def jacobian(params):
a = params[0]
i = params[1]
t = params[2]
# Get the frequencies, including the negitive ones.
df = 1.0 / dt / n_time
f = sp.arange(n_time, dtype=float)
f[n_time // 2 + 1:] -= f[-1] + 1
f = abs(f) * df
# 0th mode is meaningless. Set to unity to avoid errors.
f[0] = 1
# The power law part.
p_law = (f / f_0)**(-(params[1]**2 + min_index))
# Memory for the three derivative functions.
spec = sp.empty((3, n_time), dtype=float)
# The formula for the following derivatives derived in Kiyo's notes,
# Nov. 28, 2011.
# Derivative with respect to the amplitude parameter.
spec[0, :] = -2.0 * a * p_law
# Derivative with respect to the index parameter.
spec[1, :] = (a**2 + T_small**2) * p_law * sp.log(f / f_0) * 2.0 * i
# Derivative with respect to the thermal parameter.
spec[2, :] = -2.0 * t
# Get rid of the mean mode.
spec[:, 0] = 0
# Convolve with the window function.
spec = npow.convolve_power(spec, window[None, :], -1)
# Prune to the same size as the data.
spec = npow.prune_power(spec, -1)
spec = spec[:, 1:].real
return spec / weights
def jacobian(params):
a = params[0]
i = params[1]
t = params[2]
# Get the frequencies, including the negitive ones.
df = 1.0 / dt / n_time
f = sp.arange(n_time, dtype=float)
f[n_time // 2 + 1 :] -= f[-1] + 1
f = abs(f) * df
# 0th mode is meaningless. Set to unity to avoid errors.
f[0] = 1
# The power law part.
p_law = (f / f_0) ** (-(params[1] ** 2 + min_index))
# Memory for the three derivative functions.
spec = sp.empty((3, n_time), dtype=float)
# The formula for the following derivatives derived in Kiyo's notes,
# Nov. 28, 2011.
# Derivative with respect to the amplitude parameter.
spec[0, :] = -2.0 * a * p_law
# Derivative with respect to the index parameter.
spec[1, :] = (a ** 2 + T_small ** 2) * p_law * sp.log(f / f_0) * 2.0 * i
# Derivative with respect to the thermal parameter.
spec[2, :] = -2.0 * t
# Get rid of the mean mode.
spec[:, 0] = 0
# Convolve with the window function.
spec = npow.convolve_power(spec, window[None, :], -1)
# Prune to the same size as the data.
spec = npow.prune_power(spec, -1)
spec = spec[:, 1:].real
return spec / weights
def test_fit_over_f_plus_const(self):
dt = 0.13
n_time = 10000
amp = 0.67 # K**2/Hz
index = -1.3
f_0 = 1.0
thermal = 2.7 # K**2/Hz
BW = 1./dt/2
window = sig.get_window('hanning', n_time)
n_spec = 10
p = 0
for ii in range(n_spec):
time_stream = noise_power.generate_overf_noise(amp, index, f_0,
dt, n_time)
time_stream += rand.normal(size=n_time) * sp.sqrt(thermal * BW * 2)
time_stream -= sp.mean(time_stream)
time_stream *= window
p += noise_power.calculate_power(time_stream)
p /= n_spec
p = noise_power.make_power_physical_units(p, dt)
w = noise_power.calculate_power(window)
w_norm = sp.mean(w).real
#w /= w_norm
p = noise_power.prune_power(p).real
#p /= w_norm
f = noise_power.ps_freq_axis(dt, n_time)
p = p[1:]
f = f[1:]
amp_m, index_m, f0_m, thermal_m = mn.fit_overf_const(p, w, f)
self.assertTrue(sp.allclose(amp_m, amp, atol=0.2))
self.assertTrue(sp.allclose(index_m, index, atol=0.1))
self.assertTrue(sp.allclose(thermal_m, thermal, atol=0.1))
def test_statistical_different_windows(self):
n_trials = 1000
n_points = 200
window1 = sp.ones(n_points, dtype=float)
window1 += sp.sin(sp.arange(n_points) / 10.0)
window2 = 2 * sp.ones(n_points, dtype=float)
window2 += 2 * sp.sin(sp.arange(n_points) / 22.0)
window2[window2 < 0.5] = 0
window1[window1 < 0.5] = 0
power = sp.zeros(n_points // 2)
for ii in range(n_trials):
wave = self.amp1 * random.randn(n_points)
p = npow.windowed_power(wave * window1, window1, wave * window2,
window2)
power += npow.prune_power(p).real
power /= n_trials
self.assertTrue(
sp.allclose(power / self.amp1**2,
1.0,
atol=6.0 * (2.0 / sp.sqrt(n_trials))))
# Expect this to fail ~1/100 times.
self.assertFalse(
sp.allclose(power / self.amp1**2,
1.0,
atol=0.01 * (2.0 / sp.sqrt(n_trials))))
def test_fit_over_f_plus_const(self):
dt = 0.13
n_time = 10000
amp = 0.67 # K**2/Hz
index = -1.3
f_0 = 1.0
thermal = 2.7 # K**2/Hz
BW = 1. / dt / 2
window = sig.get_window('hanning', n_time)
n_spec = 10
p = 0
for ii in range(n_spec):
time_stream = noise_power.generate_overf_noise(
amp, index, f_0, dt, n_time)
time_stream += rand.normal(size=n_time) * sp.sqrt(thermal * BW * 2)
time_stream -= sp.mean(time_stream)
time_stream *= window
p += noise_power.calculate_power(time_stream)
p /= n_spec
p = noise_power.make_power_physical_units(p, dt)
w = noise_power.calculate_power(window)
w_norm = sp.mean(w).real
#w /= w_norm
p = noise_power.prune_power(p).real
#p /= w_norm
f = noise_power.ps_freq_axis(dt, n_time)
p = p[1:]
f = f[1:]
amp_m, index_m, f0_m, thermal_m = mn.fit_overf_const(p, w, f)
self.assertTrue(sp.allclose(amp_m, amp, atol=0.2))
self.assertTrue(sp.allclose(index_m, index, atol=0.1))
self.assertTrue(sp.allclose(thermal_m, thermal, atol=0.1))
def model(params):
a = params[0] ** 2 + T_small ** 2
i = -(params[1] ** 2 + min_index)
t = params[2] ** 2 + T_small ** 2
spec = npow.overf_power_spectrum(a, i, f_0, dt, n_time)
spec += t
spec = npow.convolve_power(spec, window)
spec = npow.prune_power(spec)
spec = spec[1:].real
return spec
def model(params):
a = params[0]**2 + T_small**2
i = -(params[1]**2 + min_index)
t = params[2]**2 + T_small**2
spec = npow.overf_power_spectrum(a, i, f_0, dt, n_time)
spec += t
spec = npow.convolve_power(spec, window)
spec = npow.prune_power(spec)
spec = spec[1:].real
return spec
def test_window_with_zeros(self) :
window = sp.ones_like(self.wave1)
window += sp.sin(sp.arange(self.n)/50.0)
self.wave1 *= window
power = npow.windowed_power(self.wave1, window)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1]/self.amp1**2/self.n*4, 1.0, 3)
self.assertTrue(sp.allclose(power[:self.mode1], 0,
atol=self.amp1**2*self.n/1e3))
self.assertTrue(sp.allclose(power[self.mode1+1:], 0,
atol=self.amp1**2*self.n/1e3))
def test_no_window(self) :
window = sp.ones_like(self.wave1)
power = npow.windowed_power(self.wave1, window)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1]/self.amp1**2/self.n*4, 1)
self.assertTrue(sp.allclose(power[:self.mode1], 0,
atol=self.amp1**2*self.n/1e15))
self.assertTrue(sp.allclose(power[self.mode1+1:], 0,
atol=self.amp1**2*self.n/1e15))
# With no window, we have a quick way to the answer
quick_power = npow.calculate_power(self.wave1)
self.assertTrue(sp.allclose(power, quick_power[:self.n//2]))
def test_statistical_no_window(self) :
n_trials = 1000
n_points = 200
window = sp.ones(n_points, dtype=float)
power = sp.zeros(n_points//2)
for ii in range(n_trials) :
wave = self.amp1*random.randn(n_points)
p = npow.windowed_power(wave, window)
power += npow.prune_power(p).real
power /= n_trials
self.assertTrue(sp.allclose(power/self.amp1**2, 1.0,
atol=4.0*(2.0/sp.sqrt(n_trials))))
# Expect this to fail ~1/100 times.
self.assertFalse(sp.allclose(power/self.amp1**2, 1.0,
atol=0.01*(2.0/sp.sqrt(n_trials))))
def test_different_windows(self) :
window1 = sp.ones_like(self.wave1)
window1 += sp.sin(sp.arange(self.n)/40.0)
window2 = 2*sp.ones_like(self.wave1)
window2 += 2*sp.sin(sp.arange(self.n)/62.0)
window2[window2<0.5] = 0
wave1 = self.wave1*window1
wave2 = self.wave1*window2
power = npow.windowed_power(wave1, window1, wave2, window2)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1]/self.amp1**2/self.n*4, 1.0, 3)
self.assertTrue(sp.allclose(power[:self.mode1], 0,
atol=self.amp1**2*self.n/1e3))
self.assertTrue(sp.allclose(power[self.mode1+1:], 0,
atol=self.amp1**2*self.n/1e3))
def test_window_with_zeros(self):
window = sp.ones_like(self.wave1)
window += sp.sin(sp.arange(self.n) / 50.0)
self.wave1 *= window
power = npow.windowed_power(self.wave1, window)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1] / self.amp1**2 / self.n * 4,
1.0, 3)
self.assertTrue(
sp.allclose(power[:self.mode1],
0,
atol=self.amp1**2 * self.n / 1e3))
self.assertTrue(
sp.allclose(power[self.mode1 + 1:],
0,
atol=self.amp1**2 * self.n / 1e3))
def test_no_window(self):
window = sp.ones_like(self.wave1)
power = npow.windowed_power(self.wave1, window)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1] / self.amp1**2 / self.n * 4,
1)
self.assertTrue(
sp.allclose(power[:self.mode1],
0,
atol=self.amp1**2 * self.n / 1e15))
self.assertTrue(
sp.allclose(power[self.mode1 + 1:],
0,
atol=self.amp1**2 * self.n / 1e15))
# With no window, we have a quick way to the answer
quick_power = npow.calculate_power(self.wave1)
self.assertTrue(sp.allclose(power, quick_power[:self.n // 2]))
def test_statistical_physical_units(self) :
n_trials = 1000
n_points = 200
dt = 0.001
window = sp.ones(n_points, dtype=float)
power = sp.zeros(n_points//2)
for ii in range(n_trials) :
wave = self.amp1*random.randn(n_points)
power += npow.prune_power(npow.calculate_power(wave)).real
power /= n_trials
power = npow.make_power_physical_units(power, dt)
freqs = npow.ps_freq_axis(dt, n_points)
df = abs(sp.mean(sp.diff(freqs)))
# The integral of the power spectrum should be the variance. Factor of
# 2 get the negitive frequencies.
integrated_power = sp.sum(power) * df * 2
self.assertTrue(sp.allclose(integrated_power/self.amp1**2, 1.0,
atol=4.0*(2.0/sp.sqrt(n_trials*n_points))))
def test_statistical_no_window(self):
n_trials = 1000
n_points = 200
window = sp.ones(n_points, dtype=float)
power = sp.zeros(n_points // 2)
for ii in range(n_trials):
wave = self.amp1 * random.randn(n_points)
p = npow.windowed_power(wave, window)
power += npow.prune_power(p).real
power /= n_trials
self.assertTrue(
sp.allclose(power / self.amp1**2,
1.0,
atol=4.0 * (2.0 / sp.sqrt(n_trials))))
# Expect this to fail ~1/100 times.
self.assertFalse(
sp.allclose(power / self.amp1**2,
1.0,
atol=0.01 * (2.0 / sp.sqrt(n_trials))))
def test_statistical_physical_units(self):
n_trials = 1000
n_points = 200
dt = 0.001
window = sp.ones(n_points, dtype=float)
power = sp.zeros(n_points // 2)
for ii in range(n_trials):
wave = self.amp1 * random.randn(n_points)
power += npow.prune_power(npow.calculate_power(wave)).real
power /= n_trials
power = npow.make_power_physical_units(power, dt)
freqs = npow.ps_freq_axis(dt, n_points)
df = abs(sp.mean(sp.diff(freqs)))
# The integral of the power spectrum should be the variance. Factor of
# 2 get the negitive frequencies.
integrated_power = sp.sum(power) * df * 2
self.assertTrue(
sp.allclose(integrated_power / self.amp1**2,
1.0,
atol=4.0 * (2.0 / sp.sqrt(n_trials * n_points))))
def test_different_windows(self):
window1 = sp.ones_like(self.wave1)
window1 += sp.sin(sp.arange(self.n) / 40.0)
window2 = 2 * sp.ones_like(self.wave1)
window2 += 2 * sp.sin(sp.arange(self.n) / 62.0)
window2[window2 < 0.5] = 0
wave1 = self.wave1 * window1
wave2 = self.wave1 * window2
power = npow.windowed_power(wave1, window1, wave2, window2)
power = npow.prune_power(power)
self.assertAlmostEqual(power[self.mode1] / self.amp1**2 / self.n * 4,
1.0, 3)
self.assertTrue(
sp.allclose(power[:self.mode1],
0,
atol=self.amp1**2 * self.n / 1e3))
self.assertTrue(
sp.allclose(power[self.mode1 + 1:],
0,
atol=self.amp1**2 * self.n / 1e3))
def test_statistical_different_windows(self) :
n_trials = 1000
n_points = 200
window1 = sp.ones(n_points, dtype=float)
window1 += sp.sin(sp.arange(n_points)/10.0)
window2 = 2*sp.ones(n_points, dtype=float)
window2 += 2*sp.sin(sp.arange(n_points)/22.0)
window2[window2<0.5] = 0
window1[window1<0.5] = 0
power = sp.zeros(n_points//2)
for ii in range(n_trials) :
wave = self.amp1*random.randn(n_points)
p = npow.windowed_power(wave*window1, window1, wave*window2,
window2)
power += npow.prune_power(p).real
power /= n_trials
self.assertTrue(sp.allclose(power/self.amp1**2, 1.0,
atol=6.0*(2.0/sp.sqrt(n_trials))))
# Expect this to fail ~1/100 times.
self.assertFalse(sp.allclose(power/self.amp1**2, 1.0,
atol=0.01*(2.0/sp.sqrt(n_trials))))
def get_freq_modes_over_f(power_mat,
window_function,
frequency,
n_modes,
plots=False):
"""Fines the most correlated frequency modes and fits thier noise."""
