Householder rank-revealing QR decomposition of a matrix with column-pivoting. More...
#include <ColPivHouseholderQR.h>
Inheritance diagram for Eigen::ColPivHouseholderQR< _MatrixType >:
Protected Member Functions | |
| void | computeInPlace () |
| Protected Member Functions inherited from Eigen::SolverBase< ColPivHouseholderQR< _MatrixType > > | |
| void | _check_solve_assertion (const Rhs &b) const |
Static Protected Member Functions | |
| static void | check_template_parameters () |
Protected Attributes | |
| MatrixType | m_qr |
| HCoeffsType | m_hCoeffs |
| PermutationType | m_colsPermutation |
| IntRowVectorType | m_colsTranspositions |
| RowVectorType | m_temp |
| RealRowVectorType | m_colNormsUpdated |
| RealRowVectorType | m_colNormsDirect |
| bool | m_isInitialized |
| bool | m_usePrescribedThreshold |
| RealScalar | m_prescribedThreshold |
| RealScalar | m_maxpivot |
| Index | m_nonzero_pivots |
| Index | m_det_pq |
Private Types | |
| typedef PermutationType::StorageIndex | PermIndexType |
Friends | |
| class | SolverBase< ColPivHouseholderQR > |
| class | CompleteOrthogonalDecomposition< MatrixType > |
Detailed Description
template<typename _MatrixType>
class Eigen::ColPivHouseholderQR< _MatrixType >
Householder rank-revealing QR decomposition of a matrix with column-pivoting.
- Template Parameters
-
_MatrixType the type of the matrix of which we are computing the QR decomposition
This class performs a rank-revealing QR decomposition of a matrix A into matrices P, Q and R such that
![\[ \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R} \]](form_174.png)
by using Householder transformations. Here, P is a permutation matrix, Q a unitary matrix and R an upper triangular matrix.
This decomposition performs column pivoting in order to be rank-revealing and improve numerical stability. It is slower than HouseholderQR, and faster than FullPivHouseholderQR.
This class supports the inplace decomposition mechanism.
Member Typedef Documentation
◆ Base
template<typename _MatrixType >
| typedef SolverBase<ColPivHouseholderQR> Eigen::ColPivHouseholderQR< _MatrixType >::Base |
◆ HCoeffsType
template<typename _MatrixType >
| typedef internal::plain_diag_type<MatrixType>::type Eigen::ColPivHouseholderQR< _MatrixType >::HCoeffsType |
◆ HouseholderSequenceType
template<typename _MatrixType >
| typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> Eigen::ColPivHouseholderQR< _MatrixType >::HouseholderSequenceType |
◆ IntRowVectorType
template<typename _MatrixType >
| typedef internal::plain_row_type<MatrixType, Index>::type Eigen::ColPivHouseholderQR< _MatrixType >::IntRowVectorType |
◆ MatrixType
template<typename _MatrixType >
| typedef _MatrixType Eigen::ColPivHouseholderQR< _MatrixType >::MatrixType |
◆ PermIndexType
template<typename _MatrixType >
|
private |
◆ PermutationType
template<typename _MatrixType >
| typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> Eigen::ColPivHouseholderQR< _MatrixType >::PermutationType |
◆ PlainObject
template<typename _MatrixType >
| typedef MatrixType::PlainObject Eigen::ColPivHouseholderQR< _MatrixType >::PlainObject |
◆ RealRowVectorType
template<typename _MatrixType >
| typedef internal::plain_row_type<MatrixType, RealScalar>::type Eigen::ColPivHouseholderQR< _MatrixType >::RealRowVectorType |
◆ RowVectorType
template<typename _MatrixType >
| typedef internal::plain_row_type<MatrixType>::type Eigen::ColPivHouseholderQR< _MatrixType >::RowVectorType |
Member Enumeration Documentation
◆ anonymous enum
Constructor & Destructor Documentation
◆ ColPivHouseholderQR() [1/4]
template<typename _MatrixType >
|
inline |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).
