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SUBROUTINE TRIDIB(N,EPS1,D,E,E2,LB,UB,M11,M,W,IND,IERR,RV4,RV5)
C
INTEGER I,J,K,L,M,N,P,Q,R,S,II,M1,M2,M11,M22,TAG,IERR,ISTURM
REAL D(N),E(N),E2(N),W(M),RV4(N),RV5(N)
REAL U,V,LB,T1,T2,UB,XU,X0,X1,EPS1,TST1,TST2,EPSLON
INTEGER IND(M)
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE BISECT,
C NUM. MATH. 9, 386-393(1967) BY BARTH, MARTIN, AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 249-256(1971).
C
C THIS SUBROUTINE FINDS THOSE EIGENVALUES OF A TRIDIAGONAL
C SYMMETRIC MATRIX BETWEEN SPECIFIED BOUNDARY INDICES,
C USING BISECTION.
C
C ON INPUT
C
C N IS THE ORDER OF THE MATRIX.
C
C EPS1 IS AN ABSOLUTE ERROR TOLERANCE FOR THE COMPUTED
C EIGENVALUES. IF THE INPUT EPS1 IS NON-POSITIVE,
C IT IS RESET FOR EACH SUBMATRIX TO A DEFAULT VALUE,
C NAMELY, MINUS THE PRODUCT OF THE RELATIVE MACHINE
C PRECISION AND THE 1-NORM OF THE SUBMATRIX.
C
C D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX.
C
C E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX
C IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY.
C
C E2 CONTAINS THE SQUARES OF THE CORRESPONDING ELEMENTS OF E.
C E2(1) IS ARBITRARY.
C
C M11 SPECIFIES THE LOWER BOUNDARY INDEX FOR THE DESIRED
C EIGENVALUES.
C
C M SPECIFIES THE NUMBER OF EIGENVALUES DESIRED. THE UPPER
C BOUNDARY INDEX M22 IS THEN OBTAINED AS M22=M11+M-1.
C
C ON OUTPUT
C
C EPS1 IS UNALTERED UNLESS IT HAS BEEN RESET TO ITS
C (LAST) DEFAULT VALUE.
C
C D AND E ARE UNALTERED.
C
C ELEMENTS OF E2, CORRESPONDING TO ELEMENTS OF E REGARDED
C AS NEGLIGIBLE, HAVE BEEN REPLACED BY ZERO CAUSING THE
C MATRIX TO SPLIT INTO A DIRECT SUM OF SUBMATRICES.
C E2(1) IS ALSO SET TO ZERO.
C
C LB AND UB DEFINE AN INTERVAL CONTAINING EXACTLY THE DESIRED
C EIGENVALUES.
C
C W CONTAINS, IN ITS FIRST M POSITIONS, THE EIGENVALUES
C BETWEEN INDICES M11 AND M22 IN ASCENDING ORDER.
C
C IND CONTAINS IN ITS FIRST M POSITIONS THE SUBMATRIX INDICES
C ASSOCIATED WITH THE CORRESPONDING EIGENVALUES IN W --
C 1 FOR EIGENVALUES BELONGING TO THE FIRST SUBMATRIX FROM
C THE TOP, 2 FOR THOSE BELONGING TO THE SECOND SUBMATRIX, ETC..
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C 3*N+1 IF MULTIPLE EIGENVALUES AT INDEX M11 MAKE
C UNIQUE SELECTION IMPOSSIBLE,
C 3*N+2 IF MULTIPLE EIGENVALUES AT INDEX M22 MAKE
C UNIQUE SELECTION IMPOSSIBLE.
C
C RV4 AND RV5 ARE TEMPORARY STORAGE ARRAYS.
C
C NOTE THAT SUBROUTINE TQL1, IMTQL1, OR TQLRAT IS GENERALLY FASTER
C THAN TRIDIB, IF MORE THAN N/4 EIGENVALUES ARE TO BE FOUND.
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