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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<HTML>
<HEAD>
<TITLE>RANDN Gaussian (Normal) Random Number Generator
</TITLE>
</HEAD>
<BODY>
<H2>RANDN Gaussian (Normal) Random Number Generator
</H2>
<P>
Section: <A HREF=sec_random.html> Random Number Generation </A>
<H3>Usage</H3>
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., <code>mu = 0, sigma = 1</code>).
Two seperate syntaxes are possible. The first syntax specifies the array
dimensions as a sequence of scalar dimensions:
<PRE>
y = randn(d1,d2,...,dn).
</PRE>
<P>
The resulting array has the given dimensions, and is filled with
random numbers. The type of <code>y</code> is <code>double</code>, 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:
<PRE>
y = randn([d1,d2,...,dn]).
</PRE>
<P>
This syntax is more convenient for calling <code>randn</code> using a
variable for the argument.
Finally, <code>randn</code> supports two additional forms that allow
you to manipulate the state of the random number generator.
The first retrieves the state
<PRE>
y = randn('state')
</PRE>
<P>
which is a 625 length integer vector. The second form sets
the state
<PRE>
randn('state',y)
</PRE>
<P>
or alternately, you can reset the random number generator with
<PRE>
randn('state',0)
</PRE>
<P>
<H3>Function Internals</H3>
Recall that the
probability density function (PDF) of a normal random variable is
<P>
<DIV ALIGN="CENTER">
<IMG SRC="randn_eqn1.png">
</DIV>
<P>
The Gaussian random numbers are generated from pairs of uniform random numbers using a transformation technique.
<H3>Example</H3>
The following example demonstrates an example of using the first form of the <code>randn</code> function.
<PRE>
--> randn(2,2,2)
ans =
(:,:,1) =
-1.7375 -0.5664
-0.2634 -1.0112
(:,:,2) =
-0.4020 0.0557
-1.8966 0.2098
</PRE>
<P>
The second example demonstrates the second form of the <code>randn</code> function.
<PRE>
--> randn([2,2,2])
ans =
(:,:,1) =
-0.7183 1.9415
0.1010 -1.1747
(:,:,2) =
0.3048 3.1685
-1.4185 -0.6130
</PRE>
<P>
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 <code>mean</code> and <code>var</code>, respectively.
<PRE>
--> x = 10+sqrt(5)*randn(1,10000);
--> mean(x)
ans =
10.0135
--> var(x)
ans =
4.9458
</PRE>
<P>
Now, we use the state manipulation functions of <code>randn</code> to exactly reproduce
a random sequence. Note that unlike using <code>seed</code>, we can exactly control where
the random number generator starts by saving the state.
<PRE>
--> 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
</PRE>
<P>
</BODY>
</HTML>
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