randi

Uniformly distributed random integers

Syntax

X = randi(imax)

X = randi(imax,n)

X = randi(imax,sz1,...,szN)

X = randi(imax,sz)

X = randi(___,typename)

X = randi(___,like=p)

X = randi([imin,imax],___)

X = randi(s,___)

Description

X = randi(imax) returns a random scalar integer between 1 and imax.

X = randi(imax,n) returns an n-by-n matrix of random integers drawn from the discrete uniform distribution on the interval [1,imax].

X = randi(imax,sz1,...,szN) returns an sz1-by-...-by-szN array where sz1,...,szN indicate the size of each dimension. For example, randi(10,3,4) returns a 3-by-4 array of random integers between 1 and 10.

X = randi(imax,sz) returns an array where size vector sz defines size(X). For example, randi(10,[3 4]) returns a 3-by-4 array of random integers between 1 and 10.

X = randi(___,typename) returns an array of random integers between 1 and imax of data type typename. The typename input can be "single", "double", "int8", "uint8", "int16", "uint16", "int32", "uint32", or "logical". You can use any of the input arguments in the previous syntaxes.

X = randi(___,like=p) returns an array of random integers like p; that is, with the same data type and complexity (real or complex) as p. You can specify either typename or like, but not both.

X = randi([imin,imax],___) returns an array containing integers drawn from the discrete uniform distribution on the interval [imin,imax], using any of the above syntaxes.

X = randi(s,___) generates integers from random number stream s instead of the default global stream. To create a stream, use RandStream. You can specify s followed by any of the input argument combinations in previous syntaxes.

Examples

Square Matrix of Random Integers

Generate a 5-by-5 matrix of random integers between 1 and 10. The first input to randi indicates the largest integer in the sampling interval (the smallest integer in the interval is 1).

r = randi(10,5)

r = 5×5

     9     1     2     2     7
    10     3    10     5     1
     2     6    10    10     9
    10    10     5     8    10
     7    10     9    10     7

Random Integers Within Specified Interval

Generate a 10-by-1 column vector of uniformly distributed random integers from the sample interval [-5,5].

r = randi([-5,5],10,1)

r = 10×1

     3
     4
    -4
     5
     1
    -4
    -2
     1
     5
     5

Control Random Number Generation

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

s = rng;
r = randi(10,1,5)

r = 1×5

     9    10     2    10     7

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

rng(s);
r1 = randi(10,1,5)

r1 = 1×5

     9    10     2    10     7

3-D Array of Random Integers

Create a 3-by-2-by-3 array of uniformly distributed random integers between 1 and 500.

X = randi(500,[3,2,3])

X = 
X(:,:,1) =

   408   457
   453   317
    64    49


X(:,:,2) =

   140   483
   274    79
   479   486


X(:,:,3) =

   479    71
   243   211
   401   458

Random Integers of Other Data Types

Create a 1-by-4 vector of random numbers between 1 and 100 whose elements are of type int16.

r = randi(100,1,4,"int16")

r = 1×4 int16 row vector

   82   91   13   92

class(r)

ans = 
'int16'

Size Defined by Existing Array

Create a matrix of uniformly distributed random integers between 1 and 10 with the same size as an existing array.

A = [3 2; -2 1];
sz = size(A);
X = randi(10,sz)

X = 2×2

     9     2
    10    10

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

X = randi(10,size(A));

Size and Numeric Data Type Defined by Existing Array

Create a 2-by-2 matrix of 8-bit signed integers.

p = int8([3 2; -2 1]);

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

X = randi(10,size(p),like=p)

X = 2×2 int8 matrix

    9    2
   10   10

class(X)

ans = 
'int8'

Random Complex Integers

Since R2022a

Generate 10 random complex integers from the discrete uniform distribution over a square domain with real and imaginary parts in the interval [-5,5].

a = randi([-5,5],10,1,like=1i)

a = 10×1 complex

   3.0000 + 4.0000i
  -4.0000 + 5.0000i
   1.0000 - 4.0000i
  -2.0000 + 1.0000i
   5.0000 + 5.0000i
  -4.0000 + 5.0000i
   5.0000 + 0.0000i
   3.0000 - 4.0000i
  -1.0000 + 5.0000i
   3.0000 + 5.0000i

Random Logical Array

Since R2023a

Create a 5-by-5 matrix of random logical values (0s and 1s) with a discrete uniform distribution.

r = randi([0 1],5,"logical")

r = 5×5 logical array

   1   0   0   0   1
   1   0   1   0   0
   0   1   1   1   1
   1   1   0   1   1
   1   1   1   1   1

Input Arguments

imax — Largest integer in sample interval

positive integer

Largest integer in sample interval, specified as a positive integer. randi draws values from the uniform distribution in the sample interval [1,imax].

Example: randi(10,5)

imin — Smallest integer in sample interval

1 (default) | scalar integer

Smallest integer in sample interval, specified as a scalar integer.

Both imin and imax must be integers that satisfy imin ≤ imax.

For example, randi([50,100],5) returns a 5-by-5 matrix of random integers between (and including) 50 and 100.

n — Size of square matrix

integer 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, randi ignores trailing dimensions with a size of 1. For example, randi([5,10],3,1,1,1) produces a 3-by-1 vector of random integers between 5 and 10.

