How to write indicator function in matlab

Question

I am a new user of matlab and I want to tackle the following problem:

I want to construct a piecewise constant function f. f should be an anonymous function like f=@(t)1[0,0.25)(t). However, the number of intervals for the piecewise constant function is not fixed in general. Instead, the piecewise interval depends on users input.

For example, if one enters 4, the piecewise interval becomes

[0,0.25), [0.25,0.5), [0.5,0.75) and [0.75,1)

then

f=@(t)a1*1[0,0.25)(t)+a2*[0.25,0.5)(t)+a3*1[0.5,0.75)(t)+a4*1[0.75,1)(t);

While if one enters 5, the piecewise interval becomes

[0,0.2), [0.2,0.4), [0.4,0.6), [0.6,0.8) and [0.8,1)

Are there any good ways to tackle the problem?

Answer 1

Assuming that the weights a1,...,ak are already defined, you can use the following approach:

%defines weight vector. for example: a1=1, a2=2, a3=3, a4=4,a5=5
A = 1:5;  
%defines a range vector
ranges = [0:(1/length(A)):1,inf];
%The padding is for handling cases where t<0 or t>=1
APadded = [0,A,0];
%define f
f=@(t)APadded(find(t<ranges,1,'first'))

Result:

f(0.1) = 1
f(0.3) = 2
f(0.5) = 3
f(0.7) = 4
f(0.9) = 5
f(-0.1) = f(1.1) = 0;