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This commit is contained in:
Benoit Jacob 2009-10-28 19:06:45 -04:00
commit e8dd552257
34 changed files with 2159 additions and 285 deletions
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1
Eigen/Core
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@ -200,6 +200,7 @@ namespace Eigen {
#include "src/Core/products/TriangularMatrixMatrix.h"
#include "src/Core/products/TriangularSolverMatrix.h"
#include "src/Core/BandMatrix.h"
#include "src/Core/ExpressionMaker.h"
} // namespace Eigen

1
Eigen/Sparse
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@ -110,6 +110,7 @@ namespace Eigen {
#include "src/Sparse/SparseLLT.h"
#include "src/Sparse/SparseLDLT.h"
#include "src/Sparse/SparseLU.h"
#include "src/Sparse/SparseExpressionMaker.h"
#ifdef EIGEN_CHOLMOD_SUPPORT
# include "src/Sparse/CholmodSupport.h"

18
Eigen/src/Core/Block.h
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@ -33,10 +33,10 @@
* \param MatrixType the type of the object in which we are taking a block
* \param BlockRows the number of rows of the block we are taking at compile time (optional)
* \param BlockCols the number of columns of the block we are taking at compile time (optional)
* \param _PacketAccess allows to enforce aligned loads and stores if set to \b ForceAligned.
* The default is \b AsRequested. This parameter is internaly used by Eigen
* in expressions such as \code mat.block() += other; \endcode and most of
* the time this is the only way it is used.
* \param _PacketAccess \internal used to enforce aligned loads in expressions such as
* \code mat.block() += other; \endcode. Possible values are
* \c AsRequested (default) and \c EnforceAlignedAccess.
* See class MapBase for more details.
* \param _DirectAccessStatus \internal used for partial specialization
*
* This class represents an expression of either a fixed-size or dynamic-size block. It is the return
@ -84,9 +84,9 @@ struct ei_traits<Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectA
CoeffReadCost = ei_traits<MatrixType>::CoeffReadCost,
PacketAccess = _PacketAccess
};
typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
typedef typename ei_meta_if<int(PacketAccess)==EnforceAlignedAccess,
Block<MatrixType, BlockRows, BlockCols, _PacketAccess, _DirectAccessStatus>&,
Block<MatrixType, BlockRows, BlockCols, ForceAligned, _DirectAccessStatus> >::ret AlignedDerivedType;
Block<MatrixType, BlockRows, BlockCols, EnforceAlignedAccess, _DirectAccessStatus> >::ret AlignedDerivedType;
};
template<typename MatrixType, int BlockRows, int BlockCols, int PacketAccess, int _DirectAccessStatus> class Block
@ -228,13 +228,13 @@ class Block<MatrixType,BlockRows,BlockCols,PacketAccess,HasDirectAccess>
class InnerIterator;
typedef typename ei_traits<Block>::AlignedDerivedType AlignedDerivedType;
friend class Block<MatrixType,BlockRows,BlockCols,PacketAccess==AsRequested?ForceAligned:AsRequested,HasDirectAccess>;
friend class Block<MatrixType,BlockRows,BlockCols,PacketAccess==EnforceAlignedAccess?AsRequested:EnforceAlignedAccess,HasDirectAccess>;
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Block)
AlignedDerivedType _convertToForceAligned()
AlignedDerivedType _convertToEnforceAlignedAccess()
{
return Block<MatrixType,BlockRows,BlockCols,ForceAligned,HasDirectAccess>
return Block<MatrixType,BlockRows,BlockCols,EnforceAlignedAccess,HasDirectAccess>
(m_matrix, Base::m_data, Base::m_rows.value(), Base::m_cols.value());
}

61
Eigen/src/Core/ExpressionMaker.h Normal file
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@ -0,0 +1,61 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_EXPRESSIONMAKER_H
#define EIGEN_EXPRESSIONMAKER_H
// computes the shape of a matrix from its traits flag
template<typename XprType> struct ei_shape_of
{
enum { ret = ei_traits<XprType>::Flags&SparseBit ? IsSparse : IsDense };
};
// Since the Sparse module is completely separated from the Core module, there is
// no way to write the type of a generic expression working for both dense and sparse
// matrix. Unless we change the overall design, here is a workaround.
// There is an example in unsuported/Eigen/src/AutoDiff/AutoDiffScalar.
template<typename XprType, int Shape = ei_shape_of<XprType>::ret>
struct MakeNestByValue
{
typedef NestByValue<XprType> Type;
};
template<typename Func, typename XprType, int Shape = ei_shape_of<XprType>::ret>
struct MakeCwiseUnaryOp
{
typedef CwiseUnaryOp<Func,XprType> Type;
};
template<typename Func, typename A, typename B, int Shape = ei_shape_of<A>::ret>
struct MakeCwiseBinaryOp
{
typedef CwiseBinaryOp<Func,A,B> Type;
};
// TODO complete the list
#endif // EIGEN_EXPRESSIONMAKER_H

35
Eigen/src/Core/Map.h
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@ -31,16 +31,14 @@
* \brief A matrix or vector expression mapping an existing array of data.
*
* \param MatrixType the equivalent matrix type of the mapped data
* \param _PacketAccess allows to enforce aligned loads and stores if set to ForceAligned.
* The default is AsRequested. This parameter is internaly used by Eigen
* in expressions such as \code Map<...>(...) += other; \endcode and most
* of the time this is the only way it is used.
* \param PointerAlignment specifies whether the pointer is \c Aligned, or \c Unaligned.
* The default is \c Unaligned.
*
* This class represents a matrix or vector expression mapping an existing array of data.
* It can be used to let Eigen interface without any overhead with non-Eigen data structures,
* such as plain C arrays or structures from other libraries.
*
* \b Tips: to change the array of data mapped by a Map object, you can use the C++
* \b Tip: to change the array of data mapped by a Map object, you can use the C++
* placement new syntax:
*
* Example: \include Map_placement_new.cpp
@ -48,22 +46,27 @@
*
* This class is the return type of Matrix::Map() but can also be used directly.
*
* \b Note \b to \b Eigen \b developers: The template parameter \c PointerAlignment
* can also be or-ed with \c EnforceAlignedAccess in order to enforce aligned read
* in expressions such as \code A += B; \endcode. See class MapBase for further details.
*
* \sa Matrix::Map()
*/
template<typename MatrixType, int _PacketAccess>
struct ei_traits<Map<MatrixType, _PacketAccess> > : public ei_traits<MatrixType>
template<typename MatrixType, int Options>
struct ei_traits<Map<MatrixType, Options> > : public ei_traits<MatrixType>
{
enum {
PacketAccess = _PacketAccess,
Flags = ei_traits<MatrixType>::Flags & ~AlignedBit
PacketAccess = Options & EnforceAlignedAccess,
Flags = (Options&Aligned)==Aligned ? ei_traits<MatrixType>::Flags | AlignedBit
: ei_traits<MatrixType>::Flags & ~AlignedBit
};
typedef typename ei_meta_if<int(PacketAccess)==ForceAligned,
Map<MatrixType, _PacketAccess>&,
Map<MatrixType, ForceAligned> >::ret AlignedDerivedType;
typedef typename ei_meta_if<int(PacketAccess)==EnforceAlignedAccess,
Map<MatrixType, Options>&,
Map<MatrixType, Options|EnforceAlignedAccess> >::ret AlignedDerivedType;
};
template<typename MatrixType, int PacketAccess> class Map
: public MapBase<Map<MatrixType, PacketAccess> >
template<typename MatrixType, int Options> class Map
: public MapBase<Map<MatrixType, Options> >
{
public:
@ -72,9 +75,9 @@ template<typename MatrixType, int PacketAccess> class Map
inline int stride() const { return this->innerSize(); }
AlignedDerivedType _convertToForceAligned()
AlignedDerivedType _convertToEnforceAlignedAccess()
{
return Map<MatrixType,ForceAligned>(Base::m_data, Base::m_rows.value(), Base::m_cols.value());
return AlignedDerivedType(Base::m_data, Base::m_rows.value(), Base::m_cols.value());
}
inline Map(const Scalar* data) : Base(data) {}

40
Eigen/src/Core/MapBase.h
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@ -32,11 +32,17 @@
*
* Expression classes inheriting MapBase must define the constant \c PacketAccess,
* and type \c AlignedDerivedType in their respective ei_traits<> specialization structure.
* The value of \c PacketAccess can be either:
* - \b ForceAligned which enforces both aligned loads and stores
* - \b AsRequested which is the default behavior
* The value of \c PacketAccess can be either \b AsRequested, or set to \b EnforceAlignedAccess which
* enforces both aligned loads and stores.
*
* \c EnforceAlignedAccess is automatically set in expressions such as
* \code A += B; \endcode where A is either a Block or a Map. Here,
* this expression is transfomed into \code A = A_with_EnforceAlignedAccess + B; \endcode
* avoiding unaligned loads from A. Indeed, since Eigen's packet evaluation mechanism
* automatically align to the destination matrix, we know that loads to A will be aligned too.
*
* The type \c AlignedDerivedType should correspond to the equivalent expression type
* with \c PacketAccess being \c ForceAligned.
* with \c PacketAccess set to \c EnforceAlignedAccess.
*
* \sa class Map, class Block
*/
@ -79,19 +85,19 @@ template<typename Derived> class MapBase
* \sa MapBase::stride() */
inline const Scalar* data() const { return m_data; }
template<bool IsForceAligned,typename Dummy> struct force_aligned_impl {
template<bool IsEnforceAlignedAccess,typename Dummy> struct force_aligned_impl {
static AlignedDerivedType run(MapBase& a) { return a.derived(); }
};
template<typename Dummy> struct force_aligned_impl<false,Dummy> {
static AlignedDerivedType run(MapBase& a) { return a.derived()._convertToForceAligned(); }
static AlignedDerivedType run(MapBase& a) { return a.derived()._convertToEnforceAlignedAccess(); }
};
/** \returns an expression equivalent to \c *this but having the \c PacketAccess constant
* set to \c ForceAligned. Must be reimplemented by the derived class. */
* set to \c EnforceAlignedAccess. Must be reimplemented by the derived class. */
AlignedDerivedType forceAligned()
{
return force_aligned_impl<int(PacketAccess)==int(ForceAligned),Derived>::run(*this);
return force_aligned_impl<int(PacketAccess)==int(EnforceAlignedAccess),Derived>::run(*this);
}
inline const Scalar& coeff(int row, int col) const
@ -131,7 +137,7 @@ template<typename Derived> class MapBase
template<int LoadMode>
inline PacketScalar packet(int row, int col) const
{
return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>
return ei_ploadt<Scalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : LoadMode>
(m_data + (IsRowMajor ? col + row * stride()
: row + col * stride()));
}
@ -139,13 +145,13 @@ template<typename Derived> class MapBase
template<int LoadMode>
inline PacketScalar packet(int index) const
{
return ei_ploadt<Scalar, int(PacketAccess) == ForceAligned ? Aligned : LoadMode>(m_data + index);
return ei_ploadt<Scalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : LoadMode>(m_data + index);
}
template<int StoreMode>
inline void writePacket(int row, int col, const PacketScalar& x)
{
ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : StoreMode>
(const_cast<Scalar*>(m_data) + (IsRowMajor ? col + row * stride()
: row + col * stride()), x);
}
@ -153,13 +159,14 @@ template<typename Derived> class MapBase
template<int StoreMode>
inline void writePacket(int index, const PacketScalar& x)
{
ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == ForceAligned ? Aligned : StoreMode>
ei_pstoret<Scalar, PacketScalar, int(PacketAccess) == EnforceAlignedAccess ? Aligned : StoreMode>
(const_cast<Scalar*>(m_data) + index, x);
}
inline MapBase(const Scalar* data) : m_data(data), m_rows(RowsAtCompileTime), m_cols(ColsAtCompileTime)
{
EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived)
checkDataAlignment();
}
inline MapBase(const Scalar* data, int size)
@ -170,6 +177,7 @@ template<typename Derived> class MapBase
EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
ei_assert(size >= 0);
ei_assert(data == 0 || SizeAtCompileTime == Dynamic || SizeAtCompileTime == size);
checkDataAlignment();
}
inline MapBase(const Scalar* data, int rows, int cols)
@ -178,6 +186,7 @@ template<typename Derived> class MapBase
ei_assert( (data == 0)
|| ( rows >= 0 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols >= 0 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)));
checkDataAlignment();
}
Derived& operator=(const MapBase& other)
@ -215,6 +224,13 @@ template<typename Derived> class MapBase
{ return derived() = forceAligned() / other; }
protected:
void checkDataAlignment() const
{
ei_assert( ((!(ei_traits<Derived>::Flags&AlignedBit))
|| ((std::size_t(m_data)&0xf)==0)) && "data is not aligned");
}
const Scalar* EIGEN_RESTRICT m_data;
const ei_int_if_dynamic<RowsAtCompileTime> m_rows;
const ei_int_if_dynamic<ColsAtCompileTime> m_cols;

