def check_input_opa(NU, femp=None):
if femp is None:
# from dolfin_navier_scipy.problem_setups import cyl_fems
# femp = cyl_fems(2)
from dolfin_navier_scipy.problem_setups import drivcav_fems
femp = drivcav_fems(20)
V = femp["V"]
Q = femp["Q"]
cdcoo = femp["cdcoo"]
# get the system matrices
stokesmats = dts.get_stokessysmats(V, Q)
# check the B
B1, Mu = cou.get_inp_opa(cdcoo=cdcoo, V=V, NU=NU, xcomp=0)
B2, Mu = cou.get_inp_opa(cdcoo=cdcoo, V=V, NU=NU, xcomp=1)
# get the rhs expression of Bu
Bu1 = spsla.spsolve(
stokesmats["M"],
B1 * np.vstack([np.linspace(0, 1, NU).reshape((NU, 1)), np.linspace(0, 1, NU).reshape((NU, 1))]),
)
Bu2 = spsla.spsolve(
stokesmats["M"],
B2 * np.vstack([np.linspace(0, 1, NU).reshape((NU, 1)), np.linspace(0, 1, NU).reshape((NU, 1))]),
)
Bu3 = spsla.spsolve(stokesmats["M"], B1 * np.vstack([1 * np.ones((NU, 1)), 0.2 * np.ones((NU, 1))]))
bu1 = dolfin.Function(V)
bu1.vector().set_local(Bu1)
bu1.vector()[2] = 1 # for scaling and illustration purposes
bu2 = dolfin.Function(V)
bu2.vector().set_local(Bu2)
bu2.vector()[2] = 1 # for scaling and illustration purposes
bu3 = dolfin.Function(V)
bu3.vector().set_local(Bu3)
bu3.vector()[2] = 1 # for scaling and illustration purposes
plt.figure(11)
dolfin.plot(bu1, title="plot of Bu - extending in x")
plt.figure(12)
dolfin.plot(bu2, title="plot of Bu - extending in y")
plt.figure(13)
dolfin.plot(bu3, title="plot of Bu - extending in y")
# dolfin.plot(V.mesh())
dolfin.interactive()
plt.show(block=False)
import numpy as np
import dolfin
import dolfin_navier_scipy.dolfin_to_sparrays as dts
import dolfin_navier_scipy.problem_setups as dnsps
N = 2
femp = dnsps.drivcav_fems(N)
mesh = dolfin.UnitSquareMesh(N, N)
stokesmats = dts.get_stokessysmats(femp['V'], femp['Q'])
# reduce the matrices by resolving the BCs
(stokesmatsc, rhsd_stbc, invinds, bcinds,
bcvals) = dts.condense_sysmatsbybcs(stokesmats, femp['diribcs'])
fv = dolfin.Constant(('0', '1'))
v = dolfin.interpolate(fv, femp['V'])
invals = np.zeros(invinds.size)
coorar, xinds, yinds, corvec = dts.get_dof_coors(femp['V'])
icoorar, ixinds, iyinds, icorvec = dts.get_dof_coors(femp['V'],
invinds=invinds)
invals[ixinds] = icoorar[:, 0]
# print coorar, xinds
# print icoorar, ixinds
# print v.vector().array()
def test_lyap_ress_compress(self):
"""comp of factrd lyap ress and compr of Z
"""
N = 15
NY = 5
verbose = True
k = None # sing vals to keep
thresh = 1e-6
nwtn_adi_dict = dict(adi_max_steps=250,
adi_newZ_reltol=1e-8,
nwtn_max_steps=24,
nwtn_upd_reltol=4e-8,
nwtn_upd_abstol=4e-8,
verbose=verbose)
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'])
M = stokesmatsc['M']
J = stokesmatsc['J']
NV = M.shape[0]
F = - stokesmatsc['M'] - 0.1*stokesmatsc['A'] - \
sps.rand(NV, NV, density=0.03, format='csr')
W = np.random.randn(NV, NY)
nwtn_adi_dict = dict(adi_max_steps=50,
adi_newZ_reltol=1e-11,
nwtn_max_steps=24,
nwtn_upd_reltol=4e-7,
nwtn_upd_abstol=4e-7,
full_upd_norm_check=True,
verbose=verbose)
