SSPFA(3F)

NAME
     SSPFA   - SSPFA factors a real symmetric matrix stored in packed form by
     elimination with symmetric pivoting.

     To solve  A*X = B , follow SSPFA by SSPSL.  To compute  INVERSE(A)*C ,
     follow SSPFA by SSPSL.  To compute  DETERMINANT(A) , follow SSPFA by
     SSPDI.  To compute  INERTIA(A) , follow SSPFA by SSPDI.  To compute
     INVERSE(A) , follow SSPFA by SSPDI.


SYNOPSYS
      SUBROUTINE SSPFA(AP,N,KPVT,INFO)

DESCRIPTION
     On Entry

     AP REAL (N*(N+1)/2)
        the packed form of a symmetric 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*TRANS(U)
        where  U  is a product of permutation and unit
        upper triangular matrices , TRANS(U) is the
        transpose of  U , and  D  is block diagonal
        with 1 by 1 and 2 by 2 blocks.

     KPVT 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 SSPSL or SSPDI may
        divide by zero if called.  Packed Storage The following program
     segment will pack the upper triangle of a symmetric 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
     SAXPY,SSWAP,ISAMAX Fortran ABS,AMAX1,SQRT