vectorize _rng functions about math

[bob-carpenter]

Would also be good if the vectorized RNGs would accept vector arguments like dnorm in R and broadcast the smaller ones. We already have the VectorView framework in place for this. With vector arguments, we don't need a redundant numerical argument, so there are really two extensions:

• vector argument(s)
• number of repetition arguments with scalars

The second is much easier as it's basically just a bunch of loops.

[bob-carpenter]

For example, for the normal distribution, we would want to support these three signatures in Stan:

vector normal_rng(vector mu, real sigma);
vector normal_rng(real mu, vector sigma);
vector normal_rng(vector mu, vector sigma);

with broadcasting of the scalar to a vector. When two vectors are present, they must be the same size.

The existing implementations can be generalized using the expression template scalar_seq_view in the same way as the log probability density functions. That lets you view either a scalar or sequence as a sequence and write a single implementation.

A second kind of vectorization that would be convenient would be to have:

vector normal_rng(int N, real mu, real sigma);

to generate N draws with a single pair of parameters.

R just uses a single function that combines the two patterns, requiring an N, and a scalar or vector location and a scalar or vector scale parameter.

[bbbales2]

I opened a pull req. to get started on this: #573 . Hopefully I didn't go too far off the beaten path.

[bob-carpenter]

I didn't realize you were working on this, as I just suggested to someone else that they work on it. I'll try to fish out your email and respond that way as I don't know the other person's GitHub handle, so I can't call it out here.

[bob-carpenter]

I will take a look when I get a chance, but I'm getting bombarded by people wanting me to look over code these days.

[bbbales2]

Haha, I wasn't working on it till yesterday -- it's no problem if the pull I made gets replaced. I was just getting annoyed at having to write for loops for things that in the model were nicely vectorized so I figured I'd give it a go.

[rok-cesnovar]

@bbbales2 We can close this one right?

[bbbales2]

I think so.