NSCS 344, Week 4: Matlab Concepts

Table of Contents

Indexing several elements of a vector Concatenating vectors

Indexing several elements of a vector

Sometimes we would like to get several elements of a vector or matrix at once. For example, if I have the vector

V = [8 84 21 3 0];

I might want the 2nd and 4th element for some reason. To do this I can us a vector as an index to the vector, like this

V([2 4])
ans = 1×2
    84     3

Another example is if I want the first 3 elements of the vector. I could refer to these like this ...

V([1 2 3])
ans = 1×3
     8    84    21

Or equally, using colon notation, like this

V(1:3)
ans = 1×3
     8    84    21

This latter notation makes things really easy if I have lots of elements in my vector and want to refer to (say) a subset of 100 of them.

Concatenating vectors

Sometimes I would like to stick two vectors together end-to-end. For example

V1 = [1 2 3];
V2 = [4 5 6];

I could stick them together like this ....

V = [V1 V2]
V = 1×6
     1     2     3     4     5     6

This is called horizontal concatenation, because we are concatentating the vectors in the horizonatal direction. Another way to do this is with the horzcat function

V = horzcat(V1, V2)
V = 1×6
     1     2     3     4     5     6

But, this isn't the only way I could stick these two vectors together. Instead of concatenating them end-to-end, I could stick one vector on top of the other to make a matrix. That is I could concatenate them vertically

vertcat(V1, V2)
ans = 2×3
     1     2     3
     4     5     6

Another way of saying the same thing is like this

[V1; V2]
ans = 2×3
     1     2     3
     4     5     6

[V1;
    V2]
ans = 2×3
     1     2     3
     4     5     6

Finally, if I want to concatenate along a generate dimension, I can use the cat function. For example, horizontal concatenation is concatenating along the second dimension (because it makes more columns, which come second by convention)

cat(2, V1, V2)
ans = 1×6
     1     2     3     4     5     6

Vertical concatenation is concatenating along the first dimension (because it makes more rows, which come first by convention)

cat(1, V1, V2)
ans = 2×3
     1     2     3
     4     5     6

Concatenating in the third dimension makes a tensor

cat(3, V1, V2)
ans = 
ans(:,:,1) =

     1     2     3


ans(:,:,2) =

     4     5     6

Although you'd be unlikely to do this with vectors. Instead you're more likely to concatenate matrices in the 3rd dimension ...

M1 = [1 2 3; 
    4 5 6];
M2 = [8 9 10;
    11 12 13];
cat(3, M1, M2)
ans = 
ans(:,:,1) =

     1     2     3
     4     5     6


ans(:,:,2) =

     8     9    10
    11    12    13

Note that you can also concatenate matrices horizontally and vertically ...

[M1 M2]
ans = 2×6
     1     2     3     8     9    10
     4     5     6    11    12    13
[M1; M2]
ans = 4×3
     1     2     3
     4     5     6
     8     9    10
    11    12    13