def _durs_withlabel(self,k):
assert k != SAMPLING
if len(self.stateseq) > 0:
stateseq_norep, durations = rle(self.stateseq)
return durations[stateseq_norep == k]
else:
return []
def plot_states(self, ax_data, ax_states, estimated_states_seq):
# We plot a pcolormesh like the statesequence to show the difference between the prior statesq and the posterior statesq
# Green is for same states and red is for different states
diff = np.array(estimated_states_seq == self.true_states, dtype=int)
state_colors = {0: 0, 1: 1}
stateseq_norep, durations = rle(diff)
datamin, datamax = 0., 1.
x, y = np.hstack((0, durations.cumsum())), np.array([datamin, datamax])
C = np.atleast_2d([state_colors[state] for state in stateseq_norep])
ax_states.pcolormesh(x, y, C, vmin=0, vmax=1, alpha=0.3, cmap='RdYlGn')
ax_states.set_ylim((datamin, datamax))
ax_states.set_xlim((0, len(diff)))
ax_states.set_yticks([])
ax_states.set_title('differences')
# We plot the data with the estimated one in red dashes
mu = self.controlled_params['air']['mu']
powers_hat = np.array(
[mu[int(state)] for state in estimated_states_seq])
ax_data.plot(self.true_powers, label='true powers')
ax_data.plot(powers_hat, 'r--', label='estimated powers')
ax_data.set_xlim((0, len(self.true_powers)))
ax_data.legend(loc='best')
return float(np.sum(diff)) / len(diff)
def __init__(self,model,beta,alpha_0,obs,dur,data=None,T=None,stateseq=None):
self.alpha_0 = alpha_0
self.model = model
self.beta = beta
self.obs = obs
self.dur = dur
self.data = data
if (data,stateseq) == (None,None):
# generating
assert T is not None, 'must pass in T when generating'
self._generate(T)
elif data is None:
self.T = stateseq.shape[0]
self.stateseq = stateseq
elif stateseq is None:
self.data = data
# self._generate(data.shape[0]) # initialized from the prior
# self.stateseq = self.stateseq[:self.T]
self.stateseq = np.random.randint(25,size=data.shape[0])
self.T = data.shape[0]
else:
assert data.shape[0] == stateseq.shape[0]
self.stateseq = stateseq
self.stateseq_norep, self.durations = rle(stateseq)
self.data = data
self.T = data.shape[0]
def _counts_to(self,k):
assert k != SAMPLING
stateseq_norep, _ = rle(self.stateseq)
temp = np.sum(stateseq_norep[1:] == k)
if SAMPLING in stateseq_norep[:-1] and \
stateseq_norep[np.where(stateseq_norep == SAMPLING)[0]+1] == k:
temp -= 1
return temp
def _counts_fromto(self,k1,k2):
assert k1 != SAMPLING and k2 != SAMPLING
if k1 not in self.stateseq or k2 not in self.stateseq or k1 == k2:
return 0
else:
stateseq_norep, _ = rle(self.stateseq)
from_indices, = np.where(stateseq_norep[:-1] == k1) # EXCEPT last
return np.sum(stateseq_norep[from_indices+1] == k2)
def plot_states_and_var(data,
hidden_states,
cmap=None,
columns=None,
by='Activity'):
"""
Make a plot of the data and the states
Parameters
----------
data : pandas DataFrame
Data to plot
hidden_states: iteretable
the hidden states corresponding to the timesteps
columns : list, optional
Which columns to plot
by : str
The column to group on
"""
fig, ax = plt.subplots(figsize=(15, 5))
if columns is None:
columns = data.columns
df = data[columns].copy()
stateseq = np.array(hidden_states)
stateseq_norep, durations = rle(stateseq)
datamin, datamax = np.array(df).min(), np.array(df).max()
y = np.array([datamin, datamax])
maxstate = stateseq.max() + 1
x = np.hstack(([0], durations.cumsum()[:-1], [len(df.index) - 1]))
C = np.array([[float(state) / maxstate]
for state in stateseq_norep]).transpose()
ax.set_xlim((min(x), max(x)))
if cmap is None:
num_states = max(hidden_states) + 1
colormap, cmap = get_color_map(num_states)
pc = ax.pcolorfast(x, y, C, vmin=0, vmax=1, alpha=0.3, cmap=cmap)
plt.plot(df.as_matrix())
locator = AutoDateLocator()
