def test_whitesignal_high_dt(Simulator, high, dt, seed, plt):
t = 1.
rms = 0.5
d = 500
process = WhiteSignal(t, high, rms=rms)
with nengo.Network() as model:
u = nengo.Node(process, size_out=d)
up = nengo.Probe(u)
with Simulator(model, seed=seed, dt=dt) as sim:
sim.run(t)
values = sim.data[up]
freq, val_psd = psd(values, dt=dt)
trange = sim.trange()
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(0, high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[npext.rfftfreq(len(trange), dt) > high] < rms * 0.5)
def make_step(self, size_in, size_out, dt, rng):
assert size_in == 0
d = size_out
n_coefficients = int(np.ceil(self.period / dt / 2.))
shape = (d, n_coefficients + 1)
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[:, 0] = 0.
coefficients[:, -1].imag = 0.
if self.high is not None:
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[:, set_to_zero] = 0.
power_correction = np.sqrt(1. - np.sum(set_to_zero, dtype=float) /
n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=1)
def step(t):
i = int(round(t / dt))
return signal[:, i % signal.shape[1]]
return step
def make_step(self, shape_in, shape_out, dt, rng):
assert shape_in == (0, )
nyquist_cutoff = 0.5 / dt
if self.high > nyquist_cutoff:
raise ValidationError("High must not exceed the Nyquist frequency "
"for the given dt (%0.3f)" % nyquist_cutoff,
attr='high',
obj=self)
n_coefficients = int(np.ceil(self.period / dt / 2.))
shape = (n_coefficients + 1, ) + shape_out
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[0] = 0.
coefficients[-1].imag = 0.
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[set_to_zero] = 0.
power_correction = np.sqrt(1. - np.sum(set_to_zero, dtype=float) /
n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=0)
def step_whitesignal(t):
i = int(round(t / dt))
return signal[i % signal.shape[0]]
return step_whitesignal
def make_step(self, shape_in, shape_out, dt, rng):
assert shape_in == (0,)
nyquist_cutoff = 0.5 / dt
if self.high > nyquist_cutoff:
raise ValidationError("High must not exceed the Nyquist frequency "
"for the given dt (%0.3f)" % nyquist_cutoff,
attr='high', obj=self)
n_coefficients = int(np.ceil(self.period / dt / 2.))
shape = (n_coefficients + 1,) + shape_out
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[0] = 0.
coefficients[-1].imag = 0.
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[set_to_zero] = 0.
power_correction = np.sqrt(
1. - np.sum(set_to_zero, dtype=float) / n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=0)
def step_whitesignal(t):
i = int(round(t / dt))
return signal[i % signal.shape[0]]
return step_whitesignal
def test_whitesignal_high_dt(Simulator, high, dt, seed, plt):
t = 1.
rms = 0.5
d = 500
process = WhiteSignal(t, high, rms=rms)
with nengo.Network() as model:
u = nengo.Node(process, size_out=d)
up = nengo.Probe(u)
with Simulator(model, seed=seed, dt=dt) as sim:
sim.run(t)
values = sim.data[up]
freq, val_psd = psd(values, dt=dt)
trange = sim.trange()
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(right=high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[npext.rfftfreq(len(trange), dt) > high] < rms * 0.5)
def make_step(self, size_in, size_out, dt, rng):
assert size_in == 0
d = size_out
n_coefficients = int(np.ceil(self.period / dt / 2.))
shape = (n_coefficients + 1, d)
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[0] = 0.
coefficients[-1].imag = 0.
if self.high is not None:
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[set_to_zero] = 0.
power_correction = np.sqrt(
1. - np.sum(set_to_zero, dtype=float) / n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=0)
def step_whitesignal(t):
i = int(round(t / dt))
return signal[i % signal.shape[0]]
return step_whitesignal
def test_rfftfreq_fallback(monkeypatch):
np_rfftfreq = np.fft.rfftfreq
monkeypatch.delattr(np.fft, "rfftfreq")
importlib.reload(npext)
for n in (3, 4, 8, 9):
for d in (1.0, 3.4, 9.8):
assert np.allclose(npext.rfftfreq(n, d=d), np_rfftfreq(n, d=d))
def make_step(self, shape_in, shape_out, dt, rng, state):
assert shape_in == (0,)
nyquist_cutoff = 0.5 / dt
if self.high > nyquist_cutoff:
raise ValidationError(
"High must not exceed the Nyquist frequency "
"for the given dt (%0.3f)" % nyquist_cutoff,
attr="high",
obj=self,
)
n_coefficients = int(np.ceil(self.period / dt / 2.0))
shape = (n_coefficients + 1,) + shape_out
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0.0, sigma, size=shape)
coefficients += rng.normal(0.0, sigma, size=shape)
coefficients[0] = 0.0
coefficients[-1].imag = 0.0
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[set_to_zero] = 0.0
power_correction = np.sqrt(
1.0 - np.sum(set_to_zero, dtype=float) / n_coefficients
)
if power_correction > 0.0:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=0)
if self.y0 is not None:
# Starts each dimension off where it is closest to y0
def shift(x):
offset = np.argmin(abs(self.y0 - x))
return np.roll(x, -offset + 1) # +1 since t starts at dt
signal = np.apply_along_axis(shift, 0, signal)
def step_whitesignal(t):
i = int(round(t / dt))
return signal[i % signal.shape[0]]
return step_whitesignal
def make_sample(self, dt, d=1, rng=np.random):
n_coefficients = int(np.ceil(self.duration / dt / 2.))
