- add diagonal * sparse product as an expression

- split sparse_basic unit test
- various fixes in sparse module
This commit is contained in:
Gael Guennebaud
2009-02-09 09:59:30 +00:00
parent e0be020622
commit a9688f0b71
18 changed files with 423 additions and 93 deletions

View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

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@@ -91,9 +91,9 @@ class SparseInnerVectorSet : ei_no_assignment_operator,
};
//----------
// specialisation for DynamicSparseMatrix
//----------
/***************************************************************************
* specialisation for DynamicSparseMatrix
***************************************************************************/
template<typename _Scalar, int _Options, int Size>
class SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options>, Size>
@@ -169,6 +169,89 @@ class SparseInnerVectorSet<DynamicSparseMatrix<_Scalar, _Options>, Size>
};
/***************************************************************************
* specialisation for SparseMatrix
***************************************************************************/
/*
template<typename _Scalar, int _Options, int Size>
class SparseInnerVectorSet<SparseMatrix<_Scalar, _Options>, Size>
: public SparseMatrixBase<SparseInnerVectorSet<SparseMatrix<_Scalar, _Options>, Size> >
{
typedef DynamicSparseMatrix<_Scalar, _Options> MatrixType;
enum { IsRowMajor = ei_traits<SparseInnerVectorSet>::IsRowMajor };
public:
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseInnerVectorSet)
class InnerIterator: public MatrixType::InnerIterator
{
public:
inline InnerIterator(const SparseInnerVectorSet& xpr, int outer)
: MatrixType::InnerIterator(xpr.m_matrix, xpr.m_outerStart + outer)
{}
};
inline SparseInnerVectorSet(const MatrixType& matrix, int outerStart, int outerSize)
: m_matrix(matrix), m_outerStart(outerStart), m_outerSize(outerSize)
{
ei_assert( (outerStart>=0) && ((outerStart+outerSize)<=matrix.outerSize()) );
}
inline SparseInnerVectorSet(const MatrixType& matrix, int outer)
: m_matrix(matrix), m_outerStart(outer)
{
ei_assert(Size==1);
ei_assert( (outer>=0) && (outer<matrix.outerSize()) );
}
template<typename OtherDerived>
inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other)
{
if (IsRowMajor != ((OtherDerived::Flags&RowMajorBit)==RowMajorBit))
{
// need to transpose => perform a block evaluation followed by a big swap
DynamicSparseMatrix<Scalar,IsRowMajor?RowMajorBit:0> aux(other);
*this = aux.markAsRValue();
}
else
{
// evaluate/copy vector per vector
for (int j=0; j<m_outerSize.value(); ++j)
{
SparseVector<Scalar,IsRowMajor ? RowMajorBit : 0> aux(other.innerVector(j));
m_matrix.const_cast_derived()._data()[m_outerStart+j].swap(aux._data());
}
}
return *this;
}
inline SparseInnerVectorSet& operator=(const SparseInnerVectorSet& other)
{
return operator=<SparseInnerVectorSet>(other);
}
inline const Scalar* _valuePtr() const
{ return m_matrix._valuePtr() + m_matrix._outerIndexPtr()[m_outerStart]; }
inline const int* _innerIndexPtr() const
{ return m_matrix._innerIndexPtr() + m_matrix._outerIndexPtr()[m_outerStart]; }
inline const int* _outerIndexPtr() const { return m_matrix._outerIndexPtr() + m_outerStart; }
// template<typename Sparse>
// inline SparseInnerVectorSet& operator=(const SparseMatrixBase<OtherDerived>& other)
// {
// return *this;
// }
EIGEN_STRONG_INLINE int rows() const { return IsRowMajor ? m_outerSize.value() : m_matrix.rows(); }
EIGEN_STRONG_INLINE int cols() const { return IsRowMajor ? m_matrix.cols() : m_outerSize.value(); }
protected:
const typename MatrixType::Nested m_matrix;
int m_outerStart;
const ei_int_if_dynamic<Size> m_outerSize;
};
*/
//----------
/** \returns the i-th row of the matrix \c *this. For row-major matrix only. */
@@ -192,7 +275,7 @@ const SparseInnerVectorSet<Derived,1> SparseMatrixBase<Derived>::row(int i) cons
template<typename Derived>
SparseInnerVectorSet<Derived,1> SparseMatrixBase<Derived>::col(int i)
{
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COL_MAJOR_MATRICES);
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
return innerVector(i);
}
@@ -201,7 +284,7 @@ SparseInnerVectorSet<Derived,1> SparseMatrixBase<Derived>::col(int i)
template<typename Derived>
const SparseInnerVectorSet<Derived,1> SparseMatrixBase<Derived>::col(int i) const
{
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COL_MAJOR_MATRICES);
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
return innerVector(i);
}
@@ -242,7 +325,7 @@ const SparseInnerVectorSet<Derived,Dynamic> SparseMatrixBase<Derived>::subrows(i
template<typename Derived>
SparseInnerVectorSet<Derived,Dynamic> SparseMatrixBase<Derived>::subcols(int start, int size)
{
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COL_MAJOR_MATRICES);
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
return innerVectors(start, size);
}
@@ -251,7 +334,7 @@ SparseInnerVectorSet<Derived,Dynamic> SparseMatrixBase<Derived>::subcols(int sta
template<typename Derived>
const SparseInnerVectorSet<Derived,Dynamic> SparseMatrixBase<Derived>::subcols(int start, int size) const
{
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COL_MAJOR_MATRICES);
EIGEN_STATIC_ASSERT(!IsRowMajor,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
return innerVectors(start, size);
}

