def test_multiple_builds(Simulator, seed):
# this is not a separate test because of nengo issue #1011
solver = BiasedSolver()
A, Y = np.ones((1, 1)), np.ones((1, 1))
assert solver.bias is None
solver(A, Y)
assert solver.bias is not None
with warns(UserWarning):
solver(A, Y)
# issue: #99
with Network(seed=seed) as model:
stim = nengo.Node(output=0)
x = nengo.Ensemble(100, 1)
out = nengo.Node(size_in=1)
nengo.Connection(stim, x, synapse=None)
conn = Connection(x, out, synapse=None)
p = nengo.Probe(out, synapse=0.1)
assert isinstance(conn.solver, BiasedSolver)
with Simulator(model):
pass
with Simulator(model) as sim:
sim.run(0.1)
assert rmse(sim.data[p], 0) < 0.01
def test_none_dt(Simulator, seed, rng):
dt = 0.0001 # approximates continuous case
T = 1.0
sys = Bandpass(8, 5)
synapse = 0.01
with Network(seed=seed) as model:
stim = nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed))
subnet = LinearNetwork(sys,
1,
synapse=synapse,
input_synapse=synapse,
dt=None,
neuron_type=nengo.neurons.Direct())
nengo.Connection(stim, subnet.input, synapse=None)
assert subnet.output_synapse is None
p_ideal = nengo.Probe(subnet.input, synapse=sys)
p_output = nengo.Probe(subnet.output, synapse=None)
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_output], sim.data[p_ideal], atol=0.1)
def test_output_filter(Simulator, seed, rng):
dt = 0.001
T = 1.0
sys = PadeDelay(0.1, order=3, p=3)
assert sys.has_passthrough
synapse = 0.01
with Network(seed=seed) as model:
stim = nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed))
subnet = LinearNetwork(sys,
1,
synapse=synapse,
output_synapse=synapse,
dt=dt,
neuron_type=nengo.neurons.Direct())
nengo.Connection(stim, subnet.input, synapse=None)
assert subnet.input_synapse is None
p_ideal = nengo.Probe(subnet.input, synapse=sys)
p_output = nengo.Probe(subnet.output, synapse=None)
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_output][:-1], sim.data[p_ideal][1:])
def test_pes_learning_rate(Simulator, plt, seed):
n = 50
dt = 0.0005
T = 1.0
initial = 0.7
desired = -0.9
epsilon = 1e-3 # get to factor epsilon with T seconds
# Get activity vector and initial decoders
with Network(seed=seed) as model:
x = nengo.Ensemble(n,
1,
seed=seed,
neuron_type=nengo.neurons.LIFRate())
y = nengo.Node(size_in=1)
conn = nengo.Connection(x, y, synapse=None)
with Simulator(model, dt=dt) as sim:
a = get_activities(sim.model, x, [initial])
d = sim.data[conn].weights
assert np.any(a > 0)
# Use util function to calculate learning_rate
init_error = float(desired - np.dot(d, a))
learning_rate, gamma = pes_learning_rate(epsilon / abs(init_error), a, T,
dt)
# Build model with no filtering on any connections
with model:
stim = nengo.Node(output=initial)
ystar = nengo.Node(output=desired)
conn.learning_rule_type = nengo.PES(pre_tau=1e-15,
learning_rate=learning_rate)
nengo.Connection(stim, x, synapse=None)
nengo.Connection(ystar, conn.learning_rule, synapse=0, transform=-1)
nengo.Connection(y, conn.learning_rule, synapse=0)
p = nengo.Probe(y, synapse=None)
decoders = nengo.Probe(conn, 'weights', synapse=None)
with Simulator(model, dt=dt) as sim:
sim.run(T)
# Check that the final error is exactly epsilon
assert np.allclose(abs(desired - sim.data[p][-1]), epsilon)
# Check that all of the errors are given exactly by gamma**k
k = np.arange(len(sim.trange()))
error = init_error * gamma**k
assert np.allclose(sim.data[p].flatten(), desired - error)
# Check that all of the decoders are equal to their analytical solution
dk = d.T + init_error * a.T[:, None] * (1 - gamma**k) / np.dot(a, a.T)
assert np.allclose(dk, np.squeeze(sim.data[decoders].T))
plt.figure()
plt.plot(sim.trange(), sim.data[p], lw=5, alpha=0.5)
plt.plot(sim.trange(), desired - error, linestyle='--', lw=5, alpha=0.5)
def test_direct_window(legendre, Simulator, seed, plt):
theta = 1.0
T = theta
assert np.allclose(t_default, np.linspace(0, 1, 1000))
with Network() as model:
stim = nengo.Node(output=lambda t: t)
rw = RollingWindow(theta, n_neurons=1, dimensions=12,
neuron_type=nengo.Direct(), process=None,
legendre=legendre)
assert rw.theta == theta
assert rw.dt == 0.001
assert rw.process is None
assert rw.synapse == nengo.Lowpass(0.1)
assert rw.input_synapse == nengo.Lowpass(0.1)
nengo.Connection(stim, rw.input, synapse=None)
output = rw.add_output(function=lambda w: np.sum(w**3)**2)
p_output = nengo.Probe(output, synapse=None)
with Simulator(model) as sim:
sim.run(T)
actual = sim.data[p_output].squeeze()
t = sim.trange()
ideal = shift(np.cumsum(t**3)**2)
plt.figure()
plt.plot(t, actual, label="Output")
plt.plot(t, ideal, label="Ideal", linestyle='--')
plt.legend()
assert nrmse(actual, ideal) < 0.005
def test_unfiltered(Simulator, seed, rng):
dt = 0.001
T = 1.0
sys = nengo.Alpha(0.1)
synapse = 0.01
with Network(seed=seed) as model:
stim = nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed))
subnet = LinearNetwork(sys,
1,
synapse=synapse,
dt=dt,
neuron_type=nengo.neurons.Direct())
nengo.Connection(stim, subnet.input, synapse=None)
assert subnet.input_synapse is None
assert subnet.output_synapse is None
p_ideal = nengo.Probe(subnet.input, synapse=sys)
p_output = nengo.Probe(subnet.output, synapse=synapse)
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_output], sim.data[p_ideal])
def test_hetero_neurons(Simulator, rng, seed):
n_neurons = 100
dt = 0.001
T = 0.1
dims_in = 2
taus = nengo.dists.Uniform(0.001, 0.1).sample(n_neurons, rng=rng)
synapses = [Lowpass(tau) for tau in taus]
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
hs = HeteroSynapse(synapses, dt)
def embed_encoders(x):
# Reshapes the vectors to be the same dimensionality as the
# encoders, and then takes the dot product row by row.
# See http://stackoverflow.com/questions/26168363/ for a more
# efficient solution.
return np.sum(encoders * hs.from_vector(x), axis=1)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed)),
stim[i],
synapse=None)
# HeteroSynapse node
syn = nengo.Node(size_in=dims_in, output=hs)
# For comparing results
x = [
nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)
] # expected, actual
# Expected
for i, synapse in enumerate(synapses):
t = np.zeros_like(encoders)
t[i, :] = encoders[i, :]
nengo.Connection(stim, x[0].neurons, transform=t, synapse=synapse)
# Actual
nengo.Connection(stim, syn, synapse=None)
nengo.Connection(syn,
x[1].neurons,
function=embed_encoders,
synapse=None)
# Probes
p_exp = nengo.Probe(x[0].neurons, synapse=None)
p_act = nengo.Probe(x[1].neurons, synapse=None)
# Check correctness
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_act], sim.data[p_exp])
def delayed_synapse():
a = 0.1 # desired delay
b = 0.01 # synapse delay
tau = 0.01 # recurrent tau
hz = 15 # input frequency
t = 1.0 # simulation time
dt = 0.00001 # simulation timestep
order = 6 # order of pade approximation
tau_probe = 0.02
dexp_synapse = DoubleExp(tau, tau / 5)
sys_lambert = lambert_delay(a, b, tau, order - 1, order)
synapse = (cont2discrete(Lowpass(tau), dt=dt) *
DiscreteDelay(int(b / dt)))
n_neurons = 2000
neuron_type = PerfectLIF()
A, B, C, D = sys_lambert.observable.transform(5*np.eye(order)).ss
sys_normal = PadeDelay(a, order)
assert len(sys_normal) == order
with Network(seed=0) as model:
stim = Node(output=WhiteSignal(t, high=hz, y0=0))
x = EnsembleArray(n_neurons / order, len(A), neuron_type=neuron_type)
output = Node(size_in=1)
Connection(x.output, x.input, transform=A, synapse=synapse)
Connection(stim, x.input, transform=B, synapse=synapse)
Connection(x.output, output, transform=C, synapse=None)
Connection(stim, output, transform=D, synapse=None)
lowpass_delay = LinearNetwork(
sys_normal, n_neurons_per_ensemble=n_neurons / order,
synapse=tau, input_synapse=tau,
dt=None, neuron_type=neuron_type, radii=1.0)
Connection(stim, lowpass_delay.input, synapse=None)
dexp_delay = LinearNetwork(
sys_normal, n_neurons_per_ensemble=n_neurons / order,
synapse=dexp_synapse, input_synapse=dexp_synapse,
dt=None, neuron_type=neuron_type, radii=1.0)
Connection(stim, dexp_delay.input, synapse=None)
p_stim = Probe(stim, synapse=tau_probe)
p_output_delayed = Probe(output, synapse=tau_probe)
p_output_lowpass = Probe(lowpass_delay.output, synapse=tau_probe)
p_output_dexp = Probe(dexp_delay.output, synapse=tau_probe)
with Simulator(model, dt=dt, seed=0) as sim:
sim.run(t)
return (a, dt, sim.trange(), sim.data[p_stim],
sim.data[p_output_delayed], sim.data[p_output_lowpass],
sim.data[p_output_dexp])
def test_mapping(Simulator, plt, seed):
sys = Alpha(0.1)
syn = Lowpass(0.01)
gsyn = 2*syn # scaled lowpass
isyn = 2/s # scaled integrator
dt = 0.001
ss = ss2sim(sys, syn, None) # normal lowpass, continuous
dss = ss2sim(sys, syn, dt) # normal lowpass, discrete
gss = ss2sim(sys, gsyn, None) # scaled lowpass, continuous
gdss = ss2sim(sys, gsyn, dt) # scaled lowpass, discrete
iss = ss2sim(sys, isyn, None) # scaled integrator, continuous
idss = ss2sim(sys, isyn, dt) # scaled integrator, discrete
assert ss.analog and gss.analog and iss.analog
assert not (dss.analog or gdss.analog or idss.analog)
with Network(seed=seed) as model:
stim = nengo.Node(output=lambda t: np.sin(20*np.pi*t))
probes = []
for mapped, synapse in ((ss, syn), (dss, syn), (gss, gsyn),
(gdss, gsyn), (iss, isyn), (idss, isyn)):
A, B, C, D = mapped.ss
x = nengo.Node(size_in=2)
y = nengo.Node(size_in=1)
nengo.Connection(stim, x, transform=B, synapse=synapse)
nengo.Connection(x, x, transform=A, synapse=synapse)
nengo.Connection(x, y, transform=C, synapse=None)
nengo.Connection(stim, y, transform=D, synapse=None)
probes.append(nengo.Probe(y))
p_stim = nengo.Probe(stim)
pss, pdss, pgss, pgdss, piss, pidss = probes
with Simulator(model, dt=dt) as sim:
sim.run(1.0)
expected = shift(sys.filt(sim.data[p_stim], dt))
plt.plot(sim.trange(), sim.data[pss], label="Continuous", alpha=0.5)
plt.plot(sim.trange(), sim.data[pdss], label="Discrete", alpha=0.5)
plt.plot(sim.trange(), sim.data[pgss], label="Gain Cont.", alpha=0.5)
plt.plot(sim.trange(), sim.data[pgdss], label="Gain Disc.", alpha=0.5)
plt.plot(sim.trange(), sim.data[piss], label="Integ Cont.", alpha=0.5)
plt.plot(sim.trange(), sim.data[pidss], label="Integ Disc.", alpha=0.5)
plt.plot(sim.trange(), expected, label="Expected", linestyle='--')
plt.legend()
assert np.allclose(sim.data[pss], expected, atol=0.01)
assert np.allclose(sim.data[pdss], expected)
assert np.allclose(sim.data[pgss], expected, atol=0.01)
assert np.allclose(sim.data[pgdss], expected)
assert np.allclose(sim.data[piss], expected, atol=0.01)
assert np.allclose(sim.data[pidss], expected)
def test_biased_solver_weights(Simulator):
solver = BiasedSolver(nengo.solvers.LstsqL2(weights=True))
assert solver.weights
with Network() as model:
x = nengo.Ensemble(100, 1)
nengo.Connection(x, x, solver=solver)
Simulator(model)
def test_network():
with Network():
x = nengo.Ensemble(100, 1)
assert isinstance(x.eval_points, ScatteredHypersphere)
assert isinstance(x.encoders, ScatteredHypersphere)
with BaseNetwork():
x = nengo.Ensemble(100, 1)
assert not isinstance(x.eval_points, ScatteredHypersphere)
assert not isinstance(x.encoders, ScatteredHypersphere)
def test_context():
with Network():
# make some arbitrary object for the reservoirs. it's okay that it's
# not within the same network, because we won't simulate it
a = nengo.Node(size_in=1)
with Network() as outer:
with Network() as inner:
assert Reservoir(a, a).network is inner
assert Reservoir(a, a, network=inner).network is inner
assert Reservoir(a, a, network=outer).network is outer
assert Reservoir(a, a).network is outer
assert Reservoir(a, a, network=inner).network is inner
assert Reservoir(a, a, network=outer).network is outer
