def test_circularconv_helpers():
"""Test the circular convolution helper functions in Numpy"""
rng = np.random.RandomState(43232)
dims = 1000
invert_a = True
invert_b = False
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
dims2 = 2 * dims - (2 if dims % 2 == 0 else 1)
inA = nengo.networks.CircularConvolution._input_transform(
dims, first=True, invert=invert_a)
inB = nengo.networks.CircularConvolution._input_transform(
dims, first=False, invert=invert_b)
outC = nengo.networks.CircularConvolution._output_transform(dims)
XY = np.zeros((dims2, 2))
XY += np.dot(inA.reshape(dims2, 2, dims), x)
XY += np.dot(inB.reshape(dims2, 2, dims), y)
C = XY[:, 0] * XY[:, 1]
z1 = np.dot(outC, C)
assert np.allclose(z0, z1)
def test_helpers(self):
"""Test the circular convolution helper functions in Numpy"""
rng = np.random.RandomState(43232)
dims = 1000
invert_a = True
invert_b = False
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
dims2 = 2 * dims - (2 if dims % 2 == 0 else 1)
inA = CircularConvolution._input_transform(dims,
first=True,
invert=invert_a)
inB = CircularConvolution._input_transform(dims,
first=False,
invert=invert_b)
outC = CircularConvolution._output_transform(dims)
XY = np.zeros((dims2, 2))
XY += np.dot(inA.reshape(dims2, 2, dims), x)
XY += np.dot(inB.reshape(dims2, 2, dims), y)
C = XY[:, 0] * XY[:, 1]
z1 = np.dot(outC, C)
assert_allclose(self, logger, z0, z1)
def test_circularconv_transforms(invert_a, invert_b):
"""Test the circular convolution transforms"""
rng = np.random.RandomState(43232)
dims = 100
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
cconv = nengo.networks.CircularConvolution(nengo.Direct(), dims, invert_a=invert_a, invert_b=invert_b)
XY = np.dot(cconv.transformA, x) * np.dot(cconv.transformB, y)
z1 = np.dot(cconv.transform_out, XY)
assert np.allclose(z0, z1)
def test_circularconv_transforms(invert_a, invert_b, rng):
"""Test the circular convolution transforms"""
dims = 100
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
tr_a = transform_in(dims, 'A', invert_a)
tr_b = transform_in(dims, 'B', invert_b)
tr_out = transform_out(dims)
XY = np.dot(tr_a, x) * np.dot(tr_b, y)
z1 = np.dot(tr_out, XY)
assert np.allclose(z0, z1)
def test_circularconv_transforms(invert_a, invert_b, rng):
"""Test the circular convolution transforms"""
dims = 100
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
tr_a = transform_in(dims, 'A', invert_a)
tr_b = transform_in(dims, 'B', invert_b)
tr_out = transform_out(dims)
XY = np.dot(tr_a, x) * np.dot(tr_b, y)
z1 = np.dot(tr_out, XY)
assert np.allclose(z0, z1)
def test_circularconv_transforms(invert_a, invert_b):
"""Test the circular convolution transforms"""
rng = np.random.RandomState(43232)
dims = 100
x = rng.randn(dims)
y = rng.randn(dims)
z0 = circconv(x, y, invert_a=invert_a, invert_b=invert_b)
cconv = nengo.networks.CircularConvolution(
1, dims, invert_a=invert_a, invert_b=invert_b)
XY = np.dot(cconv.transformA, x) * np.dot(cconv.transformB, y)
z1 = np.dot(cconv.transform_out, XY)