14
Eigen/src/Core/Matrix.h
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@ -58,6 +58,9 @@ template <typename Derived, typename OtherDerived, bool IsVector = static_cast<b
* \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
* \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
*
* \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
* \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
*
* See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
*
* You can access elements of vectors and matrices using normal subscripting:
@ -794,11 +797,20 @@ typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
/** \ingroup matrixtypedefs */ \
typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)

19
Eigen/src/Core/MatrixBase.h
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@ -190,6 +190,25 @@ template<typename Derived> class MatrixBase
* i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
int innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }
/** Only plain matrices, not expressions may be resized; therefore the only useful resize method is
* Matrix::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
void resize(int size)
{
ei_assert(size == this->size()
&& "MatrixBase::resize() does not actually allow to resize.");
}
/** Only plain matrices, not expressions may be resized; therefore the only useful resize method is
* Matrix::resize(). The present method only asserts that the new size equals the old size, and does
* nothing else.
*/
void resize(int rows, int cols)
{
ei_assert(rows == this->rows() && cols == this->cols()
&& "MatrixBase::resize() does not actually allow to resize.");
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal the plain matrix type corresponding to this expression. Note that is not necessarily
* exactly the return type of eval(): in the case of plain matrices, the return type of eval() is a const

2
Eigen/src/Core/StableNorm.h
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@ -59,7 +59,7 @@ MatrixBase<Derived>::stableNorm() const
RealScalar invScale = 1;
RealScalar ssq = 0; // sum of square
enum {
Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? ForceAligned : AsRequested
Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? EnforceAlignedAccess : AsRequested
};
int n = size();
int bi=0;

4
Eigen/src/Core/util/Constants.h
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@ -196,8 +196,8 @@ const unsigned int UnitLowerTriangular = LowerTriangularBit | UnitDiagBit;
enum { DiagonalOnTheLeft, DiagonalOnTheRight };
enum { Aligned, Unaligned };
enum { ForceAligned, AsRequested };
enum { Unaligned=0, Aligned=1 };
enum { AsRequested=0, EnforceAlignedAccess=2 };
enum { ConditionalJumpCost = 5 };
enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
enum DirectionType { Vertical, Horizontal, BothDirections };

1
Eigen/src/Core/util/ForwardDeclarations.h
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@ -130,6 +130,7 @@ template<typename Scalar> class PlanarRotation;
// Geometry module:
template<typename Derived, int _Dim> class RotationBase;
template<typename Lhs, typename Rhs> class Cross;
template<typename Derived> class QuaternionBase;
template<typename Scalar> class Quaternion;
template<typename Scalar> class Rotation2D;
template<typename Scalar> class AngleAxis;

2
Eigen/src/Core/util/Macros.h
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@ -256,7 +256,7 @@ using Eigen::ei_cos;
// C++0x features
#if defined(__GXX_EXPERIMENTAL_CXX0X__) || (defined(_MSC_VER) && (_MSC_VER >= 1600))
#define EIGEN_REF_TO_TEMPORARY &&
#define EIGEN_REF_TO_TEMPORARY const &
#else
#define EIGEN_REF_TO_TEMPORARY const &
#endif

3
Eigen/src/Core/util/StaticAssert.h
View File

@ -78,7 +78,8 @@
INVALID_MATRIX_TEMPLATE_PARAMETERS,
BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX,
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE
THE_MATRIX_OR_EXPRESSION_THAT_YOU_PASSED_DOES_NOT_HAVE_THE_EXPECTED_TYPE,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES
};
};