with pytest.raises(NetworkContextError):
Reservoir(a, a)
assert Reservoir(a, a, network=inner).network is inner
assert Reservoir(a, a, network=outer).network is outer
def test_linear_network(Simulator, plt, seed, rng, neuron_type, atol, atol_x):
n_neurons = 500
dt = 0.001
T = 1.0
sys = Lowpass(0.1)
scale_input = 2.0
synapse = 0.02
tau_probe = 0.005
with Network(seed=seed) as model:
stim = nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed))
subnet = LinearNetwork(sys,
n_neurons_per_ensemble=n_neurons,
synapse=synapse,
input_synapse=synapse,
dt=dt,
neuron_type=neuron_type)
nengo.Connection(stim,
subnet.input,
synapse=None,
transform=scale_input)
assert subnet.synapse == subnet.input_synapse
assert subnet.output_synapse is None
p_input = nengo.Probe(subnet.input, synapse=tau_probe)
p_x = nengo.Probe(subnet.state.output, synapse=tau_probe)
p_output = nengo.Probe(subnet.output, synapse=tau_probe)
with Simulator(model, dt=dt) as sim:
sim.run(T)
ideal_output = shift(sys.filt(sim.data[p_input]))
ideal_x = shift(subnet.realization.X.filt(sim.data[p_input]))
plt.plot(sim.trange(), sim.data[p_input], label="Input", alpha=0.5)
plt.plot(sim.trange(), sim.data[p_output], label="Actual y", alpha=0.5)
plt.plot(sim.trange(),
ideal_output,
label="Expected y",
alpha=0.5,
linestyle='--')
plt.plot(sim.trange(), sim.data[p_x], label="Actual x", alpha=0.5)
plt.plot(sim.trange(),
ideal_x,
label="Expected x",
alpha=0.5,
linestyle='--')
plt.legend()
assert nrmse(sim.data[p_output], ideal_output) < atol
assert nrmse(sim.data[p_x].squeeze(), ideal_x.squeeze()) < atol_x
def time_cells(order):
seed = 0
n_neurons = 300
theta = 4.784
tau = 0.1
radius = 0.3
realizer = Balanced
# The following was patched from nengolib commit
# 7e204e0c305e34a4f63d0a6fbba7197862bbcf22, prior to
# aee92b8fc45749f07f663fe696745cf0a33bfa17, so that
# the generated PDF is consistent with the version that the
# overlay was added to.
def PadeDelay(c, q):
j = np.arange(1, q+1, dtype=np.float64)
u = (q + j - 1) * (q - j + 1) / (c * j)
A = np.zeros((q, q))
B = np.zeros((q, 1))
C = np.zeros((1, q))
D = np.zeros((1,))
A[0, :] = B[0, 0] = -u[0]
A[1:, :-1][np.diag_indices(q-1)] = u[1:]
C[0, :] = - j / float(q) * (-1) ** (q - j)
return LinearSystem((A, B, C, D), analog=True)
F = PadeDelay(theta, order)
synapse = Alpha(tau)
pulse_s = 0
pulse_w = 1.0
pulse_h = 1.5
T = 6.0
dt = 0.001
pulse = np.zeros(int(T/dt))
pulse[int(pulse_s/dt):int((pulse_s + pulse_w)/dt)] = pulse_h
with Network(seed=seed) as model:
u = Node(output=PresentInput(pulse, dt))
delay = LinearNetwork(
F, n_neurons_per_ensemble=n_neurons / len(F), synapse=synapse,
input_synapse=None, radii=radius, dt=dt, realizer=realizer())
Connection(u, delay.input, synapse=None)
p_x = Probe(delay.state.input, synapse=None)
p_a = Probe(delay.state.add_neuron_output(), synapse=None)
with Simulator(model, dt=dt) as sim:
sim.run(T)
return sim.trange(), sim.data[p_x], sim.data[p_a]
def _test_temporal_solver(plt, Simulator, seed, neuron_type, tau, f, solver):
dt = 0.002
# we are cheating a bit here because we'll use the same training data as
# test data. this makes the unit testing a bit simpler since it's more
# obvious what will happen when comparing temporal to default
t = np.arange(0, 0.2, dt)
stim = np.sin(2 * np.pi * 10 * t)
function = (f(stim) if tau is None else nengo.Lowpass(tau).filt(f(stim),
dt=dt))
with Network(seed=seed) as model:
u = nengo.Node(output=nengo.processes.PresentInput(stim, dt))
x = nengo.Ensemble(100, 1, neuron_type=neuron_type)
output_ideal = nengo.Node(size_in=1)
post = dict(n_neurons=500,
dimensions=1,
neuron_type=nengo.LIFRate(),
seed=seed + 1)
output_temporal = nengo.Ensemble(**post)
output_default = nengo.Ensemble(**post)
nengo.Connection(u, output_ideal, synapse=tau, function=f)
nengo.Connection(u, x, synapse=None)
nengo.Connection(x,
output_temporal,
