Vector creation, array subscripting, and `for`

-loop
iteration

The colon is one of the most useful operators in MATLAB^{®}.
It can create vectors, subscript arrays, and specify `for`

iterations.

x = j:k x = j:i:k A(:,n) A(m,:) A(:) A(j:k)

creates
a regularly-spaced vector `x`

= `j`

:`i`

:`k`

`x`

using `i`

as
the increment between elements. The vector elements are roughly equal
to `[j,j+i,j+2*i,...,j+m*i]`

where `m = fix((k-j)/i)`

.
However, if `i`

is not an integer, then floating
point arithmetic plays a role in determining whether `colon`

includes
the endpoint `k`

in the vector, since `k`

might
not be *exactly* equal to `j+m*i`

.
If you specify nonscalar arrays, then MATLAB interprets `j:i:k`

as `j(1):i(1):k(1)`

.

`x = colon(j,k)`

and `x = colon(j,i,k)`

are
alternate ways to execute the commands `j:k`

and `j:i:k`

,
but are rarely used. These syntaxes enable operator overloading for
classes.

`A(:,n)`

, `A(m,:)`

, `A(:)`

,
and `A(j:k)`

are common indexing expressions for
a matrix `A`

that contain a colon. When you use a
colon as a subscript in an indexing expression, such as `A(:,n)`

,
it acts as shorthand to include *all* subscripts
in a particular array dimension. It is also common to create a vector
with a colon for the purposes of indexing, such as `A(j:k)`

.
Some indexing expressions combine both uses of the colon, as in `A(:,j:k)`

.

Common indexing expressions that contain a colon are:

`A(:,n)`

is the`n`

th column of matrix`A`

.`A(m,:)`

is the`m`

th row of matrix`A`

.`A(:,:,p)`

is the`p`

th page of three-dimensional array`A`

.`A(:)`

reshapes all elements of`A`

into a single column vector. This has no effect if`A`

is already a column vector.`A(:,:)`

reshapes all elements of`A`

into a two-dimensional matrix. This has no effect if`A`

is already a matrix or vector.`A(j:k)`

uses the vector`j:k`

to index into`A`

and is therefore equivalent to the vector`[A(j), A(j+1), ..., A(k)]`

.`A(:,j:k)`

includes all subscripts in the first dimension but uses the vector`j:k`

to index in the second dimension. This returns a matrix with columns`[A(:,j), A(:,j+1), ..., A(:,k)]`

.

The

`for`

reference page has a description of how to use`:`

in the context of loop statements.`linspace`

is similar to the colon operator`:`

, but it gives direct control over the number of points and always includes the endpoints. The sibling function`logspace`

generates logarithmically spaced values.When you create a vector to index into a cell array or structure array (such as

or{:}`cellName`

), MATLAB returns multiple outputs in a comma-separated list. For more information, see How to Use the Comma-Separated Lists.(:).`structName`

`fieldName`