diff --git a/examples/base/helmholtz_resonator.py b/examples/base/helmholtz_resonator.py
index 0a543b9..5c9f3e5 100644
--- a/examples/base/helmholtz_resonator.py
+++ b/examples/base/helmholtz_resonator.py
@@ -1,72 +1,71 @@
from matplotlib import pyplot as plt
import fenics as fen
import mshr
import ufl
from rrompy.hfengines.linear_problem import HelmholtzProblemEngine as HPE
p = plt.jet()
n = 50
boundary = mshr.Polygon([fen.Point(0, 0), fen.Point(6, 0), fen.Point(6, 1),
fen.Point(1.3, 1), fen.Point(1.3, 1.2),
fen.Point(1.65, 1.2), fen.Point(1.65, 2.2),
fen.Point(.65, 2.2), fen.Point(.65, 1.2),
fen.Point(1, 1.2), fen.Point(1, 1), fen.Point(0, 1)])
mesh = mshr.generate_mesh(boundary, n)
class Resonator(fen.SubDomain):
def inside(self, x, on_boundary):
return fen.between(x[1], (1.25, 2.25))
class Noslip(fen.SubDomain):
def inside(self, x, on_boundary):
return on_boundary
class Inlet(fen.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and fen.near(x[0], 0.)
class Outlet(fen.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and fen.near(x[0], 6.)
class Liner(fen.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and fen.near(x[1], 2.25)
resonator = Resonator()
noslip = Noslip()
inlet = Inlet()
outlet = Outlet()
liner = Liner()
sub_domains = fen.MeshFunction("size_t", mesh, mesh.topology().dim())
sub_domains.set_all(0)
resonator.mark(sub_domains, 1)
boundaries = fen.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
noslip.mark(boundaries, 0)
inlet.mark(boundaries, 1)
outlet.mark(boundaries, 2)
liner.mark(boundaries, 3)
for k in range(10):
kappa = .25 + .05 * k
ZR = 10.
x, y = fen.SpatialCoordinate(mesh)[:]
- solver = HPE()
+ solver = HPE(kappa)
solver.V = fen.FunctionSpace(mesh, "P", 3)
- solver.omega = kappa
solver.RobinBoundary = lambda x, on_b: on_b and (fen.near(x[0], 6.)
or fen.near(x[1], 2.25))
solver.NeumannBoundary = "REST"
solver.signR = + 1.
solver.NeumannDatum = [fen.Constant(0.),
ufl.conditional(ufl.And(ufl.gt(y, 0.), ufl.lt(y, 1.)),
fen.Constant(kappa), fen.Constant(0.))]
solver.RobinDatumH = [fen.Constant(0.),
ufl.conditional(ufl.gt(y, 1.25),
fen.Constant(kappa / ZR),
fen.Constant(kappa))]
uh = solver.solve(kappa)[0]
solver.plot(uh, name = "k={}".format(kappa))
print(solver.norm(uh))
diff --git a/examples/diapason/diapason_engine.py b/examples/diapason/diapason_engine.py
index 186cdcb..355781d 100644
--- a/examples/diapason/diapason_engine.py
+++ b/examples/diapason/diapason_engine.py
@@ -1,133 +1,131 @@
import numpy as np
import fenics as fen
import ufl
from rrompy.hfengines.vector_linear_problem import \
LinearElasticityHelmholtzProblemEngine as LEHPE
from rrompy.hfengines.vector_linear_problem import \
LinearElasticityHelmholtzProblemEngineDamped as LEHPED
class DiapasonEngine(LEHPE):
def __init__(self, kappa:float, c:float, rho:float, E:float, nu:float,
T:float, theta:float, phi:float, meshNo : int = 1,
deg : int = 1, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = kappa, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
mesh = fen.Mesh("../data/mesh/diapason_{}.xml".format(meshNo))
subdomains = fen.MeshFunction("size_t", mesh,
("../data/mesh/diapason_{}_physical_"
"region.xml").format(meshNo))
meshBall = fen.SubMesh(mesh, subdomains, 2)
meshFork = fen.SubMesh(mesh, subdomains, 1)
Hball = np.max(meshBall.coordinates()[:, 1]) #.00257
Ltot = np.max(mesh.coordinates()[:, 1]) #.1022
Lhandle = np.max(meshFork.coordinates()[:, 1]) #.026
Lrod = Ltot - Lhandle #.0762
L2var = (Lrod / 4.) ** 2.
Ehandle_ratio = 3.
rhohandle_ratio = 1.5
kWave = (np.cos(theta) * np.cos(phi), np.sin(phi),
np.sin(theta) * np.cos(phi))
x, y, z = fen.SpatialCoordinate(mesh)[:]
yCorr = y - Ltot
compPlane = kWave[0] * x + kWave[1] * y + kWave[2] * z
xPlane, yPlane, zPlane = (xx - compPlane * xx for xx in (x, y, z))
xOrtho, yOrtho, zOrtho = (compPlane * xx for xx in (x, y, z))
forcingBase = (T / (2. * np.pi * L2var)**.5
* fen.exp(- (xPlane**2. + yPlane**2. + zPlane**2.)
/ (2.*L2var)))
forcingWeight = np.real(kappa) / c * (xOrtho + yOrtho + zOrtho)
neumannDatum = [ufl.as_vector(tuple(forcingBase
* fen.cos(forcingWeight)
* kWavedir for kWavedir in kWave)),
ufl.as_vector(tuple(forcingBase
* fen.sin(forcingWeight)
* kWavedir for kWavedir in kWave))]
lambda_ = E * nu / (1. + nu) / (1. - 2. * nu)
mu_ = E / (1. + nu)
lambda_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(lambda_),
fen.Constant(Ehandle_ratio * lambda_))
mu_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(mu_),
fen.Constant(Ehandle_ratio * mu_))
rho_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(rho),
fen.Constant(rhohandle_ratio * rho))
self.lambda_ = lambda_eff
self.mu_ = mu_eff
self.rho_ = rho_eff
self.V = fen.VectorFunctionSpace(mesh, "P", deg)
self.DirichletBoundary = lambda x, on_b: on_b and x[1] < Hball
self.NeumannBoundary = "REST"
self.forcingTerm = neumannDatum
class DiapasonEngineDamped(LEHPED):
def __init__(self, kappa:float, c:float, rho:float, E:float, nu:float,
T:float, theta:float, phi:float, dampingEta:float,
meshNo : int = 1, deg : int = 1,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = kappa, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.eta = dampingEta
- self.omega = kappa
mesh = fen.Mesh("../data/mesh/diapason_{}.xml".format(meshNo))
subdomains = fen.MeshFunction("size_t", mesh,
("../data/mesh/diapason_{}_physical_"
"region.xml").format(meshNo))
meshBall = fen.SubMesh(mesh, subdomains, 2)
meshFork = fen.SubMesh(mesh, subdomains, 1)
Hball = np.max(meshBall.coordinates()[:, 1]) #.00257
Ltot = np.max(mesh.coordinates()[:, 1]) #.1022
Lhandle = np.max(meshFork.coordinates()[:, 1]) #.026
Lrod = Ltot - Lhandle #.0762
L2var = (Lrod / 4.) ** 2.
Ehandle_ratio = 3.
rhohandle_ratio = 1.5
kWave = (np.cos(theta) * np.cos(phi), np.sin(phi),
np.sin(theta) * np.cos(phi))
x, y, z = fen.SpatialCoordinate(mesh)[:]
yCorr = y - Ltot
compPlane = kWave[0] * x + kWave[1] * y + kWave[2] * z
xPlane, yPlane, zPlane = (xx - compPlane * xx for xx in (x, y, z))
xOrtho, yOrtho, zOrtho = (compPlane * xx for xx in (x, y, z))
forcingBase = (T / (2. * np.pi * L2var)**.5
* fen.exp(- (xPlane**2. + yPlane**2. + zPlane**2.)
/ (2.*L2var)))
forcingWeight = np.real(kappa) / c * (xOrtho + yOrtho + zOrtho)
neumannDatum = [ufl.as_vector(tuple(forcingBase
* fen.cos(forcingWeight)
* kWavedir for kWavedir in kWave)),
ufl.as_vector(tuple(forcingBase
* fen.sin(forcingWeight)
* kWavedir for kWavedir in kWave))]
lambda_ = E * nu / (1. + nu) / (1. - 2. * nu)
mu_ = E / (1. + nu)
lambda_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(lambda_),
fen.Constant(Ehandle_ratio * lambda_))
mu_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(mu_),
fen.Constant(Ehandle_ratio * mu_))
rho_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(rho),
fen.Constant(rhohandle_ratio * rho))
self.lambda_ = lambda_eff
self.mu_ = mu_eff
self.rho_ = rho_eff
self.V = fen.VectorFunctionSpace(mesh, "P", deg)
self.DirichletBoundary = lambda x, on_b: on_b and x[1] < Hball
self.NeumannBoundary = "REST"
self.forcingTerm = neumannDatum
diff --git a/examples/diapason/greedy.py b/examples/diapason/greedy.py
index cd24a8c..1d86efe 100644
--- a/examples/diapason/greedy.py
+++ b/examples/diapason/greedy.py
@@ -1,179 +1,178 @@
import numpy as np
import fenics as fen
import ufl
from rrompy.hfengines.vector_linear_problem import \
LinearElasticityHelmholtzProblemEngine as LEHPE
from rrompy.hfengines.vector_linear_problem import \
LinearElasticityHelmholtzProblemEngineDamped as LEHPED
from rrompy.reduction_methods.distributed_greedy import \
RationalInterpolantGreedy as Pade
from rrompy.reduction_methods.distributed_greedy import \
RBDistributedGreedy as RB
from rrompy.solver.fenics import L2NormMatrix
verb = 2
timed = False
algo = "Pade"
#algo = "RB"
polyBasis = "LEGENDRE"
polyBasis = "CHEBYSHEV"
#polyBasis = "MONOMIAL"
if timed: verb = 0
dampingEta = 0 * 1e4 / 2. / np.pi
k0s = np.linspace(2.5e2, 7.5e3, 100)
k0s = np.linspace(2.5e3, 1.5e4, 100)
k0s = np.linspace(5.0e4, 1.0e5, 100)
k0s = np.linspace(2.0e5, 2.5e5, 100)
k0 = np.mean(np.power(k0s, 2.)) ** .5 # [Hz]
kl, kr = min(k0s), max(k0s)
params = {'muBounds':[kl, kr], 'nTestPoints':500, 'Delta':0,
'greedyTol':1e-2, 'S':2, 'polybasis':polyBasis,
'robustTol':2e-16, 'interpRcond':None, 'errorEstimatorKind':'EXACT'}
theta = 20. * np.pi / 180.
phi = 10. * np.pi / 180.
mesh = fen.Mesh("../data/mesh/diapason_1.xml")
subdomains = fen.MeshFunction("size_t", mesh,
"../data/mesh/diapason_1_physical_region.xml")
meshBall = fen.SubMesh(mesh, subdomains, 2)
meshFork = fen.SubMesh(mesh, subdomains, 1)
Hball = np.max(meshBall.coordinates()[:, 1]) #.00257
Ltot = np.max(mesh.coordinates()[:, 1]) #.1022
Lhandle = np.max(meshFork.coordinates()[:, 1]) #.026
Lrod = Ltot - Lhandle #.0762
L2var = (Lrod / 4.) ** 2.
Ehandle_ratio = 3.
rhohandle_ratio = 1.5
c = 3.e2
rho = 8e3 * (2. * np.pi) ** 2.
E = 1.93e11
nu = .3
T = 1e6
lambda_ = E * nu / (1. + nu) / (1. - 2. * nu)
mu_ = E / (1. + nu)
kWave = (np.cos(theta) * np.cos(phi), np.sin(phi), np.sin(theta) * np.cos(phi))
x, y, z = fen.SpatialCoordinate(mesh)[:]
yCorr = y - Ltot
compPlane = kWave[0] * x + kWave[1] * y + kWave[2] * z
xPlane, yPlane, zPlane = (xx - compPlane * xx for xx in (x, y, z))
xOrtho, yOrtho, zOrtho = (compPlane * xx for xx in (x, y, z))
forcingBase = (T / (2. * np.pi * L2var)**.5
* fen.exp(- (xPlane**2. + yPlane**2. + zPlane**2.) / (2.*L2var)))
forcingWeight = np.real(k0) / c * (xOrtho + yOrtho + zOrtho)
neumannDatum = [ufl.as_vector(
tuple(forcingBase * fen.cos(forcingWeight) * kWavedir for kWavedir in kWave)),
ufl.as_vector(
tuple(forcingBase * fen.sin(forcingWeight) * kWavedir for kWavedir in kWave))]
lambda_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(lambda_),
fen.Constant(Ehandle_ratio * lambda_))
mu_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(mu_),
fen.Constant(Ehandle_ratio * mu_))
rho_eff = ufl.conditional(ufl.ge(y, Lhandle), fen.Constant(rho),
fen.Constant(rhohandle_ratio * rho))
###
if dampingEta > 0:
- solver = LEHPED(degree_threshold = 8, verbosity = 0)
+ solver = LEHPED(mu0 = np.real(k0), degree_threshold = 8, verbosity = 0)
solver.eta = dampingEta
else:
- solver = LEHPE(degree_threshold = 8, verbosity = 0)
-solver.omega = np.real(k0)
+ solver = LEHPE(mu0 = np.real(k0), degree_threshold = 8, verbosity = 0)
solver.lambda_ = lambda_eff
solver.mu_ = mu_eff
solver.rho_ = rho_eff
solver.V = fen.VectorFunctionSpace(mesh, "P", 1)
solver.DirichletBoundary = lambda x, on_b: on_b and x[1] < Hball
solver.NeumannBoundary = "REST"
solver.forcingTerm = neumannDatum
if algo == "Pade":
approx = Pade(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
else:
params.pop("Delta")
params.pop("polybasis")
params.pop("robustTol")
params.pop("interpRcond")
params.pop("errorEstimatorKind")
approx = RB(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
approx.initEstimatorNormEngine(L2NormMatrix(solver.V))
if timed:
from time import clock
start_time = clock()
approx.greedy()
print("Time: ", clock() - start_time)
else:
approx.greedy(True)
polesApp = approx.getPoles()
print("Poles:\n", polesApp)
approx.samplingEngine.verbosity = 0
approx.verbosity = 0
kl, kr = np.real(kl), np.real(kr)
from matplotlib import pyplot as plt
normApp = np.zeros(len(k0s))
norm = np.zeros_like(normApp)
res = np.zeros_like(normApp)
err = np.zeros_like(normApp)
for j in range(len(k0s)):
normApp[j] = approx.normApprox(k0s[j])
norm[j] = approx.normHF(k0s[j])
res[j] = (approx.estimatorNormEngine.norm(approx.getRes(k0s[j]))
/ approx.estimatorNormEngine.norm(approx.getRHS(k0s[j])))
err[j] = approx.normErr(k0s[j]) / norm[j]
resApp = approx.errorEstimator(k0s)
res[res < 1e-5 * approx.greedyTol] = np.nan
resApp[resApp < 1e-5 * approx.greedyTol] = np.nan
err[err < 1e-8 * approx.greedyTol] = np.nan
plt.figure()
plt.semilogy(k0s, norm)
plt.semilogy(k0s, normApp, '--')
plt.semilogy(np.real(approx.mus),
1.05*np.max(norm)*np.ones_like(approx.mus, dtype = float),
'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, res)
plt.semilogy(k0s, resApp, '--')
plt.semilogy(np.real(approx.mus),
approx.greedyTol*np.ones_like(approx.mus, dtype = float),
'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, err)
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
mask = (np.real(polesApp) < kl) | (np.real(polesApp) > kr)
print("Outliers:", polesApp[mask])
polesAppEff = polesApp[~mask]
plt.figure()
plt.plot(np.real(polesAppEff), np.imag(polesAppEff), 'kx')
plt.axis('equal')
plt.grid()
plt.show()
plt.close()
diff --git a/examples/from_papers/greedy_internalBox.py b/examples/from_papers/greedy_internalBox.py
index 72c798a..cf3c475 100644
--- a/examples/from_papers/greedy_internalBox.py
+++ b/examples/from_papers/greedy_internalBox.py
@@ -1,112 +1,111 @@
import numpy as np
import fenics as fen
from rrompy.hfengines.linear_problem import HelmholtzProblemEngine as HPE
from rrompy.reduction_methods.distributed_greedy import \
RationalInterpolantGreedy as Pade
from rrompy.reduction_methods.distributed_greedy import \
RBDistributedGreedy as RB
from rrompy.solver.fenics import L2NormMatrix
dim = 3
verb = 2
timed = False
algo = "Pade"
#algo = "RB"
polyBasis = "LEGENDRE"
#polyBasis = "CHEBYSHEV"
#polyBasis = "MONOMIAL"
k0s = np.power(np.linspace(500 ** 2., 2250 ** 2., 200), .5)
k0 = np.mean(np.power(k0s, 2.)) ** .5
kl, kr = min(k0s), max(k0s)
params = {'muBounds':[kl, kr], 'nTestPoints':500, 'Delta':0,
'greedyTol':1e-2, 'S':2, 'basis':polyBasis}
if dim == 2:
mesh = fen.RectangleMesh(fen.Point(0., 0.), fen.Point(.1, .15), 10, 15)
x, y = fen.SpatialCoordinate(mesh)[:]
f = fen.exp(- 1e2 * (x + y))
else:#if dim == 3:
mesh = fen.BoxMesh(fen.Point(0., 0., 0.), fen.Point(.1, .15, .25), 4, 6,10)
x, y, z = fen.SpatialCoordinate(mesh)[:]
f = fen.exp(- 1e2 * (x + y + z))
-solver = HPE(verbosity = verb)
-solver.omega = np.real(k0)
+solver = HPE(np.real(k0), verbosity = verb)
solver.V = fen.FunctionSpace(mesh, "P", 3)
solver.refractionIndex = fen.Constant(1. / 54.6)
solver.forcingTerm = f
solver.NeumannBoundary = "ALL"
#########
if algo == "Pade":
approx = Pade(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
else:
approx = RB(solver, mu0 = k0, approxParameters = params, verbosity = verb)
approx.initEstimatorNormEngine(L2NormMatrix(solver.V))
if timed:
from time import clock
start_time = clock()
approx.greedy()
print("Time: ", clock() - start_time)
else:
approx.greedy(True)
approx.samplingEngine.verbosity = 0
approx.verbosity = 0
kl, kr = np.real(kl), np.real(kr)
from matplotlib import pyplot as plt
normApp = np.zeros(len(k0s))
norm = np.zeros_like(normApp)
res = np.zeros_like(normApp)
err = np.zeros_like(normApp)
for j in range(len(k0s)):
normApp[j] = approx.normApprox(k0s[j])
norm[j] = approx.normHF(k0s[j])
res[j] = (approx.estimatorNormEngine.norm(approx.getRes(k0s[j]))
/ approx.estimatorNormEngine.norm(approx.getRHS(k0s[j])))
err[j] = approx.normErr(k0s[j]) / approx.normHF(k0s[j])
resApp = approx.errorEstimator(k0s)
plt.figure()
plt.plot(k0s, norm)
plt.plot(k0s, normApp, '--')
plt.plot(np.real(approx.mus),
1.05*np.max(norm)*np.ones_like(approx.mus, dtype = float), 'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, res)
plt.semilogy(k0s, resApp, '--')
plt.semilogy(np.real(approx.mus),
4.*np.max(resApp)*np.ones_like(approx.mus, dtype = float), 'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, err)
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
polesApp = approx.getPoles()
mask = (np.real(polesApp) < kl) | (np.real(polesApp) > kr)
print("Outliers:", polesApp[mask])
polesApp = polesApp[~mask]
plt.figure()
plt.plot(np.real(polesApp), np.imag(polesApp), 'kx')
plt.axis('equal')
plt.grid()
plt.show()
plt.close()
diff --git a/examples/from_papers/pod_membrane_centered.py b/examples/from_papers/pod_membrane_centered.py
index aada78c..fc62e55 100644
--- a/examples/from_papers/pod_membrane_centered.py
+++ b/examples/from_papers/pod_membrane_centered.py
@@ -1,71 +1,70 @@
import fenics as fen
import numpy as np
from rrompy.hfengines.linear_problem import HelmholtzProblemEngine as HPE
from rrompy.reduction_methods.centered import RationalPade as TP
verb = 0
k0 = 10
ktars = np.linspace(78**.5, 122**.5, 50)
def boundaryNeumann(x, on_boundary):
return on_boundary and x[1] > .25 and x[0] > 0.995 and x[0] < 1.005
meshname = '../data/mesh/crack_coarse.xml'
#meshname = '../data/mesh/crack_fine.xml'
mesh = fen.Mesh(meshname)
x, y = fen.SpatialCoordinate(mesh)[:]
x0, y0 = .5, .5
Rr, Ri = .1, .1
forcingTerm = fen.exp(- ((x - x0)**2 + (y - y0)**2) / 2 / Rr**2)
-solver = HPE(verbosity = verb)
-solver.omega = np.real(k0)
+solver = HPE(np.real(k0), verbosity = verb)
solver.V = fen.FunctionSpace(mesh, "P", 3)
solver.forcingTerm = forcingTerm
solver.NeumannBoundary = boundaryNeumann
solver.DirichletBoundary = 'rest'
appPoles = {}
Emax = 13
params = {'N':6, 'M':0, 'E':6, 'POD':True}
approxPade = TP(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
for E in range(6, Emax + 1):
approxPade.E = E
appPoles[E] = np.sort(approxPade.getPoles())
a = fen.dot(fen.grad(solver.u), fen.grad(solver.v)) * fen.dx
A = fen.assemble(a)
fen.DirichletBC(solver.V, fen.Constant(0.),
solver.DirichletBoundary).apply(A)
AMat = fen.as_backend_type(A).mat()
Ar, Ac, Av = AMat.getValuesCSR()
import scipy.sparse as scsp
A = scsp.csr_matrix((Av, Ac, Ar), shape = AMat.size)
m = fen.dot(solver.u, solver.v) * fen.dx
M = fen.assemble(m)
fen.DirichletBC(solver.V, fen.Constant(0.),
solver.DirichletBoundary).apply(M)
MMat = fen.as_backend_type(M).mat()
Mr, Mc, Mv = MMat.getValuesCSR()
import scipy.sparse as scsp
M = scsp.csr_matrix((Mv, Mc, Mr), shape = MMat.size)
poles = scsp.linalg.eigs(A, k = 7, M = M, sigma = 100.,
return_eigenvectors = False)
II = np.argsort(np.abs(poles - k0))
poles = poles[II]
print('Exact', end = ': ')
[print('{},{}'.format(np.real(x), np.imag(x)), end = ',') for x in poles]
print()
for E in range(6, Emax + 1):
print(E, end = ': ')
[print('{},{}'.format(np.real(x), np.imag(x)), end = ',')\
for x in np.sort(appPoles[E])]
print()
diff --git a/rrompy/hfengines/base/matrix_engine_base.py b/rrompy/hfengines/base/matrix_engine_base.py
index d132301..14d2352 100644
--- a/rrompy/hfengines/base/matrix_engine_base.py
+++ b/rrompy/hfengines/base/matrix_engine_base.py
@@ -1,362 +1,412 @@
# 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 scipy.special import binom
from matplotlib import pyplot as plt
from copy import deepcopy as copy
from rrompy.utilities.base.types import (Np1D, Np2D, ScOp, strLst, Tuple, List,
DictAny, paramVal, paramList,
sampList)
from rrompy.utilities.base import purgeList, getNewFilename, verbosityDepth
+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
__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.
"""
- npar = 1
+ npar = 0
nAs, nbs = 1, 1
- rescalingExp = 1.
+ rescalingExp = [1.]
def __init__(self, verbosity : int = 10, timestamp : bool = True):
self.verbosity = verbosity
self.timestamp = timestamp
self.resetAs()
self.resetbs()
self.setSolver("SPSOLVE", {"use_umfpack" : False})
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] != "__"]
@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.
"""
self.energyNormMatrix = np.eye(self.spacedim())
def innerProduct(self, u:Np2D, v:Np2D, onlyDiag : bool = False) -> Np2D:
"""Scalar product."""
if not hasattr(self, "energyNormMatrix"):
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling energy matrix.",
timestamp = self.timestamp)
self.buildEnergyNormForm()
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling energy matrix.",
timestamp = self.timestamp)
if not isinstance(u, (np.ndarray,)): u = u.data
if not isinstance(v, (np.ndarray,)): v = v.data
if onlyDiag:
return np.sum(self.energyNormMatrix.dot(u) * v.conj(), axis = 0)
return v.T.conj().dot(self.energyNormMatrix.dot(u))
def norm(self, u:Np2D) -> Np1D:
return np.abs(self.innerProduct(u, u, onlyDiag = True)) ** .5
- def checkAInBounds(self, der : int = 0):
+ def checkAInBounds(self, derI : int = 0):
"""Check if derivative index is oob for operator of linear system."""
