def comp_proj_lyap_res_norm(Z, amat=None, mmat=None, wmat=None,
jmat=None, umat=None, vmat=None, Sinv=None):
"""compute the squared f norm of projected lyap residual
res = Pt*[ Ft*ZZt*M + Mt*ZZt*M + W*Wt ]*P
"""
if Z.shape[1] >= Z.shape[0]:
raise Warning('TODO: catch cases where Z has more cols than rows')
if Sinv is None:
Mlu = spsla.factorized(mmat)
MinvJt = lau.app_luinv_to_spmat(Mlu, jmat.T)
Sinv = np.linalg.inv(jmat * MinvJt)
def _app_pt(Z, jmat, MinvJt, Sinv):
return Z - jmat.T * np.dot(Sinv, np.dot(MinvJt.T, Z))
if umat is None and vmat is None:
amattZ = amat.T * Z
else:
amattZ = amat.T*Z - lau.comp_uvz_spdns(vmat.T, umat.T, Z)
PtFtZ = _app_pt(amattZ, jmat, MinvJt, Sinv)
PtMtZ = _app_pt(mmat.T * Z, jmat, MinvJt, Sinv)
PtW = _app_pt(wmat, jmat, MinvJt, Sinv)
return lau.comp_sqfnrm_factrd_lyap_res(PtMtZ, PtFtZ, PtW)
def setUp(self):
self.NV = 200
self.NP = 40
self.NY = 5
self.NU = self.NY + 3
self.verbose = False
self.comprthresh = 1e-6 # threshhold for SVD trunc. for compr. of Z
self.nwtn_adi_dict = dict(adi_max_steps=300,
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=self.verbose)
# -F, M spd -- coefficient matrices
self.F = -sps.eye(self.NV) - \
sps.rand(self.NV, self.NV) * sps.rand(self.NV, self.NV)
self.M = sps.eye(self.NV) + \
sps.rand(self.NV, self.NV) * sps.rand(self.NV, self.NV)
try:
self.Mlu = spsla.factorized(self.M.tocsc())
except RuntimeError:
print 'M is not full rank'
# bmatrix that appears in the nonliner ric term X*B*B.T*X
self.bmat = np.random.randn(self.NV, self.NU)
# right-handside: C= -W*W.T
self.W = np.random.randn(self.NV, self.NY)
# smw formula Asmw = A - UV
self.U = 1e-4 * np.random.randn(self.NV, self.NY)
self.Usp = 1e-4 * sps.rand(self.NV, self.NY)
self.V = np.random.randn(self.NY, self.NV)
self.uvs = sps.csr_matrix(np.dot(self.U, self.V))
self.uvssp = sps.csr_matrix(self.Usp * self.V)
# initial value for newton adi
self.Z0 = np.random.randn(self.NV, self.NY)
# we need J sparse and of full rank
for auxk in range(10):
try:
self.J = sps.rand(self.NP, self.NV, density=0.03, format='csr')
spsla.splu((self.J * self.J.T).tocsc())
break
except RuntimeError:
if self.verbose:
print 'J not full row-rank.. I make another try'
try:
spsla.splu((self.J * self.J.T).tocsc())
except RuntimeError:
raise Warning('Fail: J is not full rank')
# the Leray projector
MinvJt = lau.app_luinv_to_spmat(self.Mlu, self.J.T)
Sinv = np.linalg.inv(self.J * MinvJt)
self.P = np.eye(self.NV) - np.dot(MinvJt, Sinv * self.J)
def test_luinv_to_spmat_complex(self):
"""check the application of the inverse
of a lu-factored matrix to a sparse mat"""
alusolve = spsla.factorized(self.A)
Z = sps.csr_matrix(self.U+1j*self.V.T)
AinvZ = lau.app_luinv_to_spmat(alusolve, Z)
self.assertTrue(np.allclose(Z.todense(), self.A * AinvZ))
def test_luinv_to_spmat_complex(self):
"""check the application of the inverse
of a lu-factored matrix to a sparse mat"""
alusolve = spsla.factorized(self.A)
Z = sps.csr_matrix(self.U + 1j * self.V.T)
AinvZ = lau.app_luinv_to_spmat(alusolve, Z)
self.assertTrue(np.allclose(Z.todense(), self.A * AinvZ))
def setUp(self):
self.NV = 200
self.NP = 40
self.NY = 5
self.NU = self.NY+3
self.verbose = False
self.comprthresh = 1e-6 # threshhold for SVD trunc. for compr. of Z
self.nwtn_adi_dict = dict(adi_max_steps=300,
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=self.verbose)
# -F, M spd -- coefficient matrices
self.F = -sps.eye(self.NV) - \
sps.rand(self.NV, self.NV) * sps.rand(self.NV, self.NV)
self.M = sps.eye(self.NV) + \
sps.rand(self.NV, self.NV) * sps.rand(self.NV, self.NV)
try:
self.Mlu = spsla.factorized(self.M.tocsc())
except RuntimeError:
print 'M is not full rank'
# bmatrix that appears in the nonliner ric term X*B*B.T*X
self.bmat = np.random.randn(self.NV, self.NU)
# right-handside: C= -W*W.T
self.W = np.random.randn(self.NV, self.NY)
# smw formula Asmw = A - UV
self.U = 1e-4 * np.random.randn(self.NV, self.NY)
self.Usp = 1e-4 * sps.rand(self.NV, self.NY)
self.V = np.random.randn(self.NY, self.NV)
self.uvs = sps.csr_matrix(np.dot(self.U, self.V))
self.uvssp = sps.csr_matrix(self.Usp * self.V)
# initial value for newton adi
self.Z0 = np.random.randn(self.NV, self.NY)
# we need J sparse and of full rank
for auxk in range(10):
try:
self.J = sps.rand(self.NP, self.NV,
density=0.03, format='csr')
spsla.splu((self.J * self.J.T).tocsc())
break
except RuntimeError:
if self.verbose:
print 'J not full row-rank.. I make another try'
try:
spsla.splu((self.J * self.J.T).tocsc())
except RuntimeError:
raise Warning('Fail: J is not full rank')
# the Leray projector
MinvJt = lau.app_luinv_to_spmat(self.Mlu, self.J.T)
Sinv = np.linalg.inv(self.J * MinvJt)
self.P = np.eye(self.NV) - np.dot(MinvJt, Sinv * self.J)
