import yoco xiao's work on reshape

This commit is contained in:
Gael Guennebaud 2017-01-29 14:29:31 +01:00
commit 0e89baa5d8
10 changed files with 566 additions and 0 deletions

View File

@ -471,6 +471,7 @@ using std::ptrdiff_t;
#include "src/Core/Map.h"
#include "src/Core/Ref.h"
#include "src/Core/Block.h"
#include "src/Core/Reshape.h"
#include "src/Core/VectorBlock.h"
#include "src/Core/IndexedView.h"
#include "src/Core/Transpose.h"

391
Eigen/src/Core/Reshape.h Normal file
View File

@ -0,0 +1,391 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2014 yoco <peter.xiau@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_RESHAPE_H
#define EIGEN_RESHAPE_H
namespace Eigen {
/** \class Reshape
* \ingroup Core_Module
*
* \brief Expression of a fixed-size or dynamic-size reshape
*
* \param XprType the type of the expression in which we are taking a reshape
* \param ReshapeRows the number of rows of the reshape we are taking at compile time (optional)
* \param ReshapeCols the number of columns of the reshape we are taking at compile time (optional)
*
* This class represents an expression of either a fixed-size or dynamic-size reshape. It is the return
* type of DenseBase::reshape(Index,Index) and DenseBase::reshape<int,int>() and
* most of the time this is the only way it is used.
*
* However, if you want to directly maniputate reshape expressions,
* for instance if you want to write a function returning such an expression, you
* will need to use this class.
*
* Here is an example illustrating the dynamic case:
* \include class_Reshape.cpp
* Output: \verbinclude class_Reshape.out
*
* \note Even though this expression has dynamic size, in the case where \a XprType
* has fixed size, this expression inherits a fixed maximal size which means that evaluating
* it does not cause a dynamic memory allocation.
*
* Here is an example illustrating the fixed-size case:
* \include class_FixedReshape.cpp
* Output: \verbinclude class_FixedReshape.out
*
* \sa DenseBase::reshape(Index,Index), DenseBase::reshape(), class VectorReshape
*/
namespace internal {
template<typename XprType, int ReshapeRows, int ReshapeCols>
struct traits<Reshape<XprType, ReshapeRows, ReshapeCols> > : traits<XprType>
{
typedef typename traits<XprType>::Scalar Scalar;
typedef typename traits<XprType>::StorageKind StorageKind;
typedef typename traits<XprType>::XprKind XprKind;
enum{
MatrixRows = traits<XprType>::RowsAtCompileTime,
MatrixCols = traits<XprType>::ColsAtCompileTime,
RowsAtCompileTime = ReshapeRows,
ColsAtCompileTime = ReshapeCols,
MaxRowsAtCompileTime = ReshapeRows,
MaxColsAtCompileTime = ReshapeCols,
XprTypeIsRowMajor = (int(traits<XprType>::Flags) & RowMajorBit) != 0,
IsRowMajor = (RowsAtCompileTime == 1 && ColsAtCompileTime != 1) ? 1
: (ColsAtCompileTime == 1 && RowsAtCompileTime != 1) ? 0
: XprTypeIsRowMajor,
HasSameStorageOrderAsXprType = (IsRowMajor == XprTypeIsRowMajor),
InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
InnerStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(inner_stride_at_compile_time<XprType>::ret)
: int(outer_stride_at_compile_time<XprType>::ret),
OuterStrideAtCompileTime = HasSameStorageOrderAsXprType
? int(outer_stride_at_compile_time<XprType>::ret)
: int(inner_stride_at_compile_time<XprType>::ret),
MaskPacketAccessBit = (InnerSize == Dynamic || (InnerSize % packet_traits<Scalar>::size) == 0)
&& (InnerStrideAtCompileTime == 1)
? PacketAccessBit : 0,
MaskAlignedBit = ((OuterStrideAtCompileTime!=Dynamic) && (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % 16) == 0)) ? AlignedBit : 0,
FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1) ? LinearAccessBit : 0,
FlagsLvalueBit = is_lvalue<XprType>::value ? LvalueBit : 0,
FlagsRowMajorBit = IsRowMajor ? RowMajorBit : 0,
Flags0 = traits<XprType>::Flags & ( (HereditaryBits & ~RowMajorBit) |
MaskPacketAccessBit |
MaskAlignedBit)
& ~DirectAccessBit,
Flags = (Flags0 | FlagsLinearAccessBit | FlagsLvalueBit | FlagsRowMajorBit)
};
};
template<typename XprType, int ReshapeRows=Dynamic, int ReshapeCols=Dynamic,
bool HasDirectAccess = internal::has_direct_access<XprType>::ret> class ReshapeImpl_dense;
} // end namespace internal
template<typename XprType, int ReshapeRows, int ReshapeCols, typename StorageKind> class ReshapeImpl;
template<typename XprType, int ReshapeRows, int ReshapeCols> class Reshape
