CXML
        	    
LAPACK version 3.0
zlasyf(3)

PURPOSE
  ZLASYF - compute a partial factorization of a complex symmetric matrix A
  using the Bunch-Kaufman diagonal pivoting method

SYNTAX
  SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, KB, LDA, LDW, N, NB

      INTEGER	     IPIV( * )

      COMPLEX*16     A( LDA, * ), W( LDW, * )

DESCRIPTION
  ZLASYF computes a partial factorization of a complex symmetric matrix A
  using the Bunch-Kaufman diagonal pivoting method. The partial factorization
  has the form:

  A  =	( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
	( 0  U22 ) (  0	  D  ) ( U12' U22' )

  A  =	( L11  0 ) ( D	  0  ) ( L11' L21' )  if UPLO = 'L'
	( L21  I ) ( 0	 A22 ) (  0    I   )

  where the order of D is at most NB. The actual order is returned in the
  argument KB, and is either NB or NB-1, or N if N <= NB.  Note that U'
  denotes the transpose of U.

  ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22
  (if UPLO = 'L').

ARGUMENTS
  UPLO	  (input) CHARACTER*1
	  Specifies whether the upper or lower triangular part of the
	  symmetric matrix A is stored:
	  = 'U':  Upper triangular
	  = 'L':  Lower triangular

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  NB	  (input) INTEGER
	  The maximum number of columns of the matrix A that should be
	  factored.  NB should be at least 2 to allow for 2-by-2 pivot
	  blocks.

  KB	  (output) INTEGER
	  The number of columns of A that were actually factored.  KB is
	  either NB-1 or NB, or N if N <= NB.

  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 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, A contains details of the partial factorization.

  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.  If UPLO
	  = 'U', only the last KB elements of IPIV are set; if UPLO = 'L',
	  only the first KB elements are set.

	  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.

  W	  (workspace) COMPLEX*16 array, dimension (LDW,NB)

  LDW	  (input) INTEGER
	  The leading dimension of the array W.	 LDW >= max(1,N).

  INFO	  (output) INTEGER
	  = 0: successful exit
	  > 0: if INFO = k, D(k,k) is exactly zero.  The factorization has
	  been completed, but the block diagonal matrix D is exactly
	  singular.