Issues with The Colon (:) Operator

Hello,

I have an issue with the colon operator which operates differently than expected.

Let's define the following vectors:

vA = 30:0.0025:60;
vB = 30:0.0025:70;

Now, since their starting point and step size are identical I'd expect their values to match in the overlap zones.

Yet, try this:

a = vA(642);
b = vB(642);

isequal(a, b)
a - b

As one could see, the result is different (46.0249999999 vs. 46.0250000006). This is very different from the documentation of the colon operator .

I was expecting its values no to be dependent on the end value (Only the number of steps depend on the end value).

Is it a bug or am I missing something?

Thank You.

Answer 1

[Guillaume]

The behaviour of colon used to be fully documented in older versions and in a technical solution on Mathworks website. Unfortunately, that documentation has been removed in newer versions and the link on Mathworks is dead.

This answer gives you the details.

Basically, with non-integer steps, colon works from both ends to avoid accumulating errors. I can't fathom why Mathworks thinks that information is no longer relevant.

[Royi Avital]

Thank You. Indeed, this should have been mentioned in the documentation of the colon in MATLAB.

[Aravind C G]

Wow, thank you for this answer that clarifies things. I stumbled upon a similar issue while using the colon operator to pass a range of decimal values into a function. Sometimes the size of the functions output would be [1 19] and at others [1 20]

Now I see where the problem is coming from.

Edit: Ah, now I see it is included in the latest documentation as:

"However, if i is not an integer, then floating point arithmetic plays a role in determining whether colon includes the endpoint k in the vector, since k might not be exactly equal to j+m*i"

[Stephen23]

The provided links are now dead, but these appear to provide the relevant information:

https://www.mathworks.com/matlabcentral/answers/53912-floating-point-accurarcy-and-colon

The original technical explanation (since removed from the TMW website) is archived here:

https://web.archive.org/web/20121120071523/http://www.mathworks.com/support/solutions/en/data/1-4FLI96/index.html?solution=1-4FLI96