inertia.hpp

//
// Copyright (c) 2015-2024 CNRS INRIA
// Copyright (c) 2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
//
 
#ifndef __pinocchio_python_spatial_inertia_hpp__
#define __pinocchio_python_spatial_inertia_hpp__
 
#include <eigenpy/exception.hpp>
#include <eigenpy/eigenpy.hpp>
#include <eigenpy/memory.hpp>
#include <boost/python/tuple.hpp>
 
#include "pinocchio/spatial/inertia.hpp"
 
#include "pinocchio/bindings/python/utils/cast.hpp"
#include "pinocchio/bindings/python/utils/copyable.hpp"
#include "pinocchio/bindings/python/utils/printable.hpp"
 
#if EIGENPY_VERSION_AT_MOST(2, 8, 1)
EIGENPY_DEFINE_STRUCT_ALLOCATOR_SPECIALIZATION(pinocchio::Inertia)
EIGENPY_DEFINE_STRUCT_ALLOCATOR_SPECIALIZATION(pinocchio::PseudoInertiaTpl)
EIGENPY_DEFINE_STRUCT_ALLOCATOR_SPECIALIZATION(pinocchio::LogCholeskyParametersTpl)
#endif
 
namespace pinocchio
{
  namespace python
  {
    namespace bp = boost::python;
 
    template<typename Inertia>
    struct InertiaPythonVisitor : public boost::python::def_visitor<InertiaPythonVisitor<Inertia>>
    {
      enum
      {
        Options = Inertia::Options
      };
      typedef typename Inertia::Scalar Scalar;
      typedef typename Inertia::Vector3 Vector3;
      typedef typename Inertia::Matrix3 Matrix3;
      typedef typename Inertia::Vector6 Vector6;
      typedef typename Inertia::Matrix6 Matrix6;
 
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1, Options> VectorXs;
      typedef MotionTpl<Scalar, Options> Motion;
      typedef ForceTpl<Scalar, Options> Force;
 
    public:
      template<class PyClass>
      void visit(PyClass & cl) const
      {
        static const Scalar dummy_precision = Eigen::NumTraits<Scalar>::dummy_precision();
        cl.def(
            "__init__",
            bp::make_constructor(
              &InertiaPythonVisitor::makeFromMCI, bp::default_call_policies(),
              bp::args("mass", "lever", "inertia")),
            "Initialize from mass, lever and 3d inertia.")
 
          .def(bp::init<>(bp::arg("self"), "Default constructor."))
          .def(bp::init<const Inertia &>((bp::arg("self"), bp::arg("clone")), "Copy constructor"))
 
          .add_property(
            "mass", &InertiaPythonVisitor::getMass, &InertiaPythonVisitor::setMass,
            "Mass of the Spatial Inertia.")
          .add_property(
            "lever",
            bp::make_function(
              (typename Inertia::Vector3 & (Inertia::*)()) & Inertia::lever,
              bp::return_internal_reference<>()),
            &InertiaPythonVisitor::setLever,
            "Center of mass location of the Spatial Inertia. It corresponds to the location of the "
            "center of mass regarding to the frame where the Spatial Inertia is expressed.")
          .add_property(
            "inertia", &InertiaPythonVisitor::getInertia, &InertiaPythonVisitor::setInertia,
            "Rotational part of the Spatial Inertia, i.e. a symmetric matrix "
            "representing the rotational inertia around the center of mass.")
 
          .def("matrix", (Matrix6(Inertia::*)() const)&Inertia::matrix, bp::arg("self"))
          .def("inverse", (Matrix6(Inertia::*)() const)&Inertia::inverse, bp::arg("self"))
          .def(
            "se3Action", &Inertia::template se3Action<Scalar, Options>, bp::args("self", "M"),
            "Returns the result of the action of M on *this.")
          .def(
            "se3ActionInverse", &Inertia::template se3ActionInverse<Scalar, Options>,
            bp::args("self", "M"), "Returns the result of the action of the inverse of M on *this.")
 
          .def(
            "setIdentity", &Inertia::setIdentity, bp::arg("self"),
            "Set *this to be the Identity inertia.")
          .def(
            "setZero", &Inertia::setZero, bp::arg("self"),
            "Set all the components of *this to zero.")
          .def(
            "setRandom", &Inertia::setRandom, bp::arg("self"),
            "Set all the components of *this to random values.")
 
