Random Number Generation

Seeds, distributions, algorithms

Use the rand, randn, and randi functions to create sequences of pseudorandom numbers, and the randperm function to create a vector of randomly permuted integers. Use the rng function to control the repeatability of your results. Use the RandStream class when you need more advanced control over random number generation.

Functions

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Create Random Values

`rand`	Uniformly distributed random numbers
`randn`	Normally distributed random numbers
`randi`	Uniformly distributed random integers
`randperm`	Random permutation of integers

Define Generator Parameters

`rng`	Control random number generator
`RandStream`	Random number stream

Topics

Generate Random Numbers

Create Arrays of Random Numbers
Use rand, randi, randn, and randperm to create arrays of random numbers.
Random Integers
This example shows how to create an array of random integer values that are drawn from a discrete uniform distribution on a specific set of numbers.
Why Do Random Numbers Repeat After Startup?
Avoid repetition of random number arrays when MATLAB^® restarts.
Replace Discouraged Syntaxes of rand and randn
Replace Discouraged Syntaxes of rand and randn.

Control Random Number Generation

Controlling Random Number Generation
This example shows how to use the rng function, which provides control over random number generation.
Generate Random Numbers That Are Repeatable
This example shows how to repeat arrays of random numbers by specifying the generator algorithm and seed first. Every time you initialize the generator using the same algorithm and seed, you always get the same result.
Generate Random Numbers That Are Different
This example shows how to avoid repeating the same random number arrays when MATLAB restarts.

Control Multiple Streams or Substreams

Managing the Global Stream Using RandStream
This example shows how to use the RandStream class to control random number generation from the global stream.
Multiple Streams
This example uses RandStream to create multiple, independent random number streams.
Creating and Controlling a Random Number Stream
This example shows how to use RandStream to create random number streams and substreams.

Related Information

Featured Examples

Random Numbers Within a Specific Range

Create an array of random floating-point numbers that are drawn from a uniform distribution in the open interval (50, 100).

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Random Numbers from Normal Distribution with Specific Mean and Variance

Create an array of random floating-point numbers that are drawn from a normal distribution having a mean of 500 and variance of 25.

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Random Numbers Within a Sphere

Create random points within the volume of a sphere, as described by Knuth [1]. The sphere in this example is centered at the origin and has a radius of 3.

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Random Numbers and Vectors from Multivariate Normal Distributions

Generate and visualize random numbers and vectors that are drawn from multivariate normal distributions. This example discusses the steps to generate and visualize random numbers and vectors that are drawn from univariate, bivariate, and trivariate normal distributions. The randn function generates random numbers from the standard normal distribution. To generate random numbers and vectors from a multivariate normal distribution with a specific mean and covariance, you can transform the data generated from the standard normal distribution. Starting from a d-dimensional random variable u=[u1,u2,...,ud] that follows a normal distribution with zero mean and a unit covariance matrix, you can transform u to v=μ+uR. The variable v follows the normal distribution with mean μ and covariance matrix Σ=RTR. The covariance matrix Σ is a symmetric and positive definite (nonsingular) matrix, which indicates that the multivariate normal distribution is also nondegenerate. Therefore, you can perform Cholesky decomposition on Σ to obtain the upper triangular matrix R. A multivariate normal distribution that is degenerate, where Σ is not full rank (or singular), is beyond the scope of this example.

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