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<hr>
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<h3 class="section">16.3 Special Utility Matrices</h3>
<!-- eye src/data.cc -->
<p><a name="doc_002deye"></a>
<div class="defun">
— Built-in Function: <b>eye</b> (<var>n</var>)<var><a name="index-eye-1684"></a></var><br>
— Built-in Function: <b>eye</b> (<var>m, n</var>)<var><a name="index-eye-1685"></a></var><br>
— Built-in Function: <b>eye</b> ([<var>m n</var>])<var><a name="index-eye-1686"></a></var><br>
— Built-in Function: <b>eye</b> (<var><small class="dots">...</small>, class</var>)<var><a name="index-eye-1687"></a></var><br>
<blockquote><p>Return an identity matrix. If invoked with a single scalar argument <var>n</var>,
return a square NxN identity matrix. If
supplied two scalar arguments (<var>m</var>, <var>n</var>), <code>eye</code> takes them to be
the number of rows and columns. If given a vector with two elements,
<code>eye</code> uses the values of the elements as the number of rows and columns,
respectively. For example:
<pre class="example"> eye (3)
⇒ 1 0 0
0 1 0
0 0 1
</pre>
<p>The following expressions all produce the same result:
<pre class="example"> eye (2)
==
eye (2, 2)
==
eye (size ([1, 2; 3, 4])
</pre>
<p>The optional argument <var>class</var>, allows <code>eye</code> to return an array of
the specified type, like
<pre class="example"> val = zeros (n,m, "uint8")
</pre>
<p>Calling <code>eye</code> with no arguments is equivalent to calling it
with an argument of 1. Any negative dimensions are treated as zero.
These odd definitions are for compatibility with <span class="sc">matlab</span>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dspeye.html#doc_002dspeye">speye</a>.
</p></blockquote></div>
<!-- ones src/data.cc -->
<p><a name="doc_002dones"></a>
<div class="defun">
— Built-in Function: <b>ones</b> (<var>n</var>)<var><a name="index-ones-1688"></a></var><br>
— Built-in Function: <b>ones</b> (<var>m, n</var>)<var><a name="index-ones-1689"></a></var><br>
— Built-in Function: <b>ones</b> (<var>m, n, k, <small class="dots">...</small></var>)<var><a name="index-ones-1690"></a></var><br>
— Built-in Function: <b>ones</b> ([<var>m n <small class="dots">...</small></var>])<var><a name="index-ones-1691"></a></var><br>
— Built-in Function: <b>ones</b> (<var><small class="dots">...</small>, class</var>)<var><a name="index-ones-1692"></a></var><br>
<blockquote><p>Return a matrix or N-dimensional array whose elements are all 1.
If invoked with a single scalar integer argument <var>n</var>, return a square
NxN matrix. If invoked with two or more scalar
integer arguments, or a vector of integer values, return an array with
the given dimensions.
<p>If you need to create a matrix whose values are all the same, you should
use an expression like
<pre class="example"> val_matrix = val * ones (m, n)
</pre>
<p>The optional argument <var>class</var> specifies the class of the return array
and defaults to double. For example:
<pre class="example"> val = ones (m,n, "uint8")
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dzeros.html#doc_002dzeros">zeros</a>.
</p></blockquote></div>
<!-- zeros src/data.cc -->
<p><a name="doc_002dzeros"></a>
<div class="defun">
— Built-in Function: <b>zeros</b> (<var>n</var>)<var><a name="index-zeros-1693"></a></var><br>
— Built-in Function: <b>zeros</b> (<var>m, n</var>)<var><a name="index-zeros-1694"></a></var><br>
— Built-in Function: <b>zeros</b> (<var>m, n, k, <small class="dots">...</small></var>)<var><a name="index-zeros-1695"></a></var><br>
— Built-in Function: <b>zeros</b> ([<var>m n <small class="dots">...</small></var>])<var><a name="index-zeros-1696"></a></var><br>
— Built-in Function: <b>zeros</b> (<var><small class="dots">...</small>, class</var>)<var><a name="index-zeros-1697"></a></var><br>
<blockquote><p>Return a matrix or N-dimensional array whose elements are all 0.
