TRBAK1(3)

SYNOPSIS
SUBROUTINE TRBAK1 (NM, N, A, E, M, Z)

NAME
trbak1 - Form the eigenvectors of real symmetric matrix from the eigenvectors of a symmetric tridiagonal matrix formed by TRED1.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C4

TYPE
SINGLE PRECISION (TRBAK1-S)

KEYWORDS
EIGENVECTORS OF A REAL SYMMETRIC MATRIX, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure TRBAK1, NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). This subroutine forms the eigenvectors of a REAL SYMMETRIC matrix by back transforming those of the corresponding symmetric tridiagonal matrix determined by TRED1. On Input NM must be set to the row dimension of the two-dimensional array parameters, A and Z, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix. N is an INTEGER variable. N must be less than or equal to NM. A contains information about the orthogonal transformations used in the reduction by TRED1 in its strict lower triangle. A is a two-dimensional REAL array, dimensioned A(NM,N). E contains the subdiagonal elements of the tridiagonal matrix in its last N-1 positions. E(1) is arbitrary. These elements provide the remaining information about the orthogonal transformations. E is a one-dimensional REAL array, dimensioned E(N). M is the number of columns of Z 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 Z contains the transformed eigenvectors in its first M columns. Note that TRBAK1 preserves vector Euclidean norms. 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)