: public ReshapeImpl<XprType, ReshapeRows, ReshapeCols, typename internal::traits<XprType>::StorageKind>
{
typedef ReshapeImpl<XprType, ReshapeRows, ReshapeCols, typename internal::traits<XprType>::StorageKind> Impl;
public:
//typedef typename Impl::Base Base;
typedef Impl Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Reshape)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Reshape)
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC
inline Reshape(XprType& xpr)
: Impl(xpr)
{
EIGEN_STATIC_ASSERT(RowsAtCompileTime!=Dynamic && ColsAtCompileTime!=Dynamic,THIS_METHOD_IS_ONLY_FOR_FIXED_SIZE)
eigen_assert(ReshapeRows * ReshapeCols == xpr.rows() * xpr.cols());
}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC
inline Reshape(XprType& xpr,
Index reshapeRows, Index reshapeCols)
: Impl(xpr, reshapeRows, reshapeCols)
{
eigen_assert((RowsAtCompileTime==Dynamic || RowsAtCompileTime==reshapeRows)
&& (ColsAtCompileTime==Dynamic || ColsAtCompileTime==reshapeCols));
eigen_assert(reshapeRows * reshapeCols == xpr.rows() * xpr.cols());
}
};
// The generic default implementation for dense reshape simplu forward to the internal::ReshapeImpl_dense
// that must be specialized for direct and non-direct access...
template<typename XprType, int ReshapeRows, int ReshapeCols>
class ReshapeImpl<XprType, ReshapeRows, ReshapeCols, Dense>
: public internal::ReshapeImpl_dense<XprType, ReshapeRows, ReshapeCols>
{
typedef internal::ReshapeImpl_dense<XprType, ReshapeRows, ReshapeCols> Impl;
typedef typename XprType::Index Index;
public:
typedef Impl Base;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapeImpl)
EIGEN_DEVICE_FUNC inline ReshapeImpl(XprType& xpr) : Impl(xpr) {}
EIGEN_DEVICE_FUNC inline ReshapeImpl(XprType& xpr, Index reshapeRows, Index reshapeCols)
: Impl(xpr, reshapeRows, reshapeCols) {}
};
namespace internal {
/** \internal Internal implementation of dense Reshapes in the general case. */
template<typename XprType, int ReshapeRows, int ReshapeCols, bool HasDirectAccess> class ReshapeImpl_dense
: public internal::dense_xpr_base<Reshape<XprType, ReshapeRows, ReshapeCols> >::type
{
typedef Reshape<XprType, ReshapeRows, ReshapeCols> ReshapeType;
public:
typedef typename internal::dense_xpr_base<ReshapeType>::type Base;
EIGEN_DENSE_PUBLIC_INTERFACE(ReshapeType)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapeImpl_dense)
class InnerIterator;
/** Fixed-size constructor
*/
EIGEN_DEVICE_FUNC
inline ReshapeImpl_dense(XprType& xpr)
: m_xpr(xpr), m_reshapeRows(ReshapeRows), m_reshapeCols(ReshapeCols)
{}
/** Dynamic-size constructor
*/
EIGEN_DEVICE_FUNC
inline ReshapeImpl_dense(XprType& xpr,
Index reshapeRows, Index reshapeCols)
: m_xpr(xpr), m_reshapeRows(reshapeRows), m_reshapeCols(reshapeCols)
{}
EIGEN_DEVICE_FUNC inline Index rows() const { return m_reshapeRows.value(); }
EIGEN_DEVICE_FUNC inline Index cols() const { return m_reshapeCols.value(); }
typedef std::pair<Index, Index> RowCol;
inline RowCol index_remap(Index rowId, Index colId) const {
const Index nth_elem_idx = colId * m_reshapeRows.value() + rowId;
const Index actual_col = nth_elem_idx / m_xpr.rows();
const Index actual_row = nth_elem_idx % m_xpr.rows();
return RowCol(actual_row, actual_col);
}
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index rowId, Index colId)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
const RowCol row_col = index_remap(rowId, colId);
return m_xpr.const_cast_derived().coeffRef(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index rowId, Index colId) const
{
const RowCol row_col = index_remap(rowId, colId);
return m_xpr.derived().coeffRef(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index rowId, Index colId) const
{
const RowCol row_col = index_remap(rowId, colId);
return m_xpr.coeff(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
inline Scalar& coeffRef(Index index)
{
EIGEN_STATIC_ASSERT_LVALUE(XprType)
const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
RowsAtCompileTime == 1 ? index : 0);
return m_xpr.const_cast_derived().coeffRef(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
inline const Scalar& coeffRef(Index index) const
{
const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
RowsAtCompileTime == 1 ? index : 0);
return m_xpr.const_cast_derived().coeffRef(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
inline const CoeffReturnType coeff(Index index) const