411
Eigen/src/Geometry/Quaternion.h
View File

@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -25,11 +26,6 @@
#ifndef EIGEN_QUATERNION_H
#define EIGEN_QUATERNION_H
template<typename Other,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct ei_quaternion_assign_impl;
/** \geometry_module \ingroup Geometry_Module
*
* \class Quaternion
@ -52,28 +48,33 @@ struct ei_quaternion_assign_impl;
* \sa class AngleAxis, class Transform
*/
template<typename _Scalar> struct ei_traits<Quaternion<_Scalar> >
template<typename Other,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct ei_quaternionbase_assign_impl;
template<typename Scalar> class Quaternion; // [XXX] => remove when Quaternion becomes Quaternion
template<typename Derived>
struct ei_traits<QuaternionBase<Derived> >
{
typedef _Scalar Scalar;
typedef typename ei_traits<Derived>::Scalar Scalar;
enum {
PacketAccess = ei_traits<Derived>::PacketAccess
};
};
template<typename _Scalar>
class Quaternion : public RotationBase<Quaternion<_Scalar>,3>
template<class Derived>
class QuaternionBase : public RotationBase<Derived, 3>
{
typedef RotationBase<Quaternion<_Scalar>,3> Base;
typedef RotationBase<Derived, 3> Base;
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,4)
using Base::operator*;
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
typedef typename ei_traits<QuaternionBase<Derived> >::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
/** the type of the Coefficients 4-vector */
typedef Matrix<Scalar, 4, 1> Coefficients;
// typedef typename Matrix<Scalar,4,1> Coefficients;
/** the type of a 3D vector */
typedef Matrix<Scalar,3,1> Vector3;
/** the equivalent rotation matrix type */
@ -82,34 +83,130 @@ public:
typedef AngleAxis<Scalar> AngleAxisType;
/** \returns the \c x coefficient */
inline Scalar x() const { return m_coeffs.coeff(0); }
inline Scalar x() const { return this->derived().coeffs().coeff(0); }
/** \returns the \c y coefficient */
inline Scalar y() const { return m_coeffs.coeff(1); }
inline Scalar y() const { return this->derived().coeffs().coeff(1); }
/** \returns the \c z coefficient */
inline Scalar z() const { return m_coeffs.coeff(2); }
inline Scalar z() const { return this->derived().coeffs().coeff(2); }
/** \returns the \c w coefficient */
inline Scalar w() const { return m_coeffs.coeff(3); }
inline Scalar w() const { return this->derived().coeffs().coeff(3); }
/** \returns a reference to the \c x coefficient */
inline Scalar& x() { return m_coeffs.coeffRef(0); }
inline Scalar& x() { return this->derived().coeffs().coeffRef(0); }
/** \returns a reference to the \c y coefficient */
inline Scalar& y() { return m_coeffs.coeffRef(1); }
inline Scalar& y() { return this->derived().coeffs().coeffRef(1); }
/** \returns a reference to the \c z coefficient */
inline Scalar& z() { return m_coeffs.coeffRef(2); }
inline Scalar& z() { return this->derived().coeffs().coeffRef(2); }
/** \returns a reference to the \c w coefficient */
inline Scalar& w() { return m_coeffs.coeffRef(3); }
inline Scalar& w() { return this->derived().coeffs().coeffRef(3); }
/** \returns a read-only vector expression of the imaginary part (x,y,z) */
inline const Block<Coefficients,3,1> vec() const { return m_coeffs.template start<3>(); }
inline const VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() const { return this->derived().coeffs().template start<3>(); }
/** \returns a vector expression of the imaginary part (x,y,z) */
inline Block<Coefficients,3,1> vec() { return m_coeffs.template start<3>(); }
inline VectorBlock<typename ei_traits<Derived>::Coefficients,3> vec() { return this->derived().coeffs().template start<3>(); }
/** \returns a read-only vector expression of the coefficients (x,y,z,w) */
inline const Coefficients& coeffs() const { return m_coeffs; }
inline const typename ei_traits<Derived>::Coefficients& coeffs() const { return this->derived().coeffs(); }
/** \returns a vector expression of the coefficients (x,y,z,w) */
inline Coefficients& coeffs() { return m_coeffs; }
inline typename ei_traits<Derived>::Coefficients& coeffs() { return this->derived().coeffs(); }
template<class OtherDerived> QuaternionBase& operator=(const QuaternionBase<OtherDerived>& other);
QuaternionBase& operator=(const AngleAxisType& aa);
template<class OtherDerived>
QuaternionBase& operator=(const MatrixBase<OtherDerived>& m);
/** \returns a quaternion representing an identity rotation
* \sa MatrixBase::Identity()
*/
inline static Quaternion<Scalar> Identity() { return Quaternion<Scalar>(1, 0, 0, 0); }
/** \sa Quaternion2::Identity(), MatrixBase::setIdentity()
*/
inline QuaternionBase& setIdentity() { coeffs() << 0, 0, 0, 1; return *this; }
/** \returns the squared norm of the quaternion's coefficients
* \sa Quaternion2::norm(), MatrixBase::squaredNorm()
*/
inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
/** \returns the norm of the quaternion's coefficients
* \sa Quaternion2::squaredNorm(), MatrixBase::norm()
*/
inline Scalar norm() const { return coeffs().norm(); }
/** Normalizes the quaternion \c *this
* \sa normalized(), MatrixBase::normalize() */
inline void normalize() { coeffs().normalize(); }
/** \returns a normalized version of \c *this
* \sa normalize(), MatrixBase::normalized() */
inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
/** \returns the dot product of \c *this and \a other
* Geometrically speaking, the dot product of two unit quaternions
* corresponds to the cosine of half the angle between the two rotations.
* \sa angularDistance()
*/
template<class OtherDerived> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
template<class OtherDerived> inline Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
Matrix3 toRotationMatrix(void) const;
template<typename Derived1, typename Derived2>
QuaternionBase& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
template<class OtherDerived> inline Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
template<class OtherDerived> inline QuaternionBase& operator*= (const QuaternionBase<OtherDerived>& q);
Quaternion<Scalar> inverse(void) const;
Quaternion<Scalar> conjugate(void) const;
template<class OtherDerived> Quaternion<Scalar> slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const;
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
* determined by \a prec.
*
* \sa MatrixBase::isApprox() */
bool isApprox(const QuaternionBase& other, RealScalar prec = precision<Scalar>()) const
{ return coeffs().isApprox(other.coeffs(), prec); }
Vector3 _transformVector(Vector3 v) const;
/** \returns \c *this with scalar type casted to \a NewScalarType
*
* Note that if \a NewScalarType is equal to the current scalar type of \c *this
* then this function smartly returns a const reference to \c *this.
*/
template<typename NewScalarType>
inline typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
{
return typename ei_cast_return_type<Derived,Quaternion<NewScalarType> >::type(
coeffs().template cast<NewScalarType>());
}
};
template<typename _Scalar>
struct ei_traits<Quaternion<_Scalar> >
{
typedef _Scalar Scalar;
typedef Matrix<_Scalar,4,1> Coefficients;
enum{
PacketAccess = Aligned
};
};
template<typename _Scalar>
class Quaternion : public QuaternionBase<Quaternion<_Scalar> >{
typedef QuaternionBase<Quaternion<_Scalar> > Base;
public:
using Base::operator=;
typedef _Scalar Scalar;
typedef typename ei_traits<Quaternion<Scalar> >::Coefficients Coefficients;
typedef typename Base::AngleAxisType AngleAxisType;
/** Default constructor leaving the quaternion uninitialized. */
inline Quaternion() {}
@ -122,10 +219,14 @@ public:
* [\c x, \c y, \c z, \c w]
*/
inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z)
{ m_coeffs << x, y, z, w; }
{ coeffs() << x, y, z, w; }
/** Constructs and initialize a quaternion from the array data
* This constructor is also used to map an array */
inline Quaternion(const Scalar* data) : m_coeffs(data) {}
/** Copy constructor */
inline Quaternion(const Quaternion& other) { m_coeffs = other.m_coeffs; }
// template<class Derived> inline Quaternion(const QuaternionBase<Derived>& other) { m_coeffs = other.coeffs(); } [XXX] redundant with 703
/** Constructs and initializes a quaternion from the angle-axis \a aa */
explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
@ -133,121 +234,96 @@ public:
/** Constructs and initializes a quaternion from either:
* - a rotation matrix expression,
* - a 4D vector expression representing quaternion coefficients.
* \sa operator=(MatrixBase<Derived>)
*/
template<typename Derived>
explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
Quaternion& operator=(const Quaternion& other);
Quaternion& operator=(const AngleAxisType& aa);
template<typename Derived>
Quaternion& operator=(const MatrixBase<Derived>& m);
/** \returns a quaternion representing an identity rotation
* \sa MatrixBase::Identity()
*/
inline static Quaternion Identity() { return Quaternion(1, 0, 0, 0); }
/** \sa Quaternion::Identity(), MatrixBase::setIdentity()
*/
inline Quaternion& setIdentity() { m_coeffs << 0, 0, 0, 1; return *this; }
/** \returns the squared norm of the quaternion's coefficients
* \sa Quaternion::norm(), MatrixBase::squaredNorm()
*/
inline Scalar squaredNorm() const { return m_coeffs.squaredNorm(); }
/** \returns the norm of the quaternion's coefficients
* \sa Quaternion::squaredNorm(), MatrixBase::norm()
*/
inline Scalar norm() const { return m_coeffs.norm(); }
/** Normalizes the quaternion \c *this
* \sa normalized(), MatrixBase::normalize() */
inline void normalize() { m_coeffs.normalize(); }
/** \returns a normalized version of \c *this
* \sa normalize(), MatrixBase::normalized() */
inline Quaternion normalized() const { return Quaternion(m_coeffs.normalized()); }
/** \returns the dot product of \c *this and \a other
* Geometrically speaking, the dot product of two unit quaternions
* corresponds to the cosine of half the angle between the two rotations.
* \sa angularDistance()
*/
inline Scalar dot(const Quaternion& other) const { return m_coeffs.dot(other.m_coeffs); }
inline Scalar angularDistance(const Quaternion& other) const;
Matrix3 toRotationMatrix(void) const;
template<typename Derived1, typename Derived2>
Quaternion& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
inline Quaternion operator* (const Quaternion& q) const;
inline Quaternion& operator*= (const Quaternion& q);
Quaternion inverse(void) const;
Quaternion conjugate(void) const;
Quaternion slerp(Scalar t, const Quaternion& other) const;
/** \returns \c *this with scalar type casted to \a NewScalarType
*
* Note that if \a NewScalarType is equal to the current scalar type of \c *this
* then this function smartly returns a const reference to \c *this.
*/
template<typename NewScalarType>
inline typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type cast() const
{ return typename ei_cast_return_type<Quaternion,Quaternion<NewScalarType> >::type(*this); }
/** Copy constructor with scalar type conversion */
template<typename OtherScalarType>
inline explicit Quaternion(const Quaternion<OtherScalarType>& other)
template<class Derived>
inline explicit Quaternion(const QuaternionBase<Derived>& other)
{ m_coeffs = other.coeffs().template cast<Scalar>(); }
/** \returns \c true if \c *this is approximately equal to \a other, within the precision
* determined by \a prec.
*
* \sa MatrixBase::isApprox() */
bool isApprox(const Quaternion& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
{ return m_coeffs.isApprox(other.m_coeffs, prec); }
Vector3 _transformVector(Vector3 v) const;
inline Coefficients& coeffs() { return m_coeffs;}
inline const Coefficients& coeffs() const { return m_coeffs;}
protected:
Coefficients m_coeffs;
};
/** \ingroup Geometry_Module
* single precision quaternion type */
typedef Quaternion<float> Quaternionf;
/** \ingroup Geometry_Module
* double precision quaternion type */
typedef Quaternion<double> Quaterniond;
/* ########### Map<Quaternion> */
/** \class Map<Quaternion>
* \nonstableyet
*
* \brief Expression of a quaternion
*
* \param Scalar the type of the vector of diagonal coefficients
*
* \sa class Quaternion, class QuaternionBase
*/
template<typename _Scalar, int _PacketAccess>
struct ei_traits<Map<Quaternion<_Scalar>, _PacketAccess> >:
ei_traits<Quaternion<_Scalar> >
{
typedef _Scalar Scalar;
typedef Map<Matrix<_Scalar,4,1> > Coefficients;
enum {
PacketAccess = _PacketAccess
};
};
template<typename _Scalar, int PacketAccess>
class Map<Quaternion<_Scalar>, PacketAccess > : public QuaternionBase<Map<Quaternion<_Scalar>, PacketAccess> >, ei_no_assignment_operator {
public:
typedef _Scalar Scalar;
typedef typename ei_traits<Map<Quaternion<Scalar>, PacketAccess> >::Coefficients Coefficients;
inline Map<Quaternion<Scalar>, PacketAccess >(const Scalar* coeffs) : m_coeffs(coeffs) {}
inline Coefficients& coeffs() { return m_coeffs;}
inline const Coefficients& coeffs() const { return m_coeffs;}
protected:
Coefficients m_coeffs;
};
typedef Map<Quaternion<double> > QuaternionMapd;
typedef Map<Quaternion<float> > QuaternionMapf;
typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
// Generic Quaternion * Quaternion product
template<int Arch,typename Scalar> inline Quaternion<Scalar>
ei_quaternion_product(const Quaternion<Scalar>& a, const Quaternion<Scalar>& b)
template<int Arch, class Derived, class OtherDerived, typename Scalar, int PacketAccess> struct ei_quat_product
{
return Quaternion<Scalar>
(
a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
);
}
inline static Quaternion<Scalar> run(const QuaternionBase<Derived>& a, const QuaternionBase<OtherDerived>& b){
return Quaternion<Scalar>
(
a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
);
}
};
/** \returns the concatenation of two rotations as a quaternion-quaternion product */
template <typename Scalar>
inline Quaternion<Scalar> Quaternion<Scalar>::operator* (const Quaternion& other) const
template <class Derived>
template <class OtherDerived>
inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
{
return ei_quaternion_product<EiArch>(*this,other);
EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename OtherDerived::Scalar>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
return ei_quat_product<EiArch, Derived, OtherDerived,
typename ei_traits<Derived>::Scalar,
ei_traits<Derived>::PacketAccess && ei_traits<OtherDerived>::PacketAccess>::run(*this, other);
}
/** \sa operator*(Quaternion) */
template <typename Scalar>
inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& other)
template <class Derived>
template <class OtherDerived>
inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
{
return (*this = *this * other);
}
@ -256,12 +332,12 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& oth
* \remarks If the quaternion is used to rotate several points (>1)
* then it is much more efficient to first convert it to a 3x3 Matrix.
* Comparison of the operation cost for n transformations:
* - Quaternion: 30n
* - Quaternion2: 30n
* - Via a Matrix3: 24 + 15n
*/
template <typename Scalar>
inline typename Quaternion<Scalar>::Vector3
Quaternion<Scalar>::_transformVector(Vector3 v) const
template <class Derived>
inline typename QuaternionBase<Derived>::Vector3
QuaternionBase<Derived>::_transformVector(Vector3 v) const
{
// Note that this algorithm comes from the optimization by hand
// of the conversion to a Matrix followed by a Matrix/Vector product.
@ -272,17 +348,18 @@ Quaternion<Scalar>::_transformVector(Vector3 v) const
return v + this->w() * uv + this->vec().cross(uv);
}
template<typename Scalar>
inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const Quaternion& other)
template<class Derived>
template<class OtherDerived>
inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
{
m_coeffs = other.m_coeffs;
coeffs() = other.coeffs();
return *this;
}
/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
*/
template<typename Scalar>
inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa)
template<class Derived>
inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
{
Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
this->w() = ei_cos(ha);
@ -295,20 +372,23 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const AngleAxisType& aa
* - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
* and \a xpr is converted to a quaternion
*/
template<typename Scalar>
template<typename Derived>
inline Quaternion<Scalar>& Quaternion<Scalar>::operator=(const MatrixBase<Derived>& xpr)
template<class Derived>
template<class MatrixDerived>
inline QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
{
ei_quaternion_assign_impl<Derived>::run(*this, xpr.derived());
EIGEN_STATIC_ASSERT((ei_is_same_type<typename Derived::Scalar, typename MatrixDerived::Scalar>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
ei_quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
return *this;
}
/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
* be normalized, otherwise the result is undefined.
*/
template<typename Scalar>
inline typename Quaternion<Scalar>::Matrix3
Quaternion<Scalar>::toRotationMatrix(void) const
template<class Derived>
inline typename QuaternionBase<Derived>::Matrix3
QuaternionBase<Derived>::toRotationMatrix(void) const
{
// NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
// if not inlined then the cost of the return by value is huge ~ +35%,
@ -352,9 +432,9 @@ Quaternion<Scalar>::toRotationMatrix(void) const
* Note that the two input vectors do \b not have to be normalized, and
* do not need to have the same norm.
*/
template<typename Scalar>
template<class Derived>
template<typename Derived1, typename Derived2>
inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
inline QuaternionBase<Derived>& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
{
Vector3 v0 = a.normalized();
Vector3 v1 = b.normalized();
@ -393,19 +473,19 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBas
* Note that in most cases, i.e., if you simply want the opposite rotation,
* and/or the quaternion is normalized, then it is enough to use the conjugate.
*
* \sa Quaternion::conjugate()
* \sa Quaternion2::conjugate()
*/
template <typename Scalar>
inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
template <class Derived>
inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::inverse() const
{
// FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
Scalar n2 = this->squaredNorm();
if (n2 > 0)
return Quaternion(conjugate().coeffs() / n2);
return Quaternion<Scalar>(conjugate().coeffs() / n2);
else
{
// return an invalid result to flag the error
return Quaternion(Coefficients::Zero());
return Quaternion<Scalar>(ei_traits<Derived>::Coefficients::Zero());
}
}
@ -413,19 +493,20 @@ inline Quaternion<Scalar> Quaternion<Scalar>::inverse() const
* if the quaternion is normalized.
* The conjugate of a quaternion represents the opposite rotation.
*
* \sa Quaternion::inverse()
* \sa Quaternion2::inverse()
*/
template <typename Scalar>
inline Quaternion<Scalar> Quaternion<Scalar>::conjugate() const
template <class Derived>
inline Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::conjugate() const
{
return Quaternion(this->w(),-this->x(),-this->y(),-this->z());
return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z());
}
/** \returns the angle (in radian) between two rotations
* \sa dot()
*/
template <typename Scalar>
inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
template <class Derived>
template <class OtherDerived>
inline typename ei_traits<QuaternionBase<Derived> >::Scalar QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
{
double d = ei_abs(this->dot(other));
if (d>=1.0)
@ -436,14 +517,15 @@ inline Scalar Quaternion<Scalar>::angularDistance(const Quaternion& other) const
/** \returns the spherical linear interpolation between the two quaternions
* \c *this and \a other at the parameter \a t
*/
template <typename Scalar>
Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other) const
template <class Derived>
template <class OtherDerived>
Quaternion<typename ei_traits<QuaternionBase<Derived> >::Scalar> QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
{
static const Scalar one = Scalar(1) - precision<Scalar>();
Scalar d = this->dot(other);
Scalar absD = ei_abs(d);
if (absD>=one)
return *this;
return Quaternion<Scalar>(*this);
// theta is the angle between the 2 quaternions
Scalar theta = std::acos(absD);
@ -454,15 +536,15 @@ Quaternion<Scalar> Quaternion<Scalar>::slerp(Scalar t, const Quaternion& other)
if (d<0)
scale1 = -scale1;
return Quaternion(scale0 * m_coeffs + scale1 * other.m_coeffs);
return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
}
// set from a rotation matrix
template<typename Other>
struct ei_quaternion_assign_impl<Other,3,3>
struct ei_quaternionbase_assign_impl<Other,3,3>
{
typedef typename Other::Scalar Scalar;
inline static void run(Quaternion<Scalar>& q, const Other& mat)
template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& mat)
{
// This algorithm comes from "Quaternion Calculus and Fast Animation",
// Ken Shoemake, 1987 SIGGRAPH course notes
@ -498,13 +580,14 @@ struct ei_quaternion_assign_impl<Other,3,3>
// set from a vector of coefficients assumed to be a quaternion
template<typename Other>
struct ei_quaternion_assign_impl<Other,4,1>
struct ei_quaternionbase_assign_impl<Other,4,1>
{
typedef typename Other::Scalar Scalar;
inline static void run(Quaternion<Scalar>& q, const Other& vec)
template<class Derived> inline static void run(QuaternionBase<Derived>& q, const Other& vec)
{
q.coeffs() = vec;
}
};
#endif // EIGEN_QUATERNION_H

