tred2.f
SUBROUTINE TRED2 (NM, N, A, D, E, Z)
C***BEGIN PROLOGUE TRED2
C***PURPOSE Reduce a real symmetric matrix to a symmetric tridiagonal
C matrix using and accumulating orthogonal transformations.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1B1
C***TYPE SINGLE PRECISION (TRED2-S)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C This subroutine is a translation of the ALGOL procedure TRED2,
C NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971).
C
C This subroutine reduces a REAL SYMMETRIC matrix to a
C symmetric tridiagonal matrix using and accumulating
C orthogonal similarity transformations.
C
C On Input
C
C NM must be set to the row dimension of the two-dimensional
C array parameters, A and Z, as declared in the calling
C program dimension statement. NM is an INTEGER variable.
C
C N is the order of the matrix A. N is an INTEGER variable.
C N must be less than or equal to NM.
C
C A contains the real symmetric input matrix. Only the lower
C triangle of the matrix need be supplied. A is a two-
C dimensional REAL array, dimensioned A(NM,N).
C
C On Output
C
C D contains the diagonal elements of the symmetric tridiagonal
C matrix. D is a one-dimensional REAL array, dimensioned D(N).
C
C E contains the subdiagonal elements of the symmetric
C tridiagonal matrix in its last N-1 positions. E(1) is set
C to zero. E is a one-dimensional REAL array, dimensioned
C E(N).
C
C Z contains the orthogonal transformation matrix produced in
C the reduction. Z is a two-dimensional REAL array,
C dimensioned Z(NM,N).
C
C A and Z may coincide. If distinct, A is unaltered.
C
C Questions and comments should be directed to B. S. Garbow,
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C ------------------------------------------------------------------
C
C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C system Routines - EISPACK Guide, Springer-Verlag,
C 1976.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 760101 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE TRED2