def testConstrainedOptimisation(self):
k = 4
g = pcb.PlaneWaves(numpy.array([[3.0/5,4.0/5]]), k).values
# g = pcb.FourierBessel(numpy.array([-2,-1]), numpy.array([5]),k)
npw = 3
nq = 8
ini = pcb.circleDirections(npw)
triquad = puq.trianglequadrature(nq)
linearopt = puo.LeastSquaresFit(g, triquad)
pwpg = puo.PWPenaltyBasisGenerator(k, 1, 2)
basis = puo.optimalbasis3(linearopt.optimise, pwpg.finalbasis, ini)
(coeffs, l2err) = linearopt.optimise(basis)
self.assertAlmostEqual(sum(l2err),0)
def testOptimalBasis3(self):
""" Can we find the right direction to approximate a plane wave?"""
k = 4
g = pcb.PlaneWaves(numpy.array([[3.0/5,4.0/5]]), k).values
# g = pcb.FourierBessel(numpy.array([-2,-1]), numpy.array([5]),k)
npw = 3
nq = 8
gen, ini = puo.pwbasisgeneration(k, npw)
triquad = puq.trianglequadrature(nq)
linearopt = puo.LeastSquaresFit(g, triquad)
basis = puo.optimalbasis3(linearopt.optimise, gen, ini)
(coeffs, l2err) = linearopt.optimise(basis)
self.assertAlmostEqual(sum(l2err),0)
def getNearbyBases(self, indices, x):
etonbcdata = {}
self.etonbcs = {}
for e in self.mesh.partition:
xe = x[indices[e]:indices[e+1]]
bc = self.etobc[e]
fs = self.mesh.etof[e]
qp = np.vstack([self.mqs.quadpoints(f) for f in fs])
qw = np.concatenate([self.mqs.quadweights(f) for f in fs])
lsf = puo.LeastSquaresFit(pcb.BasisReduce(pcb.BasisCombine(bc.getBasis()),xe).values, (qp,qw))
nbcs = bc.nearbybases(xe)
optimisednbcs = []
nbcdata = []
for i, nbc in enumerate(nbcs):
newnbc = puo.optimalbasis3(lsf.optimise, nbc.pwbasis, nbc.params, None, nbc.newparams) if nbc.npw > 0 else nbc
optimisednbcs.append(newnbc)
(_, l2err) = lsf.optimise(pcb.BasisCombine(newnbc.getBasis()))
nbcdata.append((i, newnbc.n, sum(l2err)))
etonbcdata[e] = nbcdata
self.etonbcs[e] = optimisednbcs
return etonbcdata
