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110
3party/eigen/Eigen/src/Householder/BlockHouseholder.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Vincent Lejeune
// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_BLOCK_HOUSEHOLDER_H
#define EIGEN_BLOCK_HOUSEHOLDER_H
// This file contains some helper function to deal with block householder reflectors
namespace Eigen {
namespace internal {
/** \internal */
// template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
// void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
// {
// typedef typename VectorsType::Scalar Scalar;
// const Index nbVecs = vectors.cols();
// eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
//
// for(Index i = 0; i < nbVecs; i++)
// {
// Index rs = vectors.rows() - i;
// // Warning, note that hCoeffs may alias with vectors.
// // It is then necessary to copy it before modifying vectors(i,i).
// typename CoeffsType::Scalar h = hCoeffs(i);
// // This hack permits to pass trough nested Block<> and Transpose<> expressions.
// Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);
// Scalar Vii = *Vii_ptr;
// *Vii_ptr = Scalar(1);
// triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()
// * vectors.col(i).tail(rs);
// *Vii_ptr = Vii;
// // FIXME add .noalias() once the triangular product can work inplace
// triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
// * triFactor.col(i).head(i);
// triFactor(i,i) = hCoeffs(i);
// }
// }
/** \internal */
// This variant avoid modifications in vectors
template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
{
const Index nbVecs = vectors.cols();
eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
for(Index i = nbVecs-1; i >=0 ; --i)
{
Index rs = vectors.rows() - i - 1;
Index rt = nbVecs-i-1;
if(rt>0)
{
triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint()
* vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();
// FIXME use the following line with .noalias() once the triangular product can work inplace
// triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();
for(Index j=nbVecs-1; j>i; --j)
{
typename TriangularFactorType::Scalar z = triFactor(i,j);
triFactor(i,j) = z * triFactor(j,j);
if(nbVecs-j-1>0)
triFactor.row(i).tail(nbVecs-j-1) += z * triFactor.row(j).tail(nbVecs-j-1);
}
}
triFactor(i,i) = hCoeffs(i);
}
}
/** \internal
* if forward then perform mat = H0 * H1 * H2 * mat
* otherwise perform mat = H2 * H1 * H0 * mat
*/
template<typename MatrixType,typename VectorsType,typename CoeffsType>
void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward)
{
enum { TFactorSize = MatrixType::ColsAtCompileTime };
Index nbVecs = vectors.cols();
Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs);
if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);
else make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());
const TriangularView<const VectorsType, UnitLower> V(vectors);
// A -= V T V^* A
Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,
(VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?RowMajor:ColMajor,
VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;
// FIXME add .noalias() once the triangular product can work inplace
if(forward) tmp = T.template triangularView<Upper>() * tmp;
else tmp = T.template triangularView<Upper>().adjoint() * tmp;
mat.noalias() -= V * tmp;
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BLOCK_HOUSEHOLDER_H

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3party/eigen/Eigen/src/Householder/Householder.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_HOUSEHOLDER_H
#define EIGEN_HOUSEHOLDER_H
namespace Eigen {
namespace internal {
template<int n> struct decrement_size
{
enum {
ret = n==Dynamic ? n : n-1
};
};
}
/** Computes the elementary reflector H such that:
* \f$ H *this = [ beta 0 ... 0]^T \f$
* where the transformation H is:
* \f$ H = I - tau v v^*\f$
* and the vector v is:
* \f$ v^T = [1 essential^T] \f$
*
* The essential part of the vector \c v is stored in *this.
