Eigen::SPQR< MatrixType_ > Class Template Reference

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

Inheritance diagram for Eigen::SPQR< MatrixType_ >:

Public Types
enum	{   ColsAtCompileTime ,   MaxColsAtCompileTime }
typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	MatrixType
typedef Map< PermutationMatrix< Dynamic, Dynamic, StorageIndex > >	PermutationType
typedef MatrixType_::RealScalar	RealScalar
typedef MatrixType_::Scalar	Scalar
typedef SuiteSparse_long	StorageIndex

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve_impl (const MatrixBase< Rhs > &b, MatrixBase< Dest > &dest) const
cholmod_common *	cholmodCommon () const
Index	cols () const
PermutationType	colsPermutation () const
	Get the permutation that was applied to columns of A. More...
void	compute (const MatrixType_ &matrix)
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
SPQRMatrixQReturnType< SPQR >	matrixQ () const
	Get an expression of the matrix Q. More...
const MatrixType	matrixR () const
Index	rank () const
Index	rows () const
void	setPivotThreshold (const RealScalar &tol)
	Set the tolerance tol to treat columns with 2-norm < =tol as zero. More...
void	setSPQROrdering (int ord)
	Set the fill-reducing ordering method to be used. More...
	SPQR ()
	SPQR (const MatrixType_ &matrix)
void	SPQR_free ()
	~SPQR ()
Public Member Functions inherited from Eigen::SparseSolverBase< SPQR< MatrixType_ > >
SPQR< MatrixType_ > &	derived ()
const SPQR< MatrixType_ > &	derived () const
const Solve< SPQR< MatrixType_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< SPQR< MatrixType_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()
	SparseSolverBase (SparseSolverBase &&other)
	~SparseSolverBase ()

Protected Types
typedef SparseSolverBase< SPQR< MatrixType_ > >	Base

Protected Attributes
int	m_allow_tol
bool	m_analysisIsOk
cholmod_common	m_cc
cholmod_sparse *	m_cR
StorageIndex *	m_E
bool	m_factorizationIsOk
cholmod_sparse *	m_H
StorageIndex *	m_HPinv
cholmod_dense *	m_HTau
ComputationInfo	m_info
bool	m_isRUpToDate
int	m_ordering
MatrixType	m_R
Index	m_rank
Index	m_rows
RealScalar	m_tolerance
bool	m_useDefaultThreshold
Protected Attributes inherited from Eigen::SparseSolverBase< SPQR< MatrixType_ > >
bool	m_isInitialized

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<>

This class follows the sparse solver concept .

Definition at line 62 of file SuiteSparseQRSupport.h.

Member Typedef Documentation

Base

template<typename MatrixType_ >

typedef SparseSolverBase<SPQR<MatrixType_> > Eigen::SPQR< MatrixType_ >::Base

protected

Definition at line 65 of file SuiteSparseQRSupport.h.

MatrixType

template<typename MatrixType_ >

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

Definition at line 71 of file SuiteSparseQRSupport.h.

PermutationType

template<typename MatrixType_ >

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

Definition at line 72 of file SuiteSparseQRSupport.h.

RealScalar

template<typename MatrixType_ >

typedef MatrixType_::RealScalar Eigen::SPQR< MatrixType_ >::RealScalar

Definition at line 69 of file SuiteSparseQRSupport.h.

Scalar

template<typename MatrixType_ >

typedef MatrixType_::Scalar Eigen::SPQR< MatrixType_ >::Scalar

Definition at line 68 of file SuiteSparseQRSupport.h.

StorageIndex

template<typename MatrixType_ >

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

Definition at line 70 of file SuiteSparseQRSupport.h.

Member Enumeration Documentation

anonymous enum

template<typename MatrixType_ >

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

Definition at line 73 of file SuiteSparseQRSupport.h.

         {
      ColsAtCompileTime = Dynamic,
      MaxColsAtCompileTime = Dynamic
    };

Constructor & Destructor Documentation

SPQR() [1/2]

template<typename MatrixType_ >

Eigen::SPQR< MatrixType_ >::SPQR ( )

inline

Definition at line 78 of file SuiteSparseQRSupport.h.