19
Eigen/src/Geometry/Transform.h
View File

@ -480,6 +480,15 @@ typedef Transform<double,2> Transform2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3> Transform3d;
/** \ingroup Geometry_Module */
typedef Transform<float,2,Isometry> Isometry2f;
/** \ingroup Geometry_Module */
typedef Transform<float,3,Isometry> Isometry3f;
/** \ingroup Geometry_Module */
typedef Transform<double,2,Isometry> Isometry2d;
/** \ingroup Geometry_Module */
typedef Transform<double,3,Isometry> Isometry3d;
/** \ingroup Geometry_Module */
typedef Transform<float,2> Affine2f;
/** \ingroup Geometry_Module */
@ -512,7 +521,7 @@ typedef Transform<double,3,Projective> Projective3d;
**************************/
#ifdef EIGEN_QT_SUPPORT
/** Initialises \c *this from a QMatrix assuming the dimension is 2.
/** Initializes \c *this from a QMatrix assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
@ -538,7 +547,7 @@ Transform<Scalar,Dim,Mode>& Transform<Scalar,Dim,Mode>::operator=(const QMatrix&
/** \returns a QMatrix from \c *this assuming the dimension is 2.
*
* \warning this convertion might loss data if \c *this is not affine
* \warning this conversion might loss data if \c *this is not affine
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
@ -551,7 +560,7 @@ QMatrix Transform<Scalar,Dim,Mode>::toQMatrix(void) const
matrix.coeff(0,2), matrix.coeff(1,2));
}
/** Initialises \c *this from a QTransform assuming the dimension is 2.
/** Initializes \c *this from a QTransform assuming the dimension is 2.
*
* This function is available only if the token EIGEN_QT_SUPPORT is defined.
*/
@ -899,7 +908,7 @@ struct ei_projective_transform_inverse<TransformType, Projective>
* \returns the inverse transformation according to some given knowledge
* on \c *this.
*
* \param traits allows to optimize the inversion process when the transformion
* \param traits allows to optimize the inversion process when the transformation
* is known to be not a general transformation. The possible values are:
* - Projective if the transformation is not necessarily affine, i.e., if the
* last row is not guaranteed to be [0 ... 0 1]
@ -968,7 +977,7 @@ struct ei_transform_take_affine_part<Transform<Scalar,Dim,AffineCompact> > {
};
/*****************************************************
*** Specializations of construct from matix ***
*** Specializations of construct from matrix ***
*****************************************************/
template<typename Other, int Mode, int Dim, int HDim>

12
Eigen/src/Geometry/Umeyama.h
View File

@ -117,7 +117,7 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
enum { Dimension = EIGEN_ENUM_MIN(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
typedef Matrix<Scalar, Dimension, 1> VectorType;
typedef typename ei_plain_matrix_type<Derived>::type MatrixType;
typedef Matrix<Scalar, Dimension, Dimension> MatrixType;
typedef typename ei_plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
const int m = src.rows(); // dimension
@ -131,17 +131,11 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, boo
const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
// demeaning of src and dst points
RowMajorMatrixType src_demean(m,n);
RowMajorMatrixType dst_demean(m,n);
for (int i=0; i<n; ++i)
{
src_demean.col(i) = src.col(i) - src_mean;
dst_demean.col(i) = dst.col(i) - dst_mean;
}
const RowMajorMatrixType src_demean = src.colwise() - src_mean;
const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
// Eq. (36)-(37)
const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
// const Scalar dst_var = dst_demean.rowwise().squaredNorm().sum() * one_over_n;
// Eq. (38)
const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();

36
Eigen/src/Geometry/arch/Geometry_SSE.h
View File

@ -26,24 +26,26 @@
#ifndef EIGEN_GEOMETRY_SSE_H
#define EIGEN_GEOMETRY_SSE_H
template<> inline Quaternion<float>
ei_quaternion_product<EiArch_SSE,float>(const Quaternion<float>& _a, const Quaternion<float>& _b)
template<class Derived, class OtherDerived> struct ei_quat_product<EiArch_SSE, Derived, OtherDerived, float, Aligned>
{
const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
Quaternion<float> res;
__m128 a = _a.coeffs().packet<Aligned>(0);
__m128 b = _b.coeffs().packet<Aligned>(0);
__m128 flip1 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,1,2,0,2),
ei_vec4f_swizzle1(b,2,0,1,2)),mask);
__m128 flip2 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,3,3,3,1),
ei_vec4f_swizzle1(b,0,1,2,1)),mask);
ei_pstore(&res.x(),
_mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,ei_vec4f_swizzle1(b,3,3,3,3)),
_mm_mul_ps(ei_vec4f_swizzle1(a,2,0,1,0),
ei_vec4f_swizzle1(b,1,2,0,0))),
_mm_add_ps(flip1,flip2)));
return res;
}
inline static Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
{
const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0,0,0,0x80000000));
Quaternion<float> res;
__m128 a = _a.coeffs().packet<Aligned>(0);
__m128 b = _b.coeffs().packet<Aligned>(0);
__m128 flip1 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,1,2,0,2),
ei_vec4f_swizzle1(b,2,0,1,2)),mask);
__m128 flip2 = _mm_xor_ps(_mm_mul_ps(ei_vec4f_swizzle1(a,3,3,3,1),
ei_vec4f_swizzle1(b,0,1,2,1)),mask);
ei_pstore(&res.x(),
_mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,ei_vec4f_swizzle1(b,3,3,3,3)),
_mm_mul_ps(ei_vec4f_swizzle1(a,2,0,1,0),
ei_vec4f_swizzle1(b,1,2,0,0))),
_mm_add_ps(flip1,flip2)));
return res;
}
};
template<typename VectorLhs,typename VectorRhs>
struct ei_cross3_impl<EiArch_SSE,VectorLhs,VectorRhs,float,true> {

48
Eigen/src/Sparse/SparseExpressionMaker.h Normal file
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@ -0,0 +1,48 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_SPARSE_EXPRESSIONMAKER_H
#define EIGEN_SPARSE_EXPRESSIONMAKER_H
template<typename XprType>
struct MakeNestByValue<XprType,IsSparse>
{
typedef SparseNestByValue<XprType> Type;
};
template<typename Func, typename XprType>
struct MakeCwiseUnaryOp<Func,XprType,IsSparse>
{
typedef SparseCwiseUnaryOp<Func,XprType> Type;
};
template<typename Func, typename A, typename B>
struct MakeCwiseBinaryOp<Func,A,B,IsSparse>
{
typedef SparseCwiseBinaryOp<Func,A,B> Type;
};
// TODO complete the list
#endif // EIGEN_SPARSE_EXPRESSIONMAKER_H

34
bench/BenchTimer.h
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@ -26,8 +26,14 @@
#ifndef EIGEN_BENCH_TIMER_H
#define EIGEN_BENCH_TIMER_H
#ifndef WIN32
#include <sys/time.h>
#include <unistd.h>
#else
#define NOMINMAX
#include <windows.h>
#endif
#include <cstdlib>
#include <numeric>
@ -40,7 +46,15 @@ class BenchTimer
{
public:
BenchTimer() { reset(); }
BenchTimer()
{
#ifdef WIN32
LARGE_INTEGER freq;
QueryPerformanceFrequency(&freq);
m_frequency = (double)freq.QuadPart;
#endif
reset();
}
~BenchTimer() {}
@ -51,23 +65,35 @@ public:
m_best = std::min(m_best, getTime() - m_start);
}
/** Return the best elapsed time.
/** Return the best elapsed time in seconds.
*/
inline double value(void)
{
return m_best;
return m_best;
}
#ifdef WIN32
inline double getTime(void)
#else
static inline double getTime(void)
#endif
{
#ifdef WIN32
LARGE_INTEGER query_ticks;
QueryPerformanceCounter(&query_ticks);
return query_ticks.QuadPart/m_frequency;
#else
struct timeval tv;
struct timezone tz;
gettimeofday(&tv, &tz);
return (double)tv.tv_sec + 1.e-6 * (double)tv.tv_usec;
#endif
}
protected:
#ifdef WIN32
double m_frequency;
#endif
double m_best, m_start;
};

