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All variables of all data types in MATLAB are multidimensional arrays. A vector is a one-dimensional array and a matrix is a two-dimensional array.
We have already discussed vectors and matrices. In this chapter, we will discuss multidimensional arrays. However, before that, let us discuss some special types of arrays.
Special Arrays in MATLAB
In this section, we will discuss some functions that create some special arrays. For all these functions, a single argument creates a square array, double arguments create rectangular array.
The zeros() function creates an array of all zeros −
For example −
zeros(5)
MATLAB will execute the above statement and return the following result −
ans =
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
The ones() function creates an array of all ones −
For example −
ones(4,3)
MATLAB will execute the above statement and return the following result −
ans =
1 1 1
1 1 1
1 1 1
1 1 1
The eye() function creates an identity matrix.
For example −
eye(4)
MATLAB will execute the above statement and return the following result −
ans =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
The rand() function creates an array of uniformly distributed random numbers on (0,1) −
For example −
rand(3, 5)
MATLAB will execute the above statement and return the following result −
ans = 0.8147 0.9134 0.2785 0.9649 0.9572 0.9058 0.6324 0.5469 0.1576 0.4854 0.1270 0.0975 0.9575 0.9706 0.8003
A Magic Square
A magic square is a square that produces the same sum, when its elements are added row-wise, column-wise or diagonally.
The magic() function creates a magic square array. It takes a singular argument that gives the size of the square. The argument must be a scalar greater than or equal to 3.
magic(4)
MATLAB will execute the above statement and return the following result −
ans = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
Multidimensional Arrays
An array having more than two dimensions is called a multidimensional array in MATLAB. Multidimensional arrays in MATLAB are an extension of the normal two-dimensional matrix.
Generally to generate a multidimensional array, we first create a two-dimensional array and extend it.
For example, let”s create a two-dimensional array a.
a = [7 9 5; 6 1 9; 4 3 2]
MATLAB will execute the above statement and return the following result −
a = 7 9 5 6 1 9 4 3 2
The array a is a 3-by-3 array; we can add a third dimension to a, by providing the values like −
a(:, :, 2)= [ 1 2 3; 4 5 6; 7 8 9]
MATLAB will execute the above statement and return the following result −
a = ans(:,:,1) = 0 0 0 0 0 0 0 0 0 ans(:,:,2) = 1 2 3 4 5 6 7 8 9
We can also create multidimensional arrays using the ones(), zeros() or the rand() functions.
For example,
b = rand(4,3,2)
MATLAB will execute the above statement and return the following result −
b(:,:,1) = 0.0344 0.7952 0.6463 0.4387 0.1869 0.7094 0.3816 0.4898 0.7547 0.7655 0.4456 0.2760 b(:,:,2) = 0.6797 0.4984 0.2238 0.6551 0.9597 0.7513 0.1626 0.3404 0.2551 0.1190 0.5853 0.5060
We can also use the cat() function to build multidimensional arrays. It concatenates a list of arrays along a specified dimension −
Syntax for the cat() function is −
B = cat(dim, A1, A2...)
Where,
-
B is the new array created
-
A1, A2, … are the arrays to be concatenated
-
dim is the dimension along which to concatenate the arrays
Example
Create a script file and type the following code into it −
a = [9 8 7; 6 5 4; 3 2 1]; b = [1 2 3; 4 5 6; 7 8 9]; c = cat(3, a, b, [ 2 3 1; 4 7 8; 3 9 0])
When you run the file, it displays −
c(:,:,1) =
9 8 7
6 5 4
3 2 1
c(:,:,2) =
1 2 3
4 5 6
7 8 9
c(:,:,3) =
2 3 1
4 7 8
3 9 0
Array Functions
MATLAB provides the following functions to sort, rotate, permute, reshape, or shift array contents.
