def test_vec_solve():
mu_12 = Tensor('mu_12', rank=0)
p_1, p_2 = map(lambda x: Tensor(x, rank=1), ['p_1', 'p_2'])
A = Tensor('A', rank=2)
print solve_vec_eqn(
-mu_12 * (T(p_1) * A * p_2) - mu_12 * (T(p_2) * A * p_1) +
(T(p_2) * A * p_1), mu_12)
def testZero():
A = Tensor('A', 2)
a = Tensor('a', 1)
alpha = Tensor('alpha', 0)
Z = Tensor('0', 2)
z = Tensor('0', 1)
z_0 = Tensor('0', 0)
assert(A + Z == A)
assert(Z + A == A)
assert(A * Z == Z)
assert(Z * A == Z)
assert(a + z == a)
assert(z + a == a)
assert(A * z == z)
assert(T(a) * z == z_0)
assert(T(z) * a == z_0)
assert(z * T(a) == Z)
assert(a * T(z) == Z)
assert(alpha + z_0 == alpha)
assert(alpha * z_0 == z_0)
assert(alpha * z == z)
assert(alpha * Z == Z)
assert(z_0 * A == Z)
assert(z_0 * a == z)
assert(A + z_0 == A)
assert(z_0 + A == A)
def get_chronos_eqns_1():
delta_1, omega_2, pi_1, pi_2, gamma_2, mu_12 = \
map(lambda x: Tensor(x, rank=0),
['delta_1', 'omega_2', 'pi_1', 'pi_2', 'gamma_2', 'mu_12'])
r_1, r_2, q_1, q_2, p_1, p_2, s_1, s_2 = \
map(lambda x: Tensor(x, rank=1),
['r_1', 'r_2', 'q_1', 'q_2', 'p_1', 'p_2', 's_1', 's_2'])
A, R_0, P_0 = map(lambda x: Tensor(x, rank=2), ['A', 'R_0', 'P_0'])
eqns = [
r_2 - r_1 - delta_1 * q_1,
q_2 - A * p_2,
p_2 - r_2 + p_1 * mu_12,
q_2 - A * r_2 + q_1 * mu_12,
omega_2 - T(r_2) * r_2,
pi_2 - T(p_2) * A * p_2,
T(R_0) * r_2,
T(r_1) * r_2,
T(P_0) * A * p_2,
T(p_1) * A * p_2,
T(p_2) * A * p_2 - T(r_2) * A * r_2 +
T(mu_12) * T(p_1) * A * p_1 * mu_12,
]
knowns = [p_1, r_1, q_1, pi_1, A, R_0, P_0]
return eqns, knowns
def test_latex_print():
assert (latex_print(-mu_12 * p_1 + r_2) == "-\mu_{12} p_1 + r_2")
assert (latex_print(delta_1 * A * p_1 + r_1) == "\delta_1 A p_1 + r_1")
assert (latex_print(delta_1 * p_1 + x_1) == "\delta_1 p_1 + x_1")
assert(latex_print((T(r_1) * r_1) / (T(r_1) * A * p_1)) == \
"{r_1}^t r_1 1.0 / ({p_1}^t A r_1)")
assert(latex_print((T(p_1) * A * r_2) / (T(p_1) * A * p_1)) == \
"{p_1}^t A r_2 1.0 / ({p_1}^t A p_1)")
def test_mul_inverse():
delta_11 = Tensor('delta_11', 0)
r_1, p_1 = map(lambda x: Tensor(x, 1), ['r_1', 'p_1'])
A = Tensor('A', 2)
a = Tensor('a', 0)
expr = (-(T(p_1)*A*p_1)*(T(p_1)*A*r_1)*a + (T(p_1)*A*r_1))
expr = expr.subs(a, (T(p_1)*A*p_1)**-1)
assert(simplify(expr) == S(0))
def test_numpy_print():
assert (numpy_print(-mu_12 * p_1 + r_2) == "-dot(mu_12, p_1) + r_2")
assert (numpy_print(delta_1 * A * p_1 +
r_1) == "dot(delta_1, dot(A, p_1)) + r_1")
assert (numpy_print(delta_1 * p_1 + x_1) == "dot(delta_1, p_1) + x_1")
assert(numpy_print((T(r_1) * r_1) / (T(r_1) * A * p_1)) == \
"dot(dot((r_1).transpose(), r_1), 1.0 / (dot(dot((p_1).transpose(), A), r_1)))")
assert(numpy_print((T(p_1) * A * r_2) / (T(p_1) * A * p_1)) == \
"dot(dot(dot((p_1).transpose(), A), r_2), 1.0 / (dot(dot((p_1).transpose(), A), p_1)))")
def test_chronos_cg():
skip("Test takes too long")
delta_1, omega_2, pi_1, pi_2, mu_12 = map(lambda x: Tensor(x, rank=0), \
['delta_1', 'omega_2', 'pi_1', 'pi_2', 'mu_12'])
r_1, r_2, q_1, q_2, p_1, p_2, x_1, x_2 = map(lambda x: Tensor(x, rank=1), \
['r_1', 'r_2', 'q_1', 'q_2', 'p_1', 'p_2', 'x_1', 'x_2'])
A, R_0, P_0 = map(lambda x: Tensor(x, rank=2), ['A', 'R_0', 'P_0'])
# Specify which variables are known
knowns = [pi_1, p_1, r_1, q_1, x_1, A, R_0, P_0]
