*DECK REBAK
SUBROUTINE REBAK (NM, N, B, DL, M, Z)
C***BEGIN PROLOGUE REBAK
C***PURPOSE Form the eigenvectors of a generalized symmetric
C eigensystem from the eigenvectors of derived matrix output
C from REDUC or REDUC2.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C4
C***TYPE SINGLE PRECISION (REBAK-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 REBAKA,
C NUM. MATH. 11, 99-110(1968) by Martin and Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 303-314(1971).
C
C This subroutine forms the eigenvectors of a generalized
C SYMMETRIC eigensystem by back transforming those of the
C derived symmetric matrix determined by REDUC or REDUC2.
C
C On Input
C
C NM must be set to the row dimension of the two-dimensional
C array parameters, B 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 system. N is an INTEGER
C variable. N must be less than or equal to NM.
C
C B contains information about the similarity transformation
C (Cholesky decomposition) used in the reduction by REDUC
C or REDUC2 in its strict lower triangle. B is a two-
C dimensional REAL array, dimensioned B(NM,N).
C
C DL contains further information about the transformation.
C DL is a one-dimensional REAL array, dimensioned DL(N).
C
C M is the number of eigenvectors to be back transformed.
C M is an INTEGER variable.
C
C Z contains the eigenvectors to be back transformed in its
C first M columns. Z is a two-dimensional REAL array
C dimensioned Z(NM,M).
C
C On Output
C
C Z contains the transformed eigenvectors in its first
C M columns.
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 REBAK
C
INTEGER I,J,K,M,N,I1,II,NM
REAL B(NM,*),DL(*),Z(NM,*)
REAL X
C
C***FIRST EXECUTABLE STATEMENT REBAK
IF (M .EQ. 0) GO TO 200
C
DO 100 J = 1, M
C .......... FOR I=N STEP -1 UNTIL 1 DO -- ..........
DO 100 II = 1, N
I = N + 1 - II
I1 = I + 1
X = Z(I,J)
IF (I .EQ. N) GO TO 80
C
DO 60 K = I1, N
60 X = X - B(K,I) * Z(K,J)
C
80 Z(I,J) = X / DL(I)
100 CONTINUE
C
200 RETURN
END