FIGI(3F)
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.
As shipped in IRIX 6.5.22. Unchanged since IRIX 6.5.
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