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SUBROUTINE FORIF

PURPOSE
   FOURIER ANALYSIS OF A GIVEN PERIODIC FUNCTION IN THE
   RANGE 0-2PI
   COMPUTES THE COEFFICIENTS OF THE DESIRED NUMBER OF TERMS
   IN THE FOURIER SERIES F(X)=A(0)+SUM(A(K)COS KX+B(K)SIN KX)
   WHERE K=1,2,...,M TO APPROXIMATE THE COMPUTED VALUES OF A
   GIVEN FUNCTION SUBPROGRAM

USAGE
   CALL FORIF(FUN,N,M,A,B,IER)

DESCRIPTION OF PARAMETERS
   FUN-NAME OF FUNCTION SUBPROGRAM TO BE USED FOR COMPUTING
       DATA POINTS
   N  -DEFINES THE INTERVAL SUCH THAT 2N+1 POINTS ARE TAKEN
       OVER THE INTERVAL (0,2PI). THE SPACING IS THUS 2PI/2N+1
   M  -THE MAXIMUM ORDER OF THE HARMONICS TO BE FITTED
   A  -RESULTANT VECTOR OF FOURIER COSINE COEFFICIENTS OF
       LENGTH M+1
       A SUB 0, A SUB 1,..., A SUB M
   B  -RESULTANT VECTOR OF FOURIER SINE COEFFICIENTS OF
       LENGTH M+1
       B SUB 0, B SUB 1,..., B SUB M
   IER-RESULTANT ERROR CODE WHERE
       IER=0  NO ERROR
       IER=1  N NOT GREATER OR EQUAL TO M
       IER=2  M LESS THAN 0

REMARKS
   M MUST BE GREATER THAN OR EQUAL TO ZERO
   N MUST BE GREATER THAN OR EQUAL TO M
   THE FIRST ELEMENT IN VECTOR B IS ZERO IN ALL CASES

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   FUN-NAME OF USER FUNCTION SUBPROGRAM USED FOR COMPUTING
       DATA POINTS
   CALLING PROGRAM MUST HAVE FORTRAN EXTERNAL STATEMENT
   CONTAINING NAMES OF FUNCTION SUBPROGRAMS LISTED IN CALL TO
   FORIF

METHOD
   USES RECURSIVE TECHNIQUE DESCRIBED IN A. RALSTON, H. WILF,
   'MATHEMATICAL METHODS FOR DIGITAL COMPUTERS', JOHN WILEY
   AND SONS, NEW YORK, 1960, CHAPTER 24. THE METHOD OF
   INDEXING THROUGH THE PROCEDURE HAS BEEN MODIFIED TO
   SIMPLIFY THE COMPUTATION.