ssysv - compute the solution to a real system of linear equations A * X = B,
SUBROUTINE SSYSV( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, * LDWORK, INFO) CHARACTER * 1 UPLO INTEGER N, NRHS, LDA, LDB, LDWORK, INFO INTEGER IPIVOT(*) REAL A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE SSYSV_64( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, * LDWORK, INFO) CHARACTER * 1 UPLO INTEGER*8 N, NRHS, LDA, LDB, LDWORK, INFO INTEGER*8 IPIVOT(*) REAL A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE SYSV( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], * [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER :: N, NRHS, LDA, LDB, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: A, B
SUBROUTINE SYSV_64( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], * [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, NRHS, LDA, LDB, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: A, B
#include <sunperf.h>
void ssysv(char uplo, int n, int nrhs, float *a, int lda, int *ipivot, float *b, int ldb, int *info);
void ssysv_64(char uplo, long n, long nrhs, float *a, long lda, long *ipivot, float *b, long ldb, long *info);
ssysv 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) triangular 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.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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 SSYTRF.
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 diagonal 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.
WORK(1)
returns the optimal LDWORK.
If LDWORK = -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 LDWORK is issued by XERBLA.
= 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.