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// 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 Benoit Jacob <jacob@math.jussieu.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_EXTRACT_H
#define EIGEN_EXTRACT_H
/** \class Extract
*
* \brief Expression of a triangular matrix extracted from a given matrix
*
* \param MatrixType the type of the object in which we are taking the triangular part
* \param Mode the kind of triangular matrix expression to construct. Can be Upper, StrictlyUpper,
* UnitUpper, Lower, StrictlyLower, UnitLower. This is in fact a bit field; it must have either
* UpperTriangularBit or LowerTriangularBit, and additionnaly it may have either ZeroDiagBit or
* UnitDiagBit.
*
* This class represents an expression of the upper or lower triangular part of
* a square matrix, possibly with a further assumption on the diagonal. It is the return type
* of MatrixBase::extract() and most of the time this is the only way it is used.
*
* \sa MatrixBase::extract()
*/
template<typename MatrixType, unsigned int Mode>
struct ei_traits<Extract<MatrixType, Mode> >
{
typedef typename MatrixType::Scalar Scalar;
typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
Flags = (_MatrixTypeNested::Flags & ~(VectorizableBit | Like1DArrayBit | DirectAccessBit)) | Mode,
CoeffReadCost = _MatrixTypeNested::CoeffReadCost
};
};
template<typename MatrixType, unsigned int Mode> class Extract
: public MatrixBase<Extract<MatrixType, Mode> >
{
public:
EIGEN_GENERIC_PUBLIC_INTERFACE(Extract)
inline Extract(const MatrixType& matrix) : m_matrix(matrix) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Extract)
private:
inline int _rows() const { return m_matrix.rows(); }
inline int _cols() const { return m_matrix.cols(); }
inline Scalar _coeff(int row, int col) const
{
if(Flags & LowerTriangularBit ? col>row : row>col)
return (Flags & SelfAdjointBit) ? ei_conj(m_matrix.coeff(col, row)) : (Scalar)0;
if(Flags & UnitDiagBit)
return col==row ? (Scalar)1 : m_matrix.coeff(row, col);
else if(Flags & ZeroDiagBit)
return col==row ? (Scalar)0 : m_matrix.coeff(row, col);
else
return m_matrix.coeff(row, col);
}
protected:
const typename MatrixType::Nested m_matrix;
};
/** \returns an expression of a triangular matrix extracted from the current matrix
*
* The parameter \a Mode can have the following values: \c Upper, \c StrictlyUpper, \c UnitUpper,
* \c Lower, \c StrictlyLower, \c UnitLower.
*
* Example: \include MatrixBase_extract.cpp
* Output: \verbinclude MatrixBase_extract.out
*
* \sa class Extract, part(), marked()
*/
template<typename Derived>
template<unsigned int Mode>
const Extract<Derived, Mode> MatrixBase<Derived>::extract() const
{
return derived();
}
/** \returns true if *this is approximately equal to an upper triangular matrix,
* within the precision given by \a prec.
*
* \sa isLower(), extract(), part(), marked()
*/
template<typename Derived>
bool MatrixBase<Derived>::isUpper(RealScalar prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); j++)
for(int i = 0; i <= j; i++)
{
RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
}
for(int j = 0; j < cols()-1; j++)
for(int i = j+1; i < rows(); i++)
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperPart, prec)) return false;
return true;
}
/** \returns true if *this is approximately equal to a lower triangular matrix,
* within the precision given by \a prec.
*
* \sa isUpper(), extract(), part(), marked()
*/
template<typename Derived>
bool MatrixBase<Derived>::isLower(RealScalar prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); j++)
for(int i = j; i < rows(); i++)
{
RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
}
for(int j = 1; j < cols(); j++)
for(int i = 0; i < j; i++)
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerPart, prec)) return false;
return true;
}
#endif // EIGEN_EXTRACT_H
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