Householder rank-revealing QR decomposition of a matrix with column-pivoting.
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
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.
Definition at line 51 of file QR.
Public Types | |
enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime } |
typedef _MatrixType | MatrixType |
typedef MatrixType::Scalar | Scalar |
typedef MatrixType::RealScalar | RealScalar |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixQType |
typedef internal::plain_diag_type < MatrixType >::type | HCoeffsType |
typedef PermutationMatrix < ColsAtCompileTime, MaxColsAtCompileTime > | PermutationType |
typedef internal::plain_row_type < MatrixType, Index >::type | IntRowVectorType |
typedef internal::plain_row_type < MatrixType >::type | RowVectorType |
typedef internal::plain_row_type < MatrixType, RealScalar > ::type | RealRowVectorType |
typedef HouseholderSequence < MatrixType, HCoeffsType > ::ConjugateReturnType | HouseholderSequenceType |
Public Member Functions | |
ColPivHouseholderQR () | |
Default Constructor. | |
ColPivHouseholderQR (Index rows, Index cols) | |
Default Constructor with memory preallocation. | |
ColPivHouseholderQR (const MatrixType &matrix) | |
template<typename Rhs > | |
const internal::solve_retval < ColPivHouseholderQR, Rhs > | solve (const MatrixBase< Rhs > &b) const |
This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists. | |
HouseholderSequenceType | householderQ (void) const |
const MatrixType & | matrixQR () const |
ColPivHouseholderQR & | compute (const MatrixType &matrix) |
const PermutationType & | colsPermutation () const |
MatrixType::RealScalar | absDeterminant () const |
MatrixType::RealScalar | logAbsDeterminant () const |
Index | rank () const |
Index | dimensionOfKernel () const |
bool | isInjective () const |
bool | isSurjective () const |
bool | isInvertible () const |
const internal::solve_retval < ColPivHouseholderQR, typename MatrixType::IdentityReturnType > | inverse () const |
Index | rows () const |
Index | cols () const |
const HCoeffsType & | hCoeffs () const |
ColPivHouseholderQR & | setThreshold (const RealScalar &threshold) |
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. | |
ColPivHouseholderQR & | setThreshold (Default_t) |
Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold. | |
RealScalar | threshold () const |
Returns the threshold that will be used by certain methods such as rank(). | |
Index | nonzeroPivots () const |
RealScalar | maxPivot () const |
Protected Attributes | |
MatrixType | m_qr |
HCoeffsType | m_hCoeffs |
PermutationType | m_colsPermutation |
IntRowVectorType | m_colsTranspositions |
RowVectorType | m_temp |
RealRowVectorType | m_colSqNorms |
bool | m_isInitialized |
bool | m_usePrescribedThreshold |
RealScalar | m_prescribedThreshold |
RealScalar | m_maxpivot |
Index | m_nonzero_pivots |
Index | m_det_pq |
typedef internal::plain_diag_type<MatrixType>::type Eigen::ColPivHouseholderQR< _MatrixType >::HCoeffsType |
typedef HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType Eigen::ColPivHouseholderQR< _MatrixType >::HouseholderSequenceType |
typedef MatrixType::Index Eigen::ColPivHouseholderQR< _MatrixType >::Index |
typedef internal::plain_row_type<MatrixType, Index>::type Eigen::ColPivHouseholderQR< _MatrixType >::IntRowVectorType |
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::ColPivHouseholderQR< _MatrixType >::MatrixQType |
typedef _MatrixType Eigen::ColPivHouseholderQR< _MatrixType >::MatrixType |
typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> Eigen::ColPivHouseholderQR< _MatrixType >::PermutationType |
typedef internal::plain_row_type<MatrixType, RealScalar>::type Eigen::ColPivHouseholderQR< _MatrixType >::RealRowVectorType |
typedef MatrixType::RealScalar Eigen::ColPivHouseholderQR< _MatrixType >::RealScalar |
typedef internal::plain_row_type<MatrixType>::type Eigen::ColPivHouseholderQR< _MatrixType >::RowVectorType |
typedef MatrixType::Scalar Eigen::ColPivHouseholderQR< _MatrixType >::Scalar |
anonymous enum |
Eigen::ColPivHouseholderQR< _MatrixType >::ColPivHouseholderQR | ( | ) | [inline] |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via ColPivHouseholderQR::compute(const MatrixType&).
