Templated class to perform the Cholesky decomposition on a symmetric positive-definite matrix. More...

#include <LLTMatrix.H>

Inheritance diagram for LLTMatrix< Type >:

Collaboration diagram for LLTMatrix< Type >:

Public Member Functions
	LLTMatrix ()=default
	Default construct.
	LLTMatrix (const SquareMatrix< Type > &mat)
	Construct and perform the decomposition on input square matrix.
void	decompose (const SquareMatrix< Type > &mat)
	Copy matrix and perform Cholesky decomposition.
void	solve (List< Type > &x, const UList< Type > &source) const
	Solve the linear system with the given source and return the solution in the argument x.
template<class Addr>
void	solve (List< Type > &x, const IndirectListBase< Type, Addr > &source) const
	Solve the linear system with the given source and return the solution in the argument x.
tmp< Field< Type > >	solve (const UList< Type > &source) const
	Solve the linear system with the given source return the solution.
template<class Addr>
tmp< Field< Type > >	solve (const IndirectListBase< Type, Addr > &source) const
	Solve the linear system with the given source return the solution.
template<class Addr>
Foam::tmp< Foam::Field< Type > >	solve (const IndirectListBase< Type, Addr > &source) const
Public Member Functions inherited from SquareMatrix< Type >
	SquareMatrix ()=default
	Default construct.
	SquareMatrix (const SquareMatrix &)=default
	Copy construct.
SquareMatrix &	operator= (const SquareMatrix &)=default
	Copy assignment.
	SquareMatrix (const label n)
	Construct for given size (rows == cols), uninitialised content.
	SquareMatrix (const label n, Foam::zero)
	Construct for given size (rows == cols) initializing all elements to zero.
	SquareMatrix (const label n, const Type &val)
	Construct for given size (rows == cols) initializing all elements to the given value.
template<class AnyType>
	SquareMatrix (const label n, const Identity< AnyType >)
	Construct for given size (rows == cols) initializing to the identity matrix.
template<class AnyType>
	SquareMatrix (const labelPair &dims, const Identity< AnyType >)
	Construct for given size (rows == cols) by using a labelPair initializing to the identity matrix.
	SquareMatrix (const labelPair &dims)
	Construct given number of rows/columns by using a labelPair (checked to be equal).
	SquareMatrix (const labelPair &dims, Foam::zero)
	Construct given number of rows/columns by using a labelPair (checked to be equal) and initializing all elements to zero.
	SquareMatrix (const labelPair &dims, const Type &val)
	Construct given number of rows/columns by using a labelPair (checked to be equal) and initializing all elements to the given value.
	SquareMatrix (const label m, const label n, Foam::zero)
	Construct given number of rows/columns (checked to be equal) initializing all elements to zero.
template<class MatrixType>
	SquareMatrix (const ConstMatrixBlock< MatrixType > &mat)
	Construct from const sub-matrix block.
template<class MatrixType>
	SquareMatrix (const MatrixBlock< MatrixType > &mat)
	Construct from sub-matrix block.
	SquareMatrix (const RectangularMatrix< Type > &mat)
	Construct as copy of a RectangularMatrix which is checked to be square.
	SquareMatrix (Istream &is)
	Construct from Istream.
autoPtr< SquareMatrix< Type > >	clone () const
	Clone.
void	resize (const label m)
	Resize the matrix preserving the elements.
void	resize_nocopy (const label n)
	Resize the matrix without preserving existing content.
void	resize (const label m, const label n)
	Resize the matrix preserving the elements (compatibility).
void	setSize (const label m)
	Resize the matrix preserving the elements.
void	shallowResize (const label m)
	Resize the matrix without reallocating storage (unsafe).
bool	symmetric () const
	Return true if the square matrix is effectively symmetric/Hermitian.
bool	tridiagonal () const
	Return true if the square matrix is reduced tridiagonal.
template<class CompOp>
labelList	sortPermutation (CompOp &compare) const
	Return a sort permutation using the given comparison operator on the diagonal entries.
void	applyPermutation (const labelUList &p)
	Column-reorder this Matrix according to the given permutation.
void	operator= (SquareMatrix< Type > &&mat)
	Move assignment.
void	operator= (Foam::zero)
	Assign all elements to zero.
void	operator= (const Type &val)
	Assign all elements to value.
template<class AnyType>
void	operator= (const Identity< AnyType >)
	Set to identity matrix.
template<class CompOp>
Foam::labelList	sortPermutation (CompOp &compare) const
Public Member Functions inherited from Matrix< SquareMatrix< Type >, Type >
Foam::tmp< Foam::Field< Type > >	AmulImpl (const ListType &x) const
Foam::tmp< Foam::Field< Type > >	TmulImpl (const ListType &x) const
Foam::ConstMatrixBlock< Foam::Matrix< SquareMatrix< Type >, Type > >	block (const label rowIndex, const label colIndex) const
Foam::MatrixBlock< Foam::Matrix< SquareMatrix< Type >, Type > >	block (const label rowIndex, const label colIndex)
Foam::tmp< Foam::Field< Type > >	Amul (const IndirectListBase< Type, Addr > &x) const
Foam::tmp< Foam::Field< Type > >	Tmul (const IndirectListBase< Type, Addr > &x) const