assert np.allclose(z0, z1)
def test_neural_accuracy(Simulator, seed, rng, dims, neurons_per_product=128):
a = rng.normal(scale=np.sqrt(1.0 / dims), size=dims)
b = rng.normal(scale=np.sqrt(1.0 / dims), size=dims)
result = circconv(a, b)
model = nengo.Network(label="circular conv", seed=seed)
model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
with model:
input_a = nengo.Node(a)
input_b = nengo.Node(b)
cconv = nengo.networks.CircularConvolution(neurons_per_product, dimensions=dims)
nengo.Connection(input_a, cconv.input_a, synapse=None)
nengo.Connection(input_b, cconv.input_b, synapse=None)
res_p = nengo.Probe(cconv.output)
with Simulator(model) as sim:
sim.run(0.01)
error = rms(result - sim.data[res_p][-1])
assert error < 0.1
def test_neural_accuracy(Simulator, seed, rng, dims, neurons_per_product=128):
a = rng.normal(scale=np.sqrt(1./dims), size=dims)
b = rng.normal(scale=np.sqrt(1./dims), size=dims)
result = circconv(a, b)
model = nengo.Network(label="circular conv", seed=seed)
model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
with model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
cconv = nengo.networks.CircularConvolution(
neurons_per_product, dimensions=dims)
nengo.Connection(inputA, cconv.A, synapse=None)
nengo.Connection(inputB, cconv.B, synapse=None)
res_p = nengo.Probe(cconv.output)
sim = Simulator(model)
sim.run(0.01)
error = rmse(result, sim.data[res_p][-1])
assert error < 0.1
def test_input_magnitude(Simulator, dims=16, magnitude=10):
"""Test to make sure the magnitude scaling works.
Builds two different CircularConvolution networks, one with the correct
magnitude and one with 1.0 as the input_magnitude.
"""
rng = np.random.RandomState(4238)
neurons_per_product = 128
a = rng.normal(scale=np.sqrt(1./dims), size=dims) * magnitude
b = rng.normal(scale=np.sqrt(1./dims), size=dims) * magnitude
result = circconv(a, b)
model = nengo.Network(label="circular conv", seed=1)
model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
with model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
cconv = nengo.networks.CircularConvolution(
neurons_per_product, dimensions=dims,
input_magnitude=magnitude)
nengo.Connection(inputA, cconv.A, synapse=None)
nengo.Connection(inputB, cconv.B, synapse=None)
res_p = nengo.Probe(cconv.output)
cconv_bad = nengo.networks.CircularConvolution(
neurons_per_product, dimensions=dims,
input_magnitude=1) # incorrect magnitude
nengo.Connection(inputA, cconv_bad.A, synapse=None)
nengo.Connection(inputB, cconv_bad.B, synapse=None)
res_p_bad = nengo.Probe(cconv_bad.output)
sim = Simulator(model)
sim.run(0.01)
error = rmse(result, sim.data[res_p][-1]) / (magnitude ** 2)
error_bad = rmse(result, sim.data[res_p_bad][-1]) / (magnitude ** 2)
assert error < 0.1
assert error_bad > 0.1
def test_input_magnitude(Simulator, seed, rng, dims=16, magnitude=10):
"""Test to make sure the magnitude scaling works.
Builds two different CircularConvolution networks, one with the correct
magnitude and one with 1.0 as the input_magnitude.
