CHPCO(3F)

NAME
     CHPCO   - CHPCO factors a complex Hermitian matrix stored in packed form
     by elimination with symmetric pivoting and estimates the condition of the
     matrix.

     if  RCOND  is not needed, CHPFA is slightly faster.  To solve  A*X = B ,
     follow CHPCO by CHPSL.  To compute  INVERSE(A)*C , follow CHPCO by CHPSL.
     To compute  INVERSE(A) , follow CHPCO by CHPDI.  To compute
     DETERMINANT(A) , follow CHPCO by CHPDI.  To compute  INERTIA(A), follow
     CHPCO by CHPDI.


SYNOPSYS
      SUBROUTINE CHPCO(AP,N,KPVT,RCOND,Z)

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.

     RCOND REAL
        an estimate of the reciprocal condition of  A .
        For the system  A*X = B , relative perturbations
        in  A  and  B  of size  EPSILON  may cause
        relative perturbations in  X  of size  EPSILON/RCOND .
        If  RCOND  is so small that the logical expression
        1.0 + RCOND .EQ. 1.0
        is true, then  A  may be singular to working
        precision.  In particular,  RCOND  is zero  if
        exact singularity is detected or the estimate
        underflows.

     Z COMPLEX(N)
        a work vector whose contents are usually unimportant.
        If  A  is close to a singular matrix, then  Z  is
        an approximate null vector in the sense that
        NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .  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 .  Cleve Moler,
     University of New Mexico, Argonne National Lab.  Subroutines and
     Functions LINPACK CHPFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM Fortran
     ABS,AIMAG,AMAX1,CMPLX,CONJG,IABS,REAL