{
const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
RowsAtCompileTime == 1 ? index : 0);
return m_xpr.coeff(row_col.first, row_col.second);
}
EIGEN_DEVICE_FUNC
template<int LoadMode>
inline PacketScalar packet(Index rowId, Index colId) const
{
const RowCol row_col = index_remap(rowId, colId);
return m_xpr.template packet<Unaligned>(row_col.first, row_col.second);
}
template<int LoadMode>
inline void writePacket(Index rowId, Index colId, const PacketScalar& val)
{
const RowCol row_col = index_remap(rowId, colId);
m_xpr.const_cast_derived().template writePacket<Unaligned>
(row_col.first, row_col.second, val);
}
template<int LoadMode>
inline PacketScalar packet(Index index) const
{
const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
RowsAtCompileTime == 1 ? index : 0);
return m_xpr.template packet<Unaligned>(row_col.first, row_col.second);
}
template<int LoadMode>
inline void writePacket(Index index, const PacketScalar& val)
{
const RowCol row_col = index_remap(RowsAtCompileTime == 1 ? 0 : index,
RowsAtCompileTime == 1 ? index : 0);
return m_xpr.template packet<Unaligned>(row_col.first, row_col.second, val);
}
#ifdef EIGEN_PARSED_BY_DOXYGEN
/** \sa MapBase::data() */
EIGEN_DEVICE_FUNC inline const Scalar* data() const;
EIGEN_DEVICE_FUNC inline Index innerStride() const;
EIGEN_DEVICE_FUNC inline Index outerStride() const;
#endif
EIGEN_DEVICE_FUNC
const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
{
return m_xpr;
}
protected:
const typename XprType::Nested m_xpr;
const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_reshapeRows;
const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_reshapeCols;
};
///** \internal Internal implementation of dense Reshapes in the direct access case.*/
//template<typename XprType, int ReshapeRows, int ReshapeCols>
//class ReshapeImpl_dense<XprType,ReshapeRows,ReshapeCols, true>
// : public MapBase<Reshape<XprType, ReshapeRows, ReshapeCols> >
//{
// typedef Reshape<XprType, ReshapeRows, ReshapeCols> ReshapeType;
// public:
//
// typedef MapBase<ReshapeType> Base;
// EIGEN_DENSE_PUBLIC_INTERFACE(ReshapeType)
// EIGEN_INHERIT_ASSIGNMENT_OPERATORS(ReshapeImpl_dense)
//
// /** Column or Row constructor
// */
// EIGEN_DEVICE_FUNC
// inline ReshapeImpl_dense(XprType& xpr, Index i)
// : Base(internal::const_cast_ptr(&xpr.coeffRef(
// (ReshapeRows==1) && (ReshapeCols==XprType::ColsAtCompileTime) ? i : 0,
// (ReshapeRows==XprType::RowsAtCompileTime) && (ReshapeCols==1) ? i : 0)),
// ReshapeRows==1 ? 1 : xpr.rows(),
// ReshapeCols==1 ? 1 : xpr.cols()),
// m_xpr(xpr)
// {
// init();
// }
//
// /** Fixed-size constructor
// */
// EIGEN_DEVICE_FUNC
// inline ReshapeImpl_dense(XprType& xpr)
// : Base(internal::const_cast_ptr(&xpr.coeffRef(0, 0))), m_xpr(xpr)
// {
// init();
// }
//
// /** Dynamic-size constructor
// */
// EIGEN_DEVICE_FUNC
// inline ReshapeImpl_dense(XprType& xpr,
// Index reshapeRows, Index reshapeCols)
// : Base(internal::const_cast_ptr(&xpr.coeffRef(0, 0)), reshapeRows, reshapeCols),
// m_xpr(xpr)
// {
// init();
// }
//
// EIGEN_DEVICE_FUNC
// const typename internal::remove_all<typename XprType::Nested>::type& nestedExpression() const
// {
// return m_xpr;
// }
//
// EIGEN_DEVICE_FUNC
// /** \sa MapBase::innerStride() */
// inline Index innerStride() const
// {
// return internal::traits<ReshapeType>::HasSameStorageOrderAsXprType
// ? m_xpr.innerStride()
// : m_xpr.outerStride();
// }
//
// EIGEN_DEVICE_FUNC
// /** \sa MapBase::outerStride() */
// inline Index outerStride() const
// {
// return m_outerStride;
// }
//
// #ifndef __SUNPRO_CC
// // FIXME sunstudio is not friendly with the above friend...
// // META-FIXME there is no 'friend' keyword around here. Is this obsolete?
// protected:
// #endif
//
// #ifndef EIGEN_PARSED_BY_DOXYGEN
// /** \internal used by allowAligned() */
// EIGEN_DEVICE_FUNC
// inline ReshapeImpl_dense(XprType& xpr, const Scalar* data, Index reshapeRows, Index reshapeCols)
// : Base(data, reshapeRows, reshapeCols), m_xpr(xpr)
// {
// init();
// }
// #endif
//
// protected:
// EIGEN_DEVICE_FUNC
// void init()
// {
// m_outerStride = internal::traits<ReshapeType>::HasSameStorageOrderAsXprType
// ? m_xpr.outerStride()
// : m_xpr.innerStride();
// }
//
// typename XprType::Nested m_xpr;
// Index m_outerStride;
//};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_RESHAPE_H