locator.create_dummy_axis()
num_index = pd.Index(df.index.map(date2num))
ticks_num = locator.tick_values(min(df.index), max(df.index))
ticks = [num_index.get_loc(t) for t in ticks_num]
plt.xticks(ticks, df.index.strftime('%H:%M')[ticks], rotation='vertical')
cb = plt.colorbar(pc)
cb.set_ticks(np.arange(1. / (2 * cmap.N), 1, 1. / cmap.N))
cb.set_ticklabels(np.arange(0, cmap.N))
# Plot the activities
if by is not None:
actseq = np.array(data[by])
sca = ax.scatter(
np.arange(len(hidden_states)), #data.index,
np.ones_like(hidden_states) * datamax,
c=actseq,
edgecolors='none')
plt.show()
return fig, ax
def plot_states_and_var(data, hidden_states, cmap=None, columns=None, by='Activity'):
"""
Make a plot of the data and the states
Parameters
----------
data : pandas DataFrame
Data to plot
hidden_states: iteretable
the hidden states corresponding to the timesteps
columns : list, optional
Which columns to plot
by : str
The column to group on
"""
fig, ax = plt.subplots(figsize=(15, 5))
if columns is None:
columns = data.columns
df = data[columns].copy()
stateseq = np.array(hidden_states)
stateseq_norep, durations = rle(stateseq)
datamin, datamax = np.array(df).min(), np.array(df).max()
y = np.array(
[datamin, datamax])
maxstate = stateseq.max() + 1
x = np.hstack(([0], durations.cumsum()[:-1], [len(df.index) - 1]))
C = np.array(
[[float(state) / maxstate] for state in stateseq_norep]).transpose()
ax.set_xlim((min(x), max(x)))
if cmap is None:
num_states = max(hidden_states) + 1
colormap, cmap = get_color_map(num_states)
pc = ax.pcolorfast(x, y, C, vmin=0, vmax=1, alpha=0.3, cmap=cmap)
plt.plot(df.as_matrix())
locator = AutoDateLocator()
locator.create_dummy_axis()
num_index = pd.Index(df.index.map(date2num))
ticks_num = locator.tick_values(min(df.index), max(df.index))
ticks = [num_index.get_loc(t) for t in ticks_num]
plt.xticks(ticks, df.index.strftime('%H:%M')[ticks], rotation='vertical')
cb = plt.colorbar(pc)
cb.set_ticks(np.arange(1./(2*cmap.N), 1, 1./cmap.N))
cb.set_ticklabels(np.arange(0, cmap.N))
# Plot the activities
if by is not None:
actseq = np.array(data[by])
sca = ax.scatter(
np.arange(len(hidden_states)), #data.index,
np.ones_like(hidden_states) * datamax,
c=actseq,
edgecolors='none'
)
plt.show()
return fig, ax
def resample(self,stateseqs=[]):
if type(stateseqs) != type([]):
stateseqs = [stateseqs]
states_noreps = map(lambda x: rle(x)[0], stateseqs)
if not any(len(states_norep) >= 2 for states_norep in states_noreps):
# if there is no data we just sample from the prior
self.beta = stats.gamma.rvs(self.alpha / self.state_dim, size=self.state_dim)
self.beta /= np.sum(self.beta)
self.fullA = stats.gamma.rvs(self.beta * self.gamma * np.ones((self.state_dim,1)))
self.A = (1.-np.eye(self.state_dim)) * self.fullA
self.fullA /= np.sum(self.fullA,axis=1)[:,na]
self.A /= np.sum(self.A,axis=1)[:,na]
assert not np.isnan(self.beta).any()
assert not np.isnan(self.fullA).any()
assert (self.A.diagonal() == 0).all()
else:
# make 2d array of transition counts
data = np.zeros((self.state_dim,self.state_dim))
for states_norep in states_noreps:
for idx in xrange(len(states_norep)-1):
data[states_norep[idx],states_norep[idx+1]] += 1
# we resample the children (A) then the mother (beta)
# first, we complete the data using the current parameters
# every time we transferred from a state, we had geometrically many
# self-transitions thrown away that we want to sample
assert (data.diagonal() == 0).all()
froms = np.sum(data,axis=1)
self_transitions = np.array([np.sum(stats.geom.rvs(1.-self.fullA.diagonal()[idx],size=from_num)) if from_num > 0 else 0 for idx, from_num in enumerate(froms)])
self_transitions[froms == 0] = 0 # really emphasized here!
