def numerical_norm(kappa, beta, eta, alpha, rho):
"""
Compare log-c8 (series) vs numerical integration log-c8
"""
xvals, xlabel, text, textx, args = build_args(kappa, beta, eta, alpha, rho)
plt.figure()
plt.plot(xvals, [np.log(fb8(*_).normalize()) for _ in args],
label='Series',
color='k',
linewidth=3.5)
plt.plot(xvals, [np.log(fb8(*_)._nnormalize()) for _ in args],
linestyle='--',
color='gray',
label='Numerical integration')
plt.plot(xvals, [spa(fb8(*_[:-2])).log_c3() for _ in args],
linestyle=':',
color='gray',
label='Saddlepoint')
plt.xlabel(rf'$\{xlabel}$')
plt.ylabel(rf'$\ln c_8(\{xlabel})$')
plt.legend()
plt.text(textx, 0.7, text, transform=plt.gca().transAxes, fontsize=14)
_ = fb8(0., 0., 0., 100., 10., -0.5, alpha, rho)
textnu = rf'$\vec{{\nu}}=({_.nu[0]:.3g},{_.nu[1]:.3g},{_.nu[2]:.3g})$'
plt.text(textx, 0.6, textnu, transform=plt.gca().transAxes, fontsize=14)
plt.tight_layout(0.1)
def toy(seed=92518):
from matplotlib.patches import Circle
from mpl_toolkits.mplot3d import art3d
np.random.seed(seed)
toyf8 = fb8(np.pi / 16, -np.pi / 3, 0, 55, 60, -1., 0.07, 0.3)
xs = toyf8.rvs(100)
fit5 = fb8_mle(xs, fb5_only=True)
print(fit5, -fit5.log_likelihood(xs))
plot_fb8(fit5, 200)
ax = plt.gca()
for (_z, _x, _y) in xs:
p = Circle((_x, _y), 0.01, ec='w', fc="none")
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=_z, zdir='z')
plt.savefig('figs/Fig4_toyfb5.png')
fit8 = fb8_mle(xs)
print(fit8, -fit8.log_likelihood(xs))
plot_fb8(fit8, 200)
ax = plt.gca()
for (_z, _x, _y) in xs:
p = Circle((_x, _y), 0.01, ec='w', fc="none")
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=_z)
plt.savefig('figs/Fig4_toyfb8.png')
def appendix(th, ph, ps):
for x in product([th], [ph], [ps], [
10,
], [1, 10], [-1, -0.8, 1], [0, np.pi / 2], [0]):
plot_fb8(fb8(*x), 200)
plt.savefig(
'figs/appendix/fb8_k{:.0f}_b{:.0f}_e{:.1f}_a{:.2f}.png'.format(
*x[3:-1]))
def __main__():
th, ph, ps = (np.pi / 16, -np.pi / 3, 0)
# FB4
plot_fb8(fb8(th, ph, ps, 10, 10, -1, 0, 0), 200)
plt.savefig('figs/Fig1_fb4.png')
# FB5
plot_fb8(fb8(th, ph, ps, 10, 4, 1, 0, 0), 200)
plt.savefig('figs/Fig1_fb5.png')
# FB6
plot_fb8(fb8(th + np.pi / 6, ph, ps, 10, 10, -0.5, 0, 0), 200)
plt.savefig('figs/Fig2_fb6.png')
# FB8
plot_fb8(fb8(th, ph, ps, 10, 10, -1, 0.5, 0.3), 200)
plt.savefig('figs/Fig2_fb8.png')
# approx_c6
approx_norm(None, 100., -0.5)
plt.savefig('figs/Fig3_approxc6_kappa.pdf')
approx_norm(100., None, -0.5)
plt.savefig('figs/Fig3_approxc6_beta.pdf')
approx_norm(100., 100., None)
plt.savefig('figs/Fig3_approxc6_eta.pdf')
# ln_c8
numerical_norm(None, 100., -0.5, 0.5, 0.3)
plt.savefig('figs/Fig3_lnc8_kappa.pdf')
numerical_norm(100., None, -0.5, 0.5, 0.3)
