A range is a convenient way to write a row vector with evenly spaced elements. A range expression is defined by the value of the first element in the range, an optional value for the increment between elements, and a maximum value which the elements of the range will not exceed. The base, increment, and limit are separated by colons (the ‘:’ character) and may contain any arithmetic expressions and function calls. If the increment is omitted, it is assumed to be 1. For example, the range
1 : 5
defines the set of values ‘[ 1, 2, 3, 4, 5 ]’, and the range
1 : 3 : 5
defines the set of values ‘[ 1, 4 ]’.
Although a range constant specifies a row vector, Octave does not convert range constants to vectors unless it is necessary to do so. This allows you to write a constant like ‘1 : 10000’ without using 80,000 bytes of storage on a typical 32-bit workstation.
A common example of when it does become necessary to convert ranges into vectors occurs when they appear within a vector (i.e., inside square brackets). For instance, whereas
x = 0 : 0.1 : 1;
defines x to be a variable of type
range and occupies 24
bytes of memory, the expression
y = [ 0 : 0.1 : 1];
defines y to be of type
matrix and occupies 88 bytes of
Note that the upper (or lower, if the increment is negative) bound on
the range is not always included in the set of values, and that ranges
defined by floating point values can produce surprising results because
Octave uses floating point arithmetic to compute the values in the
range. If it is important to include the endpoints of a range and the
number of elements is known, you should use the
instead (see Special Utility Matrices).
When adding a scalar to a range, subtracting a scalar from it (or subtracting a range from a scalar) and multiplying by scalar, Octave will attempt to avoid unpacking the range and keep the result as a range, too, if it can determine that it is safe to do so. For instance, doing
a = 2*(1:1e7) - 1;
will produce the same result as ‘1:2:2e7-1’, but without ever forming a vector with ten million elements.
Using zero as an increment in the colon notation, as ‘1:0:1’ is not allowed, because a division by zero would occur in determining the number of range elements. However, ranges with zero increment (i.e., all elements equal) are useful, especially in indexing, and Octave allows them to be constructed using the built-in function ones. Note that because a range must be a row vector, ‘ones (1, 10)’ produces a range, while ‘ones (10, 1)’ does not.
When Octave parses a range expression, it examines the elements of the expression to determine whether they are all constants. If they are, it replaces the range expression with a single range constant.