def plot_rates(rates):
"""Plot detection rates for askap surveys."""
plot_aa_style()
fig, (ax1) = plt.subplots(1, 1)
cmap = plt.get_cmap('tab10')
ax1.set_xlim((min(ALPHAS) + .1, max(ALPHAS) - .1))
ax1.set_yscale('log', nonposy='mask')
# Plot complex versus toy
for i, surv in enumerate(SURVEYS):
ax1.plot(ALPHAS,
rates[surv],
color=cmap(i + 1),
label=surv,
linestyle='dashed')
# Plot layout options
# Set up axes
ax1.set_xlabel(r'$\alpha$')
ax1.invert_xaxis()
ax1.set_ylabel('Events / htru')
plt.legend()
plt.savefig(rel_path('plots/askap_rates.pdf'), bbox_inches='tight')
def main():
"""Plot expected complex rates."""
plot_aa_style()
rates = complex_rates()
for surv in rates:
rate = rates[surv]
plt.plot(ALPHAS, rate, label=surv)
plt.xlabel(r'$\alpha_{\text{in}}$')
plt.ylabel(r'Events / htru')
plt.yscale('log')
plt.xlim((min(ALPHAS), max(ALPHAS)))
plt.legend()
plt.gca().invert_xaxis()
plt.tight_layout()
plt.grid()
plt.savefig(rel_path('./plots/complex_rates.pdf'))
def plot_logn_logs(data):
"""Plot log N log S data in a cumlative histogram."""
plot_aa_style()
fig, (ax1) = plt.subplots(1, 1)
for key in data:
x, y = data[key]
ax1.step(x, y, where='post', label=key)
plt.xlabel(r'S$_{\text{min}}$ (Jy)')
plt.ylabel(r'N(${>}\text{S}_{\text{min}}$)')
plt.xscale('log')
plt.yscale('log')
plt.xlim((1e-3, 1e1))
plt.legend()
plt.tight_layout()
plt.savefig(rel_path('plots/logn_logs_abc.pdf'))
def main():
"""Plot real rate regions per alpha."""
plot_aa_style()
rates = real_rates()
for surv in rates:
middle, top, bottom = rates[surv]
left = min(ALPHAS)
right = max(ALPHAS)
x = [left, right, right, left]
y = [top, top, bottom, bottom]
plt.fill(x, y, alpha=0.25)
plt.plot([left, right], [middle] * 2, label=surv, linestyle='dashed')
plt.xlabel(r'$\alpha_{\text{in}}$')
plt.ylabel(r'Events / htru')
plt.yscale('log')
plt.legend()
plt.gca().invert_xaxis()
plt.tight_layout()
plt.savefig(rel_path('./plots/real_rates.pdf'))
def plot_dm(pops):
"""Plot resulting dispersion measure."""
