FIGI(3)

SYNOPSIS
SUBROUTINE FIGI (NM, N, T, D, E, E2, IERR)

NAME
figi - Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1C

TYPE
SINGLE PRECISION (FIGI-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
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. On INPUT NM must be set to the row dimension of the two-dimensional array parameter, T, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix T. N is an INTEGER variable. N must be less than or equal to NM. T contains the nonsymmetric 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. T is a two-dimensional REAL array, dimensioned T(NM,3). On OUTPUT T is unaltered. D contains the diagonal elements of the tridiagonal symmetric matrix. D is a one-dimensional REAL array, dimensioned D(N). E contains the subdiagonal elements of the tridiagonal symmetric matrix in its last N-1 positions. E(1) is not set. E is a one-dimensional REAL array, dimensioned E(N). E2 contains the squares of the corresponding elements of E. E2 may coincide with E if the squares are not needed. E2 is a one-dimensional REAL array, dimensioned E2(N). IERR is an INTEGER flag set to Zero for normal return, N+I if T(I,1)*T(I-1,3) is negative and a symmetric matrix cannot be produced with FIGI, -(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 ------------------------------------------------------------------

REFERENCES
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- system Routines - EISPACK Guide, Springer-Verlag, 1976.

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
760101 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)