# clahef_rook.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

clahef_rook.f

## SYNOPSIS

### Functions/Subroutines

subroutine clahef_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)

## Function/Subroutine Documentation

### subroutine clahef_rook (character UPLO, integer N, integer NB, integer KB, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldw, * ) W, integer LDW, integer INFO)

Purpose:

``` CLAHEF_ROOK computes a partial factorization of a complex Hermitian
matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting
method. The partial factorization has the form:

A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
( 0  U22 ) (  0   D  ) ( U12**H U22**H )

A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
( L21  I ) (  0  A22 ) (  0      I     )

where the order of D is at most NB. The actual order is returned in
the argument KB, and is either NB or NB-1, or N if N <= NB.
Note that U**H denotes the conjugate transpose of U.

CLAHEF_ROOK is an auxiliary routine called by CHETRF_ROOK. It uses
blocked code (calling Level 3 BLAS) to update the submatrix
A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U':  Upper triangular
= 'L':  Lower triangular
```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

NB

```          NB is INTEGER
The maximum number of columns of the matrix A that should be
factored.  NB should be at least 2 to allow for 2-by-2 pivot
blocks.
```

KB

```          KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB.
```

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, A contains details of the partial factorization.
```

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 interchanges and the block structure of D.

If UPLO = 'U':
Only the last KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If UPLO = 'L':
Only the first KB elements of IPIV are set.

If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.

If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
```

W

```          W is COMPLEX array, dimension (LDW,NB)
```

LDW

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

INFO

```          INFO is INTEGER
= 0: successful exit
> 0: if INFO = k, D(k,k) is exactly zero.  The factorization
has been completed, but the block diagonal matrix D is
exactly singular.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2013

Contributors:

```  November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester
```

Definition at line 186 of file clahef_rook.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.