assert (self_transitions < 1e7).all(), 'maybe alpha is too low... code is not happy about that at the moment'
augmented_data = data + np.diag(self_transitions)
# then, compute m's and stuff
m = np.zeros((self.state_dim,self.state_dim))
for rowidx in xrange(self.state_dim):
for colidx in xrange(self.state_dim):
n = 0.
for i in xrange(int(augmented_data[rowidx,colidx])):
m[rowidx,colidx] += random() < self.alpha * self.beta[colidx] / (n + self.alpha * self.beta[colidx])
n += 1.
self.m = m # save it for possible use in any child classes
# resample mother (beta)
self.beta = stats.gamma.rvs(self.alpha / self.state_dim + np.sum(m,axis=0))
self.beta /= np.sum(self.beta)
assert not np.isnan(self.beta).any()
# resample children (fullA and A)
self.fullA = stats.gamma.rvs(self.gamma * self.beta + augmented_data)
self.fullA /= np.sum(self.fullA,axis=1)[:,na]
self.A = self.fullA * (1.-np.eye(self.state_dim))
self.A /= np.sum(self.A,axis=1)[:,na]
assert not np.isnan(self.A).any()
def slices_from_indicators(indseq):
indseq = np.asarray(indseq)
if not indseq.any():
return []
else:
vals, durs = rle(indseq)
starts, ends = cumsum(durs, strict=True), cumsum(durs, strict=False)
return [
slice(start, end) for val, start, end in zip(vals, starts, ends)
if val
]
def plot(self,colors_dict):
from matplotlib import pyplot as plt
stateseq_norep, durations = rle(self.stateseq)
X,Y = np.meshgrid(np.hstack((0,durations.cumsum())),(0,1))
if colors_dict is not None:
C = np.array([[colors_dict[state] for state in stateseq_norep]])
else:
C = stateseq_norep[na,:]
plt.pcolor(X,Y,C,vmin=0,vmax=1)
plt.ylim((0,1))
plt.xlim((0,len(self.stateseq)))
plt.yticks([])
def plot(self,colors_dict=None):
from matplotlib import pyplot as plt
from pyhsmm.util.general import rle
states,durations = rle(self.stateseq)
X,Y = np.meshgrid(np.hstack((0,durations.cumsum())),(0,1))
if colors_dict is not None:
C = np.array([[colors_dict[state] for state in states]])
else:
C = states[na,:]
plt.pcolor(X,Y,C,vmin=0,vmax=1)
plt.ylim((0,1))
plt.xlim((0,durations.sum()))
plt.yticks([])
def sample_forwards(self,betal,betastarl):
aBl = self.aBl
# stateseq = np.array(self.stateseq,dtype=np.int32)
stateseq = np.zeros(betal.shape[0],dtype=np.int32)
A = self.transition_distn.A
pi0 = self.initial_distn.pi_0
apmf = np.zeros((self.state_dim,self.T))
arg = np.arange(1,self.T+1)
for state_idx, dur_distn in enumerate(self.dur_distns):
apmf[state_idx] = dur_distn.pmf(arg)
scipy.weave.inline(self.sample_forwards_codestr,['betal','betastarl','aBl','stateseq','A','pi0','apmf'],headers=['<Eigen/Core>'],include_dirs=['/usr/local/include/eigen3'],extra_compile_args=['-O3'])#,'-march=native'])
self.stateseq_norep, self.durations = util.rle(stateseq)
self.stateseq = stateseq
def plot_observations(self,colors=None,states_objs=None):
if colors is None:
colors = self._get_colors()
if states_objs is None:
states_objs = self.states_list
cmap = cm.get_cmap()
for s in states_objs:
data = undo_AR_striding(s.data,self.nlags)
stateseq_norep, durs = rle(s.stateseq)
starts = np.concatenate(((0,),durs.cumsum()))
for state,start,dur in zip(stateseq_norep,starts,durs):
plt.plot(
np.arange(start,start+data[start:start+dur].shape[0]),
data[start:start+dur],
color=cmap(colors[state]))
plt.xlim(0,s.T-1)
def plot_stateseq(s, ax, Interval):
num_states = s.state_dim
data = s.data
stateseq = s.stateseq
# Colors
cmap = cm.get_cmap()
state_usages = np.bincount(stateseq, minlength=num_states)
freqs = state_usages / state_usages.sum()
#used_states = sorted(set(stateseq), key=lambda x: freqs[x], reverse=True)
used_states = sorted(set(stateseq), key=lambda x: s.obs_distns[x].mu)
unused_states = [
idx for idx in range(num_states) if idx not in used_states
]
colorseq = np.linspace(0, 1, num_states)
state_colors = dict((idx, v) for idx, v in zip(used_states, colorseq))
for state in unused_states:
state_colors[state] = cmap(1.)
