gtsam/gtsam/base/Manifold.h

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

 * 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

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

/**
 * @file Manifold.h
 * @brief Base class and basic functions for Manifold types
 * @author Alex Cunningham
 * @author Frank Dellaert
 * @author Mike Bosse
 */

#pragma once

#include <gtsam/base/Matrix.h>
#include <gtsam/base/Testable.h>
#include <gtsam/base/OptionalJacobian.h>

#include <boost/concept_check.hpp>
#include <boost/concept/requires.hpp>
#include <boost/type_traits/is_base_of.hpp>

namespace gtsam {

/// tag to assert a type is a manifold
struct manifold_tag {};

/**
 * A manifold defines a space in which there is a notion of a linear tangent space
 * that can be centered around a given point on the manifold.  These nonlinear
 * spaces may have such properties as wrapping around (as is the case with rotations),
 * which might make linear operations on parameters not return a viable element of
 * the manifold.
 *
 * We perform optimization by computing a linear delta in the tangent space of the
 * current estimate, and then apply this change using a retraction operation, which
 * maps the change in tangent space back to the manifold itself.
 *
 * There may be multiple possible retractions for a given manifold, which can be chosen
 * between depending on the computational complexity.  The important criteria for
 * the creation for the retract and localCoordinates functions is that they be
 * inverse operations. The new notion of a Chart guarantees that.
 *
 */

template <typename T> struct traits;

namespace internal {

/// Requirements on type to pass it to Manifold template below
template<class Class>
struct HasManifoldPrereqs {

  enum { dim = Class::dimension };

  Class p, q;
  Eigen::Matrix<double, dim, 1> v;
  OptionalJacobian<dim, dim> Hp, Hq, Hv;

  BOOST_CONCEPT_USAGE(HasManifoldPrereqs) {
    v = p.localCoordinates(q);
    q = p.retract(v);
  }
};

/// Extra manifold traits for fixed-dimension types
template<class Class, size_t N>
struct ManifoldImpl {
  // Compile-time dimensionality
  static int GetDimension(const Class&) {
    return N;
  }
};

/// Extra manifold traits for variable-dimension types
template<class Class>
struct ManifoldImpl<Class, Eigen::Dynamic> {
  // Run-time dimensionality
  static int GetDimension(const Class& m) {
    return m.dim();
  }
};

/// A helper that implements the traits interface for GTSAM manifolds.
/// To use this for your class type, define:
/// template<> struct traits<Class> : public Manifold<Class> { };
template<class Class>
struct Manifold: Testable<Class>, ManifoldImpl<Class, Class::dimension> {

  // Check that Class has the necessary machinery
  BOOST_CONCEPT_ASSERT((HasManifoldPrereqs<Class>));

  // Dimension of the manifold
  enum { dimension = Class::dimension };

  // Typedefs required by all manifold types.
  typedef Class ManifoldType;
  typedef manifold_tag structure_category;
  typedef Eigen::Matrix<double, dimension, 1> TangentVector;

  // Local coordinates
  static TangentVector Local(const Class& origin, const Class& other) {
    return origin.localCoordinates(other);
  }

  // Retraction back to manifold
  static Class Retract(const Class& origin, const TangentVector& v) {
    return origin.retract(v);
  }
};

} // \ namespace internal

/// Check invariants for Manifold type
template<typename T>
BOOST_CONCEPT_REQUIRES(((IsTestable<T>)),(bool)) //
check_manifold_invariants(const T& a, const T& b, double tol=1e-9) {
  typename traits<T>::TangentVector v0 = traits<T>::Local(a,a);
  typename traits<T>::TangentVector v = traits<T>::Local(a,b);
  T c = traits<T>::Retract(a,v);
  return v0.norm() < tol && traits<T>::Equals(b,c,tol);
}

/// Manifold concept
template<typename T>
class IsManifold {

public:

  typedef typename traits<T>::structure_category structure_category_tag;
  static const size_t dim = traits<T>::dimension;
  typedef typename traits<T>::ManifoldType ManifoldType;
  typedef typename traits<T>::TangentVector TangentVector;

  BOOST_CONCEPT_USAGE(IsManifold) {
    BOOST_STATIC_ASSERT_MSG(
        (boost::is_base_of<manifold_tag, structure_category_tag>::value),
        "This type's structure_category trait does not assert it as a manifold (or derived)");
    BOOST_STATIC_ASSERT(TangentVector::SizeAtCompileTime == dim);

    // make sure Chart methods are defined
    v = traits<T>::Local(p, q);
    q = traits<T>::Retract(p, v);
  }

private:

  TangentVector v;
  ManifoldType p, q;
};

/// Give fixed size dimension of a type, fails at compile time if dynamic
template<typename T>
struct FixedDimension {
  typedef const int value_type;
  static const int value = traits<T>::dimension;
  BOOST_STATIC_ASSERT_MSG(value != Eigen::Dynamic,
      "FixedDimension instantiated for dymanically-sized type.");
};

} // \ namespace gtsam

///**
// * Macros for using the ManifoldConcept
// *  - An instantiation for use inside unit tests
// *  - A typedef for use inside generic algorithms
// *
// * NOTE: intentionally not in the gtsam namespace to allow for classes not in
// * the gtsam namespace to be more easily enforced as testable
// */
#define GTSAM_CONCEPT_MANIFOLD_INST(T) template class gtsam::IsManifold<T>;
#define GTSAM_CONCEPT_MANIFOLD_TYPE(T) typedef gtsam::IsManifold<T> _gtsam_IsManifold_##T;