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# csysv

```
NAME
CSYSV - compute the solution to a complex system of linear
equations  A * X = B,

SYNOPSIS
SUBROUTINE CSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
LWORK, INFO )

CHARACTER     UPLO

INTEGER       INFO, LDA, LDB, LWORK, N, NRHS

INTEGER       IPIV( * )

COMPLEX       A( LDA, * ), B( LDB, * ), WORK( LWORK )

PURPOSE
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.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The number of linear equations, i.e., the order of
the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrix B.  NRHS >= 0.

A       (input/output) COMPLEX array, dimension (LDA,N)
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 triangular

part of the matrix A, and the strictly upper tri-
angular 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) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

IPIV    (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure
of D, as determined by CSYTRF.  If IPIV(k) > 0, then
rows and columns k and IPIV(k) were interchanged,
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 interchanged 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 interchanged and
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

B       (input/output) COMPLEX array, dimension (LDB,NRHS)
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) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

WORK    (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.

LWORK   (input) INTEGER
The length of WORK.  LWORK >= 1, and for best per-
formance LWORK >= N*NB, where NB is the optimal
blocksize for CSYTRF.

INFO    (output) INTEGER
= 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 fac-
torization has been completed, but the block diago-
nal matrix D is exactly singular, so the solution
could not be computed.
```