View File

@ -84,6 +84,7 @@ template<typename ExpressionType> class SwapWrapper;
template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic, bool InnerPanel = false> class Block;
template<typename XprType, typename RowIndices, typename ColIndices> class IndexedView;
template<typename XprType, int BlockRows=Dynamic, int BlockCols=Dynamic> class Reshape;
template<typename MatrixType, int Size=Dynamic> class VectorBlock;
template<typename MatrixType> class Transpose;

View File

@ -1354,3 +1354,59 @@ inline typename ConstFixedSegmentReturnType<N>::Type tail(Index n = N) const
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
return typename ConstFixedSegmentReturnType<N>::Type(derived(), size() - n);
}
/** \returns a dynamic-size expression of a reshape in *this.
*
* \param reshapeRows the number of rows in the reshape
* \param reshapeCols the number of columns in the reshape
*
* Example: \include MatrixBase_reshape_int_int.cpp
* Output: \verbinclude MatrixBase_reshape_int_int.out
*
* \note Even though the returned expression has dynamic size, in the case
* when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
* which means that evaluating it does not cause a dynamic memory allocation.
*
* \sa class Reshape, reshape()
*/
EIGEN_DEVICE_FUNC
inline Reshape<Derived> reshape(Index reshapeRows, Index reshapeCols)
{
return Reshape<Derived>(derived(), reshapeRows, reshapeCols);
}
/** This is the const version of reshape(Index,Index). */
EIGEN_DEVICE_FUNC
inline const Reshape<const Derived> reshape(Index reshapeRows, Index reshapeCols) const
{
return Reshape<const Derived>(derived(), reshapeRows, reshapeCols);
}
/** \returns a fixed-size expression of a reshape in *this.
*
* The template parameters \a ReshapeRows and \a ReshapeCols are the number of
* rows and columns in the reshape.
*
* Example: \include MatrixBase_reshape.cpp
* Output: \verbinclude MatrixBase_reshape.out
*
* \note since reshape is a templated member, the keyword template has to be used
* if the matrix type is also a template parameter: \code m.template reshape<3,3>(); \endcode
*
* \sa class Reshape, reshape(Index,Index)
*/
template<int ReshapeRows, int ReshapeCols>
EIGEN_DEVICE_FUNC
inline Reshape<Derived, ReshapeRows, ReshapeCols> reshape()
{
return Reshape<Derived, ReshapeRows, ReshapeCols>(derived());
}
/** This is the const version of reshape<>(Index, Index). */
template<int ReshapeRows, int ReshapeCols>
EIGEN_DEVICE_FUNC
inline const Reshape<const Derived, ReshapeRows, ReshapeCols> reshape() const
{
return Reshape<const Derived, ReshapeRows, ReshapeCols>(derived());
}

