# zhetrf_aa_2stage.f - Man Page

SRC/zhetrf_aa_2stage.f

## Synopsis

### Functions/Subroutines

subroutine **zhetrf_aa_2stage** (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)**ZHETRF_AA_2STAGE**

## Function/Subroutine Documentation

### subroutine zhetrf_aa_2stage (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)

**ZHETRF_AA_2STAGE**

**Purpose:**

ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A using the Aasen's algorithm. The form of the factorization is A = U**H*T*U 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS.

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

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 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. On exit, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U').

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*TB*TB is COMPLEX*16 array, dimension (LTB) On exit, details of the LU factorization of the band matrix.

*LTB*LTB is INTEGER The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA.

*IPIV*IPIV is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).

*IPIV2*IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k).

*WORK*WORK is COMPLEX*16 workspace of size LWORK

*LWORK*LWORK is INTEGER The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB. 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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, band LU factorization failed on i-th column

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **158** of file **zhetrf_aa_2stage.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhetrf_aa_2stage(3) is an alias of zhetrf_aa_2stage.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK