Parameter vector outer product

[John Reid]

Is it possible to create a matrix of the outer product between two vectors of parameters? I.e. something like?

parameters {                                                                                                                                                                                                      
    row_vector[M] colsizes;                                                                                                                                                                                       
    vector[N] rowrates;                                                                                                                                                                                           
}                                                                                                                                                                                                                 
transformed parameters {                                                                                                                                                                                          
    matrix[N,M] rates;                                                                                                                                                                                            
    rates <- rowrates * colsizes;                                                                                                                                                                                 
}

If it were possible would it be more efficient than looping in the model? That is:

model {
    for (n in 1:N) {
        for (m in 1:M) {
             rate[n,m] <- rowrates[n] * colsizes[m];
        }
    }
}

Thanks,
John.

[Bob Carpenter]

Yes, it's possible. Check out the doc for operator* to see
what the possible arguments are. For products, we have both:

outer product:

matrix operator*(vector,row_vector)

inner product:

real operator*(row_vector,vector)

and both are written just as (a * b) with a and b of different
types. Basically, Stan figures out what the operation entails and
the tightest return type that can be inferred. That way, you can
just use matrix notation for everything.

- Bob

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[John Reid]

Great. I'll try to use the documentation better.
Thanks,
John.