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RROMPy/examples/elasticity (arch) greedy.py
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elasticity (arch) greedy.py
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import numpy as np
from rrompy.hfengines.vector_linear_problem import \
LinearElasticityHelmholtzArchwayFrequency as LEHAF
from rrompy.reduction_methods.lagrange_greedy import \
ApproximantLagrangePadeGreedy as Pade
from rrompy.reduction_methods.lagrange_greedy import \
ApproximantLagrangeRBGreedy as RB
verb = 2
timed = True
algo = "Pade"
#algo = "RB"
polyBasis = "LEGENDRE"
#polyBasis = "CHEBYSHEV"
#polyBasis = "MONOMIAL"
errorEstimatorKind = "SIMPLIFIED"
errorEstimatorKind = "EXACT"
k0s = np.power(np.linspace(1e5, 3e5, 150), .5)
k0 = np.mean(k0s)
kl, kr = min(k0s), max(k0s)
params = {'muBounds':[kl, kr], 'nTrainingPoints':500, 'Delta':0,
'greedyTol':1e-2, 'nTestPoints':2, 'basis':polyBasis,
'errorEstimatorKind':errorEstimatorKind}
if timed:
verb = 0
E = 1e6
nu = .47
lambda_ = E * nu / (1. + nu) / (1. - 2. * nu)
mu_ = E / (1. + nu)
solver = LEHAF(kappa = k0, n = 200, rho_ = 1.5e3, T = 1e4, lambda_ = lambda_,
mu_ = mu_, R = 1., r = .85, verbosity = verb)
solver.omega = np.real(k0)
if algo == "Pade":
approx = Pade(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
else:
approx = RB(solver, mu0 = k0, approxParameters = params, verbosity = verb)
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
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.estNormer.norm(approx.getRes(k0s[j]))
/ approx.estNormer.norm(approx.getRHS(k0s[j])))
err[j] = approx.normErr(k0s[j]) / approx.normHF(k0s[j])
resApp = approx.errorEstimator(k0s)
plt.figure()
plt.semilogy(k0s, norm)
plt.semilogy(k0s, normApp, '--')
plt.semilogy(np.real(approx.mus),
1.25*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()
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