def static(lmax=5, res=300):
"""Plot a static PDF figure."""
# Set up the plot
fig, ax = pl.subplots(lmax + 1, 2 * lmax + 1, figsize=(9, 6))
fig.subplots_adjust(hspace=0)
for axis in ax.flatten():
axis.set_xticks([])
axis.set_yticks([])
axis.spines['top'].set_visible(False)
axis.spines['right'].set_visible(False)
axis.spines['bottom'].set_visible(False)
axis.spines['left'].set_visible(False)
for l in range(lmax + 1):
ax[l, 0].set_ylabel(r"$l = %d$" % l,
rotation='horizontal',
labelpad=30,
y=0.38,
fontsize=12)
for j, m in enumerate(range(-lmax, lmax + 1)):
if m < 0:
ax[-1, j].set_xlabel(r"$m {=} \mathrm{-}%d$" % -m,
labelpad=30,
fontsize=11)
else:
ax[-1, j].set_xlabel(r"$m = %d$" % m, labelpad=30, fontsize=11)
# Plot it
x = np.linspace(-1, 1, res)
y = np.linspace(-1, 1, res)
X, Y = np.meshgrid(x, y)
map = Map(lmax)
# Loop over the orders and degrees
for i, l in enumerate(range(lmax + 1)):
for j, m in enumerate(range(-l, l + 1)):
# Offset the index for centered plotting
j += lmax - l
# Compute the spherical harmonic
# with no rotation
map.reset()
map[l, m] = 1
flux = [map(x=X[j], y=Y[j]) for j in range(res)]
# Plot the spherical harmonic
ax[i, j].imshow(flux,
cmap='plasma',
interpolation="none",
origin="lower",
extent=(-1, 1, -1, 1))
ax[i, j].set_xlim(-1.1, 1.1)
ax[i, j].set_ylim(-1.1, 1.1)
# Save!
fig.savefig("ylms.pdf", bbox_inches="tight")
pl.close()
ax[l, 0].set_ylabel(r"$l = %d$" % l,
rotation='horizontal',
labelpad=30, y=0.38,
fontsize=12)
for j, m in enumerate(range(lmax + 1)):
ax[-1, j].set_xlabel(r"$m = %d$" % m, labelpad=30, fontsize=12)
# Occultation params
y = Map(lmax)
ro = 0.25
xo = np.linspace(-1.5, 1.5, nt)
xon = np.linspace(-1.5, 1.5, nn)
for yo, zorder, color in zip([0.25, 0.75], [1, 0], ['C0', 'C1']):
for i, l in enumerate(range(lmax + 1)):
for j, m in enumerate(range(l + 1)):
y.reset()
y.set_coeff(l, m, 1)
flux = y.flux(axis=[1, 0, 0], theta=0, xo=xo, yo=yo, ro=ro)
ax[i, j].plot(xo, flux, lw=1, zorder=zorder, color=color)
fluxn = y._flux_numerical(axis=[1, 0, 0], theta=0, xo=xon,
yo=yo, ro=ro, tol=1e-5)
ax[i, j].plot(xon, fluxn, '.', ms=2, zorder=zorder, color=color)
# Hack a legend
axleg = pl.axes([0.7, 0.7, 0.15, 0.15])
axleg.plot([0, 0], [1, 1], label=r'$y_0 = 0.25$')
axleg.plot([0, 0], [1, 1], label=r'$y_0 = 0.75$')
axleg.axis('off')
leg = axleg.legend(title=r'Occultations', fontsize=18)
leg.get_title().set_fontsize('20')
leg.get_frame().set_linewidth(0.0)
class animated():
"""Plot an animated GIF showing rotation of the Ylms."""
def __init__(self,
lmax=5,
res=300,
dpi=100,
fps=10,
frames=50,
axis=[0., 1., 0.]):
"""Initialize."""
