; $Id: chebyshev.pro,v 1.3 1997/01/15 03:11:50 ali Exp $
;
; Copyright (c) 1986-1997, Research Systems, Inc.  All rights reserved.
;	Unauthorized reproduction prohibited.
;

FUNCTION CHEBYSHEV,D,N
;+
; NAME:
;	CHEBYSHEV
;
; PURPOSE:
;	Implements forward and reverse Chebyshev polynomial expansion of
;	a set of data.
;
; CATAGORY:
;	Mathematics.
;
; CALLING SEQUENCE:
;	Result = CHEBYSHEV(D, N)
;
; INPUT:
;	D:  A vector containing the values at the zeros of Chebyshev
;	    polynomial.
;
;	N:  A flag that, if set to -1, returns a set of Chebyshev polynomials.
;	    If set to +1, the original data is returned.
;
; OUTPUT:
;	Returns either the set of Chebyshev polynomials or the original
;	data depending on the value of N.
;
; COMMON BLOCKS:
;	None.
;
; SIDE EFFECTS:
;	Results from this function are subject to roundoff error given
;	discontinuous data.
;
; RESTRICTIONS:                                           
;	Unknown.
;
; PROCEDURE:
;	Straightforward implementation of recursion formula. 
;
; REVISION HISTORY:
;	Jan, 1986  Written by Leonard Kramer, U. of Maryland
;		   University Research Foundation
;-	
	ON_ERROR,2              ;Return to caller if an error occurs	
	IF (N_PARAMS(0) NE 2 ) THEN BEGIN
	  PRINT,'two parameters required'
          STOP
	ENDIF
 	UNITY =(ABS(D[0])+1.)/(ABS(D[0])+1.)
        NL=N_ELEMENTS(D)
	NE2=(NL-1.)/2.
	C=TRANSPOSE([TRANSPOSE(D),TRANSPOSE(D)])
	C[*,0]=1.
	X = cos(!Pi * (findgen(NL) + .5)/Nl)
	C[0,1]=X
	T=D
        CASE N OF 
	-1: BEGIN
          FOR I = 0, 1 DO T[I] = 2 * TOTAL(D * C[*,I])/NL
  	  FOR I=2,NL-1 DO BEGIN
	    SAVE=C[*,1]
	    C[0,1]= 2.*X*C[*,1]-C[*,0]
	    C[0,0]=SAVE
            T[I] = 2 * TOTAL( D * C[*, 1])/NL
	  ENDFOR
	  END
	1: BEGIN
          T = fltarr(NL) - .5 * D[0]
	  FOR I=0,1 DO T = T + D[I] * C[*,I]
	  FOR I=2,NL-1 DO BEGIN
	    SAVE=C[*,1]
	    C[0,1]= 2.*X*C[*,1]-C[*,0]
	    C[0,0]=SAVE
	    T=T+D[I]*C[*,1]
	  ENDFOR
	  END
	ELSE:
	ENDCASE
	RETURN,T
END