115
bench/benchFFT.cpp Normal file
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@ -0,0 +1,115 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include <complex>
#include <vector>
#include <Eigen/Core>
#include <bench/BenchTimer.h>
#ifdef USE_FFTW
#include <fftw3.h>
#endif
#include <unsupported/Eigen/FFT>
using namespace Eigen;
using namespace std;
template <typename T>
string nameof();
template <> string nameof<float>() {return "float";}
template <> string nameof<double>() {return "double";}
template <> string nameof<long double>() {return "long double";}
#ifndef TYPE
#define TYPE float
#endif
#ifndef NFFT
#define NFFT 1024
#endif
#ifndef NDATA
#define NDATA 1000000
#endif
using namespace Eigen;
template <typename T>
void bench(int nfft,bool fwd)
{
typedef typename NumTraits<T>::Real Scalar;
typedef typename std::complex<Scalar> Complex;
int nits = NDATA/nfft;
vector<T> inbuf(nfft);
vector<Complex > outbuf(nfft);
FFT< Scalar > fft;
fft.fwd( outbuf , inbuf);
BenchTimer timer;
timer.reset();
for (int k=0;k<8;++k) {
timer.start();
for(int i = 0; i < nits; i++)
if (fwd)
fft.fwd( outbuf , inbuf);
else
fft.inv(inbuf,outbuf);
timer.stop();
}
cout << nameof<Scalar>() << " ";
double mflops = 5.*nfft*log2((double)nfft) / (1e6 * timer.value() / (double)nits );
if ( NumTraits<T>::IsComplex ) {
cout << "complex";
}else{
cout << "real ";
mflops /= 2;
}
if (fwd)
cout << " fwd";
else
cout << " inv";
cout << " NFFT=" << nfft << " " << (double(1e-6*nfft*nits)/timer.value()) << " MS/s " << mflops << "MFLOPS\n";
}
int main(int argc,char ** argv)
{
bench<complex<float> >(NFFT,true);
bench<complex<float> >(NFFT,false);
bench<float>(NFFT,true);
bench<float>(NFFT,false);
bench<complex<double> >(NFFT,true);
bench<complex<double> >(NFFT,false);
bench<double>(NFFT,true);
bench<double>(NFFT,false);
bench<complex<long double> >(NFFT,true);
bench<complex<long double> >(NFFT,false);
bench<long double>(NFFT,true);
bench<long double>(NFFT,false);
return 0;
}

24
cmake/FindFFTW.cmake Normal file
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@ -0,0 +1,24 @@
if (FFTW_INCLUDES AND FFTW_LIBRARIES)
set(FFTW_FIND_QUIETLY TRUE)
endif (FFTW_INCLUDES AND FFTW_LIBRARIES)
find_path(FFTW_INCLUDES
NAMES
fftw3.h
PATHS
$ENV{FFTWDIR}
${INCLUDE_INSTALL_DIR}
)
find_library(FFTWF_LIB NAMES fftw3f PATHS $ENV{FFTWDIR} ${LIB_INSTALL_DIR})
find_library(FFTW_LIB NAMES fftw3 PATHS $ENV{FFTWDIR} ${LIB_INSTALL_DIR})
find_library(FFTWL_LIB NAMES fftw3l PATHS $ENV{FFTWDIR} ${LIB_INSTALL_DIR})
set(FFTW_LIBRARIES "${FFTWF_LIB} ${FFTW_LIB} ${FFTWL_LIB}" )
message(STATUS "FFTW ${FFTW_LIBRARIES}" )
include(FindPackageHandleStandardArgs)
find_package_handle_standard_args(FFTW DEFAULT_MSG
FFTW_INCLUDES FFTW_LIBRARIES)
mark_as_advanced(FFTW_INCLUDES FFTW_LIBRARIES)

18
scripts/eigen_gen_credits.cpp
View File

@ -13,10 +13,24 @@ using namespace std;
std::string contributor_name(const std::string& line)
{
string result;
// let's first take care of the case of isolated email addresses, like
// "user@localhost.localdomain" entries
if(line.find("markb@localhost.localdomain") != string::npos)
{
return "Mark Borgerding";
}
// from there on we assume that we have a entry of the form
// either:
// Bla bli Blurp
// or:
// Bla bli Blurp <bblurp@email.com>
size_t position_of_email_address = line.find_first_of('<');
if(position_of_email_address != string::npos)
{
// there is an e-mail address.
// there is an e-mail address in <...>.
// Hauke once committed as "John Smith", fix that.
if(line.find("hauke.heibel") != string::npos)
@ -29,7 +43,7 @@ std::string contributor_name(const std::string& line)
}
else
{
// there is no e-mail address.
// there is no e-mail address in <...>.
if(line.find("convert-repo") != string::npos)
result = "";

3
test/geo_hyperplane.cpp
View File

@ -121,7 +121,8 @@ template<typename Scalar> void lines()
VERIFY_IS_APPROX(result, center);
// check conversions between two types of lines
CoeffsType converted_coeffs = HLine(PLine(line_u)).coeffs();
PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
CoeffsType converted_coeffs = HLine(pl).coeffs();
converted_coeffs *= (line_u.coeffs()[0])/(converted_coeffs[0]);
VERIFY(line_u.coeffs().isApprox(converted_coeffs));
}

5
test/map.cpp
View File

@ -37,13 +37,14 @@ template<typename VectorType> void map_class(const VectorType& m)
Scalar* array3unaligned = size_t(array3)%16 == 0 ? array3+1 : array3;
Map<VectorType, Aligned>(array1, size) = VectorType::Random(size);
Map<VectorType>(array2, size) = Map<VectorType>(array1, size);
Map<VectorType, Aligned>(array2, size) = Map<VectorType,Aligned>(array1, size);
Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);
VectorType ma1 = Map<VectorType>(array1, size);
VectorType ma1 = Map<VectorType, Aligned>(array1, size);
VectorType ma2 = Map<VectorType, Aligned>(array2, size);
VectorType ma3 = Map<VectorType>(array3unaligned, size);
VERIFY_IS_APPROX(ma1, ma2);
VERIFY_IS_APPROX(ma1, ma3);
VERIFY_RAISES_ASSERT((Map<VectorType,Aligned>(array3unaligned, size)));
ei_aligned_delete(array1, size);
ei_aligned_delete(array2, size);

182
unsupported/Eigen/Complex Normal file
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@ -0,0 +1,182 @@
#ifndef EIGEN_COMPLEX_H
#define EIGEN_COMPLEX_H
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// Eigen::Complex reuses as much as possible from std::complex
// and allows easy conversion to and from, even at the pointer level.
#include <complex>
namespace Eigen {
template <typename _NativePtr,typename _PunnedPtr>
struct castable_pointer
{
castable_pointer(_NativePtr ptr) : _ptr(ptr) {}
operator _NativePtr () {return _ptr;}
operator _PunnedPtr () {return reinterpret_cast<_PunnedPtr>(_ptr);}
private:
_NativePtr _ptr;
};
template <typename T>
struct Complex
{
typedef typename std::complex<T> StandardComplex;
typedef T value_type;
// constructors
Complex(const T& re = T(), const T& im = T()) : _re(re),_im(im) { }
Complex(const Complex&other ): _re(other.real()) ,_im(other.imag()) {}
template<class X>
Complex(const Complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
template<class X>
Complex(const std::complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
// allow binary access to the object as a std::complex
typedef castable_pointer< Complex<T>*, StandardComplex* > pointer_type;
typedef castable_pointer< const Complex<T>*, const StandardComplex* > const_pointer_type;
pointer_type operator & () {return pointer_type(this);}
const_pointer_type operator & () const {return const_pointer_type(this);}
operator StandardComplex () const {return std_type();}
operator StandardComplex & () {return std_type();}
StandardComplex std_type() const {return StandardComplex(real(),imag());}
StandardComplex & std_type() {return *reinterpret_cast<StandardComplex*>(this);}
// every sort of accessor and mutator that has ever been in fashion.
// For a brief history, search for "std::complex over-encapsulated"
// http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-defects.html#387
const T & real() const {return _re;}
const T & imag() const {return _im;}
T & real() {return _re;}
T & imag() {return _im;}
T & real(const T & x) {return _re=x;}
T & imag(const T & x) {return _im=x;}
void set_real(const T & x) {_re = x;}
void set_imag(const T & x) {_im = x;}
// *** complex member functions: ***
Complex<T>& operator= (const T& val) { _re=val;_im=0;return *this; }
Complex<T>& operator+= (const T& val) {_re+=val;return *this;}
Complex<T>& operator-= (const T& val) {_re-=val;return *this;}
Complex<T>& operator*= (const T& val) {_re*=val;_im*=val;return *this; }
Complex<T>& operator/= (const T& val) {_re/=val;_im/=val;return *this; }
Complex& operator= (const Complex& rhs) {_re=rhs._re;_im=rhs._im;return *this;}
Complex& operator= (const StandardComplex& rhs) {_re=rhs.real();_im=rhs.imag();return *this;}
template<class X> Complex<T>& operator= (const Complex<X>& rhs) { _re=rhs._re;_im=rhs._im;return *this;}
template<class X> Complex<T>& operator+= (const Complex<X>& rhs) { _re+=rhs._re;_im+=rhs._im;return *this;}
template<class X> Complex<T>& operator-= (const Complex<X>& rhs) { _re-=rhs._re;_im-=rhs._im;return *this;}
template<class X> Complex<T>& operator*= (const Complex<X>& rhs) { this->std_type() *= rhs.std_type(); return *this; }
template<class X> Complex<T>& operator/= (const Complex<X>& rhs) { this->std_type() /= rhs.std_type(); return *this; }
private:
T _re;
T _im;
};
template <typename T>
T ei_to_std( const T & x) {return x;}
template <typename T>
std::complex<T> ei_to_std( const Complex<T> & x) {return x.std_type();}
// 26.2.6 operators
template<class T> Complex<T> operator+(const Complex<T>& rhs) {return rhs;}
template<class T> Complex<T> operator-(const Complex<T>& rhs) {return -ei_to_std(rhs);}
template<class T> Complex<T> operator+(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) + ei_to_std(rhs);}
template<class T> Complex<T> operator-(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) - ei_to_std(rhs);}
template<class T> Complex<T> operator*(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) * ei_to_std(rhs);}
template<class T> Complex<T> operator/(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) / ei_to_std(rhs);}
template<class T> bool operator==(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) == ei_to_std(rhs);}
template<class T> bool operator!=(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) != ei_to_std(rhs);}
template<class T> Complex<T> operator+(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
template<class T> Complex<T> operator+(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
template<class T> Complex<T> operator-(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
template<class T> Complex<T> operator*(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
template<class T> Complex<T> operator/(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
template<class T> bool operator==(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
template<class T> bool operator!=(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
template<class T, class charT, class traits>
std::basic_istream<charT,traits>&
operator>> (std::basic_istream<charT,traits>& istr, Complex<T>& rhs)
{
return istr >> rhs.std_type();
}
template<class T, class charT, class traits>
std::basic_ostream<charT,traits>&
operator<< (std::basic_ostream<charT,traits>& ostr, const Complex<T>& rhs)
{
return ostr << rhs.std_type();
}
// 26.2.7 values:
template<class T> T real(const Complex<T>&x) {return real(ei_to_std(x));}
template<class T> T abs(const Complex<T>&x) {return abs(ei_to_std(x));}
template<class T> T arg(const Complex<T>&x) {return arg(ei_to_std(x));}
template<class T> T norm(const Complex<T>&x) {return norm(ei_to_std(x));}
template<class T> Complex<T> conj(const Complex<T>&x) { return conj(ei_to_std(x));}
template<class T> Complex<T> polar(const T& x, const T&y) {return polar(ei_to_std(x),ei_to_std(y));}
// 26.2.8 transcendentals:
template<class T> Complex<T> cos (const Complex<T>&x){return cos(ei_to_std(x));}
template<class T> Complex<T> cosh (const Complex<T>&x){return cosh(ei_to_std(x));}
template<class T> Complex<T> exp (const Complex<T>&x){return exp(ei_to_std(x));}
template<class T> Complex<T> log (const Complex<T>&x){return log(ei_to_std(x));}
template<class T> Complex<T> log10 (const Complex<T>&x){return log10(ei_to_std(x));}
template<class T> Complex<T> pow(const Complex<T>&x, int p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> pow(const Complex<T>&x, const T&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> pow(const Complex<T>&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> pow(const T&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
template<class T> Complex<T> sin (const Complex<T>&x){return sin(ei_to_std(x));}
template<class T> Complex<T> sinh (const Complex<T>&x){return sinh(ei_to_std(x));}
template<class T> Complex<T> sqrt (const Complex<T>&x){return sqrt(ei_to_std(x));}
template<class T> Complex<T> tan (const Complex<T>&x){return tan(ei_to_std(x));}
template<class T> Complex<T> tanh (const Complex<T>&x){return tanh(ei_to_std(x));}
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

