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Matlab Array - Indexing

Matlab ArrayCompleted

Matlab Array - Indexing

MATLAB’s array structure is well suited to accessing, modifying, and extending elements. There are three indexing modes: Position Indexing, Linear Indexing, and Logical Indexing.

  • Compared with Python, MATLAB arrays are also mutable objects.

Position Indexing

Syntax: A(ind_1,...,ind_n)

  • n equals the number of dimensions of the array
  • Each ind_i indexes the corresponding dimension
    • Can be a scalar or a vector
    • Or the operator :
      • Acts like a Python Slice
        • A bare : selects all elements along that dimension
      • Adds a special end keyword
    • Must lie within the valid range for that dimension
  • Effectively, each ind_i is an index array; the result is the array of A’s elements at those indices, arranged in the same relative positions

Example:

>> A = rand(3,3,3)
A(:,:,1) =
    0.8147    0.9134    0.2785
    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575
A(:,:,2) =
    0.9649    0.9572    0.1419
    0.1576    0.4854    0.4218
    0.9706    0.8003    0.9157
A(:,:,3) =
    0.7922    0.0357    0.6787
    0.9595    0.8491    0.7577
    0.6557    0.9340    0.7431
>> A(1,2,3)
ans =
    0.0357
>> A(1,1,[1 3])  
ans(:,:,1) =
    0.8147
ans(:,:,2) =
    0.7922
>> A(1,[1,3],1)      
ans =
    0.8147    0.2785
>> A(:,1,1)
ans =
    0.8147
    0.9058
    0.1270
>> A(1,1:2,1)
ans =
    0.8147    0.9134
>> A(1,1:3:2,1)
ans =
    0.8147
>> A(1,2:end,1)     
ans =
    0.9134    0.2785

Linear Indexing

Linear indexing is also positional, but it applies when fewer indices than dimensions are passed: the remaining dimensions are flattened into a single dimension.

In particular, a single index can reach every element.

  • While MATLAB displays arrays according to their defined sizes and shapes, they are actually stored in memory as a single column of elements.

The flattening order, illustrated for a 2-2-2-… array, is:

  1. 1-1-1-…
  2. 2-1-1-…
  3. 1-2-1-…
  4. 2-2-1-…
  5. 1-1-2-…
  6. 2-1-2-…
  7. 1-2-2-…
  8. 2-2-2-…

For matrices in particular, this is “column-major order”.

Example 1:

>> B = rand(1,1,2,2,2) 
B(:,:,1,1,1) =
    0.3500
B(:,:,2,1,1) =
    0.1966
B(:,:,1,2,1) =
    0.2511
B(:,:,2,2,1) =
    0.6160
B(:,:,1,1,2) =
    0.4733
B(:,:,2,1,2) =
    0.3517
B(:,:,1,2,2) =
    0.8308
B(:,:,2,2,2) =
    0.5853
>> C=B(1,:)   
C =
    0.3500    0.1966    0.2511    0.6160    0.4733    0.3517    0.8308    0.5853

Example 2:

>> A = rand(3,3,3)
A(:,:,1) =
    0.8147    0.9134    0.2785
    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575
A(:,:,2) =
    0.9649    0.9572    0.1419
    0.1576    0.4854    0.4218
    0.9706    0.8003    0.9157
A(:,:,3) =
    0.7922    0.0357    0.6787
    0.9595    0.8491    0.7577
    0.6557    0.9340    0.7431
>> A(4)  
ans =
    0.9134
>> A(10)
ans =
    0.9649

Logical Indexing

A conditional expression returns a logical array of the same size as the original; conversely, any logical array of matching size can be used as a logical index into the array.

Example:

>> A = rand(3)
A =
    0.5497    0.7572    0.5678
    0.9172    0.7537    0.0759
    0.2858    0.3804    0.0540
>> ind = A > 0.5
ind =
  3x3 logical array
   1   1   1
   1   1   0
   0   0   0
>> A(ind) = nan
A =
       NaN       NaN       NaN
       NaN       NaN    0.0759
    0.2858    0.3804    0.0540

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