11#ifndef EIGEN_HESSENBERGDECOMPOSITION_H
12#define EIGEN_HESSENBERGDECOMPOSITION_H
18template<
typename MatrixType>
struct HessenbergDecompositionMatrixHReturnType;
19template<
typename MatrixType>
20struct traits<HessenbergDecompositionMatrixHReturnType<MatrixType> >
22 typedef MatrixType ReturnType;
65 Size = MatrixType::RowsAtCompileTime,
67 Options = MatrixType::Options,
68 MaxSize = MatrixType::MaxRowsAtCompileTime,
73 typedef typename MatrixType::Scalar
Scalar;
87 typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
101 : m_matrix(size,size),
103 m_isInitialized(false)
118 template<
typename InputType>
120 : m_matrix(matrix.derived()),
121 m_temp(matrix.rows()),
122 m_isInitialized(false)
126 m_isInitialized =
true;
130 _compute(m_matrix, m_hCoeffs, m_temp);
131 m_isInitialized =
true;
151 template<
typename InputType>
157 m_isInitialized =
true;
161 _compute(m_matrix, m_hCoeffs, m_temp);
162 m_isInitialized =
true;
181 eigen_assert(m_isInitialized &&
"HessenbergDecomposition is not initialized.");
216 eigen_assert(m_isInitialized &&
"HessenbergDecomposition is not initialized.");
236 eigen_assert(m_isInitialized &&
"HessenbergDecomposition is not initialized.");
238 .setLength(m_matrix.rows() - 1)
264 eigen_assert(m_isInitialized &&
"HessenbergDecomposition is not initialized.");
265 return MatrixHReturnType(*
this);
271 typedef typename NumTraits<Scalar>::Real RealScalar;
278 bool m_isInitialized;
293template<
typename MatrixType>
294void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp)
296 eigen_assert(matA.rows()==matA.cols());
297 Index n = matA.rows();
299 for (Index i = 0; i<n-1; ++i)
302 Index remainingSize = n-i-1;
305 matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);
306 matA.col(i).coeffRef(i+1) = beta;
307 hCoeffs.coeffRef(i) = h;
313 matA.bottomRightCorner(remainingSize, remainingSize)
314 .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));
317 matA.rightCols(remainingSize)
318 .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1), numext::conj(h), &temp.coeffRef(0));
339template<
typename MatrixType>
struct HessenbergDecompositionMatrixHReturnType
340:
public ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> >
347 HessenbergDecompositionMatrixHReturnType(
const HessenbergDecomposition<MatrixType>& hess) : m_hess(hess) { }
354 template <
typename ResultType>
355 inline void evalTo(ResultType& result)
const
357 result = m_hess.packedMatrix();
358 Index n = result.rows();
360 result.bottomLeftCorner(n-2, n-2).template triangularView<Lower>().setZero();
363 Index rows()
const {
return m_hess.packedMatrix().rows(); }
364 Index cols()
const {
return m_hess.packedMatrix().cols(); }
367 const HessenbergDecomposition<MatrixType>& m_hess;
Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.
Definition: HessenbergDecomposition.h:58
HessenbergDecomposition & compute(const EigenBase< InputType > &matrix)
Computes Hessenberg decomposition of given matrix.
Definition: HessenbergDecomposition.h:152
HouseholderSequenceType matrixQ() const
Reconstructs the orthogonal matrix Q in the decomposition.
Definition: HessenbergDecomposition.h:234
const MatrixType & packedMatrix() const
Returns the internal representation of the decomposition.
Definition: HessenbergDecomposition.h:214
Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > CoeffVectorType
Type for vector of Householder coefficients.
Definition: HessenbergDecomposition.h:82
HouseholderSequence< MatrixType, typename internal::remove_all< typename CoeffVectorType::ConjugateReturnType >::type > HouseholderSequenceType
Return type of matrixQ()
Definition: HessenbergDecomposition.h:85
Eigen::Index Index
Definition: HessenbergDecomposition.h:74
MatrixHReturnType matrixH() const
Constructs the Hessenberg matrix H in the decomposition.
Definition: HessenbergDecomposition.h:262
_MatrixType MatrixType
Synonym for the template parameter _MatrixType.
Definition: HessenbergDecomposition.h:62
MatrixType::Scalar Scalar
Scalar type for matrices of type MatrixType.
Definition: HessenbergDecomposition.h:73
HessenbergDecomposition(const EigenBase< InputType > &matrix)
Constructor; computes Hessenberg decomposition of given matrix.
Definition: HessenbergDecomposition.h:119
HessenbergDecomposition(Index size=Size==Dynamic ? 2 :Size)
Default constructor; the decomposition will be computed later.
Definition: HessenbergDecomposition.h:100
const CoeffVectorType & householderCoefficients() const
Returns the Householder coefficients.
Definition: HessenbergDecomposition.h:179
Sequence of Householder reflections acting on subspaces with decreasing size.
Definition: HouseholderSequence.h:121
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
void resize(Index rows, Index cols)
Definition: PlainObjectBase.h:271
@ RowMajor
Definition: Constants.h:321
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const int Dynamic
Definition: Constants.h:22
Definition: EigenBase.h:30
Derived & derived()
Definition: EigenBase.h:46
EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: EigenBase.h:60