SUBROUTINE SSPFA(AP,N,KPVT,INFO)
C***BEGIN PROLOGUE  SSPFA
C***DATE WRITTEN   780814   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2B1A
C***KEYWORDS  FACTOR,LINEAR ALGEBRA,LINPACK,MATRIX,PACKED,SYMMETRIC
C***AUTHOR  BUNCH, J., (UCSD)
C***PURPOSE  Factors a real SYMMETRIC matrix stored in packed form by
C            elimination with symmetric pivoting.
C***DESCRIPTION
C
C     SSPFA factors a real symmetric matrix stored in
C     packed form by elimination with symmetric pivoting.
C
C     To solve  A*X = B , follow SSPFA by SSPSL.
C     To compute  INVERSE(A)*C , follow SSPFA by SSPSL.
C     To compute  DETERMINANT(A) , follow SSPFA by SSPDI.
C     To compute  INERTIA(A) , follow SSPFA by SSPDI.
C     To compute  INVERSE(A) , follow SSPFA by SSPDI.
C
C     On Entry
C
C        AP      REAL (N*(N+1)/2)
C                the packed form of a symmetric 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*TRANS(U)
C                where  U  is a product of permutation and unit
C                upper triangular matrices , TRANS(U) is the
C                transpose of  U , and  D  is block diagonal
C                with 1 by 1 and 2 by 2 blocks.
C
C        KPVT    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 SSPSL or SSPDI 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 symmetric 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     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 SAXPY,SSWAP,ISAMAX
C     Fortran ABS,AMAX1,SQRT
C***REFERENCES  DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C                 *LINPACK USERS  GUIDE*, SIAM, 1979.
C***ROUTINES CALLED  ISAMAX,SAXPY,SSWAP
C***END PROLOGUE  SSPFA