TRED1(3)

SYNOPSIS
SUBROUTINE TRED1 (NM, N, A, D, E, E2)

NAME
tred1 - Reduce a real symmetric matrix to symmetric tridiagonal matrix using orthogonal similarity transformations.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1B1

TYPE
SINGLE PRECISION (TRED1-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure TRED1, NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). This subroutine reduces a REAL SYMMETRIC matrix to a symmetric tridiagonal matrix using orthogonal similarity transformations. On Input NM must be set to the row dimension of the two-dimensional array parameter, A, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrix A. N is an INTEGER variable. N must be less than or equal to NM. A contains the real symmetric input matrix. Only the lower triangle of the matrix need be supplied. A is a two- dimensional REAL array, dimensioned A(NM,N). On Output A contains information about the orthogonal transformations used in the reduction in its strict lower triangle. The full upper triangle of A is unaltered. D contains the diagonal elements of the symmetric tridiagonal matrix. D is a one-dimensional REAL array, dimensioned D(N). E contains the subdiagonal elements of the symmetric tridiagonal matrix in its last N-1 positions. E(1) is set to zero. 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). 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)