## Create Arrays of Random Numbers

MATLAB^{®} uses algorithms to generate *pseudorandom* and
*pseudoindependent* numbers. These numbers are not strictly
random and independent in the mathematical sense, but they pass various statistical
tests of randomness and independence, and their calculation can be repeated for testing
or diagnostic purposes.

The `rand`

, `randi`

, `randn`

, and `randperm`

functions are the primary functions for creating arrays of
random numbers. The `rng`

function allows you to control the
seed and algorithm that generates random numbers.

### Random Number Functions

There are four fundamental random number functions: `rand`

, `randi`

, `randn`

, and `randperm`

. The
`rand`

function returns floating-point numbers between 0 and
1 that are drawn from a uniform distribution. For
example:

```
rng('default')
r1 = rand(1000,1);
```

`r1`

is a 1000-by-1 column vector containing real floating-point numbers drawn from a
uniform distribution. All the values in `r1`

are in the open
interval (0, 1). A histogram of these values is roughly flat, which indicates a
fairly uniform sampling of numbers.The `randi`

function returns `double`

integer
values drawn from a discrete uniform distribution. For
example,

r2 = randi(10,1000,1);

`r2`

is a 1000-by-1 column vector containing integer values drawn from a discrete uniform
distribution whose range is in the close interval [1, 10]. A histogram of these
values is roughly flat, which indicates a fairly uniform sampling of integers
between 1 and 10. The `randn`

function returns arrays of real floating-point
numbers that are drawn from a standard normal distribution. For
example:

r3 = randn(1000,1);

`r3`

is a 1000-by-1 column vector containing numbers drawn from a standard normal
distribution. A histogram of `r3`

looks like a roughly normal
distribution whose mean is 0 and standard deviation is 1.You can use the `randperm`

function to create a
`double`

array of random integer values that have no repeated
values. For
example,

r4 = randperm(15,5);

`r4`

is a 1-by-5 array containing integers randomly selected from the range [1, 15].
Unlike `randi`

, which can return an array containing repeated
values, the array returned by `randperm`

has no repeated
values.Successive calls to any of these functions return different results. This behavior is useful for creating several different arrays of random values.

### Random Number Generators

MATLAB offers several generator algorithm options, which are summarized in the table.

Value | Generator Name | Generator Keyword |
---|---|---|

`'twister'` | Mersenne Twister (used by default stream at MATLAB startup) | mt19937ar |

`'simdTwister'` | SIMD-oriented Fast Mersenne Twister | dsfmt19937 |

`'combRecursive'` | Combined multiple recursive | mrg32k3a |

`'multFibonacci'` | Multiplicative Lagged Fibonacci | mlfg6331_64 |

`'philox'` | Philox 4x32 generator with 10 rounds | philox4x32_10 |

`'threefry'` | Threefry 4x64 generator with 20 rounds | threefry4x64_20 |

`'v4'` | Legacy MATLAB version 4.0 generator | mcg16807 |

`'v5uniform'` | Legacy MATLAB version 5.0 uniform generator | swb2712 |

`'v5normal'` | Legacy MATLAB version 5.0 normal generator | shr3cong |

Use the `rng`

function to set the seed and
generator used by the `rand`

, `randi`

,
`randn`

, and `randperm`

functions. For
example, `rng(0,'twister')`

reset the generator to its default
state. To avoid repetition of random number arrays when MATLAB restarts, see Why Do Random Numbers Repeat After Startup?

For more information about controlling the random number generator's state to repeat calculations using the same random numbers, or to guarantee that different random numbers are used in repeated calculations, see Controlling Random Number Generation.

### Random Number Data Types

`rand`

and `randn`

functions generate values in double precision by
default.

```
rng('default')
A = rand(1,5);
class(A)
```

ans = 'double'

To specify the class as double explicitly:

rng('default') B = rand(1,5,'double'); class(B)

ans = 'double'

isequal(A,B)

ans = 1

`rand`

and `randn`

can also generate values in single precision.

rng('default') A = rand(1,5,'single'); class(A)

ans = 'single'

The values are the same as if you had cast the double precision values from the previous example. The random stream that the functions draw from advances the same way regardless of what class of values is returned.

A,B

A = 0.8147 0.9058 0.1270 0.9134 0.6324 B = 0.8147 0.9058 0.1270 0.9134 0.6324

`randi`

supports both integer types and
single or double precision.

```
A = randi([1 10],1,5,'double');
class(A)
```

ans = 'double'

```
B = randi([1 10],1,5,'uint8');
class(B)
```

ans = 'uint8'

## See Also

`rng`

| `rand`

| `randi`

| `randn`

| `randperm`