If invoked with a single scalar integer argument, return a square
NxN matrix. If invoked with two or more scalar
integer arguments, or a vector of integer values, return an array with
the given dimensions.
<p>The optional argument <var>class</var> specifies the class of the return array
and defaults to double. For example:
<pre class="example"> val = zeros (m,n, "uint8")
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dones.html#doc_002dones">ones</a>.
</p></blockquote></div>
<!-- repmat scripts/general/repmat.m -->
<p><a name="doc_002drepmat"></a>
<div class="defun">
— Function File: <b>repmat</b> (<var>A, m</var>)<var><a name="index-repmat-1698"></a></var><br>
— Function File: <b>repmat</b> (<var>A, m, n</var>)<var><a name="index-repmat-1699"></a></var><br>
— Function File: <b>repmat</b> (<var>A, m, n, p, <small class="dots">...</small></var>)<var><a name="index-repmat-1700"></a></var><br>
— Function File: <b>repmat</b> (<var>A, </var>[<var>m n</var>])<var><a name="index-repmat-1701"></a></var><br>
— Function File: <b>repmat</b> (<var>A, </var>[<var>m n p <small class="dots">...</small></var>])<var><a name="index-repmat-1702"></a></var><br>
<blockquote><p>Form a block matrix of size <var>m</var> by <var>n</var>, with a copy of matrix
<var>A</var> as each element. If <var>n</var> is not specified, form an
<var>m</var> by <var>m</var> block matrix.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drepelems.html#doc_002drepelems">repelems</a>.
</p></blockquote></div>
<!-- repelems src/data.cc -->
<p><a name="doc_002drepelems"></a>
<div class="defun">
— Built-in Function: <b>repelems</b> (<var>x, r</var>)<var><a name="index-repelems-1703"></a></var><br>
<blockquote><p>Construct a vector of repeated elements from <var>x</var>. <var>r</var>
is a 2x<var>N</var> integer matrix specifying which elements to repeat and
how often to repeat each element.
<p>Entries in the first row, <var>r</var>(1,j), select an element to repeat.
The corresponding entry in the second row, <var>r</var>(2,j), specifies
the repeat count. If <var>x</var> is a matrix then the columns of <var>x</var> are
imagined to be stacked on top of each other for purposes of the selection
index. A row vector is always returned.
<p>Conceptually the result is calculated as follows:
<pre class="example"> y = [];
for i = 1:columns (<var>r</var>)
y = [y, <var>x</var>(<var>r</var>(1,i)*ones(1, <var>r</var>(2,i)))];
endfor
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drepmat.html#doc_002drepmat">repmat</a>.
</p></blockquote></div>
<p>The functions <code>linspace</code> and <code>logspace</code> make it very easy to
create vectors with evenly or logarithmically spaced elements.
See <a href="Ranges.html#Ranges">Ranges</a>.
<!-- linspace src/data.cc -->
<p><a name="doc_002dlinspace"></a>
<div class="defun">
— Built-in Function: <b>linspace</b> (<var>base, limit</var>)<var><a name="index-linspace-1704"></a></var><br>
— Built-in Function: <b>linspace</b> (<var>base, limit, n</var>)<var><a name="index-linspace-1705"></a></var><br>
<blockquote><p>Return a row vector with <var>n</var> linearly spaced elements between
<var>base</var> and <var>limit</var>. If the number of elements is greater than one,
then the endpoints <var>base</var> and <var>limit</var> are always included in
the range. If <var>base</var> is greater than <var>limit</var>, the elements are
stored in decreasing order. If the number of points is not specified, a
value of 100 is used.
<p>The <code>linspace</code> function always returns a row vector if both
<var>base</var> and <var>limit</var> are scalars. If one, or both, of them are column
vectors, <code>linspace</code> returns a matrix.
<p>For compatibility with <span class="sc">matlab</span>, return the second argument (<var>limit</var>)
if fewer than two values are requested.
