Implement vectorize helper with similar semantics to that of NumPy

[ricardoV94]

Just a difference between providing a function or working on an existing graph.

Creating dummy inputs may not be intuitive to many users, so this helps with that. Also behaves more like NumPy.

import pytensor
import pytensor.tensor as pt

def func(x):
    return pt.exp(x) / pt.sum(pt.exp(x))

vec_func = pt.vectorize(func, signature="(a)->(a)")

x = pt.matrix("x")
y = vec_func(x)

fn = pytensor.function([x], y)
fn([[0, 1, 2], [2, 1, 0]])
# array([[0.09003057, 0.24472847, 0.66524096],
#        [0.66524096, 0.24472847, 0.09003057]])

[codecov-commenter]

Codecov Report

Merging #500 (225f429) into main (902eeb6) will increase coverage by 0.01%.
The diff coverage is 95.45%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #500      +/-   ##
==========================================
+ Coverage   80.75%   80.77%   +0.01%     
==========================================
  Files         161      162       +1     
  Lines       46078    46105      +27     
  Branches    11258    11266       +8     
==========================================
+ Hits        37212    37240      +28     
- Misses       6637     6638       +1     
+ Partials     2229     2227       -2     

Files	Coverage Δ
pytensor/tensor/blockwise.py	79.89% <100.00%> (-0.11%)	⬇️
pytensor/tensor/functional.py	100.00% <100.00%> (ø)
pytensor/graph/replace.py	84.84% <71.42%> (-1.47%)	⬇️

... and 1 file with indirect coverage changes

[twiecki]

Should this be a note further down below?

[ricardoV94]

Where would you put it?

[twiecki]

After Returns a new heading Notes

[jessegrabowski]

I was going to comment on this too; it's just not so clear what it means (since a priori everything in pytensor is a graph).

Maybe:

Vectorize a python function with symbolic pytensor inputs and outputs according to a function signature, equivalent to numpy.vectorize.

Note that this function cannot operate on pytensor variables that represent computational graphs. To vectorize an existing pytensor graph, use `pytensor.graph.replace.vectorize`. 

[twiecki]

I think this could be a bit better explained.

[ricardoV94]

I think people will be familiar with how it works in numpy, and if not they can check it. We just borrowed their API

[ricardoV94]

Updated docstrings @twiecki @jessegrabowski

[jessegrabowski]

10/10 will use