11 #ifndef EIGEN_HESSENBERGDECOMPOSITION_H 12 #define EIGEN_HESSENBERGDECOMPOSITION_H 18 template<
typename MatrixType>
struct HessenbergDecompositionMatrixHReturnType;
19 template<
typename MatrixType>
20 struct 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)
106 m_hCoeffs.resize(size-1);
118 template<
typename InputType>
120 : m_matrix(matrix.derived()),
121 m_temp(matrix.rows()),
122 m_isInitialized(false)
126 m_isInitialized =
true;
129 m_hCoeffs.resize(matrix.
rows()-1,1);
130 _compute(m_matrix, m_hCoeffs, m_temp);
131 m_isInitialized =
true;
151 template<
typename InputType>
157 m_isInitialized =
true;
160 m_hCoeffs.resize(matrix.
rows()-1,1);
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.");
237 return HouseholderSequenceType(m_matrix, m_hCoeffs.conjugate())
238 .setLength(m_matrix.rows() - 1)
264 eigen_assert(m_isInitialized &&
"HessenbergDecomposition is not initialized.");
265 return MatrixHReturnType(*
this);
272 static void _compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp);
276 CoeffVectorType m_hCoeffs;
278 bool m_isInitialized;
293 template<
typename MatrixType>
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;
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));
339 template<
typename MatrixType>
struct HessenbergDecompositionMatrixHReturnType
340 :
public ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> >
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(); }
374 #endif // EIGEN_HESSENBERGDECOMPOSITION_H const MatrixType & packedMatrix() const
Returns the internal representation of the decomposition.
Definition: HessenbergDecomposition.h:214
Namespace containing all symbols from the Eigen library.
Definition: Core:141
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:232
Derived & derived()
Definition: EigenBase.h:46
_MatrixType MatrixType
Synonym for the template parameter _MatrixType.
Definition: HessenbergDecomposition.h:62
void resize(Index rows, Index cols)
Definition: PlainObjectBase.h:271
MatrixType::Scalar Scalar
Scalar type for matrices of type MatrixType.
Definition: HessenbergDecomposition.h:73
Definition: EigenBase.h:29
Sequence of Householder reflections acting on subspaces with decreasing size.
Definition: HouseholderSequence.h:119
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:175
Eigen::Index Index
Definition: HessenbergDecomposition.h:74
HessenbergDecomposition & compute(const EigenBase< InputType > &matrix)
Computes Hessenberg decomposition of given matrix.
Definition: HessenbergDecomposition.h:152
MatrixHReturnType matrixH() const
Constructs the Hessenberg matrix H in the decomposition.
Definition: HessenbergDecomposition.h:262
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
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
Definition: Eigen_Colamd.h:50
Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.
Definition: HessenbergDecomposition.h:57
HouseholderSequenceType matrixQ() const
Reconstructs the orthogonal matrix Q in the decomposition.
Definition: HessenbergDecomposition.h:234
const CoeffVectorType & householderCoefficients() const
Returns the Householder coefficients.
Definition: HessenbergDecomposition.h:179
EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT
Definition: EigenBase.h:60
const int Dynamic
Definition: Constants.h:22
HouseholderSequence< MatrixType, typename internal::remove_all< typename CoeffVectorType::ConjugateReturnType >::type > HouseholderSequenceType
Return type of matrixQ()
Definition: HessenbergDecomposition.h:85
Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > CoeffVectorType
Type for vector of Householder coefficients.
Definition: HessenbergDecomposition.h:82