zlahef_rook (3)  Linux Man Pages
NAME
zlahef_rook.f 
SYNOPSIS
Functions/Subroutines
subroutine zlahef_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
Function/Subroutine Documentation
subroutine zlahef_rook (characterUPLO, integerN, integerNB, integerKB, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldw, * )W, integerLDW, integerINFO)

ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded BunchKaufman ("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 NB1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_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
NN is INTEGER The order of the matrix A. N >= 0.
NBNB is INTEGER The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2by2 pivot blocks.
KBKB is INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB.
AA is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading nbyn 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 nbyn 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
IPIVIPIV 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 1by1 diagonal block. If IPIV(k) < 0 and IPIV(k1) < 0, then rows and columns k and IPIV(k) were interchanged and rows and columns k1 and IPIV(k1) were inerchaged, D(k1:k,k1:k) is a 2by2 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 1by1 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 2by2 diagonal block.
WW is COMPLEX*16 array, dimension (LDW,NB)
LDWLDW is INTEGER The leading dimension of the array W. LDW >= max(1,N).
INFOINFO 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 184 of file zlahef_rook.f.
Author
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