How to `LuSolve` with Eigen Matrices with AD

[ShrutheeshIR]

I want to solve a linear systems equation AX = b where A is a Eigen::Matrix<AD<double>, Eigen::Dynamic, Eigen::Dynamic>, b and X are vectors Eigen::Matrix<AD<double>, Eigen::Dynamic, 1>.

I try to call the LuSolve function to solve for X as:

double logdet;
const int signed_det = LuSolve(nt, (size_t)1, A, b, X, logdet);

I know that we have to feed the A, b, X as FloatVectors, but I'm having some trouble converting to and from Eigen for CPPAd.

But I get two errors related to this:

deduced conflicting types for parameter 'const FloatVector' ('Eigen::Matrix<CppAD::AD<CppAD::cg<double>, -1, -1>' and 'ADVectorXs' {aka 'Eigen::Matrix<CppAD::AD<CppAD::cg<double>, -1, 1>'})

and when I force them both to be matrices (using hacky code)

convert 'Eigen::DenseCoeffsBase<Eigen::Matrix<CppAD::AD<CppAD::cg<double> >, -1, 1>, 1>::Scalar' {aka 'CppAD::AD<CppAD::cg<double> >'} to 'float'

I'm having some trouble understanding the conversions. Any help to resolve this would be appreciated, thank you

[bradbell]

The FloatVector in LuSolve can be and Eigen vector; see
https://cppad.readthedocs.io/latest/LuSolve.html#floatvector

I suggest you start by changing the example
https://cppad.readthedocs.io/latest/lu_solve.cpp.html#lu-solve-cpp-name

to use an eigen_vector as its FloatVector; see
https://cppad.readthedocs.io/latest/cppad_eigen.hpp.html#cppad-eigen-hpp-eigen-vector

It should be simple to convert an eigen_vector to and from an Eignen::Matrix