def get_admissible_projectors(dae_auto):
'get admissible projectors for the autonomous dae system'
adm_projs, _, _, _ = admissible_projectors(dae_auto.matrix_e.todense(),
dae_auto.matrix_a.todense())
print "\nadmissible projectors:"
print "\nadm_projs = {}".format(adm_projs)
print "\nQ0 = {}".format(adm_projs[0])
return adm_projs
def get_decoupled_system(self, auto_dae_automaton):
'get decoupled system from an dae automaton'
assert isinstance(auto_dae_automaton, AutonomousDaeAutomation)
matrix_e = auto_dae_automaton.matrix_e.todense()
matrix_a = auto_dae_automaton.matrix_a.todense()
matrix_c = auto_dae_automaton.matrix_c.todense()
n = matrix_a.shape[0]
In = np.eye(n, dtype=float)
adm_projs, E_list, A_list, _ = admissible_projectors(
matrix_e, matrix_a)
if adm_projs == 'error':
print "\nerror: dae system has index larger than 3"
self.status = 'error'
else:
assert isinstance(
adm_projs, list), 'error: not a list of admissible projectors'
ind = len(adm_projs)
if ind == 1:
decoupled_sys = AutonomousDecoupledIndexOne()
Q0 = adm_projs[0]
P0 = In - Q0
A0 = A_list[0]
E1_inv = np.linalg.inv(E_list[1])
E1_inv_A0 = np.dot(E1_inv, A0)
N1 = np.dot(P0, E1_inv_A0) # ode part
N2 = np.dot(Q0, E1_inv_A0) # alg part
decoupled_sys.set_dynamics(N1, N2, matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
elif ind == 2:
decoupled_sys = AutonomousDecoupledIndexTwo()
Q0 = adm_projs[0]
Q1 = adm_projs[1]
P0 = In - Q0
P1 = In - Q1
P0_P1 = np.dot(P0, P1)
A2 = A_list[2]
E2_inv = np.linalg.inv(E_list[2])
E2_inv_A2 = np.dot(E2_inv, A2)
N1 = np.dot(P0_P1, E2_inv_A2) # ode part
N2 = np.dot(P0, np.dot(Q1, E2_inv_A2)) # alg1 part
# alg2 part
Q0_P1 = np.dot(Q0, P1)
N3 = np.dot(Q0_P1, E2_inv_A2)
L3 = np.dot(Q0, Q1)
decoupled_sys.set_dynamics(N1, N2, N3, L3, matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
elif ind == 3:
decoupled_sys = AutonomousDecoupledIndexThree()
Q0 = adm_projs[0]
Q1 = adm_projs[1]
Q2 = adm_projs[2]
P0 = In - Q0
P1 = In - Q1
P2 = In - Q2
A0 = matrix_a
P0_P1_P2 = np.dot(P0, np.dot(P1, P2))
A3 = A_list[3]
E3_inv = np.linalg.inv(E_list[3])
E3_inv_A3 = np.dot(E3_inv, A3)
# ode part
N1 = np.dot(P0_P1_P2, E3_inv_A3)
# alg1 part
P0_P1_Q2 = np.dot(P0, np.dot(P1, Q2))
N2 = np.dot(P0_P1_Q2, E3_inv_A3)
# alg2 part
P0_Q1_P2 = np.dot(P0, np.dot(Q1, P2))
N3 = np.dot(P0_Q1_P2, E3_inv_A3)
L3 = np.dot(P0, np.dot(Q1, Q2))
# alg3 part
Q0_P1_P2 = np.dot(Q0, np.dot(P1, P2))
N4 = np.dot(Q0_P1_P2, E3_inv_A3)
L4 = np.dot(Q0, Q1)
Z4 = np.dot(Q0, np.dot(P1, Q2))
decoupled_sys.set_dynamics(N1, N2, N3, L3, N4, L4, Z4,
matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
# print decoupling result
print "\ndecoupling status = {}".format(self.status)
if self.status == 'success':
if ind == 1:
print "\nsystem is index 1"
print "\ndecoupled dae_auto: N1 = {}".format(decoupled_sys.N1)
print "\nnorm of N1 = {}".format(
np.linalg.norm(decoupled_sys.N1))
print "\ndecoupled dae_auto: N2 = {}".format(decoupled_sys.N2)
print "\nnorm of N2 = {}".format(
np.linalg.norm(decoupled_sys.N2))
if ind == 2:
print "\nsystem is index 2"
print "\ndecoupled dae_auto: N1 = {}".format(decoupled_sys.N1)
print "\nnorm of N1 = {}".format(
np.linalg.norm(decoupled_sys.N1))
print "\ndecoupled dae_auto: N2 = {}".format(decoupled_sys.N2)
print "\nnorm of N2 = {}".format(
np.linalg.norm(decoupled_sys.N2))
print "\ndecoupled dae_auto: N3 = {}".format(decoupled_sys.N3)
print "\nnorm of N3 = {}".format(
np.linalg.norm(decoupled_sys.N3))
print "\ndecoupled dae_auto: L3 = {}".format(decoupled_sys.L3)
print "\nnorm of L3 = {}".format(
np.linalg.norm(decoupled_sys.L3))
if ind == 3:
print "\nsystem is index 3"
print "\ndecoupled dae_auto: N1 = {}".format(decoupled_sys.N1)
print "\nnorm of N1 = {}".format(