          .def(bp::self + bp::self)
          .def(bp::self += bp::self)
          .def(bp::self - bp::self)
          .def(bp::self -= bp::self)
          .def(bp::self * bp::other<Motion>())
 
          .add_property("np", (Matrix6(Inertia::*)() const)&Inertia::matrix)
          .def(
            "vxiv", &Inertia::template vxiv<Motion>, bp::args("self", "v"),
            "Returns the result of v x Iv.")
          .def(
            "vtiv", &Inertia::template vtiv<Motion>, bp::args("self", "v"),
            "Returns the result of v.T * Iv.")
          .def(
            "vxi",
            (Matrix6(Inertia::*)(const MotionDense<Motion> &) const)&Inertia::template vxi<Motion>,
            bp::args("self", "v"), "Returns the result of v x* I, a 6x6 matrix.")
          .def(
            "ivx",
            (Matrix6(Inertia::*)(const MotionDense<Motion> &) const)&Inertia::template ivx<Motion>,
            bp::args("self", "v"), "Returns the result of I vx, a 6x6 matrix.")
          .def(
            "variation",
            (Matrix6(Inertia::*)(const MotionDense<Motion> &)
               const)&Inertia::template variation<Motion>,
            bp::args("self", "v"), "Returns the time derivative of the inertia.")
 
#ifndef PINOCCHIO_PYTHON_SKIP_COMPARISON_OPERATIONS
          .def(bp::self == bp::self)
          .def(bp::self != bp::self)
#endif
 
#ifndef PINOCCHIO_PYTHON_SKIP_COMPARISON_OPERATIONS
          .def(
            "isApprox", &Inertia::isApprox,
            (bp::arg("self"), bp::arg("other"), bp::arg("prec") = dummy_precision),
            "Returns true if *this is approximately equal to other, within the precision given "
            "by prec.")
 
          .def(
            "isZero", &Inertia::isZero, (bp::arg("self"), bp::arg("prec") = dummy_precision),
            "Returns true if *this is approximately equal to the zero Inertia, within the "
            "precision given by prec.")
#endif
 
          .def("Identity", &Inertia::Identity, "Returns the identity Inertia.")
          .staticmethod("Identity")
          .def("Zero", &Inertia::Zero, "Returns the zero Inertia.")
          .staticmethod("Zero")
          .def("Random", &Inertia::Random, "Returns a random Inertia.")
          .staticmethod("Random")
 
          .def(
            "toDynamicParameters", &InertiaPythonVisitor::toDynamicParameters_proxy,
            bp::arg("self"),
            "Returns the representation of the matrix as a vector of dynamic parameters."
            "\nThe parameters are given as v = [m, mc_x, mc_y, mc_z, I_{xx}, I_{xy}, I_{yy}, "
            "I_{xz}, I_{yz}, I_{zz}]^T "
            "where I = I_C + mS^T(c)S(c) and I_C has its origin at the barycenter")
          .def(
            "FromDynamicParameters", &InertiaPythonVisitor::fromDynamicParameters_proxy,
            bp::args("dynamic_parameters"),
            "Builds and inertia matrix from a vector of dynamic parameters."
            "\nThe parameters are given as dynamic_parameters = [m, mc_x, mc_y, mc_z, I_{xx}, "
            "I_{xy}, I_{yy}, I_{xz}, I_{yz}, I_{zz}]^T "
            "where I = I_C + mS^T(c)S(c) and I_C has its origin at the barycenter.")
          .staticmethod("FromDynamicParameters")
 
