# csytrf_aa_2stage.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine csytrf_aa_2stage (UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
CSYTRF_AA_2STAGE

## Function/Subroutine Documentation

### subroutine csytrf_aa_2stage (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV, integer, dimension( * ) IPIV2, complex, dimension( * ) WORK, integer LWORK, integer INFO)

CSYTRF_AA_2STAGE

Purpose:

``` CSYTRF_AA_2STAGE 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 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 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 subdiaonal 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 array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.```

LTB

```          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

```          IPIV 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 workspace of size LWORK`

LWORK

```          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

NAG Ltd.

Date:

November 2017

Definition at line 160 of file csytrf_aa_2stage.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page csytrf_aa_2stage(3) is an alias of csytrf_aa_2stage.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK