DecompositionOperations<TReal, TComplex>.HermitianEstimateCondition Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

Overload List

HermitianEstimateCondition(MatrixTriangle, Int32, Array2D<TComplex>, Array1D<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan2D<TComplex>, Span<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TComplex>, Int32, ReadOnlySpan<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

HermitianEstimateCondition(MatrixTriangle, Int32, Array2D<TComplex>, Array1D<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

C# 
public void HermitianEstimateCondition(
	MatrixTriangle uplo,
	int n,
	Array2D<TComplex> a,
	Array1D<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

uplo  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*UH;
            = 'L':  Lower triangular, form is A = L*D*LH.
n  Int32
            The order of the matrix A.  N >= 0.
a  Array2D<TComplex>
            A is TComplex array, dimension (LDA,N)
            The block diagonal matrix D and the multipliers used to
            obtain the factor U or L as computed by ZHETRF.
            
            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 ZHETRF.
anorm  TReal
            ANORM is TReal
            The 1-norm of the original matrix A.
rcond  TReal
            RCOND is TReal
            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
            = 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))).

HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan2D<TComplex>, Span<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

C# 
public void HermitianEstimateCondition(
	MatrixTriangle uplo,
	int n,
	ReadOnlySpan2D<TComplex> a,
	Span<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

uplo  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*UH;
            = 'L':  Lower triangular, form is A = L*D*LH.
n  Int32
            The order of the matrix A.  N >= 0.
a  ReadOnlySpan2D<TComplex>
            A is TComplex array, dimension (LDA,N)
            The block diagonal matrix D and the multipliers used to
            obtain the factor U or L as computed by ZHETRF.
            
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  Span<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by ZHETRF.
anorm  TReal
            ANORM is TReal
            The 1-norm of the original matrix A.
rcond  TReal
            RCOND is TReal
            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
            = 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))).

HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TComplex>, Int32, ReadOnlySpan<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.

C# 
public abstract void HermitianEstimateCondition(
	MatrixTriangle uplo,
	int n,
	ReadOnlySpan<TComplex> a,
	int lda,
	ReadOnlySpan<int> ipiv,
	TReal anorm,
	out TReal rcond,
	out int info
)

Parameters

uplo  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*UH;
            = 'L':  Lower triangular, form is A = L*D*LH.
n  Int32
            The order of the matrix A.  N >= 0.
a  ReadOnlySpan<TComplex>
            A is TComplex array, dimension (LDA,N)
            The block diagonal matrix D and the multipliers used to
            obtain the factor U or L as computed by ZHETRF.
lda  Int32
            The leading dimension of the array A.  LDA >= max(1,N).
ipiv  ReadOnlySpan<Int32>
            Dimension (N)
            Details of the interchanges and the block structure of D
            as determined by ZHETRF.
anorm  TReal
            ANORM is TReal
            The 1-norm of the original matrix A.
rcond  TReal
            RCOND is TReal
            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
            = 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))).

See Also