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SUBROUTINE ORTRAN(NM,N,LOW,IGH,A,ORT,Z)
C
INTEGER I,J,N,KL,MM,MP,NM,IGH,LOW,MP1
DOUBLE PRECISION A(NM,IGH),ORT(IGH),Z(NM,N)
DOUBLE PRECISION G
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE ORTRANS,
C NUM. MATH. 16, 181-204(1970) BY PETERS AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971).
C
C THIS SUBROUTINE ACCUMULATES THE ORTHOGONAL SIMILARITY
C TRANSFORMATIONS USED IN THE REDUCTION OF A REAL GENERAL
C MATRIX TO UPPER HESSENBERG FORM BY ORTHES.
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 BALANC. IF BALANC HAS NOT BEEN USED,
C SET LOW=1, IGH=N.
C
C A CONTAINS INFORMATION ABOUT THE ORTHOGONAL TRANS-
C FORMATIONS USED IN THE REDUCTION BY ORTHES
C IN ITS STRICT LOWER TRIANGLE.
C
C ORT CONTAINS FURTHER INFORMATION ABOUT THE TRANS-
C FORMATIONS USED IN THE REDUCTION BY ORTHES.
C ONLY ELEMENTS LOW THROUGH IGH ARE USED.
C
C ON OUTPUT
C
C Z CONTAINS THE TRANSFORMATION MATRIX PRODUCED IN THE
C REDUCTION BY ORTHES.
C
C ORT HAS BEEN ALTERED.
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
C