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Transpose.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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_TRANSPOSE_H
#define EIGEN_TRANSPOSE_H
namespace Eigen {
namespace internal {
template<typename MatrixType>
struct traits<Transpose<MatrixType> > : public traits<MatrixType>
{
typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedPlain;
enum {
RowsAtCompileTime = MatrixType::ColsAtCompileTime,
ColsAtCompileTime = MatrixType::RowsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxColsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
Flags0 = traits<MatrixTypeNestedPlain>::Flags & ~(LvalueBit | NestByRefBit),
Flags1 = Flags0 | FlagsLvalueBit,
Flags = Flags1 ^ RowMajorBit,
InnerStrideAtCompileTime = inner_stride_at_compile_time<MatrixType>::ret,
OuterStrideAtCompileTime = outer_stride_at_compile_time<MatrixType>::ret
};
};
}
template<typename MatrixType, typename StorageKind> class TransposeImpl;
/** \class Transpose
* \ingroup Core_Module
*
* \brief Expression of the transpose of a matrix
*
* \tparam MatrixType the type of the object of which we are taking the transpose
*
* This class represents an expression of the transpose of a matrix.
* It is the return type of MatrixBase::transpose() and MatrixBase::adjoint()
* and most of the time this is the only way it is used.
*
* \sa MatrixBase::transpose(), MatrixBase::adjoint()
*/
template<typename MatrixType> class Transpose
: public TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>
{
public:
typedef typename internal::ref_selector<MatrixType>::non_const_type MatrixTypeNested;
typedef typename TransposeImpl<MatrixType,typename internal::traits<MatrixType>::StorageKind>::Base Base;
EIGEN_GENERIC_PUBLIC_INTERFACE(Transpose)
typedef typename internal::remove_all<MatrixType>::type NestedExpression;
EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE Transpose(MatrixType& matrix) : m_matrix(matrix) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Transpose)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT { return m_matrix.cols(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT { return m_matrix.rows(); }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename internal::remove_all<MatrixTypeNested>::type&
nestedExpression() const { return m_matrix; }
/** \returns the nested expression */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
typename internal::remove_reference<MatrixTypeNested>::type&
nestedExpression() { return m_matrix; }
/** \internal */
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
void resize(Index nrows, Index ncols) {
m_matrix.resize(ncols,nrows);
}
protected:
typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
};
namespace internal {
template<typename MatrixType, bool HasDirectAccess = has_direct_access<MatrixType>::ret>
struct TransposeImpl_base
{
typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
};
template<typename MatrixType>
struct TransposeImpl_base<MatrixType, false>
{
typedef typename dense_xpr_base<Transpose<MatrixType> >::type type;
};
} // end namespace internal
// Generic API dispatcher
template<typename XprType, typename StorageKind>
class TransposeImpl
: public internal::generic_xpr_base<Transpose<XprType> >::type
{
public:
typedef typename internal::generic_xpr_base<Transpose<XprType> >::type Base;
};
template<typename MatrixType> class TransposeImpl<MatrixType,Dense>
: public internal::TransposeImpl_base<MatrixType>::type
{
public:
typedef typename internal::TransposeImpl_base<MatrixType>::type Base;
using Base::coeffRef;
EIGEN_DENSE_PUBLIC_INTERFACE(Transpose<MatrixType>)
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(TransposeImpl)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Index innerStride() const { return derived().nestedExpression().innerStride(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Index outerStride() const { return derived().nestedExpression().outerStride(); }
typedef typename internal::conditional<
internal::is_lvalue<MatrixType>::value,
Scalar,
const Scalar
>::type ScalarWithConstIfNotLvalue;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
ScalarWithConstIfNotLvalue* data() { return derived().nestedExpression().data(); }
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar* data() const { return derived().nestedExpression().data(); }
// FIXME: shall we keep the const version of coeffRef?
