CHIFA(3F)

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

DESCRIPTION
     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