zlahef_rook - compute a partial factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)
SUBROUTINE ZLAHEF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER INFO, KB, LDA, LDW, N, NB INTEGER IPIV(*) DOUBLE COMPLEX A(LDA,*), W(LDW,*) SUBROUTINE ZLAHEF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, KB, LDA, LDW, N, NB INTEGER*8 IPIV(*) DOUBLE COMPLEX A(LDA,*), W(LDW,*) F95 INTERFACE SUBROUTINE LAHEF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) INTEGER :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:,:) :: A, W SUBROUTINE LAHEF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) INTEGER(8) :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:,:) :: A, W C INTERFACE #include <sunperf.h> void zlahef_rook (char uplo, int n, int nb, int *kb, doublecomplex *a, int lda, int *ipiv, int ldw, int *info); void zlahef_rook_64 (char uplo, long n, long nb, long *kb, doublecom- plex *a, long lda, long *ipiv, long ldw, long *info);
Oracle Solaris Studio Performance Library zlahef_rook(3P)
NAME
zlahef_rook - compute a partial factorization of a complex Hermitian
indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal
pivoting method (blocked algorithm, calling Level 3 BLAS)
SYNOPSIS
SUBROUTINE ZLAHEF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CHARACTER*1 UPLO
INTEGER INFO, KB, LDA, LDW, N, NB
INTEGER IPIV(*)
DOUBLE COMPLEX A(LDA,*), W(LDW,*)
SUBROUTINE ZLAHEF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
CHARACTER*1 UPLO
INTEGER*8 INFO, KB, LDA, LDW, N, NB
INTEGER*8 IPIV(*)
DOUBLE COMPLEX A(LDA,*), W(LDW,*)
F95 INTERFACE
SUBROUTINE LAHEF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
INTEGER :: N, NB, KB, LDA, LDW, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:,:) :: A, W
SUBROUTINE LAHEF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
INTEGER(8) :: N, NB, KB, LDA, LDW, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:,:) :: A, W
C INTERFACE
#include <sunperf.h>
void zlahef_rook (char uplo, int n, int nb, int *kb, doublecomplex *a,
int lda, int *ipiv, int ldw, int *info);
void zlahef_rook_64 (char uplo, long n, long nb, long *kb, doublecom-
plex *a, long lda, long *ipiv, long ldw, long *info);
PURPOSE
zlahef_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.
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').
ARGUMENTS
UPLO (input)
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 (input)
N is INTEGER
The order of the matrix A. N >= 0.
NB (input)
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 (output)
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 (input/output)
A is COMPLEX*16 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 (input)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output)
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 diago-
nal 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 diago-
nal block.
W (output)
W is COMPLEX*16 array, dimension (LDW,NB)
LDW (input)
LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N).
INFO (output)
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.
7 Nov 2015 zlahef_rook(3P)