# clahef_aa.f

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

## SYNOPSIS

### Functions/Subroutines

subroutine clahef_aa (UPLO, J1, M, NB, A, LDA, IPIV, H, LDH, WORK)
CLAHEF_AA

## Function/Subroutine Documentation

### subroutine clahef_aa (character UPLO, integer J1, integer M, integer NB, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldh, * ) H, integer LDH, complex, dimension( * ) WORK)

CLAHEF_AA

Purpose:

``` CLAHEF_AA factorizes a panel of a complex hermitian matrix A using
the Aasen's algorithm. The panel consists of a set of NB rows of A
when UPLO is U, or a set of NB columns when UPLO is L.

In order to factorize the panel, the Aasen's algorithm requires the
last row, or column, of the previous panel. The first row, or column,
of A is set to be the first row, or column, of an identity matrix,
which is used to factorize the first panel.

The resulting J-th row of U, or J-th column of L, is stored in the
(J-1)-th row, or column, of A (without the unit diagonals), while
the diagonal and subdiagonal of A are overwritten by those of T.
```

Parameters:

UPLO

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

J1

```          J1 is INTEGER
The location of the first row, or column, of the panel
within the submatrix of A, passed to this routine, e.g.,
when called by CHETRF_AA, for the first panel, J1 is 1,
while for the remaining panels, J1 is 2.
```

M

```          M is INTEGER
The dimension of the submatrix. M >= 0.
```

NB

```          NB is INTEGER
The dimension of the panel to be facotorized.
```

A

```          A is COMPLEX array, dimension (LDA,M) for
the first panel, while dimension (LDA,M+1) for the
remaining panels.

On entry, A contains the last row, or column, of
the previous panel, and the trailing submatrix of A
to be factorized, except for the first panel, only
the panel is passed.

On exit, the leading panel is factorized.
```

LDA

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

IPIV

```          IPIV is INTEGER array, dimension (N)
Details of the row and column interchanges,
the row and column k were interchanged with the row and
column IPIV(k).
```

H

```          H is COMPLEX workspace, dimension (LDH,NB).
```

LDH

```          LDH is INTEGER
The leading dimension of the workspace H. LDH >= max(1,M).
```

WORK

```          WORK is COMPLEX workspace, dimension (M).
```

Author:

Univ. of Tennessee

Univ. of California Berkeley