</p></blockquote></div>
<!-- logspace scripts/general/logspace.m -->
<p><a name="doc_002dlogspace"></a>
<div class="defun">
— Function File: <b>logspace</b> (<var>a, b</var>)<var><a name="index-logspace-1706"></a></var><br>
— Function File: <b>logspace</b> (<var>a, b, n</var>)<var><a name="index-logspace-1707"></a></var><br>
— Function File: <b>logspace</b> (<var>a, pi, n</var>)<var><a name="index-logspace-1708"></a></var><br>
<blockquote><p>Return a row vector with <var>n</var> elements logarithmically spaced from
10^<var>a</var> to 10^<var>b</var>.
If <var>n</var> is unspecified it defaults to 50.
<p>If <var>b</var> is equal to
pi,
the points are between
10^<var>a</var> and pi,
<em>not</em>
10^<var>a</var> and 10^pi,
in order to be compatible with the corresponding <span class="sc">matlab</span> function.
<p>Also for compatibility with <span class="sc">matlab</span>, return the second argument <var>b</var>
if fewer than two values are requested.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlinspace.html#doc_002dlinspace">linspace</a>.
</p></blockquote></div>
<!-- rand src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drand"></a>
<div class="defun">
— Loadable Function: <b>rand</b> (<var>n</var>)<var><a name="index-rand-1709"></a></var><br>
— Loadable Function: <b>rand</b> (<var>n, m, <small class="dots">...</small></var>)<var><a name="index-rand-1710"></a></var><br>
— Loadable Function: <b>rand</b> ([<var>n m <small class="dots">...</small></var>])<var><a name="index-rand-1711"></a></var><br>
— Loadable Function: <var>v</var> = <b>rand</b> (<var>"state"</var>)<var><a name="index-rand-1712"></a></var><br>
— Loadable Function: <b>rand</b> (<var>"state", v</var>)<var><a name="index-rand-1713"></a></var><br>
— Loadable Function: <b>rand</b> (<var>"state", "reset"</var>)<var><a name="index-rand-1714"></a></var><br>
— Loadable Function: <var>v</var> = <b>rand</b> (<var>"seed"</var>)<var><a name="index-rand-1715"></a></var><br>
— Loadable Function: <b>rand</b> (<var>"seed", v</var>)<var><a name="index-rand-1716"></a></var><br>
— Loadable Function: <b>rand</b> (<var>"seed", "reset"</var>)<var><a name="index-rand-1717"></a></var><br>
<blockquote><p>Return a matrix with random elements uniformly distributed on the
interval (0, 1). The arguments are handled the same as the arguments
for <code>eye</code>.
<p>You can query the state of the random number generator using the
form
<pre class="example"> v = rand ("state")
</pre>
<p>This returns a column vector <var>v</var> of length 625. Later, you can
restore the random number generator to the state <var>v</var>
using the form
<pre class="example"> rand ("state", v)
</pre>
<p class="noindent">You may also initialize the state vector from an arbitrary vector of
length ≤ 625 for <var>v</var>. This new state will be a hash based on the
value of <var>v</var>, not <var>v</var> itself.
<p>By default, the generator is initialized from <code>/dev/urandom</code> if it is
available, otherwise from CPU time, wall clock time, and the current
fraction of a second.
<p>To compute the pseudo-random sequence, <code>rand</code> uses the Mersenne
Twister with a period of 2^19937-1 (See M. Matsumoto and
T. Nishimura,
<cite>Mersenne Twister: A 623-dimensionally equidistributed uniform
pseudorandom number generator</cite>, ACM Trans. on
Modeling and Computer Simulation Vol. 8, No. 1, pp. 3-30, January 1998,
<a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html">http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html</a>).
Do <strong>not</strong> use for cryptography without securely hashing
several returned values together, otherwise the generator state
can be learned after reading 624 consecutive values.
<p>Older versions of Octave used a different random number generator.
