Eigen::SparseLU< MatrixType_, OrderingType_ > Class Template Reference

Sparse supernodal LU factorization for general matrices. More...

#include <SparseLU.h>

Inheritance diagram for Eigen::SparseLU< MatrixType_, OrderingType_ >:

Public Types
enum	{ ColsAtCompileTime = MatrixType::ColsAtCompileTime , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
typedef MatrixType_	MatrixType
typedef OrderingType_	OrderingType
typedef MatrixType::Scalar	Scalar
typedef MatrixType::RealScalar	RealScalar
typedef MatrixType::StorageIndex	StorageIndex
typedef SparseMatrix< Scalar, ColMajor, StorageIndex >	NCMatrix
typedef internal::MappedSuperNodalMatrix< Scalar, StorageIndex >	SCMatrix
typedef Matrix< Scalar, Dynamic, 1 >	ScalarVector
typedef Matrix< StorageIndex, Dynamic, 1 >	IndexVector
typedef PermutationMatrix< Dynamic, Dynamic, StorageIndex >	PermutationType
typedef internal::SparseLUImpl< Scalar, StorageIndex >	Base
Public Types inherited from Eigen::internal::SparseLUImpl< MatrixType_::Scalar, MatrixType_::StorageIndex >
typedef Matrix< MatrixType_::Scalar, Dynamic, 1 >	ScalarVector
typedef Matrix< MatrixType_::StorageIndex, Dynamic, 1 >	IndexVector
typedef Matrix< MatrixType_::Scalar, Dynamic, Dynamic, ColMajor >	ScalarMatrix
typedef Map< ScalarMatrix, 0, OuterStride<> >	MappedMatrixBlock
typedef ScalarVector::RealScalar	RealScalar
typedef Ref< Matrix< MatrixType_::Scalar, Dynamic, 1 > >	BlockScalarVector
typedef Ref< Matrix< MatrixType_::StorageIndex, Dynamic, 1 > >	BlockIndexVector
typedef LU_GlobalLU_t< IndexVector, ScalarVector >	GlobalLU_t
typedef SparseMatrix< MatrixType_::Scalar, ColMajor, MatrixType_::StorageIndex >	MatrixType

Public Member Functions
	SparseLU ()
	Basic constructor of the solver. More...
	SparseLU (const MatrixType &matrix)
	Constructor of the solver already based on a specific matrix. More...
	~SparseLU ()
void	analyzePattern (const MatrixType &matrix)
	Compute the column permutation. More...
void	factorize (const MatrixType &matrix)
	Factorize the matrix to get the solver ready. More...
void	simplicialfactorize (const MatrixType &matrix)
void	compute (const MatrixType &matrix)
	Analyze and factorize the matrix so the solver is ready to solve. More...
const SparseLUTransposeView< false, SparseLU< MatrixType_, OrderingType_ > >	transpose ()
	Return a solver for the transposed matrix. More...
const SparseLUTransposeView< true, SparseLU< MatrixType_, OrderingType_ > >	adjoint ()
	Return a solver for the adjointed matrix. More...
Index	rows () const
	Give the number of rows. More...
Index	cols () const
	Give the number of columns. More...
void	isSymmetric (bool sym)
	Let you set that the pattern of the input matrix is symmetric. More...
SparseLUMatrixLReturnType< SCMatrix >	matrixL () const
	Give the matrixL. More...
SparseLUMatrixUReturnType< SCMatrix, Map< SparseMatrix< Scalar, ColMajor, StorageIndex > > >	matrixU () const
	Give the MatrixU. More...
const PermutationType &	rowsPermutation () const
	Give the row matrix permutation. More...
const PermutationType &	colsPermutation () const
	Give the column matrix permutation. More...
void	setPivotThreshold (const RealScalar &thresh)
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
std::string	lastErrorMessage () const
	Give a human readable error. More...
template<typename Rhs , typename Dest >
bool	_solve_impl (const MatrixBase< Rhs > &B, MatrixBase< Dest > &X_base) const
Scalar	absDeterminant ()
	Give the absolute value of the determinant. More...
Scalar	logAbsDeterminant () const
	Give the natural log of the absolute determinant. More...
Scalar	signDeterminant ()
	Give the sign of the determinant. More...
Scalar	determinant ()
	Give the determinant. More...
Index	nnzL () const
	Give the number of non zero in matrix L. More...
Index	nnzU () const
	Give the number of non zero in matrix U. More...
Public Member Functions inherited from Eigen::SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >
	SparseSolverBase ()
	SparseSolverBase (SparseSolverBase &&other)
	~SparseSolverBase ()
SparseLU< MatrixType_, OrderingType_ > &	derived ()
const SparseLU< MatrixType_, OrderingType_ > &	derived () const
const Solve< SparseLU< MatrixType_, OrderingType_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< SparseLU< MatrixType_, OrderingType_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
void	_solve_impl (const SparseMatrixBase< Rhs > &b, SparseMatrixBase< Dest > &dest) const

Protected Types
typedef SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >	APIBase

