Random Number Generation
R2026bUse the rand, randi, randn,
and randperm functions to generate random numbers from a shared global
stream. Control the behavior and reproducibility of this stream by using the
rng function. For more advanced control of random number streams, such as
creating multiple independent streams or choosing normal transformation algorithms, use the
RandStream object.
MATLAB provides several pseudorandom number generators that produce deterministic sequences of numbers that appear random. Given the same generator algorithm and seed, these sequences are reproducible. Although the numbers in the sequences are not truly random, they pass statistical tests of randomness and satisfy the independent and identically distributed condition. For this reason, numbers generated by pseudorandom number generators are commonly referred to as random numbers.
Functions
Topics
Generate Random Numbers
- Create Arrays of Random Numbers
Userand,randi,randn, andrandpermto 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 ofrandandrandn.
Control Random Number Generation
- Control Random Number Generation
This example shows how to control random number generation using therngfunction. - 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 theRandStreamclass to control random number generation from the global stream. - Multiple Streams
This example usesRandStreamto create multiple, independent random number streams. - Create and Control Random Number Streams
This example shows how to useRandStreamto 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).
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.
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.
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.
Teaching Resources
Descriptive Statistics and Probability Distributions
Learn the concepts of descriptive statistics, and discrete and continuous distributions.