      : m_analysisIsOk(false),
        m_factorizationIsOk(false),
        m_isRUpToDate(false),
        m_ordering(SPQR_ORDERING_DEFAULT),
        m_allow_tol(SPQR_DEFAULT_TOL),
        m_tolerance (NumTraits<Scalar>::epsilon()),
        m_cR(0),
        m_E(0),
        m_H(0),
        m_HPinv(0),
        m_HTau(0),
        m_useDefaultThreshold(true)
    { 
      cholmod_l_start(&m_cc);
    }

SPQR() [2/2]

template<typename MatrixType_ >

Eigen::SPQR< MatrixType_ >::SPQR ( const MatrixType_ &  matrix )

inlineexplicit

Definition at line 95 of file SuiteSparseQRSupport.h.

      : m_analysisIsOk(false),
        m_factorizationIsOk(false),
        m_isRUpToDate(false),
        m_ordering(SPQR_ORDERING_DEFAULT),
        m_allow_tol(SPQR_DEFAULT_TOL),
        m_tolerance (NumTraits<Scalar>::epsilon()),
        m_cR(0),
        m_E(0),
        m_H(0),
        m_HPinv(0),
        m_HTau(0),
        m_useDefaultThreshold(true)
    {
      cholmod_l_start(&m_cc);
      compute(matrix);
    }

~SPQR()

template<typename MatrixType_ >

Eigen::SPQR< MatrixType_ >::~SPQR ( )

inline

Definition at line 113 of file SuiteSparseQRSupport.h.

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

Member Function Documentation

_solve_impl()

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 174 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;
    }

cholmodCommon()

template<typename MatrixType_ >

cholmod_common* Eigen::SPQR< MatrixType_ >::cholmodCommon ( ) const

inline

Returns

a pointer to the SPQR workspace

Definition at line 242 of file SuiteSparseQRSupport.h.

{ return &m_cc; }

cols()

template<typename MatrixType_ >

Index Eigen::SPQR< MatrixType_ >::cols ( void  ) const

inline

Get the number of columns of the input matrix.

Definition at line 171 of file SuiteSparseQRSupport.h.

{ return m_cR->ncol; }

colsPermutation()

template<typename MatrixType_ >

PermutationType Eigen::SPQR< MatrixType_ >::colsPermutation ( ) const

inline

Get the permutation that was applied to columns of A.

Definition at line 218 of file SuiteSparseQRSupport.h.

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

compute()

template<typename MatrixType_ >

void Eigen::SPQR< MatrixType_ >::compute ( const MatrixType_ &  matrix )

inline

Definition at line 127 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(numext::is_exactly_zero(max2Norm))
          max2Norm = RealScalar(1);
        pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
      }
      cholmod_sparse A; 
      A = viewAsCholmod(mat);
      m_rows = matrix.rows();
      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;
    }

info()

template<typename MatrixType_ >

ComputationInfo Eigen::SPQR< MatrixType_ >::info ( ) const

inline

Reports whether previous computation was successful.

Returns

Success if computation was successful, NumericalIssue if the sparse QR can not be computed

Definition at line 250 of file SuiteSparseQRSupport.h.

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

matrixQ()

template<typename MatrixType_ >

SPQRMatrixQReturnType<SPQR> Eigen::SPQR< MatrixType_ >::matrixQ ( void  ) const

inline

Get an expression of the matrix Q.

Definition at line 213 of file SuiteSparseQRSupport.h.

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

matrixR()

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 203 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;
    }

rank()

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 227 of file SuiteSparseQRSupport.h.

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

rows()

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 166 of file SuiteSparseQRSupport.h.

{return m_rows; }

setPivotThreshold()

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 235 of file SuiteSparseQRSupport.h.

