### 4.5 Logical Values

Octave has built-in support for logical values, i.e. variables that are either `true` or `false`. When comparing two variables, the result will be a logical value whose value depends on whether or not the comparison is true.

The basic logical operations are `&`, `|`, and `!`, that corresponds to “Logical And”, “Logical Or”, and “Logical Negation”. These operations all follow the rules of logic.

It is also possible to use logical values as part of standard numerical calculations. In this case `true` is converted to `1`, and `false` to 0, both represented using double precision floating point numbers. So, the result of `true*22 - false/6` is `22`.

Logical values can also be used to index matrices and cell arrays. When indexing with a logical array the result will be a vector containing the values corresponding to `true` parts of the logical array. The following example illustrates this.

         data = [ 1, 2; 3, 4 ];
         idx = (data <= 2);
         data(idx)
              => ans = [ 1; 4 ]

Instead of creating the `idx` array it is possible to replace `data(idx)` with `data( data <= 2 )` in the above code.

Besides when doing comparisons, logical values can be constructed by casting numeric objects to logical values, or by using the `true` or `false` functions.

— Function File: logical (arg)

> Convert arg to a logical value. For example,

>               logical ([-1, 0, 1])

> is equivalent to

>               [-1, 0, 1] != 0

— Built-in Function: true (x)
— Built-in Function: true (n, m)
— Built-in Function: true (n, m, k, ...)

> Return a matrix or N-dimensional array whose elements are all logical 1. The arguments are handled the same as the arguments for `eye`.

— Built-in Function: false (x)
— Built-in Function: false (n, m)
— Built-in Function: false (n, m, k, ...)

> Return a matrix or N-dimensional array whose elements are all logical 0. The arguments are handled the same as the arguments for `eye`.