Eigen::ColPivHouseholderQR< _MatrixType >::ColPivHouseholderQR | ( | Index | rows, | |
Index | cols | |||
) | [inline] |
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
Eigen::ColPivHouseholderQR< _MatrixType >::ColPivHouseholderQR | ( | const MatrixType & | matrix | ) | [inline] |
MatrixType::RealScalar ColPivHouseholderQR< MatrixType >::absDeterminant | ( | ) | const |
Index Eigen::ColPivHouseholderQR< _MatrixType >::cols | ( | void | ) | const [inline] |
const PermutationType& Eigen::ColPivHouseholderQR< _MatrixType >::colsPermutation | ( | ) | const [inline] |
ColPivHouseholderQR< MatrixType > & ColPivHouseholderQR< MatrixType >::compute | ( | const MatrixType & | matrix | ) |
Index Eigen::ColPivHouseholderQR< _MatrixType >::dimensionOfKernel | ( | ) | const [inline] |
const HCoeffsType& Eigen::ColPivHouseholderQR< _MatrixType >::hCoeffs | ( | ) | const [inline] |
ColPivHouseholderQR< MatrixType >::HouseholderSequenceType ColPivHouseholderQR< MatrixType >::householderQ | ( | void | ) | const |
const internal::solve_retval<ColPivHouseholderQR, typename MatrixType::IdentityReturnType> Eigen::ColPivHouseholderQR< _MatrixType >::inverse | ( | ) | const [inline] |
Definition at line 263 of file QR.
Referenced by leftDivideSquare(), and rightDivideSquare().
bool Eigen::ColPivHouseholderQR< _MatrixType >::isInjective | ( | ) | const [inline] |
bool Eigen::ColPivHouseholderQR< _MatrixType >::isInvertible | ( | ) | const [inline] |
Definition at line 250 of file QR.
Referenced by leftDivideSquare(), and rightDivideSquare().
bool Eigen::ColPivHouseholderQR< _MatrixType >::isSurjective | ( | ) | const [inline] |
MatrixType::RealScalar ColPivHouseholderQR< MatrixType >::logAbsDeterminant | ( | ) | const |
const MatrixType& Eigen::ColPivHouseholderQR< _MatrixType >::matrixQR | ( | ) | const [inline] |
RealScalar Eigen::ColPivHouseholderQR< _MatrixType >::maxPivot | ( | ) | const [inline] |
Index Eigen::ColPivHouseholderQR< _MatrixType >::nonzeroPivots | ( | ) | const [inline] |
Index Eigen::ColPivHouseholderQR< _MatrixType >::rank | ( | ) | const [inline] |
Definition at line 196 of file QR.
Referenced by rank().
Index Eigen::ColPivHouseholderQR< _MatrixType >::rows | ( | void | ) | const [inline] |
ColPivHouseholderQR& Eigen::ColPivHouseholderQR< _MatrixType >::setThreshold | ( | Default_t | ) | [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&).
ColPivHouseholderQR& Eigen::ColPivHouseholderQR< _MatrixType >::setThreshold | ( | const RealScalar & | threshold | ) | [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.
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)
Definition at line 291 of file QR.
Referenced by rank().
const internal::solve_retval<ColPivHouseholderQR, Rhs> Eigen::ColPivHouseholderQR< _MatrixType >::solve | ( | const MatrixBase< Rhs > & | b | ) | const [inline] |
This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists.
b | the right-hand-side of the equation to solve. |
Example:
Output:
RealScalar Eigen::ColPivHouseholderQR< _MatrixType >::threshold | ( | ) | const [inline] |
Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
PermutationType Eigen::ColPivHouseholderQR< _MatrixType >::m_colsPermutation [protected] |
RealRowVectorType Eigen::ColPivHouseholderQR< _MatrixType >::m_colSqNorms [protected] |
IntRowVectorType Eigen::ColPivHouseholderQR< _MatrixType >::m_colsTranspositions [protected] |
Index Eigen::ColPivHouseholderQR< _MatrixType >::m_det_pq [protected] |
HCoeffsType Eigen::ColPivHouseholderQR< _MatrixType >::m_hCoeffs [protected] |
bool Eigen::ColPivHouseholderQR< _MatrixType >::m_isInitialized [protected] |
RealScalar Eigen::ColPivHouseholderQR< _MatrixType >::m_maxpivot [protected] |
Index Eigen::ColPivHouseholderQR< _MatrixType >::m_nonzero_pivots [protected] |
RealScalar Eigen::ColPivHouseholderQR< _MatrixType >::m_prescribedThreshold [protected] |
MatrixType Eigen::ColPivHouseholderQR< _MatrixType >::m_qr [protected] |
RowVectorType Eigen::ColPivHouseholderQR< _MatrixType >::m_temp [protected] |
bool Eigen::ColPivHouseholderQR< _MatrixType >::m_usePrescribedThreshold [protected] |
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