// Program to demonstrate tangent and adjoint differentiation for a simple function f(x1,x2) = 2.x1^2 + 3.x1
#include <vector>
#include <iostream>
using namespace std;
// Method to Display the Target Function and Expected Results
void showFunction(const vector<double> & x)
{
cout << "Function" << endl;
cout << "f(x1, x2) = 2.x1^2 + 3.x1" << endl;
cout << "df/dx1 = 4.x1" << endl;
cout << "df/dx2 = 3" << endl;
cout << endl;
if (x.size()!=2) return;
double x1 = x[0];
double x2 = x[1];
cout << "Expected Results" << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
cout << "f(x1,x2) = " << 2*x1*x1 + 3*x2 << endl;
cout << "df/dx1 = " << 4*x1 << endl;
cout << "df/dx2 = " << 3 << endl;
cout << endl;
}
// Forward 'Tangent' Method
// Risk variables are denoted 'dot' with '_d' suffix
// [IN] vector of input variables x (x1, x2)
// [IN] vector of risk activation variables x_d (x1_d, x2_d)
void tangent(const vector<double> & x, const vector<double> & x_d)
{
// Target Function: f(x1,x2) = 2.x1^2 + 3.x2
// Inputs: x1 and x2
if (x.size()!=2) return;
double x1 = x[0];
double x2 = x[1];
// Risk Activation Inputs: x1_d and x2_d
if (x_d.size()!=2) return;
double x1_d = x_d[0]; // Init Tangent Mode
double x2_d = x_d[1]; // Init Tangent Mode
// Forward Calculation
double a = x1 * x1; // 1. a = x1^2
double a_d = 2 * x1 * x1_d;
double b = 2 * a; // 2. b = 2.x1^2
double b_d = 2 * a_d;
double c = x2; // 3. c = x2
double c_d = x2_d;
double d = 3 * c; // 4. d = 3.x2
double d_d = 3*c_d;
double f = b + d; // 5. f = 2.x1^2 + 3.x2
double f_d = b_d + d_d;
// Tangent Results
// Tangent Mode calculates one input sensitivity at a time (similar to numerical bumping)
if(x1_d==1.0 && x2_d==0.0)
{
cout << "Tangent Results for x1_d" << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
cout << "f(x1,x2) = " << f << endl;
cout << "df/dx1 = " << f_d << endl;
cout << endl;
}
// Tangent Mode calculates one input sensitivity at a time (similar to numerical bumping)
if(x1_d==0.0 && x2_d==1.0)
{
cout << "Tangent Results for x2_d" << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
cout << "f(x1,x2) = " << f << endl;
cout << "df/dx2 = " << f_d << endl;
cout << endl;
}
}
// Backward 'Adjoint' Method
// Risk variables are denoted 'bar' with '_b' suffix
// [IN] vector of input variables x (x1, x2)
// [IN] vector of risk activation variables f_b (f1_b, f2_b)
void adjoint(const vector<double> & x, const vector<double> & f_b)
{
// Target Function: f(x1,x2) = 2.x1^2 + 3.x2
// Inputs: x1 and x2
if (x.size()!=2) return;
double x1 = x[0];
double x2 = x[1];
// Risk Activation Inputs: f1_b and f2_b
if (f_b.size()!=2) return;
double f1_b = f_b[0]; // Init Adjoint Mode
double f2_b = f_b[1]; // Init Adjoint Mode
// Forward Sweep
double a = x1 * x1; // 1. a = x1^2
double b = 2 * a; // 2. b = 2.x1^2
double c = x2; // 3. c = x2
double d = 3 * c; // 4. d = 3.x2
double f = b + d; // 5. f = 2.x1^2 + 3.x2
// Back Propogation
double b_b = f1_b; // 5.
double d_b = f2_b; // 5.
double c_b = 3 * d_b; // 4.
double x2_b = c_b; // 3.
double a_b = 2 * b_b; // 2.
double x1_b = 2 * x1 * a_b; // 1.
// Adjoint Results
cout << "Adjoint Results" << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
cout << "f(x1,x2) = " << f << endl;
cout << "df/dx1 = " << x1_b << endl;
cout << "df/dx2 = " << x2_b << endl;
cout << endl;
}
int main()
{
vector<double> x = {2, 2};
showFunction(x);
// Note: Tangent Mode calculates one input sensitivity at a time (similar to numerical bumping)
// Tangent mode for x1_d
vector<double> x1_d = {1,0};
tangent(x, x1_d);
// Tangent mode for x2_d
vector<double> x2_d = {0,1};
tangent(x, x2_d);
// Adjoint mode
vector<double> f_b = {1,1};
adjoint(x, f_b);
return 0;
}
