In c , % is the element-wise matrix multiplication operator, while * is for regular matrix multiplication.

OK,Thanks. I have one more question.

In Updata z and w，Parameters of the gamma distribution: w_beta is 2/(Y.row-mu_i_long) * lambda * (Y.row-mu_i_long).t() 4) in code. But w_beta is (Y.row-mu_i_long).t() * lambda * (Y.row-mu_i_long) 4)/2 in supplementary infomation.

There are 2 parameterizations of the gamma distribution: https://en.wikipedia.org/wiki/Gamma_distribution

In Bayesian statistics, we typically use $\alpha$ and $\beta$, but the R function we used had the other parameterization, where $\theta = 1/\beta$.

Thanks！