?hecon_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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?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, lapack.f90

Description

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	CHARACTER1. 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` = `UDU^H`. If `uplo = 'L'`, the array `a` stores the lower triangular factor `L` of the factorization `A` = `LD*L^H`.
n	INTEGER. The order of matrix `A`; `n`≥ 0.
a, work	COMPLEX for checon_rook COMPLEX16 for zhecon_rook. Arrays: `a(lda,n)`, `work()`. The array `a` contains the factored matrix `A`, as returned by ?hetrf_rook. 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.

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'.

Parent topic: Estimating the Condition Number: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hecon_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters

LAPACK 95 Interface Notes

See Also