plot_aa_style()
f, (ax1) = plt.subplots(1, 1)
for i, beam in enumerate(pops):
pop = pops[beam]
dm = pop.frbs.dm
s_peak = pop.frbs.s_peak
limit = 1e-10
dm = dm[(s_peak > limit)]
print(f'{len(dm)} FRBs in graph of {pop.name}')
n, bin_edges = np.histogram(dm, bins=75)
n = n / max(n)
bins = (bin_edges[:-1] + bin_edges[1:]) / 2
# Add edges to histogram
bin_diff = np.diff(bins)[-1]
bins = np.insert(bins, 0, bins[0] - bin_diff)
bins = np.insert(bins, len(bins), bins[-1] + bin_diff)
n = np.insert(n, 0, 0)
n = np.insert(n, len(n), 0)
ax1.step(bins, n, where='mid', label=beam)
ax1.set_xlabel(r'DM (pc cm$^{-3}$)')
ax1.set_xlim([0, 3000])
ax1.set_ylabel(r'Fraction')
ax1.set_ylim([0, 1])
ax1.legend()
plt.tight_layout()
plt.savefig(rel_path(f'./plots/dm_beams.pdf'))
if min(bin_centres) <= min_s:
min_s = min(bin_centres)
if max(bin_centres) >= max_s:
max_s = max(bin_centres)
# Add a -3/2 slope
x = np.linspace(min_s, max_s, 1000)
y = -1.5 * x
y -= min(y)
y += min(np.log10(n_gt_s))
x = x[y <= max(np.log10(n_gt_s))]
y = y[y <= max(np.log10(n_gt_s))]
ax1.step(x, y, where='mid', color='grey', alpha=0.5)
# Plot alpha over log S
# Plot a Euclidean line
x = np.linspace(min_s, max_s, 1000)
y = np.ones_like(x) * -1.5
ax2.step(x, y, where='mid', color='grey', alpha=0.5)
ax1.set_ylabel(r'log N($>$S$_{\text{peak}}$)')
ax1.legend()
ax2.set_xlabel(r'log S$_{\text{peak}}$')
ax2.set_ylabel(r'$\alpha$')
ax2.set_ylim(ax2.get_ylim()[::-1])
plt.tight_layout()
plt.savefig(rel_path(f'plots/logn_logs_si.pdf'))
f, (ax1) = plt.subplots(1, 1)
for p in BEAMPATTERNS:
pop = pop_obs[p]
limit = 1e-9
s_peak = pop.frbs.s_peak
dm_igm = pop.frbs.dm_igm
mini = min(s_peak)
maxi = max(s_peak)
bins_s_peak = np.logspace(np.log10(mini), np.log10(maxi), 50)
dm_igm = dm_igm[(s_peak > limit)]
print(f'{len(dm_igm)} FRBs in graph of {pop.name}')
n, bins = np.histogram(dm_igm, bins=50)
n = n / max(n)
bincentres = (bins[:-1] + bins[1:]) / 2
ax1.step(bincentres, n, where='mid', label=p)
ax1.set_xlabel(r'DM$_{\text{IGM}}$')
ax1.set_ylabel(r'Fraction')
ax1.set_ylim([0, 1])
ax1.legend()
plt.tight_layout()
plt.savefig(rel_path('./plots/dm_igm_beampatterns.pdf'))
plot_aa_style()
plt.rcParams["figure.figsize"] = (5.75373, 5.75373)
f, axes = plt.subplots(2, 2)
s = survey_pop.frbs
axes[0, 0].step(*hist(s.snr, bin_type='log'), where='mid')
axes[0, 0].set_title('SNR')
axes[1, 0].step(*hist(s.T_sys, bin_type='log'), where='mid')
axes[1, 0].set_title(r'T$_{\text{sys}}$')
axes[1, 0].set_xlim(1, 1e2)
axes[1, 0].set_ylim(1e-3, 1)
axes[0, 1].step(*hist(s.s_peak, bin_type='log'), where='mid')
axes[0, 1].set_title(r'S$_{\text{peak}}$')
axes[0, 1].set_xlim(1e-3, 1)
axes[0, 1].set_ylim(1e-3, 1)
axes[1, 1].step(*hist(s.w_arr, bin_type='log'), where='mid')
axes[1, 1].set_title(r'w$_{\text{arr}}$')
axes[1, 1].set_ylim(1e-3, 1)
for x in [0, 1]:
for y in [0, 1]:
axes[x, y].set_xscale('log')
axes[x, y].set_yscale('log')
plt.tight_layout()
plt.savefig(rel_path('plots/perfect.pdf'))
f, (ax1) = plt.subplots(1, 1)
for p in SIDELOBES:
pop = pop_obs[p]
limit = 1e-9
s_peak = pop.frbs.s_peak
dm_igm = pop.frbs.dm_igm
mini = min(s_peak)
maxi = max(s_peak)
bins_s_peak = np.logspace(np.log10(mini), np.log10(maxi), 50)
dm_igm = dm_igm[(s_peak > limit)]
print(f'{len(dm_igm)} FRBs in graph of {pop.name}')
n, bins = np.histogram(dm_igm, bins=50)
n = n / max(n)
bincentres = (bins[:-1] + bins[1:]) / 2
ax1.step(bincentres, n, where='mid', label=p)
ax1.set_xlabel(r'DM$_{\text{IGM}}$')
ax1.set_ylabel(r'Fraction')
ax1.set_ylim([0, 1])
ax1.legend()
plt.tight_layout()
plt.savefig(rel_path(f'./plots/dm_igm_sidelobes.pdf'))
def plot_dists(surv_pop, telescope):
"""Plot the fluence and DM distribution of a surveyed population.
