identity.h

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// Copyright (c) 2011, Hauke Strasdat
// Copyright (c) 2012, Steven Lovegrove
// Copyright (c) 2021, farm-ng, inc.
//
// Use of this source code is governed by an MIT-style
// license that can be found in the LICENSE file or at
// https://opensource.org/licenses/MIT.
 
#pragma once
 
#include "sophus/concepts/lie_group.h"
#include "sophus/manifold/unit_vector.h"
 
namespace sophus {
namespace lie {
 
template <class TScalar, int kDim>
class IdentityImpl {
 public:
  using Scalar = TScalar;
 
  static bool constexpr kIsOriginPreserving = true;
  static bool constexpr kIsAxisDirectionPreserving = true;
  static bool constexpr kIsDirectionVectorPreserving = true;
  static bool constexpr kIsShapePreserving = true;
  static bool constexpr kIisSizePreserving = true;
  static bool constexpr kIisParallelLinePreserving = true;
 
  static int const kDof = 0;
  static int const kNumParams = 0;
  static int const kPointDim = kDim;
  static int const kAmbientDim = kDim;
 
  using Tangent = Eigen::Vector<Scalar, kDof>;
  using Params = Eigen::Vector<Scalar, kNumParams>;
  using Point = Eigen::Vector<Scalar, kPointDim>;
 
  template <class TCompatibleScalar>
  using ScalarReturn = typename Eigen::
      ScalarBinaryOpTraits<Scalar, TCompatibleScalar>::ReturnType;
 
  template <class TCompatibleScalar>
  using ParamsReturn =
      Eigen::Vector<ScalarReturn<TCompatibleScalar>, kNumParams>;
 
  template <class TCompatibleScalar>
  using PointReturn = Eigen::Vector<ScalarReturn<TCompatibleScalar>, kPointDim>;
 
  template <class TCompatibleScalar>
  using UnitVectorReturn =
      UnitVector<ScalarReturn<TCompatibleScalar>, kPointDim>;
 
  // constructors and factories
 
  static auto identityParams() -> Params { return Params::Zero(); }
 
  static auto areParamsValid(Params const& scale_factors)
      -> sophus::Expected<Success> {
    return sophus::Expected<Success>{};
  }
 
  static auto adj(Params const& /*unused*/)
      -> Eigen::Matrix<Scalar, kDof, kDof> {
    return Eigen::Matrix<Scalar, kDof, kDof>::Identity();
  }
 
  static auto hasShortestPathAmbiguity(Params const&) -> bool { return false; }
 
  // Manifold / Lie Group concepts
 
  static auto exp(Tangent const& tangent) -> Params { return tangent; }
 
  static auto log(Params const& params) -> Tangent { return params; }
 
  static auto hat(Tangent const& tangent)
      -> Eigen::Matrix<Scalar, kAmbientDim, kAmbientDim> {
    Eigen::Matrix<Scalar, kAmbientDim, kAmbientDim> mat;
    mat.setZero();
    return mat;
  }
 
  static auto vee(Eigen::Matrix<Scalar, kAmbientDim, kAmbientDim> const& mat)
      -> Eigen::Matrix<Scalar, kDof, 1> {
    return Eigen::Matrix<Scalar, kDof, 1>();
  }
 
  // group operations
 
  static auto inverse(Params const& params) -> Params { return params; }
 
  template <class TCompatibleScalar>
  static auto multiplication(
      Params const& lhs_params,
      Eigen::Vector<TCompatibleScalar, kNumParams> const& rhs_params)
      -> ParamsReturn<TCompatibleScalar> {
    return ParamsReturn<TCompatibleScalar>{};
  }
 