    {
      m_useDefaultThreshold = false;
      m_tolerance = tol;
    }

setSPQROrdering()

template<typename MatrixType_ >

void Eigen::SPQR< MatrixType_ >::setSPQROrdering ( int  ord )

inline

Set the fill-reducing ordering method to be used.

Definition at line 233 of file SuiteSparseQRSupport.h.

{ m_ordering = ord;}

SPQR_free()

template<typename MatrixType_ >

void Eigen::SPQR< MatrixType_ >::SPQR_free ( )

inline

Definition at line 118 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);
    }

Member Data Documentation

m_allow_tol

template<typename MatrixType_ >

int Eigen::SPQR< MatrixType_ >::m_allow_tol

protected

Definition at line 261 of file SuiteSparseQRSupport.h.

m_analysisIsOk

template<typename MatrixType_ >

bool Eigen::SPQR< MatrixType_ >::m_analysisIsOk

protected

Definition at line 256 of file SuiteSparseQRSupport.h.

m_cc

template<typename MatrixType_ >

cholmod_common Eigen::SPQR< MatrixType_ >::m_cc

mutableprotected

Definition at line 270 of file SuiteSparseQRSupport.h.

m_cR

template<typename MatrixType_ >

cholmod_sparse* Eigen::SPQR< MatrixType_ >::m_cR

mutableprotected

Definition at line 263 of file SuiteSparseQRSupport.h.

m_E

template<typename MatrixType_ >

StorageIndex* Eigen::SPQR< MatrixType_ >::m_E

mutableprotected

Definition at line 265 of file SuiteSparseQRSupport.h.

m_factorizationIsOk

template<typename MatrixType_ >

bool Eigen::SPQR< MatrixType_ >::m_factorizationIsOk

protected

Definition at line 257 of file SuiteSparseQRSupport.h.

m_H

template<typename MatrixType_ >

cholmod_sparse* Eigen::SPQR< MatrixType_ >::m_H

mutableprotected

Definition at line 266 of file SuiteSparseQRSupport.h.

m_HPinv

template<typename MatrixType_ >

StorageIndex* Eigen::SPQR< MatrixType_ >::m_HPinv

mutableprotected

Definition at line 267 of file SuiteSparseQRSupport.h.

m_HTau

template<typename MatrixType_ >

cholmod_dense* Eigen::SPQR< MatrixType_ >::m_HTau

mutableprotected

Definition at line 268 of file SuiteSparseQRSupport.h.

m_info

template<typename MatrixType_ >

ComputationInfo Eigen::SPQR< MatrixType_ >::m_info

mutableprotected

Definition at line 259 of file SuiteSparseQRSupport.h.

m_isRUpToDate

template<typename MatrixType_ >

bool Eigen::SPQR< MatrixType_ >::m_isRUpToDate

mutableprotected

Definition at line 258 of file SuiteSparseQRSupport.h.

m_ordering

template<typename MatrixType_ >

int Eigen::SPQR< MatrixType_ >::m_ordering

protected

Definition at line 260 of file SuiteSparseQRSupport.h.

m_R

template<typename MatrixType_ >

MatrixType Eigen::SPQR< MatrixType_ >::m_R

mutableprotected

Definition at line 264 of file SuiteSparseQRSupport.h.

m_rank

template<typename MatrixType_ >

Index Eigen::SPQR< MatrixType_ >::m_rank

mutableprotected

Definition at line 269 of file SuiteSparseQRSupport.h.

m_rows

template<typename MatrixType_ >

Index Eigen::SPQR< MatrixType_ >::m_rows

protected

Definition at line 272 of file SuiteSparseQRSupport.h.

m_tolerance

template<typename MatrixType_ >

RealScalar Eigen::SPQR< MatrixType_ >::m_tolerance

protected

Definition at line 262 of file SuiteSparseQRSupport.h.

m_useDefaultThreshold

template<typename MatrixType_ >

bool Eigen::SPQR< MatrixType_ >::m_useDefaultThreshold

protected

Definition at line 271 of file SuiteSparseQRSupport.h.

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

• SuiteSparseQRSupport.h