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SUBROUTINE HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI)
C
INTEGER I,J,K,L,M,N,NM
DOUBLE PRECISION AR(NM,N),AI(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 TRBAK1, 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 HTRIDI.
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 AR AND AI CONTAIN INFORMATION ABOUT THE UNITARY TRANS-
C FORMATIONS USED IN THE REDUCTION BY HTRIDI IN THEIR
C FULL LOWER TRIANGLES EXCEPT FOR THE DIAGONAL OF AR.
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
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C