Question

I came across some MATLAB syntax with a colon that I don’t fully understand.

First Question:

The expression: 0:pi/4:pi
results in the answer: 0 0.7854 1.5708 2.3562 3.1416

Why is this the case? I thought that colon operator is used as a quick way to refer to indices so that we don’t have to write out the full list. (e.g. 1:3 -> 1 2 3)

Second Question:

Similar to above, say if I have a matrix X = [1 2 3 4 5 6 7 8 9]. How can I interpret the expression X(:,1:3)? Specifically, what does the colon operator without the left and right numbers mean?

Answer 1

Actually a:b generates a vector. You could use it as index only because the (...) accepts a list also, e.g.

octave-3.0.3:10> a = [1,4,7]
a =

   1   4   7

octave-3.0.3:11> b = [1,4,9,16,25,36,49]
b =

    1    4    9   16   25   36   49

octave-3.0.3:12> b(a)    # gets [b(1), b(4), b(7)]
ans =

    1   16   49

Now, the a:b:c syntax is equivalent to [a, a+b, a+2*b, ...] until c, e.g.

octave-3.0.3:15> 4:7:50
ans =

   4  11  18  25  32  39  46

which explains what you get in 0:pi/4:pi.

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A lone : selects the whole axes (row/column), e.g.

octave-3.0.3:16> a = [1,2,3;4,5,6;7,8,9]
a =

   1   2   3
   4   5   6
   7   8   9

octave-3.0.3:17> a(:,1)   # means a(1:3, 1)
ans =

   1
   4
   7

octave-3.0.3:18> a(1,:)   # means a(1, 1:3)
ans =

   1   2   3

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See the official MATLAB doc on colon (:) for detail.