Protected Member Functions
void	initperfvalues ()
Protected Member Functions inherited from Eigen::internal::SparseLUImpl< MatrixType_::Scalar, MatrixType_::StorageIndex >
Index	expand (VectorType &vec, Index &length, Index nbElts, Index keep_prev, Index &num_expansions)
Index	memInit (Index m, Index n, Index annz, Index lwork, Index fillratio, Index panel_size, GlobalLU_t &glu)
	Allocate various working space for the numerical factorization phase. More...
Index	memXpand (VectorType &vec, Index &maxlen, Index nbElts, MemType memtype, Index &num_expansions)
	Expand the existing storage. More...
void	heap_relax_snode (const Index n, IndexVector &et, const Index relax_columns, IndexVector &descendants, IndexVector &relax_end)
	Identify the initial relaxed supernodes. More...
void	relax_snode (const Index n, IndexVector &et, const Index relax_columns, IndexVector &descendants, IndexVector &relax_end)
	Identify the initial relaxed supernodes. More...
Index	snode_dfs (const Index jcol, const Index kcol, const MatrixType &mat, IndexVector &xprune, IndexVector &marker, GlobalLU_t &glu)
Index	snode_bmod (const Index jcol, const Index fsupc, ScalarVector &dense, GlobalLU_t &glu)
Index	pivotL (const Index jcol, const RealScalar &diagpivotthresh, IndexVector &perm_r, IndexVector &iperm_c, Index &pivrow, GlobalLU_t &glu)
	Performs the numerical pivoting on the current column of L, and the CDIV operation. More...
void	dfs_kernel (const MatrixType_::StorageIndex jj, IndexVector &perm_r, Index &nseg, IndexVector &panel_lsub, IndexVector &segrep, Ref< IndexVector > repfnz_col, IndexVector &xprune, Ref< IndexVector > marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu, Index &nextl_col, Index krow, Traits &traits)
void	panel_dfs (const Index m, const Index w, const Index jcol, MatrixType &A, IndexVector &perm_r, Index &nseg, ScalarVector &dense, IndexVector &panel_lsub, IndexVector &segrep, IndexVector &repfnz, IndexVector &xprune, IndexVector &marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu)
	Performs a symbolic factorization on a panel of columns [jcol, jcol+w) More...
void	panel_bmod (const Index m, const Index w, const Index jcol, const Index nseg, ScalarVector &dense, ScalarVector &tempv, IndexVector &segrep, IndexVector &repfnz, GlobalLU_t &glu)
	Performs numeric block updates (sup-panel) in topological order. More...
Index	column_dfs (const Index m, const Index jcol, IndexVector &perm_r, Index maxsuper, Index &nseg, BlockIndexVector lsub_col, IndexVector &segrep, BlockIndexVector repfnz, IndexVector &xprune, IndexVector &marker, IndexVector &parent, IndexVector &xplore, GlobalLU_t &glu)
	Performs a symbolic factorization on column jcol and decide the supernode boundary. More...
Index	column_bmod (const Index jcol, const Index nseg, BlockScalarVector dense, ScalarVector &tempv, BlockIndexVector segrep, BlockIndexVector repfnz, Index fpanelc, GlobalLU_t &glu)
	Performs numeric block updates (sup-col) in topological order. More...
Index	copy_to_ucol (const Index jcol, const Index nseg, IndexVector &segrep, BlockIndexVector repfnz, IndexVector &perm_r, BlockScalarVector dense, GlobalLU_t &glu)
	Performs numeric block updates (sup-col) in topological order. More...
void	pruneL (const Index jcol, const IndexVector &perm_r, const Index pivrow, const Index nseg, const IndexVector &segrep, BlockIndexVector repfnz, IndexVector &xprune, GlobalLU_t &glu)
	Prunes the L-structure. More...
void	countnz (const Index n, Index &nnzL, Index &nnzU, GlobalLU_t &glu)
	Count Nonzero elements in the factors. More...
void	fixupL (const Index n, const IndexVector &perm_r, GlobalLU_t &glu)
	Fix up the data storage lsub for L-subscripts. More...

Protected Attributes
ComputationInfo	m_info
bool	m_factorizationIsOk
bool	m_analysisIsOk
std::string	m_lastError
NCMatrix	m_mat
SCMatrix	m_Lstore
Map< SparseMatrix< Scalar, ColMajor, StorageIndex > >	m_Ustore
PermutationType	m_perm_c
PermutationType	m_perm_r
IndexVector	m_etree
Base::GlobalLU_t	m_glu
bool	m_symmetricmode
internal::perfvalues	m_perfv
RealScalar	m_diagpivotthresh
Index	m_nnzL
Index	m_nnzU
Index	m_detPermR
Index	m_detPermC
Protected Attributes inherited from Eigen::SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >
bool	m_isInitialized

Private Member Functions
	SparseLU (const SparseLU &)

Detailed Description

template<typename MatrixType_, typename OrderingType_>
class Eigen::SparseLU< MatrixType_, OrderingType_ >

Sparse supernodal LU factorization for general matrices.

This class implements the supernodal LU factorization for general matrices. It uses the main techniques from the sequential SuperLU package (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real and complex arithmetic with single and double precision, depending on the scalar type of your input matrix. The code has been optimized to provide BLAS-3 operations during supernode-panel updates. It benefits directly from the built-in high-performant Eigen BLAS routines. Moreover, when the size of a supernode is very small, the BLAS calls are avoided to enable a better optimization from the compiler. For best performance, you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.

An important parameter of this class is the ordering method. It is used to reorder the columns (and eventually the rows) of the matrix to reduce the number of new elements that are created during numerical factorization. The cheapest method available is COLAMD. See the OrderingMethods module for the list of built-in and external ordering methods.

