def check_residual(residual, initial_m):
mag_params = utils.MagParameters()
tmax = 3.0
f_residual = ft.partial(residual, mag_params)
# Timestep to a solution + convert to spherical
result_times, m_list = ode.odeint(f_residual, sp.array(initial_m),
tmax, dt=0.01)
m_sph = [utils.array2sph(m) for m in m_list]
result_pols = [m.pol for m in m_sph]
result_azis = [m.azi for m in m_sph]
# Calculate exact solutions
exact_times, exact_azis = \
mlsn.calculate_equivalent_dynamics(mag_params, result_pols)
# Check
utils.assert_list_almost_equal(exact_azis, result_azis, 1e-3)
utils.assert_list_almost_equal(exact_times, result_times, 1e-3)
def check_residual(residual, initial_m):
mag_params = utils.MagParameters()
tmax = 3.0
f_residual = ft.partial(residual, mag_params)
# Timestep to a solution + convert to spherical
result_times, m_list = ode.odeint(f_residual,
sp.array(initial_m),
tmax,
dt=0.01)
m_sph = [utils.array2sph(m) for m in m_list]
result_pols = [m.pol for m in m_sph]
result_azis = [m.azi for m in m_sph]
# Calculate exact solutions
exact_times, exact_azis = \
mlsn.calculate_equivalent_dynamics(mag_params, result_pols)
# Check
utils.assert_list_almost_equal(exact_azis, result_azis, 1e-3)
utils.assert_list_almost_equal(exact_times, result_times, 1e-3)
def test_tr_ab2_scheme_generation():
"""Make sure tr-ab can be derived using same methodology as I'm using
(also checks lte expressions).
"""
dddy = sympy.symbols("y'''")
y_np1_tr = sympy.symbols("y_{n+1}_tr")
ab_pred, ynp1_ab2_expr = generate_predictor_scheme([PTInfo(0, None, None),
PTInfo(
1,
"corr_val",
"exp test"),
PTInfo(
2, "corr_val", "exp test")],
"ab2",
symbolic=sympy.exp(St))
# ??ds hacky, have to change the symbol to represent where y''' is being
# evaluated by hand!
ynp1_ab2_expr = ynp1_ab2_expr.subs(Sdddynph, dddy)
# Check that it gives the same result as we know from the lte
utils.assert_sym_eq(y_np1_exact - ab2_lte(Sdts[0], Sdts[1], dddy),
ynp1_ab2_expr)
# Now do the solve etc.
y_np1_tr_expr = y_np1_exact - tr_lte(Sdts[0], dddy)
A = system2matrix([ynp1_ab2_expr, y_np1_tr_expr], [dddy, y_np1_exact])
x = A.inv()
exact_ynp1_symb = sum([y_est * xi.factor() for xi, y_est in
zip(x.row(1), [y_np1_p1, y_np1_tr])])
exact_ynp1_f = sympy.lambdify(
(y_np1_p1,
y_np1_tr,
Sdts[0],
Sdts[1]),
exact_ynp1_symb)
utils.assert_sym_eq(exact_ynp1_symb - y_np1_tr,
(y_np1_p1 - y_np1_tr)/(3*(1 + Sdts[1]/Sdts[0])))
# Construct an lte estimator from this estimate
def lte_est(ts, ys):
ynp1_p = ab_pred(ts, ys)
dtn = ts[-1] - ts[-2]
dtnm1 = ts[-2] - ts[-3]
ynp1_exact = exact_ynp1_f(ynp1_p, ys[-1], dtn, dtnm1)
return ynp1_exact - ys[-1]
# Solve exp using tr
t0 = 0.0
dt = 1e-2
ts, ys = ode.odeint(er.exp_residual, er.exp_exact(t0),
tmax=2.0, dt=dt, method='tr')
# Get error estimates using standard tr ab and the one we just
# constructed here, then compare.
this_ltes = ode.get_ltes_from_data(ts, ys, lte_est)
tr_ab_lte = par(ode.tr_ab_lte_estimate, dydt_func=lambda t, y: y)
standard_ltes = ode.get_ltes_from_data(ts, ys, tr_ab_lte)
# Should be the same (actually the sign is different, but this doesn't
# matter in lte).
utils.assert_list_almost_equal(
this_ltes, map(lambda a: a*-1, standard_ltes), 1e-8)
def test_tr_ab2_scheme_generation():
"""Make sure tr-ab can be derived using same methodology as I'm using
(also checks lte expressions).
"""
dddy = sympy.symbols("y'''")
y_np1_tr = sympy.symbols("y_{n+1}_tr")
ab_pred, ynp1_ab2_expr = generate_predictor_scheme([
PTInfo(0, None, None),
PTInfo(1, "corr_val", "exp test"),
PTInfo(2, "corr_val", "exp test")
],
"ab2",
symbolic=sympy.exp(St))
# ??ds hacky, have to change the symbol to represent where y''' is being
# evaluated by hand!
ynp1_ab2_expr = ynp1_ab2_expr.subs(Sdddynph, dddy)
# Check that it gives the same result as we know from the lte
utils.assert_sym_eq(y_np1_exact - ab2_lte(Sdts[0], Sdts[1], dddy),
ynp1_ab2_expr)
# Now do the solve etc.
y_np1_tr_expr = y_np1_exact - tr_lte(Sdts[0], dddy)
A = system2matrix([ynp1_ab2_expr, y_np1_tr_expr], [dddy, y_np1_exact])
x = A.inv()
exact_ynp1_symb = sum([
y_est * xi.factor()
for xi, y_est in zip(x.row(1), [y_np1_p1, y_np1_tr])
])
exact_ynp1_f = sympy.lambdify((y_np1_p1, y_np1_tr, Sdts[0], Sdts[1]),
exact_ynp1_symb)
utils.assert_sym_eq(exact_ynp1_symb - y_np1_tr,
(y_np1_p1 - y_np1_tr) / (3 * (1 + Sdts[1] / Sdts[0])))
# Construct an lte estimator from this estimate
def lte_est(ts, ys):
ynp1_p = ab_pred(ts, ys)
dtn = ts[-1] - ts[-2]
dtnm1 = ts[-2] - ts[-3]
ynp1_exact = exact_ynp1_f(ynp1_p, ys[-1], dtn, dtnm1)
return ynp1_exact - ys[-1]
# Solve exp using tr
t0 = 0.0
dt = 1e-2
ts, ys = ode.odeint(er.exp_residual,
er.exp_exact(t0),
tmax=2.0,
dt=dt,
method='tr')
# Get error estimates using standard tr ab and the one we just
# constructed here, then compare.
this_ltes = ode.get_ltes_from_data(ts, ys, lte_est)
tr_ab_lte = par(ode.tr_ab_lte_estimate, dydt_func=lambda t, y: y)
standard_ltes = ode.get_ltes_from_data(ts, ys, tr_ab_lte)
# Should be the same (actually the sign is different, but this doesn't
# matter in lte).
utils.assert_list_almost_equal(this_ltes,
map(lambda a: a * -1, standard_ltes), 1e-8)