np.linalg.norm(decoupled_sys.N1))
print "\ndecoupled dae_auto: N2 = {}".format(decoupled_sys.N2)
print "\nnorm of N2 = {}".format(
np.linalg.norm(decoupled_sys.N2))
print "\ndecoupled dae_auto: N3 = {}".format(decoupled_sys.N3)
print "\nnorm of N3 = {}".format(
np.linalg.norm(decoupled_sys.N3))
print "\ndecoupled dae_auto: L3 = {}".format(decoupled_sys.L3)
print "\nnorm of L3 = {}".format(
np.linalg.norm(decoupled_sys.L3))
print "\ndecoupled dae_auto: N4 = {}".format(decoupled_sys.N4)
print "\nnorm of N4 = {}".format(
np.linalg.norm(decoupled_sys.N4))
print "\ndecoupled dae_auto: L4 = {}".format(decoupled_sys.L4)
print "\nnorm of L4 = {}".format(
np.linalg.norm(decoupled_sys.L4))
print "\ndecoupled dae_auto: Z4 = {}".format(decoupled_sys.Z4)
print "\nnorm of Z4 = {}".format(
np.linalg.norm(decoupled_sys.Z4))
return self.decoupled_sys, self.status
def get_decoupled_system(self, dae_automaton):
'get decoupled system from an dae automaton'
assert isinstance(dae_automaton, DaeAutomation)
matrix_e = dae_automaton.matrix_e.todense()
matrix_a = dae_automaton.matrix_a.todense()
matrix_b = dae_automaton.matrix_b.todense()
print "\nmatrix_b = {}".format(matrix_b)
matrix_c = dae_automaton.matrix_c.todense()
print "\nmatrix_c = {}".format(matrix_c)
n = matrix_a.shape[0]
In = np.eye(n, dtype=float)
adm_projs, E_list, A_list, _ = admissible_projectors(
matrix_e, matrix_a)
if adm_projs == 'error':
print "\nerror: dae system has index larger than 3"
self.status = 'error'
else:
assert isinstance(
adm_projs, list), 'error: not a list of admissible projectors'
ind = len(adm_projs)
if ind == 1:
decoupled_sys = DecoupledIndexOne()
Q0 = adm_projs[0]
P0 = In - Q0
E1_inv = np.linalg.inv(E_list[1])
A0 = A_list[0]
E1_inv_A0 = np.dot(E1_inv, A0)
E1_inv_B = np.dot(E1_inv, matrix_b)
# ode part
N1 = np.dot(P0, E1_inv_A0)
M1 = np.dot(P0, E1_inv_B)
# alg part
N2 = np.dot(Q0, E1_inv_A0)
M2 = np.dot(Q0, E1_inv_B)
decoupled_sys.set_dynamics(N1, M1, N2, M2, matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
elif ind == 2:
decoupled_sys = DecoupledIndexTwo()
Q0 = adm_projs[0]
Q1 = adm_projs[1]
P0 = In - Q0
P1 = In - Q1
P0_P1 = np.dot(P0, P1)
E2_inv = np.linalg.inv(E_list[2])
A2 = A_list[2]
E2_inv_A2 = np.dot(E2_inv, A2)
E2_inv_B = np.dot(E2_inv, matrix_b)
# ode part
N1 = np.dot(P0_P1, E2_inv_A2)
M1 = np.dot(P0_P1, E2_inv_B)
# alg1 part
N2 = np.dot(P0, np.dot(Q1, E2_inv_A2))
M2 = np.dot(P0, np.dot(Q1, E2_inv_B))
# alg2 part
Q0_P1 = np.dot(Q0, P1)
N3 = np.dot(Q0_P1, E2_inv_A2)
M3 = np.dot(Q0_P1, E2_inv_B)
L3 = np.dot(Q0, Q1)
decoupled_sys.set_dynamics(N1, M1, N2, M2, N3, M3, L3,
matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
elif ind == 3:
decoupled_sys = DecoupledIndexThree()
Q0 = adm_projs[0]
Q1 = adm_projs[1]
Q2 = adm_projs[2]
P0 = In - Q0
P1 = In - Q1
P2 = In - Q2
P0_P1_P2 = np.dot(P0, np.dot(P1, P2))
A3 = A_list[3]
E3_inv = np.linalg.inv(E_list[3])
E3_inv_A3 = np.dot(E3_inv, A3)
E3_inv_B = np.dot(E3_inv, matrix_b)
# ode part
N1 = np.dot(P0_P1_P2, E3_inv_A3)
M1 = np.dot(P0_P1_P2, E3_inv_B)
# alg1 part
P0_P1_Q2 = np.dot(P0, np.dot(P1, Q2))
N2 = np.dot(P0_P1_Q2, E3_inv_A3)
M2 = np.dot(P0_P1_Q2, E3_inv_B)
# alg2 part
P0_Q1_P2 = np.dot(P0, np.dot(Q1, P2))
N3 = np.dot(P0_Q1_P2, E3_inv_A3)
M3 = np.dot(P0_Q1_P2, E3_inv_B)
L3 = np.dot(P0, np.dot(Q1, Q2))
# alg3 part
Q0_P1_P2 = np.dot(Q0, np.dot(P1, P2))
N4 = np.dot(Q0_P1_P2, E3_inv_A3)
M4 = np.dot(Q0_P1_P2, E3_inv_B)
L4 = np.dot(Q0, Q1)
Z4 = np.dot(Q0, np.dot(P1, Q2))
decoupled_sys.set_dynamics(N1, M1, N2, M2, N3, M3, L3, N4, M4,
L4, Z4, matrix_c)
decoupled_sys.set_projectors(adm_projs)
self.decoupled_sys = decoupled_sys
self.status = 'success'
return self.decoupled_sys, self.status