How to construct the document-topic matrix using the word-topic and topic-word matrix calculated using Latent Dirichlet Allocation?
using the word-topic and topic-word matrix


This would be the same, wouldn't it? The model generates a words x topics and a topics x documents matrix, there is not much left to calculate, the model practically spits it out.

Using the Gibbs method gives you the counts Ntw[1..T][1..W] and Ndt[1..D][1..T], where for example Ndt[1][5] is the amount of words assigned to topic number 5 in document number 1.