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BANDR(NM,N,MB,A,D,E,E2,MATZ,Z)

       SUBROUTINE BANDR(NM,N,MB,A,D,E,E2,MATZ,Z)
 C
       INTEGER J,K,L,N,R,I1,I2,J1,J2,KR,MB,MR,M1,NM,N2,R1,UGL,MAXL,MAXR
       REAL A(NM,MB),D(N),E(N),E2(N),Z(NM,N)
       REAL G,U,B1,B2,C2,F1,F2,S2,DMIN,DMINRT
       LOGICAL MATZ
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE BANDRD,
 C     NUM. MATH. 12, 231-241(1968) BY SCHWARZ.
 C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 273-283(1971).
 C
 C     THIS SUBROUTINE REDUCES A REAL SYMMETRIC BAND MATRIX
 C     TO A SYMMETRIC TRIDIAGONAL MATRIX USING AND OPTIONALLY
 C     ACCUMULATING ORTHOGONAL SIMILARITY TRANSFORMATIONS.
 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.
 C
 C        MB IS THE (HALF) BAND WIDTH OF THE MATRIX, DEFINED AS THE
 C          NUMBER OF ADJACENT DIAGONALS, INCLUDING THE PRINCIPAL
 C          DIAGONAL, REQUIRED TO SPECIFY THE NON-ZERO PORTION OF THE
 C          LOWER TRIANGLE OF THE MATRIX.
 C
 C        A CONTAINS THE LOWER TRIANGLE OF THE SYMMETRIC BAND INPUT
 C          MATRIX STORED AS AN N BY MB ARRAY.  ITS LOWEST SUBDIAGONAL
 C          IS STORED IN THE LAST N+1-MB POSITIONS OF THE FIRST COLUMN,
 C          ITS NEXT SUBDIAGONAL IN THE LAST N+2-MB POSITIONS OF THE
 C          SECOND COLUMN, FURTHER SUBDIAGONALS SIMILARLY, AND FINALLY
 C          ITS PRINCIPAL DIAGONAL IN THE N POSITIONS OF THE LAST COLUMN.
 C          CONTENTS OF STORAGES NOT PART OF THE MATRIX ARE ARBITRARY.
 C
 C        MATZ SHOULD BE SET TO .TRUE. IF THE TRANSFORMATION MATRIX IS
 C          TO BE ACCUMULATED, AND TO .FALSE. OTHERWISE.
 C
 C     ON OUTPUT
 C
 C        A HAS BEEN DESTROYED, EXCEPT FOR ITS LAST TWO COLUMNS WHICH
 C          CONTAIN A COPY OF THE TRIDIAGONAL MATRIX.
 C
 C        D CONTAINS THE DIAGONAL ELEMENTS OF THE TRIDIAGONAL MATRIX.
 C
 C        E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE TRIDIAGONAL
 C          MATRIX IN ITS LAST N-1 POSITIONS.  E(1) IS SET TO ZERO.
 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
 C        Z CONTAINS THE ORTHOGONAL TRANSFORMATION MATRIX PRODUCED IN
 C          THE REDUCTION IF MATZ HAS BEEN SET TO .TRUE.  OTHERWISE, Z
 C          IS NOT REFERENCED.
 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