zsysv - compute the solution to a complex system of linear equations A * X = B,
SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, * LDWORK, INFO) CHARACTER * 1 UPLO DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER N, NRHS, LDA, LDB, LDWORK, INFO INTEGER IPIVOT(*)
SUBROUTINE ZSYSV_64( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, * LDWORK, INFO) CHARACTER * 1 UPLO DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDB, LDWORK, INFO INTEGER*8 IPIVOT(*)
SUBROUTINE SYSV( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], * [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: N, NRHS, LDA, LDB, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE SYSV_64( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], * [WORK], [LDWORK], [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: N, NRHS, LDA, LDB, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIVOT
#include <sunperf.h>
void zsysv(char uplo, int n, int nrhs, doublecomplex *a, int lda, int *ipivot, doublecomplex *b, int ldb, int *info);
void zsysv_64(char uplo, long n, long nrhs, doublecomplex *a, long lda, long *ipivot, doublecomplex *b, long ldb, long *info);
zsysv computes the solution to a complex 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 CSYTRF.
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.