          .def(
            "FromSphere", &Inertia::FromSphere, bp::args("mass", "radius"),
            "Returns the Inertia of a sphere defined by a given mass and radius.")
          .staticmethod("FromSphere")
          .def(
            "FromEllipsoid", &Inertia::FromEllipsoid,
            bp::args("mass", "length_x", "length_y", "length_z"),
            "Returns the Inertia of an ellipsoid shape defined by a mass and given dimensions "
            "the semi-axis of values length_{x,y,z}.")
          .staticmethod("FromEllipsoid")
          .def(
            "FromCylinder", &Inertia::FromCylinder, bp::args("mass", "radius", "length"),
            "Returns the Inertia of a cylinder defined by its mass, radius and length along the "
            "Z axis.")
          .staticmethod("FromCylinder")
          .def(
            "FromBox", &Inertia::FromBox, bp::args("mass", "length_x", "length_y", "length_z"),
            "Returns the Inertia of a box shape with a mass and of dimension the semi axis of "
            "length_{x,y,z}.")
          .staticmethod("FromBox")
          .def(
            "FromCapsule", &Inertia::FromCapsule, bp::args("mass", "radius", "height"),
            "Computes the Inertia of a capsule defined by its mass, radius and length along the "
            "Z axis. Assumes a uniform density.")
          .staticmethod("FromCapsule")
 
          .def(
            "FromPseudoInertia", &Inertia::FromPseudoInertia, bp::args("pseudo_inertia"),
            "Returns the Inertia created from a pseudo inertia object.")
          .staticmethod("FromPseudoInertia")
 
          .def(
            "toPseudoInertia", &Inertia::toPseudoInertia, bp::arg("self"),
            "Returns the pseudo inertia representation of the inertia.")
 
          .def(
            "FromLogCholeskyParameters", &Inertia::FromLogCholeskyParameters,
            bp::args("log_cholesky_parameters"),
            "Returns the Inertia created from log Cholesky parameters.")
          .staticmethod("FromLogCholeskyParameters")
 
          .def("__array__", (Matrix6(Inertia::*)() const)&Inertia::matrix)
          .def(
            "__array__", &__array__,
            (bp::arg("self"), bp::arg("dtype") = bp::object(), bp::arg("copy") = bp::object()))
#ifndef PINOCCHIO_PYTHON_NO_SERIALIZATION
          .def_pickle(Pickle())
#endif
          ;
      }
 
      static Scalar getMass(const Inertia & self)
      {
        return self.mass();
      }
      static void setMass(Inertia & self, Scalar mass)
      {
        self.mass() = mass;
      }
 
      static void setLever(Inertia & self, const Vector3 & lever)
      {
        self.lever() = lever;
      }
 
      static Matrix3 getInertia(const Inertia & self)
      {
        return self.inertia().matrix();
      }
      //      static void setInertia(Inertia & self, const Vector6 & minimal_inertia) {
      //      self.inertia().data() = minimal_inertia; }
      static void setInertia(Inertia & self, const Matrix3 & symmetric_inertia)
      {
        if (!check_expression_if_real<Scalar>(
              isZero(symmetric_inertia - symmetric_inertia.transpose())))
          throw eigenpy::Exception("The 3d inertia should be symmetric.");
        self.inertia().data() << symmetric_inertia(0, 0), symmetric_inertia(1, 0),
          symmetric_inertia(1, 1), symmetric_inertia(0, 2), symmetric_inertia(1, 2),
          symmetric_inertia(2, 2);
      }
 
      static VectorXs toDynamicParameters_proxy(const Inertia & self)
      {
        return self.toDynamicParameters();
      }
 
      static Inertia fromDynamicParameters_proxy(const VectorXs & params)
      {
        if (params.rows() != 10 || params.cols() != 1)
        {
          std::ostringstream shape;
          shape << "(" << params.rows() << ", " << params.cols() << ")";
          throw std::invalid_argument(
            "Wrong size: params" + shape.str() + " but should have the following shape (10, 1)");
        }
        return Inertia::FromDynamicParameters(params);
      }
 
      static Inertia *
      makeFromMCI(const Scalar & mass, const Vector3 & lever, const Matrix3 & inertia)
      {
#ifndef PINOCCHIO_PYTHON_SKIP_COMPARISON_OPERATIONS
        if (!inertia.isApprox(inertia.transpose()))
          throw eigenpy::Exception("The 3d inertia should be symmetric.");
        if (
          (Vector3::UnitX().transpose() * inertia * Vector3::UnitX() < 0)
          || (Vector3::UnitY().transpose() * inertia * Vector3::UnitY() < 0)
          || (Vector3::UnitZ().transpose() * inertia * Vector3::UnitZ() < 0))
          throw eigenpy::Exception("The 3d inertia should be positive.");
#endif
        return new Inertia(mass, lever, inertia);
      }
 