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar& coeffRef(Index rowId, Index colId) const
{
return derived().nestedExpression().coeffRef(colId, rowId);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const Scalar& coeffRef(Index index) const
{
return derived().nestedExpression().coeffRef(index);
}
protected:
EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(TransposeImpl)
};
/** \returns an expression of the transpose of *this.
*
* Example: \include MatrixBase_transpose.cpp
* Output: \verbinclude MatrixBase_transpose.out
*
* \warning If you want to replace a matrix by its own transpose, do \b NOT do this:
* \code
* m = m.transpose(); // bug!!! caused by aliasing effect
* \endcode
* Instead, use the transposeInPlace() method:
* \code
* m.transposeInPlace();
* \endcode
* which gives Eigen good opportunities for optimization, or alternatively you can also do:
* \code
* m = m.transpose().eval();
* \endcode
*
* \sa transposeInPlace(), adjoint() */
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
Transpose<Derived>
DenseBase<Derived>::transpose()
{
return TransposeReturnType(derived());
}
/** This is the const version of transpose().
*
* Make sure you read the warning for transpose() !
*
* \sa transposeInPlace(), adjoint() */
template<typename Derived>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
typename DenseBase<Derived>::ConstTransposeReturnType
DenseBase<Derived>::transpose() const
{
return ConstTransposeReturnType(derived());
}
/** \returns an expression of the adjoint (i.e. conjugate transpose) of *this.
*
* Example: \include MatrixBase_adjoint.cpp
* Output: \verbinclude MatrixBase_adjoint.out
*
* \warning If you want to replace a matrix by its own adjoint, do \b NOT do this:
* \code
* m = m.adjoint(); // bug!!! caused by aliasing effect
* \endcode
* Instead, use the adjointInPlace() method:
* \code
* m.adjointInPlace();
* \endcode
* which gives Eigen good opportunities for optimization, or alternatively you can also do:
* \code
* m = m.adjoint().eval();
* \endcode
*
* \sa adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op */
template<typename Derived>
EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::AdjointReturnType
MatrixBase<Derived>::adjoint() const
{
return AdjointReturnType(this->transpose());
}
/***************************************************************************
* "in place" transpose implementation
***************************************************************************/
namespace internal {
template<typename MatrixType,
bool IsSquare = (MatrixType::RowsAtCompileTime == MatrixType::ColsAtCompileTime) && MatrixType::RowsAtCompileTime!=Dynamic,
bool MatchPacketSize =
(int(MatrixType::RowsAtCompileTime) == int(internal::packet_traits<typename MatrixType::Scalar>::size))
&& (internal::evaluator<MatrixType>::Flags&PacketAccessBit) >
struct inplace_transpose_selector;
template<typename MatrixType>
struct inplace_transpose_selector<MatrixType,true,false> { // square matrix
static void run(MatrixType& m) {
m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose().template triangularView<StrictlyUpper>());
}
};
template<typename MatrixType>
struct inplace_transpose_selector<MatrixType,true,true> { // PacketSize x PacketSize
static void run(MatrixType& m) {
typedef typename MatrixType::Scalar Scalar;
typedef typename internal::packet_traits<typename MatrixType::Scalar>::type Packet;
const Index PacketSize = internal::packet_traits<Scalar>::size;
const Index Alignment = internal::evaluator<MatrixType>::Alignment;
PacketBlock<Packet> A;
for (Index i=0; i<PacketSize; ++i)
A.packet[i] = m.template packetByOuterInner<Alignment>(i,0);
internal::ptranspose(A);
for (Index i=0; i<PacketSize; ++i)
m.template writePacket<Alignment>(m.rowIndexByOuterInner(i,0), m.colIndexByOuterInner(i,0), A.packet[i]);