synapse=tau,
eval_points=stim[:, None],
function=function[:, None],
solver=Temporal(synapse=tau, solver=solver))
nengo.Connection(x,
output_default,
synapse=tau,
eval_points=stim[:, None],
function=f,
solver=solver)
p_ideal = nengo.Probe(output_ideal, synapse=None)
p_temporal = nengo.Probe(output_temporal, synapse=None)
p_default = nengo.Probe(output_default, synapse=None)
with Simulator(model, dt) as sim:
sim.run(t[-1])
plt.plot(sim.trange(),
sim.data[p_ideal] - sim.data[p_default],
label="Default")
plt.plot(sim.trange(),
sim.data[p_ideal] - sim.data[p_temporal],
label="Temporal")
plt.legend()
return (nrmse(sim.data[p_default], target=sim.data[p_ideal]) /
nrmse(sim.data[p_temporal], target=sim.data[p_ideal]))
def discrete_example(seed, dt):
n_neurons = 1000
theta = 0.1
freq = 50
q = 27
radii = 1.0
sys = PadeDelay(theta, q)
T = 5000*(dt+0.001)
rms = 1.0
signal = WhiteSignal(T, high=freq, rms=rms, y0=0)
tau = 0.1
tau_probe = 0.02
reg = 0.1
# Determine radii using direct mode
with LinearNetwork(
sys, n_neurons_per_ensemble=1, input_synapse=tau, synapse=tau,
dt=dt, neuron_type=Direct(),
realizer=Balanced()) as model:
Connection(Node(output=signal), model.input, synapse=None)
p_x = Probe(model.state.input, synapse=None)
with Simulator(model, dt=dt, seed=seed+1) as sim:
sim.run(T)
radii *= np.max(abs(sim.data[p_x]), axis=0)
logging.info("Radii: %s", radii)
with Network(seed=seed) as model:
u = Node(output=signal)
kwargs = dict(
n_neurons_per_ensemble=n_neurons / len(sys),
input_synapse=tau, synapse=tau, radii=radii,
solver=LstsqL2(reg=reg), realizer=Balanced())
delay_disc = LinearNetwork(sys, dt=dt, **kwargs)
delay_cont = LinearNetwork(sys, dt=None, **kwargs)
Connection(u, delay_disc.input, synapse=None)
Connection(u, delay_cont.input, synapse=None)
p_u = Probe(u, synapse=tau_probe)
p_y_disc = Probe(delay_disc.output, synapse=tau_probe)
p_y_cont = Probe(delay_cont.output, synapse=tau_probe)
with Simulator(model, dt=dt, seed=seed) as sim:
sim.run(T)
return (theta, dt, sim.trange(), sim.data[p_u],
sim.data[p_y_disc], sim.data[p_y_cont])
def _test_lif(Simulator, seed, neuron_type, u, dt, n=500, t=2.0):
with Network(seed=seed) as model:
stim = nengo.Node(u)
x = nengo.Ensemble(n, 1, neuron_type=neuron_type)
nengo.Connection(stim, x, synapse=None)
p = nengo.Probe(x.neurons)
with Simulator(model, dt=dt) as sim:
sim.run(t)
expected = get_activities(sim.model, x, [u]) * t
actual = (sim.data[p] > 0).sum(axis=0)
return rmse(actual, expected, axis=0)
def _test_normalization(Simulator,
sys,
rng,
realizer,
l1_lower,
lower,
radius=5.0,
dt=0.0001,
T=1.0,
eps=1e-5):
response = sys.X.impulse(int(T / dt), dt=dt)
assert np.allclose(response[-10:], 0)
l1_norms = radius * np.sum(abs(response * dt), axis=0)
with Network() as model:
stim = nengo.Node(output=lambda t: rng.choice([-radius, radius])
if t < T / 2 else radius)
tau = 0.02
subnet = LinearNetwork(sys,
n_neurons_per_ensemble=1,
synapse=tau,
dt=dt,
input_synapse=tau,
radii=radius,
realizer=realizer,
neuron_type=nengo.neurons.Direct())
nengo.Connection(stim, subnet.input, synapse=None)
p = nengo.Probe(subnet.state.output, synapse=None)
assert np.allclose(inv(subnet.realizer_result.T),
subnet.realizer_result.Tinv)
trans = subnet.realizer_result.T
assert trans.shape == (len(sys), len(sys))
est_worst_x = np.diagonal(trans)
assert np.allclose(np.diag(est_worst_x), trans) # make sure diagonal
assert est_worst_x.shape == (len(sys), )
assert ((l1_lower * est_worst_x <= l1_norms) | (est_worst_x <= eps)).all()
assert (l1_norms <= est_worst_x + eps).all()
with Simulator(model, dt=dt) as sim:
sim.run(T)
# lower bound includes both approximation error and the gap between
# random {-1, 1} flip-flop inputs and the true worst-case input
worst_x = np.max(abs(sim.data[p]), axis=0)
assert (lower <= worst_x + eps).all()
assert (worst_x <= 1 + eps).all()
def test_sim_new_synapse(Simulator):