Simple example with key steps

VectorXd x(n), b(n);
SparseMatrix<double> A;
SparseLU<SparseMatrix<double>, COLAMDOrdering<int> > solver;
// Fill A and b.
// Compute the ordering permutation vector from the structural pattern of A.
solver.analyzePattern(A);
// Compute the numerical factorization.
solver.factorize(A);
// Use the factors to solve the linear system.
x = solver.solve(b);

We can directly call compute() instead of analyzePattern() and factorize()

VectorXd x(n), b(n);
SparseMatrix<double> A;
SparseLU<SparseMatrix<double>, COLAMDOrdering<int> > solver;
// Fill A and b.
solver.compute(A);
// Use the factors to solve the linear system.
x = solver.solve(b);

Or give the matrix to the constructor SparseLU(const MatrixType& matrix)

VectorXd x(n), b(n);
SparseMatrix<double> A;
// Fill A and b.
SparseLU<SparseMatrix<double>, COLAMDOrdering<int> > solver(A);
// Use the factors to solve the linear system.
x = solver.solve(b);

Warning

The input matrix A should be in a compressed and column-major form. Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix.

Note

Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix. For badly scaled matrices, this step can be useful to reduce the pivoting during factorization. If this is the case for your matrices, you can try the basic scaling method at "unsupported/Eigen/src/IterativeSolvers/Scaling.h"

Template Parameters

MatrixType_	The type of the sparse matrix. It must be a column-major SparseMatrix<>
OrderingType_	The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD

\implsparsesolverconcept

See also

Sparse solver concept

OrderingMethods_Module

Member Typedef Documentation

APIBase

template<typename MatrixType_ , typename OrderingType_ >

typedef SparseSolverBase<SparseLU<MatrixType_, OrderingType_> > Eigen::SparseLU< MatrixType_, OrderingType_ >::APIBase

protected

Base

template<typename MatrixType_ , typename OrderingType_ >

typedef internal::SparseLUImpl<Scalar, StorageIndex> Eigen::SparseLU< MatrixType_, OrderingType_ >::Base

IndexVector

template<typename MatrixType_ , typename OrderingType_ >

typedef Matrix<StorageIndex, Dynamic, 1> Eigen::SparseLU< MatrixType_, OrderingType_ >::IndexVector

MatrixType

template<typename MatrixType_ , typename OrderingType_ >

typedef MatrixType_ Eigen::SparseLU< MatrixType_, OrderingType_ >::MatrixType

NCMatrix

template<typename MatrixType_ , typename OrderingType_ >

typedef SparseMatrix<Scalar, ColMajor, StorageIndex> Eigen::SparseLU< MatrixType_, OrderingType_ >::NCMatrix

OrderingType

template<typename MatrixType_ , typename OrderingType_ >

typedef OrderingType_ Eigen::SparseLU< MatrixType_, OrderingType_ >::OrderingType

PermutationType

template<typename MatrixType_ , typename OrderingType_ >

typedef PermutationMatrix<Dynamic, Dynamic, StorageIndex> Eigen::SparseLU< MatrixType_, OrderingType_ >::PermutationType

RealScalar

template<typename MatrixType_ , typename OrderingType_ >

typedef MatrixType::RealScalar Eigen::SparseLU< MatrixType_, OrderingType_ >::RealScalar

Scalar

template<typename MatrixType_ , typename OrderingType_ >

typedef MatrixType::Scalar Eigen::SparseLU< MatrixType_, OrderingType_ >::Scalar

ScalarVector

template<typename MatrixType_ , typename OrderingType_ >

typedef Matrix<Scalar, Dynamic, 1> Eigen::SparseLU< MatrixType_, OrderingType_ >::ScalarVector

SCMatrix

template<typename MatrixType_ , typename OrderingType_ >

typedef internal::MappedSuperNodalMatrix<Scalar, StorageIndex> Eigen::SparseLU< MatrixType_, OrderingType_ >::SCMatrix

StorageIndex

template<typename MatrixType_ , typename OrderingType_ >

typedef MatrixType::StorageIndex Eigen::SparseLU< MatrixType_, OrderingType_ >::StorageIndex

Member Enumeration Documentation

anonymous enum

template<typename MatrixType_ , typename OrderingType_ >

anonymous enum

Enumerator
ColsAtCompileTime
MaxColsAtCompileTime

{ ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };

Constructor & Destructor Documentation

SparseLU() [1/3]

template<typename MatrixType_ , typename OrderingType_ >

Eigen::SparseLU< MatrixType_, OrderingType_ >::SparseLU ( )

inline

Basic constructor of the solver.

Construct a SparseLU. As no matrix is given as argument, compute() should be called afterward with a matrix.

      : m_lastError(""), m_Ustore(0, 0, 0, 0, 0, 0), m_symmetricmode(false), m_diagpivotthresh(1.0), m_detPermR(1) {
    initperfvalues();
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::initperfvalues().

SparseLU() [2/3]

template<typename MatrixType_ , typename OrderingType_ >

Eigen::SparseLU< MatrixType_, OrderingType_ >::SparseLU ( const MatrixType &  matrix )

inlineexplicit

Constructor of the solver already based on a specific matrix.

Construct a SparseLU. compute() is already called with the given matrix.

      : m_lastError(""), m_Ustore(0, 0, 0, 0, 0, 0), m_symmetricmode(false), m_diagpivotthresh(1.0), m_detPermR(1) {
    initperfvalues();
    compute(matrix);
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::compute(), Eigen::SparseLU< MatrixType_, OrderingType_ >::initperfvalues(), and matrix().