}
};
template <typename MatrixType, Index Alignment>
void BlockedInPlaceTranspose(MatrixType& m) {
typedef typename MatrixType::Scalar Scalar;
typedef typename internal::packet_traits<typename MatrixType::Scalar>::type Packet;
const Index PacketSize = internal::packet_traits<Scalar>::size;
eigen_assert(m.rows() == m.cols());
int row_start = 0;
for (; row_start + PacketSize <= m.rows(); row_start += PacketSize) {
for (int col_start = row_start; col_start + PacketSize <= m.cols(); col_start += PacketSize) {
PacketBlock<Packet> A;
if (row_start == col_start) {
for (Index i=0; i<PacketSize; ++i)
A.packet[i] = m.template packetByOuterInner<Alignment>(row_start + i,col_start);
internal::ptranspose(A);
for (Index i=0; i<PacketSize; ++i)
m.template writePacket<Alignment>(m.rowIndexByOuterInner(row_start + i, col_start), m.colIndexByOuterInner(row_start + i,col_start), A.packet[i]);
} else {
PacketBlock<Packet> B;
for (Index i=0; i<PacketSize; ++i) {
A.packet[i] = m.template packetByOuterInner<Alignment>(row_start + i,col_start);
B.packet[i] = m.template packetByOuterInner<Alignment>(col_start + i, row_start);
}
internal::ptranspose(A);
internal::ptranspose(B);
for (Index i=0; i<PacketSize; ++i) {
m.template writePacket<Alignment>(m.rowIndexByOuterInner(row_start + i, col_start), m.colIndexByOuterInner(row_start + i,col_start), B.packet[i]);
m.template writePacket<Alignment>(m.rowIndexByOuterInner(col_start + i, row_start), m.colIndexByOuterInner(col_start + i,row_start), A.packet[i]);
}
}
}
}
for (Index row = row_start; row < m.rows(); ++row) {
m.matrix().row(row).head(row).swap(
m.matrix().col(row).head(row).transpose());
}
}
template<typename MatrixType,bool MatchPacketSize>
struct inplace_transpose_selector<MatrixType,false,MatchPacketSize> { // non square or dynamic matrix
static void run(MatrixType& m) {
typedef typename MatrixType::Scalar Scalar;
if (m.rows() == m.cols()) {
const Index PacketSize = internal::packet_traits<Scalar>::size;
if (!NumTraits<Scalar>::IsComplex && m.rows() >= PacketSize) {
if ((m.rows() % PacketSize) == 0)
BlockedInPlaceTranspose<MatrixType,internal::evaluator<MatrixType>::Alignment>(m);
else
BlockedInPlaceTranspose<MatrixType,Unaligned>(m);
}
else {
m.matrix().template triangularView<StrictlyUpper>().swap(m.matrix().transpose().template triangularView<StrictlyUpper>());
}
} else {
m = m.transpose().eval();
}
}
};
} // end namespace internal
/** This is the "in place" version of transpose(): it replaces \c *this by its own transpose.
* Thus, doing
* \code
* m.transposeInPlace();
* \endcode
* has the same effect on m as doing
* \code
* m = m.transpose().eval();
* \endcode
* and is faster and also safer because in the latter line of code, forgetting the eval() results
* in a bug caused by \ref TopicAliasing "aliasing".
*
* Notice however that this method is only useful if you want to replace a matrix by its own transpose.
* If you just need the transpose of a matrix, use transpose().
*
* \note if the matrix is not square, then \c *this must be a resizable matrix.
* This excludes (non-square) fixed-size matrices, block-expressions and maps.
*
* \sa transpose(), adjoint(), adjointInPlace() */
template<typename Derived>
EIGEN_DEVICE_FUNC inline void DenseBase<Derived>::transposeInPlace()
{
eigen_assert((rows() == cols() || (RowsAtCompileTime == Dynamic && ColsAtCompileTime == Dynamic))
&& "transposeInPlace() called on a non-square non-resizable matrix");
internal::inplace_transpose_selector<Derived>::run(derived());
}
/***************************************************************************
* "in place" adjoint implementation
***************************************************************************/
/** This is the "in place" version of adjoint(): it replaces \c *this by its own transpose.
