user2658323 user2658323 - 1 month ago 7
C++ Question

How to retrive differentiation results with Eigen::AutoDiffScalar

I am learning to use this library. Trying to differentitate a simple function,

y = x^2
, does not yield the expected results (
dy/dx = 2x = 16
when
x = 8
).

#include <eigen3/Eigen/Core>
#include <eigen3/unsupported/Eigen/AutoDiff>
#include <iostream>

int main(int argc, char *argv[])
{
Eigen::AutoDiffScalar<Eigen::Vector2d> x(8.0), y;

y = x*x;

std::cout << y.derivatives()[0];

return 0;
}

Answer

The scalar you have declared is literally just that – a scalar, so you are finding the derivative of a scalar (8*8), which is 0. To indicate that 8 is the value of the first variable, you need to set its first derivative to 1:

#include <eigen3/Eigen/Core>
#include <eigen3/unsupported/Eigen/AutoDiff>
#include <iostream>

int main(int argc, char *argv[])
{
  // Note different initialization
  Eigen::AutoDiffScalar<Eigen::Vector2d> x(8.0, Eigen::Vector2d(1,0)), y;

  y = x*x;

  std::cout << "x = " << x << "\n"
            << "y = " << y << "\n"
            << "y' = " << y.derivatives()[0] << "\n";

  return 0;
}

This outputs

x = 8
y = 64
y' = 16

I recommend naming the variable something other than x, because it can be easily confusing if you're expecting to take the derivative with respect to something that is usually called x as well. So, let's call it a instead.

  • If da/dx=0, then a is a constant. Then, obviously, d/dx a² = 0 as well.
  • if da/dx=1, then essentially a=x. Then, d/dx a² = d/dx x² = 2x.