?hecon_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?hecon_rook

Estimates the reciprocal of the condition number of a Hermitian matrix using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges).

Syntax

call checon_rook ( uplo , n , a , lda , ipiv , anorm , rcond , work , info )

call zhecon_rook ( uplo , n , a , lda , ipiv , anorm , rcond , work , info )

call hecon_rook ( a , ipiv , anorm , rcond [ , uplo ] [ , info ] )

Include Files

mkl.fi , mkl_lapack.f90

Description

checon_rook zhecon_rook hecon_rook

The routine estimates the reciprocal of the condition number of a Hermitian matrix A using the factorization A = U * D * U^H or A = L * D * L^H computed by hetrf_rook .

An estimate is obtained for norm( A^-1 ), and the reciprocal of the condition number is computed as rcond = 1/( anorm *norm( A^-1 )).

Input Parameters

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Indicates how the input matrix A has been factored:

If uplo = 'U' , the array a stores the upper triangular factor U of the factorization A = U*D*U^{H} .

If uplo = 'L' , the array a stores the lower triangular factor L of the factorization A = L*D*L^{H} .

n

INTEGER . The order of matrix A ; n ≥ 0.

a , work

COMPLEX for checon_rook

COMPLEX*16 for zhecon_rook .

Arrays: a(lda,n) , work(*) .

The array a contains the factored matrix A , as returned by GUID-BBDF4214-702A-4F3D-BAB3-DD7A8FFF6FD7.xml#GUID-BBDF4214-702A-4F3D-BAB3-DD7A8FFF6FD7 . The second dimension of a must be at least max(1,n) .

The array work is a workspace for the routine. The dimension of work must be at least max(1, 2*n) .

lda

INTEGER . The leading dimension of a ; lda≥ max(1, n) .

ipiv

INTEGER . Array, size at least max(1, n) .

The array ipiv , as returned by hetrf_rook .

anorm

REAL for checon_rook

DOUBLE PRECISION for zhecon_rook .

The 1-norm of the original matrix A (see Description ).

Output Parameters

rcond

REAL for checon_rook

DOUBLE PRECISION for zhecon_rook .

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 A^-1 computed in this routine.

info

INTEGER .

If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.

Return Values

No return value, info is an Output Parameter.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions .

Specific details for the routine hecon_rook interface are as follows:

a

Holds the matrix A of size ( n , n ).

ipiv

Holds the vector of length n .

uplo

Must be ‘U’ or ‘L’ . The default value is ‘U’ .

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hecon_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes