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SUBROUTINE REBAK(NM,N,B,DL,M,Z)
C
INTEGER I,J,K,M,N,I1,II,NM
DOUBLE PRECISION B(NM,N),DL(N),Z(NM,M)
DOUBLE PRECISION X
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.
C
C ON INPUT
C
C NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL
C ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM
C DIMENSION STATEMENT.
C
C N IS THE ORDER OF THE MATRIX SYSTEM.
C
C B CONTAINS INFORMATION ABOUT THE SIMILARITY TRANSFORMATION
C (CHOLESKY DECOMPOSITION) USED IN THE REDUCTION BY REDUC
C IN ITS STRICT LOWER TRIANGLE.
C
C DL CONTAINS FURTHER INFORMATION ABOUT THE TRANSFORMATION.
C
C M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
C
C Z CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED
C IN ITS FIRST M COLUMNS.
C
C ON OUTPUT
C
C Z CONTAINS THE TRANSFORMED EIGENVECTORS
C IN ITS FIRST M COLUMNS.
C
C QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW,
C MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
C
C THIS VERSION DATED AUGUST 1983.
C
C ------------------------------------------------------------------
C