CHPFA(3F)

NAME
     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
      SUBROUTINE CHPFA(AP,N,KPVT,INFO)

DESCRIPTION
     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