def test_outopa_workingconfig(self):
""" The innerproducts that assemble the output operator
are accurately sampled for this parameter set (NV=25, NY=5)"""
NV = 25
NY = 5
mesh = dolfin.UnitSquareMesh(NV, NV)
V = dolfin.VectorFunctionSpace(mesh, "CG", 2)
exv = dolfin.Expression(('1', '1'))
testv = dolfin.interpolate(exv, V)
odcoo = dict(xmin=0.45,
xmax=0.55,
ymin=0.6,
ymax=0.8)
# check the C
MyC, My = cou.get_mout_opa(odcoo=odcoo, V=V, NY=NY, NV=NV)
# signal space
ymesh = dolfin.IntervalMesh(NY - 1, odcoo['ymin'], odcoo['ymax'])
Y = dolfin.FunctionSpace(ymesh, 'CG', 1)
y1 = dolfin.Function(Y)
y2 = dolfin.Function(Y)
testvi = testv.vector().array()
testy = spsla.spsolve(My, MyC * testvi)
y1 = dolfin.Expression('1')
y1 = dolfin.interpolate(y1, Y)
y2 = dolfin.Function(Y)
y2.vector().set_local(testy[NY:])
self.assertTrue(dolfin.errornorm(y2, y1) < 1e-14)
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))