"""
neurons_per_product = 128
a = rng.normal(scale=np.sqrt(1. / dims), size=dims) * magnitude
b = rng.normal(scale=np.sqrt(1. / dims), size=dims) * magnitude
result = circconv(a, b)
model = nengo.Network(label="circular conv", seed=seed)
model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
with model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
cconv = nengo.networks.CircularConvolution(neurons_per_product,
dimensions=dims,
input_magnitude=magnitude)
nengo.Connection(inputA, cconv.A, synapse=None)
nengo.Connection(inputB, cconv.B, synapse=None)
res_p = nengo.Probe(cconv.output)
cconv_bad = nengo.networks.CircularConvolution(
neurons_per_product, dimensions=dims,
input_magnitude=1) # incorrect magnitude
nengo.Connection(inputA, cconv_bad.A, synapse=None)
nengo.Connection(inputB, cconv_bad.B, synapse=None)
res_p_bad = nengo.Probe(cconv_bad.output)
sim = Simulator(model)
sim.run(0.01)
error = rmse(result, sim.data[res_p][-1]) / (magnitude**2)
error_bad = rmse(result, sim.data[res_p_bad][-1]) / (magnitude**2)
assert error < 0.1
assert error_bad > 0.1
dims = map(int, sys.argv[2].split(","))
# neurons_per_product = 128
neurons_per_product = 256
simtime = 1.0
radius = 1
records = []
for i, dim in enumerate(dims):
rng = np.random.RandomState(123)
a = rng.normal(scale=np.sqrt(1.0 / dim), size=dim)
b = rng.normal(scale=np.sqrt(1.0 / dim), size=dim)
c = circconv(a, b)
# --- Model
with nengo.Network(seed=9) as model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
A = nengo.networks.EnsembleArray(neurons_per_product,
dim,
radius=radius)
B = nengo.networks.EnsembleArray(neurons_per_product,
dim,
radius=radius)
C = nengo.networks.EnsembleArray(neurons_per_product,
dim,
radius=radius)
D = nengo.networks.CircularConvolution(neurons_per_product,
dims = map(int, sys.argv[2].split(','))
# neurons_per_product = 128
neurons_per_product = 256
simtime = 1.0
radius = 1
records = []
for i, dim in enumerate(dims):
rng = np.random.RandomState(123)
a = rng.normal(scale=np.sqrt(1./dim), size=dim)
b = rng.normal(scale=np.sqrt(1./dim), size=dim)
c = circconv(a, b)
# --- Model
with nengo.Network(seed=9) as model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
A = nengo.networks.EnsembleArray(
neurons_per_product, dim, radius=radius)
B = nengo.networks.EnsembleArray(
neurons_per_product, dim, radius=radius)
C = nengo.networks.EnsembleArray(
neurons_per_product, dim, radius=radius)
D = nengo.networks.CircularConvolution(
neurons_per_product, dim, input_magnitude=radius)
nengo.Connection(inputA, A.input, synapse=None)
def test_circularconv(Simulator, nl, dims=4, neurons_per_product=128):
rng = np.random.RandomState(42342)
n_neurons = neurons_per_product
n_neurons_d = 2 * neurons_per_product
radius = 1
a = rng.normal(scale=np.sqrt(1./dims), size=dims)
b = rng.normal(scale=np.sqrt(1./dims), size=dims)
c = circconv(a, b)
assert np.abs(a).max() < radius
assert np.abs(b).max() < radius
assert np.abs(c).max() < radius
### model
model = nengo.Model("circular convolution")
inputA = nengo.Node(output=a)
inputB = nengo.Node(output=b)
A = EnsembleArray(nl(n_neurons), dims, radius=radius)
B = EnsembleArray(nl(n_neurons), dims, radius=radius)
C = EnsembleArray(nl(n_neurons), dims, radius=radius)
