TRED3(3)

SYNOPSIS
SUBROUTINE TRED3 (N, NV, A, D, E, E2)

NAME
tred3 - Reduce a real symmetric matrix stored in packed form to symmetric tridiagonal matrix using orthogonal transformations.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1B1

TYPE
SINGLE PRECISION (TRED3-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure TRED3, 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, stored as a one-dimensional array, to a symmetric tridiagonal matrix using orthogonal similarity transformations. On Input N is the order of the matrix A. N is an INTEGER variable. NV is an INTEGER variable set equal to the dimension of the array A as specified in the calling program. NV must not be less than N*(N+1)/2. A contains the lower triangle, stored row-wise, of the real symmetric packed matrix. A is a one-dimensional REAL array, dimensioned A(NV). On Output A contains information about the orthogonal transformations used in the reduction in its first N*(N+1)/2 positions. 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)