def test_backward_sub():
q, r, s = map(lambda x: Tensor(x, rank=1), 'qrs')
s_t = Transpose(s)
delta = Tensor('delta', rank=0)
eqn1 = r - s - q * delta
eqn2 = s_t * r
sol_dict, failed_var = backward_sub([eqn1, eqn2], [q, s], [r, delta])
print sol_dict, failed_var
sol_dict, failed_var = backward_sub([eqn1, eqn2], [q, s], [delta, r])
print sol_dict, failed_var
def test_overdetermined_back_sub():
pi_1, pi_2, mu_12 = \
map(lambda x: Tensor(x, rank=0),
['pi_1', 'pi_2', 'mu_12'])
r_2, p_1, p_2 = \
map(lambda x: Tensor(x, rank=1),
['r_2', 'p_1', 'p_2'])
A = Tensor('A', rank=2)
eqns = [ pi_2 - T(r_2) * A * r_2 + T(mu_12) * pi_1 * mu_12,
p_2 - r_2 + p_1 * mu_12,
pi_2 - T(p_2) * A * p_2,
]
return backward_sub(eqns, [r_2, p_1, mu_12, A, pi_1], multiple_sols=True)
def cg_demo_eqns():
D_00, J_00, I_00, U_00, X_0 = map(lambda x: Tensor(x, rank=2),
["D_00", "J_00", "I_00", "U_00", "X_0"])
j_10, u_01, u_02 = map(lambda x: Tensor(x, rank=1),
["j_10", "u_01", "u_02"])
delta_11, su_12 = map(lambda x: Tensor(x, rank=0), ["delta_11", "su_12"])
cg_2 = [ \
r_1 * T(j_10) - R_0 * (-J_00 + I_00) + A * P_0 * D_00,
- r_1 - r_2 + delta_11 * A * p_1,
P_0 * D_00 + x_1 * T(j_10) - X_0 * (-J_00 + I_00),
- x_1 - x_2 + delta_11 * p_1,
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
- r_2 - P_0 * u_02 - su_12 * p_1 + p_2,
T(R_0) * r_2,
(T(r_1) * r_2),
T(r_2) * R_0,
(T(r_2) * r_1),
T(P_0) * A * p_2,
(T(p_1) * A * p_2),
- R_0 * (-J_00 + I_00) - r_1 * T(j_10) + A * P_0 * D_00,
P_0 * D_00 - X_0 * (-J_00 + I_00) - x_1 * T(j_10),
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
T(R_0) * r_1,
T(r_1) * R_0,
T(P_0) * A * p_1,
]
cg_2 = [ \
r_1 * T(j_10) - R_0 * (-J_00 + I_00) + A * P_0 * D_00,
- r_1 - r_2 + delta_11 * A * p_1,
P_0 * D_00 + x_1 * T(j_10) - X_0 * (-J_00 + I_00),
- x_1 - x_2 + delta_11 * p_1,
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
- r_2 - P_0 * u_02 - su_12 * p_1 + p_2,
T(R_0) * r_2,
(T(r_1) * r_2),
T(r_2) * R_0,
(T(r_2) * r_1),
T(P_0) * A * p_2,
(T(p_1) * A * p_2),
- R_0 * (-J_00 + I_00) - r_1 * T(j_10) + A * P_0 * D_00,
P_0 * D_00 - X_0 * (-J_00 + I_00) - x_1 * T(j_10),
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
T(R_0) * r_1,
T(r_1) * R_0,
T(P_0) * A * p_1,
]
knowns = set(
[U_00, p_1, X_0, u_01, x_1, I_00, j_10, D_00, R_0, r_1, A, P_0, J_00])
unknowns = [p_2, su_12, u_02, x_2, r_2, delta_11]
unknowns1 = [r_2, delta_11, p_2, su_12, x_2, u_02]
unknowns2 = [p_2, su_12, r_2, delta_11, x_2, u_02]
print("Solving for CG-Demo updates.")
