def test_proj_lyap_smw_transposeflag(self):
"""check the solution of the projected lyap eqn
via ADI iteration"""
U = self.U
V = self.V
Z = pru.solve_proj_lyap_stein(amat=self.F, mmat=self.M,
umat=U, vmat=V,
jmat=self.J, wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
Z2 = pru.solve_proj_lyap_stein(amat=self.F - self.uvs, mmat=self.M,
jmat=self.J, wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
Z3 = pru.solve_proj_lyap_stein(amat=self.F.T-self.uvs.T, mmat=self.M.T,
jmat=self.J, wmat=self.W,
adi_dict=self.nwtn_adi_dict,
transposed=True)['zfac']
Z4 = pru.solve_proj_lyap_stein(amat=self.F.T, mmat=self.M.T,
jmat=self.J, wmat=self.W,
umat=U, vmat=V,
adi_dict=self.nwtn_adi_dict,
transposed=True)['zfac']
# TEST: {smw} x {transposed}
self.assertTrue(np.allclose(Z, Z2))
self.assertTrue(np.allclose(Z2, Z3))
self.assertTrue(np.allclose(Z3, Z4))
self.assertTrue(np.allclose(Z, Z4))
def test_proj_lyap_sol(self):
"""check the solution of the projected lyap eqn
via ADI iteration"""
Z = pru.solve_proj_lyap_stein(amat=self.F, mmat=self.M,
umat=self.U, vmat=self.V,
jmat=self.J, wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
MtXM = self.M.T * np.dot(Z, Z.T) * self.M
FtXM = (self.F.T - self.uvs.T) * np.dot(Z, Z.T) * self.M
PtW = np.dot(self.P.T, self.W)
ProjRes = np.dot(self.P.T, np.dot(FtXM, self.P)) + \
np.dot(np.dot(self.P.T, FtXM.T), self.P) + \
np.dot(PtW, PtW.T)
# TEST: result is 'projected'
self.assertTrue(np.allclose(MtXM,
np.dot(self.P.T, np.dot(MtXM, self.P))))
# TEST: check projected residual
self.assertTrue(np.linalg.norm(ProjRes) / np.linalg.norm(MtXM)
< 1e-8)
def test_proj_lyap_sol(self):
"""check the solution of the projected lyap eqn
via ADI iteration"""
Z = pru.solve_proj_lyap_stein(amat=self.F,
mmat=self.M,
umat=self.U,
vmat=self.V,
jmat=self.J,
wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
MtXM = self.M.T * np.dot(Z, Z.T) * self.M
FtXM = (self.F.T - self.uvs.T) * np.dot(Z, Z.T) * self.M
PtW = np.dot(self.P.T, self.W)
ProjRes = np.dot(self.P.T, np.dot(FtXM, self.P)) + \
np.dot(np.dot(self.P.T, FtXM.T), self.P) + \
np.dot(PtW, PtW.T)
# TEST: result is 'projected'
self.assertTrue(
np.allclose(MtXM, np.dot(self.P.T, np.dot(MtXM, self.P))))
# TEST: check projected residual
self.assertTrue(np.linalg.norm(ProjRes) / np.linalg.norm(MtXM) < 1e-8)
def test_proj_lyap_smw_transposeflag(self):
"""check the solution of the projected lyap eqn
via ADI iteration"""
U = self.U
V = self.V
Z = pru.solve_proj_lyap_stein(amat=self.F,
mmat=self.M,
umat=U,
vmat=V,
jmat=self.J,
wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
Z2 = pru.solve_proj_lyap_stein(amat=self.F - self.uvs,
mmat=self.M,
jmat=self.J,
wmat=self.W,
adi_dict=self.nwtn_adi_dict)['zfac']
Z3 = pru.solve_proj_lyap_stein(amat=self.F.T - self.uvs.T,
mmat=self.M.T,
jmat=self.J,
wmat=self.W,
adi_dict=self.nwtn_adi_dict,
transposed=True)['zfac']
Z4 = pru.solve_proj_lyap_stein(amat=self.F.T,
mmat=self.M.T,
jmat=self.J,
wmat=self.W,
umat=U,
vmat=V,
adi_dict=self.nwtn_adi_dict,
transposed=True)['zfac']
# TEST: {smw} x {transposed}
self.assertTrue(np.allclose(Z, Z2))
self.assertTrue(np.allclose(Z2, Z3))
self.assertTrue(np.allclose(Z3, Z4))
self.assertTrue(np.allclose(Z, Z4))