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

 * 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 <gtsam/base/concepts.h>

#include <type_traits>
#include <utility>

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.
 *
 */

template <typename T> struct traits;

namespace internal {

/// Probe for a class member localCoordinates implementation with Jacobians.
template <class C, class ChartJacobian>
using LocalCoordinatesWithJacobians = decltype(
    std::declval<const C&>().localCoordinates(
        std::declval<const C&>(), std::declval<ChartJacobian>(),
        std::declval<ChartJacobian>()));

/// Probe for a class member retract implementation with Jacobians.
template <class C, class TangentVector, class ChartJacobian>
using RetractWithJacobians = decltype(std::declval<const C&>().retract(
    std::declval<const TangentVector&>(), std::declval<ChartJacobian>(),
    std::declval<ChartJacobian>()));

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

  inline constexpr static auto dim = Class::dimension;

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

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

/// Traits to get dimension, supporting both fixed and dynamic
template<class Class, int N>
struct GetDimensionImpl {
  // Get dimension at compile-time for fixed-size manifolds, and at
  // run-time for dynamic-size manifolds.
  static size_t GetDimension(const Class& m) {
    if constexpr (N == Eigen::Dynamic) {
      return m.dim();
    } else {
      return static_cast<size_t>(N);
    }
  }
};

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

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

  // Dimension of the manifold
  inline constexpr static auto dimension = Class::dimension;

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

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

  template <class C = Class,
            class = LocalCoordinatesWithJacobians<C, ChartJacobian>>
  static TangentVector Local(const Class& origin, const Class& other,
                             ChartJacobian H1, ChartJacobian H2 = {}) {
    return origin.localCoordinates(other, H1, H2);
  }

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

  template <class C = Class,
            class = RetractWithJacobians<C, TangentVector, ChartJacobian>>
  static Class Retract(const Class& origin, const TangentVector& v,
                       ChartJacobian H1, ChartJacobian H2 = {}) {
    return origin.retract(v, H1, H2);
  }
};

/// Detect whether a traits type provides Local with Jacobians.
template <class T, class = void>
struct HasLocalJacobians : std::false_type {};

template <class T>
struct HasLocalJacobians<
    T, std::void_t<decltype(traits<T>::Local(
           std::declval<const T&>(), std::declval<const T&>(),
           std::declval<typename traits<T>::ChartJacobian>(),
           std::declval<typename traits<T>::ChartJacobian>()))>>
    : std::true_type {};

/// Both ManifoldTraits and Testable
template<class Class> struct Manifold: ManifoldTraits<Class>, Testable<Class> {};

} // \ namespace internal

/// Check invariants for Manifold type
template<typename T>
GTSAM_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:

  using structure_category_tag = typename traits<T>::structure_category;
  static inline constexpr int dim = traits<T>::dimension;
  using ManifoldType = typename traits<T>::ManifoldType;
  using TangentVector = typename traits<T>::TangentVector;
  // Concept marker: allows checking IsManifold<T>::value in templates
  static constexpr bool value =
    std::is_base_of_v<manifold_tag, structure_category_tag>;

  GTSAM_CONCEPT_USAGE(IsManifold) {
    static_assert(
        value,
        "This type's structure_category trait does not assert it as a manifold (or derived)");
    if constexpr (dim != Eigen::Dynamic) {
      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 {
  using value_type = const int;
  static inline constexpr int value = traits<T>::dimension;
  static_assert(value != Eigen::Dynamic,
      "FixedDimension instantiated for dynamically-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) using _gtsam_IsManifold_##T = gtsam::IsManifold<T>;