FIGI2(3)

SYNOPSIS
SUBROUTINE FIGI2 (NM, N, T, D, E, Z, IERR)

NAME
figi2 - Transforms certain real non-symmetric tridiagonal matrix to symmetric tridiagonal matrix.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1C

TYPE
SINGLE PRECISION (FIGI2-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, and zero only when both factors are zero, this subroutine reduces it to a SYMMETRIC TRIDIAGONAL matrix using and accumulating diagonal similarity transformations. On INPUT NM must be set to the row dimension of the two-dimensional array parameters, T and Z, 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). Z contains the diagonal transformation matrix produced in the symmetrization. Z is a two-dimensional REAL array, dimensioned Z(NM,N). IERR is an INTEGER flag set to Zero for normal return, N+I if T(I,1)*T(I-1,3) is negative, 2*N+I if T(I,1)*T(I-1,3) is zero with one factor non-zero. In these cases, there does not exist a symmetrizing similarity transformation which is essential for the validity of the later eigenvector computation. 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)