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 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))
