chesv_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diago- nal pivoting method
SUBROUTINE CHESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, LDB, LWORK, N, NRHS INTEGER IPIV(*) COMPLEX A(LDA,*), B(LDB,*), WORK(*) SUBROUTINE CHESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, LDB, LWORK, N, NRHS INTEGER*8 IPIV(*) COMPLEX A(LDA,*), B(LDB,*), WORK(*) F95 INTERFACE SUBROUTINE HESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B SUBROUTINE HESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void chesv_rook (char uplo, int n, int nrhs, floatcomplex *a, int lda, int *ipiv, floatcomplex *b, int ldb, int *info); void chesv_rook_64 (char uplo, long n, long nrhs, floatcomplex *a, long lda, long *ipiv, floatcomplex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library chesv_rook(3P)
NAME
chesv_rook - compute the solution to a system of linear equations A*X=B
for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diago-
nal pivoting method
SYNOPSIS
SUBROUTINE CHESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
CHARACTER*1 UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
INTEGER IPIV(*)
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE CHESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
LWORK, INFO)
CHARACTER*1 UPLO
INTEGER*8 INFO, LDA, LDB, LWORK, N, NRHS
INTEGER*8 IPIV(*)
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
F95 INTERFACE
SUBROUTINE HESV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IPIV
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
SUBROUTINE HESV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
LWORK, INFO)
INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IPIV
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void chesv_rook (char uplo, int n, int nrhs, floatcomplex *a, int lda,
int *ipiv, floatcomplex *b, int ldb, int *info);
void chesv_rook_64 (char uplo, long n, long nrhs, floatcomplex *a, long
lda, long *ipiv, floatcomplex *b, long ldb, long *info);
PURPOSE
chesv_rook computes the solution to a complex system of linear equa-
tions A*X = B, where A is an N-by-N Hermitian matrix and X and B are N-
by-NRHS matrices.
The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used to
factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if
UPLO = 'L', where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
CHETRF_ROOK is called to compute the factorization of a complex Hermi-
tion matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivot-
ing method.
The factored form of A is then used to solve the system of equations A
* X = B by calling CHETRS_ROOK (uses BLAS 2).
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 number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input)
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output)
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, if INFO = 0, the block diagonal matrix D and the
multipliers used to obtain the factor U or L from the factor-
ization A = U*D*U**H or A = L*D*L**H as computed by
CHETRF_ROOK.
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.
B (input/output)
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input)
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (output)
WORK is COMPLEX 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, and for best performance
LWORK >= max(1,N*NB), where NB is the optimal blocksize for
CHETRF_ROOK.
for LWORK < N, TRS will be done with Level BLAS 2
for LWORK >= N, TRS will be done with Level BLAS 3
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, so the solution could not be computed.
7 Nov 2015 chesv_rook(3P)