## 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