~SparseLU()

template<typename MatrixType_ , typename OrderingType_ >

Eigen::SparseLU< MatrixType_, OrderingType_ >::~SparseLU ( )

inline

              {
    // Free all explicit dynamic pointers
  }

SparseLU() [3/3]

template<typename MatrixType_ , typename OrderingType_ >

Eigen::SparseLU< MatrixType_, OrderingType_ >::SparseLU ( const SparseLU< MatrixType_, OrderingType_ > &  )

private

Member Function Documentation

_solve_impl()

template<typename MatrixType_ , typename OrderingType_ >

template<typename Rhs , typename Dest >

bool Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl ( const MatrixBase< Rhs > &  B, MatrixBase< Dest > &  X_base  ) const

inline

                                                                             {
    Dest& X(X_base.derived());
    eigen_assert(m_factorizationIsOk && "The matrix should be factorized first");
    EIGEN_STATIC_ASSERT((Dest::Flags & RowMajorBit) == 0, THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
 
    // Permute the right hand side to form X = Pr*B
    // on return, X is overwritten by the computed solution
    X.resize(B.rows(), B.cols());
 
    // this ugly const_cast_derived() helps to detect aliasing when applying the permutations
    for (Index j = 0; j < B.cols(); ++j) X.col(j) = rowsPermutation() * B.const_cast_derived().col(j);
 
    // Forward substitution with L
    this->matrixL().solveInPlace(X);
    this->matrixU().solveInPlace(X);
 
    // Permute back the solution
    for (Index j = 0; j < B.cols(); ++j) X.col(j) = colsPermutation().inverse() * X.col(j);
 
    return true;
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::colsPermutation(), eigen_assert, EIGEN_STATIC_ASSERT, Eigen::PermutationBase< Derived >::inverse(), j, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk, Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixL(), Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixU(), Eigen::RowMajorBit, Eigen::SparseLU< MatrixType_, OrderingType_ >::rowsPermutation(), and X.

absDeterminant()

template<typename MatrixType_ , typename OrderingType_ >

Scalar Eigen::SparseLU< MatrixType_, OrderingType_ >::absDeterminant ( )

inline

Give the absolute value of the determinant.

Returns

the absolute value of the determinant of the matrix of which *this is the QR decomposition.

Warning

a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.

See also

logAbsDeterminant(), signDeterminant()

                          {
    using std::abs;
    eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
    // Initialize with the determinant of the row matrix
    Scalar det = Scalar(1.);
    // Note that the diagonal blocks of U are stored in supernodes,
    // which are available in the  L part :)
    for (Index j = 0; j < this->cols(); ++j) {
      for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) {
        if (it.index() == j) {
          det *= abs(it.value());
          break;
        }
      }
    }
    return det;
  }

References abs(), Eigen::SparseLU< MatrixType_, OrderingType_ >::cols(), eigen_assert, j, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk, and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore.

adjoint()

template<typename MatrixType_ , typename OrderingType_ >

const SparseLUTransposeView<true, SparseLU<MatrixType_, OrderingType_> > Eigen::SparseLU< MatrixType_, OrderingType_ >::adjoint ( )

inline

Return a solver for the adjointed matrix.

Returns

an expression of the adjoint of the factored matrix

A typical usage is to solve for the adjoint problem A' x = b:

solver.compute(A);
x = solver.adjoint().solve(b);

For real scalar types, this function is equivalent to transpose().

See also

transpose(), solve()

                                                                                    {
    SparseLUTransposeView<true, SparseLU<MatrixType_, OrderingType_>> adjointView;
    adjointView.setSparseLU(this);
    adjointView.setIsInitialized(this->m_isInitialized);
    return adjointView;
  }

References Eigen::SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >::m_isInitialized, Eigen::SparseLUTransposeView< Conjugate, SparseLUType >::setIsInitialized(), and Eigen::SparseLUTransposeView< Conjugate, SparseLUType >::setSparseLU().

analyzePattern()

template<typename MatrixType , typename OrderingType >

void Eigen::SparseLU< MatrixType, OrderingType >::analyzePattern

(

const MatrixType &

mat

)

Compute the column permutation.

Compute the column permutation to minimize the fill-in

• Apply this permutation to the input matrix -
• Compute the column elimination tree on the permuted matrix
• Postorder the elimination tree and the column permutation

It is possible to call compute() instead of analyzePattern() + factorize().

If the matrix is row-major this function will do an heavy copy.

See also

factorize(), compute()

                                                                             {
  // TODO  It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat.
 
  // Firstly, copy the whole input matrix.
  m_mat = mat;
 
  // Compute fill-in ordering
  OrderingType ord;
  ord(m_mat, m_perm_c);
 
  // Apply the permutation to the column of the input  matrix
  if (m_perm_c.size()) {
    m_mat.uncompress();  // NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This
                         // vector is filled but not subsequently used.
    // Then, permute only the column pointers
    ei_declare_aligned_stack_constructed_variable(
        StorageIndex, outerIndexPtr, mat.cols() + 1,
        mat.isCompressed() ? const_cast<StorageIndex*>(mat.outerIndexPtr()) : 0);
 
    // If the input matrix 'mat' is uncompressed, then the outer-indices do not match the ones of m_mat, and a copy is
    // thus needed.
    if (!mat.isCompressed())
      IndexVector::Map(outerIndexPtr, mat.cols() + 1) = IndexVector::Map(m_mat.outerIndexPtr(), mat.cols() + 1);
 
    // Apply the permutation and compute the nnz per column.
    for (Index i = 0; i < mat.cols(); i++) {
      m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
      m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i + 1] - outerIndexPtr[i];
    }
  }
 
  // Compute the column elimination tree of the permuted matrix
  IndexVector firstRowElt;
  internal::coletree(m_mat, m_etree, firstRowElt);
 
  // In symmetric mode, do not do postorder here
  if (!m_symmetricmode) {
    IndexVector post, iwork;
    // Post order etree
    internal::treePostorder(StorageIndex(m_mat.cols()), m_etree, post);
 