D = nengo.networks.CircularConvolution(
neurons=nl(n_neurons_d),
dimensions=A.dimensions, radius=radius)
nengo.Connection(inputA, A.input)
nengo.Connection(inputB, B.input)
nengo.Connection(A.output, D.A)
nengo.Connection(B.output, D.B)
nengo.Connection(D.output, C.input)
A_p = nengo.Probe(A.output, 'output', filter=0.03)
B_p = nengo.Probe(B.output, 'output', filter=0.03)
C_p = nengo.Probe(C.output, 'output', filter=0.03)
D_p = nengo.Probe(D.ensemble.output, 'output', filter=0.03)
# check FFT magnitude
d = np.dot(D.transformA, a) + np.dot(D.transformB, b)
assert np.abs(d).max() < radius
### simulation
sim = Simulator(model)
sim.run(1.0)
t = sim.trange()
with Plotter(Simulator, nl) as plt:
def plot(sim, a, A, title=""):
a_ref = np.tile(a, (len(t), 1))
a_sim = sim.data(A_p)
colors = ['b', 'g', 'r', 'c', 'm', 'y']
for i in range(min(dims, len(colors))):
plt.plot(t, a_ref[:, i], '--', color=colors[i])
plt.plot(t, a_sim[:, i], '-', color=colors[i])
plt.title(title)
plt.subplot(221)
plot(sim, a, A, title="A")
plt.subplot(222)
plot(sim, b, B, title="B")
plt.subplot(223)
plot(sim, c, C, title="C")
plt.subplot(224)
plot(sim, d, D.ensemble, title="D")
plt.savefig('test_circularconv.test_circularconv_%d.pdf' % dims)
plt.close()
### results
tmask = t > (0.5 + sim.model.dt/2)
assert sim.data(A_p)[tmask].shape == (499, dims)
a_sim = sim.data(A_p)[tmask].mean(axis=0)
b_sim = sim.data(B_p)[tmask].mean(axis=0)
c_sim = sim.data(C_p)[tmask].mean(axis=0)
d_sim = sim.data(D_p)[tmask].mean(axis=0)
rtol, atol = 0.1, 0.05
assert np.allclose(a, a_sim, rtol=rtol, atol=atol)
assert np.allclose(b, b_sim, rtol=rtol, atol=atol)
assert np.allclose(d, d_sim, rtol=rtol, atol=atol)
assert rmse(c, c_sim) < 0.075
def test_circularconv(Simulator, nl, dims=4, neurons_per_product=128):
rng = np.random.RandomState(4238)
n_neurons = neurons_per_product
n_neurons_d = 2 * neurons_per_product
radius = 1
a = rng.normal(scale=np.sqrt(1./dims), size=dims)
b = rng.normal(scale=np.sqrt(1./dims), size=dims)
result = circconv(a, b)
assert np.abs(a).max() < radius
assert np.abs(b).max() < radius
assert np.abs(result).max() < radius
# --- model
model = nengo.Network(label="circular convolution")
with model:
model.config[nengo.Ensemble].neuron_type = nl()
inputA = nengo.Node(a)
inputB = nengo.Node(b)
A = EnsembleArray(n_neurons, dims, radius=radius)
B = EnsembleArray(n_neurons, dims, radius=radius)
cconv = nengo.networks.CircularConvolution(
n_neurons_d, dimensions=dims)
res = EnsembleArray(n_neurons, dims, radius=radius)
nengo.Connection(inputA, A.input)
nengo.Connection(inputB, B.input)
nengo.Connection(A.output, cconv.A)
nengo.Connection(B.output, cconv.B)
nengo.Connection(cconv.output, res.input)
A_p = nengo.Probe(A.output, synapse=0.03)
B_p = nengo.Probe(B.output, synapse=0.03)
res_p = nengo.Probe(res.output, synapse=0.03)
# --- simulation
sim = Simulator(model)
sim.run(1.0)
t = sim.trange()
with Plotter(Simulator, nl) as plt:
def plot(actual, probe, title=""):
ref_y = np.tile(actual, (len(t), 1))
sim_y = sim.data[probe]
colors = ['b', 'g', 'r', 'c', 'm', 'y']
for i in range(min(dims, len(colors))):
plt.plot(t, ref_y[:, i], '--', color=colors[i])
plt.plot(t, sim_y[:, i], '-', color=colors[i])
