def testMatrix(self):
a = np.matrix([[1, 2], [1, 2]])
b = np.matrix([[1, 2], [1, 2]])
assert approxeq(a, b)
b = np.matrix([[1, 2], [1, 2.1]])
assert not approxeq(a, b)
assert approxeq(a, b, tol=1e-1, rel=True)
assert not approxeq(a, b, tol=1e-2, rel=True)
def testVector(self):
a = np.matrix([1, 2])
b = np.matrix([1, 2])
assert approxeq(a, b)
b = np.matrix([1, 2.1])
assert not approxeq(a, b)
assert approxeq(a, b, tol=1e-1, rel=True)
assert not approxeq(a, b, tol=1e-2, rel=True)
def testMatrix(self):
a = np.matrix([[1, 2],[1, 2]])
b = np.matrix([[1, 2],[1, 2]])
assert approxeq(a,b)
b = np.matrix([[1, 2],[1, 2.1]])
assert not approxeq(a,b)
assert approxeq(a,b,tol=1e-1,rel=True)
assert not approxeq(a,b,tol=1e-2,rel=True)
def testVector(self):
a = np.matrix([1, 2])
b = np.matrix([1, 2])
assert approxeq(a,b)
b = np.matrix([1, 2.1])
assert not approxeq(a,b)
assert approxeq(a,b,tol=1e-1,rel=True)
assert not approxeq(a,b,tol=1e-2,rel=True)
def mixgauss_prob(data, mu, Sigma, mixmat=None, unit_norm=False):
'''
% EVAL_PDF_COND_MOG Evaluate the pdf of a conditional mixture of Gaussians
% function [B, B2] = eval_pdf_cond_mog(data, mu, Sigma, mixmat, unit_norm)
%
% Notation: Y is observation, M is mixture component, and both may be conditioned on Q.
% If Q does not exist, ignore references to Q=j below.
% Alternatively, you may ignore M if this is a conditional Gaussian.
%
% INPUTS:
% data(:,t) = t'th observation vector
%
% mu(:,k) = E[Y(t) | M(t)=k]
% or mu(:,j,k) = E[Y(t) | Q(t)=j, M(t)=k]
%
% Sigma(:,:,j,k) = Cov[Y(t) | Q(t)=j, M(t)=k]
% or there are various faster, special cases:
% Sigma() - scalar, spherical covariance independent of M,Q.
% Sigma(:,:) diag or full, tied params independent of M,Q.
% Sigma(:,:,j) tied params independent of M.
%
% mixmat(k) = Pr(M(t)=k) = prior
% or mixmat(j,k) = Pr(M(t)=k | Q(t)=j)
% Not needed if M is not defined.
%
% unit_norm - optional; if 1, means data(:,i) AND mu(:,i) each have unit norm (slightly faster)
%
% OUTPUT:
% B(t) = Pr(y(t))
% or
% B(i,t) = Pr(y(t) | Q(t)=i)
% B2(i,k,t) = Pr(y(t) | Q(t)=i, M(t)=k)
%
% If the number of mixture components differs depending on Q, just set the trailing
% entries of mixmat to 0, e.g., 2 components if Q=1, 3 components if Q=2,
% then set mixmat(1,3)=0. In this case, B2(1,3,:)=1.0.
