Householder QR decomposition of a matrix. More...
#include <ForwardDeclarations.h>
Public Types | |
enum | { MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime } |
typedef SolverBase< HouseholderQR > | Base |
typedef internal::plain_diag_type< MatrixType >::type | HCoeffsType |
typedef HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type > | HouseholderSequenceType |
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime,(MatrixType::Flags &RowMajorBit) ? RowMajor :ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixQType |
typedef _MatrixType | MatrixType |
typedef internal::plain_row_type< MatrixType >::type | RowVectorType |
Public Member Functions | |
template<typename RhsType , typename DstType > | |
void | _solve_impl (const RhsType &rhs, DstType &dst) const |
template<bool Conjugate, typename RhsType , typename DstType > | |
void | _solve_impl_transposed (const RhsType &rhs, DstType &dst) const |
MatrixType::RealScalar | absDeterminant () const |
Index | cols () const |
template<typename InputType > | |
HouseholderQR & | compute (const EigenBase< InputType > &matrix) |
const HCoeffsType & | hCoeffs () const |
HouseholderSequenceType | householderQ () const |
HouseholderQR () | |
Default Constructor. More... | |
template<typename InputType > | |
HouseholderQR (const EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
template<typename InputType > | |
HouseholderQR (EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
HouseholderQR (Index rows, Index cols) | |
Default Constructor with memory preallocation. More... | |
MatrixType::RealScalar | logAbsDeterminant () const |
const MatrixType & | matrixQR () const |
Index | rows () const |
Protected Member Functions | |
void | computeInPlace () |
Static Protected Member Functions | |
static void | check_template_parameters () |
Protected Attributes | |
HCoeffsType | m_hCoeffs |
bool | m_isInitialized |
MatrixType | m_qr |
RowVectorType | m_temp |
Friends | |
class | SolverBase< HouseholderQR > |
Householder QR decomposition of a matrix.
_MatrixType | the type of the matrix of which we are computing the QR decomposition |
This class performs a QR decomposition of a matrix A into matrices Q and R such that
by using Householder transformations. Here, Q a unitary matrix and R an upper triangular matrix. The result is stored in a compact way compatible with LAPACK.
Note that no pivoting is performed. This is not a rank-revealing decomposition. If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.
This Householder QR decomposition is faster, but less numerically stable and less feature-full than FullPivHouseholderQR or ColPivHouseholderQR.
This class supports the inplace decomposition mechanism.
Definition at line 273 of file ForwardDeclarations.h.
Definition at line 62 of file HouseholderQR.h.
Definition at line 71 of file HouseholderQR.h.
typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> Eigen::HouseholderQR::HouseholderSequenceType |
Definition at line 73 of file HouseholderQR.h.
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::HouseholderQR::MatrixQType |
Definition at line 70 of file HouseholderQR.h.
typedef _MatrixType Eigen::HouseholderQR::MatrixType |
Definition at line 61 of file HouseholderQR.h.
Definition at line 72 of file HouseholderQR.h.
anonymous enum |
Enumerator | |
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MaxRowsAtCompileTime | |
MaxColsAtCompileTime |
Definition at line 66 of file HouseholderQR.h.
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inline |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via HouseholderQR::compute(const MatrixType&).
Definition at line 81 of file HouseholderQR.h.
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 89 of file HouseholderQR.h.
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inlineexplicit |
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 108 of file HouseholderQR.h.
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inlineexplicit |
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 126 of file HouseholderQR.h.
void Eigen::HouseholderQR::_solve_impl | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
Definition at line 361 of file HouseholderQR.h.
void Eigen::HouseholderQR::_solve_impl_transposed | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
Definition at line 379 of file HouseholderQR.h.
MatrixType::RealScalar Eigen::HouseholderQR::absDeterminant | ( | ) | const |
Definition at line 247 of file HouseholderQR.h.
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inlinestaticprotected |
Definition at line 233 of file HouseholderQR.h.
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inline |
Definition at line 215 of file HouseholderQR.h.
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inline |
Definition at line 179 of file HouseholderQR.h.
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protected |
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 404 of file HouseholderQR.h.
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inline |
Q
.For advanced uses only.
Definition at line 221 of file HouseholderQR.h.
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inline |
This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.
The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object. Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:
Example:
Output:
Definition at line 163 of file HouseholderQR.h.
MatrixType::RealScalar Eigen::HouseholderQR::logAbsDeterminant | ( | ) | const |
Definition at line 256 of file HouseholderQR.h.
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inline |
Definition at line 172 of file HouseholderQR.h.
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inline |
Definition at line 214 of file HouseholderQR.h.
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friend |
Definition at line 63 of file HouseholderQR.h.
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protected |
Definition at line 241 of file HouseholderQR.h.
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protected |
Definition at line 243 of file HouseholderQR.h.
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protected |
Definition at line 240 of file HouseholderQR.h.
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protected |
Definition at line 242 of file HouseholderQR.h.