?lahef

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

clahef zlahef

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^:code:`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 . The order of the matrix A . n≥ 0 .
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