Creating Arrays

This page introduces some commonly used methods to create arrays.

Catenation

Let us start with an example. Suppose you want to create a row vector a, which contains 1, 2 and 3. Then, you can use a = [1 2 3]. Here, two numbers are separated by a whitespace, so that they are catenated horizontally. Instead of a whitespace, you can also use a comma. For example, a = [1, 2, 3] gives the same row vector.

When two numbers are separated by a semicolon, they are catenated vertically to form a column vector. For example, b = [1; 2; 3] is a column vector of 3 numbers, and d = [1, 3; 2 4] is a $2\times 2$ array (two row vectors catenated vertically).

The catenation method is not limited to numbers, it also works for arrays. In the following example, the $2\times 2$ array c is obtained by vertically catenating a and b. Whereas, the row vector d is obtained by horizontally catenating a and b.

Input

a = [1, 3];
b = [2, 4];
c = [a; b]	% which gives a 2 x 2 array
d = [a b]		% which gives [1 3 2 4]

Output

c = 
 1.0000   3.0000
 2.0000   4.0000

d = 
 1.0000   3.0000   2.0000   4.0000

Be sure that the arrays to be catenated horizontally (vertically) have the same number of rows (columns). Otherwise, a size-mismatch error will be thrown:

Input

a = [1, 3]		% 2 columns
b = [2; 4]		% 1 columns
c = [a; b]		% size mismatch.

Output

a = 
 1.0000   3.0000

b = 
 2.0000
 4.0000

Error at Line 4(5). Dimension lengths mismatch.

More illustrative examples are shown below.

Input

[[], []]									% gives an empty array
[2 []]										% gives [2]
[[1 2 3 4]; [[5 6] 7 8]]	% Nested catenation works!

Output

ans =
 [] (double array)

ans = 
 2.0000

ans = 
 1.0000   2.0000   3.0000   4.0000
 5.0000   6.0000   7.0000   8.0000

Creating Vectors

The colon : operator and the function linspace are used frequently to create vectors.

The Colon Operator

Vectors of forms, such as $(1,2,3,\ldots,9,10)$ and $(1,3,5,\ldots,9,11)$, can be created using the colon : operator.

Input

1:10
1:2:11

Output

ans = 
Columns 1 through 7:
 1.0000   2.0000   3.0000   4.0000   5.0000   6.0000   7.0000
Columns 8 through 10:
 8.0000   9.0000   10.000

ans = 
 1.0000   3.0000   5.0000   7.0000   9.0000   11.000

This is how the colon operator : works. Assume that b is positive and a < c. The statement a:b:c starts with a and keeps adding b to it until the sum reaches the biggest number not exceeding c.

In the following example, the last number in the vector is 9, not 11, because $9 + 2 = 11$ exceeds 10.

Input

1:2:10

Output

ans = 
 1.0000   3.0000   5.0000   7.0000   9.0000

Assume that b is positive and a > c. The statement a:-b:c starts with a and keeps subtracting b from it until it is reaches the smallest number not smaller than c. For example, $(10,9,8,\ldots,2,1)$ can be obtained by

Input

10:-1:1

Output

ans = 
Columns 1 through 7:
 10.000   9.0000   8.0000   7.0000   6.0000   5.0000   4.0000
Columns 8 through 10:
 3.0000   2.0000   1.0000

The following vector excludes 1, because $4 - 2 = 2$ is smaller than 3.

Input

10:-2:3

Output

ans = 
 10.000   8.0000   6.0000   4.0000

The statement a:b:c gives an empty vector in the following cases:

• b > 0 and a > c
• b < 0 and a < c
• b == 0

For examples, each of the following gives an empty vector:

10:2:1
1:-1:10
1:0:10

linspace

We use linspace(a,b,N) to create a vector of N numbers ranging from a to b. If N is not specified, it returns a vector of 100 numbers.

Here are some examples:

Input

% A vector of 10 number in ascending order.
linspace(1,2,10)
% A vector of 11 numbers in descending order.
linspace(2,1,11)

Output

ans = 
Columns 1 through 7:
 1.0000   1.1111   1.2222   1.3333   1.4444   1.5556   1.6667
Columns 8 through 10:
 1.7778   1.8889   2.0000

ans = 
Columns 1 through 7:
 2.0000   1.9000   1.8000   1.7000   1.6000   1.5000   1.4000
Columns 8 through 11:
 1.3000   1.2000   1.1000   1.0000

More specifically, linspace(a,b,n) returns the vector $\begin{bmatrix}a&a+d&\cdots&a+(n-1)d\end{bmatrix}$, where for $n\geq 2$ the spacing $d$ is defined as

For more details, see the document page for linspace.

Constant Arrays

The following functions create constant arrays. For more details, see the respective document pages.

• ones: Array of ones.
• zeros: Array of zeros.
• eye: Identity matrix.
• true: Array of logical true values.
• false: Array of logical false values.
• inf: Array of $\infty$.
• nan: Array of nan.
• pi: Scalar approximating $\pi$.
• blanks: Array of white-spaces.

Random Arrays

The following functions create arrays of random numbers. For more details, see the respective document pages.

• randi: Array of positive random integers.
• rand: Array of uniformly distributed random numbers lying in the interval $[0,1]$.
• randn: Array of normally distributed random numbers.
• normrnd: Array of random numbers following the normal distribution of given mean and standard deviation.
• poissrnd: Array of random numbers following the Poisson distribution of a given mean.
• exprnd: Array of random numbers following the exponential distribution of a given mean.