BAKVEC(3)

SYNOPSIS
SUBROUTINE BAKVEC (NM, N, T, E, M, Z, IERR)

NAME
bakvec - Form the eigenvectors of a certain real non-symmetric tridiagonal matrix from a symmetric tridiagonal matrix output from FIGI.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (BAKVEC-S)

KEYWORDS
EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine forms the eigenvectors of a NONSYMMETRIC TRIDIAGONAL matrix by back transforming those of the corresponding symmetric matrix determined by FIGI. 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). E contains the subdiagonal elements of the symmetric matrix in its last N-1 positions. E(1) is arbitrary. E is a one-dimensional REAL array, dimensioned E(N). M is the number of eigenvectors to be back transformed. M is an INTEGER variable. Z contains the eigenvectors to be back transformed in its first M columns. Z is a two-dimensional REAL array, dimensioned Z(NM,M). On OUTPUT T is unaltered. E is destroyed. Z contains the transformed eigenvectors in its first M columns. IERR is an INTEGER flag set to Zero for normal return, 2*N+I if E(I) is zero with T(I,1) or T(I-1,3) non-zero. In this case, the symmetric matrix is not similar to the original matrix, and the eigenvectors cannot be found by this program. 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)