# Now try the chronos variant and repeat.
chronos_eqns = [
r_2 - r_1 - delta_1 * q_1,
q_2 - A * p_2,
p_2 - r_2 + p_1 * mu_12,
q_2 - A * r_2 + q_1 * mu_12,
x_2 - x_1 - delta_1 * p_1,
omega_2 - T(r_2) * r_2,
pi_2 - T(p_2) * A * p_2,
T(R_0) * r_2,
T(r_1) * r_2,
T(P_0) * A * p_2,
T(p_1) * A * p_2,
T(p_2) * A * p_2 - T(r_2) * A * r_2 + T(mu_12) * pi_1 * mu_12,
]
run_cg_algorithms(chronos_eqns, knowns)
def testUpdate():
k = Symbol('k')
A = Tensor('A', 2)
A_TL = A.update(l_ind='TL')
A_TL_2 = A_TL.update(u_ind='2', rank=2)
A_01 = A_TL.update(l_ind='01', shape=(k, k))
a_02 = T(A_TL.update(l_ind='02', shape=(1, k), rank=1))
assert(A_TL == Tensor('A_TL', 2))
assert(A_TL_2 == Tensor('A_TL^2', 2))
assert(A_01 == Tensor('A_01', 2, shape=(k, k)))
assert(a_02 == T(Tensor('a_02', 1, shape=(1, k))))
def test_overdetermined_forward_solve():
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 forward_solve(eqns, [r_2, p_1, mu_12, A, pi_1], True)
def testInverseMul():
ans = 5*I
A = Tensor('A', rank=2, has_inv=True)
A_I = Inverse(A)
e = 5*A
assert(A_I * e == ans)
assert(e*A_I == ans)
e = 5*A_I
assert(A * e == ans)
assert(e*A == ans)
ans = 5*one
p = Tensor('p', rank=1)
pAp = T(p)*A*p
pAp_I = Inverse(pAp)
e = 5*pAp
assert(e*pAp_I == ans)
assert(pAp_I*e == ans)
e = 5*pAp_I
assert(e*pAp == ans)
assert(pAp*e == ans)
e = 5*pAp*A
assert(A_I*e == 5*pAp*I)
assert(e*pAp_I == 5*A)
def test_reg_cg():
delta_1, mu_12 = map(lambda x: Tensor(x, rank=0), ['delta_1', 'mu_12'])
r_1, r_2, p_1, p_2, x_1, x_2 = map(lambda x: Tensor(x, rank=1), \
['r_1', 'r_2', 'p_1', 'p_2', 'x_1', 'x_2'])
A = Tensor('A', rank=2)
# Specify which variables are known
knowns = [p_1, r_1, x_1, A]
# Specify the CG eqns (coming from a 4x4 PME)
cg_eqns = [
delta_1 * A * p_1 - r_1 + r_2,
p_2 - r_2 + p_1 * mu_12,
x_2 - x_1 - delta_1 * p_1,
T(r_1) * r_2,
T(p_1) * A * p_2,
]
run_cg_algorithms(cg_eqns, knowns)
def test_algebra():
delta_1, omega_2, pi_1, pi_2, gamma_2, mu_12 = \
map(lambda x: Tensor(x, rank=0),
['delta_1', 'omega_2', 'pi_1', 'pi_2', 'gamma_2', 'mu_12'])
r_1, r_2, q_1, q_2, p_1, p_2, s_1, s_2 = \
map(lambda x: Tensor(x, rank=1),
['r_1', 'r_2', 'q_1', 'q_2', 'p_1', 'p_2', 's_1', 's_2'])
A, R_0, P_0 = map(lambda x: Tensor(x, rank=2), ['A', 'R_0', 'P_0'])
eqn = -2 * (T(p_1) * A * r_2) / (T(p_1) * A * p_1) * (T(p_1) * A * r_2)
eqn -= -2 * (T(p_1) * A * r_2) * (T(p_1) * A * r_2) / (T(p_1) * A * p_1)
assert (eqn == S(0))
assert (T(p_1) * A * r_2 == T(r_2) * A * p_1)
def test_algebra():
eqn = -2 * (T(p_1) * A * r_2) / (T(p_1) * A * p_1) * (T(p_1) * A * r_2)
eqn -= -2 * (T(p_1) * A * r_2) * (T(p_1) * A * r_2) / (T(p_1) * A * p_1)
assert(eqn == S(0))
assert(T(p_1) * A * r_2 == T(r_2) * A * p_1)