*
* On output:
* \param tau the scaling factor of the Householder transformation
* \param beta the result of H * \c *this
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
EIGEN_DEVICE_FUNC
void MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)
{
VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret> essentialPart(derived(), 1, size()-1);
makeHouseholder(essentialPart, tau, beta);
}
/** Computes the elementary reflector H such that:
* \f$ H *this = [ beta 0 ... 0]^T \f$
* where the transformation H is:
* \f$ H = I - tau v v^*\f$
* and the vector v is:
* \f$ v^T = [1 essential^T] \f$
*
* On output:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param beta the result of H * \c *this
*
* \sa MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void MatrixBase<Derived>::makeHouseholder(
EssentialPart& essential,
Scalar& tau,
RealScalar& beta) const
{
using std::sqrt;
using numext::conj;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
Scalar c0 = coeff(0);
const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
{
tau = RealScalar(0);
beta = numext::real(c0);
essential.setZero();
}
else
{
beta = sqrt(numext::abs2(c0) + tailSqNorm);
if (numext::real(c0)>=RealScalar(0))
beta = -beta;
essential = tail / (c0 - beta);
tau = conj((beta - c0) / beta);
}
}
/** Apply the elementary reflector H given by
* \f$ H = I - tau v v^*\f$
* with
* \f$ v^T = [1 essential^T] \f$
* from the left to a vector or matrix.
*
* On input:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param workspace a pointer to working space with at least
* this->cols() entries
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
* MatrixBase::applyHouseholderOnTheRight()
*/
template<typename Derived>
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void MatrixBase<Derived>::applyHouseholderOnTheLeft(
const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace)
{
if(rows() == 1)
{
*this *= Scalar(1)-tau;
}
else if(tau!=Scalar(0))
{
Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
tmp.noalias() = essential.adjoint() * bottom;
tmp += this->row(0);
this->row(0) -= tau * tmp;
bottom.noalias() -= tau * essential * tmp;
}
}
/** Apply the elementary reflector H given by
* \f$ H = I - tau v v^*\f$
* with
* \f$ v^T = [1 essential^T] \f$
* from the right to a vector or matrix.
*
* On input:
* \param essential the essential part of the vector \c v
* \param tau the scaling factor of the Householder transformation
* \param workspace a pointer to working space with at least
* this->rows() entries
*
* \sa MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(),
* MatrixBase::applyHouseholderOnTheLeft()
*/
template<typename Derived>
template<typename EssentialPart>
EIGEN_DEVICE_FUNC
void MatrixBase<Derived>::applyHouseholderOnTheRight(
const EssentialPart& essential,
const Scalar& tau,
Scalar* workspace)
{
if(cols() == 1)
{
*this *= Scalar(1)-tau;
}
else if(tau!=Scalar(0))
{
Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
tmp.noalias() = right * essential;
tmp += this->col(0);
this->col(0) -= tau * tmp;
right.noalias() -= tau * tmp * essential.adjoint();
}
}
} // end namespace Eigen
#endif // EIGEN_HOUSEHOLDER_H

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3party/eigen/Eigen/src/Householder/HouseholderSequence.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H
#define EIGEN_HOUSEHOLDER_SEQUENCE_H
namespace Eigen {
/** \ingroup Householder_Module
* \householder_module
* \class HouseholderSequence
* \brief Sequence of Householder reflections acting on subspaces with decreasing size
* \tparam VectorsType type of matrix containing the Householder vectors
* \tparam CoeffsType type of vector containing the Householder coefficients
* \tparam Side either OnTheLeft (the default) or OnTheRight
*
* This class represents a product sequence of Householder reflections where the first Householder reflection
* acts on the whole space, the second Householder reflection leaves the one-dimensional subspace spanned by
* the first unit vector invariant, the third Householder reflection leaves the two-dimensional subspace
* spanned by the first two unit vectors invariant, and so on up to the last reflection which leaves all but
* one dimensions invariant and acts only on the last dimension. Such sequences of Householder reflections
* are used in several algorithms to zero out certain parts of a matrix. Indeed, the methods
* HessenbergDecomposition::matrixQ(), Tridiagonalization::matrixQ(), HouseholderQR::householderQ(),
* and ColPivHouseholderQR::householderQ() all return a %HouseholderSequence.
*
* More precisely, the class %HouseholderSequence represents an \f$ n \times n \f$ matrix \f$ H \f$ of the
* form \f$ H = \prod_{i=0}^{n-1} H_i \f$ where the i-th Householder reflection is \f$ H_i = I - h_i v_i
* v_i^* \f$. The i-th Householder coefficient \f$ h_i \f$ is a scalar and the i-th Householder vector \f$
* v_i \f$ is a vector of the form
* \f[
* v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
* \f]
* The last \f$ n-i \f$ entries of \f$ v_i \f$ are called the essential part of the Householder vector.
