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Contributing New Functions to Stan
Better information on how to add a function to the Stan Math Library is available at https://mc-stan.org/math/
Instructions on adding a function that is already in Stan Math to the Stan compiler can be found at https://mc-stan.org/stanc3/stanc/exposing_new_functions.html
Sometimes a new function is needed in Stan. This function may compute some special mathematical function, or may be intended to speed up automatic differentiation by avoiding intermediate computations and directly computing the gradients. This page documents the basic steps necessary to do this.
To be available as part of the Stan language, a function must be added in two places. First, the C++ relevant code should be added to the Stan math library, along with tests that demonstrate its intended behavior. Second, the function must be added to the Stan language in the stanc3 Repository, along with tests that demonstrate that it is parsed as intended. If you only want a new function available through the Stan math library C++ API it does not need to be exposed to the Stan language.
Before doing anything, please read the Stan Developer Process document, setup your git repository and create a feature/<new function> branch. The steps below should, roughly speaking, consist of one commit each in this repository.
Functions should be implemented in the GitHub repo stan-dev/math, not in this repo, stan-dev/stan. That means you need a new issue for the math repo and unit tests there. When that's all done and tested, you can come back to do the Stan pieces of the puzzle, which are straightforward.
Implement the new function in the appropriate location, most likely in the stan/math repository and include it in the appropriate header files. The best way to figure out where this is and how to implement the function is to find a similar function already in the API and use it as a model. You can grep to see where it's included.
It is important to implement the function in such a way that it is templated such that it can be called with auto-diff variables for parameters and double values for data. Again, see the existing functions for examples.
In general, implementations should go int the lowest directory possible, subject to the orderings
scal < arr < mat
prim < rev < mix;
prim < fwd < mix;
If the left-hand type occurs, the directory has to be at least the minimum on the right
Code includes directory must be at least
------------- --------------------------
Eigen::Matrix mat
std::vector arr
stan::math::var rev
stan::math::fvar fwd
Everything else follows from these two rules. The directories are laid out two deep, with
(prim | fwd | rev | mix) / (scal | arr | mat)
Depending on where you put the function (see the rules above), you'll need to include its definition file in the appropriate header include to make sure it's visible to models. For instance, if the function is going into stan/math/rev/arr/foo.hpp then #include <stan/math/rev/arr/foo.hpp> should be included added to stan/math/rev/arr.hpp.
Implement a unit test for the function which covers both the value (i.e., that it computes the right thing), the gradients of the function, and the error behavior (e.g., when the function is passed illegal values). Looking at a unit test of a similar function will help give a sense of how to do this.
You should check all the ways in which it can be called --- that is all permutations of scalars/vectors and double and autodiff variables.
An individual unit test, e.g., test/unit/math/prim/scal/fun/abs_test.cpp, can be run with ./runTests.py test/unit/math/prim/scal/fun/abs_test.cpp.
After the individual test passes, make sure that ./runTests.py test/unit and make test-headers both pass.
Expose the function to the parser by adding the appropriate code to the stanc3 compiler (see below).
We need models in test_models instantiating all the possible ways the function can be instantiated. Examples are in src/test/test-models/good for ones that pass and in src/test/test-models/bad for ones that don't. Specifically, the function signature tests should go in src/test/test-models/good/function-signatures.
There are drivers for these tests in src/test/unit/lang/parser --- look at the ones that are in src/test/unit/lang/parser/other_test.cpp to see how to test that models don't parse or throw the right warnings when trying to parse them.
Add Doxygen docs to any new functions and reference documentation to the manual (in the Stan library). Ideally with a formula for it. Include a reference if it's uncommon.
Submit a pull request on GitHub. We'll review the code, doc and tests, perhaps iterate over fixes, verify that it passes tests, and then merge it into Stan. Details on the submission process can be found on the Git-Process wiki page.
This next section discusses how to get a stan function up and running at a C++ level.
I will use the term "parameter" to designate parameters and parameter dependent variables. Data on the other hand will refer to non-parameter variables.
Stan computes the gradient of the posterior to efficiently explore the parameter space of a model. For each parameter, stan stores the value and the derivative in a object var or fvar, respectively used for reverse and forward mode automatic differentiation.
A function acting on a parameter should be overloaded for double, var, and fvar types. The easiest way to do this is to use a template type. If you decide to code the derivatives by hand, you need to overload the function. For example sin(x) has the signatures sin(double), sin(const var& x) and template <typename T> sin(const fvar<T>& x); in the latter two, the partial derivatives are explicitly coded. If you do not explicitly code the derivative, automatic differentiation approximates the derivative.