Args:
surv_pop (Population): Population from which to plot
telescope (str): Name of the telescope with which to compare the
distribution. Necessary for Frbcat.
"""
plot_aa_style(cols=2)
# Plot dm distribution
f, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
dm_frbpoppy = surv_pop.frbs.dm
pprint(f'Number of detected FRBs: {len(dm_frbpoppy)}')
ax1.step(*hist(dm_frbpoppy), where='mid', linestyle='dashed')
df = Frbcat().df
dm_frbcat = df[df.telescope == telescope].dm
ax1.step(*hist(dm_frbcat), where='mid')
# Compare distributions
ks = ks_2samp(dm_frbpoppy, dm_frbcat)
text = fr'$p={round(ks[1], 2)}$'
anchored_text = AnchoredText(text, loc=1, borderpad=1., frameon=False)
ax1.add_artist(anchored_text)
ax1.set_xlabel(r'DM ($\textrm{pc}\ \textrm{cm}^{-3}$)')
ax1.set_ylabel('Fraction')
ax1.set_ylim([0, 1.1])
ax1.set_xlim([0, 3500])
# Plot fluence distributions
fluence_frbpoppy = surv_pop.frbs.fluence
ax2.step(*hist(fluence_frbpoppy, bin_type='log'),
where='mid',
label='frbpoppy',
linestyle='dashed')
fluence_frbcat = df[df.telescope == telescope].fluence
ax2.step(*hist(fluence_frbcat, bin_type='log'),
where='mid',
label='frbcat')
# Compare distributions
ks = ks_2samp(fluence_frbpoppy, fluence_frbcat)
text = fr'$p={round(ks[1], 2)}$'
anchored_text = AnchoredText(text, loc=1, borderpad=1., frameon=False)
ax2.add_artist(anchored_text)
ax2.set_xlabel(r'Fluence (Jy ms)')
ax2.set_ylim([0, 1.1])
ax2.set_xlim([5e-1, 1e4])
plt.xscale('log')
plt.figlegend(loc='upper center', ncol=2, framealpha=1)
plt.tight_layout()
plt.savefig(rel_path(f'plots/frbpoppy_{telescope}.pdf'))
plt.clf()
n_gt_s = np.cumsum(hist[::-1])[::-1]
# Calculate alpha
alpha, alpha_err, norm = surv_pop.calc_logn_logs(parameter='fluence',
min_p=min_p,
max_p=max_p)
print(alpha, alpha_err, norm)
xs = 10**((np.log10(edges[:-1]) + np.log10(edges[1:])) / 2)
xs = xs[xs >= min_p]
xs = xs[xs <= max_p]
ys = [norm * x**(alpha) for x in xs]
plot_aa_style()
fig = plt.figure()
ax = fig.add_subplot(111)
plt.step(edges[:-1], n_gt_s, where='post')
plt.plot(xs,
ys,
linestyle='--',
label=rf'$\alpha$ = {alpha:.3} $\pm$ {round(abs(alpha_err), 2)}')
plt.xlabel('Fluence (Jy ms)')
plt.ylabel(r'N(${>}\text{S}_{\text{min}}$)')
plt.xscale('log')
plt.yscale('log')
plt.legend()
plt.tight_layout()
plt.savefig(rel_path('plots/logn_logf_local.pdf'))
from convenience import plot_aa_style, rel_path
STEPSIZE = 1e-6
PLOT = True
x_range = np.arange(0, 50, STEPSIZE)
