sqrt.hpp

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/*
 * Copyright © 2025-2026 Akreon LLC
 * SPDX-License-Identifier: Apache-2.0
 */
 
#pragma once
 
#include "akreon/convex/canonical_form_builder.hpp"
#include "akreon/convex/cones/soc.hpp"
#include "akreon/convex/convex_traits.hpp"
 
namespace convex {
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using SqrtDom = ConvexDomain<Space, VarType::NONNEG>;
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using SqrtConvexCodom = ConvexDomain<Space, VarType::NONPOS>;
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using SqrtMeta =
    ConvexAtomMeta<SqrtDom<Space>, SqrtDom<Space>, CurvatureType::CONCAVE>;
 
template <linalg::RnSpace Space>
  requires(linalg::space_dim_v<Space> == 1)
using SqrtConvexMeta = ConvexAtomMeta<SqrtDom<Space>, SqrtConvexCodom<Space>,
                                      CurvatureType::CONVEX>;
 
template <typename Meta, typename Child>
  requires(dom_size_v<meta_dom_t<Meta>> == 1)
struct Sqrt : Atom<Meta, Sqrt<Meta, Child>, Child> {
  using ConvexBase = Atom<Meta, Sqrt<Meta, Child>, Child>;
  using ConvexBase::N;
  using typename ConvexBase::PointT;
  using typename ConvexBase::T;
 
  using Space = dom_space_t<meta_dom_t<Meta>>;
 
  static constexpr CurvatureType Tag = meta_curv_v<Meta>;
 
  constexpr explicit Sqrt(const Child& child_in)
      : ConvexBase(child_in), lift_map(affine::make_map_id<LiftedVarMat<T>>()) {
  }
 
  constexpr explicit Sqrt(const Child& child_in,
                          const affine::AffineMap<LiftedVarMat<T>>& map_in)
      : ConvexBase(child_in), lift_map(map_in) {}
 
  constexpr MonotonicityType monotonicity() const {
    if constexpr (Tag == CurvatureType::CONCAVE) {
      return MonotonicityType::NONDEC;
    } else {
      return MonotonicityType::NONINC;
    }
  }
 
  constexpr T operator()(const PointT& x) const { return eval(x); }
 
  constexpr T eval(const PointT& x) const {
    const auto alpha = lift_map.linear_part()(0, 0);
    const auto beta = lift_map.translation()(0);
    AK_ASSERT(x(0) >= T(0) && "sqrt atom expects R+ input");
 
    if constexpr (Tag == CurvatureType::CONCAVE) {
      return alpha * linalg::constexpr_sqrt_safe(x(0)) + beta;
    } else {
      return T(-1) * alpha * linalg::constexpr_sqrt_safe(x(0)) + beta;
    }
  }
 
  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());
      if constexpr (Tag == CurvatureType::CONCAVE) {
        return Sqrt<SqrtConvexMeta<Space>, Child>(std::get<0>(this->children),
                                                  new_map);
      } else {
        return Sqrt<SqrtMeta<Space>, Child>(std::get<0>(this->children),
                                            new_map);
      }
    } else {
      affine::AffineMap<LiftedVarMat<T>> new_map(
          Scalar * lift_map.linear_part(), lift_map.translation());
      return Sqrt<Meta, Child>(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 Sqrt<Meta, Child>(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 == 1,
                  "input affine map from cone block has invalid codom dim for "
                  "scalar fn domain (i.e., != 1");
 
    linalg::Matrix<T, 3, Dom + 1> F;
    F = linalg::set_block<2, 3, 0, Dom>(F, child_coord.linear_part());
    linalg::Vector<T, 3> g;
    g(1) = T(0.5);
    g(2) = child_coord.translation()(0);
 
    if constexpr (Tag == CurvatureType::CONVEX) {
      F(0, Dom) = T(-1);
    } else {
      F(0, Dom) = T(1);
    }
 
    const auto rsoc_coords = affine::AffineMap<decltype(F)>(F, g);
    const auto coord_map_up =
        conic::Rotated2SOC<decltype(rsoc_coords)>()(rsoc_coords);
    const auto rsoc = conic::SecondOrderCone<linalg::Vector<T, 3>>();
    const auto cones = std::make_tuple(rsoc);
    const auto emission =
        conic::LocalEmission(coord_map_up, cones, child_builder.eq_map);
 
    return child_builder.template realize<Type>(idx, lift_map, emission);
  }
 
  affine::AffineMap<LiftedVarMat<T>> lift_map;
  const int idx{-1};
};
 
template <typename Child>
Sqrt(const Child&)
    -> Sqrt<SqrtMeta<dom_space_t<meta_codom_t<atom_meta_t<Child>>>>,
            atom_decay_t<Child>>;
 
} // namespace convex