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

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

     CHARACTER UPLO

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

     INTEGER IPIV( * )

     COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( LWORK )



     #include <sunperf.h>

     void zsysv(char uplo, int n, int  nrhs,  doublecomplex  *za,
               int  lda, int *ipivot, doublecomplex *zb, int ldb,
               int *info);

PURPOSE
     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  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*16 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 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 ZSYTRF.

     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  struc-
               ture  of D, as determined by ZSYTRF.  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)   COMPLEX*16    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/output)  COMPLEX*16  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 ZSYTRF.

     INFO      (output) INTEGER
               = 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.

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