Is there some advantage of writing
t = linspace(0,20,21)
over
t = 0:1:20
?
I understand the former produces a vector, as the first does.
Can anyone state me some situation where linspace
is useful over t = 0:1:20
?
linspace() gives you exactly 10 elements and scales the numbers to make sure that's true. Colon steps along until the number is more than the ending number and quits without exceeding the ending number.
Colon operator (":") in R is a function that generates regular sequences. It is most commonly used in for loops, to index and to create a vector with increasing or decreasing sequence. It is a binary operator i.e. it takes two arguments.
The colon is one of the most useful operators in MATLAB®. It can create vectors, subscript arrays, and specify for iterations. example. x = j : k creates a unit-spaced vector x with elements [j,j+1,j+2,...,j+m] where m = fix(k-j) . If j and k are both integers, then this is simply [j,j+1,...,k] .
The linspace() function returns evenly spaced numbers over a specified interval [start, stop]. The endpoint of the interval can optionally be excluded. The starting value of the sequence. The end value of the sequence, unless endpoint is set to False.
It's not just the usability. Though the documentation says:
The
linspace
function generates linearly spaced vectors. It is similar to the colon operator :, but gives direct control over the number of points.
it is the same, the main difference and advantage of linspace
is that it generates a vector of integers with the desired length (or default 100) and scales it afterwards to the desired range. The :
colon creates the vector directly by increments.
Imagine you need to define bin edges for a histogram. And especially you need the certain bin edge 0.35
to be exactly on it's right place:
edges = [0.05:0.10:.55];
X = edges == 0.35
edges = 0.0500 0.1500 0.2500 0.3500 0.4500 0.5500
X = 0 0 0 0 0 0
does not define the right bin edge, but:
edges = linspace(0.05,0.55,6); %// 6 = (0.55-0.05)/0.1+1
X = edges == 0.35
edges = 0.0500 0.1500 0.2500 0.3500 0.4500 0.5500
X = 0 0 0 1 0 0
does.
Well, it's basically a floating point issue. Which can be avoided by linspace
, as a single division of an integer is not that delicate, like the cumulative sum of floting point numbers. But as Mark Dickinson pointed out in the comments:
You shouldn't rely on any of the computed values being exactly what you expect. That is not what linspace is for. In my opinion it's a matter of how likely you will get floating point issues and how much you can reduce the probabilty for them or how small can you set the tolerances. Using linspace can reduce the probability of occurance of these issues, it's not a security.
That's the code of linspace
:
n1 = n-1
c = (d2 - d1).*(n1-1) % opposite signs may cause overflow
if isinf(c)
y = d1 + (d2/n1).*(0:n1) - (d1/n1).*(0:n1)
else
y = d1 + (0:n1).*(d2 - d1)/n1
end
To sum up: linspace
and colon are reliable at doing different tasks. linspace
tries to ensure (as the name suggests) linear spacing, whereas colon
tries to ensure symmetry
In your special case, as you create a vector of integers, there is no advantage of linspace
(apart from usability), but when it comes to floating point delicate tasks, there may is.
The answer of Sam Roberts provides some additional information and clarifies further things, including some statements of MathWorks regarding the colon operator.
linspace
and the colon operator do different things.
linspace
creates a vector of integers of the specified length, and then scales it down to the specified interval with a division. In this way it ensures that the output vector is as linearly spaced as possible.
The colon operator adds increments to the starting point, and subtracts decrements from the end point to reach a middle point. In this way, it ensures that the output vector is as symmetric as possible.
The two methods thus have different aims, and will often give very slightly different answers, e.g.
>> a = 0:pi/1000:10*pi;
>> b = linspace(0,10*pi,10001);
>> all(a==b)
ans =
0
>> max(a-b)
ans =
3.5527e-15
In practice, however, the differences will often have little impact unless you are interested in tiny numerical details. I find linspace
more convenient when the number of gaps is easy to express, whereas I find the colon operator more convenient when the increment is easy to express.
See this MathWorks technical note for more detail on the algorithm behind the colon operator. For more detail on linspace
, you can just type edit linspace
to see exactly what it does.
linspace
is useful where you know the number of elements you want rather than the size of the "step" between them. So if I said make a vector with 360 elements between 0
and 2*pi
as a contrived example it's either going to be
linspace(0, 2*pi, 360)
or if you just had the colon operator you would have to manually calculate the step size:
0:(2*pi - 0)/(360-1):2*pi
linspace
is just more convenient
For a simple real world application, see this answer where linspace
is helpful in creating a custom colour map
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