function z=spintgrl(x,y,xi)%SPINTGRL Cubic Spline Integral Interpolation.% YI=SPINTRGL(X,Y,XI) uses cubic spline interpolation to fit the% data in X and Y, integrates the spline, and returns% values of the integral evaluated at the points in XI.%% PPI=SPINTGRL(PP) returns the piecewise polynomial vector PPI% describing the integral of the cubic spline described by% the piecewise polynomial in PP. PP is returned by the function% SPLINE and is a data vector containing all information to% evaluate and manipulate a spline.%% YI=SPINTGRL(PP,XI) integrates the cubic spline given by% the piecewise polynomial PP, and returns the values of the% integral evaluated at the points in XI.%% See also SPLINE, PPVAL, MKPP, UNMKPP, SPDERIV% D.C. Hanselman, University of Maine, Orono, ME 04469% 1/27/95% Copyright (c) 1996 by Prentice-Hall, Inc. if nargin==3	pp=spline(x,y);else	pp=x;end[br,co,npy,nco]=unmkpp(pp);	% take apart ppif pp(1)~=10	error('Spline data does not have the correct form.')endsf=nco:-1:1;								% scale factors for integrationico=[co./sf(ones(npy,1),:) zeros(npy,1)];	% integral coefficientsnco=nco+1;									% integral spline has higher orderfor k=2:npy									% find constant terms in polynomials	ico(k,nco)=polyval(ico(k-1,:),br(k)-br(k-1));endppi=mkpp(br,ico);							% build pp form for integralif nargin==1	z=ppi;elseif nargin==2	z=ppval(ppi,y);else	z=ppval(ppi,xi);end