# dlasyf_rook.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dlasyf_rook** (UPLO, **N**, NB, KB, A, **LDA**, IPIV, W, LDW, INFO)**DLASYF_ROOK** *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

## Function/Subroutine Documentation

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

**DLASYF_ROOK** *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method.

**Purpose:**

DLASYF_ROOK computes a partial factorization of a real symmetric 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**T U22**T ) A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) 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. DLASYF_ROOK is an auxiliary routine called by DSYTRF_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 symmetric 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 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, 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 DOUBLE PRECISION 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 dlasyf_rook.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK