#include <densemat.hpp>

Inheritance diagram for mfem::LUFactors:

Collaboration diagram for mfem::LUFactors:

Public Member Functions
	LUFactors ()

	LUFactors (double data_, int ipiv_)

virtual bool	Factor (int m, double TOL=0.0)
	Compute the LU factorization of the current matrix. More...

virtual double	Det (int m) const

void	Mult (int m, int n, double *X) const

void	LSolve (int m, int n, double *X) const

void	USolve (int m, int n, double *X) const

virtual void	Solve (int m, int n, double *X) const

void	RightSolve (int m, int n, double *X) const

virtual void	GetInverseMatrix (int m, double *X) const
	Assuming L.U = P.A factored data of size (m x m), compute X <- A^{-1}. More...

void	BlockFactor (int m, int n, double A12, double A21, double *A22) const

void	BlockForwSolve (int m, int n, int r, const double L21, double B1, double *B2) const

void	BlockBackSolve (int m, int n, int r, const double U12, const double X2, double *Y1) const

Public Member Functions inherited from mfem::Factors
	Factors ()

	Factors (double *data_)

virtual	~Factors ()

Static Public Member Functions
static void	SubMult (int m, int n, int r, const double A21, const double X1, double *X2)

Public Attributes
int *	ipiv

Public Attributes inherited from mfem::Factors
double *	data

Static Public Attributes
static const int	ipiv_base = 1

Detailed Description

Class that can compute LU factorization of external data and perform various operations with the factored data.

Definition at line 656 of file densemat.hpp.

Constructor & Destructor Documentation

◆ LUFactors() [1/2]

mfem::LUFactors::LUFactors ( )

inline

With this constructor, the (public) data and ipiv members should be set explicitly before calling class methods.

Definition at line 668 of file densemat.hpp.

◆ LUFactors() [2/2]

mfem::LUFactors::LUFactors	(	double *	data_,
		int *	ipiv_
	)

inline

Definition at line 670 of file densemat.hpp.

Member Function Documentation

◆ BlockBackSolve()

void mfem::LUFactors::BlockBackSolve	(	int	m,
		int	n,
		int	r,
		const double *	U12,
		const double *	X2,
		double *	Y1
	)		const

Given BlockFactor()'d data, perform the backward block solve in | U U12 | | X1 | = | Y1 | | 0 S22 | | X2 | | Y2 |. The input is the solution block X2 and the block Y1 resulting from BlockForwSolve(). The result block X1 overwrites input block Y1: Y1 <- X1 = U^{-1} (Y1 - U12 X2).

Definition at line 3604 of file densemat.cpp.

◆ BlockFactor()

void mfem::LUFactors::BlockFactor	(	int	m,
		int	n,
		double *	A12,
		double *	A21,
		double *	A22
	)		const

Assuming P.A = L.U factored data of size (m x m), compute the 2x2 block decomposition: | P 0 | | A A12 | = | L 0 | | U U12 | | 0 I | | A21 A22 | | L21 I | | 0 S22 | where A12, A21, and A22 are matrices of size (m x n), (n x m), and (n x n), respectively. The blocks are overwritten as follows: A12 <- U12 = L^{-1} P A12 A21 <- L21 = A21 U^{-1} A22 <- S22 = A22 - L21 U12. The block S22 is the Schur complement.

Definition at line 3569 of file densemat.cpp.

◆ BlockForwSolve()

void mfem::LUFactors::BlockForwSolve	(	int	m,
		int	n,
		int	r,
		const double *	L21,
		double *	B1,
		double *	B2
	)		const

Given BlockFactor()'d data, perform the forward block solve for the linear system: | A A12 | | X1 | = | B1 | | A21 A22 | | X2 | | B2 | written in the factored form: | L 0 | | U U12 | | X1 | = | P 0 | | B1 | | L21 I | | 0 S22 | | X2 | | 0 I | | B2 |. The resulting blocks Y1, Y2 solve the system: | L 0 | | Y1 | = | P 0 | | B1 | | L21 I | | Y2 | | 0 I | | B2 | The blocks are overwritten as follows: B1 <- Y1 = L^{-1} P B1 B2 <- Y2 = B2 - L21 Y1 = B2 - A21 A^{-1} B1 The blocks B1/Y1 and B2/Y2 are of size (m x r) and (n x r), respectively. The Schur complement system is given by: S22 X2 = Y2.

Definition at line 3595 of file densemat.cpp.

◆ Det()

double mfem::LUFactors::Det ( int m ) const

virtual

Assuming L.U = P.A factored data of size (m x m), compute |A| from the diagonal values of U and the permutation information.

Reimplemented from mfem::Factors.

Definition at line 3328 of file densemat.cpp.

◆ Factor()

bool mfem::LUFactors::Factor	(	int	m,
		double	TOL = `0.0`
	)

virtual

Compute the LU factorization of the current matrix.

Factorize the current matrix of size (m x m) overwriting it with the LU factors. The factorization is such that L.U = P.A, where A is the original matrix and P is a permutation matrix represented by ipiv.

Parameters

[in]	m	size of the square matrix
[in]	TOL	optional fuzzy comparison tolerance. Defaults to 0.0.

Returns: status set to true if successful, otherwise, false.

Reimplemented from mfem::Factors.

Definition at line 3269 of file densemat.cpp.

◆ GetInverseMatrix()

void mfem::LUFactors::GetInverseMatrix	(	int	m,
		double *	X
	)		const

virtual

Assuming L.U = P.A factored data of size (m x m), compute X <- A^{-1}.

Reimplemented from mfem::Factors.

Definition at line 3489 of file densemat.cpp.

◆ LSolve()

void mfem::LUFactors::LSolve	(	int	m,
		int	n,
		double *	X
	)		const

Assuming L.U = P.A factored data of size (m x m), compute X <- L^{-1} P X, for a matrix X of size (m x n).

Definition at line 3379 of file densemat.cpp.

◆ Mult()

void mfem::LUFactors::Mult	(	int	m,
		int	n,
		double *	X
	)		const

Assuming L.U = P.A factored data of size (m x m), compute X <- A X, for a matrix X of size (m x n).

Definition at line 3345 of file densemat.cpp.

◆ RightSolve()

void mfem::LUFactors::RightSolve	(	int	m,
		int	n,
		double *	X
	)		const

Assuming L.U = P.A factored data of size (m x m), compute X <- X A^{-1}, for a matrix X of size (n x m).

Definition at line 3434 of file densemat.cpp.

◆ Solve()

void mfem::LUFactors::Solve	(	int	m,
		int	n,
		double *	X
	)		const

virtual

Assuming L.U = P.A factored data of size (m x m), compute X <- A^{-1} X, for a matrix X of size (m x n).

Reimplemented from mfem::Factors.

Definition at line 3420 of file densemat.cpp.

◆ SubMult()

void mfem::LUFactors::SubMult	(	int	m,
		int	n,
		int	r,
		const double *	A21,
		const double *	X1,
		double *	X2
	)

static

Given an (n x m) matrix A21, compute X2 <- X2 - A21 X1, for matrices X1, and X2 of size (m x r) and (n x r), respectively.

Definition at line 3552 of file densemat.cpp.

◆ USolve()

void mfem::LUFactors::USolve	(	int	m,
		int	n,
		double *	X
	)		const

Assuming L.U = P.A factored data of size (m x m), compute X <- U^{-1} X, for a matrix X of size (m x n).

Definition at line 3402 of file densemat.cpp.

Member Data Documentation

◆ ipiv

int* mfem::LUFactors::ipiv

Definition at line 659 of file densemat.hpp.

◆ ipiv_base

static const int mfem::LUFactors::ipiv_base = 1

static

Definition at line 661 of file densemat.hpp.

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

linalg/densemat.hpp
linalg/densemat.cpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ LUFactors() [1/2]

◆ LUFactors() [2/2]

Member Function Documentation

◆ BlockBackSolve()

◆ BlockFactor()

◆ BlockForwSolve()

◆ Det()

◆ Factor()

◆ GetInverseMatrix()

◆ LSolve()

◆ Mult()

◆ RightSolve()

◆ Solve()

◆ SubMult()

◆ USolve()

Member Data Documentation

◆ ipiv

◆ ipiv_base