Inheritance diagram for Amesos_Klu:
Public Member Functions
|Amesos_Klu (const Epetra_LinearProblem &LinearProblem)|
|Amesos_Klu Constructor. |
|Amesos_Klu Destructor. |
|Performs SymbolicFactorization on the matrix A. |
|Performs NumericFactorization on the matrix A. |
|Solves A X = B (or AT x = B). |
|const Epetra_LinearProblem *||GetProblem () const|
|Get a pointer to the Problem. |
|bool||MatrixShapeOK () const|
|Returns true if KLU can handle this matrix shape. |
|int||SetUseTranspose (bool UseTranspose)|
|SetUseTranpose(true) is more efficient in Amesos_Klu. |
|bool||UseTranspose () const|
|Returns the current UseTranspose setting. |
|const Epetra_Comm &||Comm () const|
|Returns a pointer to the Epetra_Comm communicator associated with this operator. |
|int||SetParameters (Teuchos::ParameterList &ParameterList)|
|Updates internal variables. |
|int||NumSymbolicFact () const|
|Returns the number of symbolic factorizations performed by this object. |
|int||NumNumericFact () const|
|Returns the number of numeric factorizations performed by this object. |
|int||NumSolve () const|
|Returns the number of solves performed by this object. |
|void||PrintTiming () const|
|Prints timing information. |
|void||PrintStatus () const|
|Prints information about the factorization and solution phases. |
|void||GetTiming (Teuchos::ParameterList &TimingParameterList) const|
|Extracts timing information and places in parameter list. |
Class Amesos_Klu is an object-oriented wrapper for KLU. KLU, whose sources are distributed within Amesos, is a serial solver for sparse matrices. KLU will solve a linear system of equations: , where
A is an Epetra_RowMatrix and
B are Epetra_MultiVector objects.
Amesos_Klu computes more efficiently than . The latter requires a matrix transpose -- which costs both time and space.
KLU is Tim Davis' implementation of Gilbert-Peierl's left-looking sparse partial pivoting algorithm, with Eisenstat & Liu's symmetric pruning. Gilbert's version appears as
[L,U,P]=lu(A) in MATLAB. It doesn't exploit dense matrix kernels, but it is the only sparse LU factorization algorithm known to be asymptotically optimal, in the sense that it takes time proportional to the number of floating-point operations. It is the precursor to SuperLU, thus the name ("clark Kent LU"). For very sparse matrices that do not suffer much fill-in (such as most circuit matrices when permuted properly) dense matrix kernels do not help, and the asymptotic run-time is of practical importance.
klu_btf code first permutes the matrix to upper block triangular form (using two algorithms by Duff and Reid, MC13 and MC21, in the ACM Collected Algorithms). It then permutes each block via a symmetric minimum degree ordering (AMD, by Amestoy, Davis, and Duff). This ordering phase can be done just once for a sequence of matrices. Next, it factorizes each reordered block via the klu routine, which also attempts to preserve diagonal pivoting, but allows for partial pivoting if the diagonal is to small.
|Amesos_Klu::Amesos_Klu||(||const Epetra_LinearProblem &||LinearProblem||)|
|bool Amesos_Klu::MatrixShapeOK||(||)|| const
Returns true if KLU can handle this matrix shape.
Returns true if the matrix shape is one that KLU can handle. KLU only works with square matrices.
Performs NumericFactorization on the matrix A.
In addition to performing numeric factorization on the matrix A, the call to NumericFactorization() implies that no change will be made to the underlying matrix without a subsequent call to NumericFactorization().
|int Amesos_Klu::SetParameters||(||Teuchos::ParameterList &||ParameterList||)||
Updates internal variables.
Solves A X = B (or AT x = B).
Performs SymbolicFactorization on the matrix A.
In addition to performing symbolic factorization on the matrix A, the call to SymbolicFactorization() implies that no change will be made to the non-zero structure of the underlying matrix without a subsequent call to SymbolicFactorization().