## Comma-Separated Lists

### What Is a Comma-Separated List?

When you type in a series of numbers separated by commas, MATLAB^{®} creates a *comma-separated list* and returns each
value individually.

1,2,3

ans = 1 ans = 2 ans = 3

When used with large and more complex data structures like MATLAB structures and cell arrays, comma-separated lists can help simplify your code.

### Generating a Comma-Separated List

You can generate a comma-separated list from either a cell array or a MATLAB structure.

#### Generating a List from a Cell Array

When you extract multiple elements from a cell array, the result is a comma-separated list. Define a 4-by-6 cell array.

C = cell(4,6); for k = 1:24 C{k} = k*2; end C

C = 4×6 cell array {[2]} {[10]} {[18]} {[26]} {[34]} {[42]} {[4]} {[12]} {[20]} {[28]} {[36]} {[44]} {[6]} {[14]} {[22]} {[30]} {[38]} {[46]} {[8]} {[16]} {[24]} {[32]} {[40]} {[48]}

Extract the fifth column to generate a comma-separated list.

C{:,5}

ans = 34 ans = 36 ans = 38 ans = 40

This is the same as explicitly typing the list.

C{1,5},C{2,5},C{3,5},C{4,5}

#### Generating a List from a Structure

When you extract a field of a structure array across one of its dimensions, the result is a comma-separated list.

Start by converting the cell array used above into a 4-by-1 MATLAB structure with six fields: `f1`

through
`f6`

. Read field `f5`

for all rows, and
MATLAB returns a comma-separated list.

S = cell2struct(C,{'f1','f2','f3','f4','f5','f6'},2); S.f5

ans = 34 ans = 36 ans = 38 ans = 40

This is the same as explicitly typing the list.

S(1).f5,S(2).f5,S(3).f5,S(4).f5

### Assigning Output from a Comma-Separated List

You can assign any or all consecutive elements of a comma-separated list to
variables with a simple assignment statement. Define the cell array
`C`

and assign the first row to variables `c1`

through
`c6`

.

C = cell(4,6); for k = 1:24 C{k} = k*2; end [c1,c2,c3,c4,c5,c6] = C{1,1:6}; c5

c5 = 34

*N*outputs to those

*N*variables and ignores any remaining outputs. In this example, MATLAB assigns

`C{1,1:3}`

to the variables
`c1`

, `c2`

, and `c3`

and
ignores
`C{1,4:6}`

.[c1,c2,c3] = C{1,1:6};

S = cell2struct(C,{'f1','f2','f3','f4','f5','f6'},2); [sf1,sf2,sf3] = S.f5; sf3

sf3 = 38

`deal`

function for this
purpose.### Assigning to a Comma-Separated List

The simplest way to assign multiple values to a comma-separated list is to use the
`deal`

function. This function
distributes its input arguments to the elements of a comma-separated list.

This example uses `deal`

to overwrite each element in a
comma-separated list. First initialize a two-element list. This step is necessary
because you cannot use comma-separated list assignment with an undefined variable
when using `:`

as an index. See Comma-Separated List Assignment to an Undefined Variable for more
information.

c{1} = []; c{2} = []; c{:}

ans = [] ans = []

Use `deal`

to overwrite each element in the list.

[c{:}] = deal([10 20],[14 12]); c{:}

ans = 10 20 ans = 14 12

This example works in the same way, but with a comma-separated list of vectors in a structure field.

s(1).field1 = [[]]; s(2).field1 = [[]]; s.field1

ans = [] ans = []

Use `deal`

to overwrite the structure
fields.

[s.field1] = deal([10 20],[14 12]); s.field1

ans = 10 20 ans = 14 12

### How to Use Comma-Separated Lists

Common uses for comma-separated lists are:

These sections provide examples of using comma-separated lists with cell arrays. Each of these examples applies to structures as well.

#### Constructing Arrays

You can use a comma-separated list to enter a series of elements when
constructing a matrix or array. When you specify a list of elements with
`C{:,5}`

, MATLAB inserts the four individual elements.

C = cell(4,6); for k = 1:24 C{k} = k*2; end A = {'Hello',C{:,5},magic(4)}

A = 1×6 cell array {'Hello'} {[34]} {[36]} {[38]} {[40]} {4×4 double}

When you specify the `C`

cell itself, MATLAB inserts the entire cell array.

```
A = {'Hello',C,magic(4)}
```

A = 1×3 cell array {'Hello'} {4×6 cell} {4×4 double}

#### Displaying Arrays

Use a list to display all or part of a structure or cell array.

A{:}

ans = 'Hello' ans = 4×6 cell array {[2]} {[10]} {[18]} {[26]} {[34]} {[42]} {[4]} {[12]} {[20]} {[28]} {[36]} {[44]} {[6]} {[14]} {[22]} {[30]} {[38]} {[46]} {[8]} {[16]} {[24]} {[32]} {[40]} {[48]} ans = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1

#### Concatenation

Putting a comma-separated list inside square brackets extracts the specified elements from the list and concatenates them.

A = [C{:,5:6}]

A = 34 36 38 40 42 44 46 48

#### Function Call Arguments

When writing the code for a function call, you enter the input arguments as a list with each argument separated by a comma. If you have these arguments stored in a structure or cell array, then you can generate all or part of the argument list from the structure or cell array instead. This can be especially useful when passing in variable numbers of arguments.

This example passes several name-value arguments to the `plot`

function.

X = -pi:pi/10:pi; Y = tan(sin(X)) - sin(tan(X)); C = cell(2,3); C{1,1} = 'LineWidth'; C{2,1} = 2; C{1,2} = 'MarkerEdgeColor'; C{2,2} = 'k'; C{1,3} = 'MarkerFaceColor'; C{2,3} = 'g'; figure plot(X,Y,'--rs',C{:})

#### Function Return Values

MATLAB functions can also return more than one value to the caller. These values are returned in a list with each value separated by a comma. Instead of listing each return value, you can use a comma-separated list with a structure or cell array. This becomes more useful for functions that have variable numbers of return values.

This example returns three values to a cell array.

```
C = cell(1,3);
[C{:}] = fileparts('work/mytests/strArrays.mat')
```

