MATLAB Function Reference
randn

Normally distributed random numbers and arrays

Syntax

• ```Y = randn(n)
Y = randn(m,n)
Y = randn([m n])
Y = randn(m,n,p,...)
Y = randn([m n p...])
Y = randn(size(A))
randn
s = randn('state')
```

Description

The `randn` function generates arrays of random numbers whose elements are normally distributed with mean 0, variance , and standard deviation .

```Y = randn(n) ``` returns an `n`-by-`n` matrix of random entries. An error message appears if `n` is not a scalar.

```Y = randn(m,n) or Y = randn([m n]) ``` returns an `m`-by-`n` matrix of random entries.

```Y = randn(m,n,p,...) or Y = randn([m n p...]) ``` generates random arrays.

```Y = randn(size(A)) ``` returns an array of random entries that is the same size as `A`.

```randn, ``` by itself, returns a scalar whose value changes each time it's referenced.

```s = randn('state') ``` returns a 2-element vector containing the current state of the normal generator. To change the state of the generator:

 `randn('state',s)` Resets the state to `s`. `randn('state',0)` Resets the generator to its initial state. `randn('state',j)` For integer `j`, resets the generator to its `j`th state. `randn('state',sum(100*clock))` Resets it to a different state each time.

Examples

Example 1. `R` `=` `randn(3,4)` may produce

• ``` R =
1.1650    0.3516    0.0591    0.8717
0.6268   -0.6965    1.7971   -1.4462
0.0751    1.6961    0.2641   -0.7012
```

For a histogram of the `randn` distribution, see `hist`.

Example 2. Generate a random distribution with a specific mean and variance . To do this, multiply the output of `randn` by the standard deviation , and then add the desired mean. For example, to generate a 5-by-5 array of random numbers with a mean of .6 that are distributed with a variance of 0.1

• ```x = .6 + sqrt(0.1) * randn(5)
x =

0.8713    0.4735    0.8114    0.0927    0.7672
0.9966    0.8182    0.9766    0.6814    0.6694
0.0960    0.8579    0.2197    0.2659    0.3085
0.1443    0.8251    0.5937    1.0475   -0.0864
0.7806    1.0080    0.5504    0.3454    0.5813
```

`rand`, `randperm`, `sprand`, `sprandn`