- if der < 0 or der >= self.nAs:
+ 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, der : int = 0, homogeneized : bool = False):
+ 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 der < 0 or der >= 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.resetbsH()
self.setAs([None] * self.nAs)
def resetbs(self):
"""Reset (derivatives of) RHS of linear system."""
self.resetbsH()
self.setbs([None] * self.nbs)
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 A(self, mu : paramVal = (), der : int = 0) -> ScOp:
- """Return (derivative of) operator of linear system."""
+ def _assembleA(self, mu : paramVal = [], der : List[int] = 0,
+ derI : int = None) -> ScOp:
+ """Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
+ 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
- As0 = self.As[der]
- coeff = 1.
- for j in range(der + 1, self.nAs):
- coeff = coeff * mu(0, 0) * j / (j - der)
- As0 = As0 + coeff * self.As[j]
+ As0 = 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]):
+ coeff = 1.
+ for d in range(self.npar):
+ coeff *= (mu(0, d) ** (self.rescalingExp[d] * diffIdx[d])
+ * binom(derIdx[d], diffIdx[d]))
+ As0 = As0 + coeff * self.As[j]
return As0
- def affineLinearSystemA(self, mu : paramVal = ()) -> List[Np2D]:
+ @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] = 0.
+ 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, j)
return As
- def affineWeightsA(self, mu : paramVal = ()) -> List[str]:
+ 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 = ["np.ones_like(mu[0])"]
- mu0Eff = np.power(mu(0, 0), self.rescalingExp)
+ lambdasA = ["1."]
+ mu0Eff = mu ** self.rescalingExp
for j in range(1, self.nAs):
- lambdasA += ["np.power(np.power(mu[0], {1}) - {2}, {0})".format(
- j, self.rescalingExp, mu0Eff)]
+ lambdasA += ["(mu ** ({}) - {}) ** ({})".format(self.rescalingExp,
+ mu0Eff,
+ hashI(j, self.npar))]
return lambdasA
- def affineBlocksA(self, mu : paramVal = ())\
+ 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 b(self, mu : paramVal = (), der : int = 0,
- homogeneized : bool = False) -> Np1D:
- """Return (derivative of) (homogeneized) RHS of linear system."""
+ def _assembleb(self, mu : paramVal = [], der : List[int] = 0,
+ derI : int = None, homogeneized : bool = False) -> ScOp:
+ """Assemble (derivative of) (homogeneized) RHS of linear system."""
mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
+ if not hasattr(der, "__len__"): der = [der] * self.npar
+ if derI is None: derI = hashD(der)
+ bnull = self.checkbInBounds(derI)
if bnull is not None: return bnull
bs = self.bsH if homogeneized else self.bs
- b = bs[der]
- coeff = 1.
- for j in range(der + 1, len(bs)):
- coeff = coeff * mu(0, 0) * j / (j - der)
- b = b + coeff * bs[j]
+ b = 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]):
+ coeff = 1.
+ for d in range(self.npar):
+ coeff *= (mu(0, d) ** (self.rescalingExp[d] * diffIdx[d])
+ * binom(derIdx[d], diffIdx[d]))
+ b = b + coeff * bs[j]
return b
- def affineLinearSystemb(self, mu : paramVal = (),
+ @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] = 0.
+ else:
+ for j in range(derI, self.nbs):
+ if self.bs[j] is None: self.bs[j] = 0.
+ 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, j, homogeneized)
return bs
- def affineWeightsb(self, mu : paramVal = (),
+ 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 = ["np.ones_like(mu[0])"]
- mu0Eff = np.power(mu(0, 0), self.rescalingExp)
+ lambdasb = ["1."]
+ mu0Eff = mu ** self.rescalingExp
for j in range(1, nbs):
- lambdasb += ["np.power(np.power(mu[0], {1}) - {2}, {0})".format(
- j, self.rescalingExp, mu0Eff)]
+ lambdasb += ["(mu ** ({}) - {}) ** ({})".format(self.rescalingExp,
+ mu0Eff,
+ hashI(j, self.npar))]
return lambdasb
- def affineBlocksb(self, mu : paramVal = (), homogeneized : bool = False)\
+ 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,
+ 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 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")
sol = emptySampleList()
for j in range(len(mu)):
u = self._solver(self.A(mu[j]), RHS[mult * j], self._solverArgs)
if j == 0:
sol.reset((len(u), len(mu)), dtype = u.dtype)
sol[j] = u
return sol
- def residual(self, u:sampList, mu : paramList = [()],
+ def residual(self, u:sampList, mu : paramList = [],
homogeneized : bool = False) -> 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 len(mu) == 0: return
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()
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)
res[j] = r
return res
def plot(self, u:Np1D, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **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.
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))
plt.title("|{0}|".format(name))
if 'PHASE' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.angle(u))
plt.title("phase({0})".format(name))
if 'REAL' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.real(u))
plt.title("Re({0})".format(name))
if 'IMAG' in what:
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
plt.plot(idxs, np.imag(u))
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 4246b1e..8b74eba 100644
--- a/rrompy/hfengines/base/problem_engine_base.py
+++ b/rrompy/hfengines/base/problem_engine_base.py
@@ -1,361 +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 .
#
-from abc import abstractmethod
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, ScOp, strLst, FenFunc, Tuple,
- List, paramVal)
+from rrompy.utilities.base.types import (Np1D, strLst, FenFunc, Tuple, List,
+ paramVal)
from rrompy.utilities.base import purgeList, getNewFilename, verbosityDepth
from rrompy.solver.fenics import L2NormMatrix
from .boundary_conditions import BoundaryConditions
from .matrix_engine_base import MatrixEngineBase
-from rrompy.parameter import checkParameter
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.
- bsmu: Mu value of last bs evaluation.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
"""
npar = 0
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.bsmu = np.nan
self.mu0BC = np.nan
self.degree_threshold = degree_threshold
@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.
"""
self.energyNormMatrix = L2NormMatrix(self.V)
- def liftDirichletData(self, mu : paramVal = ()) -> Np1D:
+ def liftDirichletData(self, mu : paramVal = []) -> Np1D:
"""Lift Dirichlet datum."""
- mu = checkParameter(mu)
+ mu = self.checkParameter(mu)
if mu != self.mu0BC:
self.mu0BC = copy(mu)
try:
liftRe = fen.interpolate(self.DirichletDatum[0], self.V)
except:
liftRe = fen.project(self.DirichletDatum[0], self.V)
try:
liftIm = fen.interpolate(self.DirichletDatum[1], self.V)
except:
liftIm = fen.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)
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 {}
- @abstractmethod
- def A(self, mu : paramVal = (), der : int = 0) -> ScOp:
- """Assemble (derivative of) operator of linear system."""
- mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
- if self.As[der] is None:
- self.As[der] = 0.
- return self.As[der]
-
- @abstractmethod
- def b(self, mu : paramVal = (), der : int = 0,
- homogeneized : bool = False) -> Np1D:
- """Assemble (derivative of) RHS of linear system."""
- mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if bnull is not None: return bnull
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- if homogeneized:
- self.bsH[der] = 0.
- else:
- self.bs[der] = 0.
- b = 0.
- return b
-
def plot(self, u:Np1D, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **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.
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 = fen.plot(uAb, title = "|{0}|".format(name))
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 = fen.plot(uPh, title = "phase({0})".format(name))
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 = fen.plot(uRe, title = "Re({0})".format(name))
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 = fen.plot(uIm, title = "Im({0})".format(name))
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, name : str = "Mesh", save : str = None,
saveFormat : str = "eps", saveDPI : int = 100,
show : bool = True, **figspecs):
"""
Do a nice plot of the mesh.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): 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.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
plt.figure(**figspecs)
fen.plot(self.V.mesh())
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, 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.
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 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)
return filePW
def outParaviewTimeDomain(self, u:Np1D, omega:float,
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.
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
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
return filePW
diff --git a/rrompy/hfengines/base/vector_problem_engine_base.py b/rrompy/hfengines/base/vector_problem_engine_base.py
index 536aceb..73a4e4f 100644
--- a/rrompy/hfengines/base/vector_problem_engine_base.py
+++ b/rrompy/hfengines/base/vector_problem_engine_base.py
@@ -1,199 +1,199 @@
# 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 fenics as fen
import numpy as np
from matplotlib import pyplot as plt
from rrompy.utilities.base.types import Np1D, strLst
from rrompy.utilities.base import purgeList, getNewFilename
from .problem_engine_base import ProblemEngineBase
__all__ = ['VectorProblemEngineBase']
class VectorProblemEngineBase(ProblemEngineBase):
"""
Generic solver for parametric vector 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.
- bsmu: Mu value of last bs evaluation.
liftedDirichletDatum: Dofs of Dirichlet datum lifting.
mu0BC: Mu value of last Dirichlet datum lifting.
degree_threshold: Threshold for ufl expression interpolation degree.
"""
+ npar = 0
nAs, nbs = 1, 1
def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.V = fen.VectorFunctionSpace(fen.UnitSquareMesh(10, 10), "P", 1)
def plot(self, u:Np1D, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **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.
show(optional): Whether to show figure. Defaults to True.
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 'figsize' not in figspecs.keys():
figspecs['figsize'] = (13. * max(len(what), 1) / 4, 3)
if len(what) > 0:
for j in range(self.V.num_sub_spaces()):
subplotcode = 100 + len(what) * 10
II = self.V.sub(j).dofmap().dofs()
Vj = self.V.sub(j).collapse()
plt.figure(**figspecs)
plt.jet()
if 'ABS' in what:
uAb = fen.Function(Vj)
uAb.vector().set_local(np.abs(u[II]))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uAb, title = "|{}_comp{}|".format(name, j))
plt.colorbar(p)
if 'PHASE' in what:
uPh = fen.Function(Vj)
uPh.vector().set_local(np.angle(u[II]))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uPh, title = "phase({}_comp{})".format(name,
j))
plt.colorbar(p)
if 'REAL' in what:
uRe = fen.Function(Vj)
uRe.vector().set_local(np.real(u[II]))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uRe, title = "Re({}_comp{})".format(name, j))
plt.colorbar(p)
if 'IMAG' in what:
uIm = fen.Function(Vj)
uIm.vector().set_local(np.imag(u[II]))
subplotcode = subplotcode + 1
plt.subplot(subplotcode)
p = fen.plot(uIm, title = "Im({}_comp{})".format(name, j))
plt.colorbar(p)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_comp{}_fig_".format(save, j),
saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
try:
if len(what) > 1:
figspecs['figsize'] = (2. / len(what) * figspecs['figsize'][0],
figspecs['figsize'][1])
elif len(what) == 0:
figspecs['figsize'] = (2. * figspecs['figsize'][0],
figspecs['figsize'][1])
if len(what) == 0 or 'ABS' in what or 'REAL' in what:
uVRe = fen.Function(self.V)
uVRe.vector().set_local(np.real(u))
plt.figure(**figspecs)
plt.jet()
p = fen.plot(uVRe, title = "{}_Re".format(name),
mode = "displacement")
plt.colorbar(p)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_disp_Re_fig_".format(save),
saveFormat),
format = saveFormat, dpi = saveDPI)
plt.show()
plt.close()
if 'ABS' in what or 'IMAG' in what:
uVIm = fen.Function(self.V)
uVIm.vector().set_local(np.imag(u))
plt.figure(**figspecs)
plt.jet()
p = fen.plot(uVIm, title = "{}_Im".format(name),
mode = "displacement")
plt.colorbar(p)
if save is not None:
save = save.strip()
plt.savefig(getNewFilename("{}_disp_Im_fig_".format(save, j),
saveFormat),
format = saveFormat, dpi = saveDPI)
if show:
plt.show()
plt.close()
except:
pass
def plotmesh(self, name : str = "Mesh", save : str = None,
saveFormat : str = "eps", saveDPI : int = 100,
show : bool = True, **figspecs):
"""
Do a nice plot of the mesh.
Args:
u: numpy complex array with function dofs.
name(optional): Name to be shown as title of the plots. Defaults to
'u'.
save(optional): 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.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
plt.figure(**figspecs)
fen.plot(self.V.mesh())
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()
diff --git a/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
index b2728a5..4273646 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_box_scattering_problem_engine.py
@@ -1,58 +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 .
#
import numpy as np
import fenics as fen
from .scattering_problem_engine import ScatteringProblemEngine
__all__ = ['HelmholtzBoxScatteringProblemEngine']
class HelmholtzBoxScatteringProblemEngine(ScatteringProblemEngine):
"""
Solver for scattering problem outside a box with parametric wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
\partial_nu - i k u = 0 on \Gamma_R
with exact solution a transmitted plane wave.
"""
+
+ npar = 1
+
def __init__(self, R:float, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
-
import mshr
scatterer = mshr.Polygon([fen.Point(-1, -.5), fen.Point(1, -.5),
fen.Point(1, .5), fen.Point(.8, .5),
fen.Point(.8, -.3), fen.Point(-.8, -.3),
fen.Point(-.8, .5), fen.Point(-1, .5),])
mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0, 0), R)-scatterer, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
self.DirichletBoundary = (lambda x, on_boundary:
on_boundary and (x[0]**2+x[1]**2)**.5 < .95 * R)
self.RobinBoundary = "REST"
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
u0R = - fen.cos(kappa * (c * x + s * y))
u0I = - fen.sin(kappa * (c * x + s * y))
self.DirichletDatum = [u0R, u0I]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
index 6349830..6eb27e6 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_cavity_scattering_problem_engine.py
@@ -1,59 +1,60 @@
# 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 .scattering_problem_engine import ScatteringProblemEngine
__all__ = ['HelmholtzCavityScatteringProblemEngine']
class HelmholtzCavityScatteringProblemEngine(ScatteringProblemEngine):
"""
Solver for scattering problem inside a cavity with parametric wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
\partial_nu - i k u = 0 on \Gamma_R
with exact solution a transmitted plane wave.
"""
+
+ npar = 1
+
def __init__(self, kappa:float, n:int, gamma : float = 0.,
signR : int = -1, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.signR = signR
- self.omega = kappa
-
pi = np.pi
mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi), n, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
self.RobinBoundary = (lambda x, on_boundary: on_boundary
and np.isclose(x[1], np.pi))
self.DirichletBoundary = "REST"
x, y = fen.SpatialCoordinate(mesh)[:]
C = 4. / pi ** 4.
bR = C * (2 * (x * (pi - x) + y * (2 * pi - y))
+ (kappa * gamma) ** 2. * x * (pi - x) * y * (2 * pi - y))
bI = C * signR * 2 * kappa * (gamma * (pi - 2 * x) * y * (pi - y)
+ 2 * x * (pi - x) * (pi - y))
wR = fen.cos(kappa * signR * (gamma * x + y))
wI = fen.sin(kappa * signR * (gamma * x + y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
index 3b32544..3f241c9 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_problem_engine.py
@@ -1,164 +1,162 @@
# 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 .laplace_base_problem_engine import LaplaceBaseProblemEngine
-from rrompy.utilities.base.types import ScOp, paramVal
+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.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
npar = 1
nAs = 2
- rescalingExp = 2.
+ rescalingExp = [2.]
- def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
- timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ 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.omega = 1.
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 : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
- self.autoSetDS()
- if der <= 0 and self.As[0] is None:
+ if not hasattr(der, "__len__"): der = [der]
+ 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)
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))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 1 and self.As[1] is None:
+ if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
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
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * scsp.csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return self.As[0] + mu(0, 0) ** 2. * self.As[1]
- return self.As[1]
+ 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 487f10d..f55f363 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
@@ -1,250 +1,247 @@
# 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, FenExpr, paramVal
+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.parameter import checkParameter, checkParameterList
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
__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.
"""
+ npar = 1
nAs, nbs = 3, 20
- rescalingExp = 1.
+ rescalingExp = [1.]
- def __init__(self, kappa:float, theta:float, n:int, mu0 : np.complex = 1.,
+ 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__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
self.kappa = kappa
self.theta = theta
- self.mu0 = checkParameter(mu0)
+ self.mu0 = self.checkParameter(mu0)
self.forcingTermMu = np.nan
-
mesh = fen.RectangleMesh(fen.Point(0,0), fen.Point(np.pi,np.pi), n, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
def buildEnergyNormForm(self): # H1
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
mudxM = np.abs(self.mu0(0, 0)) * (fen.dot(self.u.dx(0), self.v.dx(0))
+ fen.dot(self.u, self.v))
imudy = 1. / np.abs(self.mu0(0, 0)) * fen.dot(self.u.dx(1),
self.v.dx(1))
normMatFen = fen.assemble((mudxM + imudy) * fen.dx)
normMat = fen.as_backend_type(normMatFen).mat()
self.energyNormMatrix = scsp.csr_matrix(normMat.getValuesCSR()[::-1],
shape = normMat.size)
- def getForcingTerm(self, mu : paramVal = ()) -> Tuple[FenExpr, FenExpr]:
+ def getForcingTerm(self, mu : paramVal = []) -> Tuple[FenExpr, FenExpr]:
"""Compute forcing term."""
- mu = checkParameter(mu)
+ mu = self.checkParameter(mu)
if mu != self.forcingTermMu:
if self.verbosity >= 25:
verbosityDepth("INIT", ("Assembling base expression for "
"forcing term."),
timestamp = self.timestamp)
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)
return self.forcingTerm
- def getExtraFactorB(self, mu : paramVal = (),
- der : int = 0) -> Tuple[FenExpr, FenExpr]:
+ def getExtraFactorB(self, mu : paramVal = [],
+ derI : int = 0) -> Tuple[FenExpr, FenExpr]:
"""Compute extra expression in RHS."""
- mu = checkParameter(mu)
+ 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)
from scipy.special import factorial as fact
y = fen.SpatialCoordinate(self.V.mesh())[1]
- powR, powI = [(self.kappa * np.sin(self.theta)) ** der * k\
- for k in getPowMinusj(y, der)]
+ 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 der >= 1:
+ 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)) ** (der - 1) * k\
- * der for k in getPowMinusj(y, der - 1)]
+ 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 der >= 2:
- powR, powI = [(self.kappa * np.sin(self.theta)) ** (der - 2) * k\
- * der * (der - 1) for k in getPowMinusj(y, der - 2)]
+ 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(der)
+ fac = fact(derI)
if self.verbosity >= 25:
verbosityDepth("DEL", "Done assembling auxiliary expression.",
timestamp = self.timestamp)
return [exprR / fac, exprI / fac]
- def A(self, mu : paramVal = (), der : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
- mu = checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
+ mu = self.checkParameter(mu)
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if der <= 0 and self.As[0] is None:
+ if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a0Re = fen.dot(self.u.dx(1), self.v.dx(1)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 2 and self.As[2] is None:
+ if derI <= 1 and self.As[1] is None: self.As[1] = 0.
+ if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
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
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return self.As[0] + mu(0, 0) ** 2 * self.As[2]
- if der == 1:
- return 2. * mu(0, 0) * self.As[2]
- return self.As[2]
+ return self._assembleA(mu, der, derI)
- def b(self, mu : paramVal = (), der : int = 0,
+ def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
- mu = checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if bnull is not None: return bnull
- if homogeneized and mu != self.mu0BC:
- self.u0BC = self.liftDirichletData(mu)
- if self.bsmu != mu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(der),
- timestamp = self.timestamp)
- if der < self.nbs:
- fRe, fIm = self.getForcingTerm(mu)
- cRe, cIm = self.getExtraFactorB(mu, der)
- cfRe = cRe * fRe - cIm * fIm
- cfIm = cRe * fIm + cIm * fRe
- else:
- cfRe, cfIm = fenZERO, fenZERO
- parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
- ["forcingTermDer{}Real".format(der)]))
- parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
- ["forcingTermDer{}Imag".format(der)]))
- L0Re = fen.dot(cfRe, self.v) * fen.dx
- L0Im = fen.dot(cfIm, self.v) * fen.dx
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(mu, der)
- b0Re[:] -= np.real(Ader.dot(self.u0BC))
- b0Im[:] -= np.imag(Ader.dot(self.u0BC))
- DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
- self.DirichletBoundary)
- DirichletBC0.apply(b0Re)
- DirichletBC0.apply(b0Im)
- b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
- return b
+ mu = self.checkParameter(mu)
+ if not hasattr(der, "__len__"): der = [der]
+ 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.u0BC = 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)
+ 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
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j))
+ b0Re[:] -= np.real(Ader.dot(self.u0BC))
+ b0Im[:] -= np.imag(Ader.dot(self.u0BC))
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ DirichletBC0.apply(b0Re)
+ DirichletBC0.apply(b0Im)
+ if homogeneized:
+ self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ else:
+ self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu - self.mu0, der, derI, homogeneized)
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
index 13d9c30..c268508 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_bubble_problem_engine.py
@@ -1,53 +1,54 @@
# 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 .helmholtz_problem_engine import HelmholtzProblemEngine
__all__ = ['HelmholtzSquareBubbleProblemEngine']
class HelmholtzSquareBubbleProblemEngine(HelmholtzProblemEngine):
"""
Solver for square bubble Helmholtz problems with parametric wavenumber.
- \Delta u - omega^2 * u = f in \Omega
u = 0 on \Gamma_D
with exact solution square bubble times plane wave.
"""
+
+ npar = 1
+
def __init__(self, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
-
pi = np.pi
mesh = fen.RectangleMesh(fen.Point(0, 0), fen.Point(pi, pi), n, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
c, s = np.cos(theta), np.sin(theta)
x, y = fen.SpatialCoordinate(mesh)[:]
C = 16. / pi ** 4.
bR = C * 2 * (x * (pi - x) + y * (pi - y))
bI = C * 2 * kappa * (c * (pi - 2 * x) * y * (pi - y)
+ s * x * (pi - x) * (pi - 2 * y))
wR = fen.cos(kappa * (c * x + s * y))
wI = fen.sin(kappa * (c * x + s * y))
self.forcingTerm = [bR * wR + bI * wI, bI * wR - bR * wI]
diff --git a/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py b/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
index 07b4665..8c469e7 100644
--- a/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/helmholtz_square_transmission_problem_engine.py
@@ -1,75 +1,76 @@
# 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 .helmholtz_problem_engine import HelmholtzProblemEngine
__all__ = ['HelmholtzSquareTransmissionProblemEngine']
class HelmholtzSquareTransmissionProblemEngine(HelmholtzProblemEngine):
"""
Solver for square transmission Helmholtz problems with parametric
wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
with exact solution a transmitted plane wave.
"""
+
+ npar = 1
+
def __init__(self, nT:float, nB:float, kappa:float, theta:float, n:int,
degree_threshold : int = np.inf, verbosity : int = 10,
timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
-
mesh = fen.RectangleMesh(fen.Point(-np.pi/2, -np.pi/2),
fen.Point(np.pi/2, np.pi/2), n, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
dx, dy = np.cos(theta), np.sin(theta)
Kx = kappa * nB * dx
Ky = kappa * (nT**2. - (nB * dx)**2. + 0.j)**.5
T = 2 * kappa * nB * dy / (Ky + kappa * nB * dy)
x, y = fen.SpatialCoordinate(mesh)[:]
TR, TI = np.real(T), np.imag(T)
if np.isclose(np.imag(Ky), 0.):
u0RT = (TR * fen.cos(Kx * x + np.real(Ky) * y)
- TI * fen.sin(Kx * x + np.real(Ky) * y))
u0IT = (TR * fen.sin(Kx * x + np.real(Ky) * y)
+ TI * fen.cos(Kx * x + np.real(Ky) * y))
else:
u0RT = fen.exp(- np.imag(Ky) * y) * (TR * fen.cos(Kx * x)
- TI * fen.sin(Kx * x))
u0IT = fen.exp(- np.imag(Ky) * y) * (TR * fen.sin(Kx * x)
+ TI * fen.cos(Kx * x))
u0RB = (fen.cos(kappa * nB * (dx * x + dy * y))
+ (TR - 1) * fen.cos(kappa * nB * (dx*x - dy*y))
- TI * fen.sin(kappa * nB * (dx*x - dy*y)))
u0IB = (fen.sin(kappa * nB * (dx * x + dy * y))
+ (TR - 1) * fen.sin(kappa * nB * (dx*x - dy*y))
+ TI * fen.cos(kappa * nB * (dx*x - dy*y)))
u0R = ufl.conditional(ufl.ge(y, 0.), u0RT, u0RB)
u0I = ufl.conditional(ufl.ge(y, 0.), u0IT, u0IB)
self.refractionIndex = ufl.conditional(ufl.ge(y, 0.),
fen.Constant(nT),
fen.Constant(nB))
self.DirichletDatum = [u0R, u0I]
diff --git a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
index 48aa209..b4bb816 100644
--- a/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/laplace_base_problem_engine.py
@@ -1,316 +1,321 @@
# 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.hfengines.base.problem_engine_base import ProblemEngineBase
-from rrompy.utilities.base.types import Np1D, ScOp, paramVal, paramList
+from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal, paramList
from rrompy.solver.fenics import fenZERO, fenONE, H1NormMatrix
from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
- def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
- timestamp : bool = True):
+ npar = 0
+
+ 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.omega = 0.
