FreeMat
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Section: Random Number Generation
Creates an array of pseudo-random numbers of the specified size. The numbers are normally distributed with zero mean and a unit standard deviation (i.e., mu = 0, sigma = 1
). Two seperate syntaxes are possible. The first syntax specifies the array dimensions as a sequence of scalar dimensions:
y = randn(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 = randn([d1,d2,...,dn]).
This syntax is more convenient for calling randn
using a variable for the argument.
Finally, randn
supports two additional forms that allow you to manipulate the state of the random number generator. The first retrieves the state
y = randn('state')
which is a 625 length integer vector. The second form sets the state
randn('state',y)
or alternately, you can reset the random number generator with
randn('state',0)
Recall that the probability density function (PDF) of a normal random variable is
The Gaussian random numbers are generated from pairs of uniform random numbers using a transformation technique.
The following example demonstrates an example of using the first form of the randn
function.
--> randn(2,2,2) ans = (:,:,1) = -1.3838 0.9091 -1.1738 0.1705 (:,:,2) = -0.0336 0.4572 0.7566 -1.1720
The second example demonstrates the second form of the randn
function.
--> randn([2,2,2]) ans = (:,:,1) = 1.2183 -0.5558 0.1605 0.1819 (:,:,2) = 0.5727 -0.5929 -0.3895 -0.2424
In the next example, we create a large array of 10000 normally distributed pseudo-random numbers. We then shift the mean to 10, and the variance to 5. We then numerically calculate the mean and variance using mean
and var
, respectively.
--> x = 10+sqrt(5)*randn(1,10000); --> mean(x) ans = 10.0370 --> var(x) ans = 4.9402
Now, we use the state manipulation functions of randn
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.
--> randn('state',0) % restores us to startup conditions --> a = randn(1,3) % random sequence 1 a = -0.0362 -0.1404 0.6934 --> b = randn('state'); % capture the state vector --> c = randn(1,3) % random sequence 2 c = 0.5998 0.7086 -0.9394 --> randn('state',b); % restart the random generator so... --> c = randn(1,3) % we get random sequence 2 again c = 0.5998 0.7086 -0.9394