;+ ; NAME: ; CUSPOLYN ; ; PURPOSE: ; This function returns a "cusp" polynomial determined by a given set of ; coefficients. ; ; CATEGORY: ; Curve and surface fitting. ; ; CALLING SEQUENCE: ; Result = CUSPOLYN( Degree, X, Y, Coeff [,/MATRIX]) ; ; INPUTS: ; ; Degree: The degree (in one dimension) of the 2D polynomial, [integer]. ; ; X,Y: The x- and y-vectors [double(npt)]. ; ; Coeff: The vector of coefficients for the cusp-polynomial, ; which is dimensioned as [double( (Degree+1)^2 )]. (See SFITCUSP) ; ; INPUT KEYWORDS: ; ; MATRIX: Treat X as a "row" vector and Y as a "column" vector and find ; the cusp-polynomial matrix associated with this XY-matrix. ; ; OUTPUT: ; This function returns the values of the cusp-polynomial at the values ; set by the X and Y vectors, [double(npt)] OR [double(nx,ny)] if MATRIX ; keyword is set. ; ; PROCEDURE: ; The cusp-polynomial is defined as: ; F(x,y) = Sum over i and j of coeff(i*(degree+1)+j) * abs( x^i * y^j ) ; ; MODIFICATION HISTORY: ; July, 1994 H.C. Wen ; 24-AUG-1994 Added MATRIX keyword to return a fit "matrix" ; Return a fit "matrix" whose x-component is ; defined by the x array and y-component is defined ; by the y array. (i.e. fit_matrix( x, y )) ; ;- function CUSPOLYN, degree, x, y, coeff, MATRIX=Matrix on_error, 2 nx = N_ELEMENTS(x) ny = N_ELEMENTS(y) if keyword_set( MATRIX ) then begin xm = x # REPLICATE(1.d,ny) ym = REPLICATE(1.d,nx) # y fit= dblarr(nx,ny) endif else begin if nx ne ny then message,'Incompatible arrays.' xm = x ym = y fit= dblarr(nx) endelse for j=0,degree do for k=0,degree do \$ fit = fit+coeff( j*(degree+1)+k )*abs( xm^j*ym^k ) return, REFORM( fit ) end