REDUC2(3)

SYNOPSIS
SUBROUTINE REDUC2 (NM, N, A, B, DL, IERR)

NAME
reduc2 - Reduce a certain generalized symmetric eigenproblem to a standard symmetric eigenproblem using Cholesky factorization.

LIBRARY
SLATEC (EISPACK)

CATEGORY
D4C1C

TYPE
SINGLE PRECISION (REDUC2-S)

KEYWORDS
EIGENVALUES, EIGENVECTORS, EISPACK

AUTHOR
Smith, B. T., et al.

DESCRIPTION
This subroutine is a translation of the ALGOL procedure REDUC2, NUM. MATH. 11, 99-110(1968) by Martin and Wilkinson. HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 303-314(1971). This subroutine reduces the generalized SYMMETRIC eigenproblems ABx=(LAMBDA)x OR BAy=(LAMBDA)y, where B is POSITIVE DEFINITE, to the standard symmetric eigenproblem using the Cholesky factorization of B. On Input NM must be set to the row dimension of the two-dimensional array parameters, A and B, as declared in the calling program dimension statement. NM is an INTEGER variable. N is the order of the matrices A and B. If the Cholesky factor L of B is already available, N should be prefixed with a minus sign. N is an INTEGER variable. A and B contain the real symmetric input matrices. Only the full upper triangles of the matrices need be supplied. If N is negative, the strict lower triangle of B contains, instead, the strict lower triangle of its Cholesky factor L. A and B are two-dimensional REAL arrays, dimensioned A(NM,N) and B(NM,N). DL contains, if N is negative, the diagonal elements of L. DL is a one-dimensional REAL array, dimensioned DL(N). On Output A contains in its full lower triangle the full lower triangle of the symmetric matrix derived from the reduction to the standard form. The strict upper triangle of A is unaltered. B contains in its strict lower triangle the strict lower triangle of its Cholesky factor L. The full upper triangle of B is unaltered. DL contains the diagonal elements of L. IERR is an INTEGER flag set to Zero for normal return, 7*N+1 if B is not positive definite. 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
890531 Changed all specific intrinsics to generic. (WRB)
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)