Autodiff

Reverse automatic differentiation tool in C++. Originally by https://github.com/OmarAflak/autodiff

Examples

Examples you may find helpful.

Install & Use

Then in a new main.cpp file :

#include <iostream>
#include <autodiff/node.h>

int main(int argc, char const *argv[]) {
    Node x=2, y=3;
    Node f = x*y + sin(x);

    std::cout << "f(x,y) = x*y + sin(x)" << std::endl;
    std::cout << "f(" << x << "," << y << ") = " << f << std::endl;
    std::cout << "∂f/∂x = " << f.gradient(x) << std::endl;
    std::cout << "∂f/∂y = " << f.gradient(y) << std::endl;
    return 0;
}

Compile it :

g++ main.cpp -o main -lautodiff

Clear the computational graph

You should clear the computational graph whenever a new calculation happens.

Graph::getInstance()->new_recording();

Operations Supported

Trigonometric

sin(const Node& x)
cos(const Node& x)
tan(const Node& x)
asin(const Node& x)
acos(const Node& x)
atan(const Node& x)

Hyperbolic

sinh(const Node& x)
cosh(const Node& x)
tanh(const Node& x)

Exponential and logarithmic

log(const Node& x, const Node& base)
log10(const Node& x)
ln(const Node& x)
exp(const Node& x)

Power

pow(const Node& x, const Node& p)
sqrt(const Node& x)

Others

abs(const Node& x)
min(const Node& l, const Node& r)
max(const Node& l, const Node& r)

Define your own operations

If your calculations involve functions I didn't mention above, then you can write your own operations and provide their derivative.

Thus, neither of the examples below needs to be implemented this way, they use operations already defined (*,+,exp). There are just for the sake of example.

Monadic operations

$f : R \mapsto R$

Node multBy5(const Node& node){
    return Node::monadic_operation(node, [](const double& x){
        return MonadicOperationResult(5*x, 5); // (value=5*x, d(multBy5)/dx=5)
    });
}

Dyadic operations

$f : R^2 \mapsto R$

Node multiply(const Node& left, const Node& right){
    return Node::dyadic_operation(left, right, [](const double& l, const double& r){
        return DyadicOperationResult(l*r, r, l); // (value=l*r, ∂(multiply)/∂l=r, ∂(multiply)/∂r=l)
    });
}

Polyadic operations

$f : R^n \mapsto R$

Node someRandomFunction(const std::vector<Node>& nodes){
    return Node::polyadic_operation(nodes, [](const std::vector<double>& x){
        double result=0;
        for(const double& d : x){
            result += exp(d);
        }

        std::vector<double> gradients(nodes.size());
        for(size_t i=0 ; i<gradients.size() ; i++){
            gradients[i] = exp(x[i]);
        }

        return PolyadicOperationResult(result, gradients);
    });
}

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