n_f = len(frequency)
d_f = sp.mean(sp.diff(frequency))
dt = 1. / 2. / frequency[-1]
n_chan = power_mat.shape[-1]
n_time = window_function.shape[0]
# The threshold for assuming there isn't enough data to measure anything.
no_data_thres = 10. / n_time
# Initialize the dictionary that will hold all the parameters.
output_params = {}
# First take the low frequency part of the spetrum matrix and average over
# enough bins to get a well conditioned matrix.
low_f_mat = sp.mean(power_mat[:4 * n_chan, :, :].real, 0)
# Factor the matrix to get the most correlated modes.
e, v = linalg.eigh(low_f_mat)
# Make sure they are sorted.
if not sp.alltrue(sp.diff(e) >= 0):
raise RuntimeError("Eigenvalues not sorted")
# Power matrix striped of the biggest modes.
reduced_power = sp.copy(power_mat)
mode_list = []
# Solve for the spectra of these modes.
for ii in range(n_modes):
this_mode_params = {}
# Get power spectrum and window function for this mode.
mode = v[:, -1 - ii]
mode_power = sp.sum(mode * power_mat.real, -1)
mode_power = sp.sum(mode * mode_power, -1)
mode_window = sp.sum(mode[:, None]**2 * window_function, 1)
mode_window = sp.sum(mode_window * mode[None, :]**2, 1)
# Protect against no data.
if sp.mean(mode_window).real < no_data_thres:
this_mode_params['amplitude'] = 0.
this_mode_params['index'] = 0.
this_mode_params['f_0'] = 1.
this_mode_params['thermal'] = T_infinity**2 * dt
else:
# Fit the spectrum.
p = fit_overf_const(mode_power, mode_window, frequency)
# Put all the parameters we measured into the output.
this_mode_params['amplitude'] = p[0]
this_mode_params['index'] = p[1]
this_mode_params['f_0'] = p[2]
this_mode_params['thermal'] = p[3]
this_mode_params['mode'] = mode
output_params['over_f_mode_' + str(ii)] = this_mode_params
# Remove the mode from the power matrix.
tmp_amp = sp.sum(reduced_power * mode, -1)
tmp_amp2 = sp.sum(reduced_power * mode[:, None], -2)
tmp_amp3 = sp.sum(tmp_amp2 * mode, -1)
reduced_power -= tmp_amp[:, :, None] * mode
reduced_power -= tmp_amp2[:, None, :] * mode[:, None]
reduced_power += tmp_amp3[:, None, None] * mode[:, None] * mode
mode_list.append(mode)
# Initialize the compensation matrix, that will be used to restore thermal
# noise that gets subtracted out. See Jan 29, Feb 17th, 2012 of Kiyo's
# notes.
compensation = sp.eye(n_chan, dtype=float)
for mode1 in mode_list:
compensation.flat[::n_chan + 1] -= 2 * mode1**2
for mode2 in mode_list:
mode_prod = mode1 * mode2
compensation += mode_prod[:, None] * mode_prod[None, :]
# Now that we've striped the noisiest modes, measure the auto power
# spectrum, averaged over channels.
auto_spec_mean = reduced_power.view()
auto_spec_mean.shape = (n_f, n_chan**2)
auto_spec_mean = auto_spec_mean[:, ::n_chan + 1].real
auto_spec_mean = sp.mean(auto_spec_mean, -1)
diag_window = window_function.view()
diag_window.shape = (n_time, n_chan**2)
diag_window = diag_window[:, ::n_chan + 1]
auto_spec_window = sp.mean(diag_window, -1)
if sp.mean(auto_spec_window).real < no_data_thres:
auto_cross_over = 0.
auto_index = 0.
auto_thermal = 0
else:
auto_spec_params = fit_overf_const(auto_spec_mean, auto_spec_window,
frequency)
auto_thermal = auto_spec_params[3]
if (auto_spec_params[0] <= 0 or auto_spec_params[3] <= 0
or auto_spec_params[1] > -0.599):
auto_cross_over = 0.
auto_index = 0.
else:
auto_index = auto_spec_params[1]
auto_cross_over = auto_spec_params[2] * (
auto_spec_params[0] / auto_spec_params[3])**(-1. / auto_index)
#if auto_cross_over < d_f:
# auto_index = 0.
# auto_cross_over = 0.
# Plot the mean auto spectrum if desired.
if plots:
h = plt.gcf()
a = h.add_subplot(*h.current_subplot)
norm = sp.mean(auto_spec_window).real
auto_plot = auto_spec_mean / norm
plotable = auto_plot > 0
lines = a.loglog(frequency[plotable], auto_plot[plotable])
c = lines[-1].get_color()
# And plot the fit in a light color.
if auto_cross_over > d_f / 4.:
spec = npow.overf_power_spectrum(auto_thermal, auto_index,
auto_cross_over, dt, n_time)
else:
spec = sp.zeros(n_time, dtype=float)
spec += auto_thermal
spec[0] = 0
spec = npow.convolve_power(spec, auto_spec_window)
spec = npow.prune_power(spec)
spec = spec[1:].real
if norm > no_data_thres:
spec /= norm
plotable = spec > 0
a.loglog(frequency[plotable],
spec[plotable],
c=c,
alpha=0.4,
linestyle=':')
output_params['all_channel_index'] = auto_index
output_params['all_channel_corner_f'] = auto_cross_over
# Finally measure the thermal part of the noise in each channel.
cross_over_ind = sp.digitize([auto_cross_over * 4], frequency)[0]
cross_over_ind = max(cross_over_ind, n_f // 2)
cross_over_ind = min(cross_over_ind, int(9. * n_f / 10.))
thermal = reduced_power[cross_over_ind:, :, :].real
n_high_f = thermal.shape[0]
thermal.shape = (n_high_f, n_chan**2)
thermal = sp.mean(thermal[:, ::n_chan + 1], 0)
thermal_norms = sp.mean(diag_window, 0).real
bad_inds = thermal_norms < no_data_thres
thermal_norms[bad_inds] = 1.