'''
if mu.ndim == 1:
d = len(mu)
Q = 1
M = 1
elif mu.ndim == 2:
d, Q = mu.shape
M = 1
else:
d, Q, M = mu.shape
d, T = data.shape
if mixmat == None:
mixmat = np.asmatrix(np.ones((Q, 1)))
# B2 = zeros(Q,M,T); % ATB: not needed allways
# B = zeros(Q,T);
if np.isscalar(Sigma):
mu = np.reshape(mu, (d, Q * M))
if unit_norm: # (p-q)'(p-q) = p'p + q'q - 2p'q = n+m -2p'q since p(:,i)'p(:,i)=1
# avoid an expensive repmat
print('unit norm')
# tic; D = 2 -2*(data'*mu)'; toc
D = 2 - 2 * np.dot(mu.T * data)
# tic; D2 = sqdist(data, mu)'; toc
D2 = sqdist(data, mu).T
assert (approxeq(D, D2))
else:
D = sqdist(data, mu).T
del mu
del data # ATB: clear big old data
# D(qm,t) = sq dist between data(:,t) and mu(:,qm)
logB2 = -(d / 2.) * np.log(
2 * pi * Sigma) - (1 / (2. * Sigma)) * D # det(sigma*I) = sigma^d
B2 = np.reshape(np.asarray(np.exp(logB2)), (Q, M, T))
del logB2 # ATB: clear big old data
elif Sigma.ndim == 2: # tied full
mu = np.reshape(mu, (d, Q * M))
D = sqdist(data, mu, inv(Sigma)).T
# D(qm,t) = sq dist between data(:,t) and mu(:,qm)
logB2 = -(d / 2) * np.log(2 * pi) - 0.5 * logdet(Sigma) - 0.5 * D
#denom = sqrt(det(2*pi*Sigma));
#numer = exp(-0.5 * D);
#B2 = numer/denom;
B2 = np.reshape(np.asarray(np.exp(logB2)), (Q, M, T))
elif Sigma.ndim == 3: # tied across M
B2 = np.zeros((Q, M, T))
for j in range(0, Q):
# D(m,t) = sq dist between data(:,t) and mu(:,j,m)
if isposdef(Sigma[:, :, j]):
D = sqdist(data, np.transpose(mu[:, j, :], (0, 2, 1)),
inv(Sigma[:, :, j])).T
logB2 = -(d / 2) * np.log(2 * pi) - 0.5 * logdet(
Sigma[:, :, j]) - 0.5 * D
B2[j, :, :] = np.exp(logB2)
else:
logging.error('mixgauss_prob: Sigma(:,:,q=%d) not psd\n' % j)
else: # general case
B2 = np.zeros((Q, M, T))
for j in range(0, Q):
for k in range(0, M):
# if mixmat(j,k) > 0
B2[j, k, :] = gaussian_prob(data, mu[:, j, k], Sigma[:, :, j,
k])
# B(j,t) = sum_k B2(j,k,t) * Pr(M(t)=k | Q(t)=j)
# The repmat is actually slower than the for-loop, because it uses too much memory
# (this is true even for small T).
# B = squeeze(sum(B2 .* repmat(mixmat, [1 1 T]), 2));
# B = reshape(B, [Q T]); % undo effect of squeeze in case Q = 1
B = np.zeros((Q, T))
if Q < T:
for q in range(0, Q):
# B(q,:) = mixmat(q,:) * squeeze(B2(q,:,:)); % squeeze chnages order if M=1
B[q, :] = np.dot(
mixmat[q, :], B2[q, :, :]
) # vector * matrix sums over m #TODO: had to change this. Is this correct?
else:
for t in range(0, T):
B[:, t] = np.sum(np.asarray(np.multiply(mixmat, B2[:, :, t])),
1) # sum over m
# t=toc;fprintf('%5.3f\n', t)
# tic
# A = squeeze(sum(B2 .* repmat(mixmat, [1 1 T]), 2));
# t=toc;fprintf('%5.3f\n', t)
# assert(approxeq(A,B)) % may be false because of round off error
return B, B2
def mixgauss_prob(data, mu, Sigma, mixmat = None, unit_norm = False):
'''
% EVAL_PDF_COND_MOG Evaluate the pdf of a conditional mixture of Gaussians
% function [B, B2] = eval_pdf_cond_mog(data, mu, Sigma, mixmat, unit_norm)
%
% Notation: Y is observation, M is mixture component, and both may be conditioned on Q.
% If Q does not exist, ignore references to Q=j below.
% Alternatively, you may ignore M if this is a conditional Gaussian.
%
% INPUTS:
% data(:,t) = t'th observation vector
%
% mu(:,k) = E[Y(t) | M(t)=k]
% or mu(:,j,k) = E[Y(t) | Q(t)=j, M(t)=k]
%
% Sigma(:,:,j,k) = Cov[Y(t) | Q(t)=j, M(t)=k]
% or there are various faster, special cases:
% Sigma() - scalar, spherical covariance independent of M,Q.
% Sigma(:,:) diag or full, tied params independent of M,Q.
% Sigma(:,:,j) tied params independent of M.
%
% mixmat(k) = Pr(M(t)=k) = prior
% or mixmat(j,k) = Pr(M(t)=k | Q(t)=j)
% Not needed if M is not defined.
