zhetrf_rook - nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)
SUBROUTINE ZHETRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, LWORK, N INTEGER IPIV(*) DOUBLE COMPLEX A(LDA,*), WORK(*) SUBROUTINE ZHETRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, LWORK, N INTEGER*8 IPIV(*) DOUBLE COMPLEX A(LDA,*), WORK(*) F95 INTERFACE SUBROUTINE HETRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) INTEGER :: N, LDA, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE HETRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO) INTEGER(8) :: N, LDA, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void zhetrf_rook (char uplo, int n, doublecomplex *a, int lda, int *ipiv, int *info); void zhetrf_rook_64 (char uplo, long n, doublecomplex *a, long lda, long *ipiv, long *info);
Oracle Solaris Studio Performance Library zhetrf_rook(3P)
NAME
zhetrf_rook - compute the factorization of a complex Hermitian indefi-
nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting
method (blocked algorithm, calling Level 3 BLAS)
SYNOPSIS
SUBROUTINE ZHETRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHARACTER*1 UPLO
INTEGER INFO, LDA, LWORK, N
INTEGER IPIV(*)
DOUBLE COMPLEX A(LDA,*), WORK(*)
SUBROUTINE ZHETRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHARACTER*1 UPLO
INTEGER*8 INFO, LDA, LWORK, N
INTEGER*8 IPIV(*)
DOUBLE COMPLEX A(LDA,*), WORK(*)
F95 INTERFACE
SUBROUTINE HETRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
INTEGER :: N, LDA, LWORK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
SUBROUTINE HETRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
INTEGER(8) :: N, LDA, LWORK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void zhetrf_rook (char uplo, int n, doublecomplex *a, int lda, int
*ipiv, int *info);
void zhetrf_rook_64 (char uplo, long n, doublecomplex *a, long lda,
long *ipiv, long *info);
PURPOSE
zhetrf_rook computes the factorization of a complex Hermitian matrix A
using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The
form of the factorization is
A = U*D*U**T or A = L*D*L**T
where U (or L) is a product of permutation and unit upper (lower) tri-
angular matrices, and D is Hermitian and block diagonal with 1-by-1 and
2-by-2 diagonal blocks.
This is the blocked version of the algorithm, calling Level 3 BLAS.
ARGUMENTS
UPLO (input)
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input)
N is INTEGER
The order of the matrix A. N >= 0.
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, the block diagonal matrix D and the multipliers used
to obtain the factor U or L (see below for further details).
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.
WORK (output)
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
LWORK is INTEGER
The length of WORK. LWORK >=1. For best performance LWORK >=
N*NB, where NB is the block size returned by ILAENV. If
LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output)
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal value;
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, and division by zero will occur if it is
used to solve a system of equations.
FURTHER DETAILS
If UPLO = 'U', then A = U*D*U**T, where
U = P(n)*U(n)* ... *P(k)U(k)* ...,
i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1
in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and
2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined
by IPIV(k), and U(k) is a unit upper triangular matrix, such that if
the diagonal block D(k) is of order s (s = 1 or 2), then
( I v 0 ) k-s
U(k) = ( 0 I 0 ) s
( 0 0 I ) n-k
k-s s n-k
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
and A(k,k), and v overwrites A(1:k-2,k-1:k).
If UPLO = 'L', then A = L*D*L**T, where
L = P(1)*L(1)* ... *P(k)*L(k)* ...,
i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n
in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and
2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined
by IPIV(k), and L(k) is a unit lower triangular matrix, such that if
the diagonal block D(k) is of order s (s = 1 or 2), then
( I 0 0 ) k-1
L(k) = ( 0 I 0 ) s
( 0 v I ) n-k-s+1
k-1 s n-k-s+1
If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and
A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). ~
7 Nov 2015 zhetrf_rook(3P)