y_range = 4 * (j1(x_range) / x_range)**2
nulls = []
# Find where curve changes direction
ind = np.diff(np.sign(np.diff(y_range)))
x_null = x_range[1:-1][ind > 0]
y_null = y_range[1:-1][ind > 0]
print(x_null)
if PLOT:
title = r"Bessel function over $\text{x}$"
plot_aa_style()
fig = plt.figure()
ax = fig.add_subplot(111)
plt.title(title)
plt.plot(x_range[::10], y_range[::10])
plt.scatter(x_null, y_null)
plt.yscale('log')
plt.tight_layout()
plt.savefig(rel_path('./plots/null_sidelobes.pdf'))
args = {'sidelobes': sidelobe}
s = Survey(SURVEY, gain_pattern='airy', n_sidelobes=sidelobe)
int_pro, offset = s.intensity_profile(shape=n)
# Sort the values
sorted_int = np.argsort(offset)
int_pro = int_pro[sorted_int]
offset = offset[sorted_int]
# Clean up lower limit
offset = offset[int_pro > MIN_Y]
int_pro = int_pro[int_pro > MIN_Y]
label = f'{sidelobe} sidelobes'
if sidelobe == 1:
label = label[:-1]
# Offset in degrees
offset = offset/60.
plt.plot(offset, int_pro, label=label)
plt.xlabel(r'Offset ($$^{\circ}$$)')
plt.ylabel('Intensity Profile')
plt.yscale('log')
plt.legend()
plt.tight_layout()
plt.savefig(rel_path('./plots/int_pro_sidelobes.pdf'))
# Sort the values
sorted_int = np.argsort(offset)
int_pro = int_pro[sorted_int]
offset = offset[sorted_int]
# Offset in degrees
offset = offset / 60.
bins = 1e2
bin_means, bin_edges, bin_numbers = bstat(offset,
int_pro,
statistic='mean',
bins=bins)
bin_mins, _, _ = bstat(offset, int_pro, statistic='min', bins=bins)
bin_maxs, _, _ = bstat(offset, int_pro, statistic='max', bins=bins)
center = (bin_edges[:-1] + bin_edges[1:]) / 2
plt.plot(center, bin_means, label=pattern)
plt.fill_between(center, bin_mins, bin_maxs, alpha=0.2)
plt.xlabel(r'Offset ($$^{\circ}$$)')
plt.ylabel('Intensity Profile')
plt.yscale('log')
plt.legend()
plt.tight_layout()
plt.savefig(rel_path('plots/int_pro_surveys.pdf'))
ns[s] = ns[s][1:]
bins = bins[1:]
bincentres = (bins[:-1] + bins[1:]) / 2
title = titles[i]
plt.step(bincentres, ns[s], where='mid', label=title)
i += 1
plt.xlabel('$z$')
plt.ylabel(r'$\text{d}n_{\text{FRB}}/\text{d}z$')
plt.yscale('log')
plt.legend()
plt.tight_layout()
plt.savefig(rel_path('plots/number_frbs.pdf'))
plt.clf()
if DENSITY_FRBS:
plot_aa_style()
fig = plt.figure()
ax = fig.add_subplot(111)
# Get dV
import frbpoppy.precalc as pc
d = pc.DistanceTable().lookup(z=bincentres)
dvols = d[3]
dens = {}
i = 0
for s in pop_types:
"""Check a powerlaw implementation generates the right numbers."""
