---
name: "clahef_rook.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/clahef_rook.f"
---

# clahef\_rook.f(3)

## NAME

SRC/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 () 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.

**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 **182** of file **clahef\_rook.f**.

## Author

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