randn

Normally distributed random numbers

Syntax

• X = randn
  example
• X = randn(n)
  example
• X = randn(sz1,...,szN)
  example
• X = randn(sz)
  example

• X = randn(___,typename)
  example
• X = randn(___,'like',p)
  example

Description

X = randn returns a random scalar drawn from the standard normal distribution.

X = randn(n) returns an n-by-n matrix of normally distributed random numbers.

X = randn(sz1,...,szN) returns an sz1-by-...-by-szN array of random numbers where sz1,...,szN indicate the size of each dimension. For example, randn(3,4) returns a 3-by-4 matrix.

X = randn(sz) returns an array of random numbers where size vector sz defines size(X). For example, randn([3 4]) returns a 3-by-4 matrix.

X = randn(___,typename) returns an array of random numbers of data type typename. The typename input can be either 'single' or 'double'. You can use any of the input arguments in the previous syntaxes.

X = randn(___,'like',p) returns an array of random numbers like p; that is, of the same object type as p. You can specify either typename or 'like', but not both.

The sequence of numbers produced by randn is determined by the internal settings of the uniform pseudorandom number generator that underlies rand, randi, and randn. You can control that shared random number generator using rng.

Note:   Use the rng function instead of rand or randn with the 'seed', 'state', or 'twister' inputs. For more information, see Replace Discouraged Syntaxes of rand and randn

Examples

Matrix of Random Numbers

Generate a 5-by-5 matrix of normally distributed random numbers.

r = randn(5)

r =

    1.0347    0.8884    1.4384   -0.1022   -0.0301
    0.7269   -1.1471    0.3252   -0.2414   -0.1649
   -0.3034   -1.0689   -0.7549    0.3192    0.6277
    0.2939   -0.8095    1.3703    0.3129    1.0933
   -0.7873   -2.9443   -1.7115   -0.8649    1.1093

Bivariate Normal Random Numbers

Generate values from a bivariate normal distribution with specified mean vector and covariance matrix.

mu = [1 2];
sigma = [1 0.5; 0.5 2];
R = chol(sigma);
z = repmat(mu,10,1) + randn(10,2)*R

z =

    1.3271    3.3688
    2.0826    3.3279
    2.0061    2.9663
    0.3491    3.3285
    1.2571    3.3585
    0.0556    1.8450
   -0.3218    0.4258
    1.9248    1.6005
    1.0000    3.5770
    0.9451   -0.1597

Random Complex Numbers

Generate a single random complex number with normally distributed real and imaginary parts.

a = randn + 1i*randn

a =

   0.5377 + 1.8339i

Reset Random Number Generator

Save the current state of the random number generator and create a 1-by-5 vector of random numbers.

s = rng;
r = randn(1,5)

r =

   -0.0245   -1.9488    1.0205    0.8617    0.0012

Restore the state of the random number generator to s, and then create a new 1-by-5 vector of random numbers. The values are the same as before.

rng(s);
r1 = randn(1,5)

r1 =

   -0.0245   -1.9488    1.0205    0.8617    0.0012

Always use the rng function (rather than the rand or randn functions) to specify the settings of the random number generator. For more information, see Replace Discouraged Syntaxes of rand and randn.

3-D Array of Random Numbers

Create a 3-by-2-by-3 array of random numbers.

X = randn([3,2,3])

X(:,:,1) =

   -0.0708   -2.1924
   -2.4863   -2.3193
    0.5812    0.0799


X(:,:,2) =

   -0.9485    0.8577
    0.4115   -0.6912
    0.6770    0.4494


X(:,:,3) =

    0.1006    0.8979
    0.8261   -0.1319
    0.5362   -0.1472

Specify Data Type of Random Numbers

Create a 1-by-4 vector of random numbers whose elements are single precision.

r = randn(1,4,'single')

r =

    0.5377    1.8339   -2.2588    0.8622

class(r)

ans =

single

Clone Size from Existing Array

Create a matrix of normally distributed random numbers with the same size as an existing array.

A = [3 2; -2 1];
sz = size(A);
X = randn(sz)

X =

    1.0078   -0.5046
   -2.1237   -1.2706

It is a common pattern to combine the previous two lines of code into a single line:

X = randn(size(A));

Clone Size and Data Type from Existing Array

Create a 2-by-2 matrix of single precision random numbers.

p = single([3 2; -2 1]);

Create an array of random numbers that is the same size and data type as p.

X = randn(size(p),'like',p)

X =

   -0.3826    0.8257
    0.6487   -1.0149

class(X)

ans =

single

Clone Distributed Array

If you have Parallel Computing Toolbox™, create a 1000-by-1000 distributed array of random numbers with underlying data type single. For the distributed data type, the 'like' syntax clones the underlying data type in addition to the primary data type.

p = randn(1000,'single','distributed');

Create an array of random numbers that is the same size, primary data type, and underlying data type as p.

X = randn(size(p),'like',p);

class(X)

ans =

distributed

classUnderlying(X)

ans =

single

Related Examples

• Create Arrays of Random Numbers
• Random Numbers Within a Specific Range
• Random Numbers Within a Sphere
• Random Numbers from Normal Distribution with Specific Mean and Variance

Input Arguments

n — Size of square matrixinteger value

Size of square matrix, specified as an integer value.

• If n is 0, then X is an empty matrix.

• If n is negative, then it is treated as 0.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

sz1,...,szN — Size of each dimension (as separate arguments)integer values

Size of each dimension, specified as separate arguments of integer values.

• If the size of any dimension is 0, then X is an empty array.

• If the size of any dimension is negative, then it is treated as 0.

• Beyond the second dimension, randn ignores trailing dimensions with a size of 1. For example, randn(3,1,1,1) produces a 3-by-1 vector of random numbers.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

sz — Size of each dimension (as a row vector)integer values

Size of each dimension, specified as a row vector of integer values. Each element of this vector indicates the size of the corresponding dimension:

• If the size of any dimension is 0, then X is an empty array.

• If the size of any dimension is negative, then it is treated as 0.

• Beyond the second dimension, randn ignores trailing dimensions with a size of 1. For example, randn([3,1,1,1]) produces a 3-by-1 vector of random numbers.

Example: sz = [2,3,4] creates a 2-by-3-by-4 array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

typename — Data type (class) to create'double' (default) | 'single'

Data type (class) to create, specified as the string 'double', 'single', or the name of another class that provides randn support.

Example: randn(5,'single')

p — Prototype of array to createnumeric array

Prototype of array to create, specified as a numeric array.

Example: randn(5,'like',p)

Data Types: single | double
Complex Number Support: Yes

More About

• Creating and Controlling a Random Number Stream
• Class Support for Array-Creation Functions
• Replace Discouraged Syntaxes of rand and randn
• Why Do Random Numbers Repeat After Startup?