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) = 0.8539 0.1733 0.0415 0.1300 (:,:,2) = 0.7163 0.5752 0.5953 0.3728The second example demonstrates the second form of the
rand
function.
--> rand([2,2,2]) ans = (:,:,1) = 0.4992 0.2797 0.6513 0.3209 (:,:,2) = 0.6244 0.7774 0.0934 0.1820The 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 = 0.4952 --> var(x) ans = 0.0845Now, 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