GNU Octave - Index Expressions

GNU Octave Manual Version 3
by John W. Eaton, David Bateman, Søren Hauberg
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8.1 Index Expressions

An index expression allows you to reference or extract selected elements of a matrix or vector.

Indices may be scalars, vectors, ranges, or the special operator ‘:’, which may be used to select entire rows or columns.

Vectors are indexed using a single index expression. Matrices may be indexed using one or two indices. When using a single index expression, the elements of the matrix are taken in column-first order; the dimensions of the output match those of the index expression. For example,

a (2)       # a scalar
a (1:2)     # a row vector
a ([1; 2])  # a column vector

As a special case, when a colon is used as a single index, the output is a column vector containing all the elements of the vector or matrix. For example

a (:)       # a column vector

Given the matrix

a = [1, 2; 3, 4]

all of the following expressions are equivalent

a (1, [1, 2])
a (1, 1:2)
a (1, :)

and select the first row of the matrix.

Indexing a scalar with a vector of ones can be used to create a vector the same size as the index vector, with each element equal to the value of the original scalar. For example, the following statements

a = 13;
a ([1, 1, 1, 1])

produce a vector whose four elements are all equal to 13.

Similarly, indexing a scalar with two vectors of ones can be used to create a matrix. For example the following statements

a = 13;
a ([1, 1], [1, 1, 1])

create a 2 by 3 matrix with all elements equal to 13.

This is an obscure notation and should be avoided. It is better to use the function ones to generate a matrix of the appropriate size whose elements are all one, and then to scale it to produce the desired result. See section 16.4 Special Utility Matrices.

It is also possible to create a matrix with different values. The following example creates a 10 dimensional row vector a containing the values a(i) = sqrt(i).

for i = 1:10
  a(i) = sqrt (i);
endfor

Note that it is quite inefficient to create a vector using a loop like the one shown in the example above. In this particular case, it would have been much more efficient to use the expression

a = sqrt (1:10);

thus avoiding the loop entirely. In cases where a loop is still required, or a number of values must be combined to form a larger matrix, it is generally much faster to set the size of the matrix first, and then insert elements using indexing commands. For example, given a matrix a,

[nr, nc] = size (a);
x = zeros (nr, n * nc);
for i = 1:n
  x(:,(i-1)*nc+1:i*nc) = a;
endfor

is considerably faster than

x = a;
for i = 1:n-1
  x = [x, a];
endfor

particularly for large matrices because Octave does not have to repeatedly resize the result.

Built-in Function: subsref (val, idx)

Perform the subscripted element selection operation according to the subscript specified by idx.

The subscript idx is expected to be a structure array with fields ‘type’ and ‘subs’. Valid values for ‘type’ are ‘"()"’, ‘"{}"’, and ‘"."’. The ‘subs’ field may be either ‘":"’ or a cell array of index values.

The following example shows how to extract the two first columns of a matrix

val = magic(3)
     => val = [ 8   1   6
                3   5   7
                4   9   2 ]
idx.type = "()";
idx.subs = {":", 1:2};
subsref(val, idx)
     => [ 8   1 
          3   5 
          4   9 ]

Note that this is the same as writing val(:,1:2).