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HTRID3(NM,N,A,D,E,E2,TAU)

       SUBROUTINE HTRID3(NM,N,A,D,E,E2,TAU)
 C
       INTEGER I,J,K,L,N,II,NM,JM1,JP1
       DOUBLE PRECISION A(NM,N),D(N),E(N),E2(N),TAU(2,N)
       DOUBLE PRECISION F,G,H,FI,GI,HH,SI,SCALE,PYTHAG
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF A COMPLEX ANALOGUE OF
 C     THE ALGOL PROCEDURE TRED3, 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 REDUCES A COMPLEX HERMITIAN MATRIX, STORED AS
 C     A SINGLE SQUARE ARRAY, TO A REAL SYMMETRIC TRIDIAGONAL MATRIX
 C     USING UNITARY SIMILARITY TRANSFORMATIONS.
 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 THE LOWER TRIANGLE OF THE COMPLEX HERMITIAN INPUT
 C          MATRIX.  THE REAL PARTS OF THE MATRIX ELEMENTS ARE STORED
 C          IN THE FULL LOWER TRIANGLE OF A, AND THE IMAGINARY PARTS
 C          ARE STORED IN THE TRANSPOSED POSITIONS OF THE STRICT UPPER
 C          TRIANGLE OF A.  NO STORAGE IS REQUIRED FOR THE ZERO
 C          IMAGINARY PARTS OF THE DIAGONAL ELEMENTS.
 C
 C     ON OUTPUT
 C
 C        A CONTAINS INFORMATION ABOUT THE UNITARY TRANSFORMATIONS
 C          USED IN THE REDUCTION.
 C
 C        D CONTAINS THE DIAGONAL ELEMENTS OF THE THE TRIDIAGONAL MATRIX.
 C
 C        E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE TRIDIAGONAL
 C          MATRIX IN ITS LAST N-1 POSITIONS.  E(1) IS SET TO ZERO.
 C
 C        E2 CONTAINS THE SQUARES OF THE CORRESPONDING ELEMENTS OF E.
 C          E2 MAY COINCIDE WITH E IF THE SQUARES ARE NOT NEEDED.
 C
 C        TAU CONTAINS FURTHER INFORMATION ABOUT THE TRANSFORMATIONS.
 C
 C     CALLS PYTHAG FOR  DSQRT(A*A + B*B) .
 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