SuperLU

#include \(<\tilde{ }\)/system_of_eqn/linearSOE/fullGEN/SuperLU.h\(>\)

class SuperLU: public SparseGenColLinSolver

MovableObject
Solver
LinearSOESolver
SparseGenColLinSolver

A SuperLU object can be constructed to solve a SparseGenColLinSOE object. It obtains the solution by making calls on the the SuperLU library developed at UC Berkeley by Prof. James Demmel, Xiaoye S. Li and John R. Gilbert. The SuperLU library contains a set of subroutines to solve a sparse linear system \(AX=B\). It uses Gaussian elimination with partial pivoting (GEPP). The columns of A may be preordered before factorization; the preordering for sparsity is completely separate from the factorization and a number of ordering schemes are provided.

// Constructor

// Destructor

// Public Methods

A unique class tag (defined in \(<\)classTags.h\(>\)) is passed to the SparseGenColLinSolver constructor. Saves the values for the arguments permSpec, panelSize, relax and thresh that will be used when calling the SuperLU routines in solve() and setSize().

permSpec defines the ordering routine used in defining the column permutations permC: \(0\) uses the original ordering supplied, \(1\) defines a min-degree ordering based on \(A^TA\) and \(2\) a min-degree ordering based on \(A^T + A\). relax defines the min number of columns in a subtree for the subtree to be considered a single supernode. thresh defines the pivoting threshold: at step j of the Gaussian elimination if (abs\((A_{jj}) \ge\) thresh (max\(i \ge j\) abs(\(A_{ij}\))). A value for thresh of \(0.0\) definines no pivoting, a value of \(1.0\) classical partial pivoting. panelSize defines the number of consecutive columns used as a panel in the elimination. For more information on these values see the SuperLU manual.

Invokes delete on permR, permC and etree arrays.

First copies \(B\) into \(X\) and then solves the FullGenLinSOE system it is associated with (pointer kept by parent class) by calling the SeuperLU routine dgstrf(), if the system is marked as not having been factored, or dgstrs(), if system is marked as having been factored. If the solution is successfully obtained, i.e. the SuperLU routines return \(0\) in the INFO argument, it marks the system has having been factored and returns \(0\), otherwise it prints a warning message and returns INFO. The solve process changes \(A\) and \(X\) and sets the char rafact to Y.

Obtains the size of the system from it’s associaed SparseGenColLinSOE object. With this information it creates space for the integer arrays permR, permC and etree. It then creates the a SuperMatrix for A by calling the SuperLU routine dCreate_CompCol_Matrix(), sets the column permutation permR by calling the SuperLU routine get_perm_c(permSpec, A, permC), applies this permutation and determines the elimination tree etree by calling the SuperLU routine sp_preorder(). It then creates a SuperMatrix for X by calling the SuperLU routine dCreate_Dense_Matrix(). Returns \(0\) if successful, prints a warning message and returns a \(-1\) if not enough memory is available for the arrays.

Does nothing but return \(0\).