CSYSV(l)								 )								  CSYSV(l)

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( * )

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 factored form of A is then used to solve the system of equations 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 contains 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 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) 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/output) 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 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) 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 factorization has been completed, but the block diagonal matrix D is exactly  singu-
	       lar, so the solution could not be computed.

LAPACK version 3.0						   15 June 2000 							  CSYSV(l)