matlab cell arrays greg reese, ph.d research computing support group academic technology services...

MATLAB

Cell Arrays

Greg Reese, Ph.D

Research Computing Support Group

Academic Technology Services

Miami University

MATLAB

Cell Arrays

© 2011 Greg Reese. All rights reserved

'Romeo, Romeo' 3.1415

99@my_function()

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Cell Arrays - definition

A MATLAB cell array is an array of cells. A cell can hold any data type, and data types within a cell array can differ

1 0 0

0 1 0

0 0 1

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Cell Arrays - creation

For specified content, create same way as arrays but use (curly) braces

Example>> a = { i 5:-1:2 'carrots'; magic(2) 77 NaN }

a =

[0 + 1.0000i] [1x4 double] 'carrots'

[2x2 double] [ 77] [ NaN]

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Cell Arrays - creation

Create empty cell array with cell() function

a = cell( rows, columns )

Example>> a = cell( 3, 6 )

a =

[] [] [] [] [] []

[] [] [] [] [] []

[] [] [] [] [] []>> whos a

Name Size Bytes Class

a 3x6 72 cell

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Cell Arrays - display

Various ways to display cell array. One is to type variable name with no trailing semicolon. This shows top level of array only

Example>> a = { 'AAA' 2 { {1 2; 3 4} } };

>> a

a =

'AAA' [2] {1x1 cell}

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Cell Arrays - displaycelldisp() recursively displays cell array, i.e., if content a cell array, also displays its content

Example>> a = { 'AAA' 2 { {1 2; 3 4} } };

>> celldisp( a )

a{1} = AAA

a{2} = 2

a{3}{1}{1,1} = 1

a{3}{1}{2,1} = 3

a{3}{1}{1,2} = 2

a{3}{1}{2,2} = 4

cell within cell

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Cell Arrays - display

cellplot() displays in figure window drawing of 1D or 2D cell array

Example>> a = { 'AAA' 2 { {1 2; 3 4} } };

>> cellplot( a )

AAA 2

1 2

3 4

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Cell Arrays - indexing

Two types of indexing into a cell array

•Cell indexing - access groups of cells but not their content

•Content indexing - access single cell's content

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Cell indexing

•Done by using parentheses around subscript, e.g., a(5), b(3:6,:), c(2,9)

•Can access one or more cells

•Cannot access content of cells

Use cell indexing if you want to manipulate cells of an array, regardless of what is inside them

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To delete elements of a cell array, use cell indexing ()

Examples >> a = { 'r1c1' 'r1c2' 3; [1 2; 3 4] 1:4 'The End' }

a = 'r1c1' 'r1c2' [ 3]

[2x2 double] [1x4 double] 'The End'

>> a(:,2) = [] % delete second column

a = 'r1c1' [ 3]

[2x2 double] 'The End'

>> a(2,:) = [] % delete second row

a = 'r1c1' [3]

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Content indexing

•Done by using (curly) braces around subject, e.g., a{5}, b{2,9}

•Lets you access what's inside a single cell

•Can only use on one cell at a time (sort of - will discuss this later)

Use content indexing if you want to get inside cell

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Principal rules

•Indexing a cell(s) with () always produces cells

•Indexing a cell with {} produces a data type of whatever is inside the indexed cell

– Result of {} indexing is a cell only if content is a cell

•If have cells indexed with () on left side of =, must have array of cells of same size on right side

•If array on left not subscripted, can use () or {} on right

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Examples - follow along>> a = { 'AAA' 2 { {1 2; 3 4} } }

a = 'AAA' [2] {1x1 cell}

>> whos a

Name Size Bytes Class Attributes

a 1x3 526 cell

Even though a is a cell array, output from first line is showing content of array's cells

– 'AAA' means that the content of cell 1 of a is a character array with three elements

– [2] means that the content of cell 2 of a is a numerical array with one element (the number 2)

– {1x1 cell} means that the content of cell 3 of a is a cell array with one cell

"Attributes" column always empty for these slides so will omit from now on

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Examples - follow alongFrom beforea = 'AAA' [2] {1x1 cell}

>> z = a(1)

z = 'AAA'

>> whos z


z 1x1 66 cell

>> z = a{1}

z = AAA

>> whos z


z 1x3 6 char

Why?

Why?

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Examples - follow along>> z = a(2)

z = [2]

>> whos z


z 1x1 68 cell

>> z = a{2}

z = 2

>> whos z


z 1x1 8 double

Why?

Why?

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Examples - follow along>> z = a(3)

z = {1x1 cell}

>> whos z


z 1x1 392 cell

>> z = a{3}

z = {2x2 cell}

>> whos z


z 1x1 332 cell

Why?

Why?

This means a cell containing a 1x1 cell

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Examples - follow along>> bb = { 'B' 6:9 }

bb = 'B' [1x4 double]

>> b = bb;

>> whos b


b 1x2 154 cell

>> b(1) = 6

??? Conversion to cell from double is not possible.

>> b(1) = 'Hello'

??? Conversion to cell from char is not possible.

>> b(1) = a

??? In an assignment A(:) = B, the number of elements in A and B must be the same.

