Section: Random Number Generation
[0,1).
Two seperate syntaxes are possible. The first syntax specifies the array
dimensions as a sequence of scalar dimensions:
y = rand(d1,d2,...,dn).
The resulting array has the given dimensions, and is filled with
random numbers. The type of y is double, a 64-bit floating
point array. To get arrays of other types, use the typecast
functions.
The second syntax specifies the array dimensions as a vector,
where each element in the vector specifies a dimension length:
y = rand([d1,d2,...,dn]).
This syntax is more convenient for calling rand using a
variable for the argument.
Finally, rand supports two additional forms that allow
you to manipulate the state of the random number generator.
The first retrieves the state
y = rand('state')
which is a 625 length integer vector. The second form sets the state
rand('state',y)
or alternately, you can reset the random number generator with
rand('state',0)
rand function.
--> rand(2,2,2)
ans =
(:,:,1) =
0.3478 0.5313
0.0276 0.9958
(:,:,2) =
0.2079 0.7597
0.4921 0.3365
The second example demonstrates the second form of the rand function.
--> rand([2,2,2])
ans =
(:,:,1) =
0.8670 0.2174
0.2714 0.6897
(:,:,2) =
0.2305 0.3898
0.1721 0.9545
The third example computes the mean and variance of a large number of uniform random numbers. Recall that the mean should be 1/2, and the variance should be 1/12 ~ 0.083.
--> x = rand(1,10000);
--> mean(x)
ans =
0.5023
--> var(x)
ans =
0.0840
Now, we use the state manipulation functions of rand to exactly reproduce
a random sequence. Note that unlike using seed, we can exactly control where
the random number generator starts by saving the state.
--> rand('state',0) % restores us to startup conditions
--> a = rand(1,3) % random sequence 1
a =
0.3759 0.0183 0.9134
--> b = rand('state'); % capture the state vector
--> c = rand(1,3) % random sequence 2
c =
0.3580 0.7604 0.8077
--> rand('state',b); % restart the random generator so...
--> c = rand(1,3) % we get random sequence 2 again
c =
0.3580 0.7604 0.8077