def mc_sample(prior, trans, len, numex=1):
'''
% SAMPLE_MC Generate random sequences from a Markov chain.
% STATE = SAMPLE_MC(PRIOR, TRANS, LEN) generates a sequence of length LEN.
%
% STATE = SAMPLE_MC(PRIOR, TRANS, LEN, N) generates N rows each of length LEN.
'''
trans = np.asarray(trans)
S = np.zeros((numex,len), dtype=int);
for i in range(0,numex):
S[i, 0] = sample_discrete(prior)
for t in range(1, len):
S[i, t] = sample_discrete(trans[S[i,t-1],:])
return S
def testDistSmall(self):
n = 10000
M = np.zeros((n, 2))
for i in range(n):
M[i, :] = sample_discrete(np.array([0.8, 0.1, 0.1]), 1, 2)
dist = np.bincount(M.ravel().astype(int)) / (n * 2.)
assert np.all(np.abs(dist - [0.8, 0.1, 0.1]) < 1e-2)
def testDistSmall(self):
n = 10000
M = np.zeros((n,2))
for i in range(n):
M[i,:] = sample_discrete(np.array([0.8, 0.1, 0.1]), 1, 2)
dist = np.bincount(M.ravel().astype(int)) / (n*2.)
assert np.all(np.abs(dist-[0.8, 0.1, 0.1]) < 1e-2)
def mhmm_sample(T, numex, initial_prob, transmat, mu, Sigma, mixmat=None):
'''
% SAMPLE_MHMM Generate random sequences from an HMM with (mixtures of) Gaussian output.
% [obs, hidden] = sample_mhmm(T, numex, initial_prob, transmat, mu, Sigma, mixmat)
%
% INPUTS:
% T - length of each sequence
% numex - num. sequences
% init_state_prob(i) = Pr(Q(1) = i)
% transmat(i,j) = Pr(Q(t+1)=j | Q(t)=i)
% mu(:,j,k) = mean of Y(t) given Q(t)=j, M(t)=k
% Sigma(:,:,j,k) = cov. of Y(t) given Q(t)=j, M(t)=k
% mixmat(j,k) = Pr(M(t)=k | Q(t)=j) : set to ones(Q,1) or omit if single mixture
%
% OUTPUT:
% obs(:,t,l) = observation vector at time t for sequence l
% hidden(t,l) = the hidden state at time t for sequence l
'''
assert initial_prob.ndim == 1
Q = len(initial_prob);
if mixmat==None:
mixmat = np.ones((Q,1))
O = mu.shape[0]
hidden = np.zeros((T, numex))
obs = np.zeros((O, T, numex))
hidden = mc_sample(initial_prob, transmat, T, numex).T
for i in range(0,numex):
for t in range(0,T):
q = hidden[t,i]
m = np.asscalar(sample_discrete(mixmat[q,:], 1, 1))
obs[:,t,i] = gaussian_sample(mu[:,q,m], Sigma[:,:,q,m], 1)
return obs, hidden
def testDistLarge(self):
n = 10000
M = sample_discrete(np.array([0.8, 0.2]), n, 10)
dist = np.bincount(M.ravel().astype(int)) / (n * 10.)
assert np.all(np.abs(dist - [0.8, 0.2]) < 1e-2)
def testRow(self):
assert sample_discrete(np.array([0.8, 0.2]), 1, 10).shape == (1, 10)
def testDistLarge(self):
n = 10000
M = sample_discrete(np.array([0.8, 0.2]), n, 10)
dist = np.bincount(M.ravel().astype(int)) / (n*10.)
assert np.all(np.abs(dist-[0.8, 0.2]) < 1e-2)
def testRow(self):
assert sample_discrete(np.array([0.8, 0.2]), 1, 10).shape == (1,10)