[WIP] Backport Eigen changes for proposed plugin refactor

[andrjohns]

Summary

This PR is for testing that the backported Eigen changes mentioned in #2653 will allow the proposed Eigen plugin refactor (fixing issues with val vs val_op) originally from #2604

This PR is for testing downstream compatibility only and should not be merged. Once all errors are fixed, the backported Eigen code and the plugin refactor will be proposed in separate PRs

[andrjohns]

@serban-nicusor-toptal there's a git failure in the downstream cmdstan tests for this PR, would you be able to take a look when you get a minute?

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.61	3.61	1.0	-0.26% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.97	-2.76% slower
eight_schools/eight_schools.stan	0.09	0.08	1.02	2.1% faster
gp_regr/gp_regr.stan	0.15	0.14	1.02	1.58% faster
irt_2pl/irt_2pl.stan	5.75	5.77	1.0	-0.36% slower
performance.compilation	93.26	90.95	1.03	2.48% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.07	8.12	0.99	-0.61% slower
pkpd/one_comp_mm_elim_abs.stan	31.96	31.08	1.03	2.76% faster
sir/sir.stan	119.88	127.19	0.94	-6.1% slower
gp_regr/gen_gp_data.stan	0.03	0.04	0.93	-7.04% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.02	3.1	0.97	-2.91% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.38	0.41	0.94	-6.28% slower
arK/arK.stan	2.05	2.07	0.99	-0.96% slower
arma/arma.stan	0.28	0.28	1.03	2.67% faster
garch/garch.stan	0.61	0.65	0.94	-6.18% slower
Mean result: 0.986762771383

---

Jenkins Console Log
Blue Ocean
Commit hash: b2ebd22

---

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

[serban-nicusor-toptal]

hey @andrjohns I hope it works just fine after fixing the conflicts, tbh I think it was just a network error :(

Edit: Looks like .git dir had something corrupted inside, maybe an old branch!? and it was running into kind of a conflict. Cleaned git cache and force fetched all remotes, I hope it's fine now else please tag me. Thanks!

[andrjohns]

Great, thanks!

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.56	3.58	0.99	-0.61% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.96	-3.71% slower
eight_schools/eight_schools.stan	0.09	0.09	0.98	-1.98% slower
gp_regr/gp_regr.stan	0.15	0.14	1.03	2.47% faster
irt_2pl/irt_2pl.stan	5.78	5.72	1.01	1.07% faster
performance.compilation	93.49	90.88	1.03	2.79% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.13	8.11	1.0	0.34% faster
pkpd/one_comp_mm_elim_abs.stan	30.92	30.85	1.0	0.23% faster
sir/sir.stan	124.34	129.77	0.96	-4.37% slower
gp_regr/gen_gp_data.stan	0.03	0.03	0.99	-0.65% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.0	2.99	1.0	0.4% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.38	0.43	0.88	-13.04% slower
arK/arK.stan	2.1	2.04	1.03	3.04% faster
arma/arma.stan	0.28	0.28	0.99	-1.38% slower
garch/garch.stan	0.61	0.65	0.94	-6.43% slower
Mean result: 0.987129633938

---

Jenkins Console Log
Blue Ocean
Commit hash: 1d52230

---

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

[andrjohns]

Closing for now to clear PR backlog, will re-open once ready for review