plt.title(title)
plt.subplot(311)
plot(a, A_p, title="A")
plt.subplot(312)
plot(b, B_p, title="B")
plt.subplot(313)
plot(result, res_p, title="Result")
plt.tight_layout()
plt.savefig('test_circularconv.test_circularconv_%d.pdf' % dims)
plt.close()
# --- results
tmask = t > (0.5 + sim.dt/2)
assert sim.data[A_p][tmask].shape == (499, dims)
a_sim = sim.data[A_p][tmask].mean(axis=0)
b_sim = sim.data[B_p][tmask].mean(axis=0)
res_sim = sim.data[res_p][tmask].mean(axis=0)
rtol, atol = 0.1, 0.05
assert np.allclose(a, a_sim, rtol=rtol, atol=atol)
assert np.allclose(b, b_sim, rtol=rtol, atol=atol)
assert rmse(result, res_sim) < 0.075
def test_circconv_split():
dims = 16
seed = 1
npd = 100
sim_time = 0.1
rng = np.random.RandomState(seed)
magnitude = 1.0
pstc = 0.005
a = rng.normal(scale=np.sqrt(1./dims), size=dims) * magnitude
b = rng.normal(scale=np.sqrt(1./dims), size=dims) * magnitude
result = circconv(a, b)
model = nengo.Network(label="CircConv", seed=seed)
model.config[nengo.Ensemble].neuron_type = nengo.LIFRate()
with model:
inputA = nengo.Node(a)
inputB = nengo.Node(b)
input_ea_a = nengo.networks.EnsembleArray(
npd, dims, radius=np.sqrt(1./dims), label="A")
input_ea_b = nengo.networks.EnsembleArray(
npd, dims, radius=np.sqrt(1./dims), label="B")
nengo.Connection(inputA, input_ea_a.input, synapse=None)
nengo.Connection(inputB, input_ea_b.input, synapse=None)
cconv = nengo.networks.CircularConvolution(
npd, dimensions=dims,
input_magnitude=magnitude)
nengo.Connection(input_ea_a.output, cconv.A, synapse=pstc)
nengo.Connection(input_ea_b.output, cconv.B, synapse=pstc)
output = nengo.networks.EnsembleArray(
npd, dims, radius=np.sqrt(1./dims), label="output")
nengo.Connection(cconv.output, output.input, synapse=pstc)
p = nengo.Probe(output.output)
sim_no_split = nengo.Simulator(model)
sim_no_split.run(sim_time)
splitter = EnsembleArraySplitter()
splitter.split(model, max_neurons=npd, preserve_zero_conns=False)
assert len(model.networks) == 4
assert len(model.all_networks) == 7
assert len(model.ensembles) == 0
assert len(model.all_ensembles) == 3 * dims + 2 * (2 * dims + 4)
sim_split = nengo.Simulator(model)
sim_split.run(sim_time)
pre_split_data = sim_no_split.data
post_split_data = splitter.unsplit_data(sim_split)
error = rmse(result, pre_split_data[p][-1])
assert error < 0.1
error = rmse(result, post_split_data[p][-1])
assert error < 0.1
error = rmse(pre_split_data[p][-1], post_split_data[p][-1])
assert error < 0.1
remove_log_file(splitter)
def test_circularconv(Simulator, nl, dims=4, neurons_per_product=128):
rng = np.random.RandomState(4238)
n_neurons = neurons_per_product
n_neurons_d = 2 * neurons_per_product
radius = 1
a = rng.normal(scale=np.sqrt(1.0 / dims), size=dims)
b = rng.normal(scale=np.sqrt(1.0 / dims), size=dims)
result = circconv(a, b)
assert np.abs(a).max() < radius
assert np.abs(b).max() < radius
assert np.abs(result).max() < radius
# --- model
model = nengo.Network(label="circular convolution")
with model:
inputA = nengo.Node(output=a)
inputB = nengo.Node(output=b)
A = EnsembleArray(nl(n_neurons), dims, radius=radius)
B = EnsembleArray(nl(n_neurons), dims, radius=radius)
cconv = nengo.networks.CircularConvolution(neurons=nl(n_neurons_d), dimensions=dims)