+ self.mu0 = self.checkParameter(mu0)
+ 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)
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)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
self.energyNormMatrix = H1NormMatrix(self.V, np.abs(self.omega)**2)
- def A(self, mu : paramVal = (), der : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
- self.autoSetDS()
- if self.As[0] is None:
+ if not hasattr(der, "__len__"): der = [der]
+ 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)
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))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- return self.As[0]
+ return self._assembleA(mu, der, derI)
- def b(self, mu : paramVal = (), der : int = 0,
+ def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if bnull is not None: return bnull
- if homogeneized and mu != self.mu0BC:
- self.u0BC = self.liftDirichletData(mu)
- if max(self.nbs, self.nAs * homogeneized) > 1 and self.bsmu != mu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(der),
- timestamp = self.timestamp)
- if der == 0:
- fRe, fIm = self.forcingTerm
- g1Re, g1Im = self.NeumannDatum
- g2Re, g2Im = self.RobinDatumG
- else:
- fRe, fIm = fenZERO, fenZERO
- g1Re, g1Im = fenZERO, fenZERO
- g2Re, g2Im = fenZERO, fenZERO
- termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
- parsRe = self.iterReduceQuadratureDegree(zip(
+ if not hasattr(der, "__len__"): der = [der]
+ 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.u0BC = 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)
+ if derI == 0:
+ fRe, fIm = self.forcingTerm
+ g1Re, g1Im = self.NeumannDatum
+ g2Re, g2Im = self.RobinDatumG
+ else:
+ fRe, fIm = fenZERO, fenZERO
+ g1Re, g1Im = fenZERO, fenZERO
+ g2Re, g2Im = fenZERO, fenZERO
+ termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
+ parsRe = self.iterReduceQuadratureDegree(zip(
[fRe, g1Re, g2Re],
[x + "Real" for x in termNames]))
- parsIm = self.iterReduceQuadratureDegree(zip(
+ parsIm = self.iterReduceQuadratureDegree(zip(
[fIm, g1Im, g2Im],
[x + "Imag" for x in termNames]))
- 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))
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(mu, der)
- b0Re[:] -= np.real(Ader.dot(self.u0BC))
- b0Im[:] -= np.imag(Ader.dot(self.u0BC))
- DBCR = fen.DirichletBC(self.V, fenZERO, self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, fenZERO, self.DirichletBoundary)
- else:
- DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
- self.DirichletBoundary)
- DBCR.apply(b0Re)
- DBCI.apply(b0Im)
- b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
- return b
+ 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))
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ if homogeneized:
+ Ader = self.A(self.mu0, der)
+ b0Re[:] -= np.real(Ader.dot(self.u0BC))
+ b0Im[:] -= np.imag(Ader.dot(self.u0BC))
+ DBCR = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ else:
+ DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
+ self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
+ self.DirichletBoundary)
+ DBCR.apply(b0Re)
+ DBCI.apply(b0Im)
+ b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if homogeneized:
+ self.bsH[j] = b
+ else:
+ self.bs[j] = b
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu - self.mu0, der, derI, homogeneized)
diff --git a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
index 70770ba..48b1fc4 100644
--- a/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
+++ b/rrompy/hfengines/linear_problem/laplace_disk_gaussian.py
@@ -1,163 +1,164 @@
# 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.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
__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.
"""
-
+
npar = 1
nbs = 20
- def __init__(self, n:int, degree_threshold : int = np.inf,
+ def __init__(self, n:int, mu0 : paramVal = [0.], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self.computebsFactors()
self.forcingTermMu = np.nan
import mshr
mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0., 0.), 5.), n)
self.V = fen.FunctionSpace(mesh, "P", 3)
- def getForcingTerm(self, mu : paramVal = ()) -> Tuple[FenExpr, FenExpr]:
+ 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)
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)
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 = (),
- der : int = 0) -> Tuple[FenExpr, FenExpr]:
+ 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)
muR, muI = np.real(mu(0, 0)), np.imag(mu(0, 0))
x = fen.SpatialCoordinate(self.V.mesh())[0]
- l = der % 2
+ l = derI % 2
if l == 0:
powR, powI = fenONE, fenZERO
else:
powR, powI = x - muR, fen.Constant(muI)
- exprR, exprI = [self.bsFactors[der, l] * k for k in [powR, powI]]
- for j in range(l + 2, der + 1, 2):
+ 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[der, j] * powR
- exprI += self.bsFactors[der, j] * powI
+ 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)
return[exprR, exprI]
- def b(self, mu : paramVal = (), der : int = 0,
+ def b(self, mu : paramVal = [], der : int = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if bnull is not None: return bnull
- if homogeneized and mu != self.mu0BC:
- self.u0BC = self.liftDirichletData(mu)
- if self.bsmu != mu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b{}.".format(
- der),
- timestamp = self.timestamp)
- if der < self.nbs:
- fRe, fIm = self.getForcingTerm(mu)
- cRe, cIm = self.getExtraFactorB(mu, der)
- cfRe = cRe * fRe - cIm * fIm
- cfIm = cRe * fIm + cIm * fRe
- else:
- cfRe, cfIm = fenZERO, fenZERO
- parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
- ["forcingTermDer{}Real".format(der)]))
- parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
- ["forcingTermDer{}Imag".format(der)]))
- L0Re = fen.dot(cfRe, self.v) * fen.dx
- L0Im = fen.dot(cfIm, self.v) * fen.dx
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(mu, der)
- b0Re[:] -= np.real(Ader.dot(self.u0BC))
- b0Im[:] -= np.imag(Ader.dot(self.u0BC))
- DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
- self.DirichletBoundary)
- DirichletBC0.apply(b0Re)
- DirichletBC0.apply(b0Im)
- b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
- return b
+ if not hasattr(der, "__len__"): der = [der]
+ 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.u0BC = 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)
+ 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
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j))
+ b0Re[:] -= np.real(Ader.dot(self.u0BC))
+ b0Im[:] -= np.imag(Ader.dot(self.u0BC))
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ DirichletBC0.apply(b0Re)
+ DirichletBC0.apply(b0Im)
+ if homogeneized:
+ self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ else:
+ self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu - self.mu0, der, derI, homogeneized)
diff --git a/rrompy/hfengines/linear_problem/laplace_disk_gaussian_2.py b/rrompy/hfengines/linear_problem/laplace_disk_gaussian_2.py
index 526f2c2..ce82478 100644
--- a/rrompy/hfengines/linear_problem/laplace_disk_gaussian_2.py
+++ b/rrompy/hfengines/linear_problem/laplace_disk_gaussian_2.py
@@ -1,133 +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 rrompy.utilities.base.types import Np1D, Tuple, FenExpr, paramVal
-from .laplace_base_problem_engine import LaplaceBaseProblemEngine
+from .laplace_disk_gaussian import LaplaceDiskGaussian
from rrompy.solver.fenics import fenZERO, fenONE
from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['LaplaceDiskGaussian2']
-class LaplaceDiskGaussian2(LaplaceBaseProblemEngine):
+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.
"""
-
+
npar = 2
nAs, nbs = 1, 1
- def __init__(self, n:int, degree_threshold : int = np.inf,
- verbosity : int = 10, timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ 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.computebsFactors()
- self.forcingTermMu = np.nan
-
- import mshr
- mesh = mshr.generate_mesh(mshr.Circle(fen.Point(0., 0.), 5.), n)
- self.V = fen.FunctionSpace(mesh, "P", 3)
-
- def getForcingTerm(self, mu : paramVal = ()) -> Tuple[FenExpr, FenExpr]:
+
+ 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)
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)
return self.forcingTerm
def computebsFactors(self):
- raise RROMPyException("Not implemented.")
+ pass
- def getExtraFactorB(self, mu : paramVal = (),
- der : int = 0) -> Tuple[FenExpr, FenExpr]:
+ 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 : int = 0,
+ def b(self, mu : paramVal = [], der : int = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if der > 0:
- raise RROMPyException("Not implemented.")
- if bnull is not None: return bnull
- if homogeneized and mu != self.mu0BC:
- self.u0BC = self.liftDirichletData(mu)
- if self.bsmu != mu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling forcing term b{}.".format(
- der),
- timestamp = self.timestamp)
- if der < self.nbs:
- fRe, fIm = self.getForcingTerm(mu)
-# cRe, cIm = self.getExtraFactorB(mu, der)
- cRe, cIm = fenONE, fenZERO
- cfRe = cRe * fRe - cIm * fIm
- cfIm = cRe * fIm + cIm * fRe
- else:
- cfRe, cfIm = fenZERO, fenZERO
- parsRe = self.iterReduceQuadratureDegree(zip([cfRe],
- ["forcingTermDer{}Real".format(der)]))
- parsIm = self.iterReduceQuadratureDegree(zip([cfIm],
- ["forcingTermDer{}Imag".format(der)]))
- L0Re = fen.dot(cfRe, self.v) * fen.dx
- L0Im = fen.dot(cfIm, self.v) * fen.dx
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(mu, der)
- b0Re[:] -= np.real(Ader.dot(self.u0BC))
- b0Im[:] -= np.imag(Ader.dot(self.u0BC))
- DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
- self.DirichletBoundary)
- DirichletBC0.apply(b0Re)
- DirichletBC0.apply(b0Im)
- b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
- return b
+ if not hasattr(der, "__len__"): der = [der]
+ 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.u0BC = self.liftDirichletData(self.mu0)
+ for j in range(derI, nbsTot):
+ if True or bs[j] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", ("Assembling forcing term "
+ "b{}.").format(j),
+ timestamp = self.timestamp)
+ 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
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j))
+ b0Re[:] -= np.real(Ader.dot(self.u0BC))
+ b0Im[:] -= np.imag(Ader.dot(self.u0BC))
+ DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
+ self.DirichletBoundary)
+ DirichletBC0.apply(b0Re)
+ DirichletBC0.apply(b0Im)
+ if homogeneized:
+ self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ else:
+ self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu - self.mu0, der, derI, homogeneized)
diff --git a/rrompy/hfengines/linear_problem/scattering_problem_engine.py b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
index 404341b..2ea6234 100644
--- a/rrompy/hfengines/linear_problem/scattering_problem_engine.py
+++ b/rrompy/hfengines/linear_problem/scattering_problem_engine.py
@@ -1,178 +1,175 @@
# 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 scipy.sparse as scsp
import fenics as fen
-from rrompy.utilities.base.types import ScOp, paramVal
+from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO
from rrompy.utilities.base import verbosityDepth
from .helmholtz_problem_engine import HelmholtzProblemEngine
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
from rrompy.utilities.exception_manager import RROMPyWarning
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
+ npar = 1
nAs = 3
- rescalingExp = 1.
+ rescalingExp = [1.]
signR = - 1.
- def __init__(self, degree_threshold : int = inf, verbosity : int = 10,
- timestamp : bool = True):
+ def __init__(self, mu0 : paramVal = [0.], degree_threshold : int = inf,
+ verbosity : int = 10, timestamp : bool = True):
self.silenceWarnings = True
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = mu0, degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
del self.silenceWarnings
@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 : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
- self.autoSetDS()
- if der <= 0 and self.As[0] is None:
+ if not hasattr(der, "__len__"): der = [der]
+ 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)
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
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 1 and self.As[1] is None:
+ if derI <= 1 and self.As[1] is None:
+ self.autoSetDS()
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a1 = fen.dot(self.u, self.v) * self.ds(1)
A1 = fen.assemble(a1)
DirichletBC0.zero(A1)
A1Mat = fen.as_backend_type(A1).mat()
A1r, A1c, A1v = A1Mat.getValuesCSR()
self.As[1] = self.signR * 1.j * scsp.csr_matrix((A1v, A1c, A1r),
shape = A1Mat.size)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 2 and self.As[2] is None:
+ if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
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
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return (self.As[0] + mu(0, 0) * self.As[1]
- + mu(0, 0) ** 2. * self.As[2])
- if der == 1:
- return self.As[1] + 2 * mu(0, 0) * self.As[2]
- return self.As[2]
+ return self._assembleA(mu, der, derI)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_elasticity_constants.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_elasticity_constants.py
index 5b4e880..8617a68 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_elasticity_constants.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_beam_elasticity_constants.py
@@ -1,100 +1,151 @@
# 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 .linear_elasticity_problem_engine import LinearElasticityProblemEngine
+from .linear_elasticity_beam_poisson_ratio import (
+ LinearElasticityBeamPoissonRatio)
from rrompy.solver.fenics import fenZEROS
-from rrompy.utilities.base.types import Np1D, ScOp, paramVal
+from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException
__all__ = ['LinearElasticityBeamElasticityConstants']
-class LinearElasticityBeamElasticityConstants(LinearElasticityProblemEngine):
+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
"""
npar = 2
- nAs, nbs = 1, 1
+ nAs, nbs = 5, 4
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__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [nu0, E0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.lambda_ = E0 * nu0 / (1. + nu0) / (1. - 2 * nu0)
- self.mu_ = E0 / (1. + nu0)
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 : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if der > 0:
- raise RROMPyException("Not implemented.")
- if Anull is not None: return Anull
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if self.Asmu != mu:
- self.Asmu = mu
- self.resetAs()
- A = self.As[der]
- if A is None:
+ if derI <= 0 and self.As[0] is None: self.As[0] = 0.
+ if derI <= 1 and self.As[1] is None: self.As[1] = 0.
+ if derI <= 4 and self.As[2] is None:
if self.verbosity >= 20:
- verbosityDepth("INIT", "Assembling operator term A0.",
+ verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
- m_ = mu(0, 0) / (1. + mu(0, 1))
- l_ = m_ * mu(0, 1) / (1. - 2 * mu(0, 1))
- lambda_Re, lambda_Im = np.real(l_), np.imag(l_)
- mu_Re, mu_Im = np.real(m_), np.imag(m_)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
- a0Re = (mu_Re * fen.inner(epsilon(self.u), epsilon(self.v))
- + lambda_Re * fen.div(self.u) * fen.div(self.v)) * fen.dx
- a0Im = (mu_Im * fen.inner(epsilon(self.u), epsilon(self.v))
- + lambda_Im * fen.div(self.u) * fen.div(self.v)) * fen.dx
+ a0Re = fen.inner(epsilon(self.u), epsilon(self.v)) * fen.dx
A0Re = fen.assemble(a0Re)
- A0Im = fen.assemble(a0Im)
DirichletBC0.apply(A0Re)
- DirichletBC0.apply(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
- A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
- A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
- A = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer), shape = A0ReMat.size)
- + 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr), shape = A0ImMat.size))
- self.As[0] = A
+ self.As[2] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
+ shape = A0ReMat.size,
+ dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- return A
+ if derI <= 3 and self.As[3] is None: self.As[3] = 0.
+ if derI <= 4 and self.As[4] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling operator term A4.",
+ timestamp = self.timestamp)
+ DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
+ self.DirichletBoundary)
+ a1Re = fen.div(self.u) * fen.div(self.v) * fen.dx
+ A1Re = fen.assemble(a1Re)
+ DirichletBC0.apply(A1Re)
+ A1ReMat = fen.as_backend_type(A1Re).mat()
+ A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
+ self.As[4] = 2. * (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
+ shape = A1ReMat.size,
+ dtype = np.complex)
+ - self.As[2])
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling operator term.",
+ timestamp = self.timestamp)
+ 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]
+ derI = hashD(der)
+ if derI <= 3 and self.bs[0] is None:
+ self.autoSetDS()
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling forcing term b0.",
+ timestamp = self.timestamp)
+ 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
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
+ self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
+ self.DirichletBoundary)
+ DBCR.apply(b0Re)
+ DBCI.apply(b0Im)
+ self.bs[0] = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if derI <= 1 and self.bs[1] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling forcing term b1.",
+ timestamp = self.timestamp)
+ self.bs[1] = - self.bs[0]
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ if derI <= 2 and self.bs[2] is None: self.bs[2] = 0.
+ if derI <= 3 and self.bs[3] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling forcing term b3.",
+ timestamp = self.timestamp)
+ self.bs[3] = - 2. * self.bs[0]
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ 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 4896312..0899fe4 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
@@ -1,154 +1,150 @@
# 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 .linear_elasticity_problem_engine import LinearElasticityProblemEngine
from rrompy.solver.fenics import fenZEROS
-from rrompy.utilities.base.types import Np1D, ScOp, paramVal
+from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.exception_manager import RROMPyAssert
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
__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
"""
npar = 1
nAs, nbs = 2, 3
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__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [nu0], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.lambda_ = E * nu0 / (1. + nu0) / (1. - 2 * nu0)
- self.mu_ = E / (1. + nu0)
+ 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 : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if der <= 1 and self.As[0] is None:
+ if derI <= 1 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
epsilon = lambda u: .5 * (fen.grad(u) + fen.nabla_grad(u))
- a0Re = 2 * fen.inner(epsilon(self.u), epsilon(self.v)) * fen.dx
+ a0Re = self.E_ * fen.inner(epsilon(self.u),
+ epsilon(self.v)) * fen.dx
A0Re = fen.assemble(a0Re)
DirichletBC0.apply(A0Re)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
self.As[0] = scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size,
dtype = np.complex)
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 1 and self.As[1] is None:
+ if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
DirichletBC0 = fen.DirichletBC(self.V, fenZEROS(2),
self.DirichletBoundary)
- a1Re = fen.div(self.u) * fen.div(self.v) * fen.dx
+ a1Re = self.E_ * fen.div(self.u) * fen.div(self.v) * fen.dx
A1Re = fen.assemble(a1Re)
DirichletBC0.apply(A1Re)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
- self.As[1] = (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
- shape = A1ReMat.size,
- dtype = np.complex)
- - 2. * self.As[0])
+ self.As[1] = 2. * (scsp.csr_matrix((A1Rev, A1Rec, A1Rer),
+ shape = A1ReMat.size,
+ dtype = np.complex)
+ - self.As[0])
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return self.As[0] + mu(0, 0) * self.As[1]
- return self.As[1]
+ return self._assembleA(mu, der, derI)
- def b(self, mu : paramVal = (), der : int = 0,
+ 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)
- assert homogeneized == False
- bnull = self.checkbInBounds(der)
- if bnull is not None: return bnull
- if self.nbs > 1 and self.bsmu != mu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
+ if derI <= 2 and self.bs[0] is None:
self.autoSetDS()
if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(der),
+ verbosityDepth("INIT", "Assembling forcing term b0.",
timestamp = self.timestamp)
- if self.bs[0] is None and der > 0: self.b(mu, 0)
- if der == 0:
- fRe, fIm = self.forcingTerm
- parsRe = self.iterReduceQuadratureDegree(zip(
- [fRe],
+ fRe, fIm = self.forcingTerm
+ parsRe = self.iterReduceQuadratureDegree(zip([fRe],
["forcingTermReal"]))
- parsIm = self.iterReduceQuadratureDegree(zip(
- [fIm],
+ parsIm = self.iterReduceQuadratureDegree(zip([fIm],
["forcingTermImag"]))
- L0Re = fen.inner(fRe, self.v) * fen.dx
- L0Im = fen.inner(fIm, self.v) * fen.dx
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
- self.DirichletBoundary)
- DBCR.apply(b0Re)
- DBCI.apply(b0Im)
- b = (1. - mu(0, 0) - 2 * mu(0, 0) ** 2) * np.array(
- b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- elif der == 1:
- b = ((- 1. - 4 * mu(0, 0))
- / (1. - mu(0, 0) - 2 * mu(0, 0) ** 2) * self.bs[0])
- elif der == 2:
- b = - 2. / (1. - mu(0, 0) - 2 * mu(0, 0) ** 2.) * self.bs[0]
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
+ L0Re = fen.inner(fRe, self.v) * fen.dx
+ L0Im = fen.inner(fIm, self.v) * fen.dx
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
+ self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
+ self.DirichletBoundary)
+ DBCR.apply(b0Re)
+ DBCI.apply(b0Im)
+ self.bs[0] = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
+ if derI <= 1 and self.bs[1] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling forcing term b1.",
+ timestamp = self.timestamp)
+ self.bs[1] = - self.bs[0]
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+
+ if derI <= 2 and self.bs[2] is None:
+ if self.verbosity >= 20:
+ verbosityDepth("INIT", "Assembling forcing term b2.",
+ timestamp = self.timestamp)
+ self.bs[2] = - 2. * self.bs[0]
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling forcing term.",
timestamp = self.timestamp)
- return b
+ return self._assembleb(mu, der, derI, homogeneized)
diff --git a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_archway_frequency.py b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_archway_frequency.py
index fa8ffef..eee2d90 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_archway_frequency.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_helmholtz_archway_frequency.py
@@ -1,67 +1,68 @@
# 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.solver.fenics import fenZEROS
__all__ = ['LinearElasticityHelmholtzArchwayFrequency']
class LinearElasticityHelmholtzArchwayFrequency(
LinearElasticityHelmholtzProblemEngine):
"""
Solver for archway linear elasticity Helmholtz problem with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * omega^2 * u = rho_ * g / omega in \Omega
u = 0 on \Gamma_D
\partial_nu = 0 on \Gamma_N
"""
+ npar = 1
+
def __init__(self, kappa:float, n:int, rho_:float, T:float, lambda_:float,
mu_:float, R:float, r:float, degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ super().__init__(mu0 = [kappa], degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
- self.omega = kappa
self.lambda_ = lambda_
self.mu_ = mu_
self.rho_ = rho_
import mshr
domain = (mshr.Circle(fen.Point(0, 0), R)
- mshr.Circle(fen.Point(0, 0), r)
- mshr.Rectangle(fen.Point(-1.05*R, -1.05*R),
fen.Point(1.05*R, 0)))
mesh = mshr.generate_mesh(domain, n)
self.V = fen.VectorFunctionSpace(mesh, "P", 1)
import ufl
x, y = fen.SpatialCoordinate(mesh)[:]
NeumannNonZero = ufl.And(ufl.gt(y, r),
ufl.And(ufl.ge(x, -.25 * R), ufl.le(x, .25 * R)))
self.NeumannDatum = [ufl.as_vector((0.,
ufl.conditional(NeumannNonZero,
fen.Constant(T),
0.))),
fenZEROS(2)]
self.DirichletBoundary = lambda x, on_b: on_b and fen.near(x[1], 0.)
self.NeumannBoundary = "REST"
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 1395863..c587151 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
@@ -1,183 +1,182 @@
# 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.sparse import csr_matrix
import fenics as fen
from .linear_elasticity_problem_engine import LinearElasticityProblemEngine
-from rrompy.utilities.base.types import ScOp, paramVal
+from rrompy.utilities.base.types import List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS, fenONE, elasticNormMatrix
from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
npar = 1
nAs = 2
- rescalingExp = 2.
+ rescalingExp = [2.]
- def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
- timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ 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.omega = 1.
+ self.omega = np.abs(self.mu0(0, 0))
self.rho_ = fenONE
@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.
"""
lambda_Re, _ = self.lambda_
mu_Re, _ = self.mu_
r_Re, _ = self.rho_
self.energyNormMatrix = elasticNormMatrix(self.V, lambda_Re, mu_Re,
np.abs(self.omega)**2 * r_Re)
- def A(self, mu : paramVal = (), der : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if der <= 0 and self.As[0] is None:
+ if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
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))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 1 and self.As[1] is None:
+ if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
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
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return self.As[0] + mu(0, 0) ** 2. * self.As[1]
- return self.As[1]
+ 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 c29a394..b53d4d9 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
@@ -1,210 +1,207 @@
# 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.sparse import csr_matrix
import fenics as fen
from .linear_elasticity_helmholtz_problem_engine import \
LinearElasticityHelmholtzProblemEngine
-from rrompy.utilities.base.types import ScOp, paramVal
+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.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD)
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
+ npar = 1
nAs = 3
- rescalingExp = 1.