Why?

Why?

Why?

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Examples - follow alonga = 'AAA' [2] {1x1 cell}

>> b(1) = a(1)

b = 'AAA' [1x4 double]

>> b(1) = a{1}

??? Conversion to cell from char is not possible.

>> b(1) = a(2)

b = [2] [1x4 double]

>> b(1)= a{2}

??? Conversion to cell from double is not possible.

>> b(1) = a(3)

b = {1x1 cell} [1x4 double]

>> b(1) = a{3}


Why?

Why?

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Examples - follow along

Store into single, content-indexed cell>> a

a = 'AAA' [2] {1x1 cell}

>> b = bb

b = 'B' [1x4 double]

>> b{1} = a(1)


>> b{1} = a{1}

b = 'AAA' [1x4 double]

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Examples - follow alonga = 'AAA' [2] {1x1 cell}

b = 'B' [1x4 double]

>> b{1} = a(2)


>> b{1} = a{2}

b = [2] [1x4 double]

>> b{1} = a(3)


>> b{1} = a{3}


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Tricky case - content indexing of multiple cells

•MATLAB says you can't do it

•Really means that you can do it but under many circumstances, content of all but first cell disappear

•For more information, see "comma-separated list" in MATLAB help

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Accessing a range of cells with content indexing (curly braces) produces a comma-separated list. If there are n elements in the range, there will be n members of the list and these will be assigned in order to the output variables. If there aren't enough output variables, MATLAB ignores remaining list membersdata{4:7} → data{4} data{5} data{6} data{7}[ a b c ] = data{4:7} same as

[ a b c ] = data{4} data{5} data{6} data{7}

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a = 'AAA' [2] {1x1 cell}

>> clear x

>> x = a{1:3}

x = AAA

>> whos x


x 1x3 6 char

>> x = a{2:3}

x = 2

>> whos x


x 1x1 8 double

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>> clear x y

>> [ x y ] = a{1:3}

x = AAA

y = 2

>> whos x y


x 1x3 6 char

y 1x1 8 double

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>> clear x y z

>> [ x y z ] = a{1:3}

x = AAA

y = 2

z = {2x2 cell}

>> whos x y z


x 1x3 6 char

y 1x1 8 double

z 1x1 332 cell

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TipAvoid specifying more than one cell when content indexing

a{1:4,:}

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Content of a cell-array element is often a (numerical) array. You can access multiple array elements of a single element in a cell array.

a{m,n}(r1:r2,c1:c2)

returns an array made up of rows r1 through r2 and columns c1 through c2 of the element at row m and column n of the cell array a

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Examples >> c = { 'CC' 7; [1 2; 3 4] [0+i 1+0i] }

c = 'CC' [ 7]

[2x2 double] [1x2 double]

>> c{2,1}(2,2)

ans = 4

>> c{2,1}(:,2)

ans = 2

4

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Examples >> c{2,1}(:,:)

ans = 1 2

3 4

>> c{2,1}(:)

ans = 1

3

2

4

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Cell Arrays - numbers

MATLAB functions that use numbers in computations seldom work on numbers that are in cells.

Example>> c = { 1 3 5 7 }

c = [1] [3] [5] [7]

>> mean(c)

??? Undefined function or method 'sum' for input arguments of type 'cell'.

Error in ==> mean at 28

y = sum(x)/size(x,dim);

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However, for convenience, numbers may appear in cells. To convert a cell array of numbers to a numerical array, use:

n = cell2mat( c )•c is a cell array with only numbers•n is a numerical (double) array

– If elements of c are all scalars*, n has same dimensions as c

* The elements can also be matrices. See MATLAB help on cell2mat() for details

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Example>> c = { 1 3 5 7 }

c = [1] [3] [5] [7]

>> mean(c)




>> cNum = cell2mat( c )

cNum = 1 3 5 7

>> mean( cNum )

ans = 4

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To convert an array of numbers to a cell array, use:

c = num2cell( A )•A is a numerical array•c is a cell array of same dimension as A

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Example>> a = magic( 3 )

a = 8 1 6

3 5 7

4 9 2

>> c = num2cell( a )

c = [8] [1] [6]

[3] [5] [7]

[4] [9] [2]

Try ItSuppose you are given the names and ages of three guys in two arrays, like this:>> names = { 'John' 'Joe' 'Jeff' }

names = 'John' 'Joe' 'Jeff'

>> ages = { 40 45 50 }

ages = [40] [45] [50]

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Try ItFind the mean age>> nAges = cell2mat( ages )

nAges = 40 45 50

>> mean( nAges )

ans = 45

or all at once:

>> mean( cell2mat( ages ) )

ans = 45

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Try ItStore all data in one cell array with the first column containing the names and the second the ages

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Try It>> ages = [ 40 45 50 ]

ages = 40 45 50

>> cAges = num2cell( ages )'

cAges = [40]

[45]

[50]

>> guys = cell( 3, 2 )

guys = [] []

[] []

[] []39


Try It>> guys(:,1) = names'

guys = 'John' []

'Joe' []

'Jeff' []

