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SUBROUTINE ATEIG

PURPOSE
   COMPUTE THE EIGENVALUES OF A REAL ALMOST TRIANGULAR MATRIX

USAGE
   CALL ATEIG(M,A,RR,RI,IANA,IA)

DESCRIPTION OF THE PARAMETERS
   M	  ORDER OF THE MATRIX
   A	  THE INPUT MATRIX, M BY M
   RR	  VECTOR CONTAINING THE REAL PARTS OF THE EIGENVALUES
	  ON RETURN
   RI	  VECTOR CONTAINING THE IMAGINARY PARTS OF THE EIGEN-
	  VALUES ON RETURN
   IANA   VECTOR WHOSE DIMENSION MUST BE GREATER THAN OR EQUAL
	  TO M, CONTAINING ON RETURN INDICATIONS ABOUT THE WAY
	  THE EIGENVALUES APPEARED (SEE MATH. DESCRIPTION)
   IA	  SIZE OF THE FIRST DIMENSION ASSIGNED TO THE ARRAY A
	  IN THE CALLING PROGRAM WHEN THE MATRIX IS IN DOUBLE
	  SUBSCRIPTED DATA STORAGE MODE.
	  IA=M WHEN THE MATRIX IS IN SSP VECTOR STORAGE MODE.

REMARKS
   THE ORIGINAL MATRIX IS DESTROYED
   THE DIMENSION OF RR AND RI MUST BE GREATER OR EQUAL TO M

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   QR DOUBLE ITERATION

REFERENCES
   J.G.F. FRANCIS - THE QR TRANSFORMATION---THE COMPUTER
   JOURNAL, VOL. 4, NO. 3, OCTOBER 1961, VOL. 4, NO. 4, JANUARY
   1962.  J. H. WILKINSON - THE ALGEBRAIC EIGENVALUE PROBLEM -
   CLARENDON PRESS, OXFORD, 1965.