Z = pru.solve_proj_lyap_stein(amat=F,
mmat=M,
jmat=J,
wmat=W,
adi_dict=nwtn_adi_dict)['zfac']
MtZ = M.T * Z
MtXM = np.dot(M.T * Z, Z.T * M)
FtXM = F.T * np.dot(Z, Z.T) * M
Mlu = spsla.factorized(M.tocsc())
MinvJt = lau.app_luinv_to_spmat(Mlu, J.T)
Sinv = np.linalg.inv(J * MinvJt)
P = np.eye(NV) - np.dot(MinvJt, Sinv * J)
PtW = np.dot(P.T, W)
ProjRes = np.dot(P.T, np.dot(FtXM, P)) + \
np.dot(np.dot(P.T, FtXM.T), P) + \
np.dot(PtW, PtW.T)
resn = np.linalg.norm(ProjRes)
ownresn = np.sqrt(pru.comp_proj_lyap_res_norm(Z, F, M, W, J))
# test smart fnorm comp
self.assertTrue((np.allclose(np.linalg.norm(MtXM),
np.linalg.norm(np.dot(MtZ.T, MtZ)))))
# test smart comp of ress
self.assertTrue(np.allclose(resn, ownresn))
# reduction of Z
Zred = pru.compress_Zsvd(Z, k=k, thresh=thresh, shplot=True)
MtZr = M.T * Zred
MtXMr = np.dot(MtZr, MtZr.T)
# TEST: reduction is 'projected'
self.assertTrue((np.allclose(MtXMr, np.dot(P.T, np.dot(MtXMr, P)))))
# TEST: diff in apprx
self.assertTrue(
np.allclose(np.linalg.norm(np.dot(MtZ.T, MtZ)),
np.linalg.norm(np.dot(MtZr.T, MtZr))))
# print 'norm of red res: ', np.linalg.norm(ProjRes)
ownresr = np.sqrt(pru.comp_proj_lyap_res_norm(Zred, F, M, W, J))
self.assertTrue(np.allclose(ownresr, resn))
def test_lyap_ress_compress(self):
"""comp of factrd lyap ress and compr of Z
"""
N = 15
NY = 5
verbose = True
k = None # sing vals to keep
thresh = 1e-6
nwtn_adi_dict = dict(adi_max_steps=250,
adi_newZ_reltol=1e-8,
nwtn_max_steps=24,
nwtn_upd_reltol=4e-8,
nwtn_upd_abstol=4e-8,
verbose=verbose)
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'])
M = stokesmatsc['M']
J = stokesmatsc['J']
NV = M.shape[0]
F = - stokesmatsc['M'] - 0.1*stokesmatsc['A'] - \
sps.rand(NV, NV, density=0.03, format='csr')
W = np.random.randn(NV, NY)
nwtn_adi_dict = dict(adi_max_steps=50,
adi_newZ_reltol=1e-11,
nwtn_max_steps=24,
nwtn_upd_reltol=4e-7,
nwtn_upd_abstol=4e-7,
full_upd_norm_check=True,
verbose=verbose)
Z = pru.solve_proj_lyap_stein(amat=F, mmat=M,
jmat=J, wmat=W,
adi_dict=nwtn_adi_dict)['zfac']
MtZ = M.T * Z
MtXM = np.dot(M.T*Z, Z.T*M)
FtXM = F.T * np.dot(Z, Z.T) * M
Mlu = spsla.factorized(M.tocsc())
MinvJt = lau.app_luinv_to_spmat(Mlu, J.T)
Sinv = np.linalg.inv(J * MinvJt)
P = np.eye(NV) - np.dot(MinvJt, Sinv * J)
PtW = np.dot(P.T, W)
ProjRes = np.dot(P.T, np.dot(FtXM, P)) + \
np.dot(np.dot(P.T, FtXM.T), P) + \
np.dot(PtW, PtW.T)
resn = np.linalg.norm(ProjRes)
ownresn = np.sqrt(pru.comp_proj_lyap_res_norm(Z, F, M, W, J))
# test smart fnorm comp
self.assertTrue((np.allclose(np.linalg.norm(MtXM),
np.linalg.norm(np.dot(MtZ.T, MtZ)))))
# test smart comp of ress
self.assertTrue(np.allclose(resn, ownresn))
# reduction of Z
Zred = pru.compress_Zsvd(Z, k=k, thresh=thresh, shplot=True)
MtZr = M.T * Zred
MtXMr = np.dot(MtZr, MtZr.T)
# TEST: reduction is 'projected'
self.assertTrue((np.allclose(MtXMr, np.dot(P.T, np.dot(MtXMr, P)))))
# TEST: diff in apprx
self.assertTrue(np.allclose(np.linalg.norm(np.dot(MtZ.T, MtZ)),
