_FIGI(3F)_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
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