SPLINEFIT EXAMPLES
Contents
EXAMPLE 1: Breaks and pieces
+x = 2*pi*rand(1,200);
+y = sin(x) + sin(2*x) + 0.2*randn(size(x));
+
+
+breaks = linspace(0,2*pi,41);
+pp1 = splinefit(x,y,breaks);
+
+
+pp2 = splinefit(x,y,10);
+
+
+figure(1)
+xx = linspace(0,2*pi,400);
+y1 = ppval(pp1,xx);
+y2 = ppval(pp2,xx);
+plot(x,y,'.',xx,[y1;y2])
+axis([0,2*pi,-2.5,2.5]), grid on
+legend('data','41 breaks, 40 pieces','11 breaks, 10 pieces')
+title('EXAMPLE 1: Breaks and pieces')
+
EXAMPLE 2: Spline orders
+x = 2*pi*rand(1,200);
+y = sin(x) + sin(2*x) + 0.1*randn(size(x));
+
+
+pp1 = splinefit(x,y,8,1);
+pp2 = splinefit(x,y,8,2);
+pp3 = splinefit(x,y,8,3);
+pp4 = splinefit(x,y,8,4);
+pp5 = splinefit(x,y,8,5);
+
+
+figure(2)
+xx = linspace(0,2*pi,400);
+y1 = ppval(pp1,xx);
+y2 = ppval(pp2,xx);
+y3 = ppval(pp3,xx);
+y4 = ppval(pp4,xx);
+y5 = ppval(pp5,xx);
+plot(x,y,'.',xx,[y1;y2;y3;y4;y5]), grid on
+legend('data','order 1','order 2','order 3','order 4','order 5')
+title('EXAMPLE 2: Spline orders')
+
EXAMPLE 3: Periodic boundary conditions
+x = 2*pi*[0,rand(1,98),1];
+y = sin(x) - cos(2*x) + 0.2*randn(size(x));
+
+
+pp1 = splinefit(x,y,10,5);
+
+pp2 = splinefit(x,y,10,5,'p');
+
+
+figure(3)
+xx = linspace(0,2*pi,400);
+y1 = ppval(pp1,xx);
+y2 = ppval(pp2,xx);
+plot(x,y,'.',xx,[y1;y2]), grid on
+legend('data','no constraints','periodic')
+title('EXAMPLE 3: Periodic boundary conditions')
+
+
+y0 = ppval(pp2,[0,2*pi]);
+y1 = ppval(ppdiff(pp2,1),[0,2*pi]);
+y2 = ppval(ppdiff(pp2,2),[0,2*pi]);
+y3 = ppval(ppdiff(pp2,3),[0,2*pi]);
+disp('Endpoint derivatives:')
+disp([y0;y1;y2;y3])
+Endpoint derivatives:
+ -0.9885 -0.9885
+ 0.7848 0.7848
+ 3.2802 3.2802
+ 5.6253 5.6253
+
+
EXAMPLE 4: Endpoint conditions
+x = 2*pi*rand(1,200);
+y = sin(2*x) + 0.1*randn(size(x));
+
+
+breaks = linspace(0,2*pi,10);
+
+
+xc = [0,0,2*pi,2*pi];
+cc = [eye(2),eye(2)];
+con = struct('xc',xc,'cc',cc);
+pp1 = splinefit(x,y,breaks,con);
+
+
+con = struct('xc',0);
+pp2 = splinefit(x,y,breaks,con,'p');
+
+
+figure(4)
+xx = linspace(0,2*pi,400);
+y1 = ppval(pp1,xx);
+y2 = ppval(pp2,xx);
+plot(x,y,'.',xx,[y1;y2]), grid on
+legend('data','clamped','hinged periodic')
+title('EXAMPLE 4: Endpoint conditions')
+
EXAMPLE 5: Airfoil data
+x = [0,1,2,4,8,16,24,40,56,72,80]/80;
+y = [0,28,39,53,70,86,90,79,55,22,2]/1000;
+xy = [x;y];
+
+
+ds = sqrt(diff(x).^2 + diff(y).^2);
+s = [0, cumsum(ds)];
+
+
+con = struct('xc',[0 0],'yc',[0 0; 0 1],'cc',eye(2));
+
+
+pp = splinefit(s,xy,4,con);
+
+
+figure(5)
+ss = linspace(0,s(end),400);
+xyfit = ppval(pp,ss);
+xyb = ppval(pp,pp.breaks);
+plot(x,y,'.',xyfit(1,:),xyfit(2,:),'r',xyb(1,:),xyb(2,:),'ro')
+legend('data','spline','breaks')
+grid on, axis equal
+title('EXAMPLE 5: Airfoil data')
+
EXAMPLE 6: Robust fitting
+x = linspace(0,2*pi,200);
+y = sin(x) + sin(2*x) + 0.05*randn(size(x));
+
+
+x = [x, linspace(0,2*pi,60)];
+y = [y, -ones(1,60)];
+
+
+con = struct('xc',[0,2*pi]);
+pp1 = splinefit(x,y,8,con,0.25);
+pp2 = splinefit(x,y,8,con,0.75);
+pp3 = splinefit(x,y,8,con);
+
+
+figure(6)
+xx = linspace(0,2*pi,400);
+y1 = ppval(pp1,xx);
+y2 = ppval(pp2,xx);
+y3 = ppval(pp3,xx);
+plot(x,y,'.',xx,[y1;y2;y3]), grid on
+legend('data with outliers','robust, beta = 0.25','robust, beta = 0.75',...
+ 'no robust fitting')
+title('EXAMPLE 6: Robust fitting')
+