Fix dirichlet_lpdf and multi_normal_cholesky_lpdf adjoints

[t4c1]

Summary

Fixes a bug in dirichlet_lpdf and multi_normal_cholesky_lpdf, where some overloads (ones that do broadcasting) produced wrong derivatives. The bug appeared with generalizations of the functions, so it is also present in the last release.

Tests

As far as I can see there is no test for dirichlet_lpdf that would check adjoints (ouch). Tests for multi_normal_cholesky_lpdf seem as if they should catch that, but they are quite complicated and I can't really make sense of them.

@bbbales2 can I recruit you for writing appropriate tests for this?

Side Effects

None.

Release notes

Fixed a bug in dirichlet_lpdf and multi_normal_cholesky_lpdf, where some overloads (ones that do broadcasting) produced wrong derivatives.

Checklist

• Math issue Vectorized versionf of dirichlet_lpdf and multi_normal_cholesky_lpdf broken #2332

• Copyright holder: Tadej Ciglarič

  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

[bbbales2]

Yeah sure on my list. Good catch.

[wds15]

wow! the last working version of the multivariate normal was in 2.24.1 ! Test, test, test, test... please, please, please :)

[bbbales2]

Yoyo, I have fixes, but it's not letting me push to the bstatcomp repo. I thought the pull requests to this repo granted push privileges in the source branch?

There is a branch with tests here: develop...fix_multivar_adjoints

Edit: @rok-cesnovar gave me permissions so I pushed the changes here now.

I originally added tests in the multi_normal thing too. I just left them cause it's not gonna hurt to have them. We'll need to add the ability to test these vectorized things in the varmat tests separately.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.39	3.38	1.0	0.22% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.96	-4.54% slower
eight_schools/eight_schools.stan	0.11	0.11	1.01	0.89% faster
gp_regr/gp_regr.stan	0.15	0.15	1.0	-0.11% slower
irt_2pl/irt_2pl.stan	5.21	5.23	1.0	-0.35% slower
performance.compilation	92.84	90.54	1.03	2.48% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.62	8.65	1.0	-0.35% slower
pkpd/one_comp_mm_elim_abs.stan	28.38	28.74	0.99	-1.29% slower
sir/sir.stan	135.45	127.9	1.06	5.57% faster
gp_regr/gen_gp_data.stan	0.04	0.04	1.01	1.25% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.05	3.07	0.99	-0.56% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.38	0.41	0.91	-9.29% slower
arK/arK.stan	1.81	1.82	0.99	-0.53% slower
arma/arma.stan	0.61	0.61	1.0	0.25% faster
garch/garch.stan	0.59	0.59	1.0	-0.04% slower
Mean result: 0.996689438063

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Jenkins Console Log
Blue Ocean
Commit hash: 125a4e1

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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

[bbbales2]

@rok-cesnovar @SteveBronder ready for review (and this is a bugfix for the release)

[rok-cesnovar]

Thanks to both!