* Thus, doing
* \code
* m.adjointInPlace();
* \endcode
* has the same effect on m as doing
* \code
* m = m.adjoint().eval();
* \endcode
* and is faster and also safer because in the latter line of code, forgetting the eval() results
* in a bug caused by aliasing.
*
* Notice however that this method is only useful if you want to replace a matrix by its own adjoint.
* If you just need the adjoint of a matrix, use adjoint().
*
* \note if the matrix is not square, then \c *this must be a resizable matrix.
* This excludes (non-square) fixed-size matrices, block-expressions and maps.
*
* \sa transpose(), adjoint(), transposeInPlace() */
template<typename Derived>
EIGEN_DEVICE_FUNC inline void MatrixBase<Derived>::adjointInPlace()
{
derived() = adjoint().eval();
}
#ifndef EIGEN_NO_DEBUG
// The following is to detect aliasing problems in most common cases.
namespace internal {
template<bool DestIsTransposed, typename OtherDerived>
struct check_transpose_aliasing_compile_time_selector
{
enum { ret = bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed };
};
template<bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
struct check_transpose_aliasing_compile_time_selector<DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
{
enum { ret = bool(blas_traits<DerivedA>::IsTransposed) != DestIsTransposed
|| bool(blas_traits<DerivedB>::IsTransposed) != DestIsTransposed
};
};
template<typename Scalar, bool DestIsTransposed, typename OtherDerived>
struct check_transpose_aliasing_run_time_selector
{
static bool run(const Scalar* dest, const OtherDerived& src)
{
return (bool(blas_traits<OtherDerived>::IsTransposed) != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src));
}
};
template<typename Scalar, bool DestIsTransposed, typename BinOp, typename DerivedA, typename DerivedB>
struct check_transpose_aliasing_run_time_selector<Scalar,DestIsTransposed,CwiseBinaryOp<BinOp,DerivedA,DerivedB> >
{
static bool run(const Scalar* dest, const CwiseBinaryOp<BinOp,DerivedA,DerivedB>& src)
{
return ((blas_traits<DerivedA>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.lhs())))
|| ((blas_traits<DerivedB>::IsTransposed != DestIsTransposed) && (dest!=0 && dest==(const Scalar*)extract_data(src.rhs())));
}
};
// the following selector, checkTransposeAliasing_impl, based on MightHaveTransposeAliasing,
// is because when the condition controlling the assert is known at compile time, ICC emits a warning.
// This is actually a good warning: in expressions that don't have any transposing, the condition is
// known at compile time to be false, and using that, we can avoid generating the code of the assert again
// and again for all these expressions that don't need it.
template<typename Derived, typename OtherDerived,
bool MightHaveTransposeAliasing
= check_transpose_aliasing_compile_time_selector
<blas_traits<Derived>::IsTransposed,OtherDerived>::ret
>
struct checkTransposeAliasing_impl
{
static void run(const Derived& dst, const OtherDerived& other)
{
eigen_assert((!check_transpose_aliasing_run_time_selector
<typename Derived::Scalar,blas_traits<Derived>::IsTransposed,OtherDerived>
::run(extract_data(dst), other))
&& "aliasing detected during transposition, use transposeInPlace() "
"or evaluate the rhs into a temporary using .eval()");
}
};
template<typename Derived, typename OtherDerived>
struct checkTransposeAliasing_impl<Derived, OtherDerived, false>
{
static void run(const Derived&, const OtherDerived&)
{
}
};
template<typename Dst, typename Src>
void check_for_aliasing(const Dst &dst, const Src &src)
{
if((!Dst::IsVectorAtCompileTime) && dst.rows()>1 && dst.cols()>1)
internal::checkTransposeAliasing_impl<Dst, Src>::run(dst, src);
}
} // end namespace internal
#endif // EIGEN_NO_DEBUG
} // end namespace Eigen
#endif // EIGEN_TRANSPOSE_H

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