?hetf2_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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?hetf2_rook

Computes the factorization of a complex Hermitian matrix, using the bounded Bunch-Kaufman diagonal pivoting method (unblocked algorithm).

Syntax

call chetf2_rook( uplo, n, a, lda, ipiv, info )

call zhetf2_rook( uplo, n, a, lda, ipiv, info )

Include Files

mkl.fi

Description

The routine computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:

A = U*D*U^H or A = L*D*L^H

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U^H is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling BLAS Level 2 Routines.

Input Parameters

uplo

CHARACTER*1.

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

= 'U': Upper triangular

= 'L': Lower triangular

n

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

a

COMPLEX for chetf2_rook

DOUBLE COMPLEX for zhetf2_rook.

Array, DIMENSION (lda, n).

On entry, the Hermitian matrix A.

If uplo = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

lda

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

Output Parameters

a

On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.

ipiv

INTEGER. Array, DIMENSION (n).

Details of the interchanges and the block structure of D.

If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.

If uplo = 'U' and ipiv(k) < 0 and ipiv(k - 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k - 1 and -ipiv(k - 1) were interchanged, and D_{k-1:k, k-1:k} is a 2-by-2 diagonal block.

If uplo = 'L' and ipiv(k) < 0 and ipiv(k + 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k + 1 and -ipiv(k + 1) were interchanged, and D_{k:k+1, k:k+1} is a 2-by-2 diagonal block.

info

INTEGER.

= 0: successful exit

< 0: if info = -k, the k-th argument had an illegal value

> 0: if info = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hetf2_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters