bugfix/issue-stan-2433: change step to match int_step

[roualdes]

Submission Checklist

• Run unit tests: ./runTests.py test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary:

Change stan::math::step to match stan::math::int_step as requested in stan-dev/stan issue 2433.

Intended Effect:

Consistency between step functions.

How to Verify:

./runTests.py -j3 test/unit/math/prim/scal/

and

./runTests.py -j3 test/unit/math/rev/scal/

I ran the above commands without error.

Side Effects:

Change is step function behavior.

Documentation:

Made a note about this change just above step function definition.

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): California State University, Chico

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

[bob-carpenter]

The code and doc look great. Thanks.

We need to check with @syclik to make sure this change is OK with him. I'll ping him and you via email on this.

[bob-carpenter]

@roualdes and @syclik:

I think I led @roualdes astray with the poorly formulated issue 2433 in stan-dev/math. We are very sloppy in using issues and sometimes just use them to track things that need to be fixed in some way without properly deciding how they should be fixed.

The current situation is bad---we have a step() function and int_step() function which are inconsistent. But if we change the behavior of step(), we break backward compatibility.

Here's the BUGS manual. You'll see that they define step(e) as 1 if e >= 0; 0 otherwise. BUGS followed the tradition of defining the Heaviside step function which has that pesky >= condition.

In retrospect, I think we should just deprecate int_step and keep step() matching BUGS and tradition.

[bob-carpenter]

I don't think this should be merged. The code's fine, though.

See my comment in the conversation. So I'll mark this request changes.

[syclik]

@bob-carpenter, thanks for looking into it.

[syclik]

@bob-carpenter, can you update the issue with what you're thinking about? stan-dev/stan#2433

And then we can close this PR.

[bob-carpenter]

Sorry, @roualdes but I'm going to close this and rewrite issue stan-dev/stan#2433

[bob-carpenter]

:-) I did it before reading this request to do it.