constexpr	Matrix () noexcept
	Default construct (empty matrix).
autoPtr< mType >	clone () const
	Clone.
	~Matrix ()
	Destructor.
label	mRows () const noexcept
	The number of rows.
label	nRows () const noexcept
	The number of rows.
label	m () const noexcept
	The number of rows.
label	nCols () const noexcept
	The number of columns.
label	n () const noexcept
	The number of columns.
bool	empty () const noexcept
	Return true if Matrix is empty (i.e., size() is zero).
label	size () const noexcept
	The number of elements in Matrix (m*n).
labelPair	sizes () const noexcept
	Return row/column sizes.
const Type *	cdata () const noexcept
	Return const pointer to the first data element, which can also be used to address into Matrix contents.
Type *	data () noexcept
	Return pointer to the first data element, which can also be used to address into Matrix contents.
const char *	cdata_bytes () const noexcept
	Return pointer to the underlying array serving as data storage, reinterpreted as byte data.
char *	data_bytes () noexcept
	Return pointer to the underlying array serving as data storage, reinterpreted as byte data.
std::streamsize	size_bytes () const noexcept
	Number of contiguous bytes for the Matrix data, no runtime check that the type is actually contiguous.
std::streamsize	byteSize () const
	Number of contiguous bytes for the Matrix data, runtime FatalError if type is not contiguous.
const Type *	rowData (const label irow) const
	Return const pointer to data in the specified row.
const Type &	at (const label idx) const
	Linear addressing const element access.
ConstMatrixBlock< mType >	subColumn (const label colIndex, const label rowIndex=0, label len=-1) const
	Return const column or column's subset of Matrix.
ConstMatrixBlock< mType >	subRow (const label rowIndex, const label colIndex=0, label len=-1) const
	Return const row or const row's subset of Matrix.
ConstMatrixBlock< mType >	subMatrix (const label rowIndex, const label colIndex, label szRows=-1, label szCols=-1) const
	Return const sub-block of Matrix.
void	checki (const label irow) const
	Check index i is within valid range [0, m).
void	checkj (const label jcol) const
	Check index j is within valid range [0, n).
void	checkSize () const
	Check that dimensions are positive, non-zero.
bool	uniform () const
	True if all entries have identical values, and Matrix is non-empty.
void	clear ()
	Clear Matrix, i.e. set sizes to zero.
List< Type >	release ()
	Release storage management of Matrix contents by transferring management to a List.
void	swap (Matrix< SquareMatrix< Type >, Type > &mat)
	Swap contents.
void	transfer (Matrix< SquareMatrix< Type >, Type > &mat)
	Transfer the contents of the argument Matrix into this Matrix and annul the argument Matrix.
void	resize (const label m, const label n)
	Change Matrix dimensions, preserving the elements.
void	resize_nocopy (const label mrow, const label ncol)
	Change Matrix dimensions without preserving existing content.
void	setSize (const label m, const label n)
	Change Matrix dimensions, preserving the elements.
void	shallowResize (const label m, const label n)
	Resize Matrix without reallocating storage (unsafe).
void	round (const scalar tol=SMALL)
	Round elements with magnitude smaller than tol (SMALL) to zero.
SquareMatrix< Type >	T () const
	Return conjugate transpose of Matrix.
SquareMatrix< Type >	transpose () const
	Return non-conjugate transpose of Matrix.
List< Type >	diag () const
	Extract the diagonal elements. Method may change in the future.
Type	trace () const
	Return the trace.
scalar	columnNorm (const label colIndex, const bool noSqrt=false) const
	Return L2-Norm of chosen column.
scalar	norm (const bool noSqrt=false) const
	Return Frobenius norm of Matrix.
const Type *	operator[] (const label irow) const
	Return const pointer to data in the specified row - rowData().
const Type &	operator() (const label irow, const label jcol) const
	(i, j) const element access operator
void	operator= (const Matrix< SquareMatrix< Type >, Type > &mat)
	Copy assignment. Takes linear time.
void	operator+= (const Matrix< SquareMatrix< Type >, Type > &other)
	Matrix addition.
void	operator-= (const Matrix< SquareMatrix< Type >, Type > &other)
	Matrix subtraction.
void	operator*= (const Type &s)
	Matrix scalar multiplication.
void	operator/= (const Type &s)
	Matrix scalar division.
iterator	begin () noexcept
	Return an iterator to begin traversing a Matrix.
iterator	end () noexcept
	Return an iterator to end traversing a Matrix.
const_iterator	cbegin () const noexcept
	Return const_iterator to begin traversing a constant Matrix.
const_iterator	cend () const noexcept
	Return const_iterator to end traversing a constant Matrix.
bool	readMatrix (Istream &is)
	Read Matrix from Istream, discarding existing contents.
Ostream &	writeMatrix (Ostream &os, const label shortLen=0) const
	Write Matrix, with line-breaks in ASCII when length exceeds shortLen.
const Type *	v () const
	Deprecated(2019-04) raw data pointer, const access.
ConstMatrixBlock< mType >	col (const label m, const label mStart, const label nStart) const
	Deprecated(2019-04) - use subColumn().

