ZHPTRF(l)		LAPACK routine (version	1.1)		    ZHPTRF(l)

NAME
  ZHPTRF - compute the factorization of	a complex Hermitian packed matrix A
  using	the Bunch-Kaufman diagonal pivoting method

SYNOPSIS

  SUBROUTINE ZHPTRF( UPLO, N, AP, IPIV,	INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, N

      INTEGER	     IPIV( * )

      COMPLEX*16     AP( * )

PURPOSE
  ZHPTRF computes the factorization of a complex Hermitian packed matrix A
  using	the Bunch-Kaufman diagonal pivoting method:

     A = U*D*U**H  or  A = L*D*L**H

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

ARGUMENTS

  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper	triangle of A is stored;
	  = 'L':  Lower	triangle of A is stored.

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

  AP	  (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
	  On entry, the	upper or lower triangle	of the Hermitian matrix	A,
	  packed columnwise in a linear	array.	The j-th column	of A is
	  stored in the	array AP as follows: if	UPLO = 'U', AP(i + (j-1)*j/2)
	  = A(i,j) for 1<=i<=j;	if UPLO	= 'L', AP(i + (j-1)*(2n-j)/2) =
	  A(i,j) for j<=i<=n.

	  On exit, the block diagonal matrix D and the multipliers used	to
	  obtain the factor U or L, stored as a	packed triangular matrix
	  overwriting A	(see below for further details).

  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 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	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 = -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, and division by zero will occur if it is	used to	solve a	sys-
	  tem of equations.

FURTHER	DETAILS
  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).