    // Renumber etree in postorder
    Index m = m_mat.cols();
    iwork.resize(m + 1);
    for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i));
    m_etree = iwork;
 
    // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree
    PermutationType post_perm(m);
    for (Index i = 0; i < m; i++) post_perm.indices()(i) = post(i);
 
    // Combine the two permutations : postorder the permutation for future use
    if (m_perm_c.size()) {
      m_perm_c = post_perm * m_perm_c;
    }
 
  }  // end postordering
 
  m_analysisIsOk = true;
}

References Eigen::internal::coletree(), Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::cols(), ei_declare_aligned_stack_constructed_variable, i, Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_ >::indices(), Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::isCompressed(), m, Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::outerIndexPtr(), Eigen::PlainObjectBase< Derived >::resize(), and Eigen::internal::treePostorder().

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::compute().

cols()

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::cols ( ) const

inline

Give the number of columns.

{ return m_mat.cols(); }

References Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::cols(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_mat.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::SparseLU< MatrixType_, OrderingType_ >::absDeterminant(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::logAbsDeterminant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

colsPermutation()

template<typename MatrixType_ , typename OrderingType_ >

const PermutationType& Eigen::SparseLU< MatrixType_, OrderingType_ >::colsPermutation ( ) const

inline

Give the column matrix permutation.

Returns

a reference to the column matrix permutation \( P_c^T \) such that \(P_r A P_c^T = L U\)

See also

rowsPermutation()

{ return m_perm_c; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perm_c.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), and Eigen::SparseInverse< Scalar >::computeInverse().

compute()

template<typename MatrixType_ , typename OrderingType_ >

void Eigen::SparseLU< MatrixType_, OrderingType_ >::compute ( const MatrixType &  matrix )

inline

Analyze and factorize the matrix so the solver is ready to solve.

Compute the symbolic and numeric factorization of the input sparse matrix. The input matrix should be in column-major storage, otherwise analyzePattern() will do a heavy copy.

Call analyzePattern() followed by factorize()

See also

analyzePattern(), factorize()

                                         {
    // Analyze
    analyzePattern(matrix);
    // Factorize
    factorize(matrix);
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::analyzePattern(), Eigen::SparseLU< MatrixType_, OrderingType_ >::factorize(), and matrix().

Referenced by check_sparse_inverse(), Eigen::SparseInverse< Scalar >::compute(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::SparseLU().

determinant()

template<typename MatrixType_ , typename OrderingType_ >

Scalar Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant ( )

inline

Give the determinant.

Returns

The determinant of the matrix.

See also

absDeterminant(), logAbsDeterminant()

                       {
    eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
    // Initialize with the determinant of the row matrix
    Scalar det = Scalar(1.);
    // Note that the diagonal blocks of U are stored in supernodes,
    // which are available in the  L part :)
    for (Index j = 0; j < this->cols(); ++j) {
      for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) {
        if (it.index() == j) {
          det *= it.value();
          break;
        }
      }
    }
    return (m_detPermR * m_detPermC) > 0 ? det : -det;
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::cols(), eigen_assert, j, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermC, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermR, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk, and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore.

factorize()

template<typename MatrixType , typename OrderingType >

void Eigen::SparseLU< MatrixType, OrderingType >::factorize

(

const MatrixType &

matrix

)

Factorize the matrix to get the solver ready.

• Numerical factorization
• Interleaved with the symbolic factorization

To get error of this function you should check info(), you can get more info of errors with lastErrorMessage().

In the past (before 2012 (git history is not older)), this function was returning an integer. This exit was 0 if successful factorization.

0 if info = i, and i is been completed, but the factor U is exactly singular,

and division by zero will occur if it is used to solve a system of equation.

A->ncol: number of bytes allocated when memory allocation failure occurred, plus A->ncol.

If lwork = -1, it is the estimated amount of space needed, plus A->ncol.

It seems that A was the name of the matrix in the past.

See also

analyzePattern(), compute(), SparseLU(), info(), lastErrorMessage()

                                                                           {
  using internal::emptyIdxLU;
  eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
  eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices");
 
  m_isInitialized = true;
 
  // Apply the column permutation computed in analyzepattern()
  //   m_mat = matrix * m_perm_c.inverse();
  m_mat = matrix;
  if (m_perm_c.size()) {
    m_mat.uncompress();  // NOTE: The effect of this command is only to create the InnerNonzeros pointers.
    // Then, permute only the column pointers
    const StorageIndex* outerIndexPtr;
    if (matrix.isCompressed())
      outerIndexPtr = matrix.outerIndexPtr();
    else {
      StorageIndex* outerIndexPtr_t = new StorageIndex[matrix.cols() + 1];
      for (Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i];
      outerIndexPtr = outerIndexPtr_t;
    }
    for (Index i = 0; i < matrix.cols(); i++) {
      m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i];
      m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i + 1] - outerIndexPtr[i];
    }
    if (!matrix.isCompressed()) delete[] outerIndexPtr;
  } else {  // FIXME This should not be needed if the empty permutation is handled transparently
    m_perm_c.resize(matrix.cols());
    for (StorageIndex i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i;
  }
 
  Index m = m_mat.rows();
  Index n = m_mat.cols();
  Index nnz = m_mat.nonZeros();
  Index maxpanel = m_perfv.panel_size * m;
  // Allocate working storage common to the factor routines
  Index lwork = 0;
  // Return the size of actually allocated memory when allocation failed,
  // and 0 on success.
  Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu);
  if (info) {
    m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n";
    m_factorizationIsOk = false;
    return;
  }
 
