CHIFA(3F)							     CHIFA(3F)

NAME    [Toc]    [Back]

     CHIFA   - CHIFA factors a complex Hermitian matrix	by elimination with
     symmetric pivoting.

     To	solve  A*X = B , follow	CHIFA by CHISL.	 To compute  INVERSE(A)*C ,
     follow CHIFA by CHISL.  To	compute	 DETERMINANT(A)	, follow CHIFA by
     CHIDI.  To	compute	 INERTIA(A) , follow CHIFA by CHIDI.  To compute
     INVERSE(A)	, follow CHIFA by CHIDI.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE CHIFA(A,LDA,N,KPVT,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     A COMPLEX(LDA,N)
	the Hermitian matrix to	be factored.
	Only the diagonal and upper triangle are used.

     LDA INTEGER
	the leading dimension of the array  A .

     N INTEGER
	the order of the matrix	 A .  On Return

     A a block diagonal	matrix and the multipliers which
	were used to obtain it.
	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 CHISL	or CHIDI may
	divide by zero if called.  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


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