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26 Using external C++ code

The --allow-undefined flag can be passed to the call to stanc, which will allow undefined functions in the Stan language to be parsed without an error. We can then include a definition of the function in a C++ header file.

This requires specifying two makefile variables:

STANCFLAGS=--allow-undefined
USER_HEADER=<header_file.hpp>, where <header_file.hpp> is the name of a header file that defines a function with the same name and a compatible signature. This function can appear in the global namespace or in the model namespace, which is defined as the name of the model (either the file name, or the --name argument to stanc) followed by _namespace.

This is an advanced feature which is only recommended to users familiar with the internals of Stan’s Math library. Most existing C++ code will need to be modified to work with Stan, to varying degrees.

As an example, consider the following variant of the Bernoulli example

functions {
  real make_odds(data real theta);
}
data {
  int<lower=0> N;
  array[N] int<lower=0, upper=1> y;
}
parameters {
  real<lower=0, upper=1> theta;
}
model {
  theta ~ beta(1, 1); // uniform prior on interval 0, 1
  y ~ bernoulli(theta);
}
generated quantities {
  real odds;
  odds = make_odds(theta);
}

Here the make_odds function is declared but not defined, which would ordinarily result in a parser error. However, if you put STANCFLAGS = --allow-undefined into the make/local file or into the stanc call, then the stanc compiler will translate this program to C++, but the generated C++ code will not compile unless you write a file such as examples/bernoulli/make_odds.hpp with the following lines

#include <ostream>

double make_odds(const double& theta, std::ostream *pstream__) {
  return theta / (1 - theta);
}

The signature for this function needs to fulfill all the usages in the C++ class emitted by stanc. The pstream__ argument is mandatory in the signature but need not be used if your function does not print any output. Because make_odds was declared with a data argument and only used in generated quantites, a signature which accepts and returns double is acceptable. Functions which will have parameters passed as input in the transformed parameters or model blocks will require the ability to accept Stan’s autodiff types. If you wish to autodiff through this function, the simplest option is to make it a template, like

template <typename T>
T make_odds(const T &theta, std::ostream *pstream__)
{
    return theta / (1 - theta);
}

Given the above, the following make invocation should work

> make STANCFLAGS=--allow-undefined USER_HEADER=examples/bernoulli/make_odds.hpp examples/bernoulli/bernoulli # on Windows add .exe

Alternatively, you could put STANCFLAGS and USER_HEADER into the make/local file instead of specifying them on the command-line.

If the function were more complicated and involved functions in the Stan Math Library, then you would need to add #include <stan/model/model_header.hpp> and prefix the function calls with stan::math::.

26.1 Derivative specializations

External C++ functions are currently the only way to encode a function with a known analytic gradient outside the Stan Math Library. This is done very similarly to how a function would be added to the Math library with a reverse-mode specialization. The following code is adapted from the Stan Math documentation.

Suppose you have the following (nonsensical) model which relies on a function called my_dot_self. We will implement this as a copy of the built-in dot_self function.

functions {
  // both overloads end up using the same C++ template
  real my_dot_self(vector theta);
  real my_dot_self(row_vector theta);
}
data {
  int<lower=0> N;
  vector[N] input_data;
}
transformed data {
  // no autodiff for data - will call using doubles
  real ds = my_dot_self(input_data);
}
parameters {
  row_vector[N] thetas;
}
model {
  thetas ~ normal(0,1);
  // autodiff - will call using stan::math::var types
  input_data ~ normal(thetas, my_dot_self(thetas));
}

If you wanted to autodiff through this function, the following header would suffice³:

#include <stan/model/model_header.hpp>
#include <ostream>

template <typename EigVec, stan::require_eigen_vector_t<EigVec> * = nullptr>
inline stan::value_type_t<EigVec> my_dot_self(const EigVec &x, std::ostream *pstream__)
{
    const auto &x_ref = stan::math::to_ref(x);
    stan::value_type_t<EigVec> sum_x = 0.0;
    for (int i = 0; i < x.size(); ++i)
    {
        sum_x += x_ref.coeff(i) * x_ref.coeff(i);
    }
    return sum_x;
}

However, we know the derivative of this function directly. To leverage this, we could use a more complicated form which has two function templates that differentiate themselves based on whether or not derivatives are required:

#include <stan/model/model_header.hpp>
#include <ostream>

template <typename EigVec, stan::require_eigen_vector_t<EigVec> * = nullptr,
          stan::require_not_st_var<EigVec> * = nullptr>
inline double my_dot_self(const EigVec &x, std::ostream *pstream__)
{
    auto x_ref = stan::math::to_ref(x);
    double sum = 0.0;
    for (int i = 0; i < x.size(); ++i)
    {
        sum += x_ref.coeff(i) * x_ref.coeff(i);
    }
    return sum;
}

template <typename EigVec, stan::require_eigen_vt<stan::is_var, EigVec> * = nullptr>
inline stan::math::var my_dot_self(const EigVec &v, std::ostream *pstream__)
{
    // (1) put v into our memory arena
    stan::arena_t<EigVec> arena_v(v);
    // (2) calculate forward pass using
    // (3) the .val() method for matrices of var types
    stan::math::var res = my_dot_self(arena_v.val(), pstream__);
    // (4) Place a callback for the reverse pass on the callback stack.
    stan::math::reverse_pass_callback(
        [res, arena_v]() mutable
        { arena_v.adj() += 2.0 * res.adj() * arena_v.val(); });
    return res;
}

For more details about how to write C++ code using the Stan Math Library, see the Math library documentation at https://mc-stan.org/math/ or the paper at https://arxiv.org/abs/1509.07164.

26.2 Special functions: RNGs, distributions, editing `target`

Some functions have special meanings in Stan and place additional requirements on their signatures if used in external C++.

RNGs must end with _rng. They will be passed a “base RNG object” as the second to last argument, before the pointer to the ostream. We recommend making this a template, since it may change, but at the moment it is always a boost::random::ecuyer1988 object.
Functions which edit the target directly must end with _lp and will be passed a reference to lp__ and a reference to a stan::math::accumulator object as the final parameters before the ostream pointer. They are also expected to have a boolean template parameter propto__ which controls whether or not constant terms can be dropped.
Probability distributions must end with _lpdf or _lpmf and will be passed a boolean template parameter propto__ which controls whether or not constant terms can be dropped.

Details of programming in the Stan Math style are omitted from this section, it is presented only as an example↩︎

26 Using external C++ code

26.1 Derivative specializations

26.2 Special functions: RNGs, distributions, editing target

26.2 Special functions: RNGs, distributions, editing `target`