# chpfa.f

          SUBROUTINE CHPFA (AP, N, KPVT, INFO)
    C***BEGIN PROLOGUE  CHPFA
    C***PURPOSE  Factor a complex Hermitian matrix stored in packed form by
    C            elimination with symmetric pivoting.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D1A
    C***TYPE      COMPLEX (SSPFA-S, DSPFA-D, CHPFA-C, DSPFA-C)
    C***KEYWORDS  HERMITIAN, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION,
    C             PACKED
    C***AUTHOR  Bunch, J., (UCSD)
    C***DESCRIPTION
    C
    C     CHPFA factors a complex Hermitian matrix stored in
    C     packed form by elimination with symmetric pivoting.
    C
    C     To solve  A*X = B , follow CHPFA by CHPSL.
    C     To compute  INVERSE(A)*C , follow CHPFA by CHPSL.
    C     To compute  DETERMINANT(A) , follow CHPFA by CHPDI.
    C     To compute  INERTIA(A) , follow CHPFA by CHPDI.
    C     To compute  INVERSE(A) , follow CHPFA by CHPDI.
    C
    C     On Entry
    C
    C        AP      COMPLEX (N*(N+1)/2)
    C                the packed form of a Hermitian matrix  A .  The
    C                columns of the upper triangle are stored sequentially
    C                in a one-dimensional array of length  N*(N+1)/2 .
    C                See comments below for details.
    C
    C        N       INTEGER
    C                the order of the matrix  A .
    C
    C     Output
    C
    C        AP      A block diagonal matrix and the multipliers which
    C                were used to obtain it stored in packed form.
    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 CHPSL or CHPDI may
    C                     divide by zero if called.
    C
    C     Packed Storage
    C
    C          The following program segment will pack the upper
    C          triangle of a Hermitian matrix.
    C
    C                K = 0
    C                DO 20 J = 1, N
    C                   DO 10 I = 1, J
    C                      K = K + 1
    C                      AP(K)  = A(I,J)
    C             10    CONTINUE
    C             20 CONTINUE
    C
    C***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
    C                 Stewart, LINPACK Users' Guide, SIAM, 1979.
    C***ROUTINES CALLED  CAXPY, CSWAP, ICAMAX
    C***REVISION HISTORY  (YYMMDD)
    C   780814  DATE WRITTEN
    C   890531  Changed all specific intrinsics to generic.  (WRB)
    C   890831  Modified array declarations.  (WRB)
    C   891107  Modified routine equivalence list.  (WRB)
    C   891107  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   900326  Removed duplicate information from DESCRIPTION section.
    C           (WRB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  CHPFA