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SUBROUTINE COMLR(NM,N,LOW,IGH,HR,HI,WR,WI,IERR)
C
INTEGER I,J,L,M,N,EN,LL,MM,NM,IGH,IM1,ITN,ITS,LOW,MP1,ENM1,IERR
REAL HR(NM,N),HI(NM,N),WR(N),WI(N)
REAL SI,SR,TI,TR,XI,XR,YI,YR,ZZI,ZZR,TST1,TST2
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE COMLR,
C NUM. MATH. 12, 369-376(1968) BY MARTIN AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 396-403(1971).
C
C THIS SUBROUTINE FINDS THE EIGENVALUES OF A COMPLEX
C UPPER HESSENBERG MATRIX BY THE MODIFIED LR METHOD.
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 LOW AND IGH ARE INTEGERS DETERMINED BY THE BALANCING
C SUBROUTINE CBAL. IF CBAL HAS NOT BEEN USED,
C SET LOW=1, IGH=N.
C
C HR AND HI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE COMPLEX UPPER HESSENBERG MATRIX.
C THEIR LOWER TRIANGLES BELOW THE SUBDIAGONAL CONTAIN THE
C MULTIPLIERS WHICH WERE USED IN THE REDUCTION BY COMHES,
C IF PERFORMED.
C
C ON OUTPUT
C
C THE UPPER HESSENBERG PORTIONS OF HR AND HI HAVE BEEN
C DESTROYED. THEREFORE, THEY MUST BE SAVED BEFORE
C CALLING COMLR IF SUBSEQUENT CALCULATION OF
C EIGENVECTORS IS TO BE PERFORMED.
C
C WR AND WI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE EIGENVALUES. IF AN ERROR
C EXIT IS MADE, THE EIGENVALUES SHOULD BE CORRECT
C FOR INDICES IERR+1,...,N.
C
C IERR IS SET TO
C ZERO FOR NORMAL RETURN,
C J IF THE LIMIT OF 30*N ITERATIONS IS EXHAUSTED
C WHILE THE J-TH EIGENVALUE IS BEING SOUGHT.
C
C CALLS CDIV FOR COMPLEX DIVISION.
C CALLS CSROOT FOR COMPLEX SQUARE ROOT.
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