trace_inv_quad_form_ldlt.hpp

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#ifndef STAN_MATH_REV_FUN_TRACE_INV_QUAD_FORM_LDLT_HPP
#define STAN_MATH_REV_FUN_TRACE_INV_QUAD_FORM_LDLT_HPP
 
#include <stan/math/rev/meta.hpp>
#include <stan/math/rev/core.hpp>
#include <stan/math/rev/fun/LDLT_factor.hpp>
#include <stan/math/rev/core/typedefs.hpp>
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/typedefs.hpp>
#include <type_traits>
 
namespace stan {
namespace math {
 
template <typename T1, typename T2, require_all_matrix_t<T1, T2>* = nullptr,
          require_any_st_var<T1, T2>* = nullptr>
inline var trace_inv_quad_form_ldlt(LDLT_factor<T1>& A, const T2& B) {
  check_multiplicable("trace_quad_form", "A", A.matrix(), "B", B);
 
  if (A.matrix().size() == 0)
    return 0.0;
 
  if (!is_constant<T1>::value && !is_constant<T2>::value) {
    arena_t<promote_scalar_t<var, T1>> arena_A = A.matrix();
    arena_t<promote_scalar_t<var, T2>> arena_B = B;
    auto AsolveB = to_arena(A.ldlt().solve(arena_B.val()));
 
    var res = (arena_B.val_op().transpose() * AsolveB).trace();
 
    reverse_pass_callback([arena_A, AsolveB, arena_B, res]() mutable {
      arena_A.adj() += -res.adj() * AsolveB * AsolveB.transpose();
      arena_B.adj() += 2 * res.adj() * AsolveB;
    });
 
    return res;
  } else if (!is_constant<T1>::value) {
    arena_t<promote_scalar_t<var, T1>> arena_A = A.matrix();
    const auto& B_ref = to_ref(B);
 
    auto AsolveB = to_arena(A.ldlt().solve(value_of(B_ref)));
 
    var res = (value_of(B_ref).transpose() * AsolveB).trace();
 
    reverse_pass_callback([arena_A, AsolveB, res]() mutable {
      arena_A.adj() += -res.adj() * AsolveB * AsolveB.transpose();
    });
 
    return res;
  } else {
    arena_t<promote_scalar_t<var, T2>> arena_B = B;
    auto AsolveB = to_arena(A.ldlt().solve(arena_B.val()));
 
    var res = (arena_B.val_op().transpose() * AsolveB).trace();
 
    reverse_pass_callback([AsolveB, arena_B, res]() mutable {
      arena_B.adj() += 2 * res.adj() * AsolveB;
    });
 
    return res;
  }
}
 
}  // namespace math
}  // namespace stan
#endif