135
unsupported/Eigen/FFT Normal file
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@ -0,0 +1,135 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_FFT_H
#define EIGEN_FFT_H
#include <complex>
#include <vector>
#include <map>
#ifdef EIGEN_FFTW_DEFAULT
// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
# include <fftw3.h>
namespace Eigen {
# include "src/FFT/ei_fftw_impl.h"
//template <typename T> typedef struct ei_fftw_impl default_fft_impl; this does not work
template <typename T> struct default_fft_impl : public ei_fftw_impl<T> {};
}
#elif defined EIGEN_MKL_DEFAULT
// TODO
// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form
namespace Eigen {
# include "src/FFT/ei_imklfft_impl.h"
template <typename T> struct default_fft_impl : public ei_imklfft_impl {};
}
#else
// ei_kissfft_impl: small, free, reasonably efficient default, derived from kissfft
//
namespace Eigen {
# include "src/FFT/ei_kissfft_impl.h"
template <typename T>
struct default_fft_impl : public ei_kissfft_impl<T> {};
}
#endif
namespace Eigen {
template <typename _Scalar,
typename _Impl=default_fft_impl<_Scalar> >
class FFT
{
public:
typedef _Impl impl_type;
typedef typename impl_type::Scalar Scalar;
typedef typename impl_type::Complex Complex;
FFT(const impl_type & impl=impl_type() ) :m_impl(impl) { }
template <typename _Input>
void fwd( Complex * dst, const _Input * src, int nfft)
{
m_impl.fwd(dst,src,nfft);
}
template <typename _Input>
void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src)
{
dst.resize( src.size() );
fwd( &dst[0],&src[0],src.size() );
}
template<typename InputDerived, typename ComplexDerived>
void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
dst.derived().resize( src.size() );
fwd( &dst[0],&src[0],src.size() );
}
template <typename _Output>
void inv( _Output * dst, const Complex * src, int nfft)
{
m_impl.inv( dst,src,nfft );
}
template <typename _Output>
void inv( std::vector<_Output> & dst, const std::vector<Complex> & src)
{
dst.resize( src.size() );
inv( &dst[0],&src[0],src.size() );
}
template<typename OutputDerived, typename ComplexDerived>
void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src)
{
EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time
EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
dst.derived().resize( src.size() );
inv( &dst[0],&src[0],src.size() );
}
// TODO: multi-dimensional FFTs
// TODO: handle Eigen MatrixBase
// ---> i added fwd and inv specializations above + unit test, is this enough? (bjacob)
impl_type & impl() {return m_impl;}
private:
impl_type m_impl;
};
}
#endif
/* vim: set filetype=cpp et sw=2 ts=2 ai: */

4
unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
View File

@ -50,10 +50,12 @@ public:
typedef typename Functor::InputType InputType;
typedef typename Functor::ValueType ValueType;
typedef typename Functor::JacobianType JacobianType;
typedef typename JacobianType::Scalar Scalar;
typedef Matrix<double,InputsAtCompileTime,1> DerivativeType;
typedef Matrix<Scalar,InputsAtCompileTime,1> DerivativeType;
typedef AutoDiffScalar<DerivativeType> ActiveScalar;
typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput;
typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue;

97
unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
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@ -42,9 +42,17 @@ void ei_make_coherent(const A& a, const B&b)
/** \class AutoDiffScalar
* \brief A scalar type replacement with automatic differentation capability
*
* \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
* \param _DerType the vector type used to store/represent the derivatives. The base scalar type
* as well as the number of derivatives to compute are determined from this type.
* Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
* if the number of derivatives is not known at compile time, and/or, the number
* of derivatives is large.
* Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
* existing vector into an AutoDiffScalar.
* Finally, _DerType can also be any Eigen compatible expression.
*
* This class represents a scalar value while tracking its respective derivatives.
* This class represents a scalar value while tracking its respective derivatives using Eigen's expression
* template mechanism.
*
* It supports the following list of global math function:
* - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
@ -56,10 +64,11 @@ void ei_make_coherent(const A& a, const B&b)
* while derivatives are computed right away.
*
*/
template<typename DerType>
template<typename _DerType>
class AutoDiffScalar
{
public:
typedef typename ei_cleantype<_DerType>::type DerType;
typedef typename ei_traits<DerType>::Scalar Scalar;
inline AutoDiffScalar() {}
@ -108,12 +117,28 @@ class AutoDiffScalar
inline const DerType& derivatives() const { return m_derivatives; }
inline DerType& derivatives() { return m_derivatives; }
inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
{
return AutoDiffScalar<DerType>(m_value + other, m_derivatives);
}
friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
{
return AutoDiffScalar<DerType>(a + b.value(), b.derivatives());
}
inline AutoDiffScalar& operator+=(const Scalar& other)
{
value() += other;
return *this;
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >
operator+(const AutoDiffScalar<OtherDerType>& other) const
{
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >(
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
m_value + other.value(),
m_derivatives + other.derivatives());
}
@ -127,11 +152,11 @@ class AutoDiffScalar
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >
operator-(const AutoDiffScalar<OtherDerType>& other) const
{
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >(
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
m_value - other.value(),
m_derivatives - other.derivatives());
}
@ -145,73 +170,73 @@ class AutoDiffScalar
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >
operator-() const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >(
-m_value,
-m_derivatives);
}
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator*(const Scalar& other) const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
m_value * other,
(m_derivatives * other));
}
friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator*(const Scalar& other, const AutoDiffScalar& a)
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
a.value() * other,
a.derivatives() * other);
}
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator/(const Scalar& other) const
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
m_value / other,
(m_derivatives * (Scalar(1)/other)));
}
friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
operator/(const Scalar& other, const AutoDiffScalar& a)
{
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
other / a.value(),
a.derivatives() * (-Scalar(1)/other));
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >
operator/(const AutoDiffScalar<OtherDerType>& other) const
{
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >(
m_value / other.value(),
((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
* (Scalar(1)/(other.value()*other.value())));
}
template<typename OtherDerType>
inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >
inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >
operator*(const AutoDiffScalar<OtherDerType>& other) const
{
ei_make_coherent(m_derivatives, other.derivatives());
return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >(
return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >(
m_value * other.value(),
(m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
}
@ -283,11 +308,11 @@ struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRo
#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
template<typename DerType> \
inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType> > \
inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type > \
FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
using namespace Eigen; \
typedef typename ei_traits<DerType>::Scalar Scalar; \
typedef AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> > ReturnType; \
typedef AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type > ReturnType; \
CODE; \
}
@ -314,12 +339,12 @@ namespace std
return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
template<typename DerType>
inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType> >
inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type >
pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::ei_traits<DerType>::Scalar y)
{
using namespace Eigen;
typedef typename ei_traits<DerType>::Scalar Scalar;
return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
std::pow(x.value(),y),
x.derivatives() * (y * std::pow(x.value(),y-1)));
}
@ -359,7 +384,7 @@ EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)
template<typename DerType>
inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType>::Type >
ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
{ return std::pow(x,y);}

224
unsupported/Eigen/src/FFT/ei_fftw_impl.h Normal file
View File

@ -0,0 +1,224 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// FFTW uses non-const arguments
// so we must use ugly const_cast calls for all the args it uses
//
// This should be safe as long as
// 1. we use FFTW_ESTIMATE for all our planning
// see the FFTW docs section 4.3.2 "Planner Flags"
// 2. fftw_complex is compatible with std::complex
// This assumes std::complex<T> layout is array of size 2 with real,imag
template <typename T>
inline
T * ei_fftw_cast(const T* p)
{
return const_cast<T*>( p);
}
inline
fftw_complex * ei_fftw_cast( const std::complex<double> * p)
{
return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) );
}
inline
fftwf_complex * ei_fftw_cast( const std::complex<float> * p)
{
return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) );
}
inline
fftwl_complex * ei_fftw_cast( const std::complex<long double> * p)
{
return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) );
}
template <typename T>
struct ei_fftw_plan {};
template <>
struct ei_fftw_plan<float>
{
typedef float scalar_type;
typedef fftwf_complex complex_type;
fftwf_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftwf_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftwf_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwf_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwf_execute_dft_c2r( m_plan, src,dst);
}
};
template <>
struct ei_fftw_plan<double>
{
typedef double scalar_type;
typedef fftw_complex complex_type;
fftw_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftw_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftw_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftw_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftw_execute_dft_c2r( m_plan, src,dst);
}
};
template <>
struct ei_fftw_plan<long double>
{
typedef long double scalar_type;
typedef fftwl_complex complex_type;
fftwl_plan m_plan;
ei_fftw_plan() :m_plan(NULL) {}
~ei_fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}
inline
void fwd(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
fftwl_execute_dft( m_plan, src,dst);
}
inline
void inv(complex_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
fftwl_execute_dft( m_plan, src,dst);
}
inline
void fwd(complex_type * dst,scalar_type * src,int nfft) {
if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwl_execute_dft_r2c( m_plan,src,dst);
}
inline
void inv(scalar_type * dst,complex_type * src,int nfft) {
if (m_plan==NULL)
m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
fftwl_execute_dft_c2r( m_plan, src,dst);
}
};
template <typename _Scalar>
struct ei_fftw_impl
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
inline
void clear()
{
m_plans.clear();
}
inline
void fwd( Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
}
// real-to-complex forward FFT
inline
void fwd( Complex * dst,const Scalar * src,int nfft)
{
get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src) ,nfft);
int nhbins=(nfft>>1)+1;
for (int k=nhbins;k < nfft; ++k )
dst[k] = conj(dst[nfft-k]);
}
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
//TODO move scaling to Eigen::FFT
// scaling
Scalar s = Scalar(1.)/nfft;
for (int k=0;k<nfft;++k)
dst[k] *= s;
}
// half-complex to scalar
inline
void inv( Scalar * dst,const Complex * src,int nfft)
{
get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
//TODO move scaling to Eigen::FFT
Scalar s = Scalar(1.)/nfft;
for (int k=0;k<nfft;++k)
dst[k] *= s;
}
protected:
typedef ei_fftw_plan<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
PlanMap m_plans;
inline
PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)
{
bool inplace = (dst==src);
bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
int key = (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned;
return m_plans[key];
}
};

414
unsupported/Eigen/src/FFT/ei_kissfft_impl.h Normal file
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@ -0,0 +1,414 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
// This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
// Copyright 2003-2009 Mark Borgerding
template <typename _Scalar>
struct ei_kiss_cpx_fft
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
std::vector<Complex> m_twiddles;
std::vector<int> m_stageRadix;
std::vector<int> m_stageRemainder;
std::vector<Complex> m_scratchBuf;
bool m_inverse;
void make_twiddles(int nfft,bool inverse)
{
m_inverse = inverse;
m_twiddles.resize(nfft);
Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
for (int i=0;i<nfft;++i)
m_twiddles[i] = exp( Complex(0,i*phinc) );
}
void factorize(int nfft)
{
//start factoring out 4's, then 2's, then 3,5,7,9,...
int n= nfft;
int p=4;
do {
while (n % p) {
switch (p) {
case 4: p = 2; break;
case 2: p = 3; break;
default: p += 2; break;
}
if (p*p>n)
p=n;// impossible to have a factor > sqrt(n)
}
n /= p;
m_stageRadix.push_back(p);
m_stageRemainder.push_back(n);
if ( p > 5 )
m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
}while(n>1);
}
template <typename _Src>
void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
{
int p = m_stageRadix[stage];
int m = m_stageRemainder[stage];
Complex * Fout_beg = xout;
Complex * Fout_end = xout + p*m;
if (m>1) {
do{
// recursive call:
// DFT of size m*p performed by doing
// p instances of smaller DFTs of size m,
// each one takes a decimated version of the input
work(stage+1, xout , xin, fstride*p,in_stride);
xin += fstride*in_stride;
}while( (xout += m) != Fout_end );
}else{
do{
*xout = *xin;
xin += fstride*in_stride;
}while(++xout != Fout_end );
}
xout=Fout_beg;
// recombine the p smaller DFTs
switch (p) {
case 2: bfly2(xout,fstride,m); break;
case 3: bfly3(xout,fstride,m); break;
case 4: bfly4(xout,fstride,m); break;
case 5: bfly5(xout,fstride,m); break;
default: bfly_generic(xout,fstride,m,p); break;
}
}
inline
void bfly2( Complex * Fout, const size_t fstride, int m)
{
for (int k=0;k<m;++k) {
Complex t = Fout[m+k] * m_twiddles[k*fstride];
Fout[m+k] = Fout[k] - t;
Fout[k] += t;
}
}
inline
void bfly4( Complex * Fout, const size_t fstride, const size_t m)
{
Complex scratch[6];
int negative_if_inverse = m_inverse * -2 +1;
for (size_t k=0;k<m;++k) {
scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
scratch[5] = Fout[k] - scratch[1];
Fout[k] += scratch[1];
scratch[3] = scratch[0] + scratch[2];
scratch[4] = scratch[0] - scratch[2];
scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
Fout[k+2*m] = Fout[k] - scratch[3];
Fout[k] += scratch[3];
Fout[k+m] = scratch[5] + scratch[4];
Fout[k+3*m] = scratch[5] - scratch[4];
}
}
inline
void bfly3( Complex * Fout, const size_t fstride, const size_t m)
{
size_t k=m;
const size_t m2 = 2*m;
Complex *tw1,*tw2;
Complex scratch[5];
Complex epi3;
epi3 = m_twiddles[fstride*m];
tw1=tw2=&m_twiddles[0];
do{
scratch[1]=Fout[m] * *tw1;
scratch[2]=Fout[m2] * *tw2;
scratch[3]=scratch[1]+scratch[2];
scratch[0]=scratch[1]-scratch[2];
tw1 += fstride;
tw2 += fstride*2;
Fout[m] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() );
scratch[0] *= epi3.imag();
*Fout += scratch[3];
Fout[m2] = Complex( Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
++Fout;
}while(--k);
}
inline
void bfly5( Complex * Fout, const size_t fstride, const size_t m)
{
Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
size_t u;
Complex scratch[13];
Complex * twiddles = &m_twiddles[0];
Complex *tw;
Complex ya,yb;
ya = twiddles[fstride*m];
yb = twiddles[fstride*2*m];
Fout0=Fout;
Fout1=Fout0+m;
Fout2=Fout0+2*m;
Fout3=Fout0+3*m;
Fout4=Fout0+4*m;
tw=twiddles;
for ( u=0; u<m; ++u ) {
scratch[0] = *Fout0;
scratch[1] = *Fout1 * tw[u*fstride];
scratch[2] = *Fout2 * tw[2*u*fstride];
scratch[3] = *Fout3 * tw[3*u*fstride];
scratch[4] = *Fout4 * tw[4*u*fstride];
scratch[7] = scratch[1] + scratch[4];
scratch[10] = scratch[1] - scratch[4];
scratch[8] = scratch[2] + scratch[3];
scratch[9] = scratch[2] - scratch[3];
*Fout0 += scratch[7];
*Fout0 += scratch[8];
scratch[5] = scratch[0] + Complex(
(scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
(scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
);
scratch[6] = Complex(
(scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
-(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
);
*Fout1 = scratch[5] - scratch[6];
*Fout4 = scratch[5] + scratch[6];
scratch[11] = scratch[0] +
Complex(
(scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
(scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
);
scratch[12] = Complex(
-(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
(scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
);
*Fout2=scratch[11]+scratch[12];
*Fout3=scratch[11]-scratch[12];
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
}
}
/* perform the butterfly for one stage of a mixed radix FFT */
inline
void bfly_generic(
Complex * Fout,
const size_t fstride,
int m,
int p
)
{
int u,k,q1,q;
Complex * twiddles = &m_twiddles[0];
Complex t;
int Norig = m_twiddles.size();
Complex * scratchbuf = &m_scratchBuf[0];
for ( u=0; u<m; ++u ) {
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
scratchbuf[q1] = Fout[ k ];
k += m;
}
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
int twidx=0;
Fout[ k ] = scratchbuf[0];
for (q=1;q<p;++q ) {
twidx += fstride * k;
if (twidx>=Norig) twidx-=Norig;
t=scratchbuf[q] * twiddles[twidx];
Fout[ k ] += t;
}
k += m;
}
}
}
};
template <typename _Scalar>
struct ei_kissfft_impl
{
typedef _Scalar Scalar;
typedef std::complex<Scalar> Complex;
void clear()
{
m_plans.clear();
m_realTwiddles.clear();
}
template <typename _Src>
inline
void fwd( Complex * dst,const _Src *src,int nfft)
{
get_plan(nfft,false).work(0, dst, src, 1,1);
}
// real-to-complex forward FFT
// perform two FFTs of src even and src odd
// then twiddle to recombine them into the half-spectrum format
// then fill in the conjugate symmetric half
inline
void fwd( Complex * dst,const Scalar * src,int nfft)
{
if ( nfft&3 ) {
// use generic mode for odd
get_plan(nfft,false).work(0, dst, src, 1,1);
}else{
int ncfft = nfft>>1;
int ncfft2 = nfft>>2;
Complex * rtw = real_twiddles(ncfft2);
// use optimized mode for even real
fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
Complex dc = dst[0].real() + dst[0].imag();
Complex nyquist = dst[0].real() - dst[0].imag();
int k;
for ( k=1;k <= ncfft2 ; ++k ) {
Complex fpk = dst[k];
Complex fpnk = conj(dst[ncfft-k]);
Complex f1k = fpk + fpnk;
Complex f2k = fpk - fpnk;
Complex tw= f2k * rtw[k-1];
dst[k] = (f1k + tw) * Scalar(.5);
dst[ncfft-k] = conj(f1k -tw)*Scalar(.5);
}
// place conjugate-symmetric half at the end for completeness
// TODO: make this configurable ( opt-out )
for ( k=1;k < ncfft ; ++k )
dst[nfft-k] = conj(dst[k]);
dst[0] = dc;
dst[ncfft] = nyquist;
}
}
// inverse complex-to-complex
inline
void inv(Complex * dst,const Complex *src,int nfft)
{
get_plan(nfft,true).work(0, dst, src, 1,1);
scale(dst, nfft, Scalar(1)/nfft );
}
// half-complex to scalar
inline
void inv( Scalar * dst,const Complex * src,int nfft)
{
if (nfft&3) {
m_tmpBuf.resize(nfft);
inv(&m_tmpBuf[0],src,nfft);
for (int k=0;k<nfft;++k)
dst[k] = m_tmpBuf[k].real();
}else{
// optimized version for multiple of 4
int ncfft = nfft>>1;
int ncfft2 = nfft>>2;
Complex * rtw = real_twiddles(ncfft2);
m_tmpBuf.resize(ncfft);
m_tmpBuf[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
for (int k = 1; k <= ncfft / 2; ++k) {
Complex fk = src[k];
Complex fnkc = conj(src[ncfft-k]);
Complex fek = fk + fnkc;
Complex tmp = fk - fnkc;
Complex fok = tmp * conj(rtw[k-1]);
m_tmpBuf[k] = fek + fok;
m_tmpBuf[ncfft-k] = conj(fek - fok);
}
scale(&m_tmpBuf[0], ncfft, Scalar(1)/nfft );
get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf[0], 1,1);
}
}
protected:
typedef ei_kiss_cpx_fft<Scalar> PlanData;
typedef std::map<int,PlanData> PlanMap;
PlanMap m_plans;
std::map<int, std::vector<Complex> > m_realTwiddles;
std::vector<Complex> m_tmpBuf;
inline
int PlanKey(int nfft,bool isinverse) const { return (nfft<<1) | isinverse; }
inline
PlanData & get_plan(int nfft,bool inverse)
{
// TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
if ( pd.m_twiddles.size() == 0 ) {
pd.make_twiddles(nfft,inverse);
pd.factorize(nfft);
}
return pd;
}
inline
Complex * real_twiddles(int ncfft2)
{
std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
if ( (int)twidref.size() != ncfft2 ) {
twidref.resize(ncfft2);
int ncfft= ncfft2<<1;
Scalar pi = acos( Scalar(-1) );
for (int k=1;k<=ncfft2;++k)
twidref[k-1] = exp( Complex(0,-pi * ((double) (k) / ncfft + .5) ) );
}
return &twidref[0];
}
// TODO move scaling up into Eigen::FFT
inline
void scale(Complex *dst,int n,Scalar s)
{
for (int k=0;k<n;++k)
dst[k] *= s;
}
};