plt.savefig('figs/Fig3_lnc8_beta.pdf')
numerical_norm(100., 100., None, 0.5, 0.3)
plt.savefig('figs/Fig3_lnc8_eta.pdf')
# time_c8
time_norm(None, 100., -0.5, 0.5, 0.3)
plt.savefig('figs/Fig3_timec8_kappa.pdf')
time_norm(100., None, -0.5, 0.5, 0.3)
plt.savefig('figs/Fig3_timec8_beta.pdf')
time_norm(100., 100., None, 0.5, 0.3)
plt.savefig('figs/Fig3_timec8_eta.pdf')
# toy application
toy()
# bright stars catalog
bsc5()
# appendixfb8s
appendix(0, 0, 0)
def approx_norm(kappa, beta, eta):
"""
Compare log-c6 vs approx log-c6
"""
xvals, xlabel, text, textx, args = build_args(kappa, beta, eta)
plt.figure()
plt.plot(xvals, [np.log(fb8(*_).normalize()) for _ in args], label='Series', color='k', linewidth=3.5)
plt.plot(xvals, [fb8(*_)._approx_log_normalize() for _ in args],
linestyle='--',
color='gray',
label='Approximate')
plt.plot(xvals, [spa(fb8(*_)).log_c3() for _ in args],
linestyle=':',
color='gray',
label='Saddlepoint')
plt.xlabel(rf'$\{xlabel}$')
plt.ylabel(rf'$\ln c_6(\{xlabel})$')
plt.legend()
plt.text(textx,0.7,text,
transform=plt.gca().transAxes, fontsize=14)
plt.tight_layout(0.1)
def time_norm(kappa, beta, eta, alpha, rho):
""" Plot execution time of .normalize to ._nnormalize
"""
xvals, xlabel, text, textx, args = build_args(kappa, beta, eta, alpha, rho)
tfile = os.path.join('figs', 'time', 'timec8.pkl')
if os.path.isfile(tfile) and str(args) in pickle.load(open(tfile, 'rb')):
times_normalize, times_nnormalize = pickle.load(open(tfile,
'rb'))[str(args)]
else:
times_normalize = []
times_nnormalize = []
setup = 'from sphere.distribution import fb8'
for _ in args:
times_normalize.append(
min(
timeit.repeat(
stmt=('fb8(' + ','.join(['{}'] * 8) +
').normalize(cache=dict())').format(*_),
setup=setup,
repeat=3,
number=1)))
times_nnormalize.append(
min(
timeit.repeat(stmt=('fb8(' + ','.join(['{}'] * 8) +
')._nnormalize()').format(*_),
setup=setup,
repeat=3,
number=1)))
if os.path.isfile(tfile):
ddd = pickle.load(open(tfile, 'rb'))
else:
ddd = {}
ddd[str(args)] = [times_normalize, times_nnormalize]
with open(tfile, 'wb') as f:
pickle.dump(ddd, f)
plt.figure()
plt.plot(xvals, times_normalize, label='Series', color='k', linewidth=3.5)
plt.plot(xvals,
times_nnormalize,
linestyle='--',
color='gray',
label='Numerical integration')
plt.xlabel(rf'$\{xlabel}$')
plt.ylabel(rf'Runtime [s]')
# plt.yscale('log')
plt.legend()
plt.text(0.42, 0.38, text, transform=plt.gca().transAxes, fontsize=14)
_ = fb8(0., 0., 0., 100., 10., -0.5, alpha, rho)
textnu = rf'$\vec{{\nu}}=({_.nu[0]:.3g},{_.nu[1]:.3g},{_.nu[2]:.3g})$'
plt.text(0.42, 0.28, textnu, transform=plt.gca().transAxes, fontsize=14)
plt.tight_layout(0.1)