def test_calc_Qnorm(self):
A = np.random.random((2, 5, 3))
targets = [0, 1]
volumes = np.array([1, 2, 2, 2, 4])
Qin = optimization_methods._calc_Qnorm(
A, targets, volumes,
)
currents = np.array([1, 0])
field = np.einsum('ijk, i->jk', A, currents)
avg_in = np.sum(
np.linalg.norm(field[targets], axis=1)**2 * volumes[targets])
avg_in /= np.sum(volumes[targets])
currents = np.array([-1, 1, 0])
assert np.allclose(currents.dot(Qin.dot(currents)), avg_in)
def test_norm_constrained_tes_opt_multi_infeasible(self):
np.random.seed(1)
leadfield = np.random.random((5, 10, 3))
np.random.seed(None)
tes_opt = optimization_methods.TESOptimizationProblem(leadfield)
Q = tes_opt.Q
Qnorm1 = optimization_methods._calc_Qnorm(leadfield, 0, np.ones(10))
Qnorm2 = optimization_methods._calc_Qnorm(leadfield, 1, np.ones(10))
Qnorm = np.stack([Qnorm1, Qnorm2])
max_total_current = 0.2
max_el_current = 0.1
target_norm = np.array([0.1, 0.2])
x = optimization_methods._norm_constrained_tes_opt(
Qnorm, target_norm, Q,
max_el_current, max_total_current
)
assert np.all(np.abs(x) <= max_el_current*1.001)
assert np.all(np.linalg.norm(x) <= 2*max_total_current*1.001)
assert np.isclose(np.sum(x), 0)
assert np.isclose(np.sqrt(x.dot(Qnorm).dot(x))[0], target_norm[0], rtol=1e-1)
def test_norm_constrained_tes_opt(self):
np.random.seed(1)
leadfield = np.random.random((5, 10, 3))
np.random.seed(None)
tes_opt = optimization_methods.TESOptimizationProblem(leadfield)
Q = tes_opt.Q
Qnorm = optimization_methods._calc_Qnorm(leadfield, 0, np.ones(10))
max_total_current = 0.2
max_el_current = 0.1
target_norm = 0.1
x = optimization_methods._norm_constrained_tes_opt(
Qnorm, target_norm, Q,
max_el_current, max_total_current
)
energy_bf = np.inf
directions = fibonacci_sphere(51)
directions = directions[directions[:, 2] > 0]
for d in directions:
l = optimization_methods._calc_l(
leadfield, 0, d, np.ones(10)
)
x_ = optimization_methods._linear_constrained_tes_opt(
l[None, :], np.atleast_1d(target_norm),
Q, max_el_current,
max_total_current, log_level=0
)
norm_ = np.sqrt(x_.dot(Qnorm).dot(x_))
energy_ = x_.dot(Q).dot(x_)
if np.isclose(norm_, target_norm, rtol=1e-1) and energy_ < energy_bf:
energy_bf = energy_
assert np.all(np.abs(x) <= max_el_current)
assert np.all(np.linalg.norm(x) <= 2*max_total_current)
assert np.isclose(np.sum(x), 0)
assert np.isclose(np.sqrt(x.dot(Qnorm).dot(x)), target_norm, rtol=1e-1)
assert x.dot(Q).dot(x) < energy_bf