def _gramians(self):
A, B, C, E = (getattr(self.fom, op).assemble(mu=self.mu)
for op in ['A', 'B', 'C', 'E'])
if isinstance(E, IdentityOperator):
E = None
options = self.solver_options
cf = solve_pos_ricc_lrcf(
A,
E,
B.as_range_array(),
C.as_source_array(),
R=self.gamma**2 *
np.eye(self.fom.output_dim) if self.gamma != 1 else None,
trans=False,
options=options)
of = solve_pos_ricc_lrcf(
A,
E,
B.as_range_array(),
C.as_source_array(),
R=self.gamma**2 *
np.eye(self.fom.input_dim) if self.gamma != 1 else None,
trans=True,
options=options)
return cf, of
def _gramians(self):
A = self.fom.A
B = self.fom.B
C = self.fom.C
E = self.fom.E if not isinstance(self.fom.E,
IdentityOperator) else None
options = self.solver_options
cf = solve_pos_ricc_lrcf(
A,
E,
B.as_range_array(),
C.as_source_array(),
R=self.gamma**2 *
np.eye(self.fom.output_dim) if self.gamma != 1 else None,
trans=False,
options=options)
of = solve_pos_ricc_lrcf(
A,
E,
B.as_range_array(),
C.as_source_array(),
R=self.gamma**2 *
np.eye(self.fom.input_dim) if self.gamma != 1 else None,
trans=True,
options=options)
return cf, of
def _gramians(self):
A = self.fom.A
B = self.fom.B
C = self.fom.C
E = self.fom.E if not isinstance(self.fom.E, IdentityOperator) else None
options = self.solver_options
cf = solve_pos_ricc_lrcf(A, E, B.as_range_array(), C.as_source_array(),
R=self.gamma**2 * np.eye(self.fom.output_dim) if self.gamma != 1 else None,
trans=False, options=options)
of = solve_pos_ricc_lrcf(A, E, B.as_range_array(), C.as_source_array(),
R=self.gamma**2 * np.eye(self.fom.input_dim) if self.gamma != 1 else None,
trans=True, options=options)
return cf, of
def test_pos_ricc_lrcf(n, m, p, with_E, with_R, with_S, trans, solver):
_check_availability(solver)
if not with_E:
A = conv_diff_1d_fd(n, 1, 1)
E = None
else:
A, E = conv_diff_1d_fem(n, 1, 1)
np.random.seed(0)
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
if not trans:
R0 = np.random.randn(p, p)
R = D.dot(D.T) + 10 * R0.dot(R0.T) if with_R else None
S = B.dot(D.T) if with_S else None
else:
R0 = np.random.randn(m, m)
R = D.T.dot(D) + 10 * R0.dot(R0.T) if with_R else None
S = C.T.dot(D) if with_S else None
Aop = NumpyMatrixOperator(A)
Eop = NumpyMatrixOperator(E) if with_E else None
Bva = Aop.source.from_numpy(B.T)
Cva = Aop.source.from_numpy(C)
Sva = Aop.source.from_numpy(S.T) if with_S else None
Zva = solve_pos_ricc_lrcf(Aop, Eop, Bva, Cva, R, Sva, trans=trans, options=solver)
assert len(Zva) <= n
Z = Zva.to_numpy().T
if not with_R:
R = np.eye(p if not trans else m)
assert relative_residual(A, E, B, C, -R, S, Z, trans) < 1e-8
def test_pos_ricc_lrcf(n, m, p, with_E, with_R, with_S, trans, solver):
_check_availability(solver)
if not with_E:
A = conv_diff_1d_fd(n, 1, 1)
E = None
else:
A, E = conv_diff_1d_fem(n, 1, 1)
np.random.seed(0)
B = np.random.randn(n, m)
C = np.random.randn(p, n)
D = np.random.randn(p, m)
if not trans:
R0 = np.random.randn(p, p)
R = D.dot(D.T) + 10 * R0.dot(R0.T) if with_R else None
S = B.dot(D.T) if with_S else None
else:
R0 = np.random.randn(m, m)
R = D.T.dot(D) + 10 * R0.dot(R0.T) if with_R else None
S = C.T.dot(D) if with_S else None
Aop = NumpyMatrixOperator(A)
Eop = NumpyMatrixOperator(E) if with_E else None
Bva = Aop.source.from_numpy(B.T)
Cva = Aop.source.from_numpy(C)
Sva = Aop.source.from_numpy(S.T) if with_S else None
Zva = solve_pos_ricc_lrcf(Aop,
Eop,
Bva,
Cva,
R,
Sva,
trans=trans,
options=solver)
assert len(Zva) <= n
Z = Zva.to_numpy().T
if not with_R:
R = np.eye(p if not trans else m)
assert relative_residual(A, E, B, C, -R, S, Z, trans) < 1e-8