# Compensate for power lost in mode subtraction.
compensation[:, bad_inds] = 0
compensation[bad_inds, :] = 0
for ii in xrange(n_chan):
if bad_inds[ii]:
compensation[ii, ii] = 1.
thermal = linalg.solve(compensation, thermal)
# Normalize
thermal /= thermal_norms
thermal[bad_inds] = T_infinity**2 * dt
# Occationally the compensation fails horribly on a few channels.
# When this happens, zero out the offending indices.
thermal[thermal < 0] = 0
output_params['thermal'] = thermal
# Now that we know what thermal is, we can subtract it out of the modes we
# already measured.
for ii in range(n_modes):
mode_params = output_params['over_f_mode_' + str(ii)]
thermal_contribution = sp.sum(mode_params['mode']**2 * thermal)
# Subtract a maximum of 90% of the white noise to keep things positive
# definate.
new_white = max(mode_params['thermal'] - thermal_contribution,
0.1 * mode_params['thermal'])
if mode_params['thermal'] < 0.5 * T_infinity**2 * dt:
mode_params['thermal'] = new_white
return output_params
def measure_noise_parameters(Blocks, parameters, split_scans=False, plots=False):
"""Given a set of data blocks, measure noise parameters.
Measurement done for all polarizations but only the first cal state.
"""
# Initialize the output.
out_parameters = {}
if set(parameters) == {"channel_var"}:
# Calculate the full correlated power spectrum.
power_mat, window_function, dt, channel_means = npow.full_power_diag(
Blocks,
window="hanning",
deconvolve=False,
n_time=-1.05,
normalize=False,
split_scans=split_scans,
subtract_slope=True,
)
# This shouldn't be nessisary, since I've tried to keep things finite in
# the above function. However, leave it in for now just in case.
if not sp.alltrue(sp.isfinite(power_mat)):
msg = "Non finite power spectrum calculated. Offending data in " "file starting with scan %d." % (
Blocks[0].field["SCAN"]
)
raise ce.DataError(msg)
# Get frequency axis and do unit conversions.
n_time = power_mat.shape[0]
n_chan = power_mat.shape[-1]
frequency = npow.ps_freq_axis(dt, n_time)
power_mat = npow.prune_power(power_mat, 0)
power_mat = npow.make_power_physical_units(power_mat, dt)
# Discard the mean mode.
frequency = frequency[1:]
power_mat = power_mat[1:, ...]
n_f = len(frequency)
# Loop over polarizations.
cal_ind = 0
n_pols = power_mat.shape[1]
for ii in range(n_pols):
this_pol_power = power_mat[:, ii, cal_ind, :]
this_pol_window = window_function[:, ii, cal_ind, :]
this_pol = Blocks[0].field["CRVAL4"][ii]
this_pol_parameters = {}
# If we are plotting, activate the subplot for this polarization and
# this band.
if plots:
h = plt.gcf()
# The last subplot should be hidden in the figure object.
current_subplot = h.current_subplot
current_subplot = current_subplot[:2] + (current_subplot[2] + 1,)
h.current_subplot = current_subplot
# Now figure out what we want to measure and measure it.
if "channel_var" in parameters:
power_diag = this_pol_power.view()
window_function_diag = this_pol_window.view()
# Integral of the power spectrum from -BW to BW.
channel_var = sp.mean(power_diag, 0) / dt
# Normalize for the window.
norms = sp.mean(window_function_diag, 0).real
bad_inds = norms < 10.0 / n_time
norms[bad_inds] = 1
channel_var /= norms
# If a channel is completly masked Deweight it by giving a high
# variance
channel_var[bad_inds] = T_infinity ** 2
this_pol_parameters["channel_var"] = channel_var
out_parameters[this_pol] = this_pol_parameters
return out_parameters
else:
# Calculate the full correlated power spectrum.
power_mat, window_function, dt, channel_means = npow.full_power_mat(
Blocks,
window="hanning",
deconvolve=False,
n_time=-1.05,
normalize=False,
split_scans=split_scans,
subtract_slope=True,
)
# This shouldn't be nessisary, since I've tried to keep things finite in
# the above function. However, leave it in for now just in case.
if not sp.alltrue(sp.isfinite(power_mat)):
msg = "Non finite power spectrum calculated. Offending data in " "file starting with scan %d." % (
Blocks[0].field["SCAN"]
)
raise ce.DataError(msg)
# Get frequency axis and do unit conversions.
n_time = power_mat.shape[0]
n_chan = power_mat.shape[-1]
frequency = npow.ps_freq_axis(dt, n_time)
power_mat = npow.prune_power(power_mat, 0)
power_mat = npow.make_power_physical_units(power_mat, dt)
# Discard the mean mode.
frequency = frequency[1:]
power_mat = power_mat[1:, ...]