A variable may be a function of parameters and data. In that case, if at least one of the arguments is a parameter, so is the returned object. This is consitent with the above definition of a parameter.
For example, the sum of a parameter and a datum is a parameter.
We can set this condition using boost::math::tools::promote_args:
using boost::math::tools::promote_args;
typename promote_args<T0, T1>::type scalar;The type scalar depends on the types T0 and T1. If at least one these is a parameter, then scalar is a parameter. If they are both double, then scalar is a double.
promote_args can only have up to five arguments. For more than five arguments, we can use a nested promote_args object:
typename promote_args<T0, T1, T2, T3, typename promote_args<T4, T5, T6>::type>::type scalar;When writing a function, you should keep in mind the operators you use must apply to var and fvar. This holds for most basic math functions.
There are few common C++ practices in Stan worth pointing out.
Consider the following lines of code. In this particular example, a foo returns a matrix and takes in four vectors:
template <typename T1, typename T2>
Eigen::Matrix <typename promote_args<T1, T2>::type, Dynamic, Dynamic>
foo(const std::vector<T1>& ArrayArgument1,
const std::vector<T2>& ArrayArgument2,
const std::vector<int>& IntArrayArgument1,
const std::vector<int>& IntArrayArgument2)We start with a template list. The next line gives the return type: a matrix, the elements of which have a promoted type. The arguments are standard vectors. The first two arguments contain template elements. We however do not use a template type for integers, because Stan only deals with continuous variables (integers cannot be parameters!).
Next, notice the arguments of the function are constants, as enforced by the term const. This safety measure insures the original input is not modified by the function. If the programmer inadvertently modifies a constant, the compiler returns an error.
Secondly, the & indicates we are using a reference: we are directly accessing the memory address of the variable. If we do not use a reference, the function acts on a copy of the variable, created when the function is called. With a reference, we do not waste time and memory creating a copy of the vector the function acts on.
There are many other ways of declaring a function in Stan. The best way to learn is to look at the many examples in stan/math.
A function should spot invalid arguments and produce helpful error messages. For example: one of the arguments of integrate_ode_bdf() is the maximum number of steps. This argument needs to be positive; if it isn't, the code does not run but returns an informative error message. We get this behavior with the following code:
if (max_num_steps <= 0)
invalid_argument("integrate_ode_bdf",
"max_num_steps,", max_num_steps,
"", ", must be greater than 0");
If I use
Exception thrown at line 169: integrate_ode_bdf: max_num_steps, -1, must be greater than 0
Checks for invalid arguments are helpful when a user misspecifies the value or structure of an argument (for example, a real has the wrong sign or a matrix does not have the right dimensions). There is however no need to control whether the user passes the right type of argument, say real versus integer. The stan parser controls this automatically.
Another error type we want to catch is invalid parameter values. This is not something the user controls directly, because the value of a parameter changes as the Markov Chain explores the parameter space. Our goal this time is not to abort the run, but to reject the Metropolis Proposal and make the chain "turn around". For this purpose, Stan uses "check" functions.
For example, integrate_ode_bdf requires the initial state to be finite:
stan::math::check_finite("integrate_ode_bdf", "initial state", y0);
If the initial state is infinite, the code produces the error message:
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception thrown at line 169: integrate_ode_bdf: initial state is inf, but must be finite!
There are many check functions. Here is a (far from complete) list:
| check_finite |
| check_positive |
| check_positive_finite |
| check_nonzero_size |
| check_ordered |
Contributors should look through existing examples to find more check functions.
To use a function from within the Stan language, it needs to be exposed inside the stanc3 compiler. If you'd like a function which is already in the math library exposed, you can open an issue there, or add it yourself by following the guide in the stanc developer documentation.
There are a mish-mash of testing frameworks that various developers have sprinkled throughout the unit/test directory of the stan-dev/math repo. This summarizes what is going on. It should make writing tests for functions easier.
For testing one and two scalar argument functions, there are two alternatives, depending on whether the function i vectorized or not.
For the simple unvectorized tests, you can see an example of a complete test for operator addition here:
test/unit/math/mix/core/operator_addition_test.cpp
You will see that it defines a structure
struct op_addition_f {
template <typename T1, typename T2>
static typename boost::math::tools::promote_args<T1, T2>::type
apply(const T1& x1, const T2& x2) {
return x1 + x2;
}
};
with a static tempate function apply(), which just passes through the result to operator+(). Autodiff versions will be brought in by argument-dependent lookup.
