mfem::LUFactors Class Reference

#include <densemat.hpp>

Public Member Functions
	LUFactors ()
	LUFactors (double *data_, int *ipiv_)
void	Factor (int m)
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
void	Solve (int m, int n, double *X) const
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

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

Public Attributes
double *	data
int *	ipiv

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 437 of file densemat.hpp.

Constructor & Destructor Documentation

mfem::LUFactors::LUFactors ( )

inline

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

Definition at line 450 of file densemat.hpp.

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

inline

Definition at line 452 of file densemat.hpp.

Member Function Documentation

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 4131 of file densemat.cpp.

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 4095 of file densemat.cpp.

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 4122 of file densemat.cpp.

double mfem::LUFactors::Det

(

int

m

)

const

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

Definition at line 3902 of file densemat.cpp.

void mfem::LUFactors::Factor

(

int

m

)

Factorize the current data 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.

Definition at line 3850 of file densemat.cpp.

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

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

Definition at line 4013 of file densemat.cpp.

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 3955 of file densemat.cpp.

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 3919 of file densemat.cpp.

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

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).

Definition at line 3999 of file densemat.cpp.

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 4078 of file densemat.cpp.

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 3980 of file densemat.cpp.

Member Data Documentation

double* mfem::LUFactors::data

Definition at line 440 of file densemat.hpp.

int* mfem::LUFactors::ipiv

Definition at line 441 of file densemat.hpp.

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

static

Definition at line 443 of file densemat.hpp.

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

• linalg/densemat.hpp
• linalg/densemat.cpp