◆ ColPivHouseholderQR() [2/4]
template<typename _MatrixType >
|
inline |
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
- See also
- ColPivHouseholderQR()
◆ ColPivHouseholderQR() [3/4]
template<typename _MatrixType >
template<typename InputType >
|
inlineexplicit |
◆ ColPivHouseholderQR() [4/4]
template<typename _MatrixType >
template<typename InputType >
|
inlineexplicit |
Constructs a QR factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.
- See also
- ColPivHouseholderQR(const EigenBase&)
Member Function Documentation
◆ _solve_impl()
template<typename _MatrixType >
template<typename RhsType , typename DstType >
| void Eigen::ColPivHouseholderQR< _MatrixType >::_solve_impl | ( | const RhsType & | rhs, |
| DstType & | dst | ||
| ) | const |
◆ _solve_impl_transposed()
template<typename _MatrixType >
template<bool Conjugate, typename RhsType , typename DstType >
| void Eigen::ColPivHouseholderQR< _MatrixType >::_solve_impl_transposed | ( | const RhsType & | rhs, |
| DstType & | dst | ||
| ) | const |
◆ absDeterminant()
template<typename MatrixType >
| MatrixType::RealScalar Eigen::ColPivHouseholderQR< MatrixType >::absDeterminant |
- Returns
- the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
- Note
- This is only for square matrices.
- Warning
- a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.
◆ check_template_parameters()
template<typename _MatrixType >
|
inlinestaticprotected |
◆ cols()
template<typename _MatrixType >
|
inline |
◆ colsPermutation()
template<typename _MatrixType >
|
inline |
- Returns
- a const reference to the column permutation matrix
◆ compute() [1/2]
template<typename _MatrixType >
template<typename InputType >
| ColPivHouseholderQR& Eigen::ColPivHouseholderQR< _MatrixType >::compute | ( | const EigenBase< InputType > & | matrix | ) |
◆ compute() [2/2]
template<typename _MatrixType >
template<typename InputType >
| ColPivHouseholderQR<MatrixType>& Eigen::ColPivHouseholderQR< _MatrixType >::compute | ( | const EigenBase< InputType > & | matrix | ) |
Performs the QR factorization of the given matrix matrix. The result of the factorization is stored into *this, and a reference to *this is returned.
- See also
- class ColPivHouseholderQR, ColPivHouseholderQR(const MatrixType&)
◆ computeInPlace()
template<typename MatrixType >
|
protected |
◆ dimensionOfKernel()
template<typename _MatrixType >
|
inline |
- Returns
- the dimension of the kernel of the matrix of which *this is the QR decomposition.
- Note
- This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ hCoeffs()
template<typename _MatrixType >
|
inline |
- Returns
- a const reference to the vector of Householder coefficients used to represent the factor
Q.
For advanced uses only.
◆ householderQ()
template<typename MatrixType >
| ColPivHouseholderQR< MatrixType >::HouseholderSequenceType Eigen::ColPivHouseholderQR< MatrixType >::householderQ |
- Returns
- the matrix Q as a sequence of householder transformations. You can extract the meaningful part only by using: qr.householderQ().setLength(qr.nonzeroPivots())
◆ info()
template<typename _MatrixType >
|
inline |
Reports whether the QR factorization was successful.
- Note
- This function always returns
Success. It is provided for compatibility with other factorization routines.
- Returns
Success
◆ inverse()
template<typename _MatrixType >
|
inline |
- Returns
- the inverse of the matrix of which *this is the QR decomposition.
- Note
- If this matrix is not invertible, the returned matrix has undefined coefficients. Use isInvertible() to first determine whether this matrix is invertible.
◆ isInjective()
template<typename _MatrixType >
|
inline |
- Returns
- true if the matrix of which *this is the QR decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.