# Create a new synapse object and simulate it
synapse = Lowpass(0.1) - Lowpass(0.01)
with Network() as model:
stim = nengo.Node(output=np.sin)
x = nengo.Node(size_in=1)
nengo.Connection(stim, x, synapse=synapse)
p_stim = nengo.Probe(stim, synapse=None)
p_x = nengo.Probe(x, synapse=None)
with Simulator(model) as sim:
sim.run(0.1)
assert np.allclose(shift(synapse.filt(sim.data[p_stim])),
sim.data[p_x])
def test_hetero_vector(Simulator, rng, seed):
n_neurons = 20
dt = 0.0005
T = 0.1
dims_in = 2
synapses = [Alpha(0.1), Lowpass(0.005)]
assert dims_in == len(synapses)
encoders = sphere.sample(n_neurons, dims_in, rng=rng)
with Network(seed=seed) as model:
# Input stimulus
stim = nengo.Node(size_in=dims_in)
for i in range(dims_in):
nengo.Connection(nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed)),
stim[i],
synapse=None)
# HeteroSynapse Nodes
syn_elemwise = nengo.Node(size_in=dims_in,
output=HeteroSynapse(synapses,
dt,
elementwise=True))
# For comparing results
x = [
nengo.Ensemble(n_neurons, dims_in, seed=0, encoders=encoders)
for _ in range(2)
] # expected, actual
# Expected
for j, synapse in enumerate(synapses):
nengo.Connection(stim[j], x[0][j], synapse=synapse)
# Actual
nengo.Connection(stim, syn_elemwise, synapse=None)
nengo.Connection(syn_elemwise, x[1], synapse=None)
# Probes
p_exp = nengo.Probe(x[0], synapse=None)
p_act_elemwise = nengo.Probe(x[1], synapse=None)
# Check correctness
with Simulator(model, dt=dt) as sim:
sim.run(T)
assert np.allclose(sim.data[p_act_elemwise], sim.data[p_exp])
def test_biased_solver(Simulator, seed, d):
solver = BiasedSolver()
function = solver.bias_function(d)
assert solver.bias is None
assert np.allclose(function(np.ones(d)), np.zeros(d))
with Network(seed=seed) as model:
x = nengo.Ensemble(100, d)
conn = nengo.Connection(x, x, solver=solver)
with Simulator(model) as sim:
bias = sim.data[conn].solver_info['bias']
assert np.allclose(solver.bias, bias)
assert np.allclose(function(np.ones(d)), bias)
def test_discrete_synapse(Simulator):
# Test that discrete synapses are simulated properly
delay_steps = 50
with Network() as model:
stim = nengo.Node(output=np.sin)
output = nengo.Node(size_in=1)
nengo.Connection(stim, output, synapse=z**-delay_steps)
p_stim = nengo.Probe(stim, synapse=None)
p_output = nengo.Probe(output, synapse=None)
with Simulator(model) as sim:
sim.run(1.0)
assert np.allclose(sim.data[p_output][delay_steps:],
sim.data[p_stim][:-delay_steps])
def test_tanh(Simulator, seed):
T = 0.1
with Network(seed=seed) as model:
stim = nengo.Node(
output=nengo.processes.WhiteSignal(T, high=10, seed=seed))
x = nengo.Ensemble(2, 1, neuron_type=Tanh())
nengo.Connection(stim,
x.neurons,
transform=np.ones((2, 1)),
synapse=None)
p_stim = nengo.Probe(stim, synapse=None)
p_x = nengo.Probe(x.neurons, synapse=None)
with Simulator(model) as sim:
sim.run(T)
assert np.allclose(sim.data[x].gain, 1)
assert np.allclose(sim.data[x].bias, 0)
assert np.allclose(sim.data[p_x], np.tanh(sim.data[p_stim]))
def test_echo_state(Simulator, plt, seed, rng, include_bias):
test_t = 1.0
train_t = 5.0
dt = 0.001
n_neurons = 1000
dimensions = 2
process = WhiteSignal(train_t, high=10)
with Network(seed=seed) as model:
stim = nengo.Node(output=process, size_out=dimensions)
esn = EchoState(n_neurons,
dimensions,
include_bias=include_bias,
rng=rng)
nengo.Connection(stim, esn.input, synapse=None)
p = nengo.Probe(esn.output, synapse=None)
p_stim = nengo.Probe(stim, synapse=None)
# train the reservoir to compute a highpass filter
def function(x):
return Highpass(0.01).filt(x, dt=dt)
esn.train(function, test_t, dt, process, seed=seed)
with Simulator(model, dt=dt, seed=seed + 1) as sim:
sim.run(test_t)
ideal = function(sim.data[p_stim])
plt.figure()
plt.plot(sim.trange(), sim.data[p_stim], label="Input")
plt.plot(sim.trange(), sim.data[p], label="Output")