shape = (d, n_coefficients + 1)
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[:, 0] = 0.
coefficients[:, -1].imag = 0.
if self.high is not None:
set_to_zero = rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[:, set_to_zero] = 0.
power_correction = np.sqrt(1. - np.sum(set_to_zero, dtype=float) /
n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
t = np.array([0])
signal = np.fft.irfft(coefficients, axis=1)
return functools.partial(self.sample, t=t, signal=signal)
def make_sample(self, dt, d=1, rng=np.random):
n_coefficients = int(np.ceil(self.duration / dt / 2.))
shape = (d, n_coefficients + 1)
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[:, 0] = 0.
coefficients[:, -1].imag = 0.
if self.high is not None:
set_to_zero = rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[:, set_to_zero] = 0.
power_correction = np.sqrt(
1. - np.sum(set_to_zero, dtype=float) / n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
t = np.array([0])
signal = np.fft.irfft(coefficients, axis=1)
return functools.partial(self.sample, t=t, signal=signal)
def test_whitenoise_high(high, rng, plt):
rms = 0.5
d = 500
t = 1000
dt = 0.001
process = WhiteNoise(dt * t, high, rms=rms)
values = nengo.processes.sample(t, process, dt=dt, d=d, rng=rng)
freq, val_psd = psd(values)
trange = np.arange(1, t + 1) * dt
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(right=high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[rfftfreq(t, dt) > high] < rms * 0.5)
def test_whitesignal_high(high, rng, plt):
rms = 0.5
d = 500
t = 1
dt = 0.001
process = WhiteSignal(t, high, rms=rms)
values = process.run(t, d=d, dt=dt, rng=rng)
freq, val_psd = psd(values)
trange = process.trange(t, dt=dt)
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(right=high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[npext.rfftfreq(t, dt) > high] < rms * 0.5)
def test_whitenoise_high(high, rng, plt):
rms = 0.5
d = 500
t = 1000
dt = 0.001
process = WhiteNoise(dt * t, high, rms=rms)
values = nengo.processes.sample(t, process, dt=dt, d=d, rng=rng)
freq, val_psd = psd(values)
trange = np.arange(1, t + 1) * dt
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(right=high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[rfftfreq(t, dt) > high] < rms * 0.5)
def test_whitesignal_high(high, rng, plt):
rms = 0.5
d = 500
t = 1
dt = 0.001
process = WhiteSignal(t, high, rms=rms)
values = process.run(t, d=d, dt=dt, rng=rng)
freq, val_psd = psd(values)
trange = process.trange(t, dt=dt)
plt.subplot(2, 1, 1)
plt.title("First two D of white noise process, high=%d Hz" % high)
plt.plot(trange, values[:, :2])
plt.xlim(right=trange[-1])
plt.subplot(2, 1, 2)
plt.title("Power spectrum")
plt.plot(freq, val_psd, drawstyle='steps')
plt.xlim(right=high * 2.0)
assert np.allclose(np.std(values, axis=1), rms, rtol=0.15)
assert np.all(val_psd[npext.rfftfreq(t, dt) > high] < rms * 0.5)
def make_step(self, shape_in, shape_out, dt, rng):
assert shape_in == (0,)
nyquist_cutoff = 0.5 / dt
if self.high > nyquist_cutoff:
raise ValidationError("High must not exceed the Nyquist frequency "
"for the given dt (%0.3f)" % nyquist_cutoff,
attr='high', obj=self)
n_coefficients = int(np.ceil(self.period / dt / 2.))
shape = (n_coefficients + 1,) + shape_out
sigma = self.rms * np.sqrt(0.5)
coefficients = 1j * rng.normal(0., sigma, size=shape)
coefficients += rng.normal(0., sigma, size=shape)
coefficients[0] = 0.
coefficients[-1].imag = 0.
set_to_zero = npext.rfftfreq(2 * n_coefficients, d=dt) > self.high
coefficients[set_to_zero] = 0.
power_correction = np.sqrt(
1. - np.sum(set_to_zero, dtype=float) / n_coefficients)
if power_correction > 0.:
coefficients /= power_correction
coefficients *= np.sqrt(2 * n_coefficients)
signal = np.fft.irfft(coefficients, axis=0)
if self.y0 is not None:
# Starts each dimension off where it is closest to y0
def shift(x):
offset = np.argmin(abs(self.y0 - x))
return np.roll(x, -offset+1) # +1 since t starts at dt
signal = np.apply_along_axis(shift, 0, signal)
def step_whitesignal(t):
i = int(round(t / dt))
return signal[i % signal.shape[0]]
return step_whitesignal
def psd(values, dt=0.001):
freq = npext.rfftfreq(values.shape[0], d=dt)
power = 2. * np.std(np.abs(np.fft.rfft(values, axis=0)), axis=1) / np.sqrt(
values.shape[0])
return freq, power
def psd(values, dt=0.001):
freq = npext.rfftfreq(values.shape[0], d=dt)
power = 2. * np.std(np.abs(np.fft.rfft(
values, axis=0)), axis=1) / np.sqrt(values.shape[0])
return freq, power
