def test_solve_proj_sadpnt_smw(self):
"""check the sadpnt as projection"""
n = self.n
# check whether it is a projection
AuvInvZ = lau.solve_sadpnt_smw(amat=self.A,
jmat=self.J,
rhsv=self.Z,
jmatT=self.Jt,
umat=self.U,
vmat=self.V)
auvAUVinv = self.A * AuvInvZ[:n, :] - \
lau.comp_uvz_spdns(self.U, self.V, AuvInvZ[:n, :])
AuvInv2Z = lau.solve_sadpnt_smw(amat=self.A,
jmat=self.J,
rhsv=auvAUVinv,
jmatT=self.Jt,
umat=self.U,
vmat=self.V)
self.assertTrue(np.allclose(AuvInvZ[:n, :], AuvInv2Z[:n, :]),
msg='likely to fail because of ill cond')
prjz = lau.app_prj_via_sadpnt(amat=self.A,
jmat=self.J,
rhsv=self.Z,
jmatT=self.Jt)
prprjz = lau.app_prj_via_sadpnt(amat=self.A,
jmat=self.J,
rhsv=self.Z,
jmatT=self.Jt)
# check projector
self.assertTrue(np.allclose(prprjz, prjz))
# onto kernel J
self.assertTrue(np.linalg.norm(prjz) > 1e-8)
self.assertTrue(
np.linalg.norm(self.J * prjz) / np.linalg.norm(prjz) < 1e-6)
# check transpose
idmat = np.eye(n)
prj = lau.app_prj_via_sadpnt(amat=self.A,
jmat=self.J,
rhsv=idmat,
jmatT=self.Jt)
prjT = lau.app_prj_via_sadpnt(amat=self.A,
jmat=self.J,
rhsv=idmat,
jmatT=self.Jt,
transposedprj=True)
self.assertTrue(np.allclose(prj, prjT.T))
def test_solve_proj_sadpnt_smw(self):
"""check the sadpnt as projection"""
n = self.n
# check whether it is a projection
AuvInvZ = lau.solve_sadpnt_smw(amat=self.A, jmat=self.J, rhsv=self.Z,
jmatT=self.Jt, umat=self.U, vmat=self.V)
auvAUVinv = self.A * AuvInvZ[:n, :] - \
lau.comp_uvz_spdns(self.U, self.V, AuvInvZ[:n, :])
AuvInv2Z = lau.solve_sadpnt_smw(amat=self.A, jmat=self.J,
rhsv=auvAUVinv,
jmatT=self.Jt,
umat=self.U, vmat=self.V)
self.assertTrue(np.allclose(AuvInvZ[:n, :], AuvInv2Z[:n, :]),
msg='likely to fail because of ill cond')
prjz = lau.app_prj_via_sadpnt(amat=self.A, jmat=self.J,
rhsv=self.Z, jmatT=self.Jt)
prprjz = lau.app_prj_via_sadpnt(amat=self.A, jmat=self.J,
rhsv=self.Z, jmatT=self.Jt)
# check projector
self.assertTrue(np.allclose(prprjz, prjz))
# onto kernel J
self.assertTrue(np.linalg.norm(prjz) > 1e-8)
self.assertTrue(np.linalg.norm(self.J*prjz)/np.linalg.norm(prjz)
< 1e-6)
# check transpose
idmat = np.eye(n)
prj = lau.app_prj_via_sadpnt(amat=self.A, jmat=self.J,
rhsv=idmat, jmatT=self.Jt)
prjT = lau.app_prj_via_sadpnt(amat=self.A, jmat=self.J,
rhsv=idmat, jmatT=self.Jt,
transposedprj=True)
self.assertTrue(np.allclose(prj, prjT.T))
def test_output_opa(self):
""" test the regularization of the output operator
"""
import dolfin
import dolfin_to_nparrays as dtn
import cont_obs_utils as cou
from optcont_main import drivcav_fems
dolfin.parameters.linear_algebra_backend = "uBLAS"
N = 20
mesh = dolfin.UnitSquareMesh(N, N)
V = dolfin.VectorFunctionSpace(mesh, "CG", 2)
NY = 8
odcoo = dict(xmin=0.45,
xmax=0.55,
ymin=0.6,
ymax=0.8)
# get the system matrices
femp = drivcav_fems(N)
stokesmats = dtn.get_stokessysmats(femp['V'], femp['Q'], nu=1)
# remove the freedom in the pressure
stokesmats['J'] = stokesmats['J'][:-1, :][:, :]
stokesmats['JT'] = stokesmats['JT'][:, :-1][:, :]
# reduce the matrices by resolving the BCs
# (stokesmatsc,
# rhsd_stbc,
# invinds,
# bcinds,
# bcvals) = dtn.condense_sysmatsbybcs(stokesmats, femp['diribcs'])
# check the C
MyC, My = cou.get_mout_opa(odcoo=odcoo, V=V, NY=NY)
# exv = dolfin.Expression(('x[1]', 'x[1]'))
import sympy as smp
x, y = smp.symbols('x[0], x[1]')
u_x = x * x * (1 - x) * (1 - x) * 2 * y * (1 - y) * (2 * y - 1)
u_y = y * y * (1 - y) * (1 - y) * 2 * x * (1 - x) * (1 - 2 * x)
from sympy.printing import ccode
exv = dolfin.Expression((ccode(u_x), ccode(u_y)))
testv = dolfin.interpolate(exv, V)
# plot(testv)
# the right inverse to C
Cplus = cou.get_rightinv(MyC)
self.assertTrue(np.allclose(np.eye(MyC.shape[0]), MyC * Cplus))
# MyCc = MyC[:, invinds]
ptmct = lau.app_prj_via_sadpnt(amat=stokesmats['M'],
jmat=stokesmats['J'],
rhsv=MyC.T,
transposedprj=True)
testvi = testv.vector().array()
testvi0 = np.atleast_2d(testv.vector().array()).T
testvi0 = lau.app_prj_via_sadpnt(amat=stokesmats['M'],
jmat=stokesmats['J'],
rhsv=testvi0)
# check if divfree part is not zero
self.assertTrue(np.linalg.norm(testvi0) > 1e-8,
msg='maybe nothing wrong, but this shouldnt be zero')
testyv0 = np.atleast_2d(MyC * testvi0).T
testry = np.dot(ptmct.T, testvi)
self.assertTrue(np.allclose(testyv0, testry))