*
* 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 operators.
*
* See the documentation for HouseholderSequence(const VectorsType&, const CoeffsType&) for an example.
*
* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/
namespace internal {
template<typename VectorsType, typename CoeffsType, int Side>
struct traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
{
typedef typename VectorsType::Scalar Scalar;
typedef typename VectorsType::StorageIndex StorageIndex;
typedef typename VectorsType::StorageKind StorageKind;
enum {
RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime
: traits<VectorsType>::ColsAtCompileTime,
ColsAtCompileTime = RowsAtCompileTime,
MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime
: traits<VectorsType>::MaxColsAtCompileTime,
MaxColsAtCompileTime = MaxRowsAtCompileTime,
Flags = 0
};
};
struct HouseholderSequenceShape {};
template<typename VectorsType, typename CoeffsType, int Side>
struct evaluator_traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
: public evaluator_traits_base<HouseholderSequence<VectorsType,CoeffsType,Side> >
{
typedef HouseholderSequenceShape Shape;
};
template<typename VectorsType, typename CoeffsType, int Side>
struct hseq_side_dependent_impl
{
typedef Block<const VectorsType, Dynamic, 1> EssentialVectorType;
typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;
static EIGEN_DEVICE_FUNC inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
{
Index start = k+1+h.m_shift;
return Block<const VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1);
}
};
template<typename VectorsType, typename CoeffsType>
struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>
{
typedef Transpose<Block<const VectorsType, 1, Dynamic> > EssentialVectorType;
typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;
static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
{
Index start = k+1+h.m_shift;
return Block<const VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose();
}
};
template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type
{
typedef typename ScalarBinaryOpTraits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
ResultScalar;
typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;
};
} // end namespace internal
template<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence
: public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> >
{
typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType EssentialVectorType;
public:
enum {
RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime
};
typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;
typedef HouseholderSequence<
typename internal::conditional<NumTraits<Scalar>::IsComplex,
typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,
VectorsType>::type,
typename internal::conditional<NumTraits<Scalar>::IsComplex,
typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,
CoeffsType>::type,
Side
> ConjugateReturnType;
typedef HouseholderSequence<
VectorsType,
typename internal::conditional<NumTraits<Scalar>::IsComplex,
typename internal::remove_all<typename CoeffsType::ConjugateReturnType>::type,
CoeffsType>::type,
Side
> AdjointReturnType;
typedef HouseholderSequence<
typename internal::conditional<NumTraits<Scalar>::IsComplex,
typename internal::remove_all<typename VectorsType::ConjugateReturnType>::type,
VectorsType>::type,
CoeffsType,
Side
> TransposeReturnType;
typedef HouseholderSequence<
typename internal::add_const<VectorsType>::type,
typename internal::add_const<CoeffsType>::type,
Side
> ConstHouseholderSequence;
/** \brief Constructor.
* \param[in] v %Matrix containing the essential parts of the Householder vectors
* \param[in] h Vector containing the Householder coefficients
*
* Constructs the Householder sequence with coefficients given by \p h and vectors given by \p v. The
* i-th Householder coefficient \f$ h_i \f$ is given by \p h(i) and the essential part of the i-th
* Householder vector \f$ v_i \f$ is given by \p v(k,i) with \p k > \p i (the subdiagonal part of the
* i-th column). If \p v has fewer columns than rows, then the Householder sequence contains as many
* Householder reflections as there are columns.
*
* \note The %HouseholderSequence object stores \p v and \p h by reference.
