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SUBROUTINE HSBG

PURPOSE
   TO REDUCE A REAL MATRIX INTO UPPER ALMOST TRIANGULAR FORM

USAGE
   CALL HSBG(N,A,IA)

DESCRIPTION OF THE PARAMETERS
   N	  ORDER OF THE MATRIX
   A	  THE INPUT MATRIX, N BY N
   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=N WHEN
	  THE MATRIX IS IN SSP VECTOR STORAGE MODE.

REMARKS
   THE HESSENBERG FORM REPLACES THE ORIGINAL MATRIX IN THE
   ARRAY A.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   SIMILARITY TRANSFORMATIONS USING ELEMENTARY ELIMINATION
   MATRICES, WITH PARTIAL PIVOTING.

REFERENCES
   J.H. WILKINSON - THE ALGEBRAIC EIGENVALUE PROBLEM -
   CLARENDON PRESS, OXFORD, 1965.