Additional Inherited Members
Public Types inherited from Matrix< SquareMatrix< Type >, Type >
typedef Matrix< SquareMatrix< Type >, Type >	mType
	Matrix type.
typedef Type	cmptType
	The value type the Matrix contains.
typedef Type	value_type
	The value type the Matrix contains.
typedef label	size_type
	The type to represent the size of a Matrix.
typedef Type *	iterator
	Random access iterator for traversing a Matrix.
typedef const Type *	const_iterator
	Random access iterator for traversing a Matrix.
Static Public Member Functions inherited from Matrix< SquareMatrix< Type >, Type >
static const Matrix< SquareMatrix< Type >, Type > &	null () noexcept
	Return a null Matrix (reference to a nullObject). Behaves like a empty Matrix.

Detailed Description

template<class Type>
class Foam::LLTMatrix< Type >

Templated class to perform the Cholesky decomposition on a symmetric positive-definite matrix.

Member functions are provided to solve linear systems using the LLT decomposition.

Source files

Definition at line 53 of file LLTMatrix.H.

Constructor & Destructor Documentation

◆ LLTMatrix() [1/2]

template<class Type>

LLTMatrix ( )

default

Default construct.

References SquareMatrix< Type >::SquareMatrix(), and x.

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◆ LLTMatrix() [2/2]

template<class Type>

LLTMatrix ( const SquareMatrix< Type > & mat )

Construct and perform the decomposition on input square matrix.

Definition at line 27 of file LLTMatrix.C.

References decompose(), and SquareMatrix< Type >::SquareMatrix().

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Member Function Documentation

◆ decompose()

template<class Type>

void decompose ( const SquareMatrix< Type > & mat )

Copy matrix and perform Cholesky decomposition.

Definition at line 36 of file LLTMatrix.C.

References Foam::abort(), Foam::FatalError, FatalErrorInFunction, k, Matrix< Form, Type >::m(), Matrix< SquareMatrix< Type >, Type >::m(), Foam::sqrt(), SquareMatrix< Type >::SquareMatrix(), Foam::sum(), and Foam::Zero.

Referenced by LLTMatrix().

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◆ solve() [1/5]

template<class Type>

void solve	(	List< Type > &	x,
		const UList< Type > &	source ) const

Solve the linear system with the given source and return the solution in the argument x.

This function may be called with the same field for x and source.

Definition at line 126 of file LLTMatrix.C.

References x.

◆ solve() [2/5]

template<class Type>

template<class Addr>

void solve	(	List< Type > &	x,
		const IndirectListBase< Type, Addr > &	source ) const

Solve the linear system with the given source and return the solution in the argument x.

This function may be called with the same field for x and source.

Definition at line 138 of file LLTMatrix.C.

References x.

◆ solve() [3/5]

template<class Type>

Foam::tmp< Foam::Field< Type > > solve ( const UList< Type > & source ) const

Solve the linear system with the given source return the solution.

Definition at line 148 of file LLTMatrix.C.

References Foam::New(), UList< T >::size(), and solve().

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◆ solve() [4/5]

template<class Type>

template<class Addr>

tmp< Field< Type > > solve ( const IndirectListBase< Type, Addr > & source ) const

Solve the linear system with the given source return the solution.

◆ solve() [5/5]

template<class Type>

template<class Addr>

Foam::tmp< Foam::Field< Type > > solve ( const IndirectListBase< Type, Addr > & source ) const

Definition at line 163 of file LLTMatrix.C.

References Foam::New(), IndirectListBase< T, Addr >::size(), and solve().

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

src/OpenFOAM/matrices/LLTMatrix/LLTMatrix.H
src/OpenFOAM/matrices/LLTMatrix/LLTMatrix.C

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LLTMatrix() [1/2]

◆ LLTMatrix() [2/2]

Member Function Documentation

◆ decompose()

◆ solve() [1/5]

◆ solve() [2/5]

◆ solve() [3/5]

◆ solve() [4/5]

◆ solve() [5/5]