- Note
- This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ isInvertible()
template<typename _MatrixType >
|
inline |
- Returns
- true if the matrix of which *this is the QR decomposition is invertible.
- Note
- This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ isSurjective()
template<typename _MatrixType >
|
inline |
- Returns
- true if the matrix of which *this is the QR decomposition represents a surjective linear map; false otherwise.
- Note
- This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ logAbsDeterminant()
template<typename MatrixType >
| MatrixType::RealScalar Eigen::ColPivHouseholderQR< MatrixType >::logAbsDeterminant |
- Returns
- the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
- Note
- This is only for square matrices.
- This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.
◆ matrixQ()
template<typename _MatrixType >
|
inline |
◆ matrixQR()
template<typename _MatrixType >
|
inline |
- Returns
- a reference to the matrix where the Householder QR decomposition is stored
◆ matrixR()
template<typename _MatrixType >
|
inline |
- Returns
- a reference to the matrix where the result Householder QR is stored
- Warning
- The strict lower part of this matrix contains internal values. Only the upper triangular part should be referenced. To get it, use For rank-deficient matrices, usematrixR().template triangularView<Upper>()const MatrixType & matrixR() constDefinition: ColPivHouseholderQR.h:204
◆ maxPivot()
template<typename _MatrixType >
|
inline |
- Returns
- the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of R.
◆ nonzeroPivots()
template<typename _MatrixType >
|
inline |
- Returns
- the number of nonzero pivots in the QR decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.
- See also
- rank()
◆ rank()
template<typename _MatrixType >
|
inline |
- Returns
- the rank of the matrix of which *this is the QR decomposition.
- Note
- This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ rows()
template<typename _MatrixType >
|
inline |
◆ setThreshold() [1/2]
template<typename _MatrixType >
|
inline |
Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero. This is not used for the QR decomposition itself.
When it needs to get the threshold value, Eigen calls threshold(). By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method setThreshold(const RealScalar&), your value is used instead.
- Parameters
-
threshold The new value to use as the threshold.
A pivot will be considered nonzero if its absolute value is strictly greater than 
where maxpivot is the biggest pivot.
If you want to come back to the default behavior, call setThreshold(Default_t)
◆ setThreshold() [2/2]
template<typename _MatrixType >
|
inline |
Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.
You should pass the special object Eigen::Default as parameter here.
qr.setThreshold(Eigen::Default);
See the documentation of setThreshold(const RealScalar&).
◆ threshold()
template<typename _MatrixType >
|
inline |
Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
Friends And Related Function Documentation
◆ CompleteOrthogonalDecomposition< MatrixType >
template<typename _MatrixType >
|
friend |
◆ SolverBase< ColPivHouseholderQR >
template<typename _MatrixType >
|
friend |
Member Data Documentation
◆ m_colNormsDirect
template<typename _MatrixType >
|
protected |
◆ m_colNormsUpdated
template<typename _MatrixType >
|
protected |
◆ m_colsPermutation
template<typename _MatrixType >
|
protected |
◆ m_colsTranspositions
template<typename _MatrixType >
|
protected |
◆ m_det_pq
template<typename _MatrixType >
|
protected |
◆ m_hCoeffs
template<typename _MatrixType >
|
protected |
◆ m_isInitialized
template<typename _MatrixType >
|
protected |
◆ m_maxpivot
template<typename _MatrixType >
|
protected |
◆ m_nonzero_pivots
template<typename _MatrixType >
|
protected |
◆ m_prescribedThreshold
template<typename _MatrixType >
|
protected |
◆ m_qr
template<typename _MatrixType >
|
protected |
◆ m_temp
template<typename _MatrixType >
|
protected |
◆ m_usePrescribedThreshold
template<typename _MatrixType >
|
protected |
The documentation for this class was generated from the following files:
- /home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/Core/util/ForwardDeclarations.h
- /home/runner/work/NDDEM/NDDEM/src/CoarseGraining/Eigen/src/QR/ColPivHouseholderQR.h
