 
      SUBROUTINE CHIFA(A,LDA,N,KPVT,INFO)
C***BEGIN PROLOGUE  CHIFA
C***DATE WRITTEN   780814   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2D1A
C***KEYWORDS  COMPLEX,FACTOR,HERMITIAN,LINEAR ALGEBRA,LINPACK,MATRIX
C***AUTHOR  BUNCH, J., (UCSD)
C***PURPOSE  Factors a COMPLEX HERMITIAN matrix by elimination
C            (symmetric pivoting)
C***DESCRIPTION
C
C     CHIFA factors a complex Hermitian matrix by elimination
C     with symmetric pivoting.
C
C     To solve  A*X = B , follow CHIFA by CHISL.
C     To compute  INVERSE(A)*C , follow CHIFA by CHISL.
C     To compute  DETERMINANT(A) , follow CHIFA by CHIDI.
C     To compute  INERTIA(A) , follow CHIFA by CHIDI.
C     To compute  INVERSE(A) , follow CHIFA by CHIDI.
C
C     On Entry
C
C        A       COMPLEX(LDA,N)
C                the Hermitian matrix to be factored.
C                Only the diagonal and upper triangle are used.
C
C        LDA     INTEGER
C                the leading dimension of the array  A .
C
C        N       INTEGER
C                the order of the matrix  A .
C
C     On Return
C
C        A       a block diagonal matrix and the multipliers which
C                were used to obtain it.
C                The factorization can be written  A = U*D*CTRANS(U)
C                where  U  is a product of permutation and unit
C                upper triangular matrices , CTRANS(U) is the
C                conjugate transpose of  U , and  D  is block diagonal
C                with 1 by 1 and 2 by 2 blocks.
C
C        KVPT    INTEGER(N)
C                an integer vector of pivot indices.
C
C        INFO    INTEGER
C                = 0  normal value.
C                = K  if the K-th pivot block is singular.  This is
C                     not an error condition for this subroutine,
C                     but it does indicate that CHISL or CHIDI may
C                     divide by zero if called.
C
C     LINPACK.  This version dated 08/14/78 .
C     James Bunch, Univ. Calif. San Diego, Argonne Nat. Lab.
C
C     Subroutines and Functions
C
C     BLAS CAXPY,CSWAP,ICAMAX
C     Fortran ABS,AIMAG,AMAX1,CMPLX,CONJG,REAL,SQRT
C***REFERENCES  DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C                 *LINPACK USERS  GUIDE*, SIAM, 1979.
C***ROUTINES CALLED  CAXPY,CSWAP,ICAMAX
C***END PROLOGUE  CHIFA
 
 
