def log_mvn_likelihood(mean: torch.FloatTensor, covariance: torch.FloatTensor, observation: torch.FloatTensor) -> torch.FloatTensor:
"""
all torch primitives
all non-diagonal elements of covariance matrix are assumed to be zero
"""
k = mean.shape[0]
variances = covariance.diag()
log_likelihood = 0
for i in range(k):
log_likelihood += - 0.5 * torch.log(variances[i]) \
- 0.5 * k * math.log(2 * math.pi) \
- 0.5 * ((observation[i] - mean[i])**2 / variances[i])
return log_likelihood
