RANDN Gaussian (Normal) Random Number Generator

Section: Random Number Generation

Usage

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)

Function Internals

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.

Example

The following example demonstrates an example of using the first form of the randn function. 
--> randn(2,2,2)

ans = 

(:,:,1) = 
   -1.7375   -0.5664 
   -0.2634   -1.0112 

(:,:,2) = 
   -0.4020    0.0557 
   -1.8966    0.2098

The second example demonstrates the second form of the randn function. 

--> randn([2,2,2])

ans = 

(:,:,1) = 
   -0.7183    1.9415 
    0.1010   -1.1747 

(:,:,2) = 
    0.3048    3.1685 
   -1.4185   -0.6130

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 = 
   10.0135 

--> var(x)

ans = 
    4.9458

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