dsysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. DSYTRF_ROOK is called to compute the factoriza- tion of A
SUBROUTINE DSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER N, NRHS, LDA, LDB, LWORK, INFO INTEGER IPIV(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*) SUBROUTINE DSYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER*1 UPLO INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO INTEGER*8 IPIV(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*) F95 INTERFACE SUBROUTINE SYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER, DIMENSION(:) :: IPIV REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE SYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO INTEGER(8), DIMENSION(:) :: IPIV REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dsysv_rook(char uplo, int n, int nrhs, double *a, int lda, int *ipiv, double *b, int ldb, int *info); void dsysv_rook_64(char uplo, long n, long nrhs, double *a, long lda, long *ipiv, double *b, long ldb, long *info);
Oracle Solaris Studio Performance Library dsysv_rook(3P)
NAME
dsysv_rook - compute the solution to system of linear equations A*X = B
for symmetric matrices. DSYTRF_ROOK is called to compute the factoriza-
tion of A
SYNOPSIS
SUBROUTINE DSYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
CHARACTER*1 UPLO
INTEGER N, NRHS, LDA, LDB, LWORK, INFO
INTEGER IPIV(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE DSYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
CHARACTER*1 UPLO
INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO
INTEGER*8 IPIV(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
F95 INTERFACE
SUBROUTINE SYSV_ROOK(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
LWORK, INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER, DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE SYSV_ROOK_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
LWORK, INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dsysv_rook(char uplo, int n, int nrhs, double *a, int lda, int
*ipiv, double *b, int ldb, int *info);
void dsysv_rook_64(char uplo, long n, long nrhs, double *a, long lda,
long *ipiv, double *b, long ldb, long *info);
PURPOSE
dsysv_rook computes the solution to a real system of linear equations
A * X = B, where A is an N-by-N symmetric matrix and X and B are N-
by-NRHS matrices.
The 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) tri-
angular matrices, and D is symmetric and block diagonal with 1-by-1 and
2-by-2 diagonal blocks. The factored form of A is then used to solve
the system of equations A * X = B.
DSYTRF_ROOK is called to compute the factorization of a real symmetric
matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting
method.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The number of linear equations, i.e., the order of the matrix
A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu-
lar 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**T or A = L*D*L**T as computed by
DSYTRF_ROOK.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
IPIVOT (output)
Details of the interchanges and the block structure of D, as
determined by DSYTRF_ROOK. If IPIV(k) > 0, then rows and col-
umns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.
B (input/output)
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)
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The length of WORK. LWORK >= 1, and for best performance
LWORK >= N*NB, where NB is the optimal blocksize for
DSYTRF_ROOK.
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)
= 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 dsysv_rook(3P)