*
* Example: \include HouseholderSequence_HouseholderSequence.cpp
* Output: \verbinclude HouseholderSequence_HouseholderSequence.out
*
* \sa setLength(), setShift()
*/
EIGEN_DEVICE_FUNC
HouseholderSequence(const VectorsType& v, const CoeffsType& h)
: m_vectors(v), m_coeffs(h), m_reverse(false), m_length(v.diagonalSize()),
m_shift(0)
{
}
/** \brief Copy constructor. */
EIGEN_DEVICE_FUNC
HouseholderSequence(const HouseholderSequence& other)
: m_vectors(other.m_vectors),
m_coeffs(other.m_coeffs),
m_reverse(other.m_reverse),
m_length(other.m_length),
m_shift(other.m_shift)
{
}
/** \brief Number of rows of transformation viewed as a matrix.
* \returns Number of rows
* \details This equals the dimension of the space that the transformation acts on.
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); }
/** \brief Number of columns of transformation viewed as a matrix.
* \returns Number of columns
* \details This equals the dimension of the space that the transformation acts on.
*/
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT { return rows(); }
/** \brief Essential part of a Householder vector.
* \param[in] k Index of Householder reflection
* \returns Vector containing non-trivial entries of k-th Householder vector
*
* This function returns the essential part of the Householder vector \f$ v_i \f$. This is a vector of
* length \f$ n-i \f$ containing the last \f$ n-i \f$ entries of the vector
* \f[
* v_i = [\underbrace{0, \ldots, 0}_{i-1\mbox{ zeros}}, 1, \underbrace{*, \ldots,*}_{n-i\mbox{ arbitrary entries}} ].
* \f]
* The index \f$ i \f$ equals \p k + shift(), corresponding to the k-th column of the matrix \p v
* passed to the constructor.
*
* \sa setShift(), shift()
*/
EIGEN_DEVICE_FUNC
const EssentialVectorType essentialVector(Index k) const
{
eigen_assert(k >= 0 && k < m_length);
return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k);
}
/** \brief %Transpose of the Householder sequence. */
TransposeReturnType transpose() const
{
return TransposeReturnType(m_vectors.conjugate(), m_coeffs)
.setReverseFlag(!m_reverse)
.setLength(m_length)
.setShift(m_shift);
}
/** \brief Complex conjugate of the Householder sequence. */
ConjugateReturnType conjugate() const
{
return ConjugateReturnType(m_vectors.conjugate(), m_coeffs.conjugate())
.setReverseFlag(m_reverse)
.setLength(m_length)
.setShift(m_shift);
}
/** \returns an expression of the complex conjugate of \c *this if Cond==true,
* returns \c *this otherwise.
*/
template<bool Cond>
EIGEN_DEVICE_FUNC
inline typename internal::conditional<Cond,ConjugateReturnType,ConstHouseholderSequence>::type
conjugateIf() const
{
typedef typename internal::conditional<Cond,ConjugateReturnType,ConstHouseholderSequence>::type ReturnType;
return ReturnType(m_vectors.template conjugateIf<Cond>(), m_coeffs.template conjugateIf<Cond>());
}
/** \brief Adjoint (conjugate transpose) of the Householder sequence. */
AdjointReturnType adjoint() const
{
return AdjointReturnType(m_vectors, m_coeffs.conjugate())
.setReverseFlag(!m_reverse)
.setLength(m_length)
.setShift(m_shift);
}
/** \brief Inverse of the Householder sequence (equals the adjoint). */
AdjointReturnType inverse() const { return adjoint(); }
/** \internal */
template<typename DestType>
inline EIGEN_DEVICE_FUNC
void evalTo(DestType& dst) const
{
Matrix<Scalar, DestType::RowsAtCompileTime, 1,
AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> workspace(rows());
evalTo(dst, workspace);
}
/** \internal */
template<typename Dest, typename Workspace>
EIGEN_DEVICE_FUNC
void evalTo(Dest& dst, Workspace& workspace) const
{
workspace.resize(rows());
Index vecs = m_length;
if(internal::is_same_dense(dst,m_vectors))
{
// in-place
dst.diagonal().setOnes();
