SparseSolverTransformation<T>.CreateRowColumnEquilibration Method

Creates a sparse system snapshot equilibrated by row and column maximum magnitudes.

Definition

Namespace: Numerics.NET.LinearAlgebra.IterativeSolvers
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.9.0

public static SparseSolverTransformation<T> CreateRowColumnEquilibration(
	SparseMatrix<T> matrix,
	int[]? ordering = null
)

Visual Basic

Public Shared Function CreateRowColumnEquilibration ( 
	matrix As SparseMatrix(Of T),
	Optional ordering As Integer() = Nothing
) As SparseSolverTransformation(Of T)

C++/CLI

public:
static SparseSolverTransformation<T>^ CreateRowColumnEquilibration(
	SparseMatrix<T>^ matrix, 
	array<int>^ ordering = nullptr
)

static member CreateRowColumnEquilibration : 
        matrix : SparseMatrix<'T> * 
        ?ordering : int[] 
(* Defaults:
        let _ordering = defaultArg ordering null
*)
-> SparseSolverTransformation<'T>

Parameters

matrix SparseMatrix<T>: A square sparse matrix with finite logical coefficients and magnitudes.
ordering Int32[] (Optional): An optional copied permutation mapping new coordinates to original coordinates.

Return Value

SparseSolverTransformation<T>
A transformation using reciprocal row maxima followed by reciprocal column maxima of the row-scaled matrix. Empty rows and columns use one.

Remarks

Independent row/column scaling generally changes Hermitian structure. Use it with general solvers such as GMRES, FGMRES or BiCGStab. Zero rows/columns remain zero; scaling does not repair singularity. Required factors and intermediate nonzeros must be representable.

Exceptions

ArgumentNullException	matrix is null.
DimensionMismatchException	The matrix is not square or the ordering length is incorrect.
ArgumentException	The ordering is invalid, coefficients or magnitudes are nonfinite, or a required positive scaling factor is unrepresentable.
OverflowException	A scaled nonzero or intermediate row-scaled coefficient is unrepresentable.
NotSupportedException	The sparse matrix structure is unsupported.