LieScalar.h

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/* ----------------------------------------------------------------------------

 * GTSAM Copyright 2010, Georgia Tech Research Corporation, 
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)

 * See LICENSE for the license information

 * -------------------------------------------------------------------------- */

#pragma once

#include <gtsam/dllexport.h>
#include <gtsam/base/DerivedValue.h>
#include <gtsam/base/Lie.h>

namespace gtsam {

  struct GTSAM_EXPORT LieScalar : public DerivedValue<LieScalar> {

    LieScalar() : d_(0.0) {}

    explicit LieScalar(double d) : d_(d) {}

    double value() const { return d_; }

    operator double() const { return d_; }

    void print(const std::string& name="") const;

    bool equals(const LieScalar& expected, double tol=1e-5) const {
      return fabs(expected.d_ - d_) <= tol;
    }

    // Manifold requirements

    size_t dim() const { return 1; }
    static size_t Dim() { return 1; }

    LieScalar retract(const Vector& v) const { return LieScalar(value() + v(0)); }

    Vector localCoordinates(const LieScalar& t2) const { return (Vector(1) << (t2.value() - value())); }

    // Group requirements

    static LieScalar identity() {
      return LieScalar();
    }

    LieScalar compose(const LieScalar& p,
        boost::optional<Matrix&> H1=boost::none,
        boost::optional<Matrix&> H2=boost::none) const {
      if(H1) *H1 = eye(1);
      if(H2) *H2 = eye(1);
      return LieScalar(d_ + p.d_);
    }

    LieScalar between(const LieScalar& l2,
        boost::optional<Matrix&> H1=boost::none,
        boost::optional<Matrix&> H2=boost::none) const {
      if(H1) *H1 = -eye(1);
      if(H2) *H2 = eye(1);
      return LieScalar(l2.value() - value());
    }

    LieScalar inverse() const {
      return LieScalar(-1.0 * value());
    }

    // Lie functions

    static LieScalar Expmap(const Vector& v) { return LieScalar(v(0)); }

    static Vector Logmap(const LieScalar& p) { return (Vector(1) << p.value()); }

    static Matrix dexpL(const Vector& v) {
      return eye(1);
    }

    static Matrix dexpInvL(const Vector& v) {
      return eye(1);
    }

  private:
      double d_;
  };
} // \namespace gtsam