+ rescalingExp = [1.]
- def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
- timestamp : bool = True):
- super().__init__(degree_threshold = degree_threshold,
+ 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.eta = fenZERO
@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 : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if der <= 0 and self.As[0] is None:
+ if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
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))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 1 and self.As[1] is None:
+ if derI <= 1 and self.As[1] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A1.",
timestamp = self.timestamp)
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
A1Re = fen.assemble(a1Re, form_compiler_parameters = parsRe)
A1Im = fen.assemble(a1Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A1Re)
DirichletBC0.zero(A1Im)
A1ReMat = fen.as_backend_type(A1Re).mat()
A1ImMat = fen.as_backend_type(A1Im).mat()
A1Rer, A1Rec, A1Rev = A1ReMat.getValuesCSR()
A1Imr, A1Imc, A1Imv = A1ImMat.getValuesCSR()
self.As[1] = (csr_matrix((A1Rev, A1Rec, A1Rer),
shape = A1ReMat.size)
+ 1.j * csr_matrix((A1Imv, A1Imc, A1Imr),
shape = A1ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der <= 2 and self.As[2] is None:
+ if derI <= 2 and self.As[2] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A2.",
timestamp = self.timestamp)
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
A2Re = fen.assemble(a2Re, form_compiler_parameters = parsRe)
A2Im = fen.assemble(a2Im, form_compiler_parameters = parsIm)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.As[2] = (csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- if der == 0:
- return (self.As[0] + mu(0, 0) * self.As[1]
- + mu(0, 0) ** 2. * self.As[2])
- if der == 1:
- return self.As[1] + 2 * mu(0, 0) * self.As[2]
- return self.As[2]
+ 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 fea2477..2c514ad 100644
--- a/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
+++ b/rrompy/hfengines/vector_linear_problem/linear_elasticity_problem_engine.py
@@ -1,353 +1,357 @@
# 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.sparse import csr_matrix
import fenics as fen
from rrompy.hfengines.base.vector_problem_engine_base import \
VectorProblemEngineBase
-from rrompy.utilities.base.types import Np1D, ScOp, paramVal
+from rrompy.utilities.base.types import Np1D, List, ScOp, paramVal
from rrompy.solver.fenics import fenZERO, fenZEROS, fenONE, elasticNormMatrix
from rrompy.utilities.base import verbosityDepth
+from rrompy.utilities.poly_fitting.polynomial import (
+ hashDerivativeToIdx as hashD, hashIdxToDerivative as hashI)
__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.
- bsmu: Mu value of last bs evaluation.
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.
"""
- def __init__(self, degree_threshold : int = np.inf, verbosity : int = 10,
- timestamp : bool = True):
+ npar = 0
+
+ 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 = self.checkParameter(mu0)
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)
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)
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
lambda_Re, _ = self.lambda_
mu_Re, _ = self.mu_
self.energyNormMatrix = elasticNormMatrix(self.V, lambda_Re, mu_Re)
- def A(self, mu : paramVal = (), der : int = 0) -> ScOp:
+ def A(self, mu : paramVal = [], der : List[int] = 0) -> ScOp:
"""Assemble (derivative of) operator of linear system."""
mu = self.checkParameter(mu)
- Anull = self.checkAInBounds(der)
- if Anull is not None: return Anull
+ if not hasattr(der, "__len__"): der = [der]
+ derI = hashD(der)
self.autoSetDS()
- if self.As[0] is None:
+ if derI <= 0 and self.As[0] is None:
if self.verbosity >= 20:
verbosityDepth("INIT", "Assembling operator term A0.",
timestamp = self.timestamp)
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))
A0Re = fen.assemble(a0Re, form_compiler_parameters = parsRe)
A0Im = fen.assemble(a0Im, form_compiler_parameters = parsIm)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.As[0] = (csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if self.verbosity >= 20:
verbosityDepth("DEL", "Done assembling operator term.",
timestamp = self.timestamp)
- return self.As[0]
+ return self._assembleA(mu, der, derI)
- def b(self, mu : paramVal = (), der : int = 0,
+ def b(self, mu : paramVal = [], der : List[int] = 0,
homogeneized : bool = False) -> Np1D:
"""Assemble (derivative of) RHS of linear system."""
mu = self.checkParameter(mu)
- bnull = self.checkbInBounds(der, homogeneized)
- if bnull is not None: return bnull
- if homogeneized and self.mu0BC != mu:
- self.u0BC = self.liftDirichletData(mu)
- if max(self.nbs, self.nAs * homogeneized) > 1 and mu != self.bsmu:
- self.bsmu = mu
- self.resetbs()
- b = self.bsH[der] if homogeneized else self.bs[der]
- if b is None:
- self.autoSetDS()
- if self.verbosity >= 20:
- verbosityDepth("INIT", ("Assembling forcing term "
- "b{}.").format(der),
- timestamp = self.timestamp)
- if der == 0:
- fRe, fIm = self.forcingTerm
- g1Re, g1Im = self.NeumannDatum
- g2Re, g2Im = self.RobinDatumG
- else:
- fRe = fenZEROS(self.V.mesh().topology().dim())
- fIm = fenZEROS(self.V.mesh().topology().dim())
- g1Re = fenZEROS(self.V.mesh().topology().dim())
- g1Im = fenZEROS(self.V.mesh().topology().dim())
- g2Re = fenZEROS(self.V.mesh().topology().dim())
- g2Im = fenZEROS(self.V.mesh().topology().dim())
- termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
- parsRe = self.iterReduceQuadratureDegree(zip(
+ if not hasattr(der, "__len__"): der = [der]
+ 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.u0BC = self.liftDirichletData(self.mu)
+ 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)
+ if j == 0:
+ fRe, fIm = self.forcingTerm
+ g1Re, g1Im = self.NeumannDatum
+ g2Re, g2Im = self.RobinDatumG
+ else:
+ fRe = fenZEROS(self.V.mesh().topology().dim())
+ fIm = fenZEROS(self.V.mesh().topology().dim())
+ g1Re = fenZEROS(self.V.mesh().topology().dim())
+ g1Im = fenZEROS(self.V.mesh().topology().dim())
+ g2Re = fenZEROS(self.V.mesh().topology().dim())
+ g2Im = fenZEROS(self.V.mesh().topology().dim())
+ termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
+ parsRe = self.iterReduceQuadratureDegree(zip(
[fRe, g1Re, g2Re],
[x + "Real" for x in termNames]))
- parsIm = self.iterReduceQuadratureDegree(zip(
+ 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))
- b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
- b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
- if homogeneized:
- Ader = self.A(mu, der)
- b0Re[:] -= np.real(Ader.dot(self.u0BC))
- b0Im[:] -= np.imag(Ader.dot(self.u0BC))
- DBCR = fen.DirichletBC(self.V,
+ 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))
+ b0Re = fen.assemble(L0Re, form_compiler_parameters = parsRe)
+ b0Im = fen.assemble(L0Im, form_compiler_parameters = parsIm)
+ if homogeneized:
+ Ader = self.A(self.mu0, hashI(j))
+ b0Re[:] -= np.real(Ader.dot(self.u0BC))
+ b0Im[:] -= np.imag(Ader.dot(self.u0BC))
+ DBCR = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V,
+ DBCI = fen.DirichletBC(self.V,
fenZEROS(self.V.mesh().topology().dim()),
self.DirichletBoundary)
- else:
- DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
- self.DirichletBoundary)
- DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
- self.DirichletBoundary)
- DBCR.apply(b0Re)
- DBCI.apply(b0Im)
- b = np.array(b0Re[:] + 1.j * b0Im[:], dtype = np.complex)
- if homogeneized:
- self.bsH[der] = b
- else:
- self.bs[der] = b
- if self.verbosity >= 20:
- verbosityDepth("DEL", "Done assembling forcing term.",
- timestamp = self.timestamp)
- return b
+ else:
+ DBCR = fen.DirichletBC(self.V, self.DirichletDatum[0],
+ self.DirichletBoundary)
+ DBCI = fen.DirichletBC(self.V, self.DirichletDatum[1],
+ self.DirichletBoundary)
+ DBCR.apply(b0Re)
+ DBCI.apply(b0Im)
+ if homogeneized:
+ self.bsH[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ else:
+ self.bs[j] = np.array(b0Re[:] + 1.j * b0Im[:],
+ dtype = np.complex)
+ if self.verbosity >= 20:
+ verbosityDepth("DEL", "Done assembling forcing term.",
+ timestamp = self.timestamp)
+ return self._assembleb(mu - self.mu0, der, derI, homogeneized)
diff --git a/rrompy/parameter/parameter_list.py b/rrompy/parameter/parameter_list.py
index 9cede94..184865a 100644
--- a/rrompy/parameter/parameter_list.py
+++ b/rrompy/parameter/parameter_list.py
@@ -1,218 +1,218 @@
# 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 itertools import product as iterprod
from copy import deepcopy as copy
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
from rrompy.utilities.base.types import Np2D
__all__ = ['parameterList', 'emptyParameterList', 'checkParameterList']
def checkParameterList(mu, npar = None):
if not isinstance(mu, (parameterList,)):
mu = parameterList(mu, npar)
else:
if npar is not None:
RROMPyAssert(mu.shape[1], npar, "Number of parameters")
mu = copy(mu)
return mu, len(mu) == 1
def checkParameter(mu, npar = None):
mu, wasPar = checkParameterList(mu, npar)
if not wasPar:
raise RROMPyException(("Only single parameter allowed. No parameter "
"lists here."))
return mu
+def emptyParameterList():
+ mu = parameterList([[]])
+ mu.reset((0, 0), float)
+ return mu
+
def addMemberFromNumpyArray(self, fieldName):
def objFunc(self, other):
if not isinstance(other, (self.__class__,)):
other = parameterList(other)
return parameterList(getattr(np.ndarray, fieldName)(self.data,
other.data))
setattr(self.__class__, fieldName, objFunc)
def objIFunc(self, other):
self.data = getattr(self.__class__, fieldName)(self, other).data
setattr(self.__class__, "__i" + fieldName[2:], objIFunc)
class parameterList:
"""HERE"""
__all__ += [pre + post for pre, post in iterprod(["__", "__i"],
["__add__", "__sub__", "__mul__", "__div__",
"__truediv__", "__floordiv__", "__pow__"])]
def __init__(self, data:Np2D, lengthCheck : int = None):
if not hasattr(data, "__len__"): data = [data]
elif isinstance(data, (self.__class__,)): data = data.data
elif isinstance(data, (tuple,)): data = list(data)
if (isinstance(data, (list,)) and len(data) > 0
and isinstance(data[0], (tuple,))):
data = [list(x) for x in data]
self.data = np.array(data, ndmin = 1, copy = 1)
if self.data.ndim == 1:
self.data = self.data[:, None]
if np.size(self.data) > 0:
self.data = self.data.reshape((len(self), -1))
if lengthCheck is not None:
if lengthCheck != 1 and self.shape == (lengthCheck, 1):
self.data = self.data.T
RROMPyAssert(self.shape[1], lengthCheck, "Number of parameters")
for fieldName in ["__add__", "__sub__", "__mul__", "__div__",
"__truediv__", "__floordiv__", "__pow__"]:
addMemberFromNumpyArray(self, fieldName)
def __len__(self):
return len(self.data)
def __str__(self):
if len(self) <= 3:
selfstr = str(self.data)
else:
selfstr = "[{} ..({}).. {}]".format(self[0], len(self) - 2,
self[-1])
return selfstr
def __repr__(self):
return repr(self.data)
@property
def shape(self):
return self.data.shape
@property
def re(self):
return parameterList(np.real(self.data))
@property
def im(self):
return parameterList(np.imag(self.data))
@property
def abs(self):
return parameterList(np.abs(self.data))
@property
def angle(self):
return parameterList(np.angle(self.data))
@property
def conj(self):
return parameterList(np.conj(self.data))
@property
def dtype(self):
return self.data.dtype
def __getitem__(self, key):
return self.data[key]
def __call__(self, key, idx = None):
if idx is None:
return self.data[:, key]
return self[key, idx]
def __setitem__(self, key, value):
if isinstance(key, (tuple, list,)):
RROMPyAssert(len(key), len(value), "Slice length")
for k, val in zip(key, value):
self[k] = val
else:
self.data[key] = value
def __eq__(self, other):
if not hasattr(other, "shape") or self.shape != other.shape:
return False
if isinstance(other, self.__class__):
other = other.data
return np.allclose(self.data, other)
def __contains__(self, item):
return next((x for x in self if np.allclose(x[0], item)), -1) != -1
def __iter__(self):
return iter([parameterList([x]) for x in self.data])
def __copy__(self):
return parameterList(self.data)
def __deepcopy__(self, memo):
return parameterList(copy(self.data, memo))
def __neg__(self):
return parameterList(-self.data)
def __pos__(self):
return copy(self)
def reset(self, size, dtype = complex):
self.data = np.empty(size, dtype = dtype)
self.data[:] = np.nan
def append(self, items):
if isinstance(items, self.__class__):
items = items.data
else:
items = np.array(items, ndmin = 2)
if len(self) == 0:
self.data = parameterList(items).data
else:
self.data = np.append(self.data, items, axis = 0)
def pop(self, idx = -1):
self.data = np.delete(self.data, idx, axis = 0)
def find(self, item):
if len(self) == 0: return None
return next((j for j in range(len(self))
if np.allclose(self[j], item)), None)
def findall(self, item):
if len(self) == 0: return []
return [j for j in range(len(self)) if np.allclose(self[j], item)]
def sort(self, overwrite = False, *args, **kwargs):
dataT = np.array([tuple(x[0]) for x in self],
dtype = [(str(j), self.dtype)
for j in range(self.shape[1])])
sortedP = parameterList([list(x) for x in np.sort(dataT, *args,
**kwargs)])
if overwrite: self.data = sortedP.data
return sortedP
def unique(self, overwrite = False, *args, **kwargs):
dataT = np.array([tuple(x[0]) for x in self],
dtype = [(str(j), self.dtype)
for j in range(self.shape[1])])
uniqueT = np.unique(dataT, *args, **kwargs)
if isinstance(uniqueT, (tuple,)):
extraT = uniqueT[1:]
uniqueT = uniqueT[0]
else: extraT = ()
uniqueP = parameterList([list(x) for x in uniqueT])
if overwrite: self.data = uniqueP.data
uniqueP = (uniqueP,) + extraT
if len(uniqueP) == 1: return uniqueP[0]
return uniqueP
-
-class emptyParameterList(parameterList):
- def __init__(self):
- super().__init__([[]])
- self.reset((0, 0), float)
diff --git a/rrompy/parameter/parameter_sampling/manual_sampler.py b/rrompy/parameter/parameter_sampling/manual_sampler.py
index 5965474..7465d84 100644
--- a/rrompy/parameter/parameter_sampling/manual_sampler.py
+++ b/rrompy/parameter/parameter_sampling/manual_sampler.py
@@ -1,71 +1,71 @@
# 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_sampler import GenericSampler
from rrompy.utilities.base.types import Np1D, Tuple, List, paramList
from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyAssert
from rrompy.parameter import checkParameterList
__all__ = ['ManualSampler']
class ManualSampler(GenericSampler):
"""Manual generator of sample points."""
def __init__(self, lims:paramList, points:paramList,
scaling : List[callable] = None,
scalingInv : List[callable] = None):
super().__init__(lims = lims, scaling = scaling,
scalingInv = scalingInv)
self.points = points
@property
def points(self):
"""Value of points."""
return self._points
@points.setter
def points(self, points):
- points, _ = checkParameterList(points)
- RROMPyAssert(points.shape[1], self.npar, "Number of parameters")
+ points, _ = checkParameterList(points, self.npar)
self._points = points
def __str__(self) -> str:
return "{}[{}]".format(self.name(), "_".join(map(str, self.points)))
def __repr__(self) -> str:
return self.__str__() + " at " + hex(id(self))
def generatePoints(self, n:int) -> Tuple[paramList, Np1D]:
"""Array of sample points and array of weights."""
size = 1. / n
for d in range(self.npar):
a, b = self.lims(0, d), self.lims(1, d)
if self.scaling is not None:
a, b = self.scaling[d](a), self.scaling[d](b)
size *= np.abs(a - b)
if n > len(self.points):
RROMPyWarning(("Requested more points than given. Looping over "
"first points."))
pts = copy(self.points)
for j in range(np.int(np.ceil(n / len(self.points)))):
pts.append(self.points)
else:
pts = self.points
- x, _ = checkParameterList(pts[list(range(n))])
+ x, _ = checkParameterList(pts[list(range(n))], self.npar)
return x, np.ones(n) * size
+
diff --git a/rrompy/reduction_methods/base/generic_approximant.py b/rrompy/reduction_methods/base/generic_approximant.py
index 4a0cdae..138940b 100644
--- a/rrompy/reduction_methods/base/generic_approximant.py
+++ b/rrompy/reduction_methods/base/generic_approximant.py
@@ -1,819 +1,828 @@
# 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, strLst,
paramVal, paramList, sampList)
from rrompy.utilities.base import purgeDict, verbosityDepth, 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) -> float:
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, name : str = fieldName, save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True,
homogeneized : bool = False, **figspecs):
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
for j, u in enumerate(uV):
self.HFEngine.plot(u, name = name + str(j), save = save,
what = what, saveFormat = saveFormat,
saveDPI = saveDPI, show = show, **figspecs)
setattr(self.__class__, "plot" + fieldName, objFunc)
def addOutParaviewFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, name : str = fieldName,
filename : str = "out", time : float = 0.,
what : strLst = 'all', forceNewFile : bool = True,
folder : bool = False, filePW = None,
homogeneized : bool = False):
if not hasattr(self.HFEngine, "outParaview"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
for j, u in enumerate(uV):
self.HFEngine.outParaview(u, name = name + str(j),
filename = filename, time = time,
what = what, forceNewFile = forceNewFile,
folder = folder, filePW = filePW)
setattr(self.__class__, "outParaview" + fieldName, objFunc)
def addOutParaviewTimeDomainFieldToClass(self, fieldName):
def objFunc(self, mu:paramVal, omega : float = None,
timeFinal : float = None, periodResolution : int = 20,
name : str = fieldName, filename : str = "out",
forceNewFile : bool = True, folder : bool = False,
homogeneized : bool = False):
if not hasattr(self.HFEngine, "outParaviewTimeDomain"):
raise RROMPyException(("High fidelity engine cannot output to "
"Paraview."))
uV = getattr(self.__class__, "get" + fieldName)(self, mu, homogeneized)
if omega is None: omega = np.real(mu)
for j, u in enumerate(uV):
self.HFEngine.outParaviewTimeDomain(u, omega = omega,
timeFinal = timeFinal,
periodResolution = periodResolution,
name = name + str(j),
filename = filename,
forceNewFile = forceNewFile,
folder = folder)
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.
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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: 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 = 0,
+ 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)
self._HFEngine = HFEngine
self.trainedModel = None
self.lastSolvedHF = emptyParameterList()
self.uHF = emptySampleList()
self._addParametersToList(["POD"])
- self.mu0 = mu0
+ if mu0 is None:
+ if hasattr(self.HFEngine, "mu0"):
+ self.mu0 = self.HFEngine.mu0
+ else:
+ self.mu0 = emptyParameterList()
+ else:
+ self.mu0 = checkParameter(mu0)
self.homogeneized = homogeneized
self.approxParameters = approxParameters
+ self.resetSamples()
+ RROMPyAssert(self.HFEngine.npar, 1, "Parameter dimension")
+ RROMPyAssert(self.npar, 1, "Parameter dimension")
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", "Approx", "Res", "Err"]:
addNormFieldToClass(self, objName)
### 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
def _addParametersToList(self, what:strLst):
if not hasattr(self, "parameterList"):
self.parameterList = []
self.parameterList += what
def _postInit(self):
if self.depth == 0:
if self.verbosity >= 10:
verbosityDepth("DEL", "Done initializing.",
timestamp = self.timestamp)
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)
@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())
if "POD" in keyList:
self.POD = approxParameters["POD"]
elif not hasattr(self, "_POD") or self._POD is None:
self.POD = True
@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 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
self.lastSolvedAppReduced = emptyParameterList()
self.lastSolvedApp = emptyParameterList()
self.uAppReduced = emptySampleList()
self.uApp = 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, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, **figspecs):
"""
Do some nice plots of the samples.
Args:
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.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
RROMPyAssert(self._mode, message = "Cannot plot samples.")
self.samplingEngine.plotSamples(name = name, save = save, what = what,
saveFormat = saveFormat,
saveDPI = saveDPI,
**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 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 setHF(self, muHF:paramList, uHF:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedHF, _ = checkParameterList(muHF, self.npar)
newuHF = sampleList(uHF)
if append:
self.lastSolvedHF.append(newSolvedHF)
self.uHF.append(newuHF)
return list(range(len(self.uHF) - len(newuHF), len(self.uHF)))
self.lastSolvedHF, _ = checkParameterList(newSolvedHF, self.npar)
self.uHF = sampleList(newuHF)
return list(range(len(self.uHF)))
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.
"""
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
- muKeep, _ = checkParameterList([])
+ muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedHF.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:
idx[~jExtra] = self.setHF(muKeep, self.uHF[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
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, muApp:paramList, uApp:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedApp, _ = checkParameterList(muApp, self.npar)
newuApp = sampleList(uApp)
if append:
self.lastSolvedAppReduced.append(newSolvedApp)
self.uAppReduced.append(newuApp)
return list(range(len(self.uAppReduced) - len(newuApp),
len(self.uAppReduced)))
self.lastSolvedAppReduced, _ = checkParameterList(newSolvedApp,
self.npar)
self.uAppReduced = sampleList(newuApp)
return list(range(len(self.uAppReduced)))
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.
"""
self.setupApprox()
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
- muKeep, _ = checkParameterList([])
+ muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedAppReduced.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:
idx[~jExtra] = self.setApproxReduced(muKeep,
self.uAppReduced[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
if len(muExtra) > 0:
newuApps = self.trainedModel.getApproxReduced(muExtra)
idx[jExtra] = self.setApproxReduced(muExtra, newuApps, append)
return list(idx)
def setApprox(self, muApp:paramList, uApp:sampleList,
append : bool = False) -> List[int]:
"""Assign high fidelity solution."""
newSolvedApp, _ = checkParameterList(muApp, self.npar)
newuApp = sampleList(uApp)
if append:
self.lastSolvedApp.append(newSolvedApp)
self.uApp.append(newuApp)
return list(range(len(self.uApp) - len(newuApp), len(self.uApp)))
self.lastSolvedApp, _ = checkParameterList(newSolvedApp, self.npar)
self.uApp = sampleList(newuApp)
return list(range(len(self.uApp)))
def evalApprox(self, mu:paramList, append : bool = False,
prune : bool = True) -> List[int]:
"""
Evaluate approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
self.setupApprox()
mu, _ = checkParameterList(mu, self.npar)
idx = np.empty(len(mu), dtype = np.int)
if prune:
jExtra = np.zeros(len(mu), dtype = bool)
- muKeep, _ = checkParameterList([])
+ muKeep = emptyParameterList()
muExtra = copy(muKeep)
for j in range(len(mu)):
jPos = self.lastSolvedApp.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:
idx[~jExtra] = self.setApprox(muKeep, self.uApp[idx[~jExtra]],
append)
append = True
else:
jExtra = np.ones(len(mu), dtype = bool)
muExtra = mu
if len(muExtra) > 0:
newuApps = self.trainedModel.getApprox(muExtra)
idx[jExtra] = self.setApprox(muExtra, newuApps, 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) -> 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)
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)
uAppRs = self.uAppReduced(idx)
return uAppRs
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)
uApps = self.uApp(idx)
if self.homogeneized and not homogeneized:
for j, m in enumerate(mu):
uApps[j] += self.HFEngine.liftDirichletData(m)
if not self.homogeneized and homogeneized:
for j, m in enumerate(mu):
uApps[j] -= self.HFEngine.liftDirichletData(m)
return uApps
def getRes(self, mu:paramList, homogeneized : bool = False) -> 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)
def getErr(self, mu:paramList, homogeneized : bool = False) -> 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) - self.getHF(mu, homogeneized)
def getPoles(self) -> 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)
poles = self.trainedModel.getPoles()
if self.verbosity >= 20:
verbosityDepth("DEL", "Done computing poles.",
timestamp = self.timestamp)
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)
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)
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)
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)
diff --git a/rrompy/reduction_methods/centered/generic_centered_approximant.py b/rrompy/reduction_methods/centered/generic_centered_approximant.py
index 276714e..53d2ad7 100644
--- a/rrompy/reduction_methods/centered/generic_centered_approximant.py
+++ b/rrompy/reduction_methods/centered/generic_centered_approximant.py
@@ -1,143 +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 rrompy.reduction_methods.base.generic_approximant import (
GenericApproximant)
from rrompy.utilities.base.types import DictAny, HFEng, paramVal
from rrompy.utilities.base import purgeDict, verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException, 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;
- 'E': total number of derivatives current approximant relies upon;
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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'E': total number of derivatives current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
E: Number of solution derivatives 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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
- def __init__(self, HFEngine:HFEng, mu0 : paramVal = 0,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["E"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def approxParameters(self):
"""Value of approximant parameters. Its assignment may change E."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["E"],
True, True, baselevel = 1)
GenericApproximant.approxParameters.fset(self, approxParametersCopy)
keyList = list(approxParameters.keys())
if "E" in keyList:
self.E = approxParameters["E"]
elif hasattr(self, "_E") and self._E is not None:
self.E = self.E
else:
self.E = 1
@property
def E(self):
"""Value of E."""
return self._E
@E.setter
def E(self, E):
if E < 0: raise RROMPyException("E must be non-negative.")
self._E = E
self._approxParameters["E"] = self.E
def computeDerivatives(self):
"""Compute derivatives of solution map starting from order 0."""
