CXML
        	    
LAPACK version 3.0
zhesv(3)

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

SYNTAX
  SUBROUTINE ZHESV( 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( * )

DESCRIPTION
  ZHESV computes the solution to a complex system of linear equations A * X =
  B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
  matrices.

  The diagonal pivoting method is used to factor A as
     A = U * D * U**H,	if UPLO = 'U', or
     A = L * D * L**H,	if UPLO = 'L',
  where U (or L) is a product of permutation and unit upper (lower)
  triangular matrices, and D is Hermitian 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*16 array, dimension (LDA,N)
	  On entry, the Hermitian 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**H or A = L*D*L**H as computed by ZHETRF.

  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 ZHETRF.	 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*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 performance LWORK >=
	  N*NB, where NB is the optimal blocksize for ZHETRF.

	  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
	  singular, so the solution could not be computed.