MATLAB Function Reference

rand - Uniformly distributed pseudorandom numbers

Syntax

Y = rand
Y = rand(n)
Y = rand(m,n)
Y = rand([m n])
Y = rand(m,n,p,...)
Y = rand([m n p...])
Y = rand(size(A))
rand(method,s)
s = rand(method)

Description

Y = rand returns a pseudorandom, scalar value drawn from a uniform distribution on the unit interval.

Y = rand(n) returns an n-by-n matrix of values derived as described above.

Y = rand(m,n) or Y = rand([m n]) returns an m-by-n matrix of the same.

Y = rand(m,n,p,...) or Y = rand([m n p...]) generates an m-by-n-by-p-by-... array of the same.

Note   The size inputs m, n, p, ... should be nonnegative integers. Negative integers are treated as 0.

Y = rand(size(A)) returns an array that is the same size as A.

rand(method,s) causes rand to use the generator determined by method, and initializes the state of that generator using the value of s.

The value of s is dependent upon which method is selected. If method is set to 'state' or 'twister', then s must be either a scalar integer value from 0 to 2^32-1 or the output of rand(method). If method is set to 'seed', then s must be either a scalar integer value from 0 to 2^31-2 or the output of rand(method).

The rand and randn generators each maintain their own internal state information. Initializing the state of one has no effect on the other.

Input argument method can be any of the strings shown in the table below:

For a full description of the Mersenne twister algorithm, see

http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

s = rand(method) returns in s the current internal state of the generator selected by method. It does not change the generator being used.

Remarks

The sequence of numbers produced by rand is determined by the internal state of the generator. Setting the generator to the same fixed state enables you to repeat computations. Setting the generator to different states leads to unique computations. It does not, however, improve statistical properties.

Because MATLAB software resets the rand state at startup, rand generates the same sequence of numbers in each session unless you change the value of the state input.

Examples

Example 1

Make a random choice between two equally probable alternatives:

 if rand < .5
    'heads'
 else
    'tails'
 end 

Example 2

Generate a 3-by-4 pseudorandom matrix:

R = rand(3,4)
R =

    0.8147    0.9134    0.2785    0.9649
    0.9058    0.6324    0.5469    0.1576
    0.1270    0.0975    0.9575    0.9706

Example 3

Set rand to its default initial state:

rand('twister', 5489);

Initialize rand to a different state each time:

rand('twister', sum(100*clock));

Save the current state, generate 10000 values, reset the state, and repeat the sequence:

s = rand('twister');
u1 = rand(100);
rand('twister',s);
u2 = rand(100); % contains exactly the same values as u1

Example 4

Generate uniform integers on the set 1:n:

n = 75;
f = ceil(n.*rand(100,1));

f(1:10)
ans =

    72
    37
    61
    11
    32
    69
    60
    72
    50
     3

Example 5

Generate a uniform distribution of random numbers on a specified interval [a,b]. To do this, multiply the output of rand by (b-a), then add a. For example, to generate a 5-by-5 array of uniformly distributed random numbers on the interval [10,50],

a = 10; b = 50;
x = a + (b-a) * rand(5)
x =
   19.1591   49.8454   10.1854   25.9913   17.2739
   46.5335   13.1270   40.9964   20.3948   20.5521
   16.0951   27.7071   42.6921   42.0027   15.8216
   43.0327   14.2661   44.7478   27.2566   15.4427
   31.5337   48.4759   13.3774   46.4259   44.7717

References

[1] Moler, C.B., "Numerical Computing with MATLAB," SIAM, (2004), 336 pp. Available online at http://www.mathworks.com/moler.

[2] G. Marsaglia and A. Zaman "A New Class of Random Number Generators," Annals of Applied Probability, (1991), 3:462-480.

[3] Matsumoto, M. and Nishimura, T. "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudorandom Number Generator," ACM Transactions on Modeling and Computer Simulation, (1998), 8(1):3-30.

[4] Park, S.K. and Miller, K.W. "Random Number Generators: Good Ones Are Hard to Find," Communications of the ACM, (1988), 31(10):1192-1201

See Also

randn, randperm, sprand, sprandn

qz

randn