// spline linear

figure(1)
xbasc()
x=[1 10 20 30 40];
y=[1 30 -10 20 40];
plot2d(x',y',[-3],"011"," ",[-10,-40,50,50]);
yi=interpln([x;y],-4:45);
plot2d((-4:45)',yi',[3],"000");
xtitle("spline lineare")
 
  

// continuita' della spline e della spline veloce
a = -8; b = 8;
x = linspace(a,b,20)';
y = sinc(x);
dk = splin(x,y);  // not_a_knot
df = splin(x,y, "fast");
xx = linspace(a,b,800)';
[yyk, yy1k, yy2k] = interp(xx, x, y, dk); 
[yyf, yy1f, yy2f] = interp(xx, x, y, df); 
figure(2)
xbasc()
subplot(3,1,1)
plot2d(xx, [yyk yyf])
plot2d(x, y, style=-9)
legends(["not_a_knot spline","fast sub-spline","punti di interpolazione"],...
        [1 2 -9], "ur",%f)
xtitle("spline interpolation")
subplot(3,1,2)
plot2d(xx, [yy1k yy1f])
legends(["not_a_knot spline","fast sub-spline"], [1 2], "ur",%f)
xtitle("derivata prima spline interpolante")
subplot(3,1,3)
plot2d(xx, [yy2k yy2f])
legends(["not_a_knot spline","fast sub-spline"], [1 2], "lr",%f)
xtitle("derivata seconda spline interpolante")


// estrapolazione

x = linspace(0,1,11)';
y = cosh(x-0.5);
d = splin(x,y);
xx = linspace(-0.5,1.5,401)';
yy0 = interp(xx,x,y,d,"C0");
yy1 = interp(xx,x,y,d,"linear");
yy2 = interp(xx,x,y,d,"natural");
yy3 = interp(xx,x,y,d,"periodic"); 
figure(3)
xbasc()
plot2d(xx,[yy0 yy1  yy2 yy3],[2 3 4 5],frameflag=2)

xtitle(" modi diversi per valutare la spline fuori dal suo dominio")