def post_direct(a, d, cw1, tw0):
out = np.zeros(cw1)
for i in range(cw1):
out[i] = ( libplump.logKramp(a + d, d, i)
- libplump.logKramp(a + 1, 1, i)
+ log_stirling_cached(d, cw1, i + 1)
+ log_stirling_cached(d, i + 1, tw0))
out -= np.max(out)
out = np.exp(out)
out /= np.sum(out)
return out
def post_direct(a, d, cw1, tw0):
out = np.zeros(cw1)
for i in range(cw1):
out[i] = (libplump.logKramp(a + d, d, i) -
libplump.logKramp(a + 1, 1, i) +
log_stirling_cached(d, cw1, i + 1) +
log_stirling_cached(d, i + 1, tw0))
out -= np.max(out)
out = np.exp(out)
out /= np.sum(out)
return out
def plot_posterior_components(a,
N,
ds=np.arange(0.1, 1, 0.2),
ps=np.arange(0.1, 1, 0.2)):
fig = plt.figure()
ax = fig.add_subplot(111)
# plot stirling numbers
ps = []
for d in ds:
p1, = ax.plot(range(1, N + 1),
[log_stirling_cached(d, N, i) for i in range(1, N + 1)],
':')
# plot Kramp's symbol
ax.set_color_cycle(mpl.rcParams['axes.color_cycle'])
for d in ds:
p2, = ax.plot(
range(1, N + 1),
[libplump.logKramp(a + d, d, i - 1)
for i in range(1, N + 1)], '--')
# plot sum of the two
ax.set_color_cycle(mpl.rcParams['axes.color_cycle'])
for d in ds:
p3, = ax.plot(range(1, N + 1), [
libplump.logKramp(a + d, d, i - 1) + log_stirling_cached(d, N, i)
for i in range(1, N + 1)
])
ps.append(p3)
#plt.gca().set_color_cycle(mpl.rcParams['axes.color_cycle'])
#for p in ps:
# plt.plot(range(1,N+1), [np.log(p)*i for i in range(1,N+1)],'.')
#plt.gca().set_color_cycle(mpl.rcParams['axes.color_cycle'])
# for p in ps:
# plt.plot(range(1,N+1), [np.log(p)*i for i in range(1,N+1)],'.')
ax.set_xlabel("Number of tables")
ax.set_title("Log-Posterior Parts, $\\alpha = %.1f$" % (a, ))
l1 = ax.legend([p1, p2, p3], [
"$\log S_d(c, t)$", "$\log [\\alpha + d]_d^{t-1}$",
"$\log S_d(c, t) + \log [\\alpha + d]_d^{t-1}$"
],
loc=6)
ax.legend(ps, ["$d = %.1f$" % (d, ) for d in ds],
loc=8,
ncol=len(ds),
borderaxespad=0.)
ax.add_artist(l1)
ax.grid(True)
return fig, ax
def log_post_ts(a, d, cws, tws, p0s):
# see eq. 10 in "Improvements ..." paper
return (libplump.logKramp(a + d, d,
float(np.sum(tws)) - 1) +
np.sum([
log_stirling_cached(d, cws[i], tws[i]) for i in range(len(cws))
]) + np.sum([tws[i] * math.log(p0s[i]) for i in range(len(cws))]))
def plot_posterior_components(a,N, ds=np.arange(0.1,1,0.2), ps=np.arange(0.1,1,0.2)):
fig = plt.figure()
ax = fig.add_subplot(111)
# plot stirling numbers
ps = []
for d in ds:
p1, = ax.plot(range(1,N+1), [log_stirling_cached(d,N,i) for i in range(1,N+1)], ':')
# plot Kramp's symbol
ax.set_color_cycle(mpl.rcParams['axes.color_cycle'])
for d in ds:
p2, = ax.plot(range(1,N+1), [libplump.logKramp(a + d, d, i - 1) for i in range(1,N+1)],'--')
# plot sum of the two
ax.set_color_cycle(mpl.rcParams['axes.color_cycle'])
for d in ds:
p3, = ax.plot(range(1,N+1), [libplump.logKramp(a + d, d, i - 1) + log_stirling_cached(d,N,i) for i in range(1,N+1)])
ps.append(p3)
#plt.gca().set_color_cycle(mpl.rcParams['axes.color_cycle'])
#for p in ps:
# plt.plot(range(1,N+1), [np.log(p)*i for i in range(1,N+1)],'.')
#plt.gca().set_color_cycle(mpl.rcParams['axes.color_cycle'])
# for p in ps:
# plt.plot(range(1,N+1), [np.log(p)*i for i in range(1,N+1)],'.')
ax.set_xlabel("Number of tables")
ax.set_title("Log-Posterior Parts, $\\alpha = %.1f$"%(a,))
l1 = ax.legend([p1, p2, p3],
[ "$\log S_d(c, t)$",
"$\log [\\alpha + d]_d^{t-1}$",
"$\log S_d(c, t) + \log [\\alpha + d]_d^{t-1}$"
], loc = 6)
ax.legend(ps, ["$d = %.1f$"%(d,) for d in ds], loc = 8,
ncol=len(ds) , borderaxespad=0.)
ax.add_artist(l1)
ax.grid(True)
return fig, ax
def prior_et(a, d, c):
return (np.exp(
libplump.logKramp(a + d, 1, c) - np.log(d) -
libplump.logKramp(a + 1, 1, c - 1)) - a / d)
def logcrp(a, d, c, t):
return (libplump.logKramp(a + d, d, float(t - 1)) -
libplump.logKramp(a + 1, 1, float(c - 1)) +
log_stirling_cached(d, c, t))
def log_post_t(a, d, cw, tw, T, p0):
# see eq. 10 in "Improvements ..." paper
return (libplump.logKramp(a + d, d, float(T - 1)) +
log_stirling_cached(d, cw, tw) + tw * math.log(p0))
def prior_et(a,d,c):
return (np.exp( libplump.logKramp(a + d, 1, c)
- np.log(d)
- libplump.logKramp(a + 1, 1, c - 1))
- a/d)
def logcrp(a,d,c,t):
return (libplump.logKramp(a + d, d, float(t -1)) -
libplump.logKramp(a + 1, 1, float(c-1)) +
log_stirling_cached(d, c, t))
def log_post_ts(a,d,cws,tws,p0s):
# see eq. 10 in "Improvements ..." paper
return (libplump.logKramp(a + d, d, float(np.sum(tws)) - 1) +
np.sum([log_stirling_cached(d,cws[i],tws[i]) for i in range(len(cws))]) +
np.sum([tws[i]*math.log(p0s[i]) for i in range(len(cws))])
)
def log_post_t(a,d,cw,tw,T,p0):
# see eq. 10 in "Improvements ..." paper
return (libplump.logKramp(a + d, d, float(T -1)) +
log_stirling_cached(d, cw, tw) +
tw*math.log(p0))