n_f = len(frequency)
# Loop over polarizations.
cal_ind = 0
n_pols = power_mat.shape[1]
for ii in range(n_pols):
this_pol_power = power_mat[:, ii, cal_ind, :, :]
this_pol_window = window_function[:, ii, cal_ind, :, :]
this_pol = Blocks[0].field["CRVAL4"][ii]
this_pol_parameters = {}
# If we are plotting, activate the subplot for this polarization and
# this band.
if plots:
h = plt.gcf()
# The last subplot should be hidden in the figure object.
current_subplot = h.current_subplot
current_subplot = current_subplot[:2] + (current_subplot[2] + 1,)
h.current_subplot = current_subplot
# Now figure out what we want to measure and measure it.
if "channel_var" in parameters:
power_diag = this_pol_power.view()
power_diag.shape = (n_f, n_chan ** 2)
power_diag = power_diag[:, :: n_chan + 1].real
window_function_diag = this_pol_window.view()
window_function_diag.shape = (n_time, n_chan ** 2)
window_function_diag = window_function_diag[:, :: n_chan + 1]
# Integral of the power spectrum from -BW to BW.
channel_var = sp.mean(power_diag, 0) / dt
# Normalize for the window.
norms = sp.mean(window_function_diag, 0).real
bad_inds = norms < 10.0 / n_time
norms[bad_inds] = 1
channel_var /= norms
# If a channel is completly masked Deweight it by giving a high
# variance
channel_var[bad_inds] = T_infinity ** 2
this_pol_parameters["channel_var"] = channel_var
for noise_model in parameters:
if noise_model[:18] == "freq_modes_over_f_":
n_modes = int(noise_model[18:])
this_pol_parameters[noise_model] = get_freq_modes_over_f(
this_pol_power, this_pol_window, frequency, n_modes, plots=plots
)
out_parameters[this_pol] = this_pol_parameters
return out_parameters
def get_freq_modes_over_f(power_mat, window_function, frequency, n_modes, plots=False):
"""Fines the most correlated frequency modes and fits thier noise."""
n_f = len(frequency)
d_f = sp.mean(sp.diff(frequency))
dt = 1.0 / 2.0 / frequency[-1]
n_chan = power_mat.shape[-1]
n_time = window_function.shape[0]
# The threshold for assuming there isn't enough data to measure anything.
no_data_thres = 10.0 / n_time
# Initialize the dictionary that will hold all the parameters.
output_params = {}
# First take the low frequency part of the spetrum matrix and average over
# enough bins to get a well conditioned matrix.
low_f_mat = sp.mean(power_mat[: 4 * n_chan, :, :].real, 0)
# Factor the matrix to get the most correlated modes.
e, v = linalg.eigh(low_f_mat)
# Make sure they are sorted.
if not sp.alltrue(sp.diff(e) >= 0):
raise RuntimeError("Eigenvalues not sorted")
# Power matrix striped of the biggest modes.
reduced_power = sp.copy(power_mat)
mode_list = []
# Solve for the spectra of these modes.
for ii in range(n_modes):
this_mode_params = {}
# Get power spectrum and window function for this mode.
mode = v[:, -1 - ii]
mode_power = sp.sum(mode * power_mat.real, -1)
mode_power = sp.sum(mode * mode_power, -1)
mode_window = sp.sum(mode[:, None] ** 2 * window_function, 1)
mode_window = sp.sum(mode_window * mode[None, :] ** 2, 1)
# Protect against no data.
if sp.mean(mode_window).real < no_data_thres:
this_mode_params["amplitude"] = 0.0
this_mode_params["index"] = 0.0
this_mode_params["f_0"] = 1.0
this_mode_params["thermal"] = T_infinity ** 2 * dt
else:
# Fit the spectrum.
p = fit_overf_const(mode_power, mode_window, frequency)
# Put all the parameters we measured into the output.
this_mode_params["amplitude"] = p[0]
this_mode_params["index"] = p[1]
this_mode_params["f_0"] = p[2]
this_mode_params["thermal"] = p[3]
this_mode_params["mode"] = mode
output_params["over_f_mode_" + str(ii)] = this_mode_params
# Remove the mode from the power matrix.
tmp_amp = sp.sum(reduced_power * mode, -1)
tmp_amp2 = sp.sum(reduced_power * mode[:, None], -2)
tmp_amp3 = sp.sum(tmp_amp2 * mode, -1)
reduced_power -= tmp_amp[:, :, None] * mode
reduced_power -= tmp_amp2[:, None, :] * mode[:, None]
reduced_power += tmp_amp3[:, None, None] * mode[:, None] * mode
mode_list.append(mode)
