SparseSolverTransformation<T>.CreateSymmetricEquilibration Method

Creates a Hermitian-preserving, symmetrically equilibrated sparse system snapshot.

Definition

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

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

Visual Basic

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

C++/CLI

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

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

Parameters

matrix SparseMatrix<T>: A square Hermitian 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 with identical positive row/column factors equal to the reciprocal square root of each original row's maximum magnitude. Empty rows use one.

Remarks

Positive congruence preserves Hermitian structure and positive definiteness in exact arithmetic. This is a single equilibration step; it does not guarantee a particular condition number.

Exceptions

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