added example of 2nd derivative with vector version that does not work... Also, added operator+-*/ for scalar op Dual and scalar op dualvector

AutomaticDifferentiation.hpp

@@ -119,6 +119,23 @@ class Dual
 		Scalar b;	/// Infinitesimal part
 };
 
+template<typename A, typename B, int N>
+Dual<B, N> operator+(A const& v, Dual<B, N> const& x) {
+	return (Dual<B, N>(v) + x);
+}
+template<typename A, typename B, int N>
+Dual<B, N> operator-(A const& v, Dual<B, N> const& x) {
+	return (Dual<B, N>(v) - x);
+}
+template<typename A, typename B, int N>
+Dual<B, N> operator*(A const& v, Dual<B, N> const& x) {
+	return (Dual<B, N>(v) * x);
+}
+template<typename A, typename B, int N>
+Dual<B, N> operator/(A const& v, Dual<B, N> const& x) {
+	return (Dual<B, N>(v) / x);
+}
+
 // Basic mathematical functions for Scalar numbers
 
 // Trigonometric functions

AutomaticDifferentiationVector.hpp

@@ -42,8 +42,13 @@ class DualVector
 			b = VectorT(_b, N);
 		}
 		
+		DualVector const& operator=(Scalar const& _a)
+		{
+			*this = DualVector(_a);
+		}
+
 		/// Use this function to set what variable is to be derived : x + DualVector::d(i)
-		static DualVector d(int i = 0)
+		static DualVector D(int i = 0)
 		{
 			assert(i >= 0);
 			assert(i < N);
@@ -62,6 +67,14 @@ class DualVector
 			return *this;
 		}
 		
+		/// Returns the derivative value at index i
+		Scalar const& d(int i) const
+		{
+			assert(i >= 0);
+			assert(i < N);
+			return b[i];
+		}
+
 		DualVector & operator+=(const DualVector & x)
 		{
 			a += x.a;
@@ -127,6 +140,23 @@ class DualVector
 		VectorT b;	/// Infinitesimal parts
 };
 
+template<typename A, typename B, int N>
+DualVector<B, N> operator+(A const& v, DualVector<B, N> const& x) {
+	return (DualVector<B, N>(v) + x);
+}
+template<typename A, typename B, int N>
+DualVector<B, N> operator-(A const& v, DualVector<B, N> const& x) {
+	return (DualVector<B, N>(v) - x);
+}
+template<typename A, typename B, int N>
+DualVector<B, N> operator*(A const& v, DualVector<B, N> const& x) {
+	return (DualVector<B, N>(v) * x);
+}
+template<typename A, typename B, int N>
+DualVector<B, N> operator/(A const& v, DualVector<B, N> const& x) {
+	return (DualVector<B, N>(v) / x);
+}
+
 // Basic mathematical functions for Scalar numbers
 
 // Trigonometric functions

examples/firstAndSecondDerivative.cpp

@@ -0,0 +1,66 @@
+#include "../AutomaticDifferentiationVector.hpp"
+
+#include <iostream>
+#include <iomanip>
+using std::cout;
+using std::endl;
+using std::setw;
+#define PRINT_VAR(x) std::cout << #x << "\t= " << std::setprecision(16) << (x) << std::endl
+#define PRINT_DUAL(x) std::cout << #x << "\t= " << std::fixed << std::setprecision(4) << std::setw(10) << (x).a << ", " << std::setw(10) << (x).b << std::endl
+
+template<typename T>
+T f(const T & x)
+{
+    return 1 + x + x*x + 1/x + log(x);
+}
+
+template<typename T>
+T df(const T & x)
+{
+	return 2*x + 1 + 1.0/x - 1/pow(x, 2);
+}
+
+template<typename T>
+T ddf(const T & x)
+{
+	return 2 - 1/pow(x, 2) + 2/pow(x, 3);
+}
+
+int main()
+{
+	double xdbl = 1.5;
+	
+	{
+		cout << "Analytical\n";
+		cout << "f(x)      = " << f(xdbl) << endl;
+		cout << "df(x)/dt  = " << df(xdbl) << endl;
+		cout << "d²f(x)/dt = " << ddf(xdbl) << endl;
+	}
+	
+	// 1st derivative forward
+	{
+		using Fd = DualVector<double,1>;
+		Fd x = xdbl;
+		x.diff(0);
+		Fd y = f(x);
+		cout << "\nForward\n";
+		cout << "f(x)      = " << y.a << endl;
+		cout << "df(x)/dt  = " << y.d(0) << endl;
+	}
+	
+	// 2nd derivative forward
+	/*
+	{
+		using Fdd = DualVector<DualVector<double,2>,2>;
+		Fdd x(xdbl);
+		x.diff(0);
+		x.a.diff(1);
+		Fdd y = f(x);
+		cout << "\nForward 2nd der\n";
+		cout << "f(x)      = " << y.a.a << endl;
+		cout << "df(x)/dt  = " << y.d(0).a << endl;
+		cout << "d²f(x)/dt = " << y.d(0).d(1) << endl;
+	}//*/
+
+	return 0;
+}