svd_U.hpp

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#ifndef STAN_MATH_REV_FUN_SVD_U_HPP
#define STAN_MATH_REV_FUN_SVD_U_HPP
 
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/err/check_nonzero_size.hpp>
#include <stan/math/prim/fun/typedefs.hpp>
#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/rev/fun/value_of.hpp>
 
namespace stan {
namespace math {
 
template <typename EigMat, require_rev_matrix_t<EigMat>* = nullptr>
inline auto svd_U(const EigMat& m) {
  using ret_type = return_var_matrix_t<Eigen::MatrixXd, EigMat>;
  if (unlikely(m.size() == 0)) {
    return ret_type(Eigen::MatrixXd(0, 0));
  }
 
  const int M = std::min(m.rows(), m.cols());
  auto arena_m = to_arena(m);
 
  Eigen::JacobiSVD<Eigen::MatrixXd> svd(
      arena_m.val(), Eigen::ComputeThinU | Eigen::ComputeThinV);
 
  auto arena_D = to_arena(svd.singularValues());
 
  arena_t<Eigen::MatrixXd> arena_Fp(M, M);
 
  for (int i = 0; i < M; i++) {
    for (int j = 0; j < M; j++) {
      if (j == i) {
        arena_Fp(i, j) = 0.0;
      } else {
        arena_Fp(i, j)
            = 1.0 / (arena_D[j] - arena_D[i]) + 1.0 / (arena_D[i] + arena_D[j]);
      }
    }
  }
 
  arena_t<ret_type> arena_U = svd.matrixU();
  auto arena_V = to_arena(svd.matrixV());
 
  reverse_pass_callback([arena_m, arena_U, arena_D, arena_V,
                         arena_Fp]() mutable {
    Eigen::MatrixXd UUadjT = arena_U.val_op().transpose() * arena_U.adj_op();
    arena_m.adj()
        += .5 * arena_U.val_op()
               * (arena_Fp.array() * (UUadjT - UUadjT.transpose()).array())
                     .matrix()
               * arena_V.transpose()
           + (Eigen::MatrixXd::Identity(arena_m.rows(), arena_m.rows())
              - arena_U.val_op() * arena_U.val_op().transpose())
                 * arena_U.adj_op() * arena_D.asDiagonal().inverse()
                 * arena_V.transpose();
  });
 
  return ret_type(arena_U);
}
 
}  // namespace math
}  // namespace stan
 
#endif