Is it possible to create a stairstep function?

Hi all,

I am trying to create a function that emulates what is seen below, I don't think it may be possible with stairstep but I am unsure. Does anyone know how this could be done? As I want an equation that I can have an input x value and then output a y value from the function.

% Stairstep function 
x = [0:15];
y = [19,19,19,19,19,25,25,25,25,25,25,19,19,19,19,19];

figure
stairs(x,y)
ylim([0,30]);

Much appreciated

[Image Analyst]

Let's say you have a function f() and you input a single scalar value, x. Let's say you send in 9 for the sake of illustration. How should the function know what to return? Should it return 173? How about 4.5? Sure you can define a function but you have to tell it what to return. So far I don't know what you want to send in as "x", and how the function should determine an output "y", and how stairs() has anything to do with it. If you want stairs() just use stairs().

[John Chilleri]

Not sure I understand, unless you're speaking of exactly the x and y you have above. In that case,

function y = foo(x)
    vec = [ones(1,5)+18 ones(1,6)+24 ones(1,5)+18];
    y = vec(x+1);
end

which accepts any x in [0,15].

[Tyler Bikaun]

I am using ODE45 to evaluate some equations, x being one of the variables within ODE45 will be used to evaluate a constant that is multiplied onto one of the state space equations within ODE45.

For example something along these lines

function xdot = ode(t,x)
 xdot(1) = x(2)
 xdot(2) = y_function*x(1);

The y_function is of the shape of a stairstep as shown above where the actual range I'll be using for x is approximately 0:0.001:100 (I don't need the stairstep explicitly, just need a way to call data from a function that is of the same nature).

I've done this using Simulinks 1D lookup table, but I don't want to use Simulink for this, however, I cannot find a way to do it using ODE45 and MATLAB for some reason.

Answer 1

[Walter Roberson]

Although it would be possible to program that, you should not use it in the way you propose. The ode*() routines require that the values have continuous derivatives, which you would not satisfy with a stair-steps function.

If your discontinuities are according to fixed time-points, then you need to break up your ode45 call at the timepoints, start at one end, ode45, use the result for the initial conditions of the next ode45 call and so on.

If your discontinuities are according to x rather than t, then you need to use event functions to tell it to terminate the integration at that point, and loop back and do the next ode45 call using the results from each as the boundary conditions for the next.

ode45 typically notices the discontinuity of a stairs function and considers it a singularity at which it is unable to meet integration tolerances so it gives up.