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HTRIB3(NM,N,A,TAU,M,ZR,ZI)

       SUBROUTINE HTRIB3(NM,N,A,TAU,M,ZR,ZI)
 C
       INTEGER I,J,K,L,M,N,NM
       DOUBLE PRECISION A(NM,N),TAU(2,N),ZR(NM,M),ZI(NM,M)
       DOUBLE PRECISION H,S,SI
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF A COMPLEX ANALOGUE OF
 C     THE ALGOL PROCEDURE TRBAK3, NUM. MATH. 11, 181-195(1968)
 C     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 COMPLEX HERMITIAN
 C     MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
 C     REAL SYMMETRIC TRIDIAGONAL MATRIX DETERMINED BY  HTRID3.
 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        A CONTAINS INFORMATION ABOUT THE UNITARY TRANSFORMATIONS
 C          USED IN THE REDUCTION BY  HTRID3.
 C
 C        TAU CONTAINS FURTHER INFORMATION ABOUT THE TRANSFORMATIONS.
 C
 C        M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
 C
 C        ZR CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED
 C          IN ITS 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     NOTE THAT THE LAST COMPONENT OF EACH RETURNED VECTOR
 C     IS REAL AND THAT VECTOR EUCLIDEAN NORMS ARE PRESERVED.
 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