View File

@@ -132,11 +132,10 @@ class SparseCwiseBinaryOp<BinaryOp,Lhs,Rhs>::InnerIterator
* Implementation of inner-iterators
***************************************************************************/
// template<typename T> struct ei_is_scalar_product { enum { ret = false }; };
// template<typename T> struct ei_is_scalar_product<ei_scalar_product_op<T> > { enum { ret = true }; };
// helper class
// template<typename T> struct ei_func_is_conjunction { enum { ret = false }; };
// template<typename T> struct ei_func_is_conjunction<ei_scalar_product_op<T> > { enum { ret = true }; };
// TODO generalize the ei_scalar_product_op specialization to all conjunctions if any !
// sparse - sparse (generic)
template<typename BinaryOp, typename Lhs, typename Rhs, typename Derived>
@@ -261,12 +260,13 @@ class ei_sparse_cwise_binary_op_inner_iterator_selector<ei_scalar_product_op<T>,
typedef SparseCwiseBinaryOp<BinaryFunc, Lhs, Rhs> CwiseBinaryXpr;
typedef typename CwiseBinaryXpr::Scalar Scalar;
typedef typename ei_traits<CwiseBinaryXpr>::_LhsNested _LhsNested;
typedef typename ei_traits<CwiseBinaryXpr>::RhsNested RhsNested;
typedef typename _LhsNested::InnerIterator LhsIterator;
enum { IsRowMajor = (int(Lhs::Flags)&RowMajorBit)==RowMajorBit };
public:
EIGEN_STRONG_INLINE ei_sparse_cwise_binary_op_inner_iterator_selector(const CwiseBinaryXpr& xpr, int outer)
: m_xpr(xpr), m_lhsIter(xpr.lhs(),outer), m_functor(xpr.functor()), m_outer(outer)
: m_rhs(xpr.rhs()), m_lhsIter(xpr.lhs(),outer), m_functor(xpr.functor()), m_outer(outer)
{}
EIGEN_STRONG_INLINE Derived& operator++()
@@ -277,7 +277,7 @@ class ei_sparse_cwise_binary_op_inner_iterator_selector<ei_scalar_product_op<T>,
EIGEN_STRONG_INLINE Scalar value() const
{ return m_functor(m_lhsIter.value(),
m_xpr.rhs().coeff(IsRowMajor?m_outer:m_lhsIter.index(),IsRowMajor?m_lhsIter.index():m_outer)); }
m_rhs.coeff(IsRowMajor?m_outer:m_lhsIter.index(),IsRowMajor?m_lhsIter.index():m_outer)); }
EIGEN_STRONG_INLINE int index() const { return m_lhsIter.index(); }
EIGEN_STRONG_INLINE int row() const { return m_lhsIter.row(); }
@@ -286,9 +286,9 @@ class ei_sparse_cwise_binary_op_inner_iterator_selector<ei_scalar_product_op<T>,
EIGEN_STRONG_INLINE operator bool() const { return m_lhsIter; }
protected:
const CwiseBinaryXpr& m_xpr;
const RhsNested m_rhs;
LhsIterator m_lhsIter;
const BinaryFunc& m_functor;
const BinaryFunc m_functor;
const int m_outer;
};
@@ -331,6 +331,10 @@ class ei_sparse_cwise_binary_op_inner_iterator_selector<ei_scalar_product_op<T>,
};
/***************************************************************************
* Implementation of SparseMatrixBase and SparseCwise functions/operators
***************************************************************************/
template<typename Derived>
template<typename OtherDerived>
EIGEN_STRONG_INLINE const SparseCwiseBinaryOp<ei_scalar_difference_op<typename ei_traits<Derived>::Scalar>,

