base
return [(idx, dig)] * (dig > 0) + countDerDirections(
(n - dig) // base, base, digits - 1, idx + 1)
def polyvander(x:paramList, degs:List[int], basis:str,
derIdxs : List[List[List[int]]] = None,
reorder : List[int] = None, scl : Np1D = None) -> Np2D:
"""
Compute Hermite-Vandermonde matrix with specified derivative directions.
E.g. assume that we want to obtain the Vandermonde matrix for
(value, derx, derx2) at x = [0, 0],
(value, dery) at x = [1, 0],
(dery, derxy) at x = [0, 0],
of degree 3 in x and 1 in y, using Chebyshev polynomials.
This can be done by
polyvander([[0, 0], [1, 0]], # unique sample points
[3, 1], # polynomial degree
"chebyshev", # polynomial family
[
[[0, 0], [1, 0], [2, 0], [0, 1], [1, 1]],
# derivative directions at first point
[[0, 0], [0, 1]] # derivative directions at second point
],
[0, 1, 2, 5, 6, 3, 4] # reorder indices
)
"""
if not isinstance(degs, (list,tuple,np.ndarray,)): degs = [degs]
dim = len(degs)
x, _ = checkParameterList(x, dim)
x_un, idx_un = x.unique(return_inverse = True)
if len(x_un) < len(x):
raise RROMPyException("Sample points must be distinct.")
del x_un
try:
vanderbase = {"CHEBYSHEV" : np.polynomial.chebyshev.chebvander,
"LEGENDRE" : np.polynomial.legendre.legvander,
"MONOMIAL" : np.polynomial.polynomial.polyvander
}[basis.upper()]
except:
raise RROMPyException("Polynomial basis not recognized.")
VanBase = vanderbase(x(0), degs[0])
for j in range(1, dim):
- VanBase = VanBase[..., None] * vanderbase(x(j), degs[j])[..., None, :]
+ VNext = vanderbase(x(j), degs[j])
+ for jj in range(j): VNext = np.expand_dims(VNext, 1)
+ VanBase = VanBase[..., None] * VNext
VanBase = VanBase.reshape((len(x), -1))
if derIdxs is None or VanBase.shape[-1] <= 1:
Van = VanBase
else:
derFlat, idxRep = [], []
for j, derIdx in enumerate(derIdxs):
derFlat += derIdx[:]
idxRep += [j] * len(derIdx[:])
for j in range(len(derFlat)):
if not hasattr(derFlat[j], "__len__"):
derFlat[j] = [derFlat[j]]
RROMPyAssert(len(derFlat[j]), dim, "Number of dimensions")
TDirac = [y.reshape([d + 1 for d in degs])
for y in np.eye(VanBase.shape[-1], dtype = int)]
Cs_loc = firstDerTransition(dim, TDirac, basis, scl)
Van = np.empty((len(derFlat), VanBase.shape[-1]),
dtype = VanBase.dtype)
for j in range(len(derFlat)):
Van[j, :] = VanBase[idxRep[j], :]
for k in range(dim):
for der in range(derFlat[j][k]):
Van[j, :] = Van[j, :].dot(Cs_loc[k]) / (der + 1)
if reorder is not None: Van = Van[reorder, :]
return Van