Decomposition Operations<TReal, TComplex>.Hermitian Estimate Condition Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
Hermitian | 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. |
Hermitian | 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. |
Hermitian | 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.
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.
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.
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))).