For Loop Not Executing

Hi all!

Consider the following example:

 h=(2/1000); 

 for i=8*h+h:h:9*h
     i
 end

i =

   0.0180

And similarly,

 >> for i=11*h+h:h:12*h
        i
    end

i =

    0.0240

But when I do this:

 >> for i=9*h+h:h:10*h
        i
     end

it doesn't enter the for loop! What is going on? Thanks for the help!

[Star Strider]

You can go as far as you did, but Rena Berman will reconstitute it in a few days.

Does Sisyphus begin to sound relevant?

[Rena Berman]

(Answers dev) Restored edit

Answer 1

[Mischa Kim]

Gopal, this is because

 9*h+h - 10*h
 ans =
     3.469446951953614e-18

and

 11*h+h - 12*h
 ans =
     0

Just because the terms above are all symbolically equal to zero, does not necessarily mean they are also numerically equal to zero. The first expression is not which is why the loop does not get executed.

Star Strider provides more detail below.

[Star Strider]

Almost.

In the top two, the end equals the beginning, so the loops in them execute once. The loop is satisfied after the first iteration.

In the third one, the difference between the end and the beginning is negative, so the loop is satisfied at the first iteration and never executes:

h=(2/1000); 
d = [ 9*h - (8*h+h); 12*h - (11*h+h); 10*h - (9*h+h)]

d =
            0
            0
  -3.4694e-18

Because of the negative direction:

for i=9*h+h:-h:10*h
    i
end

i =
         0.02

executes once with a step of ‘-h’.

[Mischa Kim]

Absolutely. Thanks.

[Star Strider]

As always, my pleasure.

[N/A]

Of course! Thanks so much I should have realized this.

Answer 2

[David Goodmanson]

For the floating point number h you are basically asking if n*h + h == (n+1)*h for various values of n. Well, sometimes the two sides are equal (to machine precision), sometimes not. For n=9 the left hand side is bigger than the right hand side by 3e-18, so the for loop doesn't do anything.

It's never a good idea to do exact equality tests with floating point numbers.