# Initialize the compensation matrix, that will be used to restore thermal
# noise that gets subtracted out. See Jan 29, Feb 17th, 2012 of Kiyo's
# notes.
compensation = sp.eye(n_chan, dtype=float)
for mode1 in mode_list:
compensation.flat[:: n_chan + 1] -= 2 * mode1 ** 2
for mode2 in mode_list:
mode_prod = mode1 * mode2
compensation += mode_prod[:, None] * mode_prod[None, :]
# Now that we've striped the noisiest modes, measure the auto power
# spectrum, averaged over channels.
auto_spec_mean = reduced_power.view()
auto_spec_mean.shape = (n_f, n_chan ** 2)
auto_spec_mean = auto_spec_mean[:, :: n_chan + 1].real
auto_spec_mean = sp.mean(auto_spec_mean, -1)
diag_window = window_function.view()
diag_window.shape = (n_time, n_chan ** 2)
diag_window = diag_window[:, :: n_chan + 1]
auto_spec_window = sp.mean(diag_window, -1)
if sp.mean(auto_spec_window).real < no_data_thres:
auto_cross_over = 0.0
auto_index = 0.0
auto_thermal = 0
else:
auto_spec_params = fit_overf_const(auto_spec_mean, auto_spec_window, frequency)
auto_thermal = auto_spec_params[3]
if auto_spec_params[0] <= 0 or auto_spec_params[3] <= 0 or auto_spec_params[1] > -0.599:
auto_cross_over = 0.0
auto_index = 0.0
else:
auto_index = auto_spec_params[1]
auto_cross_over = auto_spec_params[2] * (auto_spec_params[0] / auto_spec_params[3]) ** (-1.0 / auto_index)
# if auto_cross_over < d_f:
# auto_index = 0.
# auto_cross_over = 0.
# Plot the mean auto spectrum if desired.
if plots:
h = plt.gcf()
a = h.add_subplot(*h.current_subplot)
norm = sp.mean(auto_spec_window).real
auto_plot = auto_spec_mean / norm
plotable = auto_plot > 0
lines = a.loglog(frequency[plotable], auto_plot[plotable])
c = lines[-1].get_color()
# And plot the fit in a light color.
if auto_cross_over > d_f / 4.0:
spec = npow.overf_power_spectrum(auto_thermal, auto_index, auto_cross_over, dt, n_time)
else:
spec = sp.zeros(n_time, dtype=float)
spec += auto_thermal
spec[0] = 0
spec = npow.convolve_power(spec, auto_spec_window)
spec = npow.prune_power(spec)
spec = spec[1:].real
if norm > no_data_thres:
spec /= norm
plotable = spec > 0
a.loglog(frequency[plotable], spec[plotable], c=c, alpha=0.4, linestyle=":")
output_params["all_channel_index"] = auto_index
output_params["all_channel_corner_f"] = auto_cross_over
# Finally measure the thermal part of the noise in each channel.
cross_over_ind = sp.digitize([auto_cross_over * 4], frequency)[0]
cross_over_ind = max(cross_over_ind, n_f // 2)
cross_over_ind = min(cross_over_ind, int(9.0 * n_f / 10.0))
thermal = reduced_power[cross_over_ind:, :, :].real
n_high_f = thermal.shape[0]
thermal.shape = (n_high_f, n_chan ** 2)
thermal = sp.mean(thermal[:, :: n_chan + 1], 0)
thermal_norms = sp.mean(diag_window, 0).real
bad_inds = thermal_norms < no_data_thres
thermal_norms[bad_inds] = 1.0
# Compensate for power lost in mode subtraction.
compensation[:, bad_inds] = 0
compensation[bad_inds, :] = 0
for ii in xrange(n_chan):
if bad_inds[ii]:
compensation[ii, ii] = 1.0
thermal = linalg.solve(compensation, thermal)
# Normalize
thermal /= thermal_norms
thermal[bad_inds] = T_infinity ** 2 * dt
# Occationally the compensation fails horribly on a few channels.
# When this happens, zero out the offending indices.
thermal[thermal < 0] = 0
output_params["thermal"] = thermal
# Now that we know what thermal is, we can subtract it out of the modes we
# already measured.
for ii in range(n_modes):
mode_params = output_params["over_f_mode_" + str(ii)]
thermal_contribution = sp.sum(mode_params["mode"] ** 2 * thermal)
# Subtract a maximum of 90% of the white noise to keep things positive
# definate.
new_white = max(mode_params["thermal"] - thermal_contribution, 0.1 * mode_params["thermal"])
if mode_params["thermal"] < 0.5 * T_infinity ** 2 * dt:
mode_params["thermal"] = new_white
return output_params
def measure_noise_parameters(Blocks,
parameters,
split_scans=False,
plots=False):
"""Given a set of data blocks, measure noise parameters.
Measurement done for all polarizations but only the first cal state.
