?lahef

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lahef_aa

Factorizes a panel of a complex Hermitian matrix A using Aasen's algorithm.

call clahef_aa(uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)

call zlahef_aa(uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)

Description

?lahef_aa factorizes a panel of a complex Hermitian matrix A using Aasen's algorithm. The panel consists of a set of nb rows of A when uplo is 'U', or a set of nb columns when uplo is 'L'. In order to factorize the panel, Aasen's algorithm requires the last row, or column, of the previous panel. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel. The resulting j-th row of U, or j-th column of L, is stored in the (j-1)-st row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T.

Input Parameters

uplo

CHARACTER*1.

If uplo = 'U': Upper triangular of A is stored.

If uplo= 'L': Lower triangular of A is stored..

j1

INTEGER. The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, for example when called by ?hetrf_aa. For the first panel, j1 is 1, while for the remaining panels, j1 is 2.

m

INTEGER. The dimension of the submatrix. m≥ 0.

nb

INTEGER. The dimension of the panel to be factorized.

a

COMPLEX for clahef_aa

COMPLEX*16 for zlahef_aa

Array of size (lda,m) for the first panel, and size (lda,m+1) for the remaining panels. On entry, a contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed.

lda

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

h

COMPLEX for clahef_aa

COMPLEX*16 for zlahef_aa

Workspace array of size (ldh, nb).

ldh

INTEGER. The leading dimension of the workspace h. ldh≥ max(1,m).

Output Parameters

a

On exit, the leading panel is factorized.

ipiv

INTEGER . Array of size (n). Details of the row and column interchanges: the row and column k were interchanged with the row and column ipiv(k).

h

Workspace array.

work

COMPLEX for clahef_aa

COMPLEX*16 for zlahef_aa

Workspace array of size (m).

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lahef_aa