# zhesv_aa.f - Man Page

SRC/zhesv_aa.f

## Synopsis

### Functions/Subroutines

subroutine zhesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

## Function/Subroutine Documentation

### subroutine zhesv_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

``` ZHESV_AA computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.

Aasen's algorithm is used to factor A as
A = U**H * T * U,  if UPLO = 'U', or
A = L * T * L**H,  if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is Hermitian and tridiagonal. The factored form
of A is then used to solve the system of equations A * X = B.```
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 number of linear equations, i.e., the order of the
matrix A.  N >= 0.```

NRHS

```          NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**H*T*U or A = L*T*L**H as computed by
ZHETRF_AA.```

LDA

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

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).```

B

```          B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.```

LDB

```          LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).```

WORK

```          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for best
performance LWORK >= max(1,N*NB), where NB is the optimal
blocksize for ZHETRF.

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, D(i,i) is exactly zero.  The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 160 of file zhesv_aa.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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