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SUBROUTINE TRBAK3(NM,N,NV,A,M,Z)
C
INTEGER I,J,K,L,M,N,IK,IZ,NM,NV
REAL A(NV),Z(NM,M)
REAL H,S
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TRBAK3,
C NUM. MATH. 11, 181-195(1968) BY MARTIN, REINSCH, AND WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971).
C
C THIS SUBROUTINE FORMS THE EIGENVECTORS OF A REAL SYMMETRIC
C MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
C SYMMETRIC TRIDIAGONAL MATRIX DETERMINED BY TRED3.
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 NV MUST BE SET TO THE DIMENSION OF THE ARRAY PARAMETER A
C AS DECLARED IN THE CALLING PROGRAM DIMENSION STATEMENT.
C
C A CONTAINS INFORMATION ABOUT THE ORTHOGONAL TRANSFORMATIONS
C USED IN THE REDUCTION BY TRED3 IN ITS FIRST
C N*(N+1)/2 POSITIONS.
C
C M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
C
C Z CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED
C IN ITS FIRST M COLUMNS.
C
C ON OUTPUT
C
C Z CONTAINS THE TRANSFORMED EIGENVECTORS
C IN ITS FIRST M COLUMNS.
C
C NOTE THAT TRBAK3 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