_FIGI(3F)							     _FIGI(3F)

NAME    [Toc]    [Back]

     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    [Toc]    [Back]

	  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    [Toc]    [Back]

     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(I1,3)
 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


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