colon operator rounding problem

Hello everyone!

I encountered a problem in one of my code, using the semi colon operator like this:

 a = 0:0.1:120;

will not give me exactly what I want, it does return 0, 0.1, 0.2 etc, but with a small imprecision (equal to eps actually)

the following code :

 a = 0:0.1:120;
 disp(a(20));
 disp(a(20)-1.9)
 isequal(a(20),1.9)

is returning:

 1.9
 2.22044604925031e-16
 ans =
      0

Any help ? I really need this isequal(a(20),1.9) to return 1...

thanks !

[Ambroise]

actually other values have a imprecision of n*eps, sometimes n=1, or n=8...

[Stephen23]

The problem is the real value of 0.1...

http://de.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

http://de.mathworks.com/matlabcentral/answers/69-why-does-1-2-3-1-3-not-equal-zero

http://de.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

If you really want to see what the floating point values really are, try this:

http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact--exact-version-of-num2str-

Answer 1

[bio lim]

Try it like this.

a=(0:1200)/10;

 disp(a(20));

 disp(a(20)-1.9);

 isequal(a(20),1.9)

Your previous code was not returning 1 because of rounding errors when doing finite precision arithmetic.

[Ambroise]

Thanks !

[Ambroise]

and actually a=(0:1200)*0.1;

 disp(a(20));

 disp(a(20)-1.9);

 isequal(a(20),1.9)

doesnt work but this works

a=(0:1200)/(1/0.1);

 disp(a(20));

 disp(a(20)-1.9);

 isequal(a(20),1.9)

[bio lim]

If you multiply it by decimals, such as 0.1, again you get rounding errors. That is why, I specifically wrote 10 in the first place. If you actually check your initial code, you can see that until a(4), it returns 0 but starts getting rounding error from that point.

1/0.1 returns 10 because, 1 is defined and when you divide you are going to get 10 without a rounding error.

Answer 2

[Thorsten]

Use

 a = linspace(0, 120, 1201);

But in general don't use

a(20) == 1.9

but

abs(a(20) - 1.9) <= eps

If you don't want to do it this way, just define

a(20) = 1.9;

Answer 3

[Steven Lord]

See question 1 in the Mathematics section of the FAQ for a more detailed explanation of this behavior.