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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 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.

— Function File: ind = sub2ind (dims, i, j)
— Function File: ind = sub2ind (dims, s1, s2, ..., sN)

> Convert subscripts into a linear index.

> The following example shows how to convert the two-dimensional index `(2,3)` of a 3-by-3 matrix to a linear index. The matrix is linearly indexed moving from one column to next, filling up all rows in each column.

>               linear_index = sub2ind ([3, 3], 2, 3)
>                8

> See also: ind2sub.

— Function File: [s1, s2, ..., sN] = ind2sub (dims, ind)

> Convert a linear index into subscripts.

> The following example shows how to convert the linear index `8` in a 3-by-3 matrix into a subscript. The matrix is linearly indexed moving from one column to next, filling up all rows in each column.

>               [r, c] = ind2sub ([3, 3], 8)
>                r =  2
>               c =  3

> See also: sub2ind.