Sparse QR factorization based on SuiteSparseQR library. More...

#include <SuiteSparseQRSupport.h>

Inheritance diagram for Eigen::SPQR< _MatrixType >:

Collaboration diagram for Eigen::SPQR< _MatrixType >:

Public Types
enum	{ ColsAtCompileTime = Dynamic, MaxColsAtCompileTime = Dynamic }
typedef _MatrixType::Scalar	Scalar
typedef _MatrixType::RealScalar	RealScalar
typedef SuiteSparse_long	StorageIndex
typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	MatrixType
typedef Map< PermutationMatrix < Dynamic, Dynamic, StorageIndex > >	PermutationType
Public Member Functions
	SPQR ()
	SPQR (const _MatrixType &matrix)
	~SPQR ()
void	SPQR_free ()
void	compute (const _MatrixType &matrix)
Index	rows () const
Index	cols () const
template<typename Rhs , typename Dest >
void	_solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const
const MatrixType	matrixR () const
SPQRMatrixQReturnType< SPQR >	matrixQ () const
	Get an expression of the matrix Q.
PermutationType	colsPermutation () const
	Get the permutation that was applied to columns of A.
Index	rank () const
void	setSPQROrdering (int ord)
	Set the fill-reducing ordering method to be used.
void	setPivotThreshold (const RealScalar &tol)
	Set the tolerance tol to treat columns with 2-norm < =tol as zero.
cholmod_common *	cholmodCommon () const
ComputationInfo	info () const
	Reports whether previous computation was successful.
Protected Types
typedef SparseSolverBase< SPQR < _MatrixType > >	Base
Protected Attributes
bool	m_analysisIsOk
bool	m_factorizationIsOk
bool	m_isRUpToDate
ComputationInfo	m_info
int	m_ordering
int	m_allow_tol
RealScalar	m_tolerance
cholmod_sparse *	m_cR
MatrixType	m_R
StorageIndex *	m_E
cholmod_sparse *	m_H
StorageIndex *	m_HPinv
cholmod_dense *	m_HTau
Index	m_rank
cholmod_common	m_cc
bool	m_useDefaultThreshold
Friends
struct	SPQR_QProduct

Detailed Description

template<typename _MatrixType>
class Eigen::SPQR< _MatrixType >

Sparse QR factorization based on SuiteSparseQR library.

This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition of sparse matrices. The result is then used to solve linear leasts_square systems. Clearly, a QR factorization is returned such that A*P = Q*R where :

P is the column permutation. Use colsPermutation() to get it.

Q is the orthogonal matrix represented as 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 factor. Use matrixQR() to get it as SparseMatrix. NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index

Template Parameters:

_MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>

Definition at line 60 of file SuiteSparseQRSupport.h.

Member Typedef Documentation

template<typename _MatrixType >

typedef SparseSolverBase<SPQR<_MatrixType> > Eigen::SPQR< _MatrixType >::Base [protected]

Definition at line 63 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

typedef SparseMatrix<Scalar, ColMajor, StorageIndex> Eigen::SPQR< _MatrixType >::MatrixType

Definition at line 69 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

typedef Map<PermutationMatrix<Dynamic, Dynamic, StorageIndex> > Eigen::SPQR< _MatrixType >::PermutationType

Definition at line 70 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

typedef _MatrixType::RealScalar Eigen::SPQR< _MatrixType >::RealScalar

Definition at line 67 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

typedef _MatrixType::Scalar Eigen::SPQR< _MatrixType >::Scalar

Definition at line 66 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

typedef SuiteSparse_long Eigen::SPQR< _MatrixType >::StorageIndex

Definition at line 68 of file SuiteSparseQRSupport.h.

Member Enumeration Documentation

template<typename _MatrixType >

anonymous enum

Enumerator:

ColsAtCompileTime
MaxColsAtCompileTime

Definition at line 71 of file SuiteSparseQRSupport.h.

         {
      ColsAtCompileTime = Dynamic,
      MaxColsAtCompileTime = Dynamic
    };

Constructor & Destructor Documentation

template<typename _MatrixType >

Eigen::SPQR< _MatrixType >::SPQR ( ) [inline]

Definition at line 76 of file SuiteSparseQRSupport.h.

      : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
    { 
      cholmod_l_start(&m_cc);
    }

template<typename _MatrixType >

Eigen::SPQR< _MatrixType >::SPQR ( const _MatrixType & matrix ) [inline, explicit]

Definition at line 82 of file SuiteSparseQRSupport.h.

    : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
    {
      cholmod_l_start(&m_cc);
      compute(matrix);
    }

template<typename _MatrixType >

Eigen::SPQR< _MatrixType >::~SPQR ( ) [inline]

Definition at line 89 of file SuiteSparseQRSupport.h.

    {
      SPQR_free();
      cholmod_l_finish(&m_cc);
    }

Member Function Documentation

template<typename _MatrixType >

template<typename Rhs , typename Dest >

void Eigen::SPQR< _MatrixType >::_solve_impl	(	const MatrixBase< Rhs > &	b,
		MatrixBase< Dest > &	dest
	)		const `[inline]`

Definition at line 150 of file SuiteSparseQRSupport.h.

    {
      eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
      eigen_assert(b.cols()==1 && "This method is for vectors only");

      //Compute Q^T * b
      typename Dest::PlainObject y, y2;
      y = matrixQ().transpose() * b;
      
      // Solves with the triangular matrix R
      Index rk = this->rank();
      y2 = y;
      y.resize((std::max)(cols(),Index(y.rows())),y.cols());
      y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));

      // Apply the column permutation 
      // colsPermutation() performs a copy of the permutation,
      // so let's apply it manually:
      for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
      for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
      
//       y.bottomRows(y.rows()-rk).setZero();
//       dest = colsPermutation() * y.topRows(cols());
      
      m_info = Success;
    }

template<typename _MatrixType >

cholmod_common* Eigen::SPQR< _MatrixType >::cholmodCommon ( ) const [inline]

Returns:: a pointer to the SPQR workspace

Definition at line 218 of file SuiteSparseQRSupport.h.

{ return &m_cc; }

template<typename _MatrixType >

Index Eigen::SPQR< _MatrixType >::cols ( void ) const [inline]

Get the number of columns of the input matrix.

Definition at line 147 of file SuiteSparseQRSupport.h.

{ return m_cR->ncol; }

template<typename _MatrixType >

PermutationType Eigen::SPQR< _MatrixType >::colsPermutation ( ) const [inline]

Get the permutation that was applied to columns of A.

Definition at line 194 of file SuiteSparseQRSupport.h.

    { 
      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
      return PermutationType(m_E, m_cR->ncol);
    }

template<typename _MatrixType >

void Eigen::SPQR< _MatrixType >::compute ( const _MatrixType & matrix ) [inline]

Definition at line 103 of file SuiteSparseQRSupport.h.

    {
      if(m_isInitialized) SPQR_free();

      MatrixType mat(matrix);
      
      /* Compute the default threshold as in MatLab, see:
       * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
       * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 
       */
      RealScalar pivotThreshold = m_tolerance;
      if(m_useDefaultThreshold) 
      {
        RealScalar max2Norm = 0.0;
        for (int j = 0; j < mat.cols(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm());
        if(max2Norm==RealScalar(0))
          max2Norm = RealScalar(1);
        pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
      }
      
      cholmod_sparse A; 
      A = viewAsCholmod(mat);
      Index col = matrix.cols();
      m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A, 
                             &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);

      if (!m_cR)
      {
        m_info = NumericalIssue; 
        m_isInitialized = false;
        return;
      }
      m_info = Success;
      m_isInitialized = true;
      m_isRUpToDate = false;
    }

template<typename _MatrixType >

ComputationInfo Eigen::SPQR< _MatrixType >::info ( ) const [inline]

Reports whether previous computation was successful.

Returns:: Success if computation was succesful, NumericalIssue if the sparse QR can not be computed

Definition at line 226 of file SuiteSparseQRSupport.h.

    {
      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
      return m_info;
    }

template<typename _MatrixType >

SPQRMatrixQReturnType<SPQR> Eigen::SPQR< _MatrixType >::matrixQ ( void ) const [inline]

Get an expression of the matrix Q.

Definition at line 189 of file SuiteSparseQRSupport.h.

    {
      return SPQRMatrixQReturnType<SPQR>(*this);
    }

template<typename _MatrixType >

const MatrixType Eigen::SPQR< _MatrixType >::matrixR ( ) const [inline]

Returns:: the sparse triangular factor R. It is a sparse matrix

Definition at line 179 of file SuiteSparseQRSupport.h.

