Contents
csysv - compute the solution to a complex system of linear
equations A * X = B,
SUBROUTINE CSYSV(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER N, NRHS, LDA, LDB, LWORK, INFO
INTEGER IPIV(*)
SUBROUTINE CSYSV_64(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO
INTEGER*8 IPIV(*)
F95 INTERFACE
SUBROUTINE SYSV(UPLO, [N], [NRHS], A, [LDA], IPIV, B, [LDB], [WORK],
[LWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER, DIMENSION(:) :: IPIV
SUBROUTINE SYSV_64(UPLO, [N], [NRHS], A, [LDA], IPIV, B, [LDB], [WORK],
[LWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: N, NRHS, LDA, LDB, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIV
C INTERFACE
#include <sunperf.h>
void csysv(char uplo, int n, int nrhs, complex *a, int lda,
int *ipiv, complex *b, int ldb, int *info);
void csysv_64(char uplo, long n, long nrhs, complex *a, long
lda, long *ipiv, complex *b, long ldb, long
*info);
csysv 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 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 CSYTRF.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
IPIV (output)
Details of the interchanges and the block struc-
ture of D, as determined by CSYTRF. If IPIV(k) >
0, then rows and columns k and IPIV(k) were inter-
changed, 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 inter-
changed 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 inter-
changed 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 CSYTRF.
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.