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// 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_HOUSEHOLDER_SEQUENCE_H
#define EIGEN_HOUSEHOLDER_SEQUENCE_H
/** \ingroup Householder_Module
* \householder_module
* \class HouseholderSequence
* \brief Represents a sequence of householder reflections with decreasing size
*
* This class represents a product sequence of householder reflections \f$ H = \Pi_0^{n-1} H_i \f$
* where \f$ H_i \f$ is the i-th householder transformation \f$ I - h_i v_i v_i^* \f$,
* \f$ v_i \f$ is the i-th householder vector \f$ [ 1, m_vectors(i+1,i), m_vectors(i+2,i), ...] \f$
* and \f$ h_i \f$ is the i-th householder coefficient \c m_coeffs[i].
*
* Typical usages are listed below, where H is a HouseholderSequence:
* \code
* A.applyOnTheRight(H); // A = A * H
* A.applyOnTheLeft(H); // A = H * A
* A.applyOnTheRight(H.adjoint()); // A = A * H^*
* A.applyOnTheLeft(H.adjoint()); // A = H^* * A
* MatrixXd Q = H; // conversion to a dense matrix
* \endcode
* In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate.
*
* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/
template<typename VectorsType, typename CoeffsType>
struct ei_traits<HouseholderSequence<VectorsType,CoeffsType> >
{
typedef typename VectorsType::Scalar Scalar;
enum {
RowsAtCompileTime = ei_traits<VectorsType>::RowsAtCompileTime,
ColsAtCompileTime = ei_traits<VectorsType>::RowsAtCompileTime,
MaxRowsAtCompileTime = ei_traits<VectorsType>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = ei_traits<VectorsType>::MaxRowsAtCompileTime,
Flags = 0
};
};
template<typename VectorsType, typename CoeffsType> class HouseholderSequence
: public AnyMatrixBase<HouseholderSequence<VectorsType,CoeffsType> >
{
typedef typename VectorsType::Scalar Scalar;
public:
typedef HouseholderSequence<VectorsType,
typename ei_meta_if<NumTraits<Scalar>::IsComplex,
NestByValue<typename ei_cleantype<typename CoeffsType::ConjugateReturnType>::type >,
CoeffsType>::ret> ConjugateReturnType;
HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans = false)
: m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(v.diagonalSize())
{}
HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors)
: m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(actualVectors)
{}
int rows() const { return m_vectors.rows(); }
int cols() const { return m_vectors.rows(); }
HouseholderSequence transpose() const
{ return HouseholderSequence(m_vectors, m_coeffs, !m_trans, m_actualVectors); }
ConjugateReturnType conjugate() const
{ return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), m_trans, m_actualVectors); }
ConjugateReturnType adjoint() const
{ return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), !m_trans, m_actualVectors); }
ConjugateReturnType inverse() const { return adjoint(); }
/** \internal */
template<typename DestType> void evalTo(DestType& dst) const
{
int vecs = m_actualVectors;
int length = m_vectors.rows();
dst.setIdentity();
Matrix<Scalar,1,DestType::RowsAtCompileTime> temp(dst.rows());
for(int k = vecs-1; k >= 0; --k)
{
if(m_trans)
dst.corner(BottomRight, length-k, length-k)
.applyHouseholderOnTheRight(m_vectors.col(k).end(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(0));
else
dst.corner(BottomRight, length-k, length-k)
.applyHouseholderOnTheLeft(m_vectors.col(k).end(length-k-1), m_coeffs.coeff(k), &temp.coeffRef(k));
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
{
int vecs = m_actualVectors; // number of householder vectors
int length = m_vectors.rows(); // size of the largest householder vector
Matrix<Scalar,1,Dest::RowsAtCompileTime> temp(dst.rows());
for(int k = 0; k < vecs; ++k)
{
int actual_k = m_trans ? vecs-k-1 : k;
dst.corner(BottomRight, dst.rows(), length-actual_k)
.applyHouseholderOnTheRight(m_vectors.col(actual_k).end(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
{
int vecs = m_actualVectors; // number of householder vectors
int length = m_vectors.rows(); // size of the largest householder vector
Matrix<Scalar,1,Dest::ColsAtCompileTime> temp(dst.cols());
for(int k = 0; k < vecs; ++k)
{
int actual_k = m_trans ? k : vecs-k-1;
dst.corner(BottomRight, length-actual_k, dst.cols())
.applyHouseholderOnTheLeft(m_vectors.col(actual_k).end(length-actual_k-1), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
}
}
template<typename OtherDerived>
typename OtherDerived::PlainMatrixType operator*(const MatrixBase<OtherDerived>& other) const
{
typename OtherDerived::PlainMatrixType res(other);
applyThisOnTheLeft(res);
return res;
}
template<typename OtherDerived> friend
typename OtherDerived::PlainMatrixType operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence& h)
{
typename OtherDerived::PlainMatrixType res(other);
h.applyThisOnTheRight(res);
return res;
}
protected:
typename VectorsType::Nested m_vectors;
typename CoeffsType::Nested m_coeffs;
bool m_trans;
int m_actualVectors;
private:
HouseholderSequence& operator=(const HouseholderSequence&);
};
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h, bool trans=false)
{
return HouseholderSequence<VectorsType,CoeffsType>(v, h, trans);
}
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h, bool trans, int actualVectors)
{
return HouseholderSequence<VectorsType,CoeffsType>(v, h, trans, actualVectors);
}
#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H
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