The new generator is used by default
as it is significantly faster than the old generator, and produces
random numbers with a significantly longer cycle time. However, in
some circumstances it might be desirable to obtain the same random
sequences as used by the old generators. To do this the keyword
"seed" is used to specify that the old generators should be use,
as in
<pre class="example"> rand ("seed", val)
</pre>
<p class="noindent">which sets the seed of the generator to <var>val</var>. The seed of the
generator can be queried with
<pre class="example"> s = rand ("seed")
</pre>
<p>However, it should be noted that querying the seed will not cause
<code>rand</code> to use the old generators, only setting the seed will.
To cause <code>rand</code> to once again use the new generators, the
keyword "state" should be used to reset the state of the <code>rand</code>.
<p>The state or seed of the generator can be reset to a new random value
using the "reset" keyword.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drandn.html#doc_002drandn">randn</a>, <a href="doc_002drande.html#doc_002drande">rande</a>, <a href="doc_002drandg.html#doc_002drandg">randg</a>, <a href="doc_002drandp.html#doc_002drandp">randp</a>.
</p></blockquote></div>
<!-- randi scripts/general/randi.m -->
<p><a name="doc_002drandi"></a>
<div class="defun">
— Function File: <b>randi</b> (<var>imax</var>)<var><a name="index-randi-1718"></a></var><br>
— Function File: <b>randi</b> (<var>imax, n</var>)<var><a name="index-randi-1719"></a></var><br>
— Function File: <b>randi</b> (<var>imax, m, n, <small class="dots">...</small></var>)<var><a name="index-randi-1720"></a></var><br>
— Function File: <b>randi</b> ([<var>imin imax</var>]<var>, <small class="dots">...</small></var>)<var><a name="index-randi-1721"></a></var><br>
— Function File: <b>randi</b> (<var><small class="dots">...</small>, "class"</var>)<var><a name="index-randi-1722"></a></var><br>
<blockquote><p>Return random integers in the range 1:<var>imax</var>.
<p>Additional arguments determine the shape of the return matrix. When no
arguments are specified a single random integer is returned. If one
argument <var>n</var> is specified then a square matrix (<var>n</var> x <var>n</var>)<!-- /@w --> is
returned. Two or more arguments will return a multi-dimensional
matrix (<var>m</var> x <var>n</var> x <small class="dots">...</small>)<!-- /@w -->.
<p>The integer range may optionally be described by a two element matrix
with a lower and upper bound in which case the returned integers will be
on the interval [<var>imin</var>, <var>imax</var>]<!-- /@w -->.
<p>The optional argument "<var>class</var>" will return a matrix of the requested
type. The default is "double".
<p>The following example returns 150 integers in the range 1-10.
<pre class="example"> ri = randi (10, 150, 1)
</pre>
<p>Implementation Note: <code>randi</code> relies internally on <code>rand</code> which
uses class "double" to represent numbers. This limits the maximum
integer (<var>imax</var>) and range (<var>imax</var> - <var>imin</var>) to the value
returned by the <code>bitmax</code> function. For IEEE floating point numbers
this value is 2^53 - 1<!-- /@w -->.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drand.html#doc_002drand">rand</a>.
</p></blockquote></div>
<!-- randn src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drandn"></a>
<div class="defun">
— Loadable Function: <b>randn</b> (<var>n</var>)<var><a name="index-randn-1723"></a></var><br>
— Loadable Function: <b>randn</b> (<var>n, m, <small class="dots">...</small></var>)<var><a name="index-randn-1724"></a></var><br>
— Loadable Function: <b>randn</b> ([<var>n m <small class="dots">...</small></var>])<var><a name="index-randn-1725"></a></var><br>
— Loadable Function: <var>v</var> = <b>randn</b> (<var>"state"</var>)<var><a name="index-randn-1726"></a></var><br>
— Loadable Function: <b>randn</b> (<var>"state", v</var>)<var><a name="index-randn-1727"></a></var><br>
— Loadable Function: <b>randn</b> (<var>"state", "reset"</var>)<var><a name="index-randn-1728"></a></var><br>
— Loadable Function: <var>v</var> = <b>randn</b> (<var>"seed"</var>)<var><a name="index-randn-1729"></a></var><br>
— Loadable Function: <b>randn</b> (<var>"seed", v</var>)<var><a name="index-randn-1730"></a></var><br>
— Loadable Function: <b>randn</b> (<var>"seed", "reset"</var>)<var><a name="index-randn-1731"></a></var><br>
<blockquote><p>Return a matrix with normally distributed random
elements having zero mean and variance one. The arguments are
handled the same as the arguments for <code>rand</code>.
