GenericDecompositionOperations<T>.CholeskyEstimateCondition Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4

Overload List

CholeskyEstimateCondition(MatrixTriangle, Int32, Array2D<T>, T, T, Int32)

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

CholeskyEstimateCondition(MatrixTriangle, Int32, Array2D<Complex<T>>, T, T, Int32) Estimates the reciprocal of the condition number of a factored hermitian matrix.

CholeskyEstimateCondition(MatrixTriangle, Int32, Array2D<T>, T, T, Int32)

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

C# 
public override void CholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<T> a,
	T anorm,
	out T rcond,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
            = 'U':  Upper triangle of A is stored;
            = 'L':  Lower triangle of A is stored.
n  Int32
            The order of the matrix A.  N >= 0.
a  Array2D<T>
            Dimension (LDA,N)
            The triangular factor U or L from the Cholesky factorization
            A = UT*U or A = L*LT, as computed by DPOTRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
anorm  T
            The 1-norm (or infinity-norm) of the symmetric 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 DPOCON.

CholeskyEstimateCondition(MatrixTriangle, Int32, Array2D<Complex<T>>, T, T, Int32)

Estimates the reciprocal of the condition number of a factored hermitian matrix.
C# 
public override void CholeskyEstimateCondition(
	MatrixTriangle storedTriangle,
	int n,
	Array2D<Complex<T>> a,
	T aNorm,
	out T rcond,
	out int info
)

Parameters

storedTriangle  MatrixTriangle
A MatrixTriangle value that indicates whether the matrix components are stored in the upper or lower triangular part.
n  Int32
The number of rows and columns of the matrix.
a  Array2D<Complex<T>>
A complex array that contains the elements of the matrix.
aNorm  T
The norm of the matrix.
rcond  T
On return, an estimate for the reciprocal of the condition number of the matrix.
info  Int32
On return, indicates error conditions.

See Also