Contents
dsysv - compute the solution to a real system of linear
equations A * X = B,
SUBROUTINE DSYSV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDA, LDB, LWORK, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE DSYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION A(LDA,*), B(LDB,*), WORK(*)
F95 INTERFACE
SUBROUTINE SYSV(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [WORK],
[LWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE SYSV_64(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [WORK],
[LWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dsysv(char uplo, int n, int nrhs, double *a, int lda,
int *ipivot, double *b, int ldb, int *info);
void dsysv_64(char uplo, long n, long nrhs, double *a, long
lda, long *ipivot, double *b, long ldb, long
*info);
dsysv computes the solution to a real system of linear equa-
tions
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) triangular matrices, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks. The fac-
tored form of A is then used to solve the system of equa-
tions A * X = B.
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 con-
tains 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 tri-
angular 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 factorization A = U*D*U**T or A =
L*D*L**T as computed by DSYTRF.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
IPIVOT (output)
Details of the interchanges and the block struc-
ture of D, as determined by DSYTRF. If IPIVOT(k)
> 0, then rows and columns k and IPIVOT(k) were
interchanged, and D(k,k) is a 1-by-1 diagonal
block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1)
< 0, then rows and columns k-1 and -IPIVOT(k) were
interchanged and D(k-1:k,k-1:k) is a 2-by-2 diago-
nal block. If UPLO = 'L' and IPIVOT(k) =
IPIVOT(k+1) < 0, then rows and columns k+1 and
-IPIVOT(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 per-
formance LWORK >= N*NB, where NB is the optimal
blocksize for DSYTRF.
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 ille-
gal 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.