RROMPyAssert(self._mode,
message = "Cannot start derivative computation.")
if self.samplingEngine.nsamples <= self.E:
if self.verbosity >= 5:
verbosityDepth("INIT", "Starting computation of derivatives.",
timestamp = self.timestamp)
self.samplingEngine.iterSample([self.mu0[0]] * (self.E + 1),
homogeneized = self.homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done computing derivatives.",
timestamp = self.timestamp)
def normApprox(self, mu:complex, 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), axis = 0)
diff --git a/rrompy/reduction_methods/centered/rational_pade.py b/rrompy/reduction_methods/centered/rational_pade.py
index 80d08dd..f3e1d4d 100644
--- a/rrompy/reduction_methods/centered/rational_pade.py
+++ b/rrompy/reduction_methods/centered/rational_pade.py
@@ -1,442 +1,442 @@
# 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, purgeDict
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;
- 'rho': weight for computation of original Pade' approximant;
defaults to np.inf, i.e. fast approximant;
- 'M': degree of Pade' approximant numerator; defaults to 0;
- 'N': degree of Pade' approximant denominator; defaults to 0;
- 'E': total number of derivatives current approximant relies upon;
defaults to 1;
- '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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'rho': weight for computation of original Pade' approximant;
- 'M': degree of Pade' approximant numerator;
- 'N': degree of Pade' approximant denominator;
- 'E': total number of derivatives current approximant relies upon;
- 'robustTol': tolerance for robust Pade' denominator management.
POD: Whether to compute QR factorization of derivatives.
rho: Weight of approximant.
M: Numerator degree of approximant.
N: Denominator degree of approximant.
E: Number of solution derivatives over which current approximant is
based upon.
robustTol: Tolerance for robust Pade' denominator management.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: 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 = 0,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["M", "N", "robustTol", "rho"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def approxParameters(self):
"""Value of approximant parameters."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters,
["M", "N", "robustTol", "rho"],
True, True, baselevel = 1)
keyList = list(approxParameters.keys())
if "rho" in keyList:
self._rho = approxParameters["rho"]
elif not hasattr(self, "_rho") or self.rho is None:
self._rho = np.inf
GenericCenteredApproximant.approxParameters.fset(self,
approxParametersCopy)
self.rho = self._rho
if "robustTol" in keyList:
self.robustTol = approxParameters["robustTol"]
elif not hasattr(self, "_robustTol") or self._robustTol is None:
self.robustTol = 0
self._ignoreParWarnings = True
if "M" in keyList:
self.M = approxParameters["M"]
elif hasattr(self, "_M") and self._M is not None:
self.M = self.M
else:
self.M = 0
del self._ignoreParWarnings
if "N" in keyList:
self.N = approxParameters["N"]
elif hasattr(self, "_N") and self._N is not None:
self.N = self.N
else:
self.N = 0
@property
def rho(self):
"""Value of rho."""
return self._rho
@rho.setter
def rho(self, rho):
self._rho = np.abs(rho)
self._approxParameters["rho"] = self.rho
@property
def M(self):
"""Value of M. Its assignment may change E."""
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 not hasattr(self, "_ignoreParWarnings"):
self.checkMNE()
@property
def N(self):
"""Value of N. Its assignment may change E."""
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 not hasattr(self, "_ignoreParWarnings"):
self.checkMNE()
def checkMNE(self):
"""Check consistency of M, N, and E."""
if not hasattr(self, "_E") or self.E is None: return
M = self.M if (hasattr(self, "_M") and self.M is not None) else 0
N = self.N if (hasattr(self, "_N") and self.N is not None) else 0
msg = "max(M, N)" if self.rho == np.inf else "M + N"
bound = eval(msg)
if self.E < bound:
RROMPyWarning(("Prescribed E is too small. Updating E to "
"{}.").format(msg))
self.E = bound
del M, 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 E(self):
"""Value of E."""
return self._E
@E.setter
def E(self, E):
GenericCenteredApproximant.E.fset(self, E)
self.checkMNE()
def _setupDenominator(self):
"""Compute Pade' denominator."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of denominator.",
timestamp = self.timestamp)
while self.N > 0:
if self.POD:
ev, eV = self.findeveVGQR()
else:
ev, eV = self.findeveVGExplicit()
newParameters = checkRobustTolerance(ev, self.E, self.robustTol)
if not newParameters:
break
self.approxParameters = newParameters
if self.N <= 0:
eV = np.ones((1, 1))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing denominator.",
timestamp = self.timestamp)
return eV[::-1, 0]
def _setupNumerator(self):
"""Compute Pade' numerator."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of numerator.",
timestamp = self.timestamp)
P = np.zeros((self.E + 1, self.M + 1), dtype = np.complex)
for i in range(self.E + 1):
l = min(self.M + 1, i + self.N + 1)
if i < l:
P[i, i : l] = self.trainedModel.data.Q[: l - i]
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing numerator.",
timestamp = self.timestamp)
return self.rescaleParameter(P.T).T
def setupApprox(self):
"""
Compute Pade' approximant. SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
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"
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
if self.N > 0:
Q = self._setupDenominator()
else:
Q = np.ones(1, 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(self.E + 1))))
P = self._setupNumerator()
if self.POD:
P = self.samplingEngine.RPOD.dot(P)
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def rescaleParameter(self, R:Np2D, A : Np2D = None,
exponent : float = 1.) -> Np2D:
"""
Prepare parameter rescaling.
Args:
R: Matrix whose columns need rescaling.
A(optional): Matrix whose diagonal defines scaling factor. If None,
previous value of scaleFactor is used. Defaults to None.
exponent(optional): Exponent of scaling factor in matrix diagonal.
Defaults to 1.
Returns:
Rescaled matrix.
"""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
if A is not None:
aDiag = np.diag(A)
scaleCoeffs = np.polyfit(np.arange(A.shape[1]),
np.log(aDiag), 1)
self.scaleFactor = np.exp(- scaleCoeffs[0] / exponent)
return R * np.power(self.scaleFactor, np.arange(R.shape[1]))
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)
if self.rho == np.inf:
Nmin = self.E - self.N
else:
Nmin = self.M - self.N + 1
if self.POD:
RPODE = self.samplingEngine.RPOD[: self.E + 1, Nmin : self.E + 1]
RPODE = self.rescaleParameter(RPODE, RPODE[Nmin :, :])
G = RPODE.T.conj().dot(RPODE)
else:
DerE = self.samplingEngine.samples(list(range(Nmin, self.E + 1)))
G = self.HFEngine.innerProduct(DerE, DerE)
DerE = self.rescaleParameter(DerE, G, 2.)
G = self.HFEngine.innerProduct(DerE, DerE)
if self.rho == np.inf:
self.G = G
else:
Gbig = G
self.G = np.zeros((self.N + 1, self.N + 1), dtype = np.complex)
for k in range(self.E - self.M):
self.G += self.rho ** (2 * k) * Gbig[k : k + self.N + 1,
k : k + self.N + 1]
if self.verbosity >= 10:
verbosityDepth("DEL", "Done building gramian.",
timestamp = self.timestamp)
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)
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.N + 1,
condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return ev, eV
def _buildRStack(self, R:Np2D) -> Np2D:
if self.verbosity >= 10:
verbosityDepth("INIT", ("Building matrix stack for square "
"root of gramian."),
timestamp = self.timestamp)
REff = np.zeros((R.shape[0] * (self.E - self.M), self.N + 1),
dtype = np.complex)
for k in range(self.E - self.M):
RTleft = max(0, self.N - self.M - k)
Rleft = max(0, self.M - self.N + k)
REff[k * R.shape[0] : (k + 1) * R.shape[0], RTleft :] = (
self.rho ** k * R[:, Rleft : self.M + 1 + k])
if self.verbosity >= 10:
verbosityDepth("DEL", "Done building matrix stack.",
timestamp = self.timestamp)
return REff
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()
if self.rho == np.inf:
Nmin = self.E - self.N
else:
Nmin = self.M - self.N + 1
R = self.samplingEngine.RPOD[: self.E + 1, Nmin : self.E + 1]
R = self.rescaleParameter(R, R[R.shape[0] - R.shape[1] :, :])
REff = R if self.rho == np.inf else self._buildRStack(R)
if self.verbosity >= 7:
verbosityDepth("INIT", ("Solving svd for square root of "
"gramian matrix."),
timestamp = self.timestamp)
sizeI = REff.shape[0]
_, s, V = np.linalg.svd(REff, 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,
self.N + 1,
condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return s[::-1], eV
- def centerNormalize(self, mu:paramList,
+ 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 0b72361..ba82013 100644
--- a/rrompy/reduction_methods/centered/rb_centered.py
+++ b/rrompy/reduction_methods/centered/rb_centered.py
@@ -1,204 +1,204 @@
# 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 purgeDict, verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException, RROMPyWarning
__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;
- 'R': rank for Galerkin projection; defaults to E + 1;
- 'E': total number of derivatives current approximant relies upon;
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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'R': rank for Galerkin projection;
- 'E': total number of derivatives current approximant relies upon.
POD: Whether to compute QR factorization of derivatives.
R: Rank for Galerkin projection.
E: Number of solution derivatives 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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
ARBs: List of sparse matrices (in CSC format) representing RB
coefficients of linear system matrix wrt mu.
bRBs: List of numpy vectors representing RB coefficients of linear
system RHS wrt mu.
"""
- def __init__(self, HFEngine:HFEng, mu0 : paramVal = 0,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["R"])
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)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done computing affine blocks.",
timestamp = self.timestamp)
self._postInit()
@property
def approxParameters(self):
"""
Value of approximant parameters. Its assignment may change M, N and S.
"""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["R"],
True, True, baselevel = 1)
GenericCenteredApproximant.approxParameters.fset(self,
approxParametersCopy)
keyList = list(approxParameters.keys())
if "R" in keyList:
self.R = approxParameters["R"]
else:
self.R = self.E + 1
@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, "_E") and self.E + 1 < self.R:
RROMPyWarning("Prescribed E is too small. Updating E to R - 1.")
self.E = self.R - 1
def setupApprox(self):
"""Setup RB system."""
if self.checkComputedApprox():
return
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeDerivatives()
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
if self.POD:
U, _, _ = np.linalg.svd(self.samplingEngine.RPOD[: self.E + 1,
: self.E + 1])
pMat = self.samplingEngine.samples(list(range(self.E + 1))).dot(
U[:, : self.R])
else:
pMat = self.samplingEngine.samples(list(range(self.R)))
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.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
pMatOld = self.trainedModel.data.projMat
Sold = pMatOld.shape[1]
ARBs, bRBs = self.assembleReducedSystem(
pMat(list(range(Sold, pMat.shape[1]))), pMatOld)
self.trainedModel.data.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
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)
As = self.HFEngine.affineLinearSystemA(self.mu0)
bs = self.HFEngine.affineLinearSystemb(self.mu0, self.homogeneized)
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(As, bs, pMat, ARBsOld,
bRBsOld, pMatOld)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done projecting affine terms.",
timestamp = self.timestamp)
return ARBs, bRBs
diff --git a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
index a1d5edd..47a58b2 100644
--- a/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
+++ b/rrompy/reduction_methods/distributed/generic_distributed_approximant.py
@@ -1,216 +1,215 @@
# 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
+from rrompy.utilities.base.types import DictAny, HFEng, paramVal
from rrompy.utilities.base import purgeDict, verbosityDepth
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;
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': total number of samples current approximant relies upon;
defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
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.
ws: Array of snapshot weigths.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: Whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
- def __init__(self, HFEngine:HFEng, mu0 : complex = 0.,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["S", "muBounds", "sampler"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
- RROMPyAssert(self.HFEngine.npar, 1, "Number of parameters")
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.HFEngine.npar)
+ 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 approxParameters(self):
"""Value of approximant parameters. Its assignment may change S."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters,
["S", "muBounds", "sampler"],
True, True, baselevel = 1)
GenericApproximant.approxParameters.fset(self, approxParametersCopy)
keyList = list(approxParameters.keys())
if "S" in keyList:
self.S = approxParameters["S"]
elif not hasattr(self, "_S") or self._S is None:
self.S = 2
if "muBounds" in keyList:
self.muBounds = approxParameters["muBounds"]
elif not hasattr(self, "_muBounds") or self.muBounds is None:
self.muBounds = [0., 1.]
if "sampler" in keyList:
self.sampler = approxParameters["sampler"]
elif (not hasattr(self, "_sampler") or self.sampler is None):
from rrompy.parameter.parameter_sampling import QuadratureSampler
self.sampler = QuadratureSampler(self.muBounds, "UNIFORM")
del QuadratureSampler
@property
def S(self):
"""Value of S."""
return self._S
@S.setter
def S(self, S):
if S <= 0: raise RROMPyException("S must be positive.")
if hasattr(self, "_S") and self._S is not None: Sold = self.S
else: Sold = -1
self._S = S
self._approxParameters["S"] = self.S
if Sold != self.S:
self.resetSamples()
@property
def muBounds(self):
"""Value of muBounds."""
return self._muBounds
@muBounds.setter
def muBounds(self, muBounds):
- muBounds, _ = checkParameterList(muBounds)
+ muBounds, _ = checkParameterList(muBounds, self.npar)
if len(muBounds) != 2:
raise RROMPyException("2 limits must be specified.")
self._muBounds = muBounds
@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 computeSnapshots(self):
"""Compute snapshots of solution map."""
RROMPyAssert(self._mode,
message = "Cannot start snapshot computation.")
if self.samplingEngine.nsamples == 0:
if self.verbosity >= 5:
verbosityDepth("INIT", "Starting computation of snapshots.",
timestamp = self.timestamp)
self.mus, self.ws = 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)
def normApprox(self, mu:complex, 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), axis = 0)
def computeScaleFactor(self):
"""Compute parameter rescaling factor."""
RROMPyAssert(self._mode, message = "Cannot compute rescaling factor.")
self.scaleFactor = .5 * np.abs(
- np.power(self.muBounds(0, 0), self.HFEngine.rescalingExp)
- - np.power(self.muBounds(1, 0), self.HFEngine.rescalingExp))
+ 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 6117509..055ae06 100644
--- a/rrompy/reduction_methods/distributed/rational_interpolant.py
+++ b/rrompy/reduction_methods/distributed/rational_interpolant.py
@@ -1,535 +1,563 @@
# 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 scipy.special import factorial as fact
from rrompy.reduction_methods.base import checkRobustTolerance
from .generic_distributed_approximant import GenericDistributedApproximant
from rrompy.utilities.poly_fitting import customFit
from rrompy.utilities.poly_fitting.polynomial import (polybases, polyfitname,
- polyvander)
+ polyvander,
+ nextDerivativeIndices)
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
+from rrompy.utilities.base.types import (Np1D, Np2D, HFEng, DictAny, Tuple,
+ paramVal, paramList)
from rrompy.utilities.base import verbosityDepth, purgeDict
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;
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': total number of samples current approximant relies upon;
defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
muBounds;
- 'polybasis': type of polynomial basis for interpolation; allowed
values include 'MONOMIAL', 'CHEBYSHEV' and 'LEGENDRE'; defaults
to 'MONOMIAL';
- 'E': coefficient of interpolant to be minimized; defaults to
min(S, M + 1);
- 'M': degree of Pade' interpolant numerator; defaults to 0;
- 'N': degree of Pade' interpolant denominator; defaults to 0;
- '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.
ws: Array of snapshot weigths.
homogeneized: Whether to homogeneize Dirichlet BCs.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'polybasis': type of polynomial basis for interpolation;
- 'E': coefficient of interpolant to be minimized;
- 'M': degree of Pade' interpolant numerator;
- 'N': degree of Pade' interpolant denominator;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
- 'robustTol': tolerance for robust Pade' denominator management.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: Whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
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.
interpRcond: Tolerance for interpolation via numpy.polyfit.
robustTol: Tolerance for robust Pade' denominator management.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: 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 : complex = 0.,
+ 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",
"interpRcond", "robustTol"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized,
verbosity = verbosity, timestamp = timestamp)
self._postInit()
@property
def approxParameters(self):
"""
Value of approximant parameters.
"""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["polybasis",
"E", "M", "N",
"interpRcond",
"robustTol"],
True, True, baselevel = 1)
if hasattr(self, "_M") and self.M is not None:
Mold = self.M
self._M = 0
if hasattr(self, "_N") and self.N is not None:
Nold = self.N
self._N = 0
if hasattr(self, "_E") and self.E is not None:
self._E = 0
GenericDistributedApproximant.approxParameters.fset(self,
approxParametersCopy)
keyList = list(approxParameters.keys())
if "polybasis" in keyList:
self.polybasis = approxParameters["polybasis"]
elif not hasattr(self, "_polybasis") or self._polybasis is None:
self.polybasis = "MONOMIAL"
if "interpRcond" in keyList:
self.interpRcond = approxParameters["interpRcond"]
elif not hasattr(self, "interpRcond") or self.interpRcond is None:
self.interpRcond = None
if "robustTol" in keyList:
self.robustTol = approxParameters["robustTol"]
elif not hasattr(self, "_robustTol") or self._robustTol is None:
self.robustTol = 0
if "M" in keyList:
self.M = approxParameters["M"]
elif hasattr(self, "_M") and self.M is not None:
self.M = Mold
else:
self.M = 0
if "N" in keyList:
self.N = approxParameters["N"]
elif hasattr(self, "_N") and self.N is not None:
self.N = Nold
else:
self.N = 0
if "E" in keyList:
self.E = approxParameters["E"]
else:
self.E = min(self.S - 1, self.M + 1)
@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 interpRcond(self):
"""Value of interpRcond."""
return self._interpRcond
@interpRcond.setter
def interpRcond(self, interpRcond):
self._interpRcond = interpRcond
self._approxParameters["interpRcond"] = self.interpRcond
@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, "_S") and self.S < self.M + 1:
RROMPyWarning("Prescribed S is too small. Updating S to M + 1.")
self.S = self.M + 1
@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, "_S") and self.S < self.N + 1:
RROMPyWarning("Prescribed S is too small. Updating S to N + 1.")
self.S = self.N + 1
@property
def E(self):
"""Value of E. Its assignment may change S."""
return self._E
@E.setter
def E(self, E):
if E < 0: raise RROMPyException("E must be non-negative.")
self._E = E
self._approxParameters["E"] = self.E
if hasattr(self, "_S") and self.S < self.E + 1:
RROMPyWarning("Prescribed S is too small. Updating S to E + 1.")
self.S = self.E + 1
@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):
if S <= 0: raise RROMPyException("S must be positive.")
if hasattr(self, "_S"): Sold = self.S
else: Sold = -1
vals, label = [0] * 3, {0:"M", 1:"N", 2:"E"}
if hasattr(self, "_M") and self._M is not None: vals[0] = self.M
if hasattr(self, "_N") and self._N is not None: vals[1] = self.N
if hasattr(self, "_E") and self._E is not None: vals[2] = self.E
idxmax = np.argmax(vals)
if vals[idxmax] + 1 > S:
RROMPyWarning(("Prescribed S is too small. Updating S to {} + "
"1.").format(label[idxmax]))
self.S = vals[idxmax] + 1
else:
self._S = S
self._approxParameters["S"] = self.S
if Sold != self.S:
self.resetSamples()
+ def resetSamples(self):
+ """Reset samples."""
+ super().resetSamples()
+ self._musUnique = None
+ self._derIdxs = None
+ self._reorder = None
+
+ def _setupInterpolationIndices(self):
+ """Setup parameters for polyvander."""
+ if self._musUnique is None or len(self._reorder) != len(self.mus):
+ self._musUnique, musIdxs, musCount = (
+ self.centerNormalize(self.mus).unique(return_inverse = True,
+ return_counts = True))
+ self._derIdxs = [None] * len(self._musUnique)
+ 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."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of denominator.",
timestamp = self.timestamp)
while self.N > 0:
- TE = polyvander(self.centerNormalize(self.mus), self.E,
- self.polybasis,
+ self._setupInterpolationIndices()
+ TE = polyvander(self._musUnique, self.E, self.polybasis,
+ self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TE = (TE.T * self.ws).T
RHS = np.zeros(self.E + 1)
RHS[-1] = 1.
fitOut = customFit(TE.T, RHS, 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(
self.S, self.E,
polyfitname(self.polybasis),
condfit),
timestamp = self.timestamp)
if fitOut[1][1] < self.E + 1:
Enew = fitOut[1][1] - 1
Nnew = min(self.N, Enew)
Mnew = min(self.M, Enew)
if Nnew == self.N:
strN = ""
else:
strN = "N from {} to {} and ".format(self.N, Nnew)
if Mnew == self.M:
strM = ""
else:
strM = "M from {} to {} and ".format(self.M, Mnew)
RROMPyWarning(("Polyfit is poorly conditioned.\nReducing {}{}"
"E from {} to {}.").format(strN, strM,
self.E, Enew))
newParams = {"N" : Nnew, "M" : Mnew, "E" : Enew}
self.approxParameters = newParams
continue
mus_un, idx_un, cnt_un = self.mus.unique(return_inverse = True,
return_counts = True)
- TE = polyvander(self.centerNormalize(self.mus), self.N,
- self.polybasis,
+ TE = polyvander(self._musUnique, self.N, self.polybasis,
+ self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
TE = (TE.T * self.ws).T
if len(mus_un) == len(self.mus):
Ghalf = (TE.T * fitOut[0]).T
else:
pseudoInv = np.zeros((len(self.mus), len(self.mus)),
dtype = np.complex)
for j in range(len(mus_un)):
pseudoInv_loc = np.zeros((cnt_un[j], cnt_un[j]),
dtype = np.complex)
mask = np.arange(len(self.mus))[idx_un == j]
for der in range(cnt_un[j]):
fitderj = fitOut[0][mask[der]]
pseudoInv_loc = (pseudoInv_loc + fitderj
* np.diag(np.ones(1 + der),
k = der - cnt_un[j] + 1))
I = np.ix_(mask, mask)
pseudoInv[I] = np.flipud(pseudoInv_loc)
Ghalf = pseudoInv.dot(TE)
if self.POD:
self.Ghalf = self.samplingEngine.RPOD.dot(Ghalf)
ev, eV = self.findeveVGQR()
else:
self.Ghalf = self.samplingEngine.samples.dot(Ghalf)
ev, eV = self.findeveVGExplicit()
newParams = checkRobustTolerance(ev, self.E, self.robustTol)
if not newParams:
break
self.approxParameters = newParams
if self.N <= 0:
self._N = 0
eV = np.ones((1, 1))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing denominator.",
timestamp = self.timestamp)
return eV[:, 0]
def _setupNumerator(self):
"""Compute Pade' numerator."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of numerator.",
timestamp = self.timestamp)
Qevaldiag = np.diag(self.trainedModel.getQVal(self.mus))
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
mus_un, idx_un, cnt_un = self.mus.unique(return_inverse = True,
return_counts = True)
for j in range(len(mus_un)):
if cnt_un[j] > 1:
Q_loc = np.zeros((cnt_un[j], cnt_un[j]), dtype = np.complex)
for der in range(1, cnt_un[j]):
Qderj = (self.trainedModel.getQVal(mus_un[j], der,
scl = np.power(self.scaleFactor, -1.))
/ fact(der))
Q_loc = Q_loc + Qderj * np.diag(np.ones(cnt_un[j] - der),
k = - der)
I = np.ix_(idx_un == j, idx_un == j)
Qevaldiag[I] = Qevaldiag[I] + Q_loc
self.trainedModel.verbosity = verb
while self.M >= 0:
- fitVander = polyvander(self.centerNormalize(self.mus), self.M,
- self.polybasis,
+ self._setupInterpolationIndices()
+ fitVander = polyvander(self._musUnique, self.M, self.polybasis,
+ self._derIdxs, self._reorder,
scl = np.power(self.scaleFactor, -1.))
fitOut = customFit(fitVander, Qevaldiag, w = self.ws, 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(
self.S, self.M,
polyfitname(self.polybasis),
condfit),
timestamp = self.timestamp)
if fitOut[1][1] == self.M + 1:
P = fitOut[0].T
break
RROMPyWarning(("Polyfit is poorly conditioned. Reducing M from {} "
"to {}. Exact snapshot interpolation not "
"guaranteed.").format(self.M, fitOut[1][1] - 1))
self.M = fitOut[1][1] - 1
if self.M <= 0:
raise RROMPyException(("Instability in computation of numerator. "
"Aborting."))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing numerator.",
timestamp = self.timestamp)
return np.atleast_2d(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)
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.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(1, dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
P = self._setupNumerator()
if self.POD:
P = self.samplingEngine.RPOD.dot(P)
self.trainedModel.data.P = copy(P)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def findeveVGExplicit(self, verbOutput : int = 5) -> Tuple[Np1D, Np2D]:
"""
Compute explicitly eigenvalues and eigenvectors of Pade' denominator
matrix.
"""
RROMPyAssert(self._mode, message = "Cannot solve eigenvalue problem.")
if self.verbosity >= 10:
verbosityDepth("INIT", "Building gramian matrix.",
timestamp = self.timestamp)
self.G = self.HFEngine.innerProduct(self.Ghalf, self.Ghalf)
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)
ev, eV = np.linalg.eigh(self.G)
if self.verbosity >= verbOutput:
try: condev = ev[-1] / ev[0]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved eigenvalue problem of size {} "
"with condition number {:.4e}.").format(
self.N + 1, condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return ev, eV
def findeveVGQR(self, verbOutput : int = 5) -> Tuple[Np1D, Np2D]:
"""
Compute eigenvalues and eigenvectors of Pade' denominator matrix
through SVD of R factor.
"""
if self.verbosity >= 7:
verbosityDepth("INIT", ("Solving svd for square root of gramian "
"matrix."), timestamp = self.timestamp)
_, s, eV = np.linalg.svd(self.Ghalf, full_matrices = False)
ev = s[::-1]
eV = eV[::-1, :].T.conj()
if self.verbosity >= verbOutput:
try: condev = s[0] / s[-1]
except: condev = np.inf
verbosityDepth("MAIN", ("Solved svd problem of size {} x {} with "
"condition number {:.4e}.").format(
self.S, self.N + 1, condev),
timestamp = self.timestamp)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done solving eigenvalue problem.",
timestamp = self.timestamp)
return ev, eV
- def centerNormalize(self, mu:Np1D, mu0 : float = None) -> float:
+ 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 f15debf..ac27fd2 100644
--- a/rrompy/reduction_methods/distributed/rb_distributed.py
+++ b/rrompy/reduction_methods/distributed/rb_distributed.py
@@ -1,224 +1,225 @@
# 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
+from rrompy.utilities.base.types import (Np1D, Np2D, List, Tuple, DictAny,
+ HFEng, paramVal)
from rrompy.utilities.base import purgeDict, verbosityDepth
from rrompy.utilities.exception_manager import RROMPyWarning, RROMPyException
__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:
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': total number of samples current approximant relies upon;
defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
muBounds;
- 'R': rank for Galerkin projection; defaults to S.
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.
ws: Array of snapshot weigths (unused).
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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': total number of samples current approximant relies upon;
- 'sampler': sample point generator;
- 'R': rank for Galerkin projection.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: Whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
S: Number of solution snapshots over which current approximant is
based upon.
sampler: Sample point generator.
R: Rank for Galerkin projection.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: 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 : complex = 0.,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["R"])
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)
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)
self._postInit()
@property
def approxParameters(self):
"""
Value of approximant parameters. Its assignment may change M, N and S.
"""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["R"], True, True,
baselevel = 1)
GenericDistributedApproximant.approxParameters.fset(self,
approxParametersCopy)
keyList = list(approxParameters.keys())
if "R" in keyList:
self.R = approxParameters["R"]
elif hasattr(self, "_R") and self._R is not None:
self.R = self.R
else:
self.R = 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 self.S < self.R:
RROMPyWarning("Prescribed S is too small. Updating S to R.")
self.S = self.R
def setupApprox(self):
"""Compute RB projection matrix."""
if self.checkComputedApprox():
return
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeSnapshots()
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
if self.POD:
U, _, _ = np.linalg.svd(self.samplingEngine.RPOD,
full_matrices = False)
pMat = self.samplingEngine.samples.dot(U[:, : self.R])
else:
pMat = self.samplingEngine.samples[: self.R]
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.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
data.mus = copy(self.mus)
self.trainedModel.data = data
else:
self.trainedModel = self.trainedModel
pMatOld = self.trainedModel.data.projMat
Sold = pMatOld.shape[1]
ARBs, bRBs = self.assembleReducedSystem(pMat[:, Sold :], pMatOld)
self.trainedModel.data.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def assembleReducedSystem(self, pMat : Np2D = None, pMatOld : Np2D = 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)
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)
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 8c2e47e..3d4ea98 100644
--- a/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
+++ b/rrompy/reduction_methods/distributed_greedy/generic_distributed_greedy_approximant.py
@@ -1,652 +1,653 @@
# 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, paramList, sampList)
+ List, normEng, paramVal, paramList,
+ sampList)
from rrompy.utilities.base import purgeDict, verbosityDepth
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;
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': number of starting training points; defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
muBounds;
- '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 maxIter /
refinementRatio;
- '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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': number of starting training 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 test points to be exhausted before
test set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for 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.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
TOL_INSTABILITY = 1e-6
- def __init__(self, HFEngine:HFEng, mu0 : complex = 0.,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["greedyTol", "interactive", "maxIter",
"refinementRatio", "nTestPoints",
"trainSetGenerator"])
super().__init__(HFEngine = HFEngine, mu0 = mu0,
approxParameters = approxParameters,
homogeneized = homogeneized, verbosity = verbosity,
timestamp = timestamp)
self._postInit()
@property
def approxParameters(self):
"""Value of approximant parameters. Its assignment may change S."""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters,
["greedyTol", "interactive",
"maxIter", "refinementRatio",
"nTestPoints", "trainSetGenerator"],
True, True, baselevel = 1)
GenericDistributedApproximant.approxParameters.fset(self,
approxParametersCopy)
keyList = list(approxParameters.keys())
if "greedyTol" in keyList:
self.greedyTol = approxParameters["greedyTol"]
elif not hasattr(self, "_greedyTol") or self.greedyTol is None:
self.greedyTol = 1e-2
if "interactive" in keyList:
self.interactive = approxParameters["interactive"]
elif not hasattr(self, "interactive") or self.interactive is None:
self.interactive = False
if "maxIter" in keyList:
self.maxIter = approxParameters["maxIter"]
elif not hasattr(self, "_maxIter") or self.maxIter is None:
self.maxIter = 1e2
if "refinementRatio" in keyList:
self.refinementRatio = approxParameters["refinementRatio"]
elif (not hasattr(self, "_refinementRatio")
or self.refinementRatio is None):
self.refinementRatio = 0.2
if "nTestPoints" in keyList:
self.nTestPoints = approxParameters["nTestPoints"]
elif (not hasattr(self, "_nTestPoints")
or self.nTestPoints is None):
self.nTestPoints = np.int(np.ceil(self.maxIter
/ self.refinementRatio))
if "trainSetGenerator" in keyList:
self.trainSetGenerator = approxParameters["trainSetGenerator"]
elif (not hasattr(self, "_trainSetGenerator")
or self.trainSetGenerator is None):
from rrompy.parameter.parameter_sampling import QuadratureSampler
self.trainSetGenerator = QuadratureSampler(self.muBounds,
"CHEBYSHEV")
del QuadratureSampler
@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 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, "energyNormMatrix"):
self.HFEngine.buildEnergyNormForm()
estimatorEnergyMatrix = self.HFEngine.energyNormMatrix
else:
if hasattr(normEngn, "buildEnergyNormForm"):
if not hasattr(normEngn, "energyNormMatrix"):
normEngn.buildEnergyNormForm()
estimatorEnergyMatrix = normEngn.energyNormMatrix
else:
estimatorEnergyMatrix = normEngn
self.estimatorNormEngine = normEngine(estimatorEnergyMatrix)
def errorEstimator(self, mus:List[np.complex]) -> List[np.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)
RHSNorm = self.estimatorNormEngine.norm(RHS)
res = self.getRes(mus, homogeneized = self.homogeneized)
err = self.estimatorNormEngine.norm(res) / RHSNorm
else:
res = self.getRes(mus, homogeneized = self.homogeneized)
RHS = self.getRHS(mus, homogeneized = self.homogeneized)
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(0))
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(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, complex]:
"""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)
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)
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) > 1:
if self.verbosity >= 2:
verbosityDepth("MAIN",
("Adding first {} samples point at {} to "
"training set.").format(self.S - 1, self.mus),
timestamp = self.timestamp)
self.samplingEngine.iterSample(self.mus,
homogeneized = self.homogeneized)
muTestBase = pruneSamples(muTestBase, self.mus,
1e-10 * self.scaleFactor).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."""
muTestExtra, _ = self.sampler.generatePoints(2 * nTest)
muTotal = copy(self.mus)
muTotal.append(self.muTest)
muTestExtra = pruneSamples(muTestExtra, muTotal,
1e-10 * self.scaleFactor)
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.muTest = checkParameterList(muTestNew.sort(), self.npar)
if self.verbosity >= 5:
verbosityDepth("MAIN", "Enriching test set by {} elements.".format(
len(muTestExtra)),
timestamp = self.timestamp)
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)
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)
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 = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
verbosityDepth("MAIN", "Reducing value of greedyTol...",
timestamp = self.timestamp)
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 = "")
increasemaxIter = input()
if increasemaxIter.upper() == "Y":
verbosityDepth("MAIN", "Doubling value of maxIter...",
timestamp = self.timestamp)
self._maxIter *= 2
if self.verbosity >= 2:
verbosityDepth("DEL", ("Done computing snapshots (final snapshot "
"count: {}).").format(
self.samplingEngine.nsamples),
timestamp = self.timestamp)
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.,
basic : bool = False):
"""
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
if basic:
MAEnd = scaling ** nAs * As[-1].dot(pMat)
resAA = self.estimatorNormEngine.innerProduct(MAEnd, MAEnd)
else:
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:
if basic:
resAA = self.trainedModel.data.resAA[: S, : S]
else:
resAA = self.trainedModel.data.resAA[: S, :, : S, :]
else:
if not isinstance(pMat, (np.ndarray,)): pMat = pMat.data
if basic:
resAA = np.empty((S, S), dtype = np.complex)
resAA[: Sold, : Sold] = self.trainedModel.data.resAA
MAi = scaling ** nAs * As[-1].dot(pMat)
resAA[: Sold, Sold :] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, : Sold]))
resAA[Sold :, : Sold] = resAA[: Sold, Sold :].T.conj()
resAA[Sold :, Sold :] = (
self.estimatorNormEngine.innerProduct(MAi[:, Sold :],
MAi[:, Sold :]))
else:
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 f3d707e..ee67fa5 100644
--- a/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rational_interpolant_greedy.py
@@ -1,580 +1,584 @@
# 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 scipy.special import factorial as fact
from .generic_distributed_greedy_approximant import \
GenericDistributedGreedyApproximant
from rrompy.utilities.poly_fitting import customFit
from rrompy.utilities.poly_fitting.polynomial import (polybases, polyfitname,
polydomcoeff, polyvander)
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
+from rrompy.utilities.base.types import Np1D, Np2D, DictAny, HFEng, paramVal
from rrompy.utilities.base import purgeDict, verbosityDepth
from rrompy.utilities.exception_manager import RROMPyWarning
from rrompy.utilities.exception_manager import RROMPyException
__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;
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': number of starting training points; defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
muBounds;
- 'basis': 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;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'errorEstimatorKind': kind of error estimator; available values
include 'EXACT', 'BASIC', and 'BARE'; defaults to 'EXACT';
- '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 maxIter /
refinementRatio;
- 'trainSetGenerator': training sample points generator; defaults
to Chebyshev sampler within muBounds;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': number of starting training points;
- 'sampler': sample point generator;
- 'basis': type of basis for interpolation;
- 'Delta': difference between M and N in rational approximant;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'errorEstimatorKind': kind of error estimator;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of training points to be exhausted
before training set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- 'interpRcond': tolerance for interpolation via numpy.polyfit;
- 'robustTol': tolerance for robust Pade' denominator management.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
S: number of starting training points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for greedy algorithm.
errorEstimatorKind: kind of error estimator.
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.
interpRcond: Tolerance for interpolation via numpy.polyfit.
robustTol: Tolerance for robust Pade' denominator management.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: Parameter(s) corresponding to last computed approximate
solution(s) as parameterList.
"""
_allowedEstimatorKinds = ["EXACT", "BASIC", "BARE"]
- def __init__(self, HFEngine:HFEng, mu0 : complex = 0.,
+ def __init__(self, HFEngine:HFEng, mu0 : paramVal = None,
approxParameters : DictAny = {}, homogeneized : bool = False,
verbosity : int = 10, timestamp : bool = True):
self._preInit()
self._addParametersToList(["polybasis", "Delta", "errorEstimatorKind",
"interpRcond", "robustTol"])
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)
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)
self._postInit()
@property
def approxParameters(self):
"""
Value of approximant parameters. Its assignment may change robustTol.
"""
return self._approxParameters
@approxParameters.setter
def approxParameters(self, approxParams):
approxParameters = purgeDict(approxParams, self.parameterList,
dictname = self.name() + ".approxParameters",
baselevel = 1)
approxParametersCopy = purgeDict(approxParameters, ["polybasis",
"Delta",
"errorEstimatorKind",
"interpRcond",
"robustTol"],
True, True, baselevel = 1)
if "Delta" in list(approxParameters.keys()):
self._Delta = approxParameters["Delta"]
elif not hasattr(self, "_Delta") or self._Delta is None:
self._Delta = 0
GenericDistributedGreedyApproximant.approxParameters.fset(self,
approxParametersCopy)
keyList = list(approxParameters.keys())
self.Delta = self.Delta
if "polybasis" in keyList:
self.polybasis = approxParameters["polybasis"]
elif not hasattr(self, "_polybasis") or self._polybasis is None:
self.polybasis = "MONOMIAL"
if "errorEstimatorKind" in keyList:
self.errorEstimatorKind = approxParameters["errorEstimatorKind"]
elif (not hasattr(self, "_errorEstimatorKind")
or self.errorEstimatorKind is None):
self.errorEstimatorKind = "EXACT"
if "interpRcond" in keyList:
self.interpRcond = approxParameters["interpRcond"]
elif not hasattr(self, "interpRcond") or self.interpRcond is None:
self.interpRcond = None
if "robustTol" in keyList:
self.robustTol = approxParameters["robustTol"]
elif not hasattr(self, "_robustTol") or self._robustTol is None:
self.robustTol = 0
@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."""
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."""
# '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.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 * 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:complex, ratioTest:complex) -> Np1D:
"""Basic residual-based error estimator."""
resmu = self.HFEngine.residual(self.trainedModel.getApprox(muTest),
muTest, self.homogeneized)[0]
return np.abs(self.estimatorNormEngine.norm(resmu) / ratioTest)
def _errorEstimatorExact(self, muRTrain:Np1D, vanderBase:Np2D) -> Np1D:
"""Exact residual-based error estimator."""
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)
self.assembleReducedResidualBlocks(kind = self.errorEstimatorKind)
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)
muTestSample = mus[idx_muTestSample]
samplingRatioTestSample = samplingRatio[idx_muTestSample]
jOpt = self._errorEstimatorBasic(muTestSample,
samplingRatioTestSample)
else: #if self.errorEstimatorKind == "EXACT":
jOpt = self._errorEstimatorExact(muRTrain, vanderBase[: -1, :])
return jOpt * samplingRatio / RHSnorms
def _setupDenominator(self):
"""Compute Pade' denominator."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of denominator.",
timestamp = self.timestamp)
S = len(self.mus)
- TS = polyvander(self.centerNormalize(self.mus), S - 1,
- self.polybasis).T
+ self._setupInterpolationIndices()
+ TS = polyvander(self._musUnique, S - 1, self.polybasis,
+ self._derIdxs, self._reorder).T
+ #scl = np.power(self.scaleFactor, -1.))
RHS = np.zeros(S)
RHS[-1] = 1.
fitOut = customFit(TS, RHS, full = True, rcond = self.interpRcond)
if self.verbosity >= 2:
condfit = fitOut[1][2][0] / fitOut[1][2][-1]
verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
"through {}... Conditioning of system: "
"{:.4e}.").format(S, S - 1,
polyfitname(self.polybasis),
condfit),
timestamp = self.timestamp)
if fitOut[1][1] < S:
RROMPyWarning(("Polyfit is poorly conditioned. Starting "
"preemptive termination of computation of "
"approximant."))
Q = np.empty(max(self.N, 0) + 1, dtype = np.complex)
P = np.empty((len(self.mus), max(self.M, 0) + 1),
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 >= 7:
verbosityDepth("DEL", "Aborting computation of denominator.",
timestamp = self.timestamp)
return
self._fitinv = fitOut[0]
while self.N > 0:
Ghalf = (TS[: self.N + 1, :] * self._fitinv).T
if self.POD:
self.Ghalf = self.samplingEngine.RPOD.dot(Ghalf)
else:
self.Ghalf = self.samplingEngine.samples.dot(Ghalf)
ev, eV = self.findeveVGQR(2)
Nstable = np.sum(np.abs(ev) >= self.robustTol * np.linalg.norm(ev))
if self.N <= Nstable: break
if self.verbosity >= 2:
verbosityDepth("MAIN", ("Smallest {} eigenvalues below "
"tolerance. Reducing N to {}.")\
.format(self.N - Nstable + 1, Nstable),
timestamp = self.timestamp)
self._N = Nstable
if self.N <= 0:
self._N = 0
eV = np.ones((1, 1))
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing denominator.",
timestamp = self.timestamp)
return eV[:, 0]
def _setupNumerator(self):
"""Compute Pade' numerator."""
if self.verbosity >= 7:
verbosityDepth("INIT", "Starting computation of numerator.",
timestamp = self.timestamp)
Qevaldiag = np.diag(self.trainedModel.getQVal(self.mus))
verb = self.trainedModel.verbosity
self.trainedModel.verbosity = 0
mus_un, idx_un, cnt_un = self.mus.unique(return_inverse = True,
return_counts = True)
for j in range(len(mus_un)):
if cnt_un[j] > 1:
Q_loc = np.zeros((cnt_un[j], cnt_un[j]), dtype = np.complex)
for der in range(1, cnt_un[j]):
Qderj = (self.trainedModel.getQVal(mus_un[j], der)[0]
/ fact(der))
Q_loc = Q_loc + Qderj * np.diag(np.ones(cnt_un[j] - der),
k = - der)
I = idx_un == j
I = np.arange(len(self.mus))[I]
I = np.ix_(I, I)
Qevaldiag[I] = Qevaldiag[I] + Q_loc
self.trainedModel.verbosity = verb
while self.M >= 0:
- fitVander = polyvander(self.centerNormalize(self.mus), self.M,
- self.polybasis)
+ self._setupInterpolationIndices()
+ fitVander = polyvander(self._musUnique, self.M, self.polybasis,
+ self._derIdxs, self._reorder)
+ #scl = np.power(self.scaleFactor, -1.))
w = None
S = len(self.mus)
if self.M == S - 1: w = "AUTO"
fitOut = customFit(fitVander, Qevaldiag, full = True, w = w,
rcond = self.interpRcond)
if self.verbosity >= 2:
condfit = fitOut[1][2][0] / fitOut[1][2][-1]
verbosityDepth("MAIN", ("Fitting {} samples with degree {} "
"through {}... Conditioning of "
"system: {:.4e}.").format(
S, self.M,
polyfitname(self.polybasis),
condfit),
timestamp = self.timestamp)
if fitOut[1][1] == self.M + 1:
P = fitOut[0].T
break
RROMPyWarning(("Polyfit is poorly conditioned. Reducing M from {} "
"to {}. Exact snapshot interpolation not "
"guaranteed.").format(self.M, fitOut[1][1] - 1))
self._M = fitOut[1][1] - 1
if self.M < 0:
raise RROMPyException(("Instability in computation of numerator. "
"Aborting."))
return np.atleast_2d(P)
def setupApprox(self, plotEst : bool = False):
"""
Compute Pade' interpolant.
SVD-based robust eigenvalue management.
"""
if self.checkComputedApprox():
return
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.computeScaleFactor()
self.greedy(plotEst)
S = len(self.mus)
self._M = S - 1
self._N = S - 1
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.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)
Q = np.empty(max(self.N, 0) + 1, dtype = np.complex)
P = np.empty((len(self.mus), max(self.M, 0) + 1),
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)
return
if self.N > 0:
Q = self._setupDenominator()
if Q is None:
if self.verbosity >= 5:
verbosityDepth("DEL",
"Aborting computation of approximant.",
timestamp = self.timestamp)
return
else:
Q = np.ones((1,), dtype = np.complex)
self.trainedModel.data.Q = copy(Q)
P = self._setupNumerator()
if self.POD:
P = self.samplingEngine.RPOD.dot(P)
self.trainedModel.data.P = copy(P)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing numerator.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def assembleReducedResidualBlocks(self, kind : str = "EXACT"):
"""Build affine blocks of reduced linear system through projections."""
scaling = self.trainedModel.data.scaleFactor
self.assembleReducedResidualBlocksbb(self.bs, scaling)
if kind == "EXACT":
pMat = self.trainedModel.data.projMat
self.assembleReducedResidualBlocksAb(self.As, self.bs[1 :],
pMat, scaling)
self.assembleReducedResidualBlocksAA(self.As, pMat, scaling,
basic = (kind == "BASIC"))
diff --git a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
index 611a705..66bb0a7 100644
--- a/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
+++ b/rrompy/reduction_methods/distributed_greedy/rb_distributed_greedy.py
@@ -1,261 +1,261 @@
# 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
+from rrompy.utilities.base.types import Np1D, DictAny, HFEng, paramVal
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.exception_manager import RROMPyException
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;
- 'muBounds': list of bounds for parameter values; defaults to
[0, 1];
- 'S': number of starting training points; defaults to 2;
- 'sampler': sample point generator; defaults to uniform sampler on
muBounds;
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- '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 maxIter /
refinementRatio;
- '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.
parameterList: Recognized keys of approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'muBounds': list of bounds for parameter values;
- 'S': number of starting training points;
- 'sampler': sample point generator;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'refinementRatio': ratio of training points to be exhausted
before training set refinement;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator.
extraApproxParameters: List of approxParameters keys in addition to
mother class's.
POD: whether to compute POD of snapshots.
muBounds: list of bounds for parameter values.
S: number of test points.
sampler: Sample point generator.
greedyTol: uniform error tolerance for 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.
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.
uAppReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApp as sampleList.
lastSolvedAppReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApp: Approximate solution(s) with parameter(s) lastSolvedApp as
sampleList.
lastSolvedApp: 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 : complex = 0.,
+ 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)
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)
self._postInit()
@property
def R(self):
"""Value of R."""
return self._S
@R.setter
def R(self, R):
raise RROMPyException(("R is used just to simplify inheritance, and "
"its value cannot be changed from that of S."))
def errorEstimator(self, mus:Np1D) -> Np1D:
"""
Standard residual-based error estimator. Unreliable for unstable
problems (inf-sup constant is missing).