| Function | Purpose |
|---|---|
| length | Length of vector or largest array dimension |
| ndims | Number of array dimensions |
| numel | Number of array elements |
| size | Array dimensions |
| iscolumn | Determines whether input is column vector |
| isempty | Determines whether array is empty |
| ismatrix | Determines whether input is matrix |
| isrow | Determines whether input is row vector |
| isscalar | Determines whether input is scalar |
| isvector | Determines whether input is vector |
| blkdiag | Constructs block diagonal matrix from input arguments |
| circshift | Shifts array circularly |
| ctranspose | Complex conjugate transpose |
| diag | Diagonal matrices and diagonals of matrix |
| flipdim | Flips array along specified dimension |
| fliplr | Flips matrix from left to right |
| flipud | Flips matrix up to down |
| ipermute | Inverses permute dimensions of N-D array |
| permute | Rearranges dimensions of N-D array |
| repmat | Replicates and tile array |
| reshape | Reshapes array |
| rot90 | Rotates matrix 90 degrees |
| shiftdim | Shifts dimensions |
| issorted | Determines whether set elements are in sorted order |
| sort | Sorts array elements in ascending or descending order |
| sortrows | Sorts rows in ascending order |
| squeeze | Removes singleton dimensions |
| transpose | Transpose |
| vectorize | Vectorizes expression |
Examples
The following examples illustrate some of the functions mentioned above.
Length, Dimension and Number of elements −
Create a script file and type the following code into it −
x = [7.1, 3.4, 7.2, 28/4, 3.6, 17, 9.4, 8.9]; length(x) % length of x vector y = rand(3, 4, 5, 2); ndims(y) % no of dimensions in array y s = [''Zara'', ''Nuha'', ''Shamim'', ''Riz'', ''Shadab'']; numel(s) % no of elements in s
When you run the file, it displays the following result −
ans = 8 ans = 4 ans = 23
Circular Shifting of the Array Elements −
Create a script file and type the following code into it −
a = [1 2 3; 4 5 6; 7 8 9] % the original array a
b = circshift(a,1) % circular shift first dimension values down by 1.
c = circshift(a,[1 -1]) % circular shift first dimension values % down by 1
% and second dimension values to the left % by 1.
When you run the file, it displays the following result −
a = 1 2 3 4 5 6 7 8 9 b = 7 8 9 1 2 3 4 5 6 c = 8 9 7 2 3 1 5 6 4
Sorting Arrays
Create a script file and type the following code into it −
v = [ 23 45 12 9 5 0 19 17] % horizontal vector sort(v) % sorting v m = [2 6 4; 5 3 9; 2 0 1] % two dimensional array sort(m, 1) % sorting m along the row sort(m, 2) % sorting m along the column
When you run the file, it displays the following result −
v = 23 45 12 9 5 0 19 17 ans = 0 5 9 12 17 19 23 45 m = 2 6 4 5 3 9 2 0 1 ans = 2 0 1 2 3 4 5 6 9 ans = 2 4 6 3 5 9 0 1 2
Cell Array
Cell arrays are arrays of indexed cells where each cell can store an array of a different dimensions and data types.
The cell function is used for creating a cell array. Syntax for the cell function is −
C = cell(dim) C = cell(dim1,...,dimN) D = cell(obj)
Where,
-
C is the cell array;
-
dim is a scalar integer or vector of integers that specifies the dimensions of cell array C;
-
dim1, … , dimN are scalar integers that specify the dimensions of C;
-
obj is One of the following −
- Java array or object
- .NET array of type System.String or System.Object
Example
Create a script file and type the following code into it −
c = cell(2, 5);
c = {''Red'', ''Blue'', ''Green'', ''Yellow'', ''White''; 1 2 3 4 5}
When you run the file, it displays the following result −
c =
{
[1,1] = Red
[2,1] = 1
[1,2] = Blue
[2,2] = 2
[1,3] = Green
[2,3] = 3
[1,4] = Yellow
[2,4] = 4
[1,5] = White
[2,5] = 5
}
Accessing Data in Cell Arrays
There are two ways to refer to the elements of a cell array −
- Enclosing the indices in first bracket (), to refer to sets of cells
- Enclosing the indices in braces {}, to refer to the data within individual cells
When you enclose the indices in first bracket, it refers to the set of cells.
Cell array indices in smooth parentheses refer to sets of cells.
For example −
c = {''Red'', ''Blue'', ''Green'', ''Yellow'', ''White''; 1 2 3 4 5};
c(1:2,1:2)
MATLAB will execute the above statement and return the following result −
ans =
{
[1,1] = Red
[2,1] = 1
[1,2] = Blue
[2,2] = 2
}
You can also access the contents of cells by indexing with curly braces.
For example −
c = {''Red'', ''Blue'', ''Green'', ''Yellow'', ''White''; 1 2 3 4 5};
c{1, 2:4}
MATLAB will execute the above statement and return the following result −
ans = Blue ans = Green ans = Yellow
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