# csytrf_aa.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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csytrf_aa.f

## SYNOPSIS

### Functions/Subroutines

subroutine csytrf_aa (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CSYTRF_AA

## Function/Subroutine Documentation

### subroutine csytrf_aa (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( * ) WORK, integer LWORK, integer INFO)

CSYTRF_AA

Purpose:

``` CSYTRF_AA computes the factorization of a complex symmetric matrix A
using the Aasen's algorithm.  The form of the factorization is

A = U*T*U**T  or  A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a complex symmetric tridiagonal matrix.

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 REAL array, dimension (LDA,N)
On entry, the symmetric 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, 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 subdiaonals, when UPLO
is 'L' (or 'U').
```

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).
```

WORK

```          WORK is REAL 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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley