quad-costs.hpp

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#pragma once
 
#include "aligator/context.hpp"
#include "aligator/core/cost-abstract.hpp"
#include "aligator/core/manifold-base.hpp"
#include "aligator/core/vector-space.hpp"
 
namespace aligator {
 
template <typename Scalar> struct QuadraticCostDataTpl;

template <typename _Scalar> struct QuadraticCostTpl : CostAbstractTpl<_Scalar> {
public:
  using Scalar = _Scalar;
  ALIGATOR_DYNAMIC_TYPEDEFS(Scalar);
  using Base = CostAbstractTpl<Scalar>;
  using CostData = CostDataAbstractTpl<Scalar>;
 
  using Data = QuadraticCostDataTpl<Scalar>;
  using VectorSpace = ::aligator::VectorSpaceTpl<Scalar, Eigen::Dynamic>;
  using Manifold = ManifoldAbstractTpl<Scalar>;

  MatrixXs Wxx_;
  MatrixXs Wuu_;
 
protected:
  MatrixXs Wxu_;
 
public:
  VectorXs interp_x;
  VectorXs interp_u;
 
  static auto get_vector_space(Eigen::Index nx) {
    return xyz::polymorphic<Manifold>(VectorSpace((int)nx));
  }
 
  QuadraticCostTpl(const ConstMatrixRef &w_x, const ConstMatrixRef &w_u,
                   const ConstVectorRef &interp_x,
                   const ConstVectorRef &interp_u)
      : Base(get_vector_space(w_x.cols()), (int)w_u.cols())
      , Wxx_(w_x)
      , Wuu_(w_u)
      , Wxu_(this->ndx(), this->nu)
      , interp_x(interp_x)
      , interp_u(interp_u)
      , has_cross_term_(false) {
    debug_check_dims();
    Wxu_.setZero();
  }
 
  QuadraticCostTpl(const ConstMatrixRef &w_x, const ConstMatrixRef &w_u,
                   const ConstMatrixRef &w_cross,
                   const ConstVectorRef &interp_x,
                   const ConstVectorRef &interp_u)
      : Base(get_vector_space(w_x.cols()), (int)w_u.cols())
      , Wxx_(w_x)
      , Wuu_(w_u)
      , Wxu_(w_cross)
      , interp_x(interp_x)
      , interp_u(interp_u)
      , has_cross_term_(true) {
    debug_check_dims();
  }
 
  QuadraticCostTpl(const ConstMatrixRef &w_x, const ConstMatrixRef &w_u)
      : QuadraticCostTpl(w_x, w_u, VectorXs::Zero(w_x.cols()),
                         VectorXs::Zero(w_u.cols())) {}
 
  QuadraticCostTpl(const ConstMatrixRef &w_x, const ConstMatrixRef &w_u,
                   const ConstMatrixRef &w_cross)
      : QuadraticCostTpl(w_x, w_u, w_cross, VectorXs::Zero(w_x.cols()),
                         VectorXs::Zero(w_u.cols())) {}
 
  void evaluate(const ConstVectorRef &x, const ConstVectorRef &u,
                CostData &data) const {
    Data &d = static_cast<Data &>(data);
    d.w_times_x_.noalias() = Wxx_ * x;
    d.w_times_u_.noalias() = Wuu_ * u;
    if (has_cross_term_) {
      d.cross_x_.noalias() = Wxu_ * u;
      d.cross_u_.noalias() = Wxu_.transpose() * x;
 
      d.w_times_x_ += d.cross_x_;
      d.w_times_u_ += d.cross_u_;
    }
    data.value_ = Scalar(0.5) * x.dot(d.w_times_x_ + 2 * interp_x) +
                  Scalar(0.5) * u.dot(d.w_times_u_ + 2 * interp_u);
  }
 
  void computeGradients(const ConstVectorRef &, const ConstVectorRef &,
                        CostData &data) const {
    Data &d = static_cast<Data &>(data);
    d.Lx_ = d.w_times_x_ + interp_x;
    d.Lu_ = d.w_times_u_ + interp_u;
  }
 
  void computeHessians(const ConstVectorRef &, const ConstVectorRef &,
                       CostData &) const {}
 
  shared_ptr<CostData> createData() const {
    auto data = std::make_shared<Data>(this->ndx(), this->nu);
    data->Lxx_ = Wxx_;
    data->Luu_ = Wuu_;
    data->Lxu_ = Wxu_;
    data->Lux_ = Wxu_.transpose();
    return data;
  }
 
  ConstMatrixRef getCrossWeights() const { return Wxu_; }
  void setCrossWeight(const ConstMatrixRef &w) {
    Wxu_ = w;
    has_cross_term_ = true;
    debug_check_dims();
  }

  bool hasCrossTerm() const { return has_cross_term_; }
 
protected:
  bool has_cross_term_;
 
private:
  static void _check_dim_equal(long n, long m, std::string_view msg = "") {
    if (n != m)
      ALIGATOR_RUNTIME_ERROR("Dimensions inconsistent: got {:d} and {:d}{}.\n",
                             n, m, msg);
  }
 
  void debug_check_dims() const {
    _check_dim_equal(Wxx_.rows(), Wxx_.cols(), " for x weights");
    _check_dim_equal(Wuu_.rows(), Wuu_.cols(), " for u weights");
    _check_dim_equal(Wxu_.rows(), this->ndx(), " for cross-term weight");
    _check_dim_equal(Wxu_.cols(), this->nu, " for cross-term weight");
    _check_dim_equal(interp_x.rows(), Wxx_.rows(),
                     " for x weights and intercept");
    _check_dim_equal(interp_u.rows(), Wuu_.rows(),
                     " for u weights and intercept");
  }
};
 
template <typename Scalar>
struct QuadraticCostDataTpl : CostDataAbstractTpl<Scalar> {
  using Base = CostDataAbstractTpl<Scalar>;
  using VectorXs = typename Base::VectorXs;
  VectorXs w_times_x_, w_times_u_, cross_x_, cross_u_;
 
  QuadraticCostDataTpl(const int nx, const int nu)
      : Base(nx, nu)
      , w_times_x_(nx)
      , w_times_u_(nu)
      , cross_x_(nu)
      , cross_u_(nu) {
    w_times_x_.setZero();
    w_times_u_.setZero();
    cross_x_.setZero();
    cross_u_.setZero();
  }
};
 
} // namespace aligator
 
#ifdef ALIGATOR_ENABLE_TEMPLATE_INSTANTIATION
#include "./quad-costs.txx"
#endif