MFEM  v4.3.0
Finite element discretization library
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mfem::LUFactors Class Reference

#include <densemat.hpp>

Public Member Functions

 LUFactors ()
 
 LUFactors (double *data_, int *ipiv_)
 
bool Factor (int m, double TOL=0.0)
 Compute the LU factorization of the current matrix. More...
 
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 RightSolve (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 529 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 542 of file densemat.hpp.

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

Definition at line 544 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 3206 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 3170 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 3197 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 2922 of file densemat.cpp.

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

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]msize of the square matrix
[in]TOLoptional fuzzy comparison tolerance. Defaults to 0.0.
Returns
status set to true if successful, otherwise, false.

Definition at line 2863 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 3088 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 2975 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 2939 of file densemat.cpp.

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 3033 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 3019 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 3153 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 3000 of file densemat.cpp.

Member Data Documentation

double* mfem::LUFactors::data

Definition at line 532 of file densemat.hpp.

int* mfem::LUFactors::ipiv

Definition at line 533 of file densemat.hpp.

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

Definition at line 535 of file densemat.hpp.

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