csysv(3P) Sun Performance Library csysv(3P)NAMEcsysv - compute the solution to a complex system of linear equations A
* X = B,
SYNOPSIS
SUBROUTINE CSYSV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER N, NRHS, LDA, LDB, LWORK, INFO
INTEGER IPIVOT(*)
SUBROUTINE CSYSV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LWORK,
INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDB, LWORK, INFO
INTEGER*8 IPIVOT(*)
F95 INTERFACE
SUBROUTINE SYSV(UPLO, [N], [NRHS], A, [LDA], IPIVOT, 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(:) :: IPIVOT
SUBROUTINE SYSV_64(UPLO, [N], [NRHS], A, [LDA], IPIVOT, 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(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void csysv(char uplo, int n, int nrhs, complex *a, int lda, int
*ipivot, complex *b, int ldb, int *info);
void csysv_64(char uplo, long n, long nrhs, complex *a, long lda, long
*ipivot, complex *b, long ldb, long *info);
PURPOSEcsysv 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) 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.
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 CSYTRF.
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 CSYTRF. If IPIVOT(k) > 0, then rows and col‐
umns 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.
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 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 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.
6 Mar 2009 csysv(3P)