  // Point actions
  template <class TCompatibleScalar>
  static auto action(
      Params const& params,
      Eigen::Vector<TCompatibleScalar, kPointDim> const& point)
      -> PointReturn<TCompatibleScalar> {
    return Scalar(1.0) * point;
  }
 
  static auto toAmbient(Point const& point)
      -> Eigen::Vector<Scalar, kAmbientDim> {
    return point;
  }
 
  template <class TCompatibleScalar>
  static auto action(
      Params const& params, UnitVector<TCompatibleScalar, kPointDim> const& dir)
      -> UnitVectorReturn<TCompatibleScalar> {
    return UnitVectorReturn<TCompatibleScalar>::fromParams(
        Scalar(1.0) * dir.params());
  }
 
  // Matrices
 
  static auto compactMatrix(Params const& params)
      -> Eigen::Matrix<Scalar, kPointDim, kAmbientDim> {
    return Eigen::Matrix<Scalar, kPointDim, kAmbientDim>::Identity();
  }
 
  static auto matrix(Params const& params)
      -> Eigen::Matrix<Scalar, kAmbientDim, kAmbientDim> {
    return compactMatrix(params);
  }
 
  // factor group concepts
 
  static auto matV(Params const& /*unused*/, Tangent const& /*unused*/)
      -> Eigen::Matrix<Scalar, kPointDim, kPointDim> {
    return Eigen::Matrix<Scalar, kPointDim, kPointDim>::Identity();
  }
 
  static auto matVInverse(Params const& /*unused*/, Tangent const& /*unused*/)
      -> Eigen::Matrix<Scalar, kPointDim, kPointDim> {
    return Eigen::Matrix<Scalar, kPointDim, kPointDim>::Identity();
  }
 
  static auto adjOfTranslation(Params const& params, Point const& point)
      -> Eigen::Matrix<Scalar, kPointDim, kDof> {
    return Eigen::Matrix<Scalar, kPointDim, kDof>::Zero();
  }
 
  static auto adOfTranslation(Point const& point)
      -> Eigen::Matrix<Scalar, kPointDim, kDof> {
    return Eigen::Matrix<Scalar, kPointDim, kDof>::Zero();
  }
 
  // derivatives
  static auto ad(Tangent const& /*unused*/)
      -> Eigen::Matrix<Scalar, kDof, kDof> {
    return Eigen::Matrix<Scalar, kDof, kDof>::Zero();
  }
 
  static auto dxExpX(Tangent const& /*unused*/)
      -> Eigen::Matrix<Scalar, kNumParams, kDof> {
    return Eigen::Matrix<Scalar, kNumParams, 0>::Identity();
  }
 
  static auto dxExpXAt0() -> Eigen::Matrix<Scalar, kNumParams, kDof> {
    return Eigen::Matrix<Scalar, kNumParams, 0>::Identity();
  }
 
  static auto dxExpXTimesPointAt0(Point const& point)
      -> Eigen::Matrix<Scalar, kPointDim, kDof> {
    return Eigen::Matrix<Scalar, kPointDim, 0>::Identity();
  }
 
  static auto dxThisMulExpXAt0(Params const& unit_complex)
      -> Eigen::Matrix<Scalar, kNumParams, kDof> {
    return Eigen::Matrix<Scalar, kNumParams, 0>::Zero();
  }
 
  static auto dxLogThisInvTimesXAtThis(Params const& unit_quat)
      -> Eigen::Matrix<Scalar, kDof, kNumParams> {
    return Eigen::Matrix<Scalar, kDof, kNumParams>::Identity();
  }
 
  // for tests
 
  static auto tangentExamples() -> std::vector<Tangent> {
    return std::vector<Tangent>();
  }
 
  static auto paramsExamples() -> std::vector<Params> {
    return std::vector<Params>();
  }
 
  static auto invalidParamsExamples() -> std::vector<Params> {
    return std::vector<Params>();
  }
};
 
}  // namespace lie
 
template <class TScalar, int kDim>
class Identity;
 
namespace lie {
template <int kDim>
struct IdentityWithDim {
  template <class TScalar>
  using Impl = IdentityImpl<TScalar, kDim>;
 
  template <class TScalar>
  using Group = Identity<TScalar, kDim>;
};
 
}  // namespace lie
 
}  // namespace sophus