View File

@@ -89,7 +89,7 @@ class SparseCwiseUnaryOp<UnaryOp,MatrixType>::InnerIterator
protected:
MatrixTypeIterator m_iter;
const UnaryOp& m_functor;
const UnaryOp m_functor;
};
template<typename Derived>

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@@ -0,0 +1,157 @@
// 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 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_DIAGONAL_PRODUCT_H
#define EIGEN_SPARSE_DIAGONAL_PRODUCT_H
// the product a diagonal matrix with a sparse matrix can be easily
// implemented using expression template. We have two very different cases:
// 1 - diag * row-major sparse
// => each inner vector <=> scalar * sparse vector product
// => so we can reuse CwiseUnaryOp::InnerIterator
// 2 - diag * col-major sparse
// => each inner vector <=> densevector * sparse vector cwise product
// => again, we can reuse specialization of CwiseBinaryOp::InnerIterator
// for that particular case
// The two other cases are symmetric.
template<typename Lhs, typename Rhs>
struct ei_traits<SparseDiagonalProduct<Lhs, Rhs> > : ei_traits<SparseProduct<Lhs, Rhs, DiagonalProduct> >
{
typedef typename ei_cleantype<Lhs>::type _Lhs;
typedef typename ei_cleantype<Rhs>::type _Rhs;
enum {
SparseFlags = ((int(_Lhs::Flags)&Diagonal)==Diagonal) ? _Rhs::Flags : _Lhs::Flags,
Flags = SparseBit | (SparseFlags&RowMajorBit)
};
};
enum {SDP_IsDiagonal, SDP_IsSparseRowMajor, SDP_IsSparseColMajor};
template<typename Lhs, typename Rhs, typename SparseDiagonalProductType, int RhsMode, int LhsMode>
class ei_sparse_diagonal_product_inner_iterator_selector;
template<typename LhsNested, typename RhsNested>
class SparseDiagonalProduct : public SparseMatrixBase<SparseDiagonalProduct<LhsNested,RhsNested> >, ei_no_assignment_operator
{
typedef typename ei_traits<SparseDiagonalProduct>::_LhsNested _LhsNested;
typedef typename ei_traits<SparseDiagonalProduct>::_RhsNested _RhsNested;
enum {
LhsMode = (_LhsNested::Flags&Diagonal)==Diagonal ? SDP_IsDiagonal
: (_LhsNested::Flags&RowMajorBit) ? SDP_IsSparseRowMajor : SDP_IsSparseColMajor,
RhsMode = (_RhsNested::Flags&Diagonal)==Diagonal ? SDP_IsDiagonal
: (_RhsNested::Flags&RowMajorBit) ? SDP_IsSparseRowMajor : SDP_IsSparseColMajor
};
public:
EIGEN_SPARSE_GENERIC_PUBLIC_INTERFACE(SparseDiagonalProduct)
typedef ei_sparse_diagonal_product_inner_iterator_selector
<_LhsNested,_RhsNested,SparseDiagonalProduct,LhsMode,RhsMode> InnerIterator;
template<typename Lhs, typename Rhs>
EIGEN_STRONG_INLINE SparseDiagonalProduct(const Lhs& lhs, const Rhs& rhs)
: m_lhs(lhs), m_rhs(rhs)
{
ei_assert(lhs.cols() == rhs.rows() && "invalid sparse matrix * diagonal matrix product");
}
EIGEN_STRONG_INLINE int rows() const { return m_lhs.rows(); }
EIGEN_STRONG_INLINE int cols() const { return m_rhs.cols(); }
EIGEN_STRONG_INLINE const _LhsNested& lhs() const { return m_lhs; }
EIGEN_STRONG_INLINE const _RhsNested& rhs() const { return m_rhs; }
