?hetrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?hetrf_aa

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

LAPACK_DECL lapack_int LAPACKE_chetrf_aa (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * a, lapack_int lda, lapack_int * ipiv );

LAPACK_DECL lapack_int LAPACKE_zhetrf_aa (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * a, lapack_int lda, lapack_int * ipiv );

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

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

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

n

The order of the matrix A. n≥ 0.

a

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

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

lwork

See Syntax - Workspace. 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: 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: See Syntax - Workspace. Array of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

Return Values

This function returns a value info.

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.

Syntax - Workspace

Use this interface if you want to explicitly provide the workspace array.

LAPACK_DECL lapack_int LAPACKE_chetrf_aa_work (int matrix_layout, char uplo, lapack_int n, lapack_complex_float * a, lapack_int lda, lapack_int * ipiv, lapack_complex_float * work, lapack_int lwork );

LAPACK_DECL lapack_int LAPACKE_zhetrf_aa_work (int matrix_layout, char uplo, lapack_int n, lapack_complex_double * a, lapack_int lda, lapack_int * ipiv, lapack_complex_double * work, lapack_int lwork );

Parent topic: Matrix Factorization: LAPACK Computational Routines

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