def testSymmetry(self):
tag = "B1"
for k in range(1,3):
quadrule = pyramidquadrature(k+1)
for N in range(1,3):
hdivelt1 = HdivElements(k)
l2elt1 = L2Elements(k)
hdivelt2 = HdivElements(k)
l2elt2 = L2Elements(k)
system = AsymmetricSystem(hdivelt1, l2elt1, quadrule, lambda m:buildcubemesh(N,m,tag), [], [])
systemt = AsymmetricSystem(l2elt2, hdivelt2, quadrule, lambda m:buildcubemesh(N,m,tag), [], [])
SM = system.systemMatrix(True, False)
StM = system.transpose().systemMatrix(False, True)
SMt = systemt.systemMatrix(False, True)
np.testing.assert_array_almost_equal(SM.todense(), SMt.transpose().todense())
np.testing.assert_array_almost_equal(StM.todense(), SMt.todense())
def mixedpoissondual(k,N, g, f, points):
tag = "B1"
hdiveltsA = HdivElements(k)
hdiveltsB = HdivElements(k)
hdiveltsBt = HdivElements(k)
l2eltsB = L2Elements(k)
l2eltsBt = L2Elements(k)
quadrule = pyramidquadrature(k+1)
meshevents = lambda m: buildcubemesh(N,m,tag)
Asystem = SymmetricSystem(hdiveltsA, quadrule, meshevents, [])
Bsystem = AsymmetricSystem(l2eltsB, hdiveltsB, quadrule, meshevents, [],[])
Btsystem = AsymmetricSystem(hdiveltsBt, l2eltsBt, quadrule, meshevents, [],[])
A = Asystem.systemMatrix(False)
# Bt = Btsystem.systemMatrix(True, False)
B = Bsystem.systemMatrix(False, True)
print A.shape, B.shape
F = Bsystem.loadVector(f, False)
gn = lambda x,n: g(x).reshape(-1,1,1) * n.reshape(-1,1,3)
G = Btsystem.boundaryLoad({tag:gn}, squarequadrature(k+1), trianglequadrature(k+1), False)
u,p = ps.directsolve(A, B, G[tag], F)
um,pm = ps.mixedcg(A, B, G[tag], F)
# print numpy.hstack((UU[:len(u)], u))
print math.sqrt(numpy.sum((u - um)**2)/len(u))
print math.sqrt(numpy.sum((p - pm)**2)/len(p))
return Btsystem.evaluate(points, p, {}, False)
