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SUBROUTINE BANDV(NM,N,MBW,A,E21,M,W,Z,IERR,NV,RV,RV6)
C
INTEGER I,J,K,M,N,R,II,IJ,JJ,KJ,MB,M1,NM,NV,IJ1,ITS,KJ1,MBW,M21,
X IERR,MAXJ,MAXK,GROUP
DOUBLE PRECISION A(NM,MBW),W(M),Z(NM,M),RV(NV),RV6(N)
DOUBLE PRECISION U,V,UK,XU,X0,X1,E21,EPS2,EPS3,EPS4,NORM,ORDER,
X EPSLON,PYTHAG
C
C THIS SUBROUTINE FINDS THOSE EIGENVECTORS OF A REAL SYMMETRIC
C BAND MATRIX CORRESPONDING TO SPECIFIED EIGENVALUES, USING INVERSE
C ITERATION. THE SUBROUTINE MAY ALSO BE USED TO SOLVE SYSTEMS
C OF LINEAR EQUATIONS WITH A SYMMETRIC OR NON-SYMMETRIC BAND
C COEFFICIENT MATRIX.
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 MBW IS THE NUMBER OF COLUMNS OF THE ARRAY A USED TO STORE THE
C BAND MATRIX. IF THE MATRIX IS SYMMETRIC, MBW IS ITS (HALF)
C BAND WIDTH, DENOTED MB AND DEFINED AS THE NUMBER OF ADJACENT
C DIAGONALS, INCLUDING THE PRINCIPAL DIAGONAL, REQUIRED TO
C SPECIFY THE NON-ZERO PORTION OF THE LOWER TRIANGLE OF THE
C MATRIX. IF THE SUBROUTINE IS BEING USED TO SOLVE SYSTEMS
C OF LINEAR EQUATIONS AND THE COEFFICIENT MATRIX IS NOT
C SYMMETRIC, IT MUST HOWEVER HAVE THE SAME NUMBER OF ADJACENT
C DIAGONALS ABOVE THE MAIN DIAGONAL AS BELOW, AND IN THIS
C CASE, MBW=2*MB-1.
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 COLUMN MB.
C IF THE SUBROUTINE IS BEING USED TO SOLVE SYSTEMS OF LINEAR
C EQUATIONS AND THE COEFFICIENT MATRIX IS NOT SYMMETRIC, A IS
C N BY 2*MB-1 INSTEAD WITH LOWER TRIANGLE AS ABOVE AND WITH
C ITS FIRST SUPERDIAGONAL STORED IN THE FIRST N-1 POSITIONS OF
C COLUMN MB+1, ITS SECOND SUPERDIAGONAL IN THE FIRST N-2
C POSITIONS OF COLUMN MB+2, FURTHER SUPERDIAGONALS SIMILARLY,
C AND FINALLY ITS HIGHEST SUPERDIAGONAL IN THE FIRST N+1-MB
C POSITIONS OF THE LAST COLUMN.
C CONTENTS OF STORAGES NOT PART OF THE MATRIX ARE ARBITRARY.
C
C E21 SPECIFIES THE ORDERING OF THE EIGENVALUES AND CONTAINS
C 0.0D0 IF THE EIGENVALUES ARE IN ASCENDING ORDER, OR
C 2.0D0 IF THE EIGENVALUES ARE IN DESCENDING ORDER.
C IF THE SUBROUTINE IS BEING USED TO SOLVE SYSTEMS OF LINEAR
C EQUATIONS, E21 SHOULD BE SET TO 1.0D0 IF THE COEFFICIENT
C MATRIX IS SYMMETRIC AND TO -1.0D0 IF NOT.
C
C M IS THE NUMBER OF SPECIFIED EIGENVALUES OR THE NUMBER OF
C SYSTEMS OF LINEAR EQUATIONS.
C
C W CONTAINS THE M EIGENVALUES IN ASCENDING OR DESCENDING ORDER.
C IF THE SUBROUTINE IS BEING USED TO SOLVE SYSTEMS OF LINEAR
C EQUATIONS (A-W(R)*I)*X(R)=B(R), WHERE I IS THE IDENTITY
C MATRIX, W(R) SHOULD BE SET ACCORDINGLY, FOR R=1,2,...,M.
C
C Z CONTAINS THE CONSTANT MATRIX COLUMNS (B(R),R=1,2,...,M), IF
C THE SUBROUTINE IS USED TO SOLVE SYSTEMS OF LINEAR EQUATIONS.
C
C NV MUST BE SET TO THE DIMENSION OF THE ARRAY PARAMETER RV
C AS DECLARED IN THE CALLING PROGRAM DIMENSION STATEMENT.
C
C ON OUTPUT
C
C A AND W ARE UNALTERED.
C
C Z CONTAINS THE ASSOCIATED SET OF ORTHOGONAL EIGENVECTORS.
C ANY VECTOR WHICH FAILS TO CONVERGE IS SET TO ZERO. IF THE
C SUBROUTINE IS USED TO SOLVE SYSTEMS OF LINEAR EQUATIONS,
C Z CONTAINS THE SOLUTION MATRIX COLUMNS (X(R),R=1,2,...,M).
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C -R IF THE EIGENVECTOR CORRESPONDING TO THE R-TH
C EIGENVALUE FAILS TO CONVERGE, OR IF THE R-TH
C SYSTEM OF LINEAR EQUATIONS IS NEARLY SINGULAR.
C
C RV AND RV6 ARE TEMPORARY STORAGE ARRAYS. NOTE THAT RV IS
C OF DIMENSION AT LEAST N*(2*MB-1). IF THE SUBROUTINE
C IS BEING USED TO SOLVE SYSTEMS OF LINEAR EQUATIONS, THE
C DETERMINANT (UP TO SIGN) OF A-W(M)*I IS AVAILABLE, UPON
C RETURN, AS THE PRODUCT OF THE FIRST N ELEMENTS OF RV.
C
C CALLS PYTHAG FOR DSQRT(A*A + B*B) .
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