# State sequence colors
from pyhsmm.util.general import rle
stateseq_norep, durations = rle(stateseq)
datamin, datamax = data.min(), data.max()
x, y = np.hstack((0, durations.cumsum())), np.array([datamin, datamax])
C = np.atleast_2d([state_colors[state] for state in stateseq_norep])
ax.pcolormesh(x,
y,
C,
cmap=cm.get_cmap('summer'),
vmin=0,
vmax=1,
alpha=0.8)
ax.set_ylim((datamin, datamax))
ax.set_xlim((Interval[0], Interval[1]))
ax.set_yticks([])
def __init__(self,T,state_dim,obs_distns,dur_distns,transition_distn,initial_distn,
stateseq=None,trunc=None,data=None,**kwargs):
# TODO T parameter only makes sense with censoring. it should be
# removed.
self.T = T
self.state_dim = state_dim
self.obs_distns = obs_distns
self.dur_distns = dur_distns
self.transition_distn = transition_distn
self.initial_distn = initial_distn
self.trunc = T if trunc is None else trunc
self.data = data
# this arg is for initialization heuristics which may pre-determine the
# state sequence
if stateseq is not None:
self.stateseq = stateseq
# gather durations and stateseq_norep
self.stateseq_norep, self.durations = util.rle(stateseq)
else:
if data is not None:
self.resample()
else:
self.generate_states()
def __init__(self,T,state_dim,obs_distns,dur_distns,transition_distn,initial_distn,stateseq=None,trunc=None,data=None,**kwargs):
self.T = T
self.state_dim = state_dim
self.obs_distns = obs_distns
self.dur_distns = dur_distns
self.transition_distn = transition_distn
self.initial_distn = initial_distn
self.trunc = T if trunc is None else trunc
self.data = data
self.sample_forwards_codestr = hsmm_sample_forwards_codestr % {'M':state_dim,'T':T}
# self.messages_backwards_codestr = hsmm_messages_backwards_codestr % {'M':state_dim,'T':T}
# this arg is for initialization heuristics which may pre-determine the state sequence
if stateseq is not None:
self.stateseq = stateseq
# gather durations and stateseq_norep
self.stateseq_norep, self.durations = util.rle(stateseq)
else:
if data is not None:
self.resample()
else:
self.generate_states()
def durations(self):
return rle(self.stateseq)[1]
def stateseq_norep(self):
return rle(self.stateseq)[0]
def stateseqs_norep(self):
return rle(self.z)[0]
def durations(self):
return rle(self.z)[1]
def _count_transitions(self,stateseqs):
stateseq_noreps = [rle(stateseq)[0] for stateseq in stateseqs]
return super(_HSMMTransitionsBase,self)._count_transitions(stateseq_noreps)
def stateseq_norep(self):
return rle(self.stateseq)[0]
aspect="auto")
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_title("Inferred Discrete States")
ax = fig.add_subplot(gs[2, 0])
plt.plot(y[:, 0], color='k', lw=2, label="observed")
plt.plot(smoothed_data[:, 0], color=colors[0], lw=1, label="smoothed")
plt.xlabel("Time")
plt.xlim(0, min(T, 500))
plt.ylabel("Observations")
plt.legend(loc="upper center", ncol=2)
plt.tight_layout()
plt.savefig("aux/demo_smooth.png")
plt.figure()
from pyhsmm.util.general import rle
z_rle = rle(z)
offset = 0
for k, dur in zip(*z_rle):
plt.plot(x[offset:offset + dur, 0],
x[offset:offset + dur, 1],
color=colors[k])
offset += dur
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
plt.title("Continuous Latent States")
plt.show()
def durations(self):
if self._durations is None:
self._letterseq_norep, self._durations = rle(self.letterseq)
return self._durations
def generate_obs(self):
obs = []
for state, dur in zip(*rle(self.stateseq)):
obs.append(self.obs_distns[state].rvs(int(dur)))
return np.concatenate(obs)
def durations(self):
return rle(self.z)[1]
) > bestposteriormodel.log_likelihood():
print("We have a winner")
bestposteriormodel = posteriormodel
plot(bestposteriormodel)
plt.title(mode)
plt.show()
thestateseq = bestposteriormodel.states_list[-1].stateseq
# NOTE: here we fix the state-ambiguity by flipping the inferred state seq if it's become inverted
if np.mean(thestateseq) > 0.5:
thestateseq = 1 - thestateseq
resultstore[mode] = {
'stateseq': thestateseq,
'rle': rle(thestateseq),
}
# add 'true' to resultstore as if it were a result!
resultstore['true'] = {
'stateseq': trueseq,
'rle': rle(trueseq),
}
##############################################################################
#print resultstore
#print trueseq
modelist = ['true', 'geom', 'pois']
modedata = {
def stateseq_norep(self):
if self._stateseq_norep is None:
self._stateseq_norep, dur = rle(self.stateseq)
return self._stateseq_norep
Nmaxsuper = 2*Nsuper
Nmaxsub = 2*Nsub
obs_distnss = \
[[pyhsmm.distributions.Gaussian(**obs_hypparams)
for substate in range(Nmaxsub)] for superstate in range(Nmaxsuper)]
dur_distns = \
[pyhsmm.distributions.NegativeBinomialIntegerR2Duration(
**dur_hypparams) for superstate in range(Nmaxsuper)]
# !!! cheat to get the changepoints !!! #
changepointss = []
for data, labels in zip(datas,labelss):
_, durations = rle(labels)
temp = np.concatenate(((0,),durations.cumsum()))
changepoints = zip(temp[:-1],temp[1:])
changepoints[-1] = (changepoints[-1][0],T) # because last duration might be censored
changepointss.append(changepoints)
# optionally split changepoints
# changepoints = [pair for (a,b) in changepoints for pair in [(a,a+(b-a)//2), (a+(b-a)//2,b)]]
print len(changepoints)
# # plot things to check!!
# plt.figure()
# for idx, (labels, changepoints) in enumerate(zip(labelss,changepointss)):
# plt.subplot(len(changepointss),1,idx)
# plt.plot(labels)
def durations(self):
return rle(self.stateseq)[1]
Nmaxsuper = 2 * Nsuper
Nmaxsub = 2 * Nsub
obs_distnss = \
[[pyhsmm.distributions.Gaussian(**obs_hypparams)
for substate in range(Nmaxsub)] for superstate in range(Nmaxsuper)]
dur_distns = \
[pyhsmm.distributions.NegativeBinomialIntegerR2Duration(
**dur_hypparams) for superstate in range(Nmaxsuper)]
# !!! cheat to get the changepoints !!! #
changepointss = []
for data, labels in zip(datas, labelss):
_, durations = rle(labels)
temp = np.concatenate(((0, ), durations.cumsum()))
changepoints = zip(temp[:-1], temp[1:])
changepoints[-1] = (changepoints[-1][0], T
) # because last duration might be censored
changepointss.append(changepoints)
# optionally split changepoints
# changepoints = [pair for (a,b) in changepoints for pair in [(a,a+(b-a)//2), (a+(b-a)//2,b)]]
print len(changepoints)
# # plot things to check!!
# plt.figure()
# for idx, (labels, changepoints) in enumerate(zip(labelss,changepointss)):
# plt.subplot(len(changepointss),1,idx)
# plt.plot(labels)
def _count_transitions(self,stateseqs):
stateseq_noreps = [rle(stateseq)[0] for stateseq in stateseqs]
return super(_HSMMTransitionsBase,self)._count_transitions(stateseq_noreps)
ax = fig.add_subplot(gs[1,0])
ax.imshow(test_model.states_list[0].stateseq[None,:], vmin=0, vmax=max(len(colors), test_model.num_states)-1,
cmap=cmap, interpolation="nearest", aspect="auto")
ax.set_xticklabels([])
ax.set_yticks([])
ax.set_title("Inferred Discrete States")
ax = fig.add_subplot(gs[2,0])
plt.plot(y[:,0], color='k', lw=2, label="observed")
plt.plot(smoothed_data[:,0], color=colors[0], lw=1, label="smoothed")
plt.xlabel("Time")
plt.xlim(0, min(T, 500))
plt.ylabel("Observations")
plt.legend(loc="upper center", ncol=2)
plt.tight_layout()
plt.savefig("aux/demo_smooth.png")
plt.figure()
from pyhsmm.util.general import rle
z_rle = rle(z)
offset = 0
for k, dur in zip(*z_rle):
plt.plot(x[offset:offset+dur,0], x[offset:offset+dur,1], color=colors[k])
offset += dur
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
plt.title("Continuous Latent States")
plt.show()
def stateseqs_norep(self):
return rle(self.z)[0]
def durations_censored(self):
if self._durations_censored is None:
self._stateseq_norep, self._durations_censored = rle(self.stateseq)
return self._durations_censored
def durations_censored(self):
if self._durations_censored is None:
self._stateseq_norep, self._durations_censored = rle(self.stateseq)
return self._durations_censored
def plot_states(posteriormodel,data=None,powers_hat=None,cmap='summer'):
plt.rcParams['image.cmap'] = cmap
Nb_obs = posteriormodel.datas[0].shape[0]
Nb_segment = int(np.ceil(Nb_obs / 1000.))