import numpy as np
import matplotlib.pyplot as plt
from frbpoppy import distributions
from convenience import plot_aa_style, rel_path
POWER = -1
pl = distributions.powerlaw(1e35, 1e40, POWER, 100000)
minx = min(pl)
maxx = max(pl)
bins = 10 ** np.linspace(np.log10(minx), np.log10(maxx), 50)
hist, edges = np.histogram(pl, bins=bins)
plot_aa_style()
fig = plt.figure()
ax = fig.add_subplot(111)
plt.step(edges[:-1], hist, where='post')
plt.xscale('log')
plt.yscale('log')
plt.savefig(rel_path('plots/powerlaw.pdf'))
def plot(toy, simple, complex, real):
"""Plot rates panel."""
surveys = SURVEYS[:-1]
plot_aa_style(cols=2)
fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
cmap = plt.get_cmap('tab10')
ax1.set_xlim((min(ALPHAS) + .1, max(ALPHAS) - .1))
ax2.set_xlim((min(ALPHAS) + .1, max(ALPHAS) - .1))
ax1.set_yscale('log', nonposy='mask')
ax2.set_yscale('log', nonposy='mask')
# Plot simple versus toy
for i, surv in enumerate(surveys):
ax1.plot(ALPHAS,
toy[surv],
color=cmap(i),
linestyle='dotted',
zorder=0)
ax1.plot(ALPHAS, simple[surv], zorder=1)
# Plot complex expectations
for i, surv in enumerate(surveys):
ax2.plot(ALPHAS,
complex[surv],
color=cmap(i),
linestyle='dashed',
zorder=1)
# Plot real event rate boxes
ma, mi = ax2.get_xlim()
ma -= 0.05
mi += 0.05
size = 0.13
z = 0
for i, surv in enumerate(surveys):
central, min_r, max_r = real[surv]
left = mi - size
right = ma + size
x, y = zip(*[(ma, max_r), (right, max_r), (right, min_r), (ma, min_r)])
ax1.fill(x, y, color=cmap(i), zorder=z)
ax1.plot([ma, right + 0.08], [central, central],
color=cmap(i),
zorder=z)
x, y = zip(*[(mi, max_r), (left, max_r), (left, min_r), (mi, min_r)])
ax2.fill(x, y, color=cmap(i), zorder=z)
ax2.plot([mi, left - 0.08], [central, central],
color=cmap(i),
zorder=z)
size -= 0.02
z += 1
# Plot layout options
# Set up axes
ax1.set_xlabel(r'$\alpha_{\text{in}}$')
ax1.invert_xaxis()
ax1.set_ylabel('Events / htru')
ax1.yaxis.set_ticks_position('left')
ax1.title.set_text(r'\textit{Simple} populations')
ax2.set_xlabel(r'$\alpha_{\text{in}}$')
ax2.invert_xaxis()
ax2.yaxis.set_ticks_position('right')
ax2.tick_params(labelright=False)
ax2.title.set_text(r'\textit{Complex} populations')
# Set up layout options
fig.subplots_adjust(hspace=0)
fig.subplots_adjust(wspace=0)
# Add legend elements
elements = []
for i, surv in enumerate(surveys):
c = cmap(i)
line = Line2D([0], [0], color=c)
label = surv
elements.append((line, label))
# Add gap in legend
elements.append((Line2D([0], [0], color='white'), ''))
# Add line styles
n = 'analytical'
elements.append((Line2D([0], [0], color='gray', linestyle='dotted'), n))
elements.append((Line2D([0], [0], color='gray'), 'simple'))
elements.append((Line2D([0], [0], color='gray',
linestyle='dashed'), 'complex'))
# Add gap in legend
elements.append((Line2D([0], [0], color='white'), ''))
elements.append((Patch(facecolor='gray', edgecolor='gray',
alpha=0.6), 'real'))
lines, labels = zip(*elements)
plt.legend(lines, labels, bbox_to_anchor=(1.04, 0.5), loc="center left")
plt.savefig(rel_path('plots/rates.pdf'), bbox_inches='tight')