protected:
LhsNested m_lhs;
RhsNested m_rhs;
};
template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
class ei_sparse_diagonal_product_inner_iterator_selector
<Lhs,Rhs,SparseDiagonalProductType,SDP_IsDiagonal,SDP_IsSparseRowMajor>
: public SparseCwiseUnaryOp<ei_scalar_multiple_op<typename Lhs::Scalar>,Rhs>::InnerIterator
{
typedef typename SparseCwiseUnaryOp<ei_scalar_multiple_op<typename Lhs::Scalar>,Rhs>::InnerIterator Base;
public:
inline ei_sparse_diagonal_product_inner_iterator_selector(
const SparseDiagonalProductType& expr, int outer)
: Base(expr.rhs()*(expr.lhs().diagonal().coeff(outer)), outer)
{}
};
template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
class ei_sparse_diagonal_product_inner_iterator_selector
<Lhs,Rhs,SparseDiagonalProductType,SDP_IsDiagonal,SDP_IsSparseColMajor>
: public SparseCwiseBinaryOp<
ei_scalar_product_op<typename Lhs::Scalar>,
SparseInnerVectorSet<Rhs,1>,
typename Lhs::_CoeffsVectorType>::InnerIterator
{
typedef typename SparseCwiseBinaryOp<
ei_scalar_product_op<typename Lhs::Scalar>,
SparseInnerVectorSet<Rhs,1>,
typename Lhs::_CoeffsVectorType>::InnerIterator Base;
public:
inline ei_sparse_diagonal_product_inner_iterator_selector(
const SparseDiagonalProductType& expr, int outer)
: Base(expr.rhs().innerVector(outer) .cwise()* expr.lhs().diagonal(), 0)
{}
};
template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
class ei_sparse_diagonal_product_inner_iterator_selector
<Lhs,Rhs,SparseDiagonalProductType,SDP_IsSparseColMajor,SDP_IsDiagonal>
: public SparseCwiseUnaryOp<ei_scalar_multiple_op<typename Rhs::Scalar>,Lhs>::InnerIterator
{
typedef typename SparseCwiseUnaryOp<ei_scalar_multiple_op<typename Rhs::Scalar>,Lhs>::InnerIterator Base;
public:
inline ei_sparse_diagonal_product_inner_iterator_selector(
const SparseDiagonalProductType& expr, int outer)
: Base(expr.lhs()*expr.rhs().diagonal().coeff(outer), outer)
{}
};
template<typename Lhs, typename Rhs, typename SparseDiagonalProductType>
class ei_sparse_diagonal_product_inner_iterator_selector
<Lhs,Rhs,SparseDiagonalProductType,SDP_IsSparseRowMajor,SDP_IsDiagonal>
: public SparseCwiseBinaryOp<
ei_scalar_product_op<typename Rhs::Scalar>,
SparseInnerVectorSet<Lhs,1>,
NestByValue<Transpose<typename Rhs::_CoeffsVectorType> > >::InnerIterator
{
typedef typename SparseCwiseBinaryOp<
ei_scalar_product_op<typename Rhs::Scalar>,
SparseInnerVectorSet<Lhs,1>,
NestByValue<Transpose<typename Rhs::_CoeffsVectorType> > >::InnerIterator Base;
public:
inline ei_sparse_diagonal_product_inner_iterator_selector(
const SparseDiagonalProductType& expr, int outer)
: Base(expr.lhs().innerVector(outer) .cwise()* expr.rhs().diagonal().transpose().nestByValue(), 0)
{}
};
#endif // EIGEN_SPARSE_DIAGONAL_PRODUCT_H

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@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