res = EnsembleArray(nl(n_neurons), dims, radius=radius)
nengo.Connection(inputA, A.input)
nengo.Connection(inputB, B.input)
nengo.Connection(A.output, cconv.A)
nengo.Connection(B.output, cconv.B)
nengo.Connection(cconv.output, res.input)
A_p = nengo.Probe(A.output, synapse=0.03)
B_p = nengo.Probe(B.output, synapse=0.03)
res_p = nengo.Probe(res.output, synapse=0.03)
# --- simulation
sim = Simulator(model)
sim.run(1.0)
t = sim.trange()
with Plotter(Simulator, nl) as plt:
def plot(actual, probe, title=""):
ref_y = np.tile(actual, (len(t), 1))
sim_y = sim.data[probe]
colors = ["b", "g", "r", "c", "m", "y"]
for i in range(min(dims, len(colors))):
plt.plot(t, ref_y[:, i], "--", color=colors[i])
plt.plot(t, sim_y[:, i], "-", color=colors[i])
plt.title(title)
plt.subplot(311)
plot(a, A_p, title="A")
plt.subplot(312)
plot(b, B_p, title="B")
plt.subplot(313)
plot(result, res_p, title="Result")
plt.tight_layout()
plt.savefig("test_circularconv.test_circularconv_%d.pdf" % dims)
plt.close()
# --- results
tmask = t > (0.5 + sim.dt / 2)
assert sim.data[A_p][tmask].shape == (499, dims)
a_sim = sim.data[A_p][tmask].mean(axis=0)
b_sim = sim.data[B_p][tmask].mean(axis=0)
res_sim = sim.data[res_p][tmask].mean(axis=0)
rtol, atol = 0.1, 0.05
assert np.allclose(a, a_sim, rtol=rtol, atol=atol)
assert np.allclose(b, b_sim, rtol=rtol, atol=atol)
assert rmse(result, res_sim) < 0.075
def _test_circularconv(self, dims=5, neurons_per_product=128):
rng = np.random.RandomState(42342)
n_neurons = neurons_per_product * dims
n_neurons_d = 2 * neurons_per_product * (2 * dims -
(2 if dims % 2 == 0 else 1))
radius = 1
a = rng.normal(scale=np.sqrt(1. / dims), size=dims)
b = rng.normal(scale=np.sqrt(1. / dims), size=dims)
c = circconv(a, b)
self.assertTrue(np.abs(a).max() < radius)
self.assertTrue(np.abs(b).max() < radius)
self.assertTrue(np.abs(c).max() < radius)
### model
model = nengo.Model("circular convolution")
inputA = model.make_node("inputA", output=a)
inputB = model.make_node("inputB", output=b)
A = model.add(
EnsembleArray('A', nengo.LIF(n_neurons), dims, radius=radius))
B = model.add(
EnsembleArray('B', nengo.LIF(n_neurons), dims, radius=radius))
C = model.add(
EnsembleArray('C', nengo.LIF(n_neurons), dims, radius=radius))
D = model.add(
CircularConvolution('D',
neurons=nengo.LIF(n_neurons_d),
dimensions=A.dimensions,
radius=radius))
inputA.connect_to(A)
inputB.connect_to(B)
A.connect_to(D.A)
B.connect_to(D.B)
D.output.connect_to(C)
model.probe(A, filter=0.03)
model.probe(B, filter=0.03)
model.probe(C, filter=0.03)
model.probe(D.ensemble, filter=0.03)
# check FFT magnitude
d = np.dot(D.transformA, a) + np.dot(D.transformB, b)
self.assertTrue(np.abs(d).max() < radius)
### simulation
sim = model.simulator(sim_class=self.Simulator)
sim.run(1.0)
t = sim.data(model.t).flatten()
with Plotter(self.Simulator) as plt:
def plot(sim, a, A, title=""):
a_ref = np.tile(a, (len(t), 1))
a_sim = sim.data(A)
colors = ['b', 'g', 'r', 'c', 'm', 'y']
for i in xrange(min(dims, len(colors))):
plt.plot(t, a_ref[:, i], '--', color=colors[i])
plt.plot(t, a_sim[:, i], '-', color=colors[i])
plt.title(title)
plt.subplot(221)
plot(sim, a, A, title="A")
plt.subplot(222)
