How to fit a step function?

The problem is only the first parameter (p(1)) is fitted, but p1(2) = p0(2), unchanged! Why?

X = [-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0];
Y = [0.1 -0.15 0.05 0.0 -0.05 10.2 10.5 11.5 8.2 9.2 10.0 10.5 10.2 10.9 10.5 11.5];

plot(X,Y)

step = @(x)x > 0;

fun = @(p,x) p(1)*step(x-p(2))

p0 = [9,-0.5];

p1 = lsqcurvefit(fun,p0,X,Y);

Z = fun(p1,linspace(min(X),max(X)));

hold on

plot(linspace(min(X),max(X)),Z,'r')

[Adam Danz]

It's not clear to me what the fit should look like or the resolution of the steps. For example,

X = [-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0];
Y = [0.1 -0.15 0.05 0.0 -0.05 10.2 10.5 11.5 8.2 9.2 10.0 10.5 10.2 10.9 10.5 11.5];

plot(X,Y, 'b-o')

xr = [X(1),repelem(X(2:end),1,2)];       % X is row vec
yr = [repelem(Y(1:end-1),1,2),Y(end)];   % Y is row vec

hold on
plot(xr, yr, 'r-','LineWidth',2)

Answer 1

[Figen Ece Demirer]

X = [-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0];

Y = [0.1 -0.15 0.05 0.0 -0.05 10.2 10.5 11.5 8.2 9.2 10.0 10.5 10.2 10.9 10.5 11.5];

cut=0;

plot(X,Y,'g--o')

step = @(x)x > cut;

step2 = @(x)x < cut;

fun = @(p,x) p(1)*step(x)+p(2)*step2(x);

p0 = [9,-0.5];

p1 = lsqcurvefit(fun,p0,X,Y);

Z = fun(p1,linspace(min(X),max(X)));

hold on

plot(linspace(min(X),max(X)),Z,'r')

[Jörn Froböse]

lsqcurvefit works for continous functions only