View File

@@ -29,7 +29,9 @@ template<typename Lhs, typename Rhs> struct ei_sparse_product_mode
{
enum {
value = (Rhs::Flags&Lhs::Flags&SparseBit)==SparseBit
value = ((Lhs::Flags&Diagonal)==Diagonal || (Rhs::Flags&Diagonal)==Diagonal)
? DiagonalProduct
: (Rhs::Flags&Lhs::Flags&SparseBit)==SparseBit
? SparseTimeSparseProduct
: (Lhs::Flags&SparseBit)==SparseBit
? SparseTimeDenseProduct
@@ -45,6 +47,15 @@ struct SparseProductReturnType
typedef SparseProduct<LhsNested, RhsNested, ProductMode> Type;
};
template<typename Lhs, typename Rhs>
struct SparseProductReturnType<Lhs,Rhs,DiagonalProduct>
{
typedef const typename ei_nested<Lhs,Rhs::RowsAtCompileTime>::type LhsNested;
typedef const typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
typedef SparseDiagonalProduct<LhsNested, RhsNested> Type;
};
// sparse product return type specialization
template<typename Lhs, typename Rhs>
struct SparseProductReturnType<Lhs,Rhs,SparseTimeSparseProduct>
@@ -95,7 +106,7 @@ struct ei_traits<SparseProduct<LhsNested, RhsNested, ProductMode> >
// RhsIsRowMajor = (RhsFlags & RowMajorBit)==RowMajorBit,
EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit),
ResultIsSparse = ProductMode==SparseTimeSparseProduct,
ResultIsSparse = ProductMode==SparseTimeSparseProduct || ProductMode==DiagonalProduct,
RemovedBits = ~( (EvalToRowMajor ? 0 : RowMajorBit) | (ResultIsSparse ? 0 : SparseBit) ),
@@ -112,7 +123,8 @@ struct ei_traits<SparseProduct<LhsNested, RhsNested, ProductMode> >
};
template<typename LhsNested, typename RhsNested, int ProductMode>
class SparseProduct : ei_no_assignment_operator, public ei_traits<SparseProduct<LhsNested, RhsNested, ProductMode> >::Base
class SparseProduct : ei_no_assignment_operator,
public ei_traits<SparseProduct<LhsNested, RhsNested, ProductMode> >::Base
{
public:
@@ -285,7 +297,6 @@ template<typename Derived>
template<typename Lhs, typename Rhs>
inline Derived& SparseMatrixBase<Derived>::operator=(const SparseProduct<Lhs,Rhs,SparseTimeSparseProduct>& product)
{
// std::cout << "sparse product to sparse\n";
ei_sparse_product_selector<
typename ei_cleantype<Lhs>::type,
typename ei_cleantype<Rhs>::type,
@@ -311,7 +322,7 @@ inline Derived& SparseMatrixBase<Derived>::operator=(const SparseProduct<Lhs,Rhs
template<typename Derived>
template<typename Lhs, typename Rhs>
Derived& MatrixBase<Derived>::lazyAssign(const SparseProduct<Lhs,Rhs,SparseTimeDenseProduct>& product)
{
{
typedef typename ei_cleantype<Lhs>::type _Lhs;
typedef typename ei_cleantype<Rhs>::type _Rhs;
typedef typename _Lhs::InnerIterator LhsInnerIterator;
@@ -333,7 +344,7 @@ Derived& MatrixBase<Derived>::lazyAssign(const SparseProduct<Lhs,Rhs,SparseTimeD
derived().row(j) += i.value() * product.rhs().row(j);
++i;
}
Block<Derived,1,Derived::ColsAtCompileTime> foo = derived().row(j);
Block<Derived,1,Derived::ColsAtCompileTime> res(derived().row(LhsIsRowMajor ? j : 0));
for (; (ProcessFirstHalf ? i && i.index() < j : i) ; ++i)
{
if (LhsIsSelfAdjoint)
@@ -345,7 +356,7 @@ Derived& MatrixBase<Derived>::lazyAssign(const SparseProduct<Lhs,Rhs,SparseTimeD
derived().row(b) += ei_conj(v) * product.rhs().row(a);
}
else if (LhsIsRowMajor)
foo += i.value() * product.rhs().row(i.index());
res += i.value() * product.rhs().row(i.index());
else
derived().row(i.index()) += i.value() * product.rhs().row(j);
}

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@@ -113,6 +113,7 @@ template<typename UnaryOp, typename MatrixType> class SparseCwiseUnaryO
template<typename BinaryOp, typename Lhs, typename Rhs> class SparseCwiseBinaryOp;
template<typename ExpressionType,
unsigned int Added, unsigned int Removed> class SparseFlagged;
template<typename Lhs, typename Rhs> class SparseDiagonalProduct;
template<typename Lhs, typename Rhs> struct ei_sparse_product_mode;
template<typename Lhs, typename Rhs, int ProductMode = ei_sparse_product_mode<Lhs,Rhs>::value> struct SparseProductReturnType;

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@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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

View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2008-2009 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