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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
DOUBLE PRECISION A(NM,MB),D(N),E(N),E2(N),Z(NM,N)
DOUBLE PRECISION 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
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C