tred3.f
SUBROUTINE TRED3 (N, NV, A, D, E, E2)
C***BEGIN PROLOGUE TRED3
C***PURPOSE Reduce a real symmetric matrix stored in packed form to
C symmetric tridiagonal matrix using orthogonal
C transformations.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1B1
C***TYPE SINGLE PRECISION (TRED3-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 TRED3,
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, stored as
C a one-dimensional array, to a symmetric tridiagonal matrix
C using orthogonal similarity transformations.
C
C On Input
C
C N is the order of the matrix A. N is an INTEGER variable.
C
C NV is an INTEGER variable set equal to the dimension of the
C array A as specified in the calling program. NV must not
C be less than N*(N+1)/2.
C
C A contains the lower triangle, stored row-wise, of the real
C symmetric packed matrix. A is a one-dimensional REAL
C array, dimensioned A(NV).
C
C On Output
C
C A contains information about the orthogonal transformations
C used in the reduction in its first N*(N+1)/2 positions.
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 E2 contains the squares of the corresponding elements of E.
C E2 may coincide with E if the squares are not needed.
C E2 is a one-dimensional REAL array, dimensioned E2(N).
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 TRED3