?hetrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?hetrf_aa

Computes the factorization of a complex hermitian matrix using Aasen's algorithm.

call chetrf_aa(uplo, n, a, lda, ipiv, work, lwork, info)

call zhetrf_aa(uplo, n, a, lda, ipiv, work, lwork, info)

Description

?hetrf_aa computes the factorization of a complex Hermitian matrix A using Aasen's algorithm. The form of the factorization is A = U * T * U^H or a = L*T*L^H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a Hermitian tridiagonal matrix. This is the blocked version of the algorithm, calling Level 3 BLAS.

Input Parameters

uplo

CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of a is stored.

n

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

a

COMPLEX for chetrf_aa

COMPLEX*16 for zhetrf_aa

Array of size (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).

lwork

INTEGER. The length of work. lwork≥ 2*n. For optimum performance lwork≥n*(1 + nb), where nb is the optimal block size. If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

Output Parameters

a

On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of a just below (or above) the diagonals, and L is stored below (or above) the subdiagonals, when uplo is 'L' (or 'U').

ipiv

INTEGER . array, dimension (n) On exit, it contains the details of the interchanges: the row and column k of a were interchanged with the row and column ipiv(k).

work

COMPLEX for chetrf_aa

COMPLEX*16 for zhetrf_aa

Array of size (max(1, lwork)). On exit, if info = 0, work(1) returns the optimal lwork.

info

INTEGER.

If info = 0: successful exit < 0: if info = -i, the i-th argument had an illegal value,

If info > 0: if info = i, D_{i, i} 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: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hetrf_aa