# cppfa.f

          SUBROUTINE CPPFA (AP, N, INFO)
    C***BEGIN PROLOGUE  CPPFA
    C***PURPOSE  Factor a complex Hermitian positive definite matrix stored
    C            in packed form.
    C***LIBRARY   SLATEC (LINPACK)
    C***CATEGORY  D2D1B
    C***TYPE      COMPLEX (SPPFA-S, DPPFA-D, CPPFA-C)
    C***KEYWORDS  LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED,
    C             POSITIVE DEFINITE
    C***AUTHOR  Moler, C. B., (U. of New Mexico)
    C***DESCRIPTION
    C
    C     CPPFA factors a complex Hermitian positive definite matrix
    C     stored in packed form.
    C
    C     CPPFA is usually called by CPPCO, but it can be called
    C     directly with a saving in time if  RCOND  is not needed.
    C     (Time for CPPCO) = (1 + 18/N)*(Time for CPPFA) .
    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     On Return
    C
    C        AP      an upper triangular matrix  R , stored in packed
    C                form, so that  A = CTRANS(R)*R .
    C
    C        INFO    INTEGER
    C                = 0  for normal return.
    C                = K  If the leading minor of order  K  is not
    C                     positive definite.
    C
    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  CDOTC
    C***REVISION HISTORY  (YYMMDD)
    C   780814  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  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  CPPFA