Vectorised versions of composed functions

[avehtari]

Version

2.8.0

Category

improved functions

Description

Stan reference section 31.13 lists several composed functions, which accept only real argument and return value is real. It would be useful if they would accept also vector argument and return vector. And same for array, row_vector and matrix...

Example

For example, in addition to

real log1p(real x);

it would be useful to have also the following defined pointwise

vector log1p(vector x)
row_vector log1p(row_vector x);
matrix log1p(matrix x);
real[] log1p(real[]);

We could also extend this so that it handled arbitrary containers, so arrays of vectors or matrices, 2D arrays, etc. The main issue is going to be checking that the shapes are the same for functions of more than one argument.

Example Stan model can be found in
https://groups.google.com/forum/#!topic/stan-users/C6IxqRU1Cuw
This Stan model includes user defined function

vector log1pv(vector y)

which is used in user defined functions gpareto_log and gpareto_ccdf.

Multi-argument functions, shape matching, and broadcasting

• Allow any number of arguments with matching shapes
• Broadcast lower-dimensional up to higher-dimensional

Thus if we have a function of signature

foo(real, real) : real

and v is a vector of size N and c is a scalar, then

foo(v, a)  =def=  { foo(v[1], a), foo(v[2], a), ..., foo(v[N], a) }

[bob-carpenter]

Thanks, Aki. I'm assigning myself to this at least temporarily and targeting v3.

1. We need to scope out which functions to vectorize. We should really do them all.
2. I think this should be done via class static template functions which we can easily pass in via generic template functions to do this for 1, 2, and 3 arguments. I'll code up examples.

[bob-carpenter]

This first has to be done in stan-dev/math; see stan-dev/math#202

[bob-carpenter]

This is already finished for unary functions and underway for binary functions working up from stan-dev/math, so I'm closing this issue.