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SUBROUTINE IMTQLV(N,D,E,E2,W,IND,IERR,RV1)
C
INTEGER I,J,K,L,M,N,II,MML,TAG,IERR
REAL D(N),E(N),E2(N),W(N),RV1(N)
REAL B,C,F,G,P,R,S,TST1,TST2,PYTHAG
INTEGER IND(N)
C
C THIS SUBROUTINE IS A VARIANT OF IMTQL1 WHICH IS A TRANSLATION OF
C ALGOL PROCEDURE IMTQL1, NUM. MATH. 12, 377-383(1968) BY MARTIN AND
C WILKINSON, AS MODIFIED IN NUM. MATH. 15, 450(1970) BY DUBRULLE.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 241-248(1971).
C
C THIS SUBROUTINE FINDS THE EIGENVALUES OF A SYMMETRIC TRIDIAGONAL
C MATRIX BY THE IMPLICIT QL METHOD AND ASSOCIATES WITH THEM
C THEIR CORRESPONDING SUBMATRIX INDICES.
C
C ON INPUT
C
C N IS THE ORDER OF THE MATRIX.
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 ON OUTPUT
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C AS NEGLIGIBLE, HAVE BEEN REPLACED BY ZERO CAUSING THE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 W CONTAINS THE EIGENVALUES IN ASCENDING ORDER. IF AN
C ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT AND
C ORDERED FOR INDICES 1,2,...IERR-1, BUT MAY NOT BE
C THE SMALLEST EIGENVALUES.
C
C IND CONTAINS THE SUBMATRIX INDICES ASSOCIATED WITH THE
C CORRESPONDING EIGENVALUES IN W -- 1 FOR EIGENVALUES
C BELONGING TO THE FIRST SUBMATRIX FROM THE TOP,
C 2 FOR THOSE BELONGING TO THE SECOND SUBMATRIX, ETC..
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C J IF THE J-TH EIGENVALUE HAS NOT BEEN
C DETERMINED AFTER 30 ITERATIONS.
C
C RV1 IS A TEMPORARY STORAGE ARRAY.
C
C CALLS PYTHAG FOR SQRT(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