  // Set up pointers for integer working arrays
  IndexVector segrep(m);
  segrep.setZero();
  IndexVector parent(m);
  parent.setZero();
  IndexVector xplore(m);
  xplore.setZero();
  IndexVector repfnz(maxpanel);
  IndexVector panel_lsub(maxpanel);
  IndexVector xprune(n);
  xprune.setZero();
  IndexVector marker(m * internal::LUNoMarker);
  marker.setZero();
 
  repfnz.setConstant(-1);
  panel_lsub.setConstant(-1);
 
  // Set up pointers for scalar working arrays
  ScalarVector dense;
  dense.setZero(maxpanel);
  ScalarVector tempv;
  tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/ m));
 
  // Compute the inverse of perm_c
  PermutationType iperm_c(m_perm_c.inverse());
 
  // Identify initial relaxed snodes
  IndexVector relax_end(n);
  if (m_symmetricmode == true)
    Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
  else
    Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
 
  m_perm_r.resize(m);
  m_perm_r.indices().setConstant(-1);
  marker.setConstant(-1);
  m_detPermR = 1;  // Record the determinant of the row permutation
 
  m_glu.supno(0) = emptyIdxLU;
  m_glu.xsup.setConstant(0);
  m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0);
 
  // Work on one 'panel' at a time. A panel is one of the following :
  //  (a) a relaxed supernode at the bottom of the etree, or
  //  (b) panel_size contiguous columns, <panel_size> defined by the user
  Index jcol;
  Index pivrow;  // Pivotal row number in the original row matrix
  Index nseg1;   // Number of segments in U-column above panel row jcol
  Index nseg;    // Number of segments in each U-column
  Index irep;
  Index i, k, jj;
  for (jcol = 0; jcol < n;) {
    // Adjust panel size so that a panel won't overlap with the next relaxed snode.
    Index panel_size = m_perfv.panel_size;  // upper bound on panel width
    for (k = jcol + 1; k < (std::min)(jcol + panel_size, n); k++) {
      if (relax_end(k) != emptyIdxLU) {
        panel_size = k - jcol;
        break;
      }
    }
    if (k == n) panel_size = n - jcol;
 
    // Symbolic outer factorization on a panel of columns
    Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune,
                    marker, parent, xplore, m_glu);
 
    // Numeric sup-panel updates in topological order
    Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu);
 
    // Sparse LU within the panel, and below the panel diagonal
    for (jj = jcol; jj < jcol + panel_size; jj++) {
      k = (jj - jcol) * m;  // Column index for w-wide arrays
 
      nseg = nseg1;  // begin after all the panel segments
      // Depth-first-search for the current column
      VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m);
      VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
      // Return 0 on success and > 0 number of bytes allocated when run out of space.
      info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune,
                              marker, parent, xplore, m_glu);
      if (info) {
        m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() ";
        m_info = NumericalIssue;
        m_factorizationIsOk = false;
        return;
      }
      // Numeric updates to this column
      VectorBlock<ScalarVector> dense_k(dense, k, m);
      VectorBlock<IndexVector> segrep_k(segrep, nseg1, m - nseg1);
      // Return 0 on success and > 0 number of bytes allocated when run out of space.
      info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu);
      if (info) {
        m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() ";
        m_info = NumericalIssue;
        m_factorizationIsOk = false;
        return;
      }
 
      // Copy the U-segments to ucol(*)
      // Return 0 on success and > 0 number of bytes allocated when run out of space.
      info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k, m_perm_r.indices(), dense_k, m_glu);
      if (info) {
        m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() ";
        m_info = NumericalIssue;
        m_factorizationIsOk = false;
        return;
      }
 
      // Form the L-segment
      // Return O if success, i > 0 if U(i, i) is exactly zero.
      info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu);
      if (info) {
        m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR";
#ifndef EIGEN_NO_IO
        std::ostringstream returnInfo;
        returnInfo << " ... ZERO COLUMN AT ";
        returnInfo << info;
        m_lastError += returnInfo.str();
#endif
        m_info = NumericalIssue;
        m_factorizationIsOk = false;
        return;
      }
 
      // Update the determinant of the row permutation matrix
      // FIXME: the following test is not correct, we should probably take iperm_c into account and pivrow is not
      // directly the row pivot.
      if (pivrow != jj) m_detPermR = -m_detPermR;
 
      // Prune columns (0:jj-1) using column jj
      Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu);
 
      // Reset repfnz for this column
      for (i = 0; i < nseg; i++) {
        irep = segrep(i);
        repfnz_k(irep) = emptyIdxLU;
      }
    }                    // end SparseLU within the panel
    jcol += panel_size;  // Move to the next panel
  }                      // end for -- end elimination
 
  m_detPermR = m_perm_r.determinant();
  m_detPermC = m_perm_c.determinant();
 
  // Count the number of nonzeros in factors
  Base::countnz(n, m_nnzL, m_nnzU, m_glu);
  // Apply permutation  to the L subscripts
  Base::fixupL(n, m_perm_r.indices(), m_glu);
 
  // Create supernode matrix L
  m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup);
  // Create the column major upper sparse matrix  U;
  new (&m_Ustore) Map<SparseMatrix<Scalar, ColMajor, StorageIndex>>(m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(),
                                                                    m_glu.ucol.data());
 
  m_info = Success;
  m_factorizationIsOk = true;
}

References countnz(), eigen_assert, Eigen::internal::emptyIdxLU, fixupL(), heap_relax_snode(), i, Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_ >::indices(), info, k, Eigen::internal::LUNoMarker, Eigen::internal::LUnumTempV(), m, matrix(), min, n, Eigen::NumericalIssue, relax_snode(), Eigen::PlainObjectBase< Derived >::setConstant(), Eigen::PlainObjectBase< Derived >::setZero(), and Eigen::Success.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::compute().

info()

template<typename MatrixType_ , typename OrderingType_ >

ComputationInfo Eigen::SparseLU< MatrixType_, OrderingType_ >::info ( ) const

inline

Reports whether previous computation was successful.

Returns

Success if computation was successful, NumericalIssue if the LU factorization reports a problem, zero diagonal for instance InvalidInput if the input matrix is invalid

You can get a readable error message with lastErrorMessage().

See also

lastErrorMessage()

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

References eigen_assert, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_info, and Eigen::SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >::m_isInitialized.

Referenced by Eigen::SparseInverse< Scalar >::computeInverse().

initperfvalues()

template<typename MatrixType_ , typename OrderingType_ >

void Eigen::SparseLU< MatrixType_, OrderingType_ >::initperfvalues ( )

inlineprotected

                        {
    m_perfv.panel_size = 16;
    m_perfv.relax = 1;
    m_perfv.maxsuper = 128;
    m_perfv.rowblk = 16;
    m_perfv.colblk = 8;
    m_perfv.fillfactor = 20;
  }

References Eigen::internal::perfvalues::colblk, Eigen::internal::perfvalues::fillfactor, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perfv, Eigen::internal::perfvalues::maxsuper, Eigen::internal::perfvalues::panel_size, Eigen::internal::perfvalues::relax, and Eigen::internal::perfvalues::rowblk.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::SparseLU().

isSymmetric()

template<typename MatrixType_ , typename OrderingType_ >

void Eigen::SparseLU< MatrixType_, OrderingType_ >::isSymmetric ( bool  sym )

inline

Let you set that the pattern of the input matrix is symmetric.

{ m_symmetricmode = sym; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_symmetricmode.

lastErrorMessage()

template<typename MatrixType_ , typename OrderingType_ >

std::string Eigen::SparseLU< MatrixType_, OrderingType_ >::lastErrorMessage ( ) const

inline

Give a human readable error.

Returns

A string describing the type of error

{ return m_lastError; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_lastError.

logAbsDeterminant()

template<typename MatrixType_ , typename OrderingType_ >

Scalar Eigen::SparseLU< MatrixType_, OrderingType_ >::logAbsDeterminant ( ) const

inline

Give the natural log of the absolute determinant.

Returns

the natural log of the absolute value of the determinant of the matrix of which **this is the QR decomposition

Note

This method is useful to work around the risk of overflow/underflow that's inherent to the determinant computation.

See also

absDeterminant(), signDeterminant()

                                   {
    using std::abs;
    using std::log;
 
    eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
    Scalar det = Scalar(0.);
    for (Index j = 0; j < this->cols(); ++j) {
      for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) {
        if (it.row() < j) continue;
        if (it.row() == j) {
          det += log(abs(it.value()));
          break;
        }
      }
    }
    return det;
  }

References abs(), Eigen::SparseLU< MatrixType_, OrderingType_ >::cols(), eigen_assert, j, Eigen::bfloat16_impl::log(), Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk, and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore.

matrixL()

template<typename MatrixType_ , typename OrderingType_ >

SparseLUMatrixLReturnType<SCMatrix> Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixL ( ) const

inline

Give the matrixL.

Returns

an expression of the matrix L, internally stored as supernodes The only operation available with this expression is the triangular solve

y = b; matrixL().solveInPlace(y);

{ return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore); }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), and Eigen::SparseInverse< Scalar >::computeInverse().

matrixU()

template<typename MatrixType_ , typename OrderingType_ >

SparseLUMatrixUReturnType<SCMatrix, Map<SparseMatrix<Scalar, ColMajor, StorageIndex> > > Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixU ( ) const

inline

Give the MatrixU.

Returns

an expression of the matrix U, The only operation available with this expression is the triangular solve

y = b; matrixU().solveInPlace(y);

                                                                                                         {
    return SparseLUMatrixUReturnType<SCMatrix, Map<SparseMatrix<Scalar, ColMajor, StorageIndex>>>(m_Lstore, m_Ustore);
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore, and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Ustore.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), and Eigen::SparseInverse< Scalar >::computeInverse().

nnzL()

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::nnzL ( ) const

inline

Give the number of non zero in matrix L.

{ return m_nnzL; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_nnzL.

nnzU()

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::nnzU ( ) const

inline

Give the number of non zero in matrix U.

{ return m_nnzU; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_nnzU.

rows()

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::rows ( ) const

inline

Give the number of rows.

{ return m_mat.rows(); }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_mat, and Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::rows().

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

rowsPermutation()

template<typename MatrixType_ , typename OrderingType_ >

const PermutationType& Eigen::SparseLU< MatrixType_, OrderingType_ >::rowsPermutation ( ) const

inline

Give the row matrix permutation.

Returns

a reference to the row matrix permutation \( P_r \) such that \(P_r A P_c^T = L U\)

See also

colsPermutation()

{ return m_perm_r; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perm_r.

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), and Eigen::SparseInverse< Scalar >::computeInverse().

setPivotThreshold()

template<typename MatrixType_ , typename OrderingType_ >

void Eigen::SparseLU< MatrixType_, OrderingType_ >::setPivotThreshold ( const RealScalar &  thresh )

inline

Set the threshold used for a diagonal entry to be an acceptable pivot.