%
% unit_norm - optional; if 1, means data(:,i) AND mu(:,i) each have unit norm (slightly faster)
%
% OUTPUT:
% B(t) = Pr(y(t))
% or
% B(i,t) = Pr(y(t) | Q(t)=i)
% B2(i,k,t) = Pr(y(t) | Q(t)=i, M(t)=k)
%
% If the number of mixture components differs depending on Q, just set the trailing
% entries of mixmat to 0, e.g., 2 components if Q=1, 3 components if Q=2,
% then set mixmat(1,3)=0. In this case, B2(1,3,:)=1.0.
'''
if mu.ndim == 1:
d = len(mu)
Q = 1
M = 1
elif mu.ndim == 2:
d, Q = mu.shape
M = 1
else:
d, Q, M = mu.shape;
d, T = data.shape
if mixmat == None:
mixmat = np.asmatrix(np.ones((Q,1)))
# B2 = zeros(Q,M,T); % ATB: not needed allways
# B = zeros(Q,T);
if np.isscalar(Sigma):
mu = np.reshape(mu, (d, Q * M))
if unit_norm: # (p-q)'(p-q) = p'p + q'q - 2p'q = n+m -2p'q since p(:,i)'p(:,i)=1
# avoid an expensive repmat
print('unit norm')
# tic; D = 2 -2*(data'*mu)'; toc
D = 2 - 2 * np.dot(mu.T * data)
# tic; D2 = sqdist(data, mu)'; toc
D2 = sqdist(data, mu).T
assert(approxeq(D,D2))
else:
D = sqdist(data, mu).T
del mu
del data # ATB: clear big old data
# D(qm,t) = sq dist between data(:,t) and mu(:,qm)
logB2 = -(d / 2.) * np.log(2 * pi * Sigma) - (1 / (2. * Sigma)) * D # det(sigma*I) = sigma^d
B2 = np.reshape(np.asarray(np.exp(logB2)), (Q, M, T))
del logB2 # ATB: clear big old data
elif Sigma.ndim == 2: # tied full
mu = np.reshape(mu, (d, Q * M))
D = sqdist(data, mu, inv(Sigma)).T
# D(qm,t) = sq dist between data(:,t) and mu(:,qm)
logB2 = -(d/2)*np.log(2*pi) - 0.5*logdet(Sigma) - 0.5*D;
#denom = sqrt(det(2*pi*Sigma));
#numer = exp(-0.5 * D);
#B2 = numer/denom;
B2 = np.reshape(np.asarray(np.exp(logB2)), (Q, M, T))
elif Sigma.ndim==3: # tied across M
B2 = np.zeros((Q,M,T))
for j in range(0,Q):
# D(m,t) = sq dist between data(:,t) and mu(:,j,m)
if isposdef(Sigma[:,:,j]):
D = sqdist(data, np.transpose(mu[:,j,:], (0, 2, 1)), inv(Sigma[:,:,j])).T
logB2 = -(d / 2) * np.log(2 * pi) - 0.5 * logdet(Sigma[:, :, j]) - 0.5 * D;
B2[j, :, :] = np.exp(logB2);
else:
logging.error('mixgauss_prob: Sigma(:,:,q=%d) not psd\n' % j)
else: # general case
B2 = np.zeros((Q, M, T))
for j in range(0, Q):
for k in range(0, M):
# if mixmat(j,k) > 0
B2[j, k, :] = gaussian_prob(data, mu[:, j, k], Sigma[:, :, j, k]);
# B(j,t) = sum_k B2(j,k,t) * Pr(M(t)=k | Q(t)=j)
# The repmat is actually slower than the for-loop, because it uses too much memory
# (this is true even for small T).
# B = squeeze(sum(B2 .* repmat(mixmat, [1 1 T]), 2));
# B = reshape(B, [Q T]); % undo effect of squeeze in case Q = 1
B = np.zeros((Q, T))
if Q < T:
for q in range(0, Q):
# B(q,:) = mixmat(q,:) * squeeze(B2(q,:,:)); % squeeze chnages order if M=1
B[q, :] = np.dot(mixmat[q, :], B2[q, :, :]) # vector * matrix sums over m #TODO: had to change this. Is this correct?
else:
for t in range(0, T):
B[:, t] = np.sum(np.asarray(np.multiply(mixmat, B2[:, :, t])), 1) # sum over m
# t=toc;fprintf('%5.3f\n', t)
# tic
# A = squeeze(sum(B2 .* repmat(mixmat, [1 1 T]), 2));
# t=toc;fprintf('%5.3f\n', t)
# assert(approxeq(A,B)) % may be false because of round off error
return B, B2