fig = plt.figure(figsize=(16,(5+2)*Nb_segment))
height_ratios = ([5]+[2])*Nb_segment
gs = GridSpec(2*Nb_segment,2,width_ratios=[15, 1],height_ratios=height_ratios,wspace=0.05)
for t in np.arange(0,Nb_obs,1000):
# We plot the data with the estimated one in red dashes
data_ax = plt.subplot(gs[(t//1000)*2,0])
data_ax.plot(data,color='red',label='true powers')
data_ax.plot(powers_hat,'b--',label='estimated powers')
data_ax.set_xlim((t,t+1000))
data_ax.legend(loc='best')
rect = data_ax.axis() # xmin xmax ymin ymax
#data_ax.vlines([c[1] for c in posteriormodel.states_list[0].changepoints[:-1]],rect[2],rect[3],color='black',linestyles='dashed')
stateseq = posteriormodel.stateseqs[0]
num_states = len(set(stateseq))
# Colors
state_usages = np.bincount(stateseq,minlength=num_states)
freqs = state_usages / state_usages.sum()
used_states = sorted(set(stateseq), key=lambda x: posteriormodel.obs_distns[x].mu)
#used_states = sorted(set(stateseq), key=lambda x: np.mean([c.mu for c in posteriormodel.obs_distns[x].components]))
unused_states = [idx for idx in range(num_states) if idx not in used_states]
colorseq = np.linspace(0,1,num_states)
state_colors = dict((idx, v) for idx, v in zip(used_states,colorseq))
for state in unused_states:
state_colors[state] = 1.
# Colorbar
unique_states = np.sort(list(set(stateseq)))
n = len(unique_states)
C_bar = np.atleast_2d([state_colors[state] for state in unique_states])
x_bar, y_bar = np.array([0.,1.]), np.arange(n+1)/n
# State sequence
stateseq_norep, durations = rle(stateseq)
x, y = np.hstack((0,durations.cumsum())), np.array([0.,1.])
C = np.atleast_2d([state_colors[state] for state in stateseq_norep])
for t in np.arange(0,Nb_obs,1000):
stateseq_ax = plt.subplot(gs[(t//1000)*2 + 1,0])
colorbar_ax = plt.subplot(gs[(t//1000)*2 + 1,1])
colorbar_ax.set_ylim((0.,1.))
colorbar_ax.set_xlim((0.,1.))
colorbar_ax.set_xticks([])
colorbar_ax.yaxis.set_label_position("right")
colorbar_ax.get_yaxis().set_ticks([])
# State sequence
stateseq_ax.pcolormesh(x,y,C,cmap=cmap,vmin=0,vmax=1,alpha=0.5)
stateseq_ax.set_ylim((0.,1.))
stateseq_ax.set_xlim((t,t+1000))
stateseq_ax.set_yticks([])
stateseq_ax.set_title('Hidden states sequence')
# We plot a colorbar to indicate the color of each state
colorbar_ax.pcolormesh(x_bar,y_bar,C_bar.T,vmin=0,vmax=1,alpha=0.5,cmap=cmap)
for j in range(n):
colorbar_ax.text(.5, (1+j*2)/(2*n), str(unique_states[j]), ha='center', va='center')
colorbar_ax.get_yaxis().labelpad = 15
colorbar_ax.set_ylabel('States', rotation=270)
gs.tight_layout(fig, rect=[0, 0.03, 1, 0.97])
return fig