*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