Sparse left-looking rank-revealing QR factorization. More...
#include <SparseQR.h>
Public Types | |
typedef MatrixType::Index | Index |
typedef Matrix< Index, Dynamic, 1 > | IndexVector |
typedef _MatrixType | MatrixType |
typedef _OrderingType | OrderingType |
typedef PermutationMatrix< Dynamic, Dynamic, Index > | PermutationType |
typedef SparseMatrix< Scalar, ColMajor, Index > | QRMatrixType |
typedef MatrixType::RealScalar | RealScalar |
typedef MatrixType::Scalar | Scalar |
typedef Matrix< Scalar, Dynamic, 1 > | ScalarVector |
Public Member Functions | |
template<typename Rhs , typename Dest > | |
bool | _solve (const MatrixBase< Rhs > &B, MatrixBase< Dest > &dest) const |
void | analyzePattern (const MatrixType &mat) |
Preprocessing step of a QR factorization. More... | |
Index | cols () const |
const PermutationType & | colsPermutation () const |
void | compute (const MatrixType &mat) |
void | factorize (const MatrixType &mat) |
Performs the numerical QR factorization of the input matrix. More... | |
ComputationInfo | info () const |
Reports whether previous computation was successful. More... | |
std::string | lastErrorMessage () const |
SparseQRMatrixQReturnType< SparseQR > | matrixQ () const |
const QRMatrixType & | matrixR () const |
Index | rank () const |
Index | rows () const |
void | setPivotThreshold (const RealScalar &threshold) |
template<typename Rhs > | |
const internal::solve_retval< SparseQR, Rhs > | solve (const MatrixBase< Rhs > &B) const |
template<typename Rhs > | |
const internal::sparse_solve_retval< SparseQR, Rhs > | solve (const SparseMatrixBase< Rhs > &B) const |
SparseQR () | |
SparseQR (const MatrixType &mat) | |
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void | sort_matrix_Q () |
Protected Attributes | |
bool | m_analysisIsok |
IndexVector | m_etree |
bool | m_factorizationIsok |
IndexVector | m_firstRowElt |
ScalarVector | m_hcoeffs |
ComputationInfo | m_info |
bool | m_isInitialized |
bool | m_isQSorted |
std::string | m_lastError |
Index | m_nonzeropivots |
PermutationType | m_outputPerm_c |
PermutationType | m_perm_c |
PermutationType | m_pivotperm |
QRMatrixType | m_pmat |
QRMatrixType | m_Q |
QRMatrixType | m_R |
RealScalar | m_threshold |
bool | m_useDefaultThreshold |
Friends | |
template<typename , typename > | |
struct | SparseQR_QProduct |
template<typename > | |
struct | SparseQRMatrixQReturnType |
Sparse left-looking rank-revealing QR factorization.
This class implements a left-looking rank-revealing QR decomposition of sparse matrices. When a column has a norm less than a given tolerance it is implicitly permuted to the end. The QR factorization thus obtained is given by A*P = Q*R where R is upper triangular or trapezoidal.
P is the column permutation which is the product of the fill-reducing and the rank-revealing permutations. Use colsPermutation() to get it.
Q is the orthogonal matrix represented as products of Householder reflectors. Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose. You can then apply it to a vector.
R is the sparse triangular or trapezoidal matrix. The later occurs when A is rank-deficient. matrixR().topLeftCorner(rank(), rank()) always returns a triangular factor of full rank.
_MatrixType | The type of the sparse matrix A, must be a column-major SparseMatrix<> |
_OrderingType | The fill-reducing ordering method. See the OrderingMethods module for the list of built-in and external ordering methods. |
Definition at line 16 of file SparseQR.h.
typedef MatrixType::Index Eigen::SparseQR< _MatrixType, _OrderingType >::Index |
Definition at line 71 of file SparseQR.h.
typedef Matrix<Index, Dynamic, 1> Eigen::SparseQR< _MatrixType, _OrderingType >::IndexVector |
Definition at line 73 of file SparseQR.h.
typedef _MatrixType Eigen::SparseQR< _MatrixType, _OrderingType >::MatrixType |
Definition at line 67 of file SparseQR.h.
typedef _OrderingType Eigen::SparseQR< _MatrixType, _OrderingType >::OrderingType |
Definition at line 68 of file SparseQR.h.
typedef PermutationMatrix<Dynamic, Dynamic, Index> Eigen::SparseQR< _MatrixType, _OrderingType >::PermutationType |
Definition at line 75 of file SparseQR.h.
typedef SparseMatrix<Scalar,ColMajor,Index> Eigen::SparseQR< _MatrixType, _OrderingType >::QRMatrixType |
Definition at line 72 of file SparseQR.h.
typedef MatrixType::RealScalar Eigen::SparseQR< _MatrixType, _OrderingType >::RealScalar |
Definition at line 70 of file SparseQR.h.
typedef MatrixType::Scalar Eigen::SparseQR< _MatrixType, _OrderingType >::Scalar |
Definition at line 69 of file SparseQR.h.
typedef Matrix<Scalar, Dynamic, 1> Eigen::SparseQR< _MatrixType, _OrderingType >::ScalarVector |
Definition at line 74 of file SparseQR.h.
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Definition at line 77 of file SparseQR.h.
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Definition at line 80 of file SparseQR.h.
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Definition at line 151 of file SparseQR.h.
void Eigen::SparseQR< MatrixType, OrderingType >::analyzePattern | ( | const MatrixType & | mat | ) |
Preprocessing step of a QR factorization.
In this step, the fill-reducing permutation is computed and applied to the columns of A and the column elimination tree is computed as well. Only the sparcity pattern of mat is exploited.
Definition at line 264 of file SparseQR.h.
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Definition at line 98 of file SparseQR.h.
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Definition at line 138 of file SparseQR.h.
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Definition at line 84 of file SparseQR.h.
void Eigen::SparseQR< MatrixType, OrderingType >::factorize | ( | const MatrixType & | mat | ) |
Performs the numerical QR factorization of the input matrix.
The function SparseQR::analyzePattern(const MatrixType&) must have been called beforehand with a matrix having the same sparcity pattern than mat.
mat | The sparse column-major matrix |
Definition at line 300 of file SparseQR.h.
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Reports whether previous computation was successful.
Success
if computation was succesful, NumericalIssue
if the QR factorization reports a numerical problem InvalidInput
if the input matrix is invalidDefinition at line 214 of file SparseQR.h.
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Definition at line 147 of file SparseQR.h.
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To get a plain SparseMatrix representation of Q:
Internally, this call simply performs a sparse product between the matrix Q and a sparse identity matrix. However, due to the fact that the sparse reflectors are stored unsorted, two transpositions are needed to sort them before performing the product.
Definition at line 132 of file SparseQR.h.
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Definition at line 94 of file SparseQR.h.
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Sets the threshold that is used to determine linearly dependent columns during the factorization.
In practice, if during the factorization the norm of the column that has to be eliminated is below this threshold, then the entire column is treated as zero, and it is moved at the end.
Definition at line 181 of file SparseQR.h.
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