"""
# Initialize the output.
out_parameters = {}
if set(parameters) == {"channel_var"}:
# Calculate the full correlated power spectrum.
power_mat, window_function, dt, channel_means = npow.full_power_diag(
Blocks,
window="hanning",
deconvolve=False,
n_time=-1.05,
normalize=False,
split_scans=split_scans,
subtract_slope=True)
# This shouldn't be nessisary, since I've tried to keep things finite in
# the above function. However, leave it in for now just in case.
if not sp.alltrue(sp.isfinite(power_mat)):
msg = ("Non finite power spectrum calculated. Offending data in "
"file starting with scan %d." % (Blocks[0].field['SCAN']))
raise ce.DataError(msg)
# Get frequency axis and do unit conversions.
n_time = power_mat.shape[0]
n_chan = power_mat.shape[-1]
frequency = npow.ps_freq_axis(dt, n_time)
power_mat = npow.prune_power(power_mat, 0)
power_mat = npow.make_power_physical_units(power_mat, dt)
# Discard the mean mode.
frequency = frequency[1:]
power_mat = power_mat[1:, ...]
n_f = len(frequency)
# Loop over polarizations.
cal_ind = 0
n_pols = power_mat.shape[1]
for ii in range(n_pols):
this_pol_power = power_mat[:, ii, cal_ind, :]
this_pol_window = window_function[:, ii, cal_ind, :]
this_pol = Blocks[0].field['CRVAL4'][ii]
this_pol_parameters = {}
# If we are plotting, activate the subplot for this polarization and
# this band.
if plots:
h = plt.gcf()
# The last subplot should be hidden in the figure object.
current_subplot = h.current_subplot
current_subplot = current_subplot[:2] + (current_subplot[2] +
1, )
h.current_subplot = current_subplot
# Now figure out what we want to measure and measure it.
if "channel_var" in parameters:
power_diag = this_pol_power.view()
window_function_diag = this_pol_window.view()
# Integral of the power spectrum from -BW to BW.
channel_var = sp.mean(power_diag, 0) / dt
# Normalize for the window.
norms = sp.mean(window_function_diag, 0).real
bad_inds = norms < 10. / n_time
norms[bad_inds] = 1
channel_var /= norms
# If a channel is completly masked Deweight it by giving a high
# variance
channel_var[bad_inds] = T_infinity**2
this_pol_parameters["channel_var"] = channel_var
out_parameters[this_pol] = this_pol_parameters
return out_parameters
else:
# Calculate the full correlated power spectrum.
power_mat, window_function, dt, channel_means = npow.full_power_mat(
Blocks,
window="hanning",
deconvolve=False,
n_time=-1.05,
normalize=False,
split_scans=split_scans,
subtract_slope=True)
# This shouldn't be nessisary, since I've tried to keep things finite in
# the above function. However, leave it in for now just in case.
if not sp.alltrue(sp.isfinite(power_mat)):
msg = ("Non finite power spectrum calculated. Offending data in "
"file starting with scan %d." % (Blocks[0].field['SCAN']))
raise ce.DataError(msg)
# Get frequency axis and do unit conversions.
n_time = power_mat.shape[0]
n_chan = power_mat.shape[-1]
frequency = npow.ps_freq_axis(dt, n_time)
power_mat = npow.prune_power(power_mat, 0)
power_mat = npow.make_power_physical_units(power_mat, dt)
# Discard the mean mode.
frequency = frequency[1:]
power_mat = power_mat[1:, ...]
n_f = len(frequency)
# Loop over polarizations.
cal_ind = 0
n_pols = power_mat.shape[1]
for ii in range(n_pols):
this_pol_power = power_mat[:, ii, cal_ind, :, :]
this_pol_window = window_function[:, ii, cal_ind, :, :]
this_pol = Blocks[0].field['CRVAL4'][ii]
this_pol_parameters = {}
# If we are plotting, activate the subplot for this polarization and
# this band.
if plots:
h = plt.gcf()
# The last subplot should be hidden in the figure object.
current_subplot = h.current_subplot
current_subplot = current_subplot[:2] + (current_subplot[2] +
1, )
h.current_subplot = current_subplot
# Now figure out what we want to measure and measure it.
if "channel_var" in parameters:
power_diag = this_pol_power.view()
power_diag.shape = (n_f, n_chan**2)
power_diag = power_diag[:, ::n_chan + 1].real
window_function_diag = this_pol_window.view()
window_function_diag.shape = (n_time, n_chan**2)
window_function_diag = window_function_diag[:, ::n_chan + 1]
# Integral of the power spectrum from -BW to BW.
channel_var = sp.mean(power_diag, 0) / dt
# Normalize for the window.
norms = sp.mean(window_function_diag, 0).real
bad_inds = norms < 10. / n_time
norms[bad_inds] = 1
channel_var /= norms
# If a channel is completly masked Deweight it by giving a high
# variance
channel_var[bad_inds] = T_infinity**2
this_pol_parameters["channel_var"] = channel_var
for noise_model in parameters:
if noise_model[:18] == "freq_modes_over_f_":
n_modes = int(noise_model[18:])
this_pol_parameters[noise_model] = \
get_freq_modes_over_f(this_pol_power, this_pol_window,
frequency, n_modes, plots=plots)
out_parameters[this_pol] = this_pol_parameters
return out_parameters