self.lmax = lmax
self.map = Map(lmax)
self.res = res
self.axis = axis
self.frames = frames
x = np.linspace(-1, 1, res)
y = np.linspace(-1, 1, res)
self.X, self.Y = np.meshgrid(x, y)
# Set up the plot
self.fig, self.ax = pl.subplots(self.lmax + 1,
2 * self.lmax + 1,
figsize=(9, 6))
self.fig.subplots_adjust(hspace=0)
for axis in self.ax.flatten():
axis.set_xticks([])
axis.set_yticks([])
axis.spines['top'].set_visible(False)
axis.spines['right'].set_visible(False)
axis.spines['bottom'].set_visible(False)
axis.spines['left'].set_visible(False)
for l in range(self.lmax + 1):
self.ax[l, 0].set_ylabel(r"$l = %d$" % l,
rotation='horizontal',
labelpad=30,
y=0.38,
fontsize=12)
for j, m in enumerate(range(-self.lmax, self.lmax + 1)):
self.ax[-1, j].set_xlabel(r"$m = %d$" % m,
labelpad=30,
fontsize=12)
# Loop over the orders and degrees
self.img = []
for i, l in enumerate(range(self.lmax + 1)):
for j, m in enumerate(range(-l, l + 1)):
# Offset the index for centered plotting
j += self.lmax - l
# Compute the spherical harmonic
self.map.reset()
self.map[l, m] = 1
flux = [
self.map(theta=0, x=self.X[j], y=self.Y[j])
for j in range(res)
]
# Plot the spherical harmonic
img = self.ax[i, j].imshow(flux,
cmap='plasma',
interpolation="none",
origin="lower")
self.img.append(img)
# Set up the animation
self.theta = np.linspace(0, 360, frames, endpoint=False)
self.animation = animation.FuncAnimation(self.fig,
self.animate,
frames=self.frames,
interval=50,
repeat=True,
blit=True)
# Save
self.animation.save('ylms.gif', writer='imagemagick', fps=fps, dpi=dpi)
pl.close()
def animate(self, j):
"""Run the animation."""
print("Rendering frame %d/%d..." % (j + 1, self.frames))
# Rotate the spherical harmonics
n = 0
theta = self.theta[j]
for i, l in enumerate(range(self.lmax + 1)):
for j, m in enumerate(range(-l, l + 1)):
self.map.reset()
self.map[l, m] = 1
self.map.axis = self.axis
flux = self.map(theta=theta, x=self.X, y=self.Y)
self.img[n].set_data(flux)
n += 1
return self.img
ax[l, 0].set_ylabel(r"$l = %d$" % l,
rotation='horizontal',
labelpad=30, y=0.38,
fontsize=12)
for j, m in enumerate(range(lmax + 1)):
ax[-1, j].set_xlabel(r"$m = %d$" % m, labelpad=30, fontsize=12)
# Occultation params
map = Map(lmax)
ro = 0.25
xo = np.linspace(-1.5, 1.5, nt)
xon = np.linspace(-1.5, 1.5, nn)
for yo, zorder, color in zip([0.25, 0.75], [1, 0], ['C0', 'C1']):
for i, l in enumerate(range(lmax + 1)):
for j, m in enumerate(range(l + 1)):
map.reset()
map[0, 0] = 0
map[l, m] = 1
flux = map.flux(theta=0, xo=xo, yo=yo, ro=ro)
ax[i, j].plot(xo, flux, lw=1, zorder=zorder, color=color)
fluxn = map.flux(theta=0, xo=xon, yo=yo, ro=ro, numerical=True)
ax[i, j].plot(xon, fluxn, '.', ms=2, zorder=zorder, color=color)
# Hack a legend
axleg = pl.axes([0.7, 0.7, 0.15, 0.15])
axleg.plot([0, 0], [1, 1], label=r'$y_0 = 0.25$')
axleg.plot([0, 0], [1, 1], label=r'$y_0 = 0.75$')
axleg.axis('off')
leg = axleg.legend(title=r'Occultations', fontsize=18)
leg.get_title().set_fontsize('20')
leg.get_frame().set_linewidth(0.0)