Adding const quietly invalidates results

[alecjacobson]

This code works correctly

#include <autodiff/reverse/var.hpp>
#include <autodiff/reverse/var/eigen.hpp>

Eigen::MatrixXd matrix_gradient(
  const autodiff::var& f, 
  autodiff::MatrixXvar & x)
{
  autodiff::VectorXvar x_vec = autodiff::VectorXvar{x.reshaped()};
  Eigen::VectorXd dfdx_vec = gradient(f, x_vec);
  return dfdx_vec.reshaped(x.rows(), x.cols());
}

int main(int argc, char *argv[])
{
  // Autodiff requires variables to be put into a vector
  autodiff::MatrixXvar U(2,2);
  U << 1, 2, 3, 4;
  // Expression using U as a matrix
  autodiff::var f = U(0,0)*U(1,1) - U(0,1)*U(1,0);
  Eigen::MatrixXd dfdU = matrix_gradient(f, U);
  std::cout<<dfdU<<std::endl;
}

Producing:

 4 -3
-2  1

But if I change autodiff::MatrixXvar & x → const autodiff::MatrixXvar & x then I get no compilation error but the incorrect result at runtime:

0 0 
0 0

Is there a way to detect this as compilation error to avoid this gotcha?

(meanwhile, is there a better way for me to create a helper function to get gradients in the shape of my parameters?)