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SUBROUTINE TINVIT(NM,N,D,E,E2,M,W,IND,Z, X IERR,RV1,RV2,RV3,RV4,RV6) C INTEGER I,J,M,N,P,Q,R,S,II,IP,JJ,NM,ITS,TAG,IERR,GROUP DOUBLE PRECISION D(N),E(N),E2(N),W(M),Z(NM,M), X RV1(N),RV2(N),RV3(N),RV4(N),RV6(N) DOUBLE PRECISION U,V,UK,XU,X0,X1,EPS2,EPS3,EPS4,NORM,ORDER,EPSLON, X PYTHAG INTEGER IND(M) C C THIS SUBROUTINE IS A TRANSLATION OF THE INVERSE ITERATION TECH- C NIQUE IN THE ALGOL PROCEDURE TRISTURM BY PETERS AND WILKINSON. C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 418-439(1971). C C THIS SUBROUTINE FINDS THOSE EIGENVECTORS OF A TRIDIAGONAL C SYMMETRIC MATRIX CORRESPONDING TO SPECIFIED EIGENVALUES, C USING INVERSE ITERATION. 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 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 WITH ZEROS CORRESPONDING TO NEGLIGIBLE ELEMENTS OF E. C E(I) IS CONSIDERED NEGLIGIBLE IF IT IS NOT LARGER THAN C THE PRODUCT OF THE RELATIVE MACHINE PRECISION AND THE SUM C OF THE MAGNITUDES OF D(I) AND D(I-1). E2(1) MUST CONTAIN C 0.0D0 IF THE EIGENVALUES ARE IN ASCENDING ORDER, OR 2.0D0 C IF THE EIGENVALUES ARE IN DESCENDING ORDER. IF BISECT, C TRIDIB, OR IMTQLV HAS BEEN USED TO FIND THE EIGENVALUES, C THEIR OUTPUT E2 ARRAY IS EXACTLY WHAT IS EXPECTED HERE. C C M IS THE NUMBER OF SPECIFIED EIGENVALUES. C C W CONTAINS THE M EIGENVALUES IN ASCENDING OR DESCENDING 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 ON OUTPUT C C ALL INPUT ARRAYS ARE UNALTERED. C C Z CONTAINS THE ASSOCIATED SET OF ORTHONORMAL EIGENVECTORS. C ANY VECTOR WHICH FAILS TO CONVERGE IS SET TO ZERO. 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 IN 5 ITERATIONS. C C RV1, RV2, RV3, RV4, AND RV6 ARE TEMPORARY STORAGE ARRAYS. 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 C ------------------------------------------------------------------ C