FIGI(3F)

NAME
     FIGI, SFIGI    -  EISPACK routine.  Given a NONSYMMETRIC TRIDIAGONAL
     matrix such that the products of corresponding pairs of off-diagonal
     elements are all non-negative, this subroutine reduces it to a symmetric
     tridiagonal matrix with the same eigenvalues.  If, further, a zero
     product only occurs when both factors are zero, the reduced matrix is
     similar to the original matrix.


SYNOPSYS
          subroutine  figi(nm, n, t, d, e, e2, ierr)
             integer          n, nm, ierr
             double precision t(nm,3), d(n), e(n), e2(n)


          subroutine sfigi(nm, n, t, d, e, e2, ierr)
             integer          n, nm, ierr
             real             t(nm,3), d(n), e(n), e2(n)



DESCRIPTION
     On INPUT

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     N is the order of the matrix.

     T contains the input matrix.  Its subdiagonal is stored in the last N-1
     positions of the first column, its diagonal in the N positions of the
     second column, and its superdiagonal in the first N-1 positions of the
     third column.  T(1,1) and T(N,3) are arbitrary.  On OUTPUT

     T is unaltered.

     D contains the diagonal elements of the symmetric matrix.

     E contains the subdiagonal elements of the symmetric matrix in its last
     N-1 positions.  E(1) is not set.

     E2 contains the squares of the corresponding elements of E. E2 may
     coincide with E if the squares are not needed.

     IERR is set to Zero       for normal return, N+I        if T(I,1)*T(I-
     1,3) is negative, -(3*N+I)   if T(I,1)*T(I-1,3) is zero with one factor
        non-zero.  In this case, the eigenvectors of
        the symmetric matrix are not simply related
        to those of  T  and should not be sought.  Questions and comments
     should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
     NATIONAL LABORATORY