plt.plot(sim.trange(), ideal, label="Ideal")
plt.legend()
if include_bias:
assert rmse(sim.data[p], ideal) <= 0.5 * rms(ideal)
else:
assert rmse(sim.data[p], ideal) <= 0.7 * rms(ideal)
def test_radii(Simulator, seed, plt):
sys = canonical(PadeDelay(0.2, order=3))
dt = 0.001
T = 0.5
plt.figure()
# Precompute the exact bounds for an impulse stimulus
radii = []
for sub in sys:
response = sub.impulse(int(T / dt), dt=dt)
amplitude = np.max(abs(response))
assert amplitude >= 1e-4 # otherwise numerical issues
radii.append(amplitude)
plt.plot(response / amplitude, linestyle='--')
with Network(seed=seed) as model:
# Impulse stimulus
stim = nengo.Node(output=lambda t: 1 / dt if t <= dt else 0)
# Set explicit radii for controllable realization
subnet = LinearNetwork(sys,
n_neurons_per_ensemble=1,
synapse=0.2,
input_synapse=0.2,
dt=dt,
radii=radii,
realizer=Identity(),
neuron_type=nengo.neurons.Direct())
nengo.Connection(stim, subnet.input, synapse=None)
p = nengo.Probe(subnet.state.output, synapse=None)
with Simulator(model, dt=dt) as sim:
sim.run(T)
plt.plot(sim.data[p], lw=5, alpha=0.5)
assert np.allclose(np.max(abs(sim.data[p]), axis=0), 1, atol=1e-4)
def test_simulation(sys, Simulator, plt, seed):
assert isinstance(sys, LinearSystem)
old_sys = nengo.LinearFilter(sys.num, sys.den)
assert sys == old_sys
with Network() as model:
stim = nengo.Node(output=nengo.processes.WhiteSignal(
1.0, high=10, seed=seed))
out_new = nengo.Node(size_in=2)
out_old = nengo.Node(size_in=2)
nengo.Connection(stim, out_new, transform=[[1], [-1]], synapse=sys)
nengo.Connection(stim, out_old, transform=[[1], [-1]], synapse=old_sys)
p_new = nengo.Probe(out_new)
p_old = nengo.Probe(out_old)
with Simulator(model) as sim:
sim.run(1.0)
plt.figure()
plt.plot(sim.trange(), sim.data[p_new])
plt.plot(sim.trange(), sim.data[p_old])
assert np.allclose(sim.data[p_new], sim.data[p_old])
def test_connection(Simulator, seed, d):
with Network(seed=seed) as model:
stim = nengo.Node(output=lambda t: np.sin(t*2*np.pi), size_out=d)
x = nengo.Ensemble(1, d, intercepts=[-1], neuron_type=nengo.LIFRate())
default = nengo.Node(size_in=d)
improved = nengo.Node(size_in=d)
stim_conn = Connection(stim, x, synapse=None)
default_conn = nengo.Connection(x, default)
improved_conn = Connection(x, improved)
p_default = nengo.Probe(default)
p_improved = nengo.Probe(improved)
p_stim = nengo.Probe(stim, synapse=0.005)
assert not isinstance(stim_conn.solver, BiasedSolver)
assert not isinstance(default_conn.solver, BiasedSolver)
assert isinstance(improved_conn.solver, BiasedSolver)
with Simulator(model) as sim:
sim.run(1.0)
assert (rmse(sim.data[p_default], sim.data[p_stim]) >
rmse(sim.data[p_improved], sim.data[p_stim]))
def test_bad_inputs_outputs():
with Network():
only_out = nengo.Node(output=[0])
no_out = nengo.Node(size_out=0)
okay = nengo.Ensemble(1, 1)
bad = nengo.Network()
with pytest.raises(ValueError): # must contain at least one input
Reservoir([], okay)
with pytest.raises(ValueError): # must contain at least one output
Reservoir(okay, [])
with pytest.raises(ValueError): # must contain at least one input
Reservoir(only_out, okay)
with pytest.raises(ValueError): # must contain at least one output
Reservoir(okay, no_out)
with pytest.raises(TypeError): # must be connectable object
Reservoir(bad, okay)
with pytest.raises(TypeError): # must be connectable object
Reservoir(okay, bad)
def test_ensemble_array():
with Network():
ea = nengo.networks.EnsembleArray(100, 2)
for ens in ea.ea_ensembles:
assert isinstance(ens.eval_points, ScatteredHypersphere)
assert isinstance(ens.encoders, ScatteredHypersphere)
def __init__(self, n_neurons, dimensions, recurrent_synapse=0.005,
readout_synapse=None, radii=1.0, gain=1.25, rng=None,
neuron_type=Tanh(), include_bias=True, ens_seed=None,
label=None, seed=None, add_to_container=None, **ens_kwargs):
"""Initializes the Echo State Network.