dst.template triangularView<StrictlyUpper>().setZero();
for(Index k = vecs-1; k >= 0; --k)
{
Index cornerSize = rows() - k - m_shift;
if(m_reverse)
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
else
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
// clear the off diagonal vector
dst.col(k).tail(rows()-k-1).setZero();
}
// clear the remaining columns if needed
for(Index k = 0; k<cols()-vecs ; ++k)
dst.col(k).tail(rows()-k-1).setZero();
}
else if(m_length>BlockSize)
{
dst.setIdentity(rows(), rows());
if(m_reverse)
applyThisOnTheLeft(dst,workspace,true);
else
applyThisOnTheLeft(dst,workspace,true);
}
else
{
dst.setIdentity(rows(), rows());
for(Index k = vecs-1; k >= 0; --k)
{
Index cornerSize = rows() - k - m_shift;
if(m_reverse)
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), workspace.data());
else
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), workspace.data());
}
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
{
Matrix<Scalar,1,Dest::RowsAtCompileTime,RowMajor,1,Dest::MaxRowsAtCompileTime> workspace(dst.rows());
applyThisOnTheRight(dst, workspace);
}
/** \internal */
template<typename Dest, typename Workspace>
inline void applyThisOnTheRight(Dest& dst, Workspace& workspace) const
{
workspace.resize(dst.rows());
for(Index k = 0; k < m_length; ++k)
{
Index actual_k = m_reverse ? m_length-k-1 : k;
dst.rightCols(rows()-m_shift-actual_k)
.applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheLeft(Dest& dst, bool inputIsIdentity = false) const
{
Matrix<Scalar,1,Dest::ColsAtCompileTime,RowMajor,1,Dest::MaxColsAtCompileTime> workspace;
applyThisOnTheLeft(dst, workspace, inputIsIdentity);
}
/** \internal */
template<typename Dest, typename Workspace>
inline void applyThisOnTheLeft(Dest& dst, Workspace& workspace, bool inputIsIdentity = false) const
{
if(inputIsIdentity && m_reverse)
inputIsIdentity = false;
// if the entries are large enough, then apply the reflectors by block
if(m_length>=BlockSize && dst.cols()>1)
{
// Make sure we have at least 2 useful blocks, otherwise it is point-less:
Index blockSize = m_length<Index(2*BlockSize) ? (m_length+1)/2 : Index(BlockSize);
for(Index i = 0; i < m_length; i+=blockSize)
{
Index end = m_reverse ? (std::min)(m_length,i+blockSize) : m_length-i;
Index k = m_reverse ? i : (std::max)(Index(0),end-blockSize);
Index bs = end-k;
Index start = k + m_shift;
typedef Block<typename internal::remove_all<VectorsType>::type,Dynamic,Dynamic> SubVectorsType;
SubVectorsType sub_vecs1(m_vectors.const_cast_derived(), Side==OnTheRight ? k : start,
Side==OnTheRight ? start : k,
Side==OnTheRight ? bs : m_vectors.rows()-start,
Side==OnTheRight ? m_vectors.cols()-start : bs);
typename internal::conditional<Side==OnTheRight, Transpose<SubVectorsType>, SubVectorsType&>::type sub_vecs(sub_vecs1);
Index dstStart = dst.rows()-rows()+m_shift+k;
Index dstRows = rows()-m_shift-k;
Block<Dest,Dynamic,Dynamic> sub_dst(dst,
dstStart,
inputIsIdentity ? dstStart : 0,
dstRows,
inputIsIdentity ? dstRows : dst.cols());
apply_block_householder_on_the_left(sub_dst, sub_vecs, m_coeffs.segment(k, bs), !m_reverse);
}
}
else
{
workspace.resize(dst.cols());
for(Index k = 0; k < m_length; ++k)
{
Index actual_k = m_reverse ? k : m_length-k-1;
Index dstStart = rows()-m_shift-actual_k;
dst.bottomRightCorner(dstStart, inputIsIdentity ? dstStart : dst.cols())
.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), workspace.data());
}
}
}
/** \brief Computes the product of a Householder sequence with a matrix.
* \param[in] other %Matrix being multiplied.
* \returns Expression object representing the product.
*
* This function computes \f$ HM \f$ where \f$ H \f$ is the Householder sequence represented by \p *this
* and \f$ M \f$ is the matrix \p other.
