?lahef

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?lahef

Computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.

Syntax

call clahef(uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
call zlahef(uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)

Include Files

mkl.fi

Description

The routine ?lahef computes a partial factorization of a complex Hermitian matrix A , using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form:

If uplo = 'U' :

If uplo = 'U' :

where the order of D is at most nb .

The actual order is returned in the argument kb , and is either nb or nb -1, or n if n ≤ nb .

Note that U^H denotes the conjugate transpose of U .

This is an auxiliary routine called by ?hetrf (Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.) . It uses blocked code (calling Level 3 BLAS) to update the submatrix A₁₁ (if uplo = 'U' ) or A₂₂ (if uplo = 'L' ).

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. Specifies the order of the matrix A. The value of n must be at least zero.

nb: INTEGER . The maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.
a: COMPLEX for clahef DOUBLE COMPLEX for zlahef . 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) .
w: COMPLEX for clahef DOUBLE COMPLEX for zlahef . Workspace array, DIMENSION ( ldw , nb ).
ldw: INTEGER . The leading dimension of the array w . ldw≥ max(1,n) .

Output Parameters

kb: INTEGER . The number of columns of A that were actually factored kb is either nb -1 or nb , or n if n ≤ nb .
a: On exit, A contains details of the partial factorization.
ipiv: INTEGER . Array, DIMENSION ( n ). Details of the interchanges and the block structure of D . If uplo = 'U' , only the last kb elements of ipiv are set; if uplo = 'L' , only the first kb elements are set. If ipiv(k) > 0, then rows and columns k and ipiv(k) are interchanged and D ( k , k ) is a 1-by-1 diagonal block. If uplo = 'U' and ipiv(k) = ipiv(k-1) < 0 , then rows and columns k -1 and - ipiv(k) are interchanged and D(k-1:k, k-1:k) is a 2-by-2 diagonal block. If uplo = 'L' and ipiv(k) = ipiv(k+1) < 0 , then rows and columns k +1 and -ipiv ( k ) are 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 , D ( k , k ) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lahef

Syntax

Include Files

Description

Input Parameters

Output Parameters