Reverse mode autodiff for diag_post_multiply

[gregorp90]

Summary

Implemented custom reverse mode AD for diag_post_multiply() function. The implementation is based on the reverse mode implementation of diag_pre_multiply().

Tests

Added a test for prim where the arguments are of length zero.

Removed manual ad_tolerances from the mix test, similar to diag_pre_multiply(). Also added 4 mix tests, where the matrix is non-square.

Side Effects

None.

Release notes

Added custom reverse mode for diag_post_multiply() function.

Checklist

• Math issue Functions in prim/mat/fun that could use custom reverse mode autodiff implementations #989

• Copyright holder: Gregor Pirš

[rok-cesnovar]

@gregorp90 I pushed a fix for an OpenCL test issue that surfaced here.

@t4c1 @bbbales2 can I interest any one of you for a review?

[gregorp90]

@gregorp90 I pushed a fix for an OpenCL test issue that surfaced here.

@rok-cesnovar Thank you!

[t4c1]

Looks good, just one question.

[t4c1]

Why the change to this require to not allow vectors?

[t4c1]

As far as I can see this is what required the change to OpenCL tests (although new test is fine as well).

[gregorp90]

I see, so this should be require_eigen_t instead of require_eigen_matrix_dynamic_t?

I based this implementation on the implementation of diag_pre_multiply. In that implementation, Ben made this change, as you can see here. Maybe @bbbales2 can provide some more details on this change?

Also, if we are already on this subject. Why does the prim test with 1x1 matrix not fail, if we have require_eigen_matrix_dynamic_t?

[t4c1]

Yeah require_eigen_t or require_eigen_matrix_t is fine.

Also, if we are already on this subject. Why does the prim test with 1x1 matrix not fail, if we have require_eigen_matrix_dynamic_t?

It is not the shape of the input that is the issue, but type. We have general matrix type (that can also contain a vector) and special types for row or column vector. The new require does not accept the specialized vector types, while the test probably uses general matrix type.

[gregorp90]

So should I revert back to require_eigen_t or leave the implementation as it is?

Thanks for the answer, makes things more clear now!

[t4c1]

I think you should revert.

[gregorp90]

OK.
Should I make the same changes for diag_pre_multiply?

[gregorp90]

@t4c1 I made the changes to both, diag_pre_multiply and diag_post_multiply.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.45	3.4	1.01	1.46% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	1.04	4.07% faster
eight_schools/eight_schools.stan	0.11	0.11	1.01	1.0% faster
gp_regr/gp_regr.stan	0.16	0.16	0.98	-1.86% slower
irt_2pl/irt_2pl.stan	5.38	5.37	1.0	0.19% faster
performance.compilation	91.5	89.4	1.02	2.29% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.68	8.72	1.0	-0.45% slower
pkpd/one_comp_mm_elim_abs.stan	30.46	31.1	0.98	-2.09% slower
sir/sir.stan	126.08	120.07	1.05	4.77% faster
gp_regr/gen_gp_data.stan	0.04	0.04	1.0	-0.29% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.02	3.05	0.99	-0.77% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.39	0.39	1.01	0.84% faster
arK/arK.stan	1.85	1.89	0.98	-1.98% slower
arma/arma.stan	0.79	0.77	1.03	2.62% faster
garch/garch.stan	0.64	0.64	1.01	0.67% faster
Mean result: 1.00744965818

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Jenkins Console Log
Blue Ocean
Commit hash: d7be4a8

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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