plot(sim, b, B, title="B")
plt.subplot(223)
plot(sim, c, C, title="C")
plt.subplot(224)
plot(sim, d, D.ensemble, title="D")
plt.savefig('test_circularconv.test_circularconv_%d.pdf' % dims)
plt.close()
### results
tmask = t > (0.5 + sim.model.dt / 2)
self.assertEqual(sim.data(A)[tmask].shape, (499, dims))
a_sim = sim.data(A)[tmask].mean(axis=0)
b_sim = sim.data(B)[tmask].mean(axis=0)
c_sim = sim.data(C)[tmask].mean(axis=0)
d_sim = sim.data(D.ensemble)[tmask].mean(axis=0)
rtol, atol = 0.1, 0.05
self.assertTrue(np.allclose(a, a_sim, rtol=rtol, atol=atol))
self.assertTrue(np.allclose(b, b_sim, rtol=rtol, atol=atol))
self.assertTrue(np.allclose(d, d_sim, rtol=rtol, atol=atol))
self.assertTrue(rmse(c, c_sim) < 0.075)
def _test_circularconv(self, dims=5, neurons_per_product=128):
rng = np.random.RandomState(42342)
n_neurons = neurons_per_product * dims
n_neurons_d = 2 * neurons_per_product * (
2*dims - (2 if dims % 2 == 0 else 1))
radius = 1
a = rng.normal(scale=np.sqrt(1./dims), size=dims)
b = rng.normal(scale=np.sqrt(1./dims), size=dims)
c = circconv(a, b)
self.assertTrue(np.abs(a).max() < radius)
self.assertTrue(np.abs(b).max() < radius)
self.assertTrue(np.abs(c).max() < radius)
### model
model = nengo.Model("circular convolution")
inputA = model.make_node("inputA", output=a)
inputB = model.make_node("inputB", output=b)
A = model.add(EnsembleArray(
'A', nengo.LIF(n_neurons), dims, radius=radius))
B = model.add(EnsembleArray(
'B', nengo.LIF(n_neurons), dims, radius=radius))
C = model.add(EnsembleArray(
'C', nengo.LIF(n_neurons), dims, radius=radius))
D = model.add(CircularConvolution(
'D', neurons=nengo.LIF(n_neurons_d),
dimensions=A.dimensions, radius=radius))
inputA.connect_to(A)
inputB.connect_to(B)
A.connect_to(D.A)
B.connect_to(D.B)
D.output.connect_to(C)
model.probe(A, filter=0.03)
model.probe(B, filter=0.03)
model.probe(C, filter=0.03)
model.probe(D.ensemble, filter=0.03)
# check FFT magnitude
d = np.dot(D.transformA, a) + np.dot(D.transformB, b)
self.assertTrue(np.abs(d).max() < radius)
### simulation
sim = model.simulator(sim_class=self.Simulator)
sim.run(1.0)
t = sim.data(model.t).flatten()
with Plotter(self.Simulator) as plt:
def plot(sim, a, A, title=""):
a_ref = np.tile(a, (len(t), 1))
a_sim = sim.data(A)
colors = ['b', 'g', 'r', 'c', 'm', 'y']
for i in xrange(min(dims, len(colors))):
plt.plot(t, a_ref[:,i], '--', color=colors[i])
plt.plot(t, a_sim[:,i], '-', color=colors[i])
plt.title(title)
plt.subplot(221)
plot(sim, a, A, title="A")
plt.subplot(222)
plot(sim, b, B, title="B")
plt.subplot(223)
plot(sim, c, C, title="C")
plt.subplot(224)
plot(sim, d, D.ensemble, title="D")
plt.savefig('test_circularconv.test_circularconv_%d.pdf' % dims)
plt.close()
### results
tmask = t > (0.5 + sim.model.dt/2)
self.assertEqual(sim.data(A)[tmask].shape, (499, dims))
a_sim = sim.data(A)[tmask].mean(axis=0)
b_sim = sim.data(B)[tmask].mean(axis=0)
c_sim = sim.data(C)[tmask].mean(axis=0)
d_sim = sim.data(D.ensemble)[tmask].mean(axis=0)
rtol, atol = 0.1, 0.05
self.assertTrue(np.allclose(a, a_sim, rtol=rtol, atol=atol))
self.assertTrue(np.allclose(b, b_sim, rtol=rtol, atol=atol))
self.assertTrue(np.allclose(d, d_sim, rtol=rtol, atol=atol))
self.assertTrue(rmse(c, c_sim) < 0.075)