np.linalg.norm(np.dot(MtZr.T, MtZr))))
# print 'norm of red res: ', np.linalg.norm(ProjRes)
ownresr = np.sqrt(pru.comp_proj_lyap_res_norm(Zred, F, M, W, J))
self.assertTrue(np.allclose(ownresr, resn))
def check_output_opa(NY, femp=None):
if femp is None:
# from dolfin_navier_scipy.problem_setups import cyl_fems
# femp = cyl_fems(2)
from dolfin_navier_scipy.problem_setups import drivcav_fems
femp = drivcav_fems(20)
V = femp['V']
Q = femp['Q']
odcoo = femp['odcoo']
testcase = 2 # 1,2
# testvelocities
if testcase == 1:
"""case 1 -- not div free"""
exv = dolfin.Expression(('x[1]', 'x[1]'), element=V.ufl_element())
if testcase == 2:
"""case 2 -- disc div free"""
exv = dolfin.Expression(('1', '1'), element=V.ufl_element())
testv = dolfin.interpolate(exv, V)
odcoo = femp['odcoo']
stokesmats = dts.get_stokessysmats(V, Q, nu=1)
# remove the freedom in the pressure
stokesmats['J'] = stokesmats['J'][:-1, :][:, :]
stokesmats['JT'] = stokesmats['JT'][:, :-1][:, :]
bc = dolfin.DirichletBC(V, exv, 'on_boundary')
# reduce the matrices by resolving the BCs
(stokesmatsc,
rhsd_stbc,
invinds,
bcinds,
bcvals) = dts.condense_sysmatsbybcs(stokesmats, [bc])
# check the C
MyC, My = cou.get_mout_opa(odcoo=odcoo, V=V, NY=NY)
# MyC = MyC[:, invinds][:, :]
# 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)
# y3 = dolfin.Function(Y)
# dolfin.plot(V.mesh())
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)
print "||J*v|| = {0}".format(np.linalg.norm(stokesmats['J'] * testvi))
print "||J* v_df|| = {0}".format(np.linalg.norm(stokesmats['J'] * testvi0))
# # testsignals from the test velocities
testy = spsla.spsolve(My, MyC * testvi)
testyv0 = spsla.spsolve(My, MyC * testvi0)
# testyg = spsla.spsolve(My, MyC * (testvi.flatten() - testvi0))
testry = spsla.spsolve(My, np.dot(ptmct.T, testvi))
print "||C v_df - C_df v|| = {0}".format(np.linalg.norm(testyv0 - testry))
plt.figure(1)
y1.vector().set_local(testy[:NY])
dolfin.plot(y1, title="x-comp of C*v")
plt.figure(2)
y2.vector().set_local(testy[NY:])
dolfin.plot(y2, title="y-comp of C*v")
# y2.vector().set_local(testyv0[:NY])
# dolfin.plot(y2, title="x-comp of $C*(P_{df}v)$")
# y3.vector().set_local(testyg[:NY])
# dolfin.plot(y3, title="x-comp of $C*(v - P_{df}v)$")
plt.show(block=False)
import numpy as np
import dolfin
import dolfin_navier_scipy.dolfin_to_sparrays as dts
import dolfin_navier_scipy.problem_setups as dnsps
N = 2
femp = dnsps.drivcav_fems(N)
mesh = dolfin.UnitSquareMesh(N, N)
stokesmats = dts.get_stokessysmats(femp['V'], femp['Q'])
# reduce the matrices by resolving the BCs
(stokesmatsc,
rhsd_stbc,
invinds,
bcinds,
bcvals) = dts.condense_sysmatsbybcs(stokesmats,
femp['diribcs'])
fv = dolfin.Constant(('0', '1'))
v = dolfin.interpolate(fv, femp['V'])
invals = np.zeros(invinds.size)
coorar, xinds, yinds, corvec = dts.get_dof_coors(femp['V'])
icoorar, ixinds, iyinds, icorvec = dts.get_dof_coors(femp['V'],
invinds=invinds)
invals[ixinds] = icoorar[:, 0]
# print coorar, xinds