CHPFA(3F)							     CHPFA(3F)

NAME    [Toc]    [Back]

     CHPFA   - CHPFA factors a complex Hermitian matrix	stored in packed form
     by	elimination with symmetric pivoting.

     To	solve  A*X = B , follow	CHPFA by CHPSL.	 To compute  INVERSE(A)*C ,
     follow CHPFA by CHPSL.  To	compute	 DETERMINANT(A)	, follow CHPFA by
     CHPDI.  To	compute	 INERTIA(A) , follow CHPFA by CHPDI.  To compute
     INVERSE(A)	, follow CHPFA by CHPDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE CHPFA(AP,N,KPVT,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     AP	COMPLEX	(N*(N+1)/2)
	the packed form	of a Hermitian matrix  A .  The
	columns	of the upper triangle are stored sequentially
	in a one-dimensional array of length  N*(N+1)/2	.
	See comments below for details.

     N INTEGER
	the order of the matrix	 A .  Output

     AP	A block	diagonal matrix	and the	multipliers which
	were used to obtain it stored in packed	form.
	The factorization can be written  A = U*D*CTRANS(U)
	where  U  is a product of permutation and unit
	upper triangular matrices , CTRANS(U) is the
	conjugate transpose of	U , and	 D  is block diagonal
	with 1 by 1 and	2 by 2 blocks.	KVPT	INTEGER(N)
	an integer vector of pivot indices.

     INFO INTEGER
	= 0  normal value.
	= K  if	the K-th pivot block is	singular.  This	is
	not an error condition for this	subroutine,
	but it does indicate that CHPSL	or CHPDI may
	divide by zero if called.  Packed Storage The following	program
     segment will pack the upper triangle of a Hermitian matrix.
	K = 0
	DO 20 J	= 1, N
	DO 10 I	= 1, J
	K = K +	1
	AP(K)  = A(I,J)
	10    CONTINUE
	20 CONTINUE LINPACK.  This version dated 08/14/78 .  James Bunch,
     Univ. Calif. San Diego, Argonne Nat. Lab.	Subroutines and	Functions BLAS
     CAXPY,CSWAP,ICAMAX	Fortran	ABS,AIMAG,AMAX1,CMPLX,CONJG,REAL,SQRT


									PPPPaaaaggggeeee 1111