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SUBROUTINE COMBAK(NM,LOW,IGH,AR,AI,INT,M,ZR,ZI)
C
INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
DOUBLE PRECISION AR(NM,IGH),AI(NM,IGH),ZR(NM,M),ZI(NM,M)
DOUBLE PRECISION XR,XI
INTEGER INT(IGH)
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE COMBAK,
C NUM. MATH. 12, 349-368(1968) BY MARTIN AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971).
C
C THIS SUBROUTINE FORMS THE EIGENVECTORS OF A COMPLEX GENERAL
C MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
C UPPER HESSENBERG MATRIX DETERMINED BY COMHES.
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 LOW AND IGH ARE INTEGERS DETERMINED BY THE BALANCING
C SUBROUTINE CBAL. IF CBAL HAS NOT BEEN USED,
C SET LOW=1 AND IGH EQUAL TO THE ORDER OF THE MATRIX.
C
C AR AND AI CONTAIN THE MULTIPLIERS WHICH WERE USED IN THE
C REDUCTION BY COMHES IN THEIR LOWER TRIANGLES
C BELOW THE SUBDIAGONAL.
C
C INT CONTAINS INFORMATION ON THE ROWS AND COLUMNS
C INTERCHANGED IN THE REDUCTION BY COMHES.
C ONLY ELEMENTS LOW THROUGH IGH ARE USED.
C
C M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
C
C ZR AND ZI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE EIGENVECTORS TO BE
C BACK TRANSFORMED IN THEIR FIRST M COLUMNS.
C
C ON OUTPUT
C
C ZR AND ZI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE TRANSFORMED EIGENVECTORS
C IN THEIR FIRST M COLUMNS.
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