add autodiff

Automatic-Differentiation/.gitignore

-obj/
-bin/
-main
-.gmake

Automatic-Differentiation/Makefile

-CXX = g++
-BIN = bin
-LIB = lib
-OBJS_MAIN = root/obj/dual.o root/obj/gradient.o root/obj/main.o
-
-all : main
-
-main : $(BIN)
-	$(MAKE) -C root obj obj/dual.o obj/gradient.o obj/main.o
-	$(CXX) -o $(BIN)/main $(OBJS_MAIN) $(LIBS)
-
-$(BIN) :
-	if [ ! -d $(BIN) ]; then mkdir $(BIN); fi
-
-$(LIB) :
-	if [ ! -d $(LIB) ]; then mkdir $(LIB); fi
-
-clean :
-	$(MAKE) -C root clean
-	if [ -d $(BIN) ]; then rm $(BIN) -r; fi
-
-install : $(LIB)
-	ar rcs $(LIB)/libgradient.a root/obj/dual.o root/obj/gradient.o
-	sudo mv $(LIB)/libgradient.a /usr/local/lib/mylibs
-	sudo ln -sf /usr/local/lib/mylibs/libgradient.a /usr/local/lib/libgradient.a
-	sudo cp root/include/gradient.h /usr/local/include/mylibs
-
-.PHONY : all
-.PHONY : install
-.PHONY : main
-.PHONY : clean

Automatic-Differentiation/README.md

-# Automatic Differentiation
-
-Very simple automatic differentiation tool, implemented using dual numbers and operator overloading.
-
-This code is part of my article on **Medium** : **[Automatic Differentiation](https://medium.com/@omaraflak/automatic-differentiation-4d26d03b7508)**.
-
-# Example
-
-```c++
-// Dual(value, derivative=0)
-Dual x(5, 1); // derivative=1 means we are going to derive with respect to this variable.
-Dual y(6);
-Dual f = pow(x,2)*y; // the derivative is calculated when the function is computed.
-std::cout << f.getDerivative() << std::endl; // get the derivative of y*x^2 with respect to x, evaluated at (x=5,y=6).
-```

Automatic-Differentiation/root/Makefile

-CXX = g++
-ODIR = obj
-CXXFLAGS = -std=c++14
-OBJS = $(ODIR)/gradient.o $(ODIR)/dual.o $(ODIR)/main.o 
-
-all : $(ODIR) $(OBJS) 
-
-$(ODIR)/gradient.o : src/gradient.cpp include/gradient.h 
-	$(CXX) -c $< -o $@ $(CXXFLAGS)
-
-$(ODIR)/dual.o : src/dual.cpp include/dual.h 
-	$(CXX) -c $< -o $@ $(CXXFLAGS)
-
-$(ODIR)/main.o : src/main.cpp include/dual.h include/gradient.h 
-	$(CXX) -c $< -o $@ $(CXXFLAGS)
-
-$(ODIR) : 
-	if [ ! -d $(ODIR) ]; then mkdir $(ODIR); fi
-
-clean : 
-	if [ -d $(ODIR) ]; then rm $(ODIR) -r; fi
-
-.PHONY : all
-.PHONY : clean
-

Automatic-Differentiation/root/include/dual.h

-#ifndef DUAL
-#define DUAL
-
-#include <iostream>
-#include <cmath>
-
-class Dual {
-    private:
-        double val;
-        double der;
-
-    public:
-        Dual();
-        Dual(double val);
-        Dual(double val, double der);
-
-        void setValue(double value);
-        void setDerivative(double derivative);
-
-        double getValue() const;
-        double getDerivative() const;
-
-        // operators
-        friend Dual operator+(const Dual& u, const Dual& v);
-        friend Dual operator-(const Dual& u, const Dual& v);
-        friend Dual operator*(const Dual& u, const Dual& v);
-        friend Dual operator/(const Dual& u, const Dual& v);
-
-        Dual operator+=(const Dual& u);
-        Dual operator-=(const Dual& u);
-        Dual operator*=(const Dual& u);
-        Dual operator/=(const Dual& u);
-
-        friend std::ostream& operator<<(std::ostream& os, const Dual& a);
-
-        // maths
-        friend Dual sin(Dual d);
-        friend Dual cos(Dual d);
-        friend Dual exp(Dual d);
-        friend Dual log(Dual d);
-        friend Dual abs(Dual d);
-        friend Dual pow(Dual d, double p);
-};
-
-#endif

Automatic-Differentiation/root/include/gradient.h

-#ifndef GRADIENT
-#define GRADIENT
-
-#include "dual.h"
-#include <vector>
-
-namespace dual{
-    namespace{
-        typedef std::vector<Dual> Vector;
-        typedef std::vector<Vector> Matrix;
-    }
-
-    void resetDerivatives(Vector& input);
-    Vector gradient(Dual (*f)(Vector&), Vector& input);
-    Matrix jacobian(Vector (*f)(Vector&), Vector& input);
-}
-
-#endif

