[WIP] Complex numbers vals_c

[nickdidio]

Submission Checklist

• Run unit tests: ./runTests.py src/test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary

Allow for intake of complex numbers in Stan. This PR mainly adds a new function called vals_c which allow for intake of complex numbers in a Stan program.

Documentation

All documentation for complex numbers is available at stan-dev/docs#378.

How to Verify

Testing is available in src/test/unit/io/array_var_context_test.cpp

Side Effects

None

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Nicholas DiDio

By submitting this pull request, the copyright holder is agreeing to 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/)

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.01	3.01	1.0	0.23% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	1.0	-0.47% slower
eight_schools/eight_schools.stan	0.1	0.1	0.99	-0.63% slower
gp_regr/gp_regr.stan	0.16	0.16	0.98	-2.39% slower
irt_2pl/irt_2pl.stan	5.84	5.96	0.98	-2.07% slower
performance.compilation	89.81	87.66	1.02	2.4% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.54	8.63	0.99	-0.99% slower
pkpd/one_comp_mm_elim_abs.stan	32.19	29.57	1.09	8.14% faster
sir/sir.stan	128.93	125.97	1.02	2.29% faster
gp_regr/gen_gp_data.stan	0.03	0.03	1.0	-0.48% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.98	2.96	1.01	0.71% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.4	0.39	1.03	2.48% faster
arK/arK.stan	1.92	2.52	0.76	-31.56% slower
arma/arma.stan	0.83	0.91	0.91	-9.46% slower
garch/garch.stan	0.53	0.61	0.87	-15.32% slower
Mean result: 0.97621803717

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Jenkins Console Log
Blue Ocean
Commit hash: 5a18ead

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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

[bob-carpenter]

Looks good. This can be merged when tests pass.