Updates LLT to inplace decomposition per eigen 3.3 doc

[rtrangucci]

Submission Checklist

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

Summary:

Inplace LLT saves memory and one copy. Addresses #359

Intended Effect:

Reduction in memory, reduction in copies.

How to Verify:

./runTests.py test/unit/math/rev/mat/fun/cholesky_decompose_test.cp

Side Effects:

None

Documentation:

None

Reviewer Suggestions:

@bob-carpenter

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):

Rob Trangucci

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]

More questions than requested changes!

[bob-carpenter]

Is this doc broken now? You've removed the selfadjointView<Lower> bit of the code.

[rtrangucci]

Fixed the doc. Thanks for the review.

[bob-carpenter]

Is there a reason we're no longer using a selfadjointView of L_A? Have the input requirements changed now that we use all of it?

[rtrangucci]

Good question! I'm not sure if I can do a Ref to a triangular view of a matrix. I'll see if I can figure it out.

[rtrangucci]

I used the selfadjointViewEigen::Lower() to cut down on the copy when L_factor was instantiated, but I'm fairly certain that LLT defaults to a lower triangular view. In any case, the inplace decomposition obviates the need for any selfadjointView() instantiation here. I've added an explicit Eigen::Lower template argument, but that's the default for the class.