def plot(self,
data=None,
indices=None,
color='b',
plot_params=True,
label=''):
from util import project_data, plot_gaussian_projection, plot_gaussian_2D
if data is not None:
data = flattendata_distribution(data)
D = self.mu.shape[0]
if D > 2 and ((not hasattr(self, 'plotting_subspace_basis')) or
(self.plotting_subspace_basis.shape[1] != D)):
# TODO improve this bookkeeping. need a notion of collection. it's
# totally potentially broken and confusing to set class members like
# this!
subspace = np.random.randn(D, 2)
self.__class__.plotting_subspace_basis = np.linalg.qr(
subspace)[0].T.copy()
if data is not None:
if D > 2:
data = project_data(data, self.plotting_subspace_basis)
plt.plot(data[:, 0],
data[:, 1],
marker='.',
linestyle=' ',
color=color)
if plot_params:
if D > 2:
plot_gaussian_projection(self.mu,
self.sigma,
self.plotting_subspace_basis,
color=color,
label=label)
else:
plot_gaussian_2D(self.mu, self.sigma, color=color, label=label)
def plot(self,
data=None,
indices=None,
color='b',
plot_params=True,
label=''):
from util import project_data, plot_gaussian_projection, plot_gaussian_2D
if data is not None:
data = util.flattendata(data)
D = len(self.mu) if isinstance(self.mu, np.ndarray) else 1
assert D >= 2
if D > 2 and ((not hasattr(self, 'plotting_subspace_basis')) or
(self.plotting_subspace_basis.shape[1] != D)):
subspace = np.random.randn(D, 2)
self.__class__.plotting_subspace_basis = np.linalg.qr(
subspace)[0].T.copy()
if data is not None:
if D > 2:
data = project_data(data, self.plotting_subspace_basis)
plt.plot(data[:, 0],
data[:, 1],
marker='.',
linestyle=' ',
color=color)
if plot_params:
if D > 2:
plot_gaussian_projection(self.mu,
self.Sigma,
self.plotting_subspace_basis,
color=color,
label=label)
else:
plot_gaussian_2D(self.mu, self.Sigma, color=color, label=label)
def test_ukf():
### generate some spiral data passed through some nonlinear business
theta = 0.05*np.pi
A = 1.01*np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta),np.cos(theta)]])
B = np.eye(2)
d = 5*np.ones(2)
x = np.zeros((100,2))
x[0] = (0,5)
for i in range(1,100):
x[i] = A.dot(x[i-1]) + B.dot(np.random.randn(2))
f = lambda x: x**2
y = f(x) + d*np.random.normal(size=x.shape)
### run unscented kalman filter
initial_distn = Gaussian(x[0],0.1*np.eye(2))
filtered_distns = kalman.ukf_optimized(A,B,f,d,initial_distn,y,1,1)
### plot things
filtered_mus = np.array([d.mu for d in filtered_distns])
plt.figure()
plt.subplot(2,1,1)
plt.plot(y[:,0],y[:,1],'bx-',label='observations')
plt.legend()
plt.subplot(2,1,2)
plt.plot(filtered_mus[:,0],filtered_mus[:,1],'g.-',label='filtered')
plt.plot(x[:,0],x[:,1],'kx-.',label='true state')
for df in filtered_distns:
plot_gaussian_2D(df.mu,df.Sigma,color='g',centermarker=False)
plt.legend()
def test_linear():
### generate some noisy spiral data
theta = 0.1*np.pi
A = 1.02*np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta),np.cos(theta)]])
B = 0.25*np.eye(2)
C = np.eye(2)
D = np.eye(2)
x = np.zeros((100,2))
x[0] = (0,2)
for i in range(1,100):
x[i] = A.dot(x[i-1]) + B.dot(np.random.randn(2))
y = (C.dot(x.T) + D.dot(np.random.normal(size=x.shape).T)).T
### run Kalman filters and smoothers (so easy!)
initial_distn = Gaussian(np.zeros(2),np.eye(2))
filtered_distns = kalman.filter_generic(A,B,C,D,initial_distn,y)
smoothed_distns = kalman.smooth_rts_optimized(A,B,C,D,initial_distn,y)
### plot things
filtered_mus = np.array([d.mu for d in filtered_distns])
smoothed_mus = np.array([d.mu for d in smoothed_distns])
plt.plot(y[:,0],y[:,1],'bx-',label='observations')
plt.plot(filtered_mus[:,0],filtered_mus[:,1],'g.-',label='filtered')
plt.plot(smoothed_mus[:,0],smoothed_mus[:,1],'r.-',label='smoothed')
for df,ds in zip(filtered_distns,smoothed_distns):
plot_gaussian_2D(df.mu,df.Sigma,color='g',centermarker=False)
plot_gaussian_2D(ds.mu,ds.Sigma,color='r',centermarker=False)
plt.plot(x[:,0],x[:,1],'ko-.',label='true state',markersize=8)
plt.legend()
plt.figure(figsize=(15,10))
# true stateseq
plt.subplot(3,1,1)
states, durs = util.rle(labels)
X,Y = np.meshgrid(np.hstack((0,durs.cumsum())),[1,2]);
plt.pcolor(X,Y,states[na,:],edgecolors='k',alpha=0.8);
# inferred stateseq
states, durs = util.rle(posteriormodel.states.stateseq)
X,Y = np.meshgrid(np.hstack((0,durs.cumsum())),[0,1]);
plt.pcolor(X,Y,states[na,:],edgecolors='k',alpha=0.8,vmin=0,vmax=Nmax);
plt.ylim((0,2)); plt.xlim((0,T))
plt.title('true stateseq (top, colors arbitrary) vs sampled stateseq (bottom)')
# observations
plt.subplot(3,1,2)
plt.title('data and inferred observation distributions')
plt.plot(data[:,0],data[:,1],'kx')
for state, (c,o) in enumerate(zip(colors,obs_distns)):
if np.sum(posteriormodel.states.stateseq == state) > 1:
util.plot_gaussian_2D(o.mu,o.sigma,color=c,centermarker=True)
# durations
plt.subplot(3,1,3)
t = np.arange(1,2*N*10)
for state,(c,d) in enumerate(zip(colors,posteriormodel.dur_distns)):
if np.sum(posteriormodel.states.stateseq == state) > 1:
plt.plot(t,d.pmf(t),label='state %d, %s' % (state,d),color=c)
plt.hist(durs[states == state],normed=True,color=c,bins=t)
plt.legend()
plt.title('inferred duration distributions and normalized histograms of sampled durations')
plt.show()