    {
      eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
      if(!m_isRUpToDate) {
        m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::StorageIndex>(*m_cR);
        m_isRUpToDate = true;
      }
      return m_R;
    }

template<typename _MatrixType >

Index Eigen::SPQR< _MatrixType >::rank ( ) const [inline]

Gets the rank of the matrix. It should be equal to matrixQR().cols if the matrix is full-rank

Definition at line 203 of file SuiteSparseQRSupport.h.

    {
      eigen_assert(m_isInitialized && "Decomposition is not initialized.");
      return m_cc.SPQR_istat[4];
    }

template<typename _MatrixType >

Index Eigen::SPQR< _MatrixType >::rows ( void ) const [inline]

Get the number of rows of the input matrix and the Q matrix

Definition at line 142 of file SuiteSparseQRSupport.h.

{return m_cR->nrow; }

template<typename _MatrixType >

void Eigen::SPQR< _MatrixType >::setPivotThreshold ( const RealScalar & tol ) [inline]

Set the tolerance tol to treat columns with 2-norm < =tol as zero.

Definition at line 211 of file SuiteSparseQRSupport.h.

    {
      m_useDefaultThreshold = false;
      m_tolerance = tol;
    }

template<typename _MatrixType >

void Eigen::SPQR< _MatrixType >::setSPQROrdering ( int ord ) [inline]

Set the fill-reducing ordering method to be used.

Definition at line 209 of file SuiteSparseQRSupport.h.

{ m_ordering = ord;}

template<typename _MatrixType >

void Eigen::SPQR< _MatrixType >::SPQR_free ( ) [inline]

Definition at line 94 of file SuiteSparseQRSupport.h.

    {
      cholmod_l_free_sparse(&m_H, &m_cc);
      cholmod_l_free_sparse(&m_cR, &m_cc);
      cholmod_l_free_dense(&m_HTau, &m_cc);
      std::free(m_E);
      std::free(m_HPinv);
    }

Friends And Related Function Documentation

template<typename _MatrixType >

friend struct SPQR_QProduct [friend]

Definition at line 248 of file SuiteSparseQRSupport.h.

Member Data Documentation

template<typename _MatrixType >

int Eigen::SPQR< _MatrixType >::m_allow_tol [protected]

Definition at line 237 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

bool Eigen::SPQR< _MatrixType >::m_analysisIsOk [protected]

Definition at line 232 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

cholmod_common Eigen::SPQR< _MatrixType >::m_cc [mutable, protected]

Definition at line 246 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

cholmod_sparse* Eigen::SPQR< _MatrixType >::m_cR [mutable, protected]

Definition at line 239 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

StorageIndex* Eigen::SPQR< _MatrixType >::m_E [mutable, protected]

Definition at line 241 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

bool Eigen::SPQR< _MatrixType >::m_factorizationIsOk [protected]

Definition at line 233 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

cholmod_sparse* Eigen::SPQR< _MatrixType >::m_H [mutable, protected]

Definition at line 242 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

StorageIndex* Eigen::SPQR< _MatrixType >::m_HPinv [mutable, protected]

Definition at line 243 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

cholmod_dense* Eigen::SPQR< _MatrixType >::m_HTau [mutable, protected]

Definition at line 244 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

ComputationInfo Eigen::SPQR< _MatrixType >::m_info [mutable, protected]

Definition at line 235 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

bool Eigen::SPQR< _MatrixType >::m_isRUpToDate [mutable, protected]

Definition at line 234 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

int Eigen::SPQR< _MatrixType >::m_ordering [protected]

Definition at line 236 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

MatrixType Eigen::SPQR< _MatrixType >::m_R [mutable, protected]

Definition at line 240 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

Index Eigen::SPQR< _MatrixType >::m_rank [mutable, protected]

Definition at line 245 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

RealScalar Eigen::SPQR< _MatrixType >::m_tolerance [protected]

Definition at line 238 of file SuiteSparseQRSupport.h.

template<typename _MatrixType >

bool Eigen::SPQR< _MatrixType >::m_useDefaultThreshold [protected]

Definition at line 247 of file SuiteSparseQRSupport.h.

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

SuiteSparseQRSupport.h

Public Types

Public Member Functions

Protected Types

Protected Attributes

Friends

Detailed Description

template<typename _MatrixType> class Eigen::SPQR< _MatrixType >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename _MatrixType>
class Eigen::SPQR< _MatrixType >