def plot_2d_hist(x,
y,
z,
ax=None,
xrange=None,
yrange=None,
show=True,
smooth=None,
contour=False):
"""
"""
if ax is None:
fig, ax = plt.subplots()
xsorted = np.unique(x)
ysorted = np.unique(y)
dx2 = (xsorted[1] - xsorted[0]) / 2
dy2 = (ysorted[1] - ysorted[0]) / 2
extent = (x.min() - dx2, x.max() + dx2, y.min() - dy2, y.max() + dy2
) # l r b t
nx = np.unique(x).size
ny = np.unique(y).size
zz = z.reshape(nx, ny).T
if smooth:
zz = gaussian_filter(zz, smooth)
# Display the thresholded image
ax.imshow(zz, origin="lower", cmap="binary", extent=extent, aspect="auto")
if contour:
levels = [
confidence_threshold(zz, 0.997),
confidence_threshold(zz, 0.95),
confidence_threshold(zz, 0.68)
]
ax.contour(zz,
colors="b",
linewidths=1,
zorder=10,
levels=levels,
extent=extent)
# Format axes
if xrange is not None:
ax.set_xlim(*xrange)
if yrange is not None:
ax.set_ylim(*yrange)
if (xrange is not None) and (yrange is not None):
ax.set_aspect((xrange[1] - xrange[0]) / (yrange[1] - yrange[0]))
if show:
plt.show(block=False)
return ax
def contour_plot_threshold(ax, df, legend=True, fontsize=15):
xkey = "rec_phys_alpha"
ykey = "uae_phys_k"
zkey = "poisson_likelihood_2d"
x = df[xkey].values
y = df[ykey].values
z = df[zkey].values
extent = (y.min(), y.max(), x.min(), x.max())
nx = np.unique(x).size
ny = np.unique(y).size
zz = z.reshape(nx, ny)
zzexp = np.exp(zz+1000)
levels = (confidence_threshold(zzexp, 0.999999426696856),
confidence_threshold(zzexp, 0.999936657516334),
confidence_threshold(zzexp, 0.997),
confidence_threshold(zzexp, 0.95),
confidence_threshold(zzexp, 0.68))
labels = r">$5\sigma$", r"$5\sigma$", r"$4\sigma$", r"$3\sigma$", r"$2\sigma$", r"$1\sigma$"
tmap = np.zeros_like(zz)
for level in levels:
tmap[zzexp >= level] += 1
ax.imshow(tmap, origin="lower", cmap="binary", extent=extent, aspect="auto")
xrange = 0, 1.2
yrange = 2.4, 5.2
# ax.plot(xrange, [4.4, 4.4], 'r--')
# ax.plot(xrange, [3.71, 3.71], 'b--')
plot_ext(ax)
bounds = np.array([0, 1, 2, 3, 4, 5, 6])
cmap = plt.cm.binary
norm = mpl.colors.BoundaryNorm(bounds, cmap.N)
axb = inset_axes(ax, width="55%", height="3%", loc=1, borderpad=0.8)
ticks = bounds+0.5
cb = mpl.colorbar.ColorbarBase(axb, cmap=cmap, norm=norm, spacing='proportional', ticks=ticks,
boundaries=bounds, format='%1i', orientation='horizontal')
cb.ax.set_xticklabels(labels, fontsize=fontsize-4)
ax.set_xlim(*xrange)
ax.set_ylim(*yrange)
ax.set_aspect((xrange[1]-xrange[0])/(yrange[1]-yrange[0]))
ax.set_xlabel("$k$", fontsize=fontsize)
ax.set_ylabel(r"$\alpha$", fontsize=fontsize)
if legend:
ax.legend(loc="lower left", frameon=False, fontsize=fontsize-4)
def contour_plot_gauss(ax, df, fontsize=15):
xkey = "rec_phys_alpha"
ykey = "uae_phys_k"
zkey = "poisson_likelihood_2d"
x = df[xkey].values
y = df[ykey].values
z = np.exp(df[zkey].values + 1000)
extent = (y.min(), y.max(), x.min(), x.max())
nx = np.unique(x).size
ny = np.unique(y).size
mean = (np.average(x, weights=z), np.average(y, weights=z))
cov = np.cov(x, y, aweights=z)
norm = stats.multivariate_normal(mean=mean, cov=cov)
zz = norm.pdf(np.vstack([x, y]).T).reshape(nx, ny)
levels = (confidence_threshold(zz, 0.999999426696856),
confidence_threshold(zz, 0.997),
confidence_threshold(zz, 0.95),
confidence_threshold(zz, 0.68))
colors = "k"
contour_labels = r"$5\sigma$", r"$3\sigma$", r"$2\sigma$", r"$1\sigma$"
cs = ax.contour(zz, linewidths=0.8, colors=colors, extent=extent, levels=levels)
fmt = {}
for l, s in zip(cs.levels, contour_labels):
fmt[l] = s
ax.clabel(cs, cs.levels, inline=True, fmt=fmt, fontsize=10)
xrange = 0, 1.2
yrange = 2.5, 5.2
ax.plot(xrange, [4.4, 4.4], 'b--')
ax.plot(xrange, [3.71, 3.71], 'r--')
ax.axhspan(4.4-0.19, 4.4+0.19, color="b", alpha=0.2,
label="vdB+16 (clusters), Amorisco+16")
ax.axhspan(3.71-0.33, 3.71+0.33, color="r", alpha=0.2,
label="vdB+17 (groups)")
ax.set_xlim(*xrange)
ax.set_ylim(2.5, 5.2)
ax.set_aspect((xrange[1]-xrange[0])/(yrange[1]-yrange[0]))
ax.set_xlabel("$k$", fontsize=fontsize)
ax.set_ylabel(r"$\alpha$", fontsize=fontsize)
ax.legend(loc="best")
def contour_plot(ax, df, smooth=False):
xkey = "rec_phys_alpha"
ykey = "uae_phys_k"
zkey = "poisson_likelihood_2d"
x = df[xkey].values
y = df[ykey].values
z = df[zkey].values
extent = (y.min(), y.max(), x.min(), x.max())
nx = np.unique(x).size
ny = np.unique(y).size
zz = z.reshape(nx, ny)
zzexp = np.exp(zz+1000)
if smooth:
zzexp = gaussian_filter(zzexp, 0.5)
levels = (confidence_threshold(zzexp, 0.999999426696856),
confidence_threshold(zzexp, 0.997),
confidence_threshold(zzexp, 0.95),
confidence_threshold(zzexp, 0.68))
colors = "k"
contour_labels = r"$5\sigma$", r"$3\sigma$", r"$2\sigma$", r"$1\sigma$"
cs = ax.contour(zzexp, linewidths=0.8, colors=colors, extent=extent, levels=levels)
fmt = {}
for l, s in zip(cs.levels, contour_labels):
fmt[l] = s
ax.clabel(cs, cs.levels, inline=True, fmt=fmt, fontsize=10)
xrange = 0, 1.2
yrange = 2.5, 5.2
fontsize = 15
ax.plot(xrange, [4.4, 4.4], 'b--', label="van der Burg +16 (clusters), Amorisco +16")
ax.plot(xrange, [3.71, 3.71], 'r--', label="van der Burg +17 (groups)")
ax.axhspan(4.4-0.19, 4.4+0.19, color="b", alpha=0.2)
ax.axhspan(3.71-0.33, 3.71+0.33, color="r", alpha=0.2)
ax.set_xlim(*xrange)
ax.set_ylim(2.5, 5.2)
ax.set_aspect((xrange[1]-xrange[0])/(yrange[1]-yrange[0]))
ax.set_xlabel("$k$", fontsize=fontsize)
ax.set_ylabel(r"$\alpha$", fontsize=fontsize)
ax.legend(loc="best")
def _identify_confident(self, metric=None, q=0.9):
""" Identify best models within confidence interval. """
if metric is None:
metric = self._default_metric
df = self.load_metrics()
values = df[metric].values
threshold = confidence_threshold(values, q=q)
cond = values >= threshold
self.logger.debug(f"Identified {cond.sum()} models for q={q:.2f}.")
return cond
def threshold_plot(x,
y,
z,
ax=None,
legend=True,
xrange=None,
yrange=None,
fontsize=15,
show=True,
xlabel=None,
ylabel=None,
smooth=None,
**kwargs):
"""
"""
if ax is None:
fig, ax = plt.subplots(**kwargs)
extent = (x.min(), x.max(), y.min(), y.max()) # l r b t
nx = np.unique(x).size
ny = np.unique(y).size
zz = z.reshape(nx, ny).T
if smooth is not None:
zz = gaussian_filter(zz, smooth)
# Identify the thresholds and make thresholded image
levels = (confidence_threshold(zz, 0.999999426696856),
confidence_threshold(zz, 0.999936657516334),
confidence_threshold(zz, 0.997), confidence_threshold(zz, 0.95),
confidence_threshold(zz, 0.68))
labels = r">$5\sigma$", r"$5\sigma$", r"$4\sigma$", r"$3\sigma$", r"$2\sigma$", r"$1\sigma$"
levels = list(levels)[1:]
labels = list(labels)[1:]
labels[0] = ">" + labels[1]
tmap = np.zeros_like(zz)
for level in levels:
tmap[zz >= level] += 1
# Display the thresholded image
ax.imshow(tmap,
origin="lower",
cmap="binary",
extent=extent,
aspect="auto")
# Add the inset discrete threshold colourbar
# bounds = np.array([0, 1, 2, 3, 4, 5, 6])
bounds = np.arange(len(levels) + 2)
cmap = plt.cm.binary
norm = mpl.colors.BoundaryNorm(bounds, cmap.N)
axb = inset_axes(ax, width="55%", height="3%", loc=1, borderpad=0.8)
ticks = bounds + 0.5
cb = mpl.colorbar.ColorbarBase(axb,
cmap=cmap,
norm=norm,
spacing='proportional',
ticks=ticks,
boundaries=bounds,
format='%1i',
orientation='horizontal')
cb.ax.set_xticklabels(labels, fontsize=fontsize - 4)
# Format axes
if xrange is not None:
ax.set_xlim(*xrange)
if yrange is not None:
ax.set_ylim(*yrange)
if (xrange is not None) and (yrange is not None):
ax.set_aspect((xrange[1] - xrange[0]) / (yrange[1] - yrange[0]))
ax.set_xlabel(xlabel, fontsize=fontsize)
ax.set_ylabel(ylabel, fontsize=fontsize)
if legend:
ax.legend(loc="lower left", frameon=False, fontsize=fontsize - 4)
if show:
plt.show(block=False)
return ax