# sols = all_back_sub(cg_2, knowns, levels= -1)
# print "solve_vec_eqn(T(P_0)*A*r_2 + T(P_0)*A*P_0*u_02, u_02)"
# print solve_vec_eqn(T(P_0) * A * r_2 + T(P_0) * A * P_0 * u_02, u_02)
# print_sols(sols)
sol = backward_sub(cg_2, knowns, unknowns1, False, False)
print "Sol:", pprint.pformat(sol)
def test_cyclic_solve ():
a, b = map(lambda x: Tensor(x, rank=0), 'ab')
assert(backward_sub([a + b], [], [a, b]) == (None, b))
def cg_demo_eqns ():
D_00, J_00, I_00, U_00, X_0 = map(lambda x: Tensor(x, rank=2),
["D_00", "J_00", "I_00", "U_00", "X_0"])
j_10, u_01, u_02 = map(lambda x: Tensor(x, rank=1),
["j_10", "u_01", "u_02"])
delta_11, su_12 = map(lambda x: Tensor(x, rank=0),
["delta_11", "su_12"])
cg_2 = [ \
r_1 * T(j_10) - R_0 * (-J_00 + I_00) + A * P_0 * D_00,
- r_1 - r_2 + delta_11 * A * p_1,
P_0 * D_00 + x_1 * T(j_10) - X_0 * (-J_00 + I_00),
- x_1 - x_2 + delta_11 * p_1,
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
- r_2 - P_0 * u_02 - su_12 * p_1 + p_2,
T(R_0) * r_2,
(T(r_1) * r_2),
T(r_2) * R_0,
(T(r_2) * r_1),
T(P_0) * A * p_2,
(T(p_1) * A * p_2),
- R_0 * (-J_00 + I_00) - r_1 * T(j_10) + A * P_0 * D_00,
P_0 * D_00 - X_0 * (-J_00 + I_00) - x_1 * T(j_10),
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
T(R_0) * r_1,
T(r_1) * R_0,
T(P_0) * A * p_1,
]
cg_2 = [ \
r_1 * T(j_10) - R_0 * (-J_00 + I_00) + A * P_0 * D_00,
- r_1 - r_2 + delta_11 * A * p_1,
P_0 * D_00 + x_1 * T(j_10) - X_0 * (-J_00 + I_00),
- x_1 - x_2 + delta_11 * p_1,
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
- r_2 - P_0 * u_02 - su_12 * p_1 + p_2,
T(R_0) * r_2,
(T(r_1) * r_2),
T(r_2) * R_0,
(T(r_2) * r_1),
T(P_0) * A * p_2,
(T(p_1) * A * p_2),
- R_0 * (-J_00 + I_00) - r_1 * T(j_10) + A * P_0 * D_00,
P_0 * D_00 - X_0 * (-J_00 + I_00) - x_1 * T(j_10),
- R_0 + P_0 * (-U_00 + I_00),
- r_1 - P_0 * u_01 + p_1,
T(R_0) * r_1,
T(r_1) * R_0,
T(P_0) * A * p_1,
]
knowns = set([U_00, p_1, X_0, u_01, x_1, I_00, j_10, D_00, R_0, r_1, A,
P_0, J_00 ])
unknowns = [p_2, su_12, u_02, x_2, r_2, delta_11]
unknowns1 = [r_2, delta_11, p_2, su_12, x_2, u_02]
unknowns2 = [p_2, su_12, r_2, delta_11, x_2, u_02]
print("Solving for CG-Demo updates.")
# sols = all_back_sub(cg_2, knowns, levels= -1)
# print "solve_vec_eqn(T(P_0)*A*r_2 + T(P_0)*A*P_0*u_02, u_02)"
# print solve_vec_eqn(T(P_0) * A * r_2 + T(P_0) * A * P_0 * u_02, u_02)
# print_sols(sols)
sol = backward_sub(cg_2, knowns, unknowns1, False, False)
print "Sol:", pprint.pformat(sol)
