matrix_exp_pade.hpp

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#ifndef STAN_MATH_PRIM_FUN_MATRIX_EXP_PADE_HPP
#define STAN_MATH_PRIM_FUN_MATRIX_EXP_PADE_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/MatrixExponential.h>
 
namespace stan {
namespace math {
 
template <typename EigMat, require_eigen_t<EigMat>* = nullptr>
Eigen::Matrix<value_type_t<EigMat>, EigMat::RowsAtCompileTime,
              EigMat::ColsAtCompileTime>
matrix_exp_pade(const EigMat& arg) {
  using MatrixType
      = Eigen::Matrix<value_type_t<EigMat>, EigMat::RowsAtCompileTime,
                      EigMat::ColsAtCompileTime>;
  check_square("matrix_exp_pade", "arg", arg);
  if (arg.size() == 0) {
    return {};
  }
 
  MatrixType U, V;
  int squarings;
 
  Eigen::matrix_exp_computeUV<MatrixType>::run(arg, U, V, squarings, arg(0, 0));
  // Pade approximant is
  // (U+V) / (-U+V)
  MatrixType numer = U + V;
  MatrixType denom = -U + V;
  MatrixType pade_approximation = denom.partialPivLu().solve(numer);
  for (int i = 0; i < squarings; ++i) {
    pade_approximation *= pade_approximation;  // undo scaling by
  }
  // repeated squaring
  return pade_approximation;
}
 
}  // namespace math
}  // namespace stan
 
#endif