"""
self.setupApprox()
self.assembleReducedResidualBlocks()
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)
- parmus, _ = checkParameterList(mus)
+ parmus, _ = checkParameterList(mus, self.npar)
uApps = self.getApproxReduced(parmus)
for j, muPL in enumerate(parmus):
mu = muPL[0]
uApp = uApps[j]
for i in range(nAs):
radiusA[:, i, j] = eval(thetaAs[i]) * uApp
for i in range(nbs):
radiusb[i, j] = eval(thetabs[i])
if verb >= 5:
verbosityDepth("DEL", "Done computing RB solution.",
timestamp = self.timestamp)
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
if self.verbosity >= 5:
verbosityDepth("INIT", "Setting up {}.". format(self.name()),
timestamp = self.timestamp)
self.greedy(plotEst)
if self.verbosity >= 7:
verbosityDepth("INIT", "Computing projection matrix.",
timestamp = self.timestamp)
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)
data.ARBs, data.bRBs = self.assembleReducedSystem(pMat)
data.mus = copy(self.mus)
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.ARBs = ARBs
self.trainedModel.data.bRBs = bRBs
self.trainedModel.data.projMat = copy(pMat)
self.trainedModel.data.mus = copy(self.mus)
if self.verbosity >= 7:
verbosityDepth("DEL", "Done computing projection matrix.",
timestamp = self.timestamp)
self.trainedModel.data.approxParameters = copy(self.approxParameters)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done setting up approximant.",
timestamp = self.timestamp)
def assembleReducedResidualBlocks(self):
"""Build affine blocks of RB linear system through projections."""
computeResbb = not hasattr(self.trainedModel.data, "resbb")
computeResAb = (not hasattr(self.trainedModel.data, "resAb")
or self.trainedModel.data.resAb.shape[1] != len(self.mus))
computeResAA = (not hasattr(self.trainedModel.data, "resAA")
or self.trainedModel.data.resAA.shape[0] != len(self.mus))
if computeResbb or computeResAb or computeResAA:
if self.verbosity >= 7:
verbosityDepth("INIT", "Projecting affine terms of residual.",
timestamp = self.timestamp)
if computeResAb or computeResAA:
pMat = self.trainedModel.data.projMat
if computeResbb:
self.assembleReducedResidualBlocksbb(self.bs)
if computeResAb:
self.assembleReducedResidualBlocksAb(self.As, self.bs, pMat)
if computeResAA:
self.assembleReducedResidualBlocksAA(self.As, pMat)
if self.verbosity >= 7:
verbosityDepth("DEL", ("Done setting up affine decomposition "
"of residual."),
timestamp = self.timestamp)
diff --git a/rrompy/reduction_methods/trained_model/trained_model.py b/rrompy/reduction_methods/trained_model/trained_model.py
index 58415b8..eb310e9 100644
--- a/rrompy/reduction_methods/trained_model/trained_model.py
+++ b/rrompy/reduction_methods/trained_model/trained_model.py
@@ -1,87 +1,87 @@
# 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
from rrompy.utilities.base.types import Np1D, paramList, sampList
from rrompy.parameter import checkParameterList
from rrompy.sampling import sampleList, emptySampleList
__all__ = ['TrainedModel']
class TrainedModel:
"""
ABSTRACT
ROM approximant evaluation.
Attributes:
Data: dictionary with all that can be pickled.
"""
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))
@abstractmethod
- def getApproxReduced(self, mu:paramList) -> sampList:
+ def getApproxReduced(self, mu : paramList = []) -> sampList:
"""
Evaluate reduced representation of approximant at arbitrary parameter.
(ABSTRACT)
Args:
mu: Target parameter.
"""
pass
- def getApprox(self, mu:paramList) -> sampList:
+ def getApprox(self, mu : paramList = []) -> sampList:
"""
Evaluate approximant at arbitrary parameter.
Args:
mu: Target parameter.
"""
mu, _ = checkParameterList(mu, self.data.npar)
if not hasattr(self, "lastSolvedApp") or self.lastSolvedApp != mu:
uAppRed = self.getApproxReduced(mu)
self.uApp = emptySampleList()
self.uApp.reset((self.data.projMat.shape[0], len(mu)),
self.data.projMat.dtype)
for i in range(len(mu)):
if isinstance(self.data.projMat, (list, sampleList,)):
self.uApp[i] = uAppRed[i][0] * self.data.projMat[0]
for j in range(1, uAppRed.shape[0]):
self.uApp[i] += uAppRed[i][j] * self.data.projMat[j]
else:
self.uApp[i] = self.data.projMat.dot(uAppRed[i])
self.lastSolvedApp = mu
return self.uApp
@abstractmethod
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
pass
diff --git a/rrompy/reduction_methods/trained_model/trained_model_data.py b/rrompy/reduction_methods/trained_model/trained_model_data.py
index 1806897..9215ea9 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_data.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_data.py
@@ -1,32 +1,32 @@
# 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.utilities.base.types import Np2D, paramVal
+from rrompy.utilities.base.types import Np2D, List, paramVal
__all__ = ['TrainedModelData']
class TrainedModelData:
"""ROM approximant evaluation data (must be pickle-able)."""
def __init__(self, name:str, mu0:paramVal, projMat:Np2D,
- rescalingExp : float = 1., npar : int = 1):
+ rescalingExp : List[float] = [1.], npar : int = 1):
self.name = name
self.mu0 = mu0
self.projMat = copy(projMat)
self.rescalingExp = rescalingExp
self.npar = npar
diff --git a/rrompy/reduction_methods/trained_model/trained_model_pade.py b/rrompy/reduction_methods/trained_model/trained_model_pade.py
index d2bf232..10fe356 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_pade.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_pade.py
@@ -1,145 +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
from . import TrainedModel
-from rrompy.utilities.base.types import Np1D, List, paramList, sampList
+from rrompy.utilities.base.types import (Np1D, List, paramVal, paramList,
+ sampList)
from rrompy.utilities.base import verbosityDepth
from rrompy.utilities.poly_fitting.polynomial import polyval, polyroots
from rrompy.utilities.exception_manager import RROMPyAssert
from rrompy.parameter import 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 : float = None) -> float:
+ 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:
+ 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 >= 10:
verbosityDepth("INIT", ("Evaluating numerator at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
muCenter = self.centerNormalize(mu)
p = sampleList(polyval(muCenter, self.data.P.T,
self.data.polytype, der))
if self.verbosity >= 10:
verbosityDepth("DEL", "Done evaluating numerator.",
timestamp = self.timestamp)
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 >= 10:
verbosityDepth("INIT", ("Evaluating denominator at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
muCenter = self.centerNormalize(mu)
q = polyval(muCenter, self.data.Q, self.data.polytype, der, scl)
if self.verbosity >= 10:
verbosityDepth("DEL", "Done evaluating denominator.",
timestamp = self.timestamp)
return q
- def getApproxReduced(self, mu:paramList) -> sampList:
+ 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, "lastSolvedAppReduced")
or self.lastSolvedAppReduced != mu):
if self.verbosity >= 5:
verbosityDepth("INIT", ("Evaluating approximant at mu = "
"{}.").format(mu),
timestamp = self.timestamp)
self.uAppReduced = self.getPVal(mu) / self.getQVal(mu)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done evaluating approximant.",
timestamp = self.timestamp)
self.lastSolvedAppReduced = mu
return self.uAppReduced
def getPoles(self) -> Np1D:
"""
Obtain approximant poles.
Returns:
Numpy complex vector of poles.
"""
- return np.power(self.data.mu0(0) ** self.data.rescalingExp
+ RROMPyAssert(self.data.npar, 1, "Number of parameters")
+ return np.power(self.data.mu0(0) ** self.data.rescalingExp[0]
+ self.data.scaleFactor
* polyroots(self.data.Q, self.data.polytype),
- 1. / self.data.rescalingExp)
+ 1. / self.data.rescalingExp[0])
def getResidues(self) -> Np1D:
"""
Obtain approximant residues.
Returns:
Numpy matrix with residues as columns.
"""
- RROMPyAssert(self.data.npar, 1, "Number of parameters")
pls = self.getPoles()
- poles, _ = checkParameterList(pls)
+ poles, _ = checkParameterList(pls, 1)
print(self.data.projMat.dot(self.getPVal(poles).data).shape)
print(self.getQVal(poles, 1).shape)
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 fcb46a9..ce630fe 100644
--- a/rrompy/reduction_methods/trained_model/trained_model_rb.py
+++ b/rrompy/reduction_methods/trained_model/trained_model_rb.py
@@ -1,113 +1,113 @@
# 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.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:
+ 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, "lastSolvedAppReduced")
or self.lastSolvedAppReduced != mus):
if self.verbosity >= 5:
verbosityDepth("INIT", ("Computing RB solution at mu = "
"{}.").format(mus),
timestamp = self.timestamp)
thetaAs, thetabs = self.data.thetaAs, self.data.thetabs
ARBs, bRBs = self.data.ARBs, self.data.bRBs
self.uAppReduced = emptySampleList()
self.uAppReduced.reset((ARBs[0].shape[0], len(mu)),
self.data.projMat.dtype)
for i, muPL in enumerate(mus):
mu = muPL[0]
if self.verbosity >= 10:
verbosityDepth("INIT", ("Assembling reduced model for mu "
"= {}.").format(mu),
timestamp = self.timestamp)
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 >= 10:
verbosityDepth("DEL", "Done assembling reduced model.",
timestamp = self.timestamp)
if self.verbosity >= 5:
verbosityDepth("INIT", ("Solving reduced model for mu = "
"{}.").format(mu),
timestamp = self.timestamp)
self.uAppReduced[i] = np.linalg.solve(ARBmu, bRBmu)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done solving reduced model.",
timestamp = self.timestamp)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done computing RB solution.",
timestamp = self.timestamp)
self.lastSolvedAppReduced = mus
return self.uAppReduced
def getPoles(self) -> 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)
- + self.data.mu0(0) ** self.data.rescalingExp,
- 1. / self.data.rescalingExp)
+ + 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 601662a..529aeac 100644
--- a/rrompy/sampling/base/sampling_engine_base.py
+++ b/rrompy/sampling/base/sampling_engine_base.py
@@ -1,193 +1,194 @@
# 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, strLst, paramVal,
paramList, sampList)
from rrompy.utilities.base import verbosityDepth
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):
self.verbosity = verbosity
self.timestamp = timestamp
if self.verbosity >= 10:
verbosityDepth("INIT",
"Initializing sampling engine of type {}.".format(
self.name()),
timestamp = self.timestamp)
self.HFEngine = HFEngine
if self.verbosity >= 10:
verbosityDepth("DEL", "Done initializing sampling engine.",
timestamp = self.timestamp)
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
-
+
@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,
+ 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)
+ mu, _ = checkParameterList(mu, self.HFEngine.npar)
if self.verbosity >= 5:
verbosityDepth("INIT", "Solving HF model for mu = {}.".format(mu),
timestamp = self.timestamp)
u = self.HFEngine.solve(mu, RHS, homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Done solving HF model.",
timestamp = self.timestamp)
return u
def plotSamples(self, name : str = "u", save : str = None,
what : strLst = 'all', saveFormat : str = "eps",
saveDPI : int = 100, show : bool = True, **figspecs):
"""
Do some nice plots of the samples.
Args:
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.
figspecs(optional key args): Optional arguments for matplotlib
figure creation.
"""
for j in range(self.nsamples):
self.HFEngine.plot(self.samples[j], name = "{}_{}".format(name, j),
save = save, what = what,
saveFormat = saveFormat, saveDPI = saveDPI,
show = show, **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 d908e04..f0ac79c 100644
--- a/rrompy/sampling/linear_problem/sampling_engine_linear.py
+++ b/rrompy/sampling/linear_problem/sampling_engine_linear.py
@@ -1,97 +1,105 @@
# 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.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.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 u
def _getSampleConcurrence(self, mu:paramVal, previous:Np1D,
homogeneized : bool = False) -> sampList:
- mu = checkParameter(mu, 1)
+ 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, len(previous), homogeneized = homogeneized)
- for i in range(1, len(previous) + 1):
- RHS -= self.HFEngine.A(mu, i).dot(samplesOld[- i])
+ 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,
+ def nextSample(self, mu : paramVal = [], overwrite : bool = False,
homogeneized : bool = False) -> Np1D:
- mu = checkParameter(mu, self.HFEngine.npar)[0]
+ mu = checkParameter(mu, self.HFEngine.npar)
ns = self.nsamples
- muidxs = self.mus.findall(mu)
+ 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
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)
n = len(mus)
if n <= 0:
raise RROMPyException(("Number of samples must be positive."))
self.resetHistory()
if self.verbosity >= 7:
verbosityDepth("MAIN", "Computing sample {}/{}.".format(1, n),
timestamp = self.timestamp)
u = self.nextSample(mus[0], homogeneized = homogeneized)
if n > 1:
self.preallocateSamples(u, mus[0], n)
for j in range(1, n):
if self.verbosity >= 7:
verbosityDepth("MAIN",
"Computing sample {}/{}.".format(j + 1, n),
timestamp = self.timestamp)
self.nextSample(mus[j], overwrite = True,
homogeneized = homogeneized)
if self.verbosity >= 5:
verbosityDepth("DEL", "Finished sampling iterations.",
timestamp = self.timestamp)
return self.samples
diff --git a/rrompy/utilities/poly_fitting/polynomial/__init__.py b/rrompy/utilities/poly_fitting/polynomial/__init__.py
index c2a210d..5ba2478 100644
--- a/rrompy/utilities/poly_fitting/polynomial/__init__.py
+++ b/rrompy/utilities/poly_fitting/polynomial/__init__.py
@@ -1,35 +1,40 @@
# 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 .base import (polybases, polyfitname, polydomcoeff)
from .der import polyder
from .val import polyval
from .vander import polyvander
from .roots import polyroots
+from .derivative import nextDerivativeIndices
+from .hash_derivative import hashDerivativeToIdx, hashIdxToDerivative
__all__ = [
'polybases',
'polyfitname',
'polydomcoeff',
'polyder',
'polyval',
'polyvander',
- 'polyroots'
+ 'polyroots',
+ 'nextDerivativeIndices',
+ 'hashDerivativeToIdx',
+ 'hashIdxToDerivative'
]
diff --git a/rrompy/utilities/poly_fitting/polynomial/derivative.py b/rrompy/utilities/poly_fitting/polynomial/derivative.py
new file mode 100644
index 0000000..ba9fab4
--- /dev/null
+++ b/rrompy/utilities/poly_fitting/polynomial/derivative.py
@@ -0,0 +1,72 @@
+# 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 scipy.special import binom
+from rrompy.utilities.base.types import List
+from rrompy.utilities.exception_manager import RROMPyException
+
+__all__ = ['nextDerivativeIndices']
+
+def nextDerivativeIndices(derIdxs:List[List[int]], dim:int,
+ count : int = 1) -> List[List[int]]:
+ out = []
+ if count <= 0: return out
+ derIdxs = copy(derIdxs)
+ sumDer, sumInverse, sumCount = np.unique(
+ [np.sum(derIdx) for derIdx in derIdxs],
+ return_inverse = True, return_counts = True)
+ if len(derIdxs) == 0 or 0 not in sumDer:
+ out += [[0] * dim]
+ count -= 1
+ if count <= 0: return out
+ derIdxs += [[0] * dim]
+ shellIncomplete = 1
+ _, sumInverse = np.unique([np.sum(derIdx) for derIdx in derIdxs],
+ return_inverse = True)
+ else:
+ sumCount = np.cumsum(sumCount)
+ shellIncomplete = 1
+ for shellIncomplete in range(1, len(sumDer) + 1):
+ theoreticalCount = binom(shellIncomplete + dim, dim)
+ if (shellIncomplete not in sumDer
+ or theoreticalCount > sumCount[shellIncomplete]):
+ break
+ if theoreticalCount < sumCount[shellIncomplete]:
+ raise RROMPyException("Starting index list is redundant.")
+ shell_previous = [derIdxs[x] for x in
+ np.nonzero(sumInverse == shellIncomplete - 1)[0]]
+ while count > 0:
+ shell_current = [derIdxs[x] for x in
+ np.nonzero(sumInverse == shellIncomplete)[0]]
+ for prev in shell_previous:
+ prevC = copy(prev)
+ for d in range(dim):
+ prevC[d] += 1
+ if prevC not in shell_current:
+ out += [copy(prevC)]
+ shell_current += [copy(prevC)]
+ derIdxs += [copy(prevC)]
+ count -= 1
+ if count <= 0: return out
+ prevC[d] -= 1
+ shell_previous = copy(shell_current)
+ _, sumInverse = np.unique([np.sum(derIdx) for derIdx in derIdxs],
+ return_inverse = True)
+ shellIncomplete += 1
diff --git a/rrompy/utilities/poly_fitting/polynomial/hash_derivative.py b/rrompy/utilities/poly_fitting/polynomial/hash_derivative.py
new file mode 100644
index 0000000..bb75b18
--- /dev/null
+++ b/rrompy/utilities/poly_fitting/polynomial/hash_derivative.py
@@ -0,0 +1,44 @@
+# 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 scipy.special import binom
+from rrompy.utilities.base.types import List
+
+__all__ = ['hashDerivativeToIdx', 'hashIdxToDerivative']
+
+def shellCount(shell:int, dim:int) -> int:
+ return int(binom(shell + dim, dim))
+
+def hashDerivativeToIdx(derIdx:List[int]) -> int:
+ dim = len(derIdx)
+ derMag = sum(derIdx)
+ base = shellCount(derMag - 1, dim)
+ if derMag == derIdx[0]: return base
+ return base + hashDerivativeToIdx(derIdx[1:])
+
+def hashIdxToDerivative(n:int, dim:int) -> List[int]:
+ if n == 0: return [0] * dim
+ shell = 0
+ shellOld = -1
+ shellNew = 1
+ while shellNew <= n:
+ shell += 1
+ shellOld = shellNew
+ shellNew = shellCount(shell, dim)
+ rest = hashIdxToDerivative(n - shellOld, dim - 1)
+ return [shell - sum(rest)] + rest
diff --git a/rrompy/utilities/poly_fitting/polynomial/vander.py b/rrompy/utilities/poly_fitting/polynomial/vander.py
index ea16477..ed4984c 100644
--- a/rrompy/utilities/poly_fitting/polynomial/vander.py
+++ b/rrompy/utilities/poly_fitting/polynomial/vander.py
@@ -1,82 +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 .
#
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
+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,
- scl : Np1D = None) -> Np2D:
- """Compute Vandermonde matrix even in case of confluence."""
+ 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, wasPar = 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.")
- x_un, idx_un, cnt_un = x.unique(return_inverse = True,
- return_counts = True)
- Van = vanderbase(x(0), degs[0])
+ VanBase = vanderbase(x(0), degs[0])
for j in range(1, dim):
- Van = Van[..., None] * vanderbase(x(j), degs[j])[..., None, :]
- Van = Van.reshape((len(x), -1))
- if max(cnt_un) > 1:
- degsp1 = [d + 1 for d in degs]
- TDirac = [x.reshape(degsp1)
- for x in np.eye(np.prod(degsp1), dtype = int)]
+ VanBase = VanBase[..., None] * vanderbase(x(j), degs[j])[..., None, :]
+ VanBase = VanBase.reshape((len(x), -1))
+
+ if derIdxs is None:
+ 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 = [x.reshape([d + 1 for d in degs])
+ for x in np.eye(VanBase.shape[-1], dtype = int)]
Cs_loc = firstDerTransition(dim, TDirac, basis, scl)
- for j, c in enumerate(cnt_un):
- idx_loc = np.nonzero(idx_un == j)[0]
- der_max = int(c ** (1. / dim))
- if der_max ** dim != c:
- raise RROMPyException(("Number of occurrences of each sample "
- "point must be exact {}-th "
- "power.").format(dim))
- for i, idx in enumerate(idx_loc[1 :]):
- for (k, ct) in countDerDirections(i + 1, der_max, dim, 0):
- for der in range(ct):
- Van[idx, :] = Van[idx, :].dot(Cs_loc[k]) / (der + 1)
+ 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
-
diff --git a/rrompy/utilities/poly_fitting/radial_basis/radial_basis_fitter.py b/rrompy/utilities/poly_fitting/radial_basis/radial_basis_fitter.py
index 7c8b0f2..dec76f5 100644
--- a/rrompy/utilities/poly_fitting/radial_basis/radial_basis_fitter.py
+++ b/rrompy/utilities/poly_fitting/radial_basis/radial_basis_fitter.py
@@ -1,229 +1,229 @@
# 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, Np2D, List, ListAny, paramList
from rrompy.solver import Np2DLikeEye, normEngine
from rrompy.parameter import checkParameterList
from rrompy.utilities.exception_manager import RROMPyException, RROMPyAssert
__all__ = ['radialBasisFitter', 'radialGaussian', 'thinPlateSpline',
'multiQuadric']
def radialGaussian(r2):
return np.exp(- r2)
def thinPlateSpline(r2):
return .5 * r2 * np.log(np.finfo(float).eps + r2)
def multiQuadric(r2):
return np.power(r2 + 1, .5)
class radialBasisFitter:
"""HERE"""
allowedModes = ["PARAMETERS", "VALUES"]
def __init__(self, mus:paramList, basisFun : callable = radialGaussian,
massMatrix : Np2D = None, mode : str = "PARAMETERS",
scl : float = 1.):
self.mus = mus
self.basisFun = basisFun
if massMatrix is None: massMatrix = normEngine(Np2DLikeEye())
self.massMatrix = massMatrix
self.mode = mode
self.scl = scl
@property
def d(self):
"""Number of parameters."""
return self.mus.shape[1]
@property
def n(self):
"""Number of parameter points."""
return len(self.mus)
@property
def basisFun(self):
"""Value of basisFun. Its assignment resets all."""
return self._basisFun
@basisFun.setter
def basisFun(self, basisFun):
self.reset()
self._basisFun = basisFun
@property
def mus(self):
"""Value of mus. Its assignment resets all."""
return self._mus
@mus.setter
def mus(self, mus):
mus, _ = checkParameterList(mus)
self.reset()
self._mus = mus
@property
def massMatrix(self):
"""Value of massMatrix. Its assignment resets all."""
return self._massMatrix
@massMatrix.setter
def massMatrix(self, massMatrix):
self.reset()
self._massMatrix = massMatrix
@property
def mode(self):
"""Value of mode. Its assignment resets all."""
return self._mode
@mode.setter
def mode(self, mode):
self.reset()
self._mode = mode.upper()
@property
def scl(self):
"""Value of scl. Its assignment resets all."""
return self._scl
@scl.setter
def scl(self, scl):
self.reset()
self._scl = scl
def reset(self):
self.vander = None
self.offDiag = None
self.offDiagT = None
self.matrixInv = None
self.probeParameters = None
self.probeValues = None
def buildMatrixBlocks(self):
if self.offDiag is None:
self.reset()
self.offDiagT = np.array([[1] + list(x[0]) for x in self.mus])
self.offDiag = self.offDiagT.T
muDiff = np.empty((self.d, self.n * (self.n - 1) // 2 + 1),
dtype = self.mus.dtype)
muDiff[:, 0] = 0.
idxInv = np.zeros(self.n ** 2, dtype = int)
for j in range(self.n):
idx = j * (self.n - 1) - j * (j + 1) // 2
for i in range(j + 1, self.n):
muDiff[:, idx + i] = (self.offDiag[1:, j]
- self.offDiag[1:, i])
idxInv[j * self.n + i] = idx + i
idxInv[i * self.n + j] = idx + i
self.vander = self.basisFun(np.power(self.scl *
self.massMatrix.norm(muDiff), 2.))[idxInv]
self.vander = self.vander.reshape((self.n, -1))
self.vanderProj = self.offDiag.dot(self.vander.dot(self.offDiag.T))
def buildMatrixInvBlocks(self):
if self.matrixInv is None:
self.buildMatrixBlocks()
vanderInv = np.linalg.inv(self.vander)
vanderProjInv = np.linalg.solve(self.vanderProj,
self.offDiag.dot(vanderInv))
self.matrixInv = np.empty((self.n + self.d + 1, self.n),
dtype = vanderProjInv.dtype)
self.matrixInv[self.n :, :] = vanderProjInv
self.matrixInv[: self.n, :] = vanderInv - vanderInv.dot(
self.offDiagT.dot(vanderProjInv))
- def setupProbeParameters(self, mu:paramList) -> List[Np1D]:
+ def setupProbeParameters(self, mu : paramList = []) -> List[Np1D]:
mu, _ = checkParameterList(mu, self.d)
self.buildMatrixInvBlocks()
self.probeParameters = [None] * len(mu)
for j, m in enumerate(mu):
probe = np.ones(self.n + self.d + 1, dtype = m.dtype)
probe[self.n + 1 :] = m.data # flatten?
mDiff = (probe[self.n + 1:] - self.offDiagT[:, 1:]).T
probe[: self.n] = self.basisFun(np.power(self.scl *
self.massMatrix.norm(mDiff), 2.))
self.probeParameters[j] = probe.dot(self.matrixInv)
def setupProbeValues(self, vals:ListAny) -> ListAny:
RROMPyAssert(len(vals), self.n, "Number of samples")
self.buildMatrixInvBlocks()
if isinstance(vals, (np.ndarray,)):
self.probeValues = np.tensordot(self.matrixInv, vals,
axes = ([-1], [0]))
else:
self.probeValues = [None] * (self.n + self.d + 1)
for j in range(self.n + self.d + 1):
self.probeValues[j] = self.matrixInv[j, 0] * vals[0]
for i in range(1, self.n):
self.probeValues[j] += self.matrixInv[j, i] * vals[i]
def interpolateParameters(self, vals:ListAny) -> ListAny:
if self.probeParameters is None:
raise RROMPyException(("Parameter probe must be set up before "
"interpolation."))
