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CppADCodeGen with an easy Eigen interface and Python bindings.

This project has been tested on Ubuntu 16.04, 18.04, and 20.04. It may work on other Linux systems as well.


I want to be able to prototype code in Python while making use of fast, compiled auto-differentiated code. Autodiff tools in Python, such as JAX, typically just-in-time (JIT) compile code rather than ahead-of-time compile it. I would like to avoid waiting for a JIT compile every time I run my script if the functions being differentiated haven't actually changed.

The goal of CppADCodeGenEigenPy is to take the auto-diff and compilation capabilities of CppADCodeGen, wrap it up in an easy-to-use C++ interface, and provide built-in Python bindings to the compiled auto-differentiated model. The upshot is that the functions being differentiated need to be written in C++, but they need only be compiled once and they run very fast.

This project was heavily inspired by larger frameworks that incorporate auto-diff functionality via CppADCodeGen for convenience; in particular, the automatic_differentiation module from OCS2 was a big influence.

An alterntive approach is something like PyCppAd. Instead of just binding the resulting auto-differentiated model like CppADCodeGenEigenPy, PyCppAd actually binds the underlying CppADCodeGen types to enable the auto-diff + code-gen pipeline to be implemented directly from Python.

How it works

This project provides a simple interface to CppADCodeGen to define the required function in C++, which is then compiled (along with its automatically-computed derivatives) into a dynamic library. This dynamic library can then be easily used from C++ or imported into Python via bindings based on pybind11.

CppADCodeGenEigenPy is built around two classes. The first is the ADModel, which defines the function to be auto-differentiated. It is compiled into a dynamic library which can then be loaded by the CompiledModel class. The CompiledModel can evaluate the function itself as well as its first and second derivatives.


First ensure you have the required dependencies:

Clone CppADCodeGenEigenPy:

git clone
cd CppADCodeGenEigenPy

The main C++ part of CppADCodeGenEigenPy uses cmake. The library itself is header-only, so you need only do:

mkdir build
cmake -S . -B build
cmake --install build  # may require sudo

To build and install the Python bindings, pip is used. Python 3 is strongly preferred. Note that pip version 10+ is required in order to parse pyproject.toml. Run

python -m pip install .


To build the tests, run

cmake --build build

To run the C++ tests:

cd build

To run the Python tests:

python -m pytest

Note that the tests assume that the name of the build directory is build in order to find the required dynamic libraries. If this is not the case, you can pass --builddir NAME to pytest to change it.


All examples are found in the examples directory. These include the simple weighted sum-of-squares example described below, an example for differentiating the forward dynamics of a 3D rigid body, and an example of inverse dynamics using Pinocchio.

Simple weighted sum-of-squares

A minimal example of the C++ code to define and generate an auto-diff model would look something like:

#include <CppADCodeGenEigenPy/ADModel.h>
#include <Eigen/Eigen>

namespace ad = CppADCodeGenEigenPy;

// Our custom model extends the ad::ADModel class
template <typename Scalar>
struct ExampleModel : public ad::ADModel<Scalar> {
    using typename ad::ADModel<Scalar>::ADVector;

    // Generate the input used when differentiating the function
    ADVector input() const override { return ADVector::Ones(3); }

    // Generate parameters used when differentiating the function
    // This can be skipped if the function takes no parameters
    ADVector parameters() const override { return ADVector::Ones(3); }

    // Implement a weighted sum-of-squares function.
    ADVector function(const ADVector& input,
                      const ADVector& parameters) const override {
        ADVector output(1);
        for (int i = 0; i < 3; ++i) {
            output(0) += 0.5 * parameters(i) * input(i) * input(i);
        return output;

int main() {
    // Compile model named ExampleModel and save in the current directory; the
    // model is saved as a shared object file named
    ExampleModel<double>().compile("ExampleModel", ".",

Compile the code and generate the model:

g++ -std=c++11 -I/usr/local/include/eigen3 model.cpp -ldl -o make_model

If you get an error about not being able to find an Eigen header, you may have to change the path to the Eigen include directory.

This code can then be called from Python using:

import numpy as np
from CppADCodeGenEigenPy import CompiledModel

# note that the .so file extension not included on the second argument
model = CompiledModel("ExampleModel", "libExampleModel")

inputs = np.array([1, 2, 3])
params = np.ones(3)

# compute model output and first derivative
output = model.evaluate(inputs, params)
jacobian = model.jacobian(inputs, params)

print(f"output = {output}")
print(f"jacobian = {jacobian}")

This C++ and Python code can be found here.




CppADCodeGen with an easy Eigen interface and Python bindings.







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