      static void expose()
      {
#if PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION == 6 && EIGENPY_VERSION_AT_LEAST(2, 9, 0)
        typedef PINOCCHIO_SHARED_PTR_HOLDER_TYPE(Inertia) HolderType;
#else
        typedef ::boost::python::detail::not_specified HolderType;
#endif
        bp::class_<Inertia, HolderType>(
          "Inertia",
          "This class represenses a sparse version of a Spatial Inertia and its is defined by its "
          "mass, its center of mass location and the rotational inertia expressed around this "
          "center of mass.\n\n"
          "Supported operations ...",
          bp::no_init)
          .def(InertiaPythonVisitor<Inertia>())
          .def(CastVisitor<Inertia>())
          .def(ExposeConstructorByCastVisitor<Inertia, ::pinocchio::Inertia>())
          .def(CopyableVisitor<Inertia>())
          .def(PrintableVisitor<Inertia>());
      }
 
    private:
      static Matrix6 __array__(const Inertia & self, bp::object, bp::object)
      {
        return self.matrix();
      }
 
      struct Pickle : bp::pickle_suite
      {
        static boost::python::tuple getinitargs(const Inertia & I)
        {
          return bp::make_tuple(I.mass(), (Vector3)I.lever(), I.inertia().matrix());
        }
 
        static bool getstate_manages_dict()
        {
          return true;
        }
      };
 
    }; // struct InertiaPythonVisitor
 
    template<typename PseudoInertia>
    struct PseudoInertiaPythonVisitor
    : public boost::python::def_visitor<PseudoInertiaPythonVisitor<PseudoInertia>>
    {
      enum
      {
        Options = PseudoInertia::Options
      };
      typedef typename PseudoInertia::Scalar Scalar;
      typedef typename PseudoInertia::Vector3 Vector3;
      typedef typename PseudoInertia::Matrix3 Matrix3;
      typedef typename PseudoInertia::Vector10 Vector10;
      typedef typename PseudoInertia::Matrix4 Matrix4;
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1, Options> VectorXs;
 
    public:
      template<class PyClass>
      void visit(PyClass & cl) const
      {
        cl.def(bp::init<const Scalar &, const Vector3 &, const Matrix3 &>(
                 (bp::arg("self"), bp::arg("mass"), bp::arg("h"), bp::arg("sigma")),
                 "Initialize from mass, vector part of the pseudo inertia and matrix part of the "
                 "pseudo inertia."))
          .def(bp::init<const PseudoInertia &>(
            (bp::arg("self"), bp::arg("clone")), "Copy constructor"))
          .add_property(
            "mass", &PseudoInertiaPythonVisitor::getMass, &PseudoInertiaPythonVisitor::setMass,
            "Mass of the Pseudo Inertia.")
          .add_property(
            "h", &PseudoInertiaPythonVisitor::getH, &PseudoInertiaPythonVisitor::setH,
            "Vector part of the Pseudo Inertia.")
          .add_property(
            "sigma", &PseudoInertiaPythonVisitor::getSigma, &PseudoInertiaPythonVisitor::setSigma,
            "Matrix part of the Pseudo Inertia.")
 
          .def(
            "toMatrix", &PseudoInertia::toMatrix, bp::arg("self"),
            "Returns the pseudo inertia as a 4x4 matrix.")
          .def(
            "toDynamicParameters", &PseudoInertiaPythonVisitor::toDynamicParameters_proxy,
            bp::arg("self"), "Returns the dynamic parameters representation.")
          .def(
            "toInertia", &PseudoInertia::toInertia, bp::arg("self"),
            "Returns the inertia representation.")
          .def(
            "FromDynamicParameters", &PseudoInertiaPythonVisitor::fromDynamicParameters_proxy,
            bp::args("dynamic_parameters"),
            "Builds a pseudo inertia matrix from a vector of dynamic parameters."
            "\nThe parameters are given as dynamic_parameters = [m, h_x, h_y, h_z, I_{xx}, "
            "I_{xy}, I_{yy}, I_{xz}, I_{yz}, I_{zz}]^T.")
          .staticmethod("FromDynamicParameters")
 
          .def(
            "FromMatrix", &PseudoInertia::FromMatrix, bp::args("pseudo_inertia_matrix"),
            "Returns the Pseudo Inertia from a 4x4 matrix.")
          .staticmethod("FromMatrix")
 
          .def(
            "FromInertia", &PseudoInertia::FromInertia, bp::args("inertia"),
            "Returns the Pseudo Inertia from an Inertia object.")
          .staticmethod("FromInertia")
 
          .def("__array__", &PseudoInertia::toMatrix)
          .def(
            "__array__", &__array__,
            (bp::arg("self"), bp::arg("dtype") = bp::object(), bp::arg("copy") = bp::object()))
#ifndef PINOCCHIO_PYTHON_NO_SERIALIZATION
          .def_pickle(Pickle())
#endif
          ;
      }
 
      static Scalar getMass(const PseudoInertia & self)
      {
        return self.mass;
      }
      static void setMass(PseudoInertia & self, Scalar mass)
      {
        self.mass = mass;
      }
 
      static Vector3 getH(const PseudoInertia & self)
      {
        return self.h;
      }
      static void setH(PseudoInertia & self, const Vector3 & h)
      {
        self.h = h;
      }
 
      static Matrix3 getSigma(const PseudoInertia & self)
      {
        return self.sigma;
      }
      static void setSigma(PseudoInertia & self, const Matrix3 & sigma)
      {
        self.sigma = sigma;
      }
 
      static VectorXs toDynamicParameters_proxy(const PseudoInertia & self)
      {
        return self.toDynamicParameters();
      }
 
      static PseudoInertia fromDynamicParameters_proxy(const VectorXs & params)
      {
        if (params.rows() != 10 || params.cols() != 1)
        {
          std::ostringstream shape;
          shape << "(" << params.rows() << ", " << params.cols() << ")";
          throw std::invalid_argument(
            "Wrong size: params" + shape.str() + " but should have the following shape (10, 1)");
        }
        return PseudoInertia::FromDynamicParameters(params);
      }
 
      static void expose()
      {
#if PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION == 6 && EIGENPY_VERSION_AT_LEAST(2, 9, 0)
        typedef PINOCCHIO_SHARED_PTR_HOLDER_TYPE(PseudoInertia) HolderType;
#else
        typedef ::boost::python::detail::not_specified HolderType;
#endif
        bp::class_<PseudoInertia, HolderType>(
          "PseudoInertia",
          "This class represents a pseudo inertia matrix and it is defined by its mass, vector "
          "part, and 3x3 matrix part.\n\n"
          "Supported operations ...",
          bp::no_init)
          .def(PseudoInertiaPythonVisitor<PseudoInertia>())
          .def(CopyableVisitor<PseudoInertia>())
          .def(PrintableVisitor<PseudoInertia>())
          .def(CastVisitor<PseudoInertia>())
          .def(ExposeConstructorByCastVisitor<PseudoInertia, ::pinocchio::PseudoInertia>());
      }
 
    private:
      static Matrix4 __array__(const PseudoInertia & self, bp::object, bp::object)
      {
        return self.toMatrix();
      }
 
      struct Pickle : bp::pickle_suite
      {
        static boost::python::tuple getinitargs(const PseudoInertia & pi)
        {
          return bp::make_tuple(pi.mass, pi.h, pi.sigma);
        }
 
        static bool getstate_manages_dict()
        {
          return true;
        }
      };
 
    }; // struct PseudoInertiaPythonVisitor
 
    template<typename LogCholeskyParameters>
    struct LogCholeskyParametersPythonVisitor
    : public boost::python::def_visitor<LogCholeskyParametersPythonVisitor<LogCholeskyParameters>>
    {
      enum
      {
        Options = LogCholeskyParameters::Options
      };
      typedef typename LogCholeskyParameters::Scalar Scalar;
      typedef typename LogCholeskyParameters::Vector10 Vector10;
      typedef typename LogCholeskyParameters::Matrix10 Matrix10;
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1, Options> VectorXs;
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Options> MatrixXs;
 
    public:
      template<class PyClass>
      void visit(PyClass & cl) const
      {
        cl.def(
            "__init__",
            bp::make_constructor(
              &LogCholeskyParametersPythonVisitor::makeFromParameters, bp::default_call_policies(),
              bp::args("log_cholesky_parameters")),
            "Initialize from log cholesky parameters.")
          .def(bp::init<const LogCholeskyParameters &>(
            (bp::arg("self"), bp::arg("clone")), "Copy constructor"))
 
          .add_property(
            "parameters", &LogCholeskyParametersPythonVisitor::getParameters,
            &LogCholeskyParametersPythonVisitor::setParameters, "Log Cholesky parameters.")
 
