Householder rank-revealing QR decomposition of a matrix with full pivoting. More...
#include <ForwardDeclarations.h>
Public Member Functions | |
template<typename RhsType , typename DstType > | |
EIGEN_DEVICE_FUNC void | _solve_impl (const RhsType &rhs, DstType &dst) const |
template<typename RhsType , typename DstType > | |
void | _solve_impl (const RhsType &rhs, DstType &dst) const |
MatrixType::RealScalar | absDeterminant () const |
Index | cols () const |
const PermutationType & | colsPermutation () const |
template<typename InputType > | |
FullPivHouseholderQR & | compute (const EigenBase< InputType > &matrix) |
template<typename InputType > | |
FullPivHouseholderQR< MatrixType > & | compute (const EigenBase< InputType > &matrix) |
Index | dimensionOfKernel () const |
FullPivHouseholderQR () | |
Default Constructor. More... | |
FullPivHouseholderQR (Index rows, Index cols) | |
Default Constructor with memory preallocation. More... | |
template<typename InputType > | |
FullPivHouseholderQR (const EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
template<typename InputType > | |
FullPivHouseholderQR (EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
const HCoeffsType & | hCoeffs () const |
const Inverse< FullPivHouseholderQR > | inverse () const |
bool | isInjective () const |
bool | isInvertible () const |
bool | isSurjective () const |
MatrixType::RealScalar | logAbsDeterminant () const |
MatrixQReturnType | matrixQ (void) const |
const MatrixType & | matrixQR () const |
RealScalar | maxPivot () const |
Index | nonzeroPivots () const |
Index | rank () const |
Index | rows () const |
const IntDiagSizeVectorType & | rowsTranspositions () const |
FullPivHouseholderQR & | setThreshold (const RealScalar &threshold) |
FullPivHouseholderQR & | setThreshold (Default_t) |
template<typename Rhs > | |
const Solve< FullPivHouseholderQR, Rhs > | solve (const MatrixBase< Rhs > &b) const |
RealScalar | threshold () const |
Protected Member Functions | |
void | computeInPlace () |
Static Protected Member Functions | |
static void | check_template_parameters () |
Householder rank-revealing QR decomposition of a matrix with full 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, P', Q and R such that
by using Householder transformations. Here, P and P' are permutation matrices, Q a unitary matrix and R an upper triangular matrix.
This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
This class supports the inplace decomposition mechanism.
Definition at line 256 of file ForwardDeclarations.h.
typedef internal::plain_col_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::ColVectorType |
Definition at line 79 of file FullPivHouseholderQR.h.
typedef internal::plain_diag_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::HCoeffsType |
Definition at line 73 of file FullPivHouseholderQR.h.
Definition at line 76 of file FullPivHouseholderQR.h.
typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> Eigen::FullPivHouseholderQR< _MatrixType >::MatrixQReturnType |
Definition at line 72 of file FullPivHouseholderQR.h.
typedef _MatrixType Eigen::FullPivHouseholderQR< _MatrixType >::MatrixType |
Definition at line 61 of file FullPivHouseholderQR.h.
typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> Eigen::FullPivHouseholderQR< _MatrixType >::PermutationType |
Definition at line 77 of file FullPivHouseholderQR.h.
typedef MatrixType::PlainObject Eigen::FullPivHouseholderQR< _MatrixType >::PlainObject |
Definition at line 80 of file FullPivHouseholderQR.h.
typedef MatrixType::RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::RealScalar |
Definition at line 69 of file FullPivHouseholderQR.h.
typedef internal::plain_row_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::RowVectorType |
Definition at line 78 of file FullPivHouseholderQR.h.
typedef MatrixType::Scalar Eigen::FullPivHouseholderQR< _MatrixType >::Scalar |
Definition at line 68 of file FullPivHouseholderQR.h.
typedef MatrixType::StorageIndex Eigen::FullPivHouseholderQR< _MatrixType >::StorageIndex |
Definition at line 71 of file FullPivHouseholderQR.h.
anonymous enum |
Enumerator | |
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RowsAtCompileTime | |
ColsAtCompileTime | |
MaxRowsAtCompileTime | |
MaxColsAtCompileTime |
Definition at line 62 of file FullPivHouseholderQR.h.
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Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).
Definition at line 87 of file FullPivHouseholderQR.h.
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Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
Definition at line 103 of file FullPivHouseholderQR.h.
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Constructs a QR factorization from a given matrix.
This constructor computes the QR factorization of the matrix matrix by calling the method compute(). It is a short cut for:
Definition at line 126 of file FullPivHouseholderQR.h.
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Constructs a QR factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType
is a Eigen::Ref.
Definition at line 146 of file FullPivHouseholderQR.h.
EIGEN_DEVICE_FUNC void Eigen::FullPivHouseholderQR< _MatrixType >::_solve_impl | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
void Eigen::FullPivHouseholderQR< _MatrixType >::_solve_impl | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
Definition at line 542 of file FullPivHouseholderQR.h.
MatrixType::RealScalar Eigen::FullPivHouseholderQR< MatrixType >::absDeterminant | ( | ) | const |
Definition at line 425 of file FullPivHouseholderQR.h.
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Definition at line 404 of file FullPivHouseholderQR.h.
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Definition at line 319 of file FullPivHouseholderQR.h.
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Definition at line 198 of file FullPivHouseholderQR.h.
FullPivHouseholderQR& Eigen::FullPivHouseholderQR< _MatrixType >::compute | ( | const EigenBase< InputType > & | matrix | ) |
FullPivHouseholderQR<MatrixType>& Eigen::FullPivHouseholderQR< _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.
Definition at line 449 of file FullPivHouseholderQR.h.
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Definition at line 457 of file FullPivHouseholderQR.h.
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Definition at line 263 of file FullPivHouseholderQR.h.
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Q
.For advanced uses only.
Definition at line 325 of file FullPivHouseholderQR.h.
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Definition at line 312 of file FullPivHouseholderQR.h.
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Definition at line 276 of file FullPivHouseholderQR.h.
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Definition at line 301 of file FullPivHouseholderQR.h.
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Definition at line 289 of file FullPivHouseholderQR.h.
MatrixType::RealScalar Eigen::FullPivHouseholderQR< MatrixType >::logAbsDeterminant | ( | ) | const |
Definition at line 434 of file FullPivHouseholderQR.h.
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Definition at line 657 of file FullPivHouseholderQR.h.
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Definition at line 188 of file FullPivHouseholderQR.h.
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Definition at line 394 of file FullPivHouseholderQR.h.
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Definition at line 246 of file FullPivHouseholderQR.h.
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Definition at line 318 of file FullPivHouseholderQR.h.
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Definition at line 205 of file FullPivHouseholderQR.h.
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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 344 of file FullPivHouseholderQR.h.
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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.
See the documentation of setThreshold(const RealScalar&).
Definition at line 359 of file FullPivHouseholderQR.h.
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This method finds a solution x to the equation Ax=b, where A is the matrix of which *this
is the QR decomposition.
b | the right-hand-side of the equation to solve. |
Example:
Output:
Definition at line 176 of file FullPivHouseholderQR.h.
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Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
Definition at line 369 of file FullPivHouseholderQR.h.
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Definition at line 415 of file FullPivHouseholderQR.h.
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Definition at line 414 of file FullPivHouseholderQR.h.
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Definition at line 417 of file FullPivHouseholderQR.h.