Using rows_dot_product in a loop to set column contents; any optimization ideas?

Modeling
,
1

Removing extraneous structures, I have:

data{
	int m ;
	int n ;
	matrix[m,n] X ;
	int p ;
	...
}
parameters{
	matrix[n,p] Z ;
	...
}
model{
	matrix[m,p] Q ;
	for(i_p in 1:p){
		Q[,i_p]= rows_dot_product(
			rep_matrix(to_row_vector(Z[,i_p]),m)
			, X
		) ;
	}
	...
}

I’m sure that loop can be made into a single call to rows_dot_product but I’ve been I’ve been looking at this model for too long and am having trouble “seeing” it. Any suggestions?

2

Solved it! Just need to index to expand the matrices for a single rows_dot_product call, then wrap the resulting vector to a matrix:

data{
	int m ;
	int n ;
	matrix[m,n] X ;
	int p ;
	...
}
transformed data{
	array[m*p] int mp ; //will be rep(1:m,times=p)
	array[p*m] int pm ; // will be rep(1:p,each=m)
	int i_mp = 0 ;
	for(i_p in 1:p){
		for(i_m in 1:m){
			i_mp += 1 ;
			mp[i_mp] = i_m ;
			pm[i_mp] = i_p ;
		}
	}
}
parameters{
	matrix[p,n] Z ; //n.b. transposed wrt original, obviating to_row_vector
	...
}
model{
	matrix[m,p] Q = to_matrix( rows_dot_product(Z[pm],X[mp]) , m, p)
	...
}

Now to check if I got the indexing right…

Yup, had an indexing error, but worked it out and edited the above to have the correct solution.

3

Wonder if it would be slightly more efficient to pre-define X[mp] as a TD variable:

data{
	int m ;
	int n ;
	matrix[m,n] X ;
	int p ;
	...
}
transformed data{
	array[m*p] int mp ; //will be rep(1:m,times=p)
	array[p*m] int pm ; // will be rep(1:p,each=m)
	int i_mp = 0 ;
	for(i_p in 1:p){
		for(i_m in 1:m){
			i_mp += 1 ;
			mp[i_mp] = i_m ;
			pm[i_mp] = i_p ;
		}
	}
	matrix[m*p,n] X_mp = X[mp] ;
}
parameters{
	matrix[p,n] Z ; //n.b. transposed wrt original, obviating to_row_vector
	...
}
model{
	matrix[m,p] Q = to_matrix( rows_dot_product(Z[pm],X_mp) , m, p)
	...
}