*/
template<typename OtherDerived>
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const
{
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type
res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar,OtherDerived>::ResultScalar>());
applyThisOnTheLeft(res, internal::is_identity<OtherDerived>::value && res.rows()==res.cols());
return res;
}
template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl;
/** \brief Sets the length of the Householder sequence.
* \param [in] length New value for the length.
*
* By default, the length \f$ n \f$ of the Householder sequence \f$ H = H_0 H_1 \ldots H_{n-1} \f$ is set
* to the number of columns of the matrix \p v passed to the constructor, or the number of rows if that
* is smaller. After this function is called, the length equals \p length.
*
* \sa length()
*/
EIGEN_DEVICE_FUNC
HouseholderSequence& setLength(Index length)
{
m_length = length;
return *this;
}
/** \brief Sets the shift of the Householder sequence.
* \param [in] shift New value for the shift.
*
* By default, a %HouseholderSequence object represents \f$ H = H_0 H_1 \ldots H_{n-1} \f$ and the i-th
* column of the matrix \p v passed to the constructor corresponds to the i-th Householder
* reflection. After this function is called, the object represents \f$ H = H_{\mathrm{shift}}
* H_{\mathrm{shift}+1} \ldots H_{n-1} \f$ and the i-th column of \p v corresponds to the (shift+i)-th
* Householder reflection.
*
* \sa shift()
*/
EIGEN_DEVICE_FUNC
HouseholderSequence& setShift(Index shift)
{
m_shift = shift;
return *this;
}
EIGEN_DEVICE_FUNC
Index length() const { return m_length; } /**< \brief Returns the length of the Householder sequence. */
EIGEN_DEVICE_FUNC
Index shift() const { return m_shift; } /**< \brief Returns the shift of the Householder sequence. */
/* Necessary for .adjoint() and .conjugate() */
template <typename VectorsType2, typename CoeffsType2, int Side2> friend class HouseholderSequence;
protected:
/** \internal
* \brief Sets the reverse flag.
* \param [in] reverse New value of the reverse flag.
*
* By default, the reverse flag is not set. If the reverse flag is set, then this object represents
* \f$ H^r = H_{n-1} \ldots H_1 H_0 \f$ instead of \f$ H = H_0 H_1 \ldots H_{n-1} \f$.
* \note For real valued HouseholderSequence this is equivalent to transposing \f$ H \f$.
*
* \sa reverseFlag(), transpose(), adjoint()
*/
HouseholderSequence& setReverseFlag(bool reverse)
{
m_reverse = reverse;
return *this;
}
bool reverseFlag() const { return m_reverse; } /**< \internal \brief Returns the reverse flag. */
typename VectorsType::Nested m_vectors;
typename CoeffsType::Nested m_coeffs;
bool m_reverse;
Index m_length;
Index m_shift;
enum { BlockSize = 48 };
};
/** \brief Computes the product of a matrix with a Householder sequence.
* \param[in] other %Matrix being multiplied.
* \param[in] h %HouseholderSequence being multiplied.
* \returns Expression object representing the product.
*
* This function computes \f$ MH \f$ where \f$ M \f$ is the matrix \p other and \f$ H \f$ is the
* Householder sequence represented by \p h.
*/
template<typename OtherDerived, typename VectorsType, typename CoeffsType, int Side>
typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence<VectorsType,CoeffsType,Side>& h)
{
typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::Type
res(other.template cast<typename internal::matrix_type_times_scalar_type<typename VectorsType::Scalar,OtherDerived>::ResultScalar>());
h.applyThisOnTheRight(res);
return res;
}
/** \ingroup Householder_Module \householder_module
* \brief Convenience function for constructing a Householder sequence.
* \returns A HouseholderSequence constructed from the specified arguments.
*/
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h);
}
/** \ingroup Householder_Module \householder_module
* \brief Convenience function for constructing a Householder sequence.
* \returns A HouseholderSequence constructed from the specified arguments.
* \details This function differs from householderSequence() in that the template argument \p OnTheSide of
* the constructed HouseholderSequence is set to OnTheRight, instead of the default OnTheLeft.
*/
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType,OnTheRight> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h);
}
} // end namespace Eigen
#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H