{ m_diagpivotthresh = thresh; }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::m_diagpivotthresh.

signDeterminant()

template<typename MatrixType_ , typename OrderingType_ >

Scalar Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant ( )

inline

Give the sign of the determinant.

Returns

A number representing the sign of the determinant

See also

absDeterminant(), logAbsDeterminant()

                           {
    eigen_assert(m_factorizationIsOk && "The matrix should be factorized first.");
    // Initialize with the determinant of the row matrix
    Index det = 1;
    // Note that the diagonal blocks of U are stored in supernodes,
    // which are available in the  L part :)
    for (Index j = 0; j < this->cols(); ++j) {
      for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) {
        if (it.index() == j) {
          if (it.value() < 0)
            det = -det;
          else if (it.value() == 0)
            return 0;
          break;
        }
      }
    }
    return det * m_detPermR * m_detPermC;
  }

References Eigen::SparseLU< MatrixType_, OrderingType_ >::cols(), eigen_assert, j, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermC, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermR, Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk, and Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore.

simplicialfactorize()

template<typename MatrixType_ , typename OrderingType_ >

void Eigen::SparseLU< MatrixType_, OrderingType_ >::simplicialfactorize

(

const MatrixType &

matrix

)

transpose()

template<typename MatrixType_ , typename OrderingType_ >

const SparseLUTransposeView<false, SparseLU<MatrixType_, OrderingType_> > Eigen::SparseLU< MatrixType_, OrderingType_ >::transpose ( )

inline

Return a solver for the transposed matrix.

Returns

an expression of the transposed of the factored matrix.

A typical usage is to solve for the transposed problem A^T x = b:

solver.compute(A);
x = solver.transpose().solve(b);

See also

adjoint(), solve()

                                                                                       {
    SparseLUTransposeView<false, SparseLU<MatrixType_, OrderingType_>> transposeView;
    transposeView.setSparseLU(this);
    transposeView.setIsInitialized(this->m_isInitialized);
    return transposeView;
  }

References Eigen::SparseSolverBase< SparseLU< MatrixType_, OrderingType_ > >::m_isInitialized, Eigen::SparseLUTransposeView< Conjugate, SparseLUType >::setIsInitialized(), and Eigen::SparseLUTransposeView< Conjugate, SparseLUType >::setSparseLU().

Member Data Documentation

m_analysisIsOk

template<typename MatrixType_ , typename OrderingType_ >

bool Eigen::SparseLU< MatrixType_, OrderingType_ >::m_analysisIsOk

protected

m_detPermC

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermC

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant().

m_detPermR

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::m_detPermR

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant().

m_diagpivotthresh

template<typename MatrixType_ , typename OrderingType_ >

RealScalar Eigen::SparseLU< MatrixType_, OrderingType_ >::m_diagpivotthresh

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::setPivotThreshold().

m_etree

template<typename MatrixType_ , typename OrderingType_ >

IndexVector Eigen::SparseLU< MatrixType_, OrderingType_ >::m_etree

protected

m_factorizationIsOk

template<typename MatrixType_ , typename OrderingType_ >

bool Eigen::SparseLU< MatrixType_, OrderingType_ >::m_factorizationIsOk

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), Eigen::SparseLU< MatrixType_, OrderingType_ >::absDeterminant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::logAbsDeterminant(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant().

m_glu

template<typename MatrixType_ , typename OrderingType_ >

Base::GlobalLU_t Eigen::SparseLU< MatrixType_, OrderingType_ >::m_glu

protected

m_info

template<typename MatrixType_ , typename OrderingType_ >

ComputationInfo Eigen::SparseLU< MatrixType_, OrderingType_ >::m_info

mutableprotected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::info().

m_lastError

template<typename MatrixType_ , typename OrderingType_ >

std::string Eigen::SparseLU< MatrixType_, OrderingType_ >::m_lastError

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::lastErrorMessage().

m_Lstore

template<typename MatrixType_ , typename OrderingType_ >

SCMatrix Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Lstore

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::absDeterminant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::determinant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::logAbsDeterminant(), Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixL(), Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixU(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::signDeterminant().

m_mat

template<typename MatrixType_ , typename OrderingType_ >

NCMatrix Eigen::SparseLU< MatrixType_, OrderingType_ >::m_mat

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::cols(), and Eigen::SparseLU< MatrixType_, OrderingType_ >::rows().

m_nnzL

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::m_nnzL

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::nnzL().

m_nnzU

template<typename MatrixType_ , typename OrderingType_ >

Index Eigen::SparseLU< MatrixType_, OrderingType_ >::m_nnzU

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::nnzU().

m_perfv

template<typename MatrixType_ , typename OrderingType_ >

internal::perfvalues Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perfv

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::initperfvalues().

m_perm_c

template<typename MatrixType_ , typename OrderingType_ >

PermutationType Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perm_c

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::colsPermutation().

m_perm_r

template<typename MatrixType_ , typename OrderingType_ >

PermutationType Eigen::SparseLU< MatrixType_, OrderingType_ >::m_perm_r

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::rowsPermutation().

m_symmetricmode

template<typename MatrixType_ , typename OrderingType_ >

bool Eigen::SparseLU< MatrixType_, OrderingType_ >::m_symmetricmode

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::isSymmetric().

m_Ustore

template<typename MatrixType_ , typename OrderingType_ >

Map<SparseMatrix<Scalar, ColMajor, StorageIndex> > Eigen::SparseLU< MatrixType_, OrderingType_ >::m_Ustore

protected

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::matrixU().

---

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

• SparseLU.h