subroutine figi(nm,n,t,d,e,e2,ierr)
c
integer i,n,nm,ierr
double precision t(nm,3),d(n),e(n),e2(n)
c
c given a nonsymmetric tridiagonal matrix such that the products
c of corresponding pairs of off-diagonal elements are all
c non-negative, this subroutine reduces it to a symmetric
c tridiagonal matrix with the same eigenvalues. if, further,
c a zero product only occurs when both factors are zero,
c the reduced matrix is similar to the original matrix.
c
c on input
c
c nm must be set to the row dimension of two-dimensional
c array parameters as declared in the calling program
c dimension statement.
c
c n is the order of the matrix.
c
c t contains the input matrix. its subdiagonal is
c stored in the last n-1 positions of the first column,
c its diagonal in the n positions of the second column,
c and its superdiagonal in the first n-1 positions of
c the third column. t(1,1) and t(n,3) are arbitrary.
c
c on output
c
c t is unaltered.
c
c d contains the diagonal elements of the symmetric matrix.
c
c e contains the subdiagonal elements of the symmetric
c matrix in its last n-1 positions. e(1) is not set.
c
c e2 contains the squares of the corresponding elements of e.
c e2 may coincide with e if the squares are not needed.
c
c ierr is set to
c zero for normal return,
c n+i if t(i,1)*t(i-1,3) is negative,
c -(3*n+i) if t(i,1)*t(i-1,3) is zero with one factor
c non-zero. in this case, the eigenvectors of
c the symmetric matrix are not simply related
c to those of t and should not be sought.
c
c questions and comments should be directed to burton s. garbow,
c mathematics and computer science div, argonne national laboratory
c
c this version dated august 1983.
c
c ------------------------------------------------------------------
c
ierr = 0
c
do 100 i = 1, n
if (i .eq. 1) go to 90
e2(i) = t(i,1) * t(i-1,3)
if (e2(i)) 1000, 60, 80
60 if (t(i,1) .eq. 0.0d0 .and. t(i-1,3) .eq. 0.0d0) go to 80
c .......... set error -- product of some pair of off-diagonal
c elements is zero with one member non-zero ..........
ierr = -(3 * n + i)
80 e(i) = dsqrt(e2(i))
90 d(i) = t(i,2)
100 continue
c
go to 1001
c .......... set error -- product of some pair of off-diagonal
c elements is negative ..........
1000 ierr = n + i
1001 return
end