<p>By default, <code>randn</code> uses the Marsaglia and Tsang “Ziggurat technique”
to transform from a uniform to a normal distribution.
<p>Reference: G. Marsaglia and W.W. Tsang,
<cite>Ziggurat Method for Generating Random Variables</cite>,
J. Statistical Software, vol 5, 2000,
<a href="http://www.jstatsoft.org/v05/i08/">http://www.jstatsoft.org/v05/i08/</a>)
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drand.html#doc_002drand">rand</a>, <a href="doc_002drande.html#doc_002drande">rande</a>, <a href="doc_002drandg.html#doc_002drandg">randg</a>, <a href="doc_002drandp.html#doc_002drandp">randp</a>.
</p></blockquote></div>
<!-- rande src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drande"></a>
<div class="defun">
— Loadable Function: <b>rande</b> (<var>n</var>)<var><a name="index-rande-1732"></a></var><br>
— Loadable Function: <b>rande</b> (<var>n, m, <small class="dots">...</small></var>)<var><a name="index-rande-1733"></a></var><br>
— Loadable Function: <b>rande</b> ([<var>n m <small class="dots">...</small></var>])<var><a name="index-rande-1734"></a></var><br>
— Loadable Function: <var>v</var> = <b>rande</b> (<var>"state"</var>)<var><a name="index-rande-1735"></a></var><br>
— Loadable Function: <b>rande</b> (<var>"state", v</var>)<var><a name="index-rande-1736"></a></var><br>
— Loadable Function: <b>rande</b> (<var>"state", "reset"</var>)<var><a name="index-rande-1737"></a></var><br>
— Loadable Function: <var>v</var> = <b>rande</b> (<var>"seed"</var>)<var><a name="index-rande-1738"></a></var><br>
— Loadable Function: <b>rande</b> (<var>"seed", v</var>)<var><a name="index-rande-1739"></a></var><br>
— Loadable Function: <b>rande</b> (<var>"seed", "reset"</var>)<var><a name="index-rande-1740"></a></var><br>
<blockquote><p>Return a matrix with exponentially distributed random elements. The
arguments are handled the same as the arguments for <code>rand</code>.
<p>By default, <code>randn</code> uses the Marsaglia and Tsang “Ziggurat technique”
to transform from a uniform to an exponential distribution.
<p>Reference: G. Marsaglia and W.W. Tsang,
<cite>Ziggurat Method for Generating Random Variables</cite>,
J. Statistical Software, vol 5, 2000,
<a href="http://www.jstatsoft.org/v05/i08/">http://www.jstatsoft.org/v05/i08/</a>)
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drand.html#doc_002drand">rand</a>, <a href="doc_002drandn.html#doc_002drandn">randn</a>, <a href="doc_002drandg.html#doc_002drandg">randg</a>, <a href="doc_002drandp.html#doc_002drandp">randp</a>.
