Add vectorized versions of the free functions

[SteveBronder]

Summary

This is for stan-dev/stanc3#947 and allows the compiler to simply call the free functions for standard vectors holding containers instead of generating a for loop and iterating over them.

All the functions here are pretty much the same with the scheme being

template <typename T, require_std_vector_t<T>* = nullptr>
auto <constrain>_free(const T& x) {
  std::vector<decltype(<constrain>_free(x[0]))> x_free(x.size());
  std::transform(x.begin(), x.end(), x_free.begin(), [](auto&& xx) {
    return <constrain>_free(xx);
  });
  return x_free;
}

Tests

Tests are added in each *_constrain_test.cpp to run the standard test to check input/output but instead uses a standard vector of eigen types. Change tests can be run using

./runTests.py -j4 test/unit/math/prim/fun/cholesky_corr_transform_test.cpp \
test/unit/math/prim/fun/cholesky_factor_transform_test.cpp \
test/unit/math/prim/fun/corr_matrix_transform_test.cpp \
test/unit/math/prim/fun/cov_matrix_transform_test.cpp \
test/unit/math/prim/fun/ordered_transform_test.cpp \
test/unit/math/prim/fun/positive_ordered_transform_test.cpp \
test/unit/math/prim/fun/simplex_transform_test.cpp \
test/unit/math/prim/fun/unit_vector_transform_test.cpp

Side Effects

Nope!

Release notes

Vectorize unconstrain functions

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

[bob-carpenter]

Thanks. This looks good.

I have a question about whether this will work for size 0 vectors as I don't know enough about decltype actually works. Assuming that's OK, this is OK to merge.

I made a suggestion for eliminating boilerplate, but it should be considered optional. It also contains a suggestion for solving the x[0] not existing problem brought up in the first comment.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.55	3.48	1.02	1.95% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.98	-2.31% slower
eight_schools/eight_schools.stan	0.09	0.09	1.0	-0.23% slower
gp_regr/gp_regr.stan	0.14	0.14	1.0	-0.34% slower
irt_2pl/irt_2pl.stan	5.07	5.06	1.0	0.28% faster
performance.compilation	90.9	88.77	1.02	2.35% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.14	8.24	0.99	-1.23% slower
pkpd/one_comp_mm_elim_abs.stan	31.82	29.56	1.08	7.12% faster
sir/sir.stan	124.02	120.32	1.03	2.98% faster
gp_regr/gen_gp_data.stan	0.03	0.03	0.98	-1.87% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.96	3.05	0.97	-3.21% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.37	0.39	0.95	-5.39% slower
arK/arK.stan	2.04	2.05	1.0	-0.48% slower
arma/arma.stan	0.25	0.25	1.02	1.83% faster
garch/garch.stan	0.6	0.61	0.98	-1.73% slower
Mean result: 1.00065898959

---

Jenkins Console Log
Blue Ocean
Commit hash: f35f8f1

---

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

[bob-carpenter]

Thanks! So glad you could get rid of all that boilerplate and use an existing framework. Feel free to merge if tests pass.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.5	3.51	1.0	-0.36% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.99	-0.57% slower
eight_schools/eight_schools.stan	0.09	0.09	1.01	1.41% faster
gp_regr/gp_regr.stan	0.14	0.14	1.0	0.06% faster
irt_2pl/irt_2pl.stan	5.09	5.08	1.0	0.22% faster
performance.compilation	91.07	88.83	1.03	2.47% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.33	8.13	1.02	2.41% faster
pkpd/one_comp_mm_elim_abs.stan	29.65	31.09	0.95	-4.84% slower
sir/sir.stan	121.3	121.39	1.0	-0.07% slower
gp_regr/gen_gp_data.stan	0.03	0.03	0.99	-1.03% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.96	2.99	0.99	-1.07% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.37	0.39	0.96	-3.85% slower
arK/arK.stan	2.05	2.04	1.0	0.43% faster
arma/arma.stan	0.25	0.25	0.99	-1.52% slower
garch/garch.stan	0.6	0.6	1.0	0.42% faster
Mean result: 0.996448210928

---

Jenkins Console Log
Blue Ocean
Commit hash: 45dd53f

---

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