# dsytrf_aa_2stage.f - Man Page

SRC/dsytrf_aa_2stage.f

## Synopsis

### Functions/Subroutines

subroutine dsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
DSYTRF_AA_2STAGE

## Function/Subroutine Documentation

### subroutine dsytrf_aa_2stage (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRF_AA_2STAGE

Purpose:

``` DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
using the Aasen's algorithm.  The form of the factorization is

A = U**T*T*U  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 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 DOUBLE PRECISION 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, 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 DOUBLE PRECISION 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 IPIV2(k).```

WORK

`          WORK is DOUBLE PRECISION 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

NAG Ltd.

Definition at line 158 of file dsytrf_aa_2stage.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsytrf_aa_2stage(3) is an alias of dsytrf_aa_2stage.f(3).

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