C = 1×3 cell array {'work/mytests'} {'strArrays'} {'.mat'}

### Fast Fourier Transform Example

The `fftshift`

function swaps the left
and right halves of each dimension of an array. For the vector ```
[0 2 4 6 8
10]
```

, the output is `[6 8 10 0 2 4]`

. For a
multidimensional array, `fftshift`

performs this swap along each
dimension.

`fftshift`

uses vectors of indices to perform the swap. For the
vector shown above, the index `[1 2 3 4 5 6]`

is rearranged to form
a new index `[4 5 6 1 2 3]`

. The function then uses this index
vector to reposition the elements. For a multidimensional array,
`fftshift`

constructs an index vector for each dimension. A
comma-separated list makes this task much simpler.

Here is the `fftshift`

function.

function y = fftshift(x) numDims = ndims(x); idx = cell(1,numDims); for k = 1:numDims m = size(x,k); p = ceil(m/2); idx{k} = [p+1:m 1:p]; end y = x(idx{:}); end

The function stores the index vectors in cell array `idx`

.
Building this cell array is relatively simple. For each of the *N*
dimensions, determine the size of that dimension and find the integer index nearest
the midpoint. Then, construct a vector that swaps the two halves of that
dimension.

By using a cell array to store the index vectors and a comma-separated list for
the indexing operation, `fftshift`

shifts arrays of any dimension
using just a single operation: `y = x(idx{:})`

. If you use explicit
indexing, you need to write one `if`

statement for each dimension
you want the function to handle.

if ndims(x) == 1 y = x(index1); else if ndims(x) == 2 y = x(index1,index2); end end

Another way to handle this without a comma-separated list is to loop over each dimension, converting one dimension at a time and moving data each time. With a comma-separated list, you move the data just once. A comma-separated list makes it easy to generalize the swapping operation to any number of dimensions.

### Troubleshooting Operations with Comma-Separated Lists

Some common MATLAB operations and indexing techniques do not work directly on comma-separated lists. This section details several errors you can encounter when working with comma-separated lists and explains how to resolve the underlying issues.

#### Intermediate Indexing Produced a Comma-Separated List

Compound indexing expressions with braces or dots can produce comma-separated lists. You must index into the individual elements of the list to access them.

For example, create a 1-by-2 cell array that contains two 3-by-3 matrices of doubles.

A = {magic(3),rand(3)}

A = 1×2 cell array {3×3 double} {3×3 double}

Use brace indexing to display both elements.

A{1,:}

ans = 8 1 6 3 5 7 4 9 2 ans = 0.7922 0.0357 0.6787 0.9595 0.8491 0.7577 0.6557 0.9340 0.7431

Indexing into `A`

this way produces a comma-separated list
that includes both matrices contained by the cell array. You cannot use
parentheses indexing to retrieve the entries at `(1,2)`

in both
matrices in the list.

A{1,:}(1,2)

Intermediate brace '{}' indexing produced a comma-separated list with 2 values, but it must produce a single value when followed by subsequent indexing operations.

To retrieve the entries at `(1,2)`

in both of the matrices in
the cell array, index into the cells individually.

A{1,1}(1,2) A{1,2}(1,2)

ans = 1 ans = 0.0357

#### Expression Produced a Comma-Separated List Instead of a Single Value

Arguments for conditional statements, logical operators, loops, and
`switch`

statements cannot be comma-separated lists. For
example, you cannot directly loop through the contents of a comma-separated list
using a `for`

loop.

Create a cell array of the first three prime numbers.

A = cell(1,3); A{1} = 2; A{2} = 3; A{3} = 5;

`A{:}`

produces a comma-separated list of the three
values.

A{:}

ans = 2 ans = 3 ans = 5

Using `for`

to loop through the comma-separated list
generated by `A{:}`

errors.

for c = A{:} disp(c) end

A brace '{}' indexing expression produced a comma-separated list with 3 values where only a single value is allowed.

To loop over the contents of `A`

, enclose
`A{:}`

in square brackets to concatenate the values into a
vector.

for c = [A{:}] disp(c) end

2 3 5

#### Assigning Multiple Elements Using Simple Assignment

Unlike with arrays, using simple assignment to assign values to multiple elements of a comma-separated list errors. For example, define a 2-by-3 cell array.

B = cell(2,3);

Assigning a value of 5 to all cells of the array using `:`

as
an index for `B`

errors.

B{:} = 5

Assigning to 6 elements using a simple assignment statement is not supported. Consider using comma-separated list assignment.

One way to accomplish this assignment is to enclose `B{:}`

in
square brackets and use the `deal`

function.

[B{:}] = deal(5)

B = 2×3 cell array {[5]} {[5]} {[5]} {[5]} {[5]} {[5]}

#### Comma-Separated List Assignment to an Undefined Variable

You cannot assign a comma-separated list to an undefined variable using
`:`

as an index. In the example in Assigning to a Comma-Separated List, the variable `x`

is
defined as a comma-separated list with explicit indices before assigning new
values to it using `:`

as an index.

x{1} = []; x{2} = []; [x{:}] = deal([10 20],[14 12]); x{:}

ans = 10 20 ans = 14 12

Performing the same assignment with a variable that has not been initialized errors.

[y{:}] = deal([10 20],[14 12]);

Comma-separated list assignment to a nonexistent variable is not supported when any index is a colon (:). Use explicit indices or define the variable before performing the assignment.

To solve this problem, initialize `y`

in the same way as
`x`

, or create `y`

using enough explicit
indices to accommodate the number of values produced by the
`deal`

function.

[y{1:2}] = deal([10 20],[14 12])

y = 1×2 cell array {[10 20]} {[14 12]}