csr_matrix_time_vector data * var specialization

[SteveBronder]

Summary

This adds a SparseMatrix<data> * Vector<var> specialization in rev. I think this is a pretty common case. For instance in brms for random effects models this can optionally be used. I think the pattern here should be faster than the alternative of doing a multi-index

Tests

Tests were added in mix for the csr matrix times vector

./runTests.py ./test/unit/math/mix/fun/csr_matrix_times_vector_test

Side Effects

I can also do this for sparse var on the lhs, though I think it requires a little extra fiddling and that would be a bit more of an involved PR

Release notes

Adds reverse mode specialization for `csr_matrix_times_vector(sparse data, dense parameter)

Checklist

• Math issue #(issue number)

• Copyright holder: Steve Bronder

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the 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/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.38	3.41	0.99	-0.81% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.97	-3.58% slower
eight_schools/eight_schools.stan	0.11	0.12	0.95	-4.88% slower
gp_regr/gp_regr.stan	0.16	0.16	1.04	3.7% faster
irt_2pl/irt_2pl.stan	6.02	6.12	0.98	-1.68% slower
performance.compilation	92.29	89.15	1.04	3.4% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.6	8.75	0.98	-1.75% slower
pkpd/one_comp_mm_elim_abs.stan	28.46	29.96	0.95	-5.28% slower
sir/sir.stan	128.58	133.86	0.96	-4.11% slower
gp_regr/gen_gp_data.stan	0.04	0.04	1.03	2.92% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.08	3.01	1.02	2.17% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.4	0.38	1.06	5.33% faster
arK/arK.stan	1.86	1.87	1.0	-0.48% slower
arma/arma.stan	0.76	0.77	0.99	-0.9% slower
garch/garch.stan	0.56	0.59	0.95	-5.41% slower
Mean result: 0.993637150405

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Jenkins Console Log
Blue Ocean
Commit hash: 2a39e03

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Machine information

ProductName: Mac OS X ProductVersion: 10.11.6 BuildVersion: 15G22010

CPU:
Intel(R) Xeon(R) CPU E5-1680 v2 @ 3.00GHz

G++:
Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr --with-gxx-include-dir=/usr/include/c++/4.2.1
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

Clang:
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

[SteveBronder]

@t4c1 do you have time to take a look at this?