Automatic-Differentiation/root/src/dual.cpp

-#include "../include/dual.h"
-
-Dual::Dual(){
-    this->val = 0;
-    this->der = 0;
-}
-
-Dual::Dual(double val){
-    this->val = val;
-    this->der = 0;
-}
-
-Dual::Dual(double val, double der){
-    this->val = val;
-    this->der = der;
-}
-
-void Dual::setValue(double value){
-    this->val = value;
-}
-
-void Dual::setDerivative(double derivative){
-    this->der = derivative;
-}
-
-double Dual::getValue() const{
-    return val;
-}
-
-double Dual::getDerivative() const{
-    return der;
-}
-
-// operators
-Dual operator+(const Dual& u, const Dual& v){
-    return Dual(u.val+v.val, u.der+v.der);
-}
-
-Dual operator-(const Dual& u, const Dual& v){
-    return Dual(u.val-v.val, u.der-v.der);
-}
-
-Dual operator*(const Dual& u, const Dual& v){
-    return Dual(u.val*v.val, u.der*v.val+u.val*v.der);
-}
-
-Dual operator/(const Dual& u, const Dual& v){
-    return Dual(u.val/v.val, (u.der*v.val-u.val*v.der)/(v.val*v.val));
-}
-
-Dual Dual::operator+=(const Dual& u){
-    *this = *this+u;
-    return *this;
-}
-
-Dual Dual::operator-=(const Dual& u){
-    *this = *this-u;
-    return *this;
-}
-
-Dual Dual::operator*=(const Dual& u){
-    *this = *this*u;
-    return *this;
-}
-
-Dual Dual::operator/=(const Dual& u){
-    *this = *this/u;
-    return *this;
-}
-
-std::ostream& operator<<(std::ostream& os, const Dual& a){
-    os << a.val;
-    return os;
-}
-
-// maths
-Dual sin(Dual d){
-    return Dual(::sin(d.val), d.der*::cos(d.val));
-}
-
-Dual cos(Dual d){
-    return Dual(::cos(d.val), -d.der*::sin(d.val));
-}
-
-Dual exp(Dual d){
-    return Dual(::exp(d.val), d.der*::exp(d.val));
-}
-
-Dual log(Dual d){
-    return Dual(::log(d.val), d.der/d.val);
-}
-
-Dual abs(Dual d){
-    int sign = d.val==0 ? 0 : d.val/::abs(d.val);
-    return Dual(::abs(d.val), d.der*sign);
-}
-
-Dual pow(Dual d, double p){
-    return Dual(::pow(d.val, p), p*d.der*::pow(d.val, p-1));
-}

Automatic-Differentiation/root/src/gradient.cpp

-#include "../include/gradient.h"
-
-void dual::resetDerivatives(dual::Vector& input){
-    for(auto& e : input){
-        e.setDerivative(0);
-    }
-}
-
-dual::Vector dual::gradient(Dual (*f)(dual::Vector&), dual::Vector& input){
-    resetDerivatives(input);
-    dual::Vector grad(input.size());
-    for(size_t i=0 ; i<grad.size() ; i++){
-        input[i].setDerivative(1);
-        grad[i] = f(input).getDerivative();
-        input[i].setDerivative(0);
-    }
-    return grad;
-}
-
-dual::Matrix dual::jacobian(dual::Vector (*f)(dual::Vector&), dual::Vector& input){
-    resetDerivatives(input);
-    dual::Matrix jac(f(input).size(), dual::Vector(input.size()));
-    for(size_t i=0 ; i<jac.size() ; i++){
-        for(size_t j=0 ; j<jac[i].size() ; j++){
-            input[j].setDerivative(1);
-            jac[i][j] = f(input)[i].getDerivative();
-            input[j].setDerivative(0);
-        }
-    }
-    return jac;
-}

Automatic-Differentiation/root/src/main.cpp

-#include <iostream>
-#include "../include/dual.h"
-#include "../include/gradient.h"
-
-typedef std::vector<Dual> Vector;
-
-std::ostream& operator<<(std::ostream& os, const Vector& v){
-    os << "[";
-    for(size_t i=0 ; i<v.size() ; i++){
-        os << v[i] << (i<v.size()-1?", ":"");
-    }
-    os << "]";
-    return os;
-}
-
-Dual function(Vector& x){
-    return x[0]*x[0]+x[1]*x[1]; // f(x1,x2) = x1^2 + x2^2
-}
-
-int main() {
-    
-    Vector x = {50, 70}; // random default values
-
-    // hyperparameters
-    int epochs = 30;
-    float learningRate = 0.3;
-
-    // gradient descent
-    for(size_t i=0 ; i<epochs ; i++){
-        Vector gradient = dual::gradient(function, x);
-        for(size_t j=0 ; j<x.size() ; j++){
-            x[j] -= learningRate*gradient[j];
-        }
-    }
-
-    // check new values
-    std::cout << "x = " << x << std::endl;
-    std::cout << "f(x) = " << function(x) << std::endl;
-    
-    return 0;
-}