Parameters
----------
n_neurons : int
The number of neurons to use in the reservoir.
dimensions : int
The dimensionality of the input signal.
recurrent_synapse : nengo.synapses.Synapse (Default: ``0.005``)
Synapse used to filter the recurrent connection.
readout_synapse : nengo.synapses.Synapse (Default: ``None``)
Optional synapse to filter all of the outputs before solving
for the linear readout. This is included in the connection to the
``output`` Node created within the network.
radii : scalar or array_like, optional (Default: ``1``)
The radius of each dimension of the input signal, used to normalize
the incoming connection weights.
gain : scalar, optional (Default: ``1.25``)
A scalar gain on the recurrent connection weight matrix.
rng : ``numpy.random.RandomState``, optional (Default: ``None``)
Random state used to initialize all weights.
neuron_type : ``nengo.neurons.NeuronType`` optional \
(Default: ``Tanh()``)
Neuron model to use within the reservoir.
include_bias : ``bool`` (Default: ``True``)
Whether to include a bias current to the neural nonlinearity.
This should be ``False`` if the neuron model already has a bias,
e.g., ``LIF`` or ``LIFRate``.
ens_seed : int, optional (Default: ``None``)
Seed passed to the ensemble of neurons.
"""
Network.__init__(self, label, seed, add_to_container)
self.n_neurons = n_neurons
self.dimensions = dimensions
self.recurrent_synapse = recurrent_synapse
self.radii = radii # TODO: make array or scalar parameter?
self.gain = gain
self.rng = np.random if rng is None else rng
self.neuron_type = neuron_type
self.include_bias = include_bias
self.W_in = (
self.rng.rand(self.n_neurons, self.dimensions) - 0.5) / self.radii
if self.include_bias:
self.W_bias = self.rng.rand(self.n_neurons, 1) - 0.5
else:
self.W_bias = np.zeros((self.n_neurons, 1))
self.W = self.rng.rand(self.n_neurons, self.n_neurons) - 0.5
self.W *= self.gain / max(abs(eig(self.W)[0]))
with self:
self.ensemble = nengo.Ensemble(
self.n_neurons, 1, neuron_type=self.neuron_type, seed=ens_seed,
**ens_kwargs)
self.input = nengo.Node(size_in=self.dimensions)
pool = self.ensemble.neurons
nengo.Connection(
self.input, pool, transform=self.W_in, synapse=None)
nengo.Connection( # note the bias will be active during training
nengo.Node(output=1, label="bias"), pool,
transform=self.W_bias, synapse=None)
nengo.Connection(
self.ensemble.neurons, pool, transform=self.W,
synapse=self.recurrent_synapse)
Reservoir.__init__(
self, self.input, pool, readout_synapse=readout_synapse,
network=self)
def test_alpha_whitesignal(Simulator, seed, rng, plt):
# Pick test LinearSystem
sys = Alpha(0.1)
state = sys.X
assert state.shape == (2, 1)
# Pick test process
n_steps = 1000
dt = 0.01
process = WhiteSignal(5.0, high=10, default_dt=dt, seed=seed)
# Sample evaluation points
dist = EvalPoints(state, process, n_steps=n_steps)
assert dist.n_steps == n_steps
assert dist.dt == dt # taken from process
assert isinstance(repr(dist), str)
n_eval_points = 500
eval_points = dist.sample(n_eval_points, 2, rng=rng)
assert eval_points.shape == (n_eval_points, 2)
# Sample encoders
encoders = Encoders(state, process).sample(n_eval_points, 2, rng=rng)
assert encoders.shape == (n_eval_points, 2)
plt.figure()
# plt.scatter(*encoders.T, label="Encoders")
plt.scatter(*eval_points.T, s=2, marker='*', label="Eval Points")
# Check that most evaluation points fall within radii
x_m, zero, x_p = sorted(np.unique(encoders[:, 0]))
assert np.allclose(-x_m, x_p)
assert np.allclose(zero, 0)
sl = (1 / x_m < eval_points[:, 0]) & (eval_points[:, 0] < 1 / x_p)
assert np.count_nonzero(sl) / float(n_eval_points) >= 0.99
y_m, zero, y_p = sorted(np.unique(encoders[:, 1]))
assert np.allclose(zero, 0)
assert np.allclose(-y_m, y_p)
sl = (1 / y_m < eval_points[:, 1]) & (eval_points[:, 1] < 1 / y_p)
assert np.count_nonzero(sl) / float(n_eval_points) >= 0.99
# Simulate same process / system in nengo network
with Network() as model:
output = nengo.Node(output=process)
probes = [nengo.Probe(output, synapse=sub) for sub in sys]
with Simulator(model, dt=dt) as sim:
sim.run(n_steps * dt)
plt.scatter(sim.data[probes[0]],
sim.data[probes[1]],
s=1,
alpha=0.5,
label="Simulated")
plt.legend()
# Check that each eval_point is a subset / sample from the ideal
ideal = np.asarray(
[sim.data[probes[0]].squeeze(), sim.data[probes[1]].squeeze()]).T
assert ideal.shape == (n_steps, 2)
for pt in eval_points:
dists = np.linalg.norm(ideal - pt[None, :], axis=1)
assert dists.shape == (n_steps, )
assert np.allclose(np.min(dists), 0)