>> guys(:,2) = cAges

guys = 'John' [40]

'Joe' [45]

'Jeff' [50]

Can do this a little more easily by concatenating the two cell arrays. See MATLAB help 40


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Cell Arrays - functions on

Some MATLAB functions will take a cell array as input, e.g., cell2mat(), isvector(), and deal(). Others, such as mean(), eval(), and not(), won't. If one of the latter functions can accept the content of the elements of the cell array as input, we can process those cells with the MATLAB function cellfun()

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Even if a function can take a cell array as an input, we may want to apply a function that can accept cell-array arguments to the content of a cell array, not to the array itself

ExampleFind the length of each word in a string array>> c = { 'a' 'bb' 'cccc' }

c = 'a' 'bb' 'cccc'

>> length(c)

ans = 3 length of cell array c, not lengths of content (1, 2, 4)

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The MATLAB function cellfun() applies a specified function to the content of every element of a cell array

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We'll use a basic version of cellfun, namely,

A = cellfun( fun, C )•C is a cell array•fun is a function that takes exactly one input value and produces exactly one, scalar output

– fun must be able to accept the type of input in the cells of C, e.g., character array, numerical array, etc.

•A is an array of same dimension as C

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A = cellfun( fun, C )

To specify the function, use the at-sign @ followed by the function name without parentheses. (This is called a function handle)

Examples– If C is a cell array of strings, cellfun( @length, c ) finds the length of each of the strings in the array

– If C is a cell array of strings, cellfun( @isempty, c ) tells whether or not each cell in the array is empty

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ExampleFind the means of four data sets:>> data = { 1 [0 2 4] [ -1 0 1] randn(1,1000) }

data = [1] [1x3 double] [1x3 double] [1x1000 double]

>> mean( data )




>> dataMeans = cellfun( @mean, data )

dataMeans = 1.0000 2.0000 0 -0.0326

>> whos data dataMeans


data 1x4 8296 cell

dataMeans 1x4 32 double

mean() doesn't accept cell arrays as input, but contents of each array is okay because those are numerical arrays

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tf = isempty( C )

isempty() is a useful function which returns 1 (true) if its input array is empty and 0 (false) if the array is not empty. (An empty array is one that has at least one dimension of size zero, e.g., 0x0, 0x5, 3x7x0 )

Try ItMake a cell array of four cells whose contents are 'a', 'bb', empty ( {} ), and 'ccc'. Determine if the array is empty and if each cell is empty>> c = { 'a' 'bb' {} 'cccc' }

c = 'a' 'bb' {} 'cccc'

>> isempty( c )

ans = 0

>> cellfun( @isempty, c )

ans = 0 0 1 0 49


Try ItUse the previous array and find the length of the array and the number of characters in each string in the array

>> length( c )

ans = 4

>> cellfun( @length, c )

ans = 1 2 0 4

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It's common to want to know if any element of a cell array meets a certain condition. Do this with the MATLAB function:

B = any( A )•A is a numerical vector (not a cell array)•B is a scalar that is 1 if any element of A is not zero and 0 otherwise, i.e., if all elements of A are zero

any() also works on matrices. See MATLAB help for details

Try ItUse the previous array and determine if any of the strings have at least one character>> lengths = cellfun( @length, c )

lengths = 1 2 0 4

>> any( lengths )

ans = 1

>> any( cellfun( @length, c ) )

ans = 152


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It's also common to want to know if all elements of a cell array meet a certain condition. Do this with the MATLAB function:

B = all( A )•A is a numerical vector (not a cell array)•B is a scalar that is 1 if all elements of A are not zero and 0 otherwise, i.e., if at least one element of A is zero

all() also works on matrices. See MATLAB help for details

Try ItUse the previous array and determine if all of the strings have at least one character>> lengths = cellfun( @length, c )

lengths = 1 2 0 4

>> all( lengths )

ans = 0

>> all( cellfun( @length, c ) )

ans = 054


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Cell Arrays - finding

Often it's useful to know which cells in a cell array meet a certain condition. One way to find out is with the MATLAB function:

indexes = find( A )•A is a numerical vector (not a cell array)•indexes is a vector of the indexes of the cells whose content is not 0

– If no such cells, indexes is empty

•find() also works on matrices. See MATLAB help for details

Try ItUse the previous array and find the indexes of all empty cells>> c = { 'a' 'bb' {} 'cccc' }

c = 'a' 'bb' {} 'cccc'

>> empty = cellfun( @isempty, c )

empty = 0 0 1 0

>> indexes = find( empty )

indexes = 3

>> c{3}

ans = {}

Often just do it all at once>> indexes = find( cellfun( @isempty, c ) )

indexes = 356


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Can also use find() to determine if any of the cell array members meet a criterion and if so, how many meet it:

•Length of returned index vector is number of cells meeting criterion

– If length is zero or returned vector is empty (same thing), no cells meet criterion

Try ItUse the previous array and find() to determine how many empty cells are in the array>> length( find( cellfun( @isempty, c ) ) )

ans = 1

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Cell Arrays

Questions?

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The End

matlab cell arrays greg reese, ph.d research computing support group academic technology services...

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