          .def(
            "toDynamicParameters", &LogCholeskyParametersPythonVisitor::toDynamicParameters_proxy,
            bp::arg("self"), "Returns the dynamic parameters representation.")
          .def(
            "toPseudoInertia", &LogCholeskyParameters::toPseudoInertia, bp::arg("self"),
            "Returns the Pseudo Inertia representation.")
          .def(
            "toInertia", &LogCholeskyParameters::toInertia, bp::arg("self"),
            "Returns the Inertia representation.")
          .def(
            "calculateJacobian", &LogCholeskyParametersPythonVisitor::calculateJacobian_proxy,
            bp::arg("self"), "Calculates the Jacobian of the log Cholesky parameters.")
 
          .def("__array__", &LogCholeskyParametersPythonVisitor::getParameters)
          .def(
            "__array__", &__array__,
            (bp::arg("self"), bp::arg("dtype") = bp::object(), bp::arg("copy") = bp::object()))
#ifndef PINOCCHIO_PYTHON_NO_SERIALIZATION
          .def_pickle(Pickle())
#endif
          ;
      }
 
      static LogCholeskyParameters * makeFromParameters(const VectorXs & params)
      {
        if (params.rows() != 10 || params.cols() != 1)
        {
          std::ostringstream shape;
          shape << "(" << params.rows() << ", " << params.cols() << ")";
          throw std::invalid_argument(
            "Wrong size: params" + shape.str() + " but should have the following shape (10, 1)");
        }
        return new LogCholeskyParameters(params);
      }
 
      static VectorXs getParameters(const LogCholeskyParameters & self)
      {
        return self.parameters;
      }
      static void setParameters(LogCholeskyParameters & self, const Vector10 & parameters)
      {
        self.parameters = parameters;
      }
 
      static VectorXs toDynamicParameters_proxy(const LogCholeskyParameters & self)
      {
        return self.toDynamicParameters();
      }
 
      static MatrixXs calculateJacobian_proxy(const LogCholeskyParameters & self)
      {
        return self.calculateJacobian();
      }
 
      static void expose()
      {
#if PY_MAJOR_VERSION == 3 && PY_MINOR_VERSION == 6 && EIGENPY_VERSION_AT_LEAST(2, 9, 0)
        typedef PINOCCHIO_SHARED_PTR_HOLDER_TYPE(LogCholeskyParameters) HolderType;
#else
        typedef ::boost::python::detail::not_specified HolderType;
#endif
        bp::class_<LogCholeskyParameters, HolderType>(
          "LogCholeskyParameters",
          "This class represents log Cholesky parameters.\n\n"
          "Supported operations ...",
          bp::no_init)
          .def(LogCholeskyParametersPythonVisitor<LogCholeskyParameters>())
          .def(CopyableVisitor<LogCholeskyParameters>())
          .def(PrintableVisitor<LogCholeskyParameters>())
          .def(CastVisitor<LogCholeskyParameters>())
          .def(ExposeConstructorByCastVisitor<
               LogCholeskyParameters, ::pinocchio::LogCholeskyParameters>());
      }
 
    private:
      static VectorXs __array__(const LogCholeskyParameters & self, bp::object, bp::object)
      {
        return self.parameters;
      }
 
      struct Pickle : bp::pickle_suite
      {
        static boost::python::tuple getinitargs(const LogCholeskyParameters & lcp)
        {
          return bp::make_tuple(lcp.parameters);
        }
 
        static bool getstate_manages_dict()
        {
          return true;
        }
      };
 
    }; // struct LogCholeskyParametersPythonVisitor
 
  } // namespace python
} // namespace pinocchio
 
#endif // ifndef __pinocchio_python_spatial_inertia_hpp__