allows complex abs() to be vectorized

[SteveBronder]

Summary

Alternative to #2734 that uses apply_scalar_unary to vectorize abs() for complex types and containers of complex types. Mostly we just remove the explicit instantiations for std::vector<> and Eigen::Matrix types and use the apply_scalar_unary scheme to do the vectorization.

Tests

@bob-carpenter I kept the tests you added in the above PR and added a few more to make sure everything still works with the new matrix type as well.

Side Effects

idt so, but adding as a note @andrjohns we should add a doc page describing how to write vectorized versions of scalar functions.

Release notes

• Allows complex abs() to be vectorized

Checklist

• Math issue fully vectorize abs for int, real, complex #2729

• 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 so much @SteveBronder. I think given that I've worked on this and don't clearly understand the current math requirements, that @rok-cesnovar or someone else is going to have to review this.

[rok-cesnovar]

Looks great! Thanks.

[WardBrian]

Did this also vectorize the integer signature of abs?

[rok-cesnovar]

Yes.

std::vector<int> t{1,2,-3,4,-5,6,-1};
EXPECT_EQ(stan::math::abs(t), std::vector<int>({1, 2, 3, 4,5,6, 1}));

passes.

[WardBrian]

The relevant stanc pr is failing to compile the example model still:
https://jenkins.flatironinstitute.org/blue/rest/organizations/jenkins/pipelines/Stan/pipelines/Stanc3/branches/PR-1195/runs/8/nodes/298/steps/416/log/?start=0

/home/jenkins/workspace/Stan_Stanc3_PR-1195/performance-tests-cmdstan/cmdstan/stan/src/stan/model/indexing/assign.hpp:782:7: note: in instantiation of function template specialization 'stan::model::assign<std::vector<double, std::allocator<double> > &, std::vector<std::complex<double>, std::allocator<std::complex<double> > >, nullptr, nullptr>' requested here
../../test/integration/good/function-signatures/math/matrix/abs.hpp:1563:20: note: in instantiation of function template specialization 'stan::model::assign<std::vector<std::vector<double, std::allocator<double> >, std::allocator<std::vector<double, std::allocator<double> > > > &, std::vector<std::vector<std::complex<double>, std::allocator<std::complex<double> > >, std::allocator<std::vector<std::complex<double>, std::allocator<std::complex<double> > > > >, nullptr, nullptr>' requested here
      stan::model::assign(trans_x2z, stan::math::abs(cx2z),
                   ^

It seems like the return type of the vectorized version may be incorrect?

[WardBrian]

I can confirm this PR is broken for vectors of complex values.

Adding this test exposes the issue:

  std::vector<std::complex<stan::math::var>> vc {3};
  std::vector<stan::math::var> vr = abs(vc);

Failure:

------------------------------------------------------------
make -j1 test/unit/math/mix/fun/abs_test
g++ -DSTAN_TEST_PRINT_MATRIX_FAILURE -std=c++1y -pthread -D_REENTRANT -Wno-sign-compare -Wno-ignored-attributes      -I lib/tbb_2020.3/include    -O0  -I . -I lib/eigen_3.3.9 -I lib/boost_1.78.0 -I lib/sundials_6.1.1/include -I lib/sundials_6.1.1/src/sundials -I lib/benchmark_1.5.1/googletest/googletest/include -I lib/benchmark_1.5.1/googletest/googletest     -DBOOST_DISABLE_ASSERTS         -DGTEST_HAS_PTHREAD=0  -c -MT test/unit/math/mix/fun/abs_test.o -MM -E -MG -MP -MF test/unit/math/mix/fun/abs_test.d test/unit/math/mix/fun/abs_test.cpp
g++ -DSTAN_TEST_PRINT_MATRIX_FAILURE -std=c++1y -pthread -D_REENTRANT -Wno-sign-compare -Wno-ignored-attributes      -I lib/tbb_2020.3/include    -O0  -I . -I lib/eigen_3.3.9 -I lib/boost_1.78.0 -I lib/sundials_6.1.1/include -I lib/sundials_6.1.1/src/sundials -I lib/benchmark_1.5.1/googletest/googletest/include -I lib/benchmark_1.5.1/googletest/googletest -I lib/benchmark_1.5.1/googletest/googletest/include -I lib/benchmark_1.5.1/googletest/googletest      -DBOOST_DISABLE_ASSERTS         -DGTEST_HAS_PTHREAD=0 -DGTEST_HAS_PTHREAD=0  -c -o test/unit/math/mix/fun/abs_test.o test/unit/math/mix/fun/abs_test.cpp
test/unit/math/mix/fun/abs_test.cpp: In member function ‘virtual void mixFun_absReturnType_Test::TestBody()’:
test/unit/math/mix/fun/abs_test.cpp:228:40: error: conversion from ‘vector<std::complex<stan::math::var_value<double> >,allocator<std::complex<stan::math::var_value<double> >>>’ to non-scalar type ‘vector<stan::math::var_value<double>,allocator<stan::math::var_value<double>>>’ requested
  228 |   std::vector<stan::math::var> vr = abs(vc);
      |                                     ~~~^~~~
make: *** [<builtin>: test/unit/math/mix/fun/abs_test.o] Error 1
make -j1 test/unit/math/mix/fun/abs_test failed
exit now (05/16/22 09:53:37 EDT)

[WardBrian]

  Eigen::MatrixXcd mc(0, 0);
  Eigen::MatrixXd mr = abs(mc);

Also fails with a similar error ("cannot convert 'const std::complex<double>' to 'double' in assignment")

[WardBrian]

Here's a version of the test which I think should pass at a minimum. The first two sections are already tested and pass, and the integer section also passes. The middle versions which use containers of complex values fail to compile.

TEST(mixFun, absReturnType) {
  using stan::math::abs;

  // validate return types not overpromoted to complex by assignability
  std::complex<stan::math::var> a = 3;
  stan::math::var b = abs(a);

  std::complex<stan::math::fvar<double>> c = 3;
  stan::math::fvar<double> d = abs(c);

  std::vector<std::complex<stan::math::var>> vc{3};
  std::vector<stan::math::var> vr = abs(vc);

  Eigen::MatrixXcd mc(0, 0);
  Eigen::MatrixXd mr = abs(mc);

  std::vector<Eigen::MatrixXcd> vmc{mc};
  std::vector<Eigen::MatrixXd> vmr = abs(vmc);

  std::vector<int> t{1, 2, -3, 4, -5, 6, -1};
  // does not promote to real
  t = abs(t);

  SUCCEED();
}

It wouldn't hurt to add tests which also check that the correct values are returned for abs(complex) and its containers - that probably also would have caught this

[rok-cesnovar]

Will look into this tomorrow. Thanks for digging all this up!

[SteveBronder]

I have a fix for this sorted out I'll put up in a little bit

[bob-carpenter]

You can write tests using std::is_same<> for checking return types:

#include <typetraits>

template <typename E, typename T>
bool is_type(const T& x) {
  return std::is_same<T, E>::value;
}

and then call it with something like is_type<int>(abs(1)) to check. I think I wrote that into the primitive tests.