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, randi ignores trailing dimensions with a size of 1. For example, randi([5,10],[3 1 1 1]) produces a 3-by-1 vector of random integers between 5 and 10.

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

typename — Data type (class) to create

"double" (default) | "single" | "int8" | "uint8" | "int16" | "uint16" | ...

Data type (class) to create, specified as "double", "single", "int8", "uint8", "int16", "uint16", "int32", "uint32", "logical", or the name of another class that provides randi support.

Example: randi(5,5,"int8")

p — Prototype of array to create

numeric array | logical array

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

Example: randi(5,5,like=p)

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | logical
Complex Number Support: Yes

s — Random number stream

RandStream object

Random number stream, specified as a RandStream object.

Example: s = RandStream("dsfmt19937"); randi(s,[5,10],[3 1])

Output Arguments

X — Output array

scalar | vector | matrix | multidimensional array

Output array, returned as a scalar, vector, matrix, or multidimensional array.

More About

Pseudorandom Number Generator

The underlying number generator for randi is a pseudorandom number generator, which creates a deterministic sequence of numbers that appear random. These numbers are predictable if the seed and the deterministic algorithm of the generator are known. While not truly random, the generated numbers pass various statistical tests of randomness, satisfying the independent and identically distributed (i.i.d.) condition, and justifying the name pseudorandom.

Tips

• The sequence of numbers produced by randi 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.

• The arrays returned by randi can contain repeated integer values. This behavior is sometimes referred to as sampling with replacement. Use randperm if you require all unique values.

• If imin and imax are outside the range of the output type (as specified by typename or by the prototype p), then randi first creates random integers within the interval [imin,imax] and converts any resulting out-of-range integers to the minimum or maximum value of the output type. For example:

  rng default;
  r = randi([-10 10],1,10)

  r =
  
       7     9    -8     9     3    -8    -5     1    10    10

  rng default;
  r = randi([-10 10],1,10,"logical")

  r =
  
    1×10 logical array
  
     1   1   0   1   1   0   0   1   1   1

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If used, the input argument typename must be "double","single", "int8", "uint8", "int16", "uint16", "int32", "uint32", or "logical". Other classes are not supported, even if the class defines a static randi method.

• If used, size arguments n, sz, and sz1,...,szN must be fixed size.

• The code generator uses double-precision math to compute single-precision outputs.

• In most cases, generated MEX files use the same random number state as MATLAB^®. If you disable extrinsic calls or you call randi from inside a parfor-loop, the generated MEX code and standalone code maintain their own random number state that is initialized to the MATLAB default, which is rng(0,"twister").

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The randi function supports GPU array input with these usage notes and limitations:

• You can specify typename as 'gpuArray'. If you specify typename as 'gpuArray', the default underlying type of the array is double.

  To create a GPU array with underlying type datatype, specify the underlying type as an additional argument before typename. For example, X = randi(imax,3,datatype,'gpuArray') creates a 3-by-3 GPU array of random integers in the range [1 imax] with underlying type datatype.

  You can specify the underlying type datatype as one of these options:

  • 'double'

  • 'single'

  • 'logical'

  • 'int8'

  • 'uint8'

  • 'int16'

  • 'uint16'

  • 'int32'

  • 'uint32'

• You can also specify the numeric variable p as a gpuArray.

  If you specify p as a gpuArray, the underlying type of the returned array is the same as p.

• To use the stream syntax, randi(s,___), on a GPU, s must be a parallel.gpu.RandStream (Parallel Computing Toolbox) object.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Usage notes and limitations:

• The stream syntax randi(s,___) is not supported for codistributed or distributed arrays.

• You can specify typename as 'codistributed' or 'distributed'. If you specify typename as 'codistributed' or 'distributed', the default underlying type of the returned array is double.

  To create a distributed or codistributed array with underlying type datatype, specify the underlying type as an additional argument before typename. For example, X = randi(imax,3,datatype,'distributed') creates a 3-by-3 distributed matrix of random integers in the range [1 imax] with underlying type datatype.

  You can specify the underlying type datatype as one of these options:

  • 'double'

  • 'single'

  • 'int8'

  • 'uint8'

  • 'int16'

  • 'uint16'

  • 'int32'

  • 'uint32'

  • 'logical'

• You can also specify p as a codistributed or distributed array.

  If you specify p as a codistributed or distributed array, the underlying type of the returned array is the same as p.

• For additional codistributed syntaxes, see randi (codistributed) (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced in R2008b

R2023a: Create random logical array

You can create a random logical array by specifying typename as "logical" or the prototype p as a logical array. For example, see Random Logical Array.

R2022a: Match complexity with like, and use like with RandStream object

The like name-value argument supports both real and complex prototype arrays. For example:

r = randi(2,2,like=1i)

r =

   2.0000 + 2.0000i   2.0000 + 1.0000i
   1.0000 + 2.0000i   1.0000 + 2.0000i

All syntaxes support this feature. Also, you can now use like with a RandStream object as the first input of randi.

R2014a: Match data type of an existing variable with 'like'

To generate random numbers with the same data type as an existing variable, use the syntax randi(__,'like',p). For example:

A = single(pi);
r = randi(4,4,'like',A);
class(r)

ans = 
single

This feature is not available when passing a RandStream object as the first input to randi.

R2013b: Non-integer size inputs are not supported

Specifying a dimension that is not an integer causes an error. Use floor to convert non-integer size inputs to integers.