CXML
        	    
LAPACK version 3.0
chetf2(3)

PURPOSE
  CHETF2 - compute the factorization of a complex Hermitian matrix A using
  the Bunch-Kaufman diagonal pivoting method

SYNTAX
  SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, LDA, N

      INTEGER	     IPIV( * )

      COMPLEX	     A( LDA, * )

DESCRIPTION
  CHETF2 computes the factorization of a complex Hermitian matrix A using the
  Bunch-Kaufman diagonal pivoting method:
     A = U*D*U'	 or  A = L*D*L'

  where U (or L) is a product of permutation and unit upper (lower)
  triangular matrices, U' is the conjugate transpose of U, and D is Hermitian
  and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

  This is the unblocked version of the algorithm, calling Level 2 BLAS.

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

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

  A	  (input/output) COMPLEX 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, the block diagonal matrix D and the multipliers used to
	  obtain the factor U or L (see below for further details).

  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
	  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.

  INFO	  (output) INTEGER
	  = 0: successful exit
	  < 0: if INFO = -k, the k-th argument had an illegal value
	  > 0: if INFO = k, D(k,k) is exactly zero.  The factorization has
	  been completed, but the block diagonal matrix D is exactly
	  singular, and division by zero will occur if it is used to solve a
	  system of equations.

FURTHER DETAILS
  1-96 - Based on modifications by
    J. Lewis, Boeing Computer Services Company
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

  If UPLO = 'U', then A = U*D*U', where
     U = P(n)*U(n)* ... *P(k)U(k)* ...,
  i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in
  steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
  diagonal blocks D(k).	 P(k) is a permutation matrix as defined by IPIV(k),
  and U(k) is a unit upper triangular matrix, such that if the diagonal block
  D(k) is of order s (s = 1 or 2), then

	     (	 I    v	   0   )   k-s
     U(k) =  (	 0    I	   0   )   s
	     (	 0    0	   I   )   n-k
		k-s   s	  n-k

  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).  If s = 2,
  the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and
  v overwrites A(1:k-2,k-1:k).

  If UPLO = 'L', then A = L*D*L', where
     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in
  steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2
  diagonal blocks D(k).	 P(k) is a permutation matrix as defined by IPIV(k),
  and L(k) is a unit lower triangular matrix, such that if the diagonal block
  D(k) is of order s (s = 1 or 2), then

	     (	 I    0	    0	)  k-1
     L(k) =  (	 0    I	    0	)  s
	     (	 0    v	    I	)  n-k-s+1
		k-1   s	 n-k-s+1

  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).  If s = 2,
  the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and
  v overwrites A(k+2:n,k:k+1).