def test_compress_algric_Z(self):
Z = pru.proj_alg_ric_newtonadi(mmat=self.M, amat=self.F,
jmat=self.J, bmat=self.bmat,
wmat=self.W, z0=self.bmat,
nwtn_adi_dict=
self.nwtn_adi_dict)['zfac']
Zred = pru.compress_Zsvd(Z, thresh=self.comprthresh)
print '\ncompressing Z from {0} to {1} columns:'.\
format(Z.shape[1], Zred.shape[1])
difn, zzn, zzrn = \
lau.comp_sqfnrm_factrd_diff(Z, Zred, ret_sing_norms=True)
print '\n || ZZ - ZZred||_F || / ||ZZ|| = {0}\n'.\
format(np.sqrt(difn/zzn))
vec = np.random.randn(Z.shape[0], 1)
print '||(ZZ_red - ZZ )*testvec|| / ||ZZ*testvec|| = {0}'.\
format(np.linalg.norm(np.dot(Z, np.dot(Z.T, vec)) -
np.dot(Zred, np.dot(Zred.T, vec))) /
np.linalg.norm(np.dot(Zred, np.dot(Zred.T, vec))))
self.assertTrue(True)
def test_compress_algric_Z(self):
Z = pru.proj_alg_ric_newtonadi(
mmat=self.M,
amat=self.F,
jmat=self.J,
bmat=self.bmat,
wmat=self.W,
z0=self.bmat,
nwtn_adi_dict=self.nwtn_adi_dict)['zfac']
Zred = pru.compress_Zsvd(Z, thresh=self.comprthresh)
print '\ncompressing Z from {0} to {1} columns:'.\
format(Z.shape[1], Zred.shape[1])
difn, zzn, zzrn = \
lau.comp_sqfnrm_factrd_diff(Z, Zred, ret_sing_norms=True)
print '\n || ZZ - ZZred||_F || / ||ZZ|| = {0}\n'.\
format(np.sqrt(difn/zzn))
vec = np.random.randn(Z.shape[0], 1)
print '||(ZZ_red - ZZ )*testvec|| / ||ZZ*testvec|| = {0}'.\
format(np.linalg.norm(np.dot(Z, np.dot(Z.T, vec)) -
np.dot(Zred, np.dot(Zred.T, vec))) /
np.linalg.norm(np.dot(Zred, np.dot(Zred.T, vec))))
self.assertTrue(True)
def test_proj_alg_ric_sol(self):
"""check the sol of the projected alg. Riccati Eqn
via Newton ADI"""
Z = pru.proj_alg_ric_newtonadi(
mmat=self.M,
amat=self.F,
jmat=self.J,
bmat=self.bmat,
wmat=self.W,
z0=self.bmat,
nwtn_adi_dict=self.nwtn_adi_dict)['zfac']
# for '0' initial value --> z0 = None
Z0 = pru.proj_alg_ric_newtonadi(
mmat=self.M,
amat=self.F,
jmat=self.J,
bmat=self.bmat,
wmat=self.W,
nwtn_adi_dict=self.nwtn_adi_dict)['zfac']
MtXM = self.M.T * np.dot(Z, Z.T) * self.M
MtX0M = self.M.T * np.dot(Z0, Z0.T) * self.M
self.assertTrue(np.allclose(MtXM, MtX0M))
MtXb = self.M.T * np.dot(np.dot(Z, Z.T), self.bmat)
FtXM = self.F.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(MtXb, MtXb.T) + \
np.dot(PtW, PtW.T)
# TEST: result is 'projected' - riccati sol
self.assertTrue(
np.allclose(MtXM, np.dot(self.P.T, np.dot(MtXM, self.P))))
# TEST: check projected residual - riccati sol
print np.linalg.norm(ProjRes) / np.linalg.norm(MtXM)
self.assertTrue(np.linalg.norm(ProjRes) / np.linalg.norm(MtXM) < 1e-7)
def test_proj_alg_ric_sol(self):
"""check the sol of the projected alg. Riccati Eqn
via Newton ADI"""
Z = pru.proj_alg_ric_newtonadi(mmat=self.M, amat=self.F,
jmat=self.J, bmat=self.bmat,
wmat=self.W, z0=self.bmat,
nwtn_adi_dict=
self.nwtn_adi_dict)['zfac']
# for '0' initial value --> z0 = None
Z0 = pru.proj_alg_ric_newtonadi(mmat=self.M, amat=self.F,
jmat=self.J, bmat=self.bmat,
wmat=self.W,
nwtn_adi_dict=
self.nwtn_adi_dict)['zfac']
MtXM = self.M.T * np.dot(Z, Z.T) * self.M
MtX0M = self.M.T * np.dot(Z0, Z0.T) * self.M
self.assertTrue(np.allclose(MtXM, MtX0M))
MtXb = self.M.T * np.dot(np.dot(Z, Z.T), self.bmat)
FtXM = self.F.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(MtXb, MtXb.T) + \
np.dot(PtW, PtW.T)
# TEST: result is 'projected' - riccati sol
self.assertTrue(np.allclose(MtXM,
np.dot(self.P.T, np.dot(MtXM, self.P))))
# TEST: check projected residual - riccati sol
print np.linalg.norm(ProjRes) / np.linalg.norm(MtXM)
self.assertTrue(np.linalg.norm(ProjRes) / np.linalg.norm(MtXM)
< 1e-7)