The test itself is then run with:
TEST(mathMixCore, opratorAddition) {
stan::math::test::test_common_args<op_addition_f, false>();
}
The first template parameter is the name of the structure defining the function, here op_addition_f. The second argument is true if the function is a comparison operator (they return integer values, not real values, so are tested slightly differently). This function then cycles through various typical arguments, positive, zero, negative, infinite, and not-a-number, making sure that the result of the basic function on double values matches and the derivatives match at all levels of autodiff.
The actual code for testing each level of autodiff is in the framework file:
test/unit/math/mix/mat/util/autodiff_tester.hpp
The tests cover all the autodiff cases.
- reverse:
var, - forward:
fvar<double>,fvar<fvar<double>> - mixed:
fvar<var>,fvar<fvar<var>>
Warning: The test framework assumes you already have tests for primitives, double and int.
Follow the example in test/unit/math/mix/mat/fun/acosh_test.cpp.
You'll see that there's a required static apply function, as before, that wraps up the acosh() function and has a using stan::math::acosh file to allow it to be found along with the std:: namespace version.
There is then an integer and templated apply_base function which just call the static function above. The reason int is broken out is that it uses the template argument of the apply function called to explicitly promote to double.
The rest of the static functiosn provide definitions of valid and invalid inputs of both double and int varieties.
Then there are four macro calls at the end of the file to test at each level. These get played out in test harnesses in each of the included files with the actual tests, such as
test/unit/math/rev/mat/vectorize/rev_scalar_unary_test.hpp
If you dive into that file, it's just more includes of files starting with expect_ (named following google test conventions) that instantiate the test macros and register them with a testing harness.
One of the exciting items on the horizon for Stan is incorporating more and more Gaussian process covariance functions, especially those that exploit structure for faster computations. At the same time, that structure will be cumbersome to propagate through the various computations needed to incorporate a Gaussian process in Stan, including determinant calculations and matrix divisions. To ensure that Gaussian processes in Stan can take advantage of as much intrinsic structure as possible without requiring a completely suite of specialized linear algebra we have decided that each specialized Gaussian process covariance function introduced in Stan must have three implementations.
Note that if the covariance matrix is likely to be ill-posed then it is probably best to implement not the covariance function in isolation but rather it's sum with a diagonal jitter, ideally given as a parameter that can be set by the user either as data or as a parameter.
Each Gaussian process implementation must have a function that returns a dense covariance matrix,
matrix gp_name_cov(real[] x, ..., data real jitter),
where ... refers to the hyperparameters specific to the Gaussian process.
This dense matrix will lose any structure inherent to the specific Gaussian process, but ensure that it can always be incorporated into composite Gaussian processes that combine different covariance functions.
Additionally, each implementation must have a function that returns a non-centered parameterization of a zero-mean Gaussian process, y = mu + L * z,
vector gp_name_ncp(vector mu, vector z, real[] x, ..., data real jitter)
If the covariance function is structured then that structure can be exploited in the C++ implementation of this function to realize the corresponding speed up.
Each implementation must also have a function that returns the log probability density function of a zero-mean multivariate normal with the Gaussian process's covariance matrix,
real gp_name_lpdf(vector y, vector mu, real[] x, ..., data real jitter)
from which we can implement a centered parameterization of the Gaussian process.
Again, if the covariance function is structured then that structure can be exploited in the C++ implementation of the log density function, in particular the calculation of the log determinant and precision quadratic form. If there is no structure to exploit then this will reduce to the multi_normal_lpdf function, which can be called directly to avoid code duplication.
Finally, each implementation must have a function that returns a realization of the Gaussian process,
real gp_name_rng(vector mu, real[] x, ..., data real jitter)
If you have a function and know its partial derivatives, there are several ways to code this in the Stan math library.
If your function is templated separately on all of its arguments and bottoms out only in functions built into the C++ standard library or into Stan, there's nothing to do other than add it to the Stan namespace. For example, if we want to code in a simple z-score calculation, we can do it very easily as follows, because the mean and sd function are built into Stan's math library:
#include <stan/math/rev/core.hpp>
namespace stan {
namespace math {
vector<T> z(const vector<T>& x) {
T mean = mean(x);
T sd = sd(x);
vector<T> result;
for (size_t i = 0; i < x.size(); ++i)
result[i] = (x[i] - mean) / sd;
return result;
}
}
}
This will even work for higher-order autodiff if you include the top-level header <stan/math.hpp>.
