user2658323 - 3 months ago 15

C++ Question

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

`y = x^2`

`dy/dx = 2x = 16`

`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.