View File

@ -0,0 +1,22 @@
#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;
template<typename Derived>
Eigen::Reshape<Derived, 4, 2>
reshape_helper(MatrixBase<Derived>& m)
{
return Eigen::Reshape<Derived, 4, 2>(m.derived());
}
int main(int, char**)
{
MatrixXd m(2, 4);
m << 1, 2, 3, 4,
5, 6, 7, 8;
MatrixXd n = reshape_helper(m);
cout << "matrix m is:" << endl << m << endl;
cout << "matrix n is:" << endl << n << endl;
return 0;
}

View File

@ -0,0 +1,23 @@
#include <Eigen/Core>
#include <iostream>
using namespace std;
using namespace Eigen;
template<typename Derived>
const Reshape<const Derived>
reshape_helper(const MatrixBase<Derived>& m, int rows, int cols)
{
return Reshape<const Derived>(m.derived(), rows, cols);
}
int main(int, char**)
{
MatrixXd m(3, 4);
m << 1, 4, 7, 10,
2, 5, 8, 11,
3, 6, 9, 12;
cout << m << endl;
auto n = reshape_helper(m, 2, 6);
cout << "Matrix m is:" << endl << m << endl;
cout << "Matrix n is:" << endl << n << endl;
}

View File

@ -0,0 +1,3 @@
Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshape<2,8>():" << endl << m.reshape<2,8>() << endl;

View File

@ -0,0 +1,3 @@
Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is m.reshape(2, 8):" << endl << m.reshape(2, 8) << endl;

View File

@ -160,6 +160,7 @@ endif()
ei_add_test(redux)
ei_add_test(visitor)
ei_add_test(block)
ei_add_test(reshape)
ei_add_test(corners)
ei_add_test(symbolic_index)
ei_add_test(indexed_view)

65
test/reshape.cpp Normal file
View File

@ -0,0 +1,65 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 yoco <peter.xiau@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
using Eigen::Map;
using Eigen::MatrixXi;
// just test a 4x4 matrix, enumerate all combination manually,
// so I don't have to do template-meta-programming here.
template <typename MatType>
void reshape_all_size(MatType m) {
typedef Eigen::Map<MatrixXi> MapMat;
// dynamic
VERIFY_IS_EQUAL((m.template reshape( 1, 16)), MapMat(m.data(), 1, 16));
VERIFY_IS_EQUAL((m.template reshape( 2, 8)), MapMat(m.data(), 2, 8));
VERIFY_IS_EQUAL((m.template reshape( 4, 4)), MapMat(m.data(), 4, 4));
VERIFY_IS_EQUAL((m.template reshape( 8, 2)), MapMat(m.data(), 8, 2));
VERIFY_IS_EQUAL((m.template reshape(16, 1)), MapMat(m.data(), 16, 1));
// static
VERIFY_IS_EQUAL((m.template reshape< 1, 16>()), MapMat(m.data(), 1, 16));
VERIFY_IS_EQUAL((m.template reshape< 2, 8>()), MapMat(m.data(), 2, 8));
VERIFY_IS_EQUAL((m.template reshape< 4, 4>()), MapMat(m.data(), 4, 4));
VERIFY_IS_EQUAL((m.template reshape< 8, 2>()), MapMat(m.data(), 8, 2));
VERIFY_IS_EQUAL((m.template reshape<16, 1>()), MapMat(m.data(), 16, 1));
// reshape chain
VERIFY_IS_EQUAL(
(m
.template reshape( 1, 16)
.template reshape< 2, 8>()
.template reshape(16, 1)
.template reshape< 8, 2>()
.template reshape( 2, 8)
.template reshape< 1, 16>()
.template reshape( 4, 4)
.template reshape<16, 1>()
.template reshape( 8, 2)
.template reshape< 4, 4>()
),
MapMat(m.data(), 4, 4)
);
}
void test_reshape()
{
Eigen::MatrixXi mx = Eigen::MatrixXi::Random(4, 4);
Eigen::Matrix4i m4 = Eigen::Matrix4i::Random(4, 4);
// test dynamic-size matrix
CALL_SUBTEST(reshape_all_size(mx));
// test static-size matrix
CALL_SUBTEST(reshape_all_size(m4));
// test dynamic-size const matrix
CALL_SUBTEST(reshape_all_size(static_cast<const Eigen::MatrixXi>(mx)));
// test static-size const matrix
CALL_SUBTEST(reshape_all_size(static_cast<const Eigen::Matrix4i>(m4)));
}