Previous: minfit Up: ../eispas.html Next: orthes
SUBROUTINE ORTBAK(NM,LOW,IGH,A,ORT,M,Z)
C
INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
REAL A(NM,IGH),ORT(IGH),Z(NM,M)
REAL G
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE ORTBAK,
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 REAL GENERAL
C MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
C UPPER HESSENBERG MATRIX DETERMINED 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 LOW AND IGH ARE INTEGERS DETERMINED BY THE BALANCING
C SUBROUTINE BALANC. IF BALANC HAS NOT BEEN USED,
C SET LOW=1 AND IGH EQUAL TO THE ORDER OF THE MATRIX.
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 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 ORT HAS BEEN ALTERED.
C
C NOTE THAT ORTBAK PRESERVES VECTOR EUCLIDEAN NORMS.
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