How to create a piecewise function using if and else statements?

I am trying to plot over an interval of -5 <= x <= 5 with the following conditions:

if x <= -3 then y = -x -3;

if -3 < x < 0 then y = x + 3;

if 0 < x < 3 then y = -2.*x + 3;

if x >= 3 then y = 0.5.*x - 4.5;

This is what I have:

x = -5:5
if x <= -3
y = -x -3;
elseif x > -3 & x < 0
y = x + 3;

elseif x > 0 & x < 3
y = -2.*x + 3;

elseif x >= 3
y = 0.5.*x - 4.5;

end
plot(x,y)

I get often get errors saying "Operands to the and && operators must be convertible to logical scalar values." Most of the time, however, it will give me unhelpful answers like:

 x =

Columns 1 through 10

    -5    -4    -3    -2    -1     0     1     2     3     4

Column 11

     5

All I want to do is plot a piecewise with if/ elseif/ etc. statements.

Answer 1

[Torsten]

x = -5:5
for i=1:numel(x)
  if x(i) <= -3
    y(i) = -x(i) -3;
  elseif (x(i) > -3) && (x(i) < 0)
    y(i) = x(i) + 3;
  elseif (x(i) > 0) && (x(i) < 3)
    y(i) = -2*x(i) + 3;
  elseif x(i) >= 3
    y(i) = 0.5*x(i) - 4.5;
  end
end
plot(x,y)

Best wishes

Torsten.

Answer 2

[A Mackie]

Im not sure how you are receiving that error without using '&&' or '||' in your code. But the issue with what you are doing is that you are always using the full 'x' vector whenever you are setting y - in whichever part of your if statements pass.

You don't need to use if statements necessarily to do the piecewise and could just use logical indexing. For your example this would look a little like:

x = -5:5

y = zeros(size(x)) % this creates the y vector to be same size

y(x<= -3) = -x(x<=-3) -3; %this selects only the points when x <= -3
y(x> -3 & x <0) = x(x>-3 & x<0) + 3 
y(x > 0 & x < 3) = -2.*x(x > 0 & x < 3) + 3;
y(x>=3) = 0.5.*x(x>=3) - 4.5;

plot(x,y)

By placing the logic into the indexing we gather a vector the same length as x that is a list of true false values. When true we select those values and act only on these.

Is this what you are looking for or do you require IF statements to be used?

Answer 3

[Rik]

Or without a loop:

x=-5:5;
y=NaN(size(x));%pre-allocate to NaN so you notice it if some values are outside all your conditions
cond=x <= -3;
y(cond) = -x(cond) -3;
cond= -3 < x & x < 0;
y(cond) = x(cond) + 3;
cond= 0 < x & x < 3;
y(cond) = -2.*x(cond) + 3;
cond=x >= 3;
y(cond) = 0.5.*x(cond) - 4.5;