Suppose have a code to calculate a univariate function and its derivative:
namespace bar {
double foo(double x);
double d_foo(double x);
}
We can implement foo for Stan as follows, making sure to put it in the stan::math namespace so that argument-dependnet lookup (ADL) can work. We'll assume the two relevant functions are defined in my_foo.hpp
#include "my_foo.hpp"
#include <stan/math/rev/core.hpp>
namespace stan {
namespace math {
double foo(double x) {
return bar::foo(x);
}
var foo(const var& x) {
double a = x.val();
double fa = bar::foo(a);
double dfa_da = bar::d_foo(a);
return precomp_v_vari(fa, x.vi_, dfa_da);
}
}
}
There are similar functions precomp_vv_vari for two-argument functions and so on.
For most efficiency, each argument should independently allow var or double arguments (int arguments don't need gradients---those can just get carried along). So if you're writing a two-argument function of scalars, you want to do this:
namespace bar {
double foo(double x, double y);
double dfoo_dx(double x, double y);
double dfoo_dy(double x, double y);
}
This can be coded as follows
#include "my_foo.hpp"
#include <stan/math/rev/core.hpp>
namespace stan {
namespace math {
double foo(double x, double y) {
return bar::foo(x, y);
}
var foo(const var& x, double y) {
double a = x.val();
double fay = bar::foo(a, y);
double dfay_da = bar::foo_dx(a, y);
return return precomp_v_vari(fay, x.vi_, dfay_da);
}
var foo(double x, const var& y) {
double b = y.val();
double fxb = bar::foo(x, b);
double dfxb_db = bar::foo_dy(x, b);
return return precomp_v_vari(fxb, y.vi_, dfxb_db);
}
var foo(const var& x, const var& y) {
double a = x.val();
double b = y.val();
double fab = bar::foo(a, b);
double dfab_da = bar::foo_dx(a, b);
double dfab_db = bar::foo_dy(a, b);
return precomp_vv_vari(fab, x.vi_, y.vi_, dfab_da, dfab_db);
}
}
}
Same thing works for three scalars.
Now suppose the signatures you have give you a function and a gradient using standard vectors (you can also use Eigen vectors or matrices in a similar way):
namespace bar {
double foo(const vector<double>& x);
vector<double> grad_foo(const vector<double>& x);
}
Of course, it's often more efficient to compute these at the same time---if you can do that, replace the lines for fa and grad_fa witha more efficient call. Otherwise, the code follows the previous version:
#include "my_foo.hpp"
#include <stan/math/rev/core.hpp>
namespace stan {
namespace math {
vector<double> foo(const vector<double>& x) {
return bar::foo(x);
}
vector<var> foo(const vector<var>& x) {
vector<double> a = value_of(x);
double fa = bar::foo(a);
vector<double> grad_fa = bar::grad_foo(a);
return precomputed_gradients(fa, x, grad_fa);
}
}
}
The precomputed_gradients class can be used to deal with any form of inputs and outputs. All you need to do is pack all the var arguments into one vector and their matching gradients into another.
If you have a function with more than one output, you'll need the full Jacobian matrix. You create each output var the same way you create a univariate output, using precomputed_gradients. Then you just put them all together. This time, I'll use Eigen matrices assuming that's how you get your Jacobian:
namespace bar {
Eigen::VectorXd foo(const Eigen::VectorXd& x);
Eigen::MatrixXd foo_jacobian(const Eigen::VectorXd& x);
}
You can code this up the same way as before (with the same includes):
namespace stan {
namespace math {
Eigen::VectorXd foo(const Eigen::VectorXd& x) {
return bar::foo(x);
}
Eigen::Matrix<var, -1, 1> foo(const Eigen::Matrix<var,-1,1>& x,
std::ostream* pstream__) {
// extract parameter values from x
const var * x_data = x.data();
int x_size = x.size();
vector<var> x_std_var(x_data, x_data + x_size );
VectorXd a = value_of( x );
// evaluate f
VectorXd f_val = bar::foo(a);
// f_val_jacobian[i][j] is the partial derivative of f_i w.r.t. parameter j
vector<vector<double>> f_val_jacobian = bar::foo_jacobian(a);
int f_size = f_val_jacobian.size();
Eigen::Matrix<var, -1, 1> f_var_jacobian(f_size);
for (int i=0; i < f_size; i++) {
f_var_jacobian(i) = precomputed_gradients(f_val(i), x_std_var, f_val_jacobian[i]);
}
return f_var_jacobian;
}
}
}
We could obviously use a form of precomputed_gradients that takes in an entire Jacobian to remove the error-prone and non-memory-local loops (by default, matrices are stored column-major in Eigen).