117
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@ -0,0 +1,117 @@
// To use the simple FFT implementation
// g++ -o demofft -I.. -Wall -O3 FFT.cpp
// To use the FFTW implementation
// g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l
#ifdef USE_FFTW
#include <fftw3.h>
#endif
#include <vector>
#include <complex>
#include <algorithm>
#include <iterator>
#include <Eigen/Core>
#include <unsupported/Eigen/FFT>
using namespace std;
using namespace Eigen;
template <typename T>
T mag2(T a)
{
return a*a;
}
template <typename T>
T mag2(std::complex<T> a)
{
return norm(a);
}
template <typename T>
T mag2(const std::vector<T> & vec)
{
T out=0;
for (size_t k=0;k<vec.size();++k)
out += mag2(vec[k]);
return out;
}
template <typename T>
T mag2(const std::vector<std::complex<T> > & vec)
{
T out=0;
for (size_t k=0;k<vec.size();++k)
out += mag2(vec[k]);
return out;
}
template <typename T>
vector<T> operator-(const vector<T> & a,const vector<T> & b )
{
vector<T> c(a);
for (size_t k=0;k<b.size();++k)
c[k] -= b[k];
return c;
}
template <typename T>
void RandomFill(std::vector<T> & vec)
{
for (size_t k=0;k<vec.size();++k)
vec[k] = T( rand() )/T(RAND_MAX) - .5;
}
template <typename T>
void RandomFill(std::vector<std::complex<T> > & vec)
{
for (size_t k=0;k<vec.size();++k)
vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - .5, T( rand() )/T(RAND_MAX) - .5);
}
template <typename T_time,typename T_freq>
void fwd_inv(size_t nfft)
{
typedef typename NumTraits<T_freq>::Real Scalar;
vector<T_time> timebuf(nfft);
RandomFill(timebuf);
vector<T_freq> freqbuf;
static FFT<Scalar> fft;
fft.fwd(freqbuf,timebuf);
vector<T_time> timebuf2;
fft.inv(timebuf2,freqbuf);
long double rmse = mag2(timebuf - timebuf2) / mag2(timebuf);
cout << "roundtrip rmse: " << rmse << endl;
}
template <typename T_scalar>
void two_demos(int nfft)
{
cout << " scalar ";
fwd_inv<T_scalar,std::complex<T_scalar> >(nfft);
cout << " complex ";
fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft);
}
void demo_all_types(int nfft)
{
cout << "nfft=" << nfft << endl;
cout << " float" << endl;
two_demos<float>(nfft);
cout << " double" << endl;
two_demos<double>(nfft);
cout << " long double" << endl;
two_demos<long double>(nfft);
}
int main()
{
demo_all_types( 2*3*4*5*7 );
demo_all_types( 2*9*16*25 );
demo_all_types( 1024 );
return 0;
}

7
unsupported/test/CMakeLists.txt
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@ -19,3 +19,10 @@ ei_add_test(autodiff)
ei_add_test(BVH)
ei_add_test(matrixExponential)
ei_add_test(alignedvector3)
ei_add_test(FFT)
find_package(FFTW)
if(FFTW_FOUND)
ei_add_test(FFTW "-DEIGEN_FFTW_DEFAULT " "-lfftw3 -lfftw3f -lfftw3l" )
endif(FFTW_FOUND)

200
unsupported/test/FFT.cpp Normal file
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@ -0,0 +1,200 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <unsupported/Eigen/FFT>
using namespace std;
float norm(float x) {return x*x;}
double norm(double x) {return x*x;}
long double norm(long double x) {return x*x;}
template < typename T>
complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
complex<long double> promote(float x) { return complex<long double>( x); }
complex<long double> promote(double x) { return complex<long double>( x); }
complex<long double> promote(long double x) { return complex<long double>( x); }
template <typename VectorType1,typename VectorType2>
long double fft_rmse( const VectorType1 & fftbuf,const VectorType2 & timebuf)
{
long double totalpower=0;
long double difpower=0;
cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
for (size_t k0=0;k0<size_t(fftbuf.size());++k0) {
complex<long double> acc = 0;
long double phinc = -2.*k0* M_PIl / timebuf.size();
for (size_t k1=0;k1<size_t(timebuf.size());++k1) {
acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
}
totalpower += norm(acc);
complex<long double> x = promote(fftbuf[k0]);
complex<long double> dif = acc - x;
difpower += norm(dif);
cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
}
cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
return sqrt(difpower/totalpower);
}
template <typename VectorType1,typename VectorType2>
long double dif_rmse( const VectorType1& buf1,const VectorType2& buf2)
{
long double totalpower=0;
long double difpower=0;
size_t n = min( buf1.size(),buf2.size() );
for (size_t k=0;k<n;++k) {
totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
difpower += norm(buf1[k] - buf2[k]);
}
return sqrt(difpower/totalpower);
}
enum { StdVectorContainer, EigenVectorContainer };
template<int Container, typename Scalar> struct VectorType;
template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
{
typedef vector<Scalar> type;
};
template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
{
typedef Matrix<Scalar,Dynamic,1> type;
};
template <int Container, typename T>
void test_scalar_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename FFT<T>::Scalar Scalar;
typedef typename VectorType<Container,Scalar>::type ScalarVector;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ScalarVector inbuf(nfft);
ComplexVector outbuf;
for (int k=0;k<nfft;++k)
inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
fft.fwd( outbuf,inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
ScalarVector buf3;
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <typename T>
void test_scalar(int nfft)
{
test_scalar_generic<StdVectorContainer,T>(nfft);
test_scalar_generic<EigenVectorContainer,T>(nfft);
}
template <int Container, typename T>
void test_complex_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ComplexVector inbuf(nfft);
ComplexVector outbuf;
ComplexVector buf3;
for (int k=0;k<nfft;++k)
inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
fft.fwd( outbuf , inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <typename T>
void test_complex(int nfft)
{
test_complex_generic<StdVectorContainer,T>(nfft);
test_complex_generic<EigenVectorContainer,T>(nfft);
}
void test_FFT()
{
CALL_SUBTEST( test_complex<float>(32) );
CALL_SUBTEST( test_complex<double>(32) );
CALL_SUBTEST( test_complex<long double>(32) );
CALL_SUBTEST( test_complex<float>(256) );
CALL_SUBTEST( test_complex<double>(256) );
CALL_SUBTEST( test_complex<long double>(256) );
CALL_SUBTEST( test_complex<float>(3*8) );
CALL_SUBTEST( test_complex<double>(3*8) );
CALL_SUBTEST( test_complex<long double>(3*8) );
CALL_SUBTEST( test_complex<float>(5*32) );
CALL_SUBTEST( test_complex<double>(5*32) );
CALL_SUBTEST( test_complex<long double>(5*32) );
CALL_SUBTEST( test_complex<float>(2*3*4) );
CALL_SUBTEST( test_complex<double>(2*3*4) );
CALL_SUBTEST( test_complex<long double>(2*3*4) );
CALL_SUBTEST( test_complex<float>(2*3*4*5) );
CALL_SUBTEST( test_complex<double>(2*3*4*5) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
CALL_SUBTEST( test_complex<float>(2*3*4*5*7) );
CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<float>(32) );
CALL_SUBTEST( test_scalar<double>(32) );
CALL_SUBTEST( test_scalar<long double>(32) );
CALL_SUBTEST( test_scalar<float>(45) );
CALL_SUBTEST( test_scalar<double>(45) );
CALL_SUBTEST( test_scalar<long double>(45) );
CALL_SUBTEST( test_scalar<float>(50) );
CALL_SUBTEST( test_scalar<double>(50) );
CALL_SUBTEST( test_scalar<long double>(50) );
CALL_SUBTEST( test_scalar<float>(256) );
CALL_SUBTEST( test_scalar<double>(256) );
CALL_SUBTEST( test_scalar<long double>(256) );
CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
}

136
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@ -0,0 +1,136 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <fftw3.h>
#include <unsupported/Eigen/FFT>
using namespace std;
float norm(float x) {return x*x;}
double norm(double x) {return x*x;}
long double norm(long double x) {return x*x;}
template < typename T>
complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
complex<long double> promote(float x) { return complex<long double>( x); }
complex<long double> promote(double x) { return complex<long double>( x); }
complex<long double> promote(long double x) { return complex<long double>( x); }
template <typename T1,typename T2>
long double fft_rmse( const vector<T1> & fftbuf,const vector<T2> & timebuf)
{
long double totalpower=0;
long double difpower=0;
cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
for (size_t k0=0;k0<fftbuf.size();++k0) {
complex<long double> acc = 0;
long double phinc = -2.*k0* M_PIl / timebuf.size();
for (size_t k1=0;k1<timebuf.size();++k1) {
acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
}
totalpower += norm(acc);
complex<long double> x = promote(fftbuf[k0]);
complex<long double> dif = acc - x;
difpower += norm(dif);
cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(norm(dif)) << endl;
}
cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
return sqrt(difpower/totalpower);
}
template <typename T1,typename T2>
long double dif_rmse( const vector<T1> buf1,const vector<T2> buf2)
{
long double totalpower=0;
long double difpower=0;
size_t n = min( buf1.size(),buf2.size() );
for (size_t k=0;k<n;++k) {
totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
difpower += norm(buf1[k] - buf2[k]);
}
return sqrt(difpower/totalpower);
}
template <class T>
void test_scalar(int nfft)
{
typedef typename Eigen::FFT<T>::Complex Complex;
typedef typename Eigen::FFT<T>::Scalar Scalar;
FFT<T> fft;
vector<Scalar> inbuf(nfft);
vector<Complex> outbuf;
for (int k=0;k<nfft;++k)
inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
fft.fwd( outbuf,inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
vector<Scalar> buf3;
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
template <class T>
void test_complex(int nfft)
{
typedef typename Eigen::FFT<T>::Complex Complex;
FFT<T> fft;
vector<Complex> inbuf(nfft);
vector<Complex> outbuf;
vector<Complex> buf3;
for (int k=0;k<nfft;++k)
inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
fft.fwd( outbuf , inbuf);
VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>() );// gross check
}
void test_FFTW()
{
CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); CALL_SUBTEST( test_complex<long double>(32) );
CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); CALL_SUBTEST( test_complex<long double>(256) );
CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); CALL_SUBTEST( test_complex<long double>(3*8) );
CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); CALL_SUBTEST( test_complex<long double>(5*32) );
CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); CALL_SUBTEST( test_complex<long double>(2*3*4) );
CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); CALL_SUBTEST( test_scalar<long double>(32) );
CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); CALL_SUBTEST( test_scalar<long double>(45) );
CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); CALL_SUBTEST( test_scalar<long double>(50) );
CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); CALL_SUBTEST( test_scalar<long double>(256) );
CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
}