kl_div.hpp

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/*
 * Copyright © 2025-2026 Akreon LLC
 * SPDX-License-Identifier: Apache-2.0
 */
 
#pragma once
 
#include "akreon/linalg/assert.hpp"
#include "akreon/convex/canonical_form_builder.hpp"
#include "akreon/convex/convex_traits.hpp"
 
namespace convex {
 
template <linalg::RnSpace Space>
using KLDivDom = ConvexDomain<Space, VarType::POS>;
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using KLDivCodom = ConvexDomain<Space, VarType::NONNEG>;
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using KLDivConcaveCodom = ConvexDomain<Space, VarType::NEG>;
 
template <linalg::RnSpace Dom, linalg::RnSpace Codom>
using KLDivMeta =
    ConvexAtomMeta<KLDivDom<Dom>, KLDivCodom<Codom>, CurvatureType::CONVEX>;
 
template <linalg::RnSpace Dom, linalg::RnSpace Codom>
using KLDivConcaveMeta = ConvexAtomMeta<KLDivDom<Dom>, KLDivConcaveCodom<Codom>,
                                        CurvatureType::CONCAVE>;
 
template <typename Meta, typename Child>
struct KLDivergence : Atom<Meta, KLDivergence<Meta, Child>, Child> {
  using ConvexBase = Atom<Meta, KLDivergence<Meta, Child>, Child>;
  using ConvexBase::N;
  using typename ConvexBase::PointT;
  using typename ConvexBase::T;
 
  static constexpr CurvatureType Tag = meta_curv_v<Meta>;
 
  constexpr explicit KLDivergence(const PointT& p_in, const Child& child_in)
      : ConvexBase(child_in), p(p_in),
        lift_map(affine::make_map_id<LiftedVarMat<T>>()) {
    for (const auto& x : p) {
      AK_ASSERT(x > T(0) &&
                "KLDivergence expects each fixed p entry to satisfy x > 0");
      (void)x;
    }
  }
 
  constexpr explicit KLDivergence(
      const PointT& p_in, const Child& child_in,
      const affine::AffineMap<LiftedVarMat<T>>& map_in)
      : ConvexBase(child_in), p(p_in), lift_map(map_in) {
    for (const auto& x : p) {
      AK_ASSERT(x > T(0) &&
                "KLDivergence expects each fixed p entry to satisfy x > 0");
      (void)x;
    }
  }
 
  constexpr MonotonicityType monotonicity() const {
    return MonotonicityType::UNKNOWN;
  }
 
  constexpr T operator()(const PointT& q) const { return eval(q); }
 
  constexpr T eval(const PointT& q) const {
    T res(0);
    for (std::size_t i = 0; i < N; ++i) {
      AK_ASSERT(p(i) >= T(0) && q(i) > T(0) && "Invalid domain for kl div");
      res += p(i) * linalg::constexpr_ln(p(i) / q(i)).value();
    }
 
    if constexpr (Tag == CurvatureType::CONVEX) return res;
    else return T(-1) * res;
  }
 
  template <T Scalar>
  constexpr auto mul() const {
    if constexpr (Scalar < T(0)) {
      const auto alpha = T(-1) * Scalar;
      affine::AffineMap<LiftedVarMat<T>> new_map(alpha * lift_map.linear_part(),
                                                 lift_map.translation());
 
      using Dom = dom_space_t<meta_dom_t<Meta>>;
      using Codom = dom_space_t<meta_codom_t<Meta>>;
      if constexpr (Tag == CurvatureType::CONCAVE) {
        return KLDivergence<KLDivMeta<Dom, Codom>, Child>(
            p, std::get<0>(this->children), new_map);
      } else {
        return KLDivergence<KLDivConcaveMeta<Dom, Codom>, Child>(
            p, std::get<0>(this->children), new_map);
      }
    } else {
      affine::AffineMap<LiftedVarMat<T>> new_map(
          Scalar * lift_map.linear_part(), lift_map.translation());
      return KLDivergence<Meta, Child>(p, std::get<0>(this->children), new_map);
    }
  }
 
  constexpr auto add(T beta) const {
    LiftedVarBias<T> bias{beta + lift_map.translation()(0)};
    affine::AffineMap<LiftedVarMat<T>> new_map(lift_map.linear_part(), bias);
    return KLDivergence<Meta, Child>(p, std::get<0>(this->children), new_map);
  }
 
  template <AtomType Type, conic::BuilderLike Builder>
  constexpr auto canonicalize_impl(const Builder& builder) const {
    const auto child_builder =
        std::get<0>(this->children)
            .template canonicalize<AtomType::FN>(builder);
    const auto child_coord = child_builder.coord_map;
 
    using AffineMatT = affine::affine_mat_t<decltype(child_coord)>;
    static constexpr std::size_t Dom = linalg::mat_cols_v<AffineMatT>;
    static constexpr std::size_t Codom = linalg::mat_rows_v<AffineMatT>;
    static_assert(Codom == N,
                  "Input affine map from cone block has invalid dom which is a "
                  "mismatch between domain in the convex function");
    static_assert(Dom == N,
                  "Expecting child affine map to have square linear part");
    linalg::Matrix<T, 3 * N + 1, 3 * N + 1> F;
    linalg::Vector<T, 3 * N + 1> g;
    for (std::size_t i = 0; i < N; ++i)
      g(2 * N + i) = child_coord.translation()(i);
 
    const auto I = linalg::make_identity<T, N>();
    if constexpr (Tag == CurvatureType::CONVEX)
      F = linalg::set_block<0, N, 2 * N, 3 * N>(F, T(-1) * I);
    else F = linalg::set_block<0, N, 2 * N, 3 * N>(F, I);
 
    F = linalg::set_block<N, 2 * N, 0, N>(F, I);
    F = linalg::set_block<2 * N, 3 * N, N, 2 * N>(F, child_coord.linear_part());
    for (std::size_t i = 0; i < N; ++i) F(3 * N, 2 * N + i) = T(-1);
    F(3 * N, 3 * N) = T(1);
 
    const auto coord_map_up = affine::AffineMap<decltype(F)>(F, g);
    const auto exp_cone = conic::ExpCone<linalg::Vector<T, 3 * N>>();
    const auto rplus = conic::NonnegOrthantCone<linalg::Vector<T, 1>>();
    const auto cones = std::make_tuple(exp_cone, rplus);
    const auto emission =
        conic::LocalEmission(coord_map_up, cones, child_builder.eq_map);
 
    return child_builder.template realize<Type>(idx, lift_map, emission);
  }
 
  PointT p;
  affine::AffineMap<LiftedVarMat<T>> lift_map;
  const int idx{-1};
};
 
template <typename Point, typename Child>
KLDivergence(const Point&, const Child&) -> KLDivergence<
    KLDivMeta<
        dom_space_t<meta_codom_t<atom_meta_t<Child>>>,
        linalg::Matrix<dom_type_t<meta_codom_t<atom_meta_t<Child>>>, 1, 1>>,
    atom_decay_t<Child>>;
 
} // namespace convex