SSIFA(3F)

NAME
     SSIFA   - SSIFA factors a real symmetric matrix by elimination with
     symmetric pivoting.

     To solve  A*X = B , follow SSIFA by SSISL.  To compute  INVERSE(A)*C ,
     follow SSIFA by SSISL.  To compute  DETERMINANT(A) , follow SSIFA by
     SSIDI.  To compute  INERTIA(A) , follow SSIFA by SSIDI.  To compute
     INVERSE(A) , follow SSIFA by SSIDI.


SYNOPSYS
      SUBROUTINE SSIFA(A,LDA,N,KPVT,INFO)

DESCRIPTION
     On Entry

     A REAL(LDA,N)
        the symmetric matrix to be factored.
        Only the diagonal and upper triangle are used.

     LDA INTEGER
        the leading dimension of the array  A .

     N INTEGER
        the order of the matrix  A .  On Return

     A a block diagonal matrix and the multipliers which
        were used to obtain it.
        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 SSISL or SSIDI may
        divide by zero if called.  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