GenericDecompositionOperations<T>.SymmetricEstimateCondition Method

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4
C# 
public override void SymmetricEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<T> a,
	Array1D<int> ipiv,
	T anorm,
	out T rcond,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            Specifies whether the details of the factorization are stored
            as an upper or lower triangular matrix.
            = 'U':  Upper triangular, form is A = U*D*UT;
            = 'L':  Lower triangular, form is A = L*D*LT.
n  Int32
            The order of the matrix A.  N >= 0.
a  Array2D<T>
            Dimension (LDA,N)
            The block diagonal matrix D and the multipliers used to
            obtain the factor U or L as computed by DSYTRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  Array1D<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by DSYTRF.
anorm  T
            The 1-norm of the original matrix A.
rcond  T
            The reciprocal of the condition number of the matrix A,
            computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
            estimate of the 1-norm of inv(A) computed in this routine.
info  Int32
info is INTEGER
            = 0:  successful exit
            < 0:  if info = -i, the i-th argument had an illegal value

Remarks

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

This method corresponds to the LAPACK routine DSYCON.

See Also