Eigen  3.3.90 (mercurial changeset d63bd3cb7378)
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Eigen::SparseQR< MatrixType, OrderingType > Class Template Reference

Detailed Description

template<typename MatrixType, typename OrderingType>
class Eigen::SparseQR< MatrixType, OrderingType >

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.

Template Parameters
_MatrixTypeThe type of the sparse matrix A, must be a column-major SparseMatrix<>
_OrderingTypeThe fill-reducing ordering method. See the OrderingMethods module for the list of built-in and external ordering methods.

This class follows the sparse solver concept .

Warning
The input sparse matrix A must be in compressed mode (see SparseMatrix::makeCompressed()).
+ Inheritance diagram for Eigen::SparseQR< MatrixType, OrderingType >:

Public Member Functions

void analyzePattern (const MatrixType &mat)
 Preprocessing step of a QR factorization. More...
 
Index cols () const
 
const PermutationTypecolsPermutation () 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 QRMatrixTypematrixR () const
 
Index rank () const
 
Index rows () const
 
void setPivotThreshold (const RealScalar &threshold)
 
template<typename Rhs >
const Solve< SparseQR, Rhs > solve (const MatrixBase< Rhs > &B) const
 
 SparseQR (const MatrixType &mat)
 
- Public Member Functions inherited from Eigen::SparseSolverBase< SparseQR< _MatrixType, _OrderingType > >
const Solve< SparseQR
< _MatrixType, _OrderingType >
, Rhs > 
solve (const MatrixBase< Rhs > &b) const
 
const Solve< SparseQR
< _MatrixType, _OrderingType >
, Rhs > 
solve (const SparseMatrixBase< Rhs > &b) const
 
 SparseSolverBase ()
 

Constructor & Destructor Documentation

template<typename MatrixType , typename OrderingType >
Eigen::SparseQR< MatrixType, OrderingType >::SparseQR ( const MatrixType &  mat)
inlineexplicit

Construct a QR factorization of the matrix mat.

Warning
The matrix mat must be in compressed mode (see SparseMatrix::makeCompressed()).
See Also
compute()

Member Function Documentation

template<typename MatrixType , typename OrderingType >
void Eigen::SparseQR< MatrixType, OrderingType >::analyzePattern ( const MatrixType &  mat)

Preprocessing step of a QR factorization.

Warning
The matrix mat must be in compressed mode (see SparseMatrix::makeCompressed()).

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 sparsity pattern of mat is exploited.

Note
In this step it is assumed that there is no empty row in the matrix mat.
template<typename MatrixType , typename OrderingType >
Index Eigen::SparseQR< MatrixType, OrderingType >::cols ( void  ) const
inline
Returns
the number of columns of the represented matrix.
template<typename MatrixType , typename OrderingType >
const PermutationType& Eigen::SparseQR< MatrixType, OrderingType >::colsPermutation ( ) const
inline
Returns
a const reference to the column permutation P that was applied to A such that A*P = Q*R It is the combination of the fill-in reducing permutation and numerical column pivoting.
template<typename MatrixType , typename OrderingType >
void Eigen::SparseQR< MatrixType, OrderingType >::compute ( const MatrixType &  mat)
inline

Computes the QR factorization of the sparse matrix mat.

Warning
The matrix mat must be in compressed mode (see SparseMatrix::makeCompressed()).
See Also
analyzePattern(), factorize()
template<typename MatrixType , typename OrderingType >
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 sparsity pattern than mat.

Parameters
matThe sparse column-major matrix
template<typename MatrixType , typename OrderingType >
ComputationInfo Eigen::SparseQR< MatrixType, OrderingType >::info ( ) const
inline

Reports whether previous computation was successful.

Returns
Success if computation was successful, NumericalIssue if the QR factorization reports a numerical problem InvalidInput if the input matrix is invalid
See Also
iparm()
template<typename MatrixType , typename OrderingType >
std::string Eigen::SparseQR< MatrixType, OrderingType >::lastErrorMessage ( ) const
inline
Returns
A string describing the type of error. This method is provided to ease debugging, not to handle errors.
template<typename MatrixType , typename OrderingType >
SparseQRMatrixQReturnType<SparseQR> Eigen::SparseQR< MatrixType, OrderingType >::matrixQ ( void  ) const
inline
\returns an expression of the matrix Q as products of sparse Householder reflectors.

The common usage of this function is to apply it to a dense matrix or vector

* VectorXd B1, B2;
* // Initialize B1
* B2 = matrixQ() * B1;
*

To get a plain SparseMatrix representation of Q:

* SparseMatrix<double> Q;
* Q = SparseQR<SparseMatrix<double> >(A).matrixQ();
*

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.

template<typename MatrixType , typename OrderingType >
const QRMatrixType& Eigen::SparseQR< MatrixType, OrderingType >::matrixR ( ) const
inline
Returns
a const reference to the sparse upper triangular matrix R of the QR factorization.
Warning
The entries of the returned matrix are not sorted. This means that using it in algorithms expecting sorted entries will fail. This include random coefficient accesses (SpaseMatrix::coeff()), and coefficient-wise operations. Matrix products and triangular solves are fine though.

To sort the entries, you can assign it to a row-major matrix, and if a column-major matrix is required, you can copy it again:

* SparseMatrix<double> R = qr.matrixR(); // column-major, not sorted!
* SparseMatrix<double,RowMajor> Rr = qr.matrixR(); // row-major, sorted
* SparseMatrix<double> Rc = Rr; // column-major, sorted
*
template<typename MatrixType , typename OrderingType >
Index Eigen::SparseQR< MatrixType, OrderingType >::rank ( ) const
inline
Returns
the number of non linearly dependent columns as determined by the pivoting threshold.
See Also
setPivotThreshold()
template<typename MatrixType , typename OrderingType >
Index Eigen::SparseQR< MatrixType, OrderingType >::rows ( void  ) const
inline
Returns
the number of rows of the represented matrix.
template<typename MatrixType , typename OrderingType >
void Eigen::SparseQR< MatrixType, OrderingType >::setPivotThreshold ( const RealScalar &  threshold)
inline

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.

template<typename MatrixType , typename OrderingType >
template<typename Rhs >
const Solve<SparseQR, Rhs> Eigen::SparseQR< MatrixType, OrderingType >::solve ( const MatrixBase< Rhs > &  B) const
inline
Returns
the solution X of $ A X = B $ using the current decomposition of A.
See Also
compute()

The documentation for this class was generated from the following file: