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SUBROUTINE BALBAK(NM,N,LOW,IGH,SCALE,M,Z)
C
INTEGER I,J,K,M,N,II,NM,IGH,LOW
DOUBLE PRECISION SCALE(N),Z(NM,M)
DOUBLE PRECISION S
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE BALBAK,
C NUM. MATH. 13, 293-304(1969) BY PARLETT AND REINSCH.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 315-326(1971).
C
C THIS SUBROUTINE FORMS THE EIGENVECTORS OF A REAL GENERAL
C MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
C BALANCED MATRIX DETERMINED BY BALANC.
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 BALANC.
C
C SCALE CONTAINS INFORMATION DETERMINING THE PERMUTATIONS
C AND SCALING FACTORS USED BY BALANC.
C
C M IS THE NUMBER OF COLUMNS OF Z TO BE BACK TRANSFORMED.
C
C Z CONTAINS THE REAL AND IMAGINARY PARTS OF THE EIGEN-
C VECTORS TO BE BACK TRANSFORMED IN ITS FIRST M COLUMNS.
C
C ON OUTPUT
C
C Z CONTAINS THE REAL AND IMAGINARY PARTS OF THE
C TRANSFORMED EIGENVECTORS IN ITS 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
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C