RROMPyAssert(len(vals), self.n, "Number of samples")
interpolated = [None] * len(self.probeParameters)
if isinstance(vals, (np.ndarray,)):
if vals.ndim == 1:
for j, pUp in enumerate(self.probeParameters):
interpolated[j] = pUp.dot(vals)
else:
for j, pUp in enumerate(self.probeParameters):
interpolated[j] = np.tensordot(pUp, vals,
axes = ([0], [0]))
else:
for j, pUp in enumerate(self.probeParameters):
interpolated[j] = self.probeParameters[j][0] * vals[0]
for i in range(1, self.n):
interpolated[j] += self.probeParameters[j][i] * vals[i]
return interpolated
- def interpolateValues(self, mu:paramList) -> ListAny:
+ def interpolateValues(self, mu : paramList = []) -> ListAny:
if self.probeValues is None:
raise RROMPyException(("Value probe must be set up before "
"interpolation."))
mu, _ = checkParameterList(mu, self.d)
probeLs = [None] * len(mu)
for j, m in enumerate(mu):
probeLs[j] = np.ones(self.n + self.d + 1, dtype = m.dtype)
probeLs[j][self.n + 1 :] = m.data # flatten?
mDiff = (probeLs[j][self.n + 1:] - self.offDiagT[:, 1:]).T
probeLs[j][: self.n] = self.basisFun(np.power(self.scl *
self.massMatrix.norm(mDiff), 2.))
interpolated = [None] * len(mu)
if isinstance(self.probeValues, (np.ndarray,)):
if self.probeValues.ndim == 1:
for j, pL in enumerate(probeLs):
interpolated[j] = pL.dot(self.probeValues)
else:
for j, pL in enumerate(probeLs):
interpolated[j] = np.tensordot(pL, self.probeValues,
axes = ([-1], [0]))
else:
for j, pL in enumerate(probeLs):
interpolated[j] = pL[0] * self.probeValues[0]
for i in range(1, self.n + self.d + 1):
interpolated[j] += pL[i] * self.probeValues[i]
return interpolated
def interpolate(self, x) -> ListAny:
if self.mode == "PARAMETERS":
return self.interpolateParameters(x)
if self.mode == "VALUES":
return self.interpolateValues(x)
raise RROMPyException("Not implemented")
diff --git a/tests/test_1_utilities/fitting.py b/tests/test_1_utilities/fitting.py
index e16a855..936b051 100644
--- a/tests/test_1_utilities/fitting.py
+++ b/tests/test_1_utilities/fitting.py
@@ -1,106 +1,116 @@
# 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 import customFit
from rrompy.utilities.poly_fitting.polynomial import (polybases, polyfitname,
polydomcoeff, polyval,
- polyroots, polyvander)
+ polyroots, polyvander,
+ nextDerivativeIndices)
from rrompy.parameter import checkParameterList
def test_chebyshev():
assert "CHEBYSHEV" in polybases
fitname = polyfitname("CHEBYSHEV")
domcoeff = polydomcoeff(5, "CHEBYSHEV")
assert fitname == "chebfit"
assert np.isclose(domcoeff, 16, rtol = 1e-5)
assert np.allclose(polyroots((-1, 1, -1, 1), "CHEBYSHEV"),
np.array([-.5, 0., 1.]), rtol = 1e-5)
Phi = polyvander(np.arange(5), 4, "CHEBYSHEV")
y = 2. * np.arange(5)
cFit = customFit(Phi, y)
assert np.allclose(cFit, [0, 2, 0, 0, 0], rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "CHEBYSHEV"), y,
rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "CHEBYSHEV", m = 1),
2. * np.ones(5), rtol = 1e-5)
def test_legendre():
assert "LEGENDRE" in polybases
fitname = polyfitname("LEGENDRE")
domcoeff = polydomcoeff([0, 5], "LEGENDRE")
assert fitname == "legfit"
assert np.allclose(domcoeff, [1., 63. / 8], rtol = 1e-5)
assert np.allclose(polyroots((1, 2, 3, 4), "LEGENDRE"),
np.array([-0.85099543, -0.11407192, 0.51506735]),
rtol = 1e-5)
Phi = polyvander(np.arange(5), 4, "LEGENDRE")
y = 2. * np.arange(5)
cFit = customFit(Phi, y)
assert np.allclose(cFit, [0, 2, 0, 0, 0], rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "LEGENDRE"), y, rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "LEGENDRE", m = 1),
2. * np.ones(5), rtol = 1e-5)
def test_monomial():
assert "MONOMIAL" in polybases
fitname = polyfitname("MONOMIAL")
domcoeff = polydomcoeff(5, "MONOMIAL")
assert fitname == "polyfit"
assert np.isclose(domcoeff, 1., rtol = 1e-5)
assert np.allclose(polyroots([0.+0.j, 1.+0.j, 0.+0.j, 1.+0.j], "MONOMIAL"),
np.array([0., 1.j, -1.j]), rtol = 1e-5)
Phi = polyvander(np.arange(5), 4, "MONOMIAL")
y = 2. * np.arange(5)
cFit = customFit(Phi, y)
assert np.allclose(cFit, [0, 2, 0, 0, 0], rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "MONOMIAL"), y, rtol = 1e-5)
assert np.allclose(polyval(np.arange(5), cFit, "MONOMIAL", m = 1),
2. * np.ones(5), rtol = 1e-5)
def test_cheb_confluence():
x = np.arange(5)
- x[3] = 0
- Phi = polyvander(x, 4, "CHEBYSHEV")
- y = 2. * x
+ x = np.delete(x, 3)
+ Phi = polyvander(x, 4, "CHEBYSHEV", [[0, 1]] + [[0]] * 3,
+ reorder = [0, 2, 3, 1, 4])
+ y = 2. * np.arange(5)
y[3] = 2.
cFit = customFit(Phi, y)
- mask = np.arange(len(x)) != 3
+ mask = np.arange(len(y)) != 3
assert np.allclose(cFit, [0, 2, 0, 0, 0], rtol = 1e-5)
- assert np.allclose(polyval(x[mask], cFit, "CHEBYSHEV"), y[mask],
+ assert np.allclose(polyval(x, cFit, "CHEBYSHEV"), y[mask],
rtol = 1e-5)
- assert np.allclose(polyval(x[~mask], cFit, "CHEBYSHEV", m = 1), y[~mask],
+ assert np.allclose(polyval(x[0], cFit, "CHEBYSHEV", m = 1), y[~mask],
rtol = 1e-5)
def test_mon_confluence_2d():
- x, _ = checkParameterList([[0, 0], [0, 0], [0, 0], [0, 0],
- [1, 1], [-1, -1]])
+ x, _ = checkParameterList([[0, 0], [1, 1], [-1, -1]])
y = np.array([3., 5., 1., 2., 12., -2.]).reshape((-1, 1)) # 3+y+5x+2xy+x2y
- Phi = polyvander(x, [2, 1], "MONOMIAL")
+ Phi = polyvander(x, [2, 1], "MONOMIAL",
+ [[[0, 0], [1, 0], [0, 1], [1, 1]]] + [[[0, 0]]] * 2)
cFit = customFit(Phi, y).reshape((3, 2))
mask = np.array([0, 4, 5])
assert np.allclose(cFit.flatten(), [3, 1, 5, 2, 0, 1], atol = 1e-5)
- assert np.allclose(polyval(x[mask], cFit, "MONOMIAL").flatten(),
+ assert np.allclose(polyval(x, cFit, "MONOMIAL").flatten(),
y[mask].flatten(), rtol = 1e-5)
- assert np.allclose(polyval([x[1]], cFit, "MONOMIAL", m = [1, 0]), y[1],
+ assert np.allclose(polyval([x[0]], cFit, "MONOMIAL", m = [1, 0]), y[1],
rtol = 1e-5)
- assert np.allclose(polyval([x[2]], cFit, "MONOMIAL", m = [0, 1]), y[2],
+ assert np.allclose(polyval([x[0]], cFit, "MONOMIAL", m = [0, 1]), y[2],
rtol = 1e-5)
- assert np.allclose(polyval([x[3]], cFit, "MONOMIAL", m = [1, 1]), y[3],
+ assert np.allclose(polyval([x[0]], cFit, "MONOMIAL", m = [1, 1]), y[3],
rtol = 1e-5)
+
+def test_derivative_indices_4d():
+ idxs = nextDerivativeIndices([], 4, 70)
+ idxMag = [np.sum(idx) for idx in idxs]
+ idxMagUnique, idxMagCount = np.unique(idxMag, return_counts = True)
+ idxMagCount = np.cumsum(idxMagCount)
+ assert np.allclose(idxMagUnique, np.arange(5), atol = 1e-10)
+ assert np.allclose(idxMagCount, [1, 5, 15, 35, 70], atol = 1e-10)
diff --git a/tests/test_1_utilities/sampling.py b/tests/test_1_utilities/sampling.py
index 370ada6..f1b2975 100644
--- a/tests/test_1_utilities/sampling.py
+++ b/tests/test_1_utilities/sampling.py
@@ -1,74 +1,78 @@
# 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 sp
from rrompy.hfengines.base import MatrixEngineBase as MEB
from rrompy.sampling.linear_problem import (SamplingEngineLinear,
SamplingEngineLinearPOD)
from rrompy.parameter import parameterList
def test_krylov():
N = 100
mu = 10. + .5j
solver = MEB(verbosity = 0)
+ solver.npar = 1
solver.nAs = 2
solver.As = [sp.spdiags([np.arange(1, 1 + N)], [0], N, N),
- sp.eye(N)]
solver.nbs = 1
solver.bs = [np.exp(1.j * np.linspace(0, -np.pi, N))]
samplingEngine = SamplingEngineLinear(solver, verbosity = 0)
samples = samplingEngine.iterSample([mu] * 5).data
assert samples.shape == (100, 5)
assert np.isclose(np.linalg.norm(samples), 37.02294804524299, rtol = 1e-5)
def test_distributed():
N = 100
mus = parameterList(np.linspace(5, 15, 11) + .5j)
solver = MEB(verbosity = 0)
+ solver.npar = 1
solver.nAs = 2
solver.As = [sp.spdiags([np.arange(1, 1 + N)], [0], N, N),
- sp.eye(N)]
solver.nbs = 1
solver.bs = [np.exp(1.j * np.linspace(0, -np.pi, N))]
samplingEngine = SamplingEngineLinear(solver, verbosity = 0)
samples = samplingEngine.iterSample(mus).data
assert samples.shape == (100, 11)
assert np.isclose(np.linalg.norm(samples), 8.59778606421386, rtol = 1e-5)
def test_distributed_pod():
N = 100
mus = np.linspace(5, 15, 11) + .5j
solver = MEB(verbosity = 0)
+ solver.npar = 1
solver.nAs = 2
solver.As = [sp.spdiags([np.arange(1, 1 + N)], [0], N, N),
- sp.eye(N)]
solver.nbs = 1
solver.bs = [np.exp(1.j * np.linspace(0, -np.pi, N))]
samplingEngine = SamplingEngineLinearPOD(solver, verbosity = 0)
samples = samplingEngine.iterSample(mus).data
assert samples.shape == (100, 11)
assert np.isclose(np.linalg.norm(samples), 3.3166247903553994, rtol = 1e-5)
assert np.isclose(np.linalg.cond(samples.conj().T.dot(samples)), 1.,
rtol = 1e-5)
+
diff --git a/tests/test_2_hfengines/helmholtz_elasticity.py b/tests/test_2_hfengines/helmholtz_elasticity.py
index 84793b6..32e8ce9 100644
--- a/tests/test_2_hfengines/helmholtz_elasticity.py
+++ b/tests/test_2_hfengines/helmholtz_elasticity.py
@@ -1,66 +1,66 @@
# 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.hfengines.vector_linear_problem import (
LinearElasticityHelmholtzProblemEngine,
LinearElasticityHelmholtzProblemEngineDamped,
LinearElasticityHelmholtzArchwayFrequency)
from rod_3d import rod3Dsolver
def test_helmholtz_elastic_arch():
solver = LinearElasticityHelmholtzArchwayFrequency(kappa = 10, n = 30,
rho_ = 1e4, T = 1e5, lambda_ = 4e6, mu_ = 7e5,
R = 2e1, r = 1.5e1, verbosity = 0)
mu = 10
uh = solver.solve(mu)[0]
assert np.isclose(solver.norm(uh), 3188.9960782143194, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 3.025504915e-05,
rtol = 1e-1)
def test_helmholtz_elastic_rod():
solverBase = rod3Dsolver()
solver = LinearElasticityHelmholtzProblemEngine()
solver.V = solverBase.V
solver.lambda_ = solverBase.lambda_
solver.mu_ = solverBase.mu_
solver.forcingTerm = solverBase.forcingTerm
solver.DirichletBoundary = solverBase.DirichletBoundary
solver.NeumannBoundary = solverBase.NeumannBoundary
mu = 10
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 0.17847395043115702, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 0.17836028624665373, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, 10)[0]), 7.030048088e-08,
rtol = 1e-1)
def test_helmholtz_elastic_rod_damped():
solverBase = rod3Dsolver()
solver = LinearElasticityHelmholtzProblemEngineDamped()
solver.V = solverBase.V
solver.lambda_ = solverBase.lambda_
solver.mu_ = solverBase.mu_
solver.forcingTerm = solverBase.forcingTerm
solver.DirichletBoundary = solverBase.DirichletBoundary
solver.NeumannBoundary = solverBase.NeumannBoundary
solver.eta = 10
mu = 10
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 0.17657773579415595, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 0.1583390058791357, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, 10)[0]), 6.802444e-08,
rtol = 1e-1)
diff --git a/tests/test_2_hfengines/helmholtz_external.py b/tests/test_2_hfengines/helmholtz_external.py
index 451d699..d3be9ad 100644
--- a/tests/test_2_hfengines/helmholtz_external.py
+++ b/tests/test_2_hfengines/helmholtz_external.py
@@ -1,64 +1,64 @@
# 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.hfengines.linear_problem import (
HelmholtzCavityScatteringProblemEngine, HelmholtzBoxScatteringProblemEngine)
def test_helmholtz_square_scattering():
solver = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 0)
mu = 5
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 20.719752682674923, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 15.448200380615363, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 4.25056407e-13,
rtol = 1e-1)
def test_helmholtz_scattering_copy(capsys):
solver1 = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 0)
mu = 5
uh1 = solver1.solve(mu)[0]
solver2 = HelmholtzCavityScatteringProblemEngine(kappa = 4, gamma = 2.,
n = 20, verbosity = 100)
assert solver1.As[0] is not None and solver1.bs[0] is not None
assert solver2.As[0] is None and solver2.bs[0] is None
solver2.setAs(solver1.As)
solver2.setbs(solver1.bs)
uh2 = solver2.solve(mu)[0]
assert np.allclose(uh1, uh2, rtol = 1e-8)
out, err = capsys.readouterr()
assert ("Assembling operator term" not in out
and "Assembling forcing term" not in out)
assert len(err) == 0
def test_helmholtz_box_scattering():
solver = HelmholtzBoxScatteringProblemEngine(R = 2, kappa = 10.,
theta = np.pi * 30 / 180, n = 20, verbosity = 0)
mu = 15
uh = solver.solve(mu)[0]
solver.plotmesh(show = False, figsize = (7, 7))
- assert np.isclose(solver.norm(uh), 63.98946657389119, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 26.753778500929478, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 9.62989935e-13,
rtol = 1e-1)
from matplotlib import pyplot as plt
plt.close('all')
diff --git a/tests/test_2_hfengines/helmholtz_internal.py b/tests/test_2_hfengines/helmholtz_internal.py
index 005f95d..9ab3d59 100644
--- a/tests/test_2_hfengines/helmholtz_internal.py
+++ b/tests/test_2_hfengines/helmholtz_internal.py
@@ -1,95 +1,95 @@
# 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 os, shutil
import numpy as np
from rrompy.hfengines.linear_problem import (
HelmholtzSquareBubbleDomainProblemEngine, HelmholtzSquareBubbleProblemEngine,
HelmholtzSquareTransmissionProblemEngine)
def test_helmholtz_square_io():
solver = HelmholtzSquareBubbleProblemEngine(kappa = 4, theta = 1., n = 50,
verbosity = 0)
mu = 5
uh = solver.solve(mu)[0]
assert np.isclose(solver.norm(uh), 70762597.99694124, rtol = 1e-3)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 2.1855986e-06,
rtol = 1e-1)
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pvd" and x[:9] == "outSquare")]
filesOutData = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".vtu" and x[:9] == "outSquare")]
for fileOut in filesOut:
os.remove("./.pytest_cache/" + fileOut)
for fileOut in filesOutData:
os.remove("./.pytest_cache/" + fileOut)
solver.outParaview(uh, what = ["MESH", "ABS"],
filename = ".pytest_cache/outSquare",
forceNewFile = False)
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".pvd" and x[:9] == "outSquare")]
filesOutData = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".vtu" and x[:9] == "outSquare")]
assert len(filesOut) == 1
assert len(filesOutData) == 1
os.remove("./.pytest_cache/" + filesOut[0])
os.remove("./.pytest_cache/" + filesOutData[0])
def test_helmholtz_transmission_io():
solver = HelmholtzSquareTransmissionProblemEngine(nT = 1, nB = 2,
theta = np.pi * 40 / 180, kappa = 4., n = 50, verbosity = 0)
mu = 5.
uh = solver.solve(mu)[0]
assert np.isclose(solver.norm(uh), 46.4528217234862, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 3.7288565e-12,
rtol = 1e-1)
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
solver.outParaviewTimeDomain(uh, omega = mu,
filename = ".pytest_cache/outTrans",
forceNewFile = False, folder = True)
filesOut = [x for x in os.listdir("./.pytest_cache/outTrans") if
(x[-4:] == ".pvd" and x[:8] == "outTrans")]
filesOutData = [x for x in os.listdir("./.pytest_cache/outTrans") if
(x[-4:] == ".vtu" and x[:8] == "outTrans")]
assert len(filesOut) == 1
assert len(filesOutData) == 20
shutil.rmtree("./.pytest_cache/outTrans")
def test_helmholtz_domain_io():
solver = HelmholtzSquareBubbleDomainProblemEngine(kappa = 4, theta = 1.,
n = 50, mu0 = 1.5, verbosity = 0)
mu = 1.5
uh = solver.solve(mu)[0]
if not os.path.isdir("./.pytest_cache"): os.mkdir("./.pytest_cache")
solver.plot(uh, save = "./.pytest_cache/outDomain", show = False)
filesOut = [x for x in os.listdir("./.pytest_cache") if
(x[-4:] == ".eps" and x[:9] == "outDomain")]
assert len(filesOut) == 1
os.remove("./.pytest_cache/" + filesOut[0])
- assert np.isclose(solver.norm(uh), 263.91673976964546, rtol = 1e-5)
- assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 1.734638595e-11,
+ assert np.isclose(solver.norm(uh), 59864887.596, rtol = 1e-5)
+ assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 4.210429353e-06,
rtol = 1e-1)
diff --git a/tests/test_2_hfengines/laplace.py b/tests/test_2_hfengines/laplace.py
index 2a3351d..a9d0679 100644
--- a/tests/test_2_hfengines/laplace.py
+++ b/tests/test_2_hfengines/laplace.py
@@ -1,38 +1,39 @@
# 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.hfengines.linear_problem import (LaplaceDiskGaussian,
LaplaceDiskGaussian2)
def test_laplace_disk():
solver = LaplaceDiskGaussian(n = 20, verbosity = 0)
mu = 1.5
solver.setSolver("BICG", {"tol" : 1e-15})
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 1.0534030774205372, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 1.00259477236834, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 5.27345e-13,
rtol = 1e-1)
def test_laplace_disk_2():
solver = LaplaceDiskGaussian2(n = 20, verbosity = 0)
mu = [[0., 1.5]]
+ mu = [0., 1.5]
uh = solver.solve(mu)[0]
assert np.isclose(solver.norm(uh), 1.0534030774205372, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 5.27345e-13,
rtol = 1e-1)
diff --git a/tests/test_2_hfengines/linear_elasticity.py b/tests/test_2_hfengines/linear_elasticity.py
index 1e15baa..7540d2c 100644
--- a/tests/test_2_hfengines/linear_elasticity.py
+++ b/tests/test_2_hfengines/linear_elasticity.py
@@ -1,38 +1,38 @@
# 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.hfengines.vector_linear_problem import (
LinearElasticityBeamPoissonRatio)
from rod_3d import rod3Dsolver
def test_elastic_beam():
solver = LinearElasticityBeamPoissonRatio(n = 10, rho_ = 1e3, g = 3,
E = 1e6, nu0 = .45, length = 5, verbosity = 0)
mu = .45
uh = solver.solve(mu)[0]
- assert np.isclose(solver.norm(uh), 58.54349189072907, rtol = 1e-5)
+ assert np.isclose(solver.norm(uh), 6.583911304578e-07, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh, mu)[0]), 8.4545952e-13,
rtol = 1e-1)
def test_elastic_rod():
solver = rod3Dsolver()
uh = solver.solve()[0]
assert np.isclose(solver.norm(uh), 0.15563476339534466, rtol = 1e-5)
assert np.isclose(solver.norm(solver.residual(uh)[0]), 5.708389944e-08,
rtol = 1e-1)
diff --git a/tests/test_2_hfengines/matrix.py b/tests/test_2_hfengines/matrix.py
index 4390daf..db2f54a 100644
--- a/tests/test_2_hfengines/matrix.py
+++ b/tests/test_2_hfengines/matrix.py
@@ -1,60 +1,62 @@
# 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 sp
from rrompy.hfengines.base import MatrixEngineBase as MEB
def test_deterministic():
N = 100
verb = 0
solver = MEB(verbosity = verb)
+ solver.npar = 1
solver.nAs = 2
mu = 10. + .5j
solver.As = [sp.spdiags([np.arange(1, 1 + N)], [0], N, N),
- sp.eye(N)]
solver.nbs = 1
solver.bs = [np.exp(1.j * np.linspace(0, -np.pi, N))]
uh = solver.solve(mu)[0]
assert np.isclose(np.linalg.norm(solver.residual(uh, mu)[0]), 1.088e-15,
rtol = 1e-1)
def test_random():
N = 100
verb = 0
solver = MEB(verbosity = verb)
+ solver.npar = 1
solver.nAs = 2
mu = 1. + .5j
np.random.seed(420)
solver.setSolver("SOLVE")
fftB = np.fft.fft(np.eye(N)) * N**-.5
solver.As = [fftB.dot(np.multiply(np.arange(1, 1 + N), fftB.conj()).T),
- np.eye(N)]
solver.nbs = 1
solver.bs = [np.random.randn(N) + 1.j * np.random.randn(N)]
uh = solver.solve(mu)[0]
assert np.isclose(np.linalg.norm(solver.residual(uh, mu)[0]), 7.18658e-14,
rtol = 1e-1)
diff --git a/tests/test_3_reduction_methods/matrix_fft.py b/tests/test_3_reduction_methods/matrix_fft.py
index cb54bd9..d5ea4c0 100644
--- a/tests/test_3_reduction_methods/matrix_fft.py
+++ b/tests/test_3_reduction_methods/matrix_fft.py
@@ -1,33 +1,35 @@
# 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.hfengines.base import MatrixEngineBase as MEB
def matrixFFT():
N = 100
solver = MEB(verbosity = 0)
np.random.seed(420)
solver.setSolver("SOLVE")
fftB = np.fft.fft(np.eye(N)) * N**-.5
+ solver.npar = 1
+ solver.mu0 = 0.
solver.nAs = 2
solver.As = [fftB.dot(np.multiply(np.arange(1, 1 + N), fftB.conj()).T),
- np.eye(N)]
solver.nbs = 1
solver.bs = [np.random.randn(N) + 1.j * np.random.randn(N)]
return solver