Generalize normal

[t4c1]

Summary

Generalizes normal distribution related fucntions to accept Eigen expressions.

Tests

Tested using expression testing framework.

Side Effects

None.

Release notes

Generalized normal distribution related fucntions to accept Eigen expressions.

Checklist

• Math issue Generalize matrix function signatures #1470

• 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

[t4c1]

@bbbales2 This PR also contains those moves you did not like. However I just remembered that fwd implementation of ops_partials_edge uses regular Eigen matrices for partials_, so doing moves can benefit fwd (and it does not hurt rev).

[bbbales2]

Good

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	4.24	3.92	1.08	7.51% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.96	-3.69% slower
eight_schools/eight_schools.stan	0.09	0.12	0.78	-28.05% slower
gp_regr/gp_regr.stan	0.18	0.18	1.01	1.01% faster
irt_2pl/irt_2pl.stan	6.53	6.11	1.07	6.47% faster
performance.compilation	88.29	88.77	0.99	-0.55% slower
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.34	9.16	0.91	-9.92% slower
pkpd/one_comp_mm_elim_abs.stan	29.55	29.4	1.01	0.5% faster
sir/sir.stan	130.83	135.88	0.96	-3.86% slower
gp_regr/gen_gp_data.stan	0.05	0.05	0.99	-1.09% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.33	3.17	1.05	4.86% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.39	0.38	1.05	4.36% faster
arK/arK.stan	2.56	1.85	1.39	27.8% faster
arma/arma.stan	0.72	0.74	0.97	-3.6% slower
garch/garch.stan	0.73	0.7	1.04	3.43% faster
Mean result: 1.01665117111

---

Jenkins Console Log
Blue Ocean
Commit hash: f7de716

---

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

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	4.28	3.78	1.13	11.72% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.97	-3.47% slower
eight_schools/eight_schools.stan	0.09	0.12	0.76	-31.49% slower
gp_regr/gp_regr.stan	0.18	0.18	0.97	-2.98% slower
irt_2pl/irt_2pl.stan	6.61	6.04	1.09	8.64% faster
performance.compilation	88.72	88.56	1.0	0.17% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.2	9.15	0.9	-11.58% slower
pkpd/one_comp_mm_elim_abs.stan	28.95	30.18	0.96	-4.25% slower
sir/sir.stan	128.97	131.62	0.98	-2.06% slower
gp_regr/gen_gp_data.stan	0.05	0.05	1.0	-0.18% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.3	3.17	1.04	3.89% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.4	0.39	1.03	2.89% faster
arK/arK.stan	2.56	1.94	1.32	24.31% faster
arma/arma.stan	0.73	0.75	0.97	-3.4% slower
garch/garch.stan	0.73	0.7	1.04	3.47% faster
Mean result: 1.01033361315

---

Jenkins Console Log
Blue Ocean
Commit hash: f7de716

---

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]

Good!