</p></blockquote></div>
<!-- randp src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drandp"></a>
<div class="defun">
— Loadable Function: <b>randp</b> (<var>l, n</var>)<var><a name="index-randp-1741"></a></var><br>
— Loadable Function: <b>randp</b> (<var>l, n, m, <small class="dots">...</small></var>)<var><a name="index-randp-1742"></a></var><br>
— Loadable Function: <b>randp</b> (<var>l, </var>[<var>n m <small class="dots">...</small></var>])<var><a name="index-randp-1743"></a></var><br>
— Loadable Function: <var>v</var> = <b>randp</b> (<var>"state"</var>)<var><a name="index-randp-1744"></a></var><br>
— Loadable Function: <b>randp</b> (<var>"state", v</var>)<var><a name="index-randp-1745"></a></var><br>
— Loadable Function: <b>randp</b> (<var>"state", "reset"</var>)<var><a name="index-randp-1746"></a></var><br>
— Loadable Function: <var>v</var> = <b>randp</b> (<var>"seed"</var>)<var><a name="index-randp-1747"></a></var><br>
— Loadable Function: <b>randp</b> (<var>"seed", v</var>)<var><a name="index-randp-1748"></a></var><br>
— Loadable Function: <b>randp</b> (<var>"seed", "reset"</var>)<var><a name="index-randp-1749"></a></var><br>
<blockquote><p>Return a matrix with Poisson distributed random elements with mean value
parameter given by the first argument, <var>l</var>. The arguments
are handled the same as the arguments for <code>rand</code>, except for the
argument <var>l</var>.
<p>Five different algorithms are used depending on the range of <var>l</var>
and whether or not <var>l</var> is a scalar or a matrix.
<dl>
<dt>For scalar <var>l</var> ≤ 12, use direct method.<dd>W.H. Press, et al., <cite>Numerical Recipes in C</cite>,
Cambridge University Press, 1992.
<br><dt>For scalar <var>l</var> > 12, use rejection method.[1]<dd>W.H. Press, et al., <cite>Numerical Recipes in C</cite>,
Cambridge University Press, 1992.
<br><dt>For matrix <var>l</var> ≤ 10, use inversion method.[2]<dd>E. Stadlober, et al., WinRand source code, available via FTP.
<br><dt>For matrix <var>l</var> > 10, use patchwork rejection method.<dd>E. Stadlober, et al., WinRand source code, available via FTP, or
H. Zechner, <cite>Efficient sampling from continuous and discrete
unimodal distributions</cite>, Doctoral Dissertation, 156pp., Technical
University Graz, Austria, 1994.
<br><dt>For <var>l</var> > 1e8, use normal approximation.<dd>L. Montanet, et al., <cite>Review of Particle Properties</cite>, Physical Review
D 50 p1284, 1994.
</dl>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drand.html#doc_002drand">rand</a>, <a href="doc_002drandn.html#doc_002drandn">randn</a>, <a href="doc_002drande.html#doc_002drande">rande</a>, <a href="doc_002drandg.html#doc_002drandg">randg</a>.
</p></blockquote></div>
<!-- randg src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drandg"></a>
<div class="defun">
— Loadable Function: <b>randg</b> (<var>n</var>)<var><a name="index-randg-1750"></a></var><br>
— Loadable Function: <b>randg</b> (<var>n, m, <small class="dots">...</small></var>)<var><a name="index-randg-1751"></a></var><br>
— Loadable Function: <b>randg</b> ([<var>n m <small class="dots">...</small></var>])<var><a name="index-randg-1752"></a></var><br>
— Loadable Function: <var>v</var> = <b>randg</b> (<var>"state"</var>)<var><a name="index-randg-1753"></a></var><br>
— Loadable Function: <b>randg</b> (<var>"state", v</var>)<var><a name="index-randg-1754"></a></var><br>
— Loadable Function: <b>randg</b> (<var>"state", "reset"</var>)<var><a name="index-randg-1755"></a></var><br>
— Loadable Function: <var>v</var> = <b>randg</b> (<var>"seed"</var>)<var><a name="index-randg-1756"></a></var><br>
— Loadable Function: <b>randg</b> (<var>"seed", v</var>)<var><a name="index-randg-1757"></a></var><br>
— Loadable Function: <b>randg</b> (<var>"seed", "reset"</var>)<var><a name="index-randg-1758"></a></var><br>
<blockquote><p>Return a matrix with <code>gamma(</code><var>a</var><code>,1)</code> distributed random elements.
The arguments are handled the same as the arguments for <code>rand</code>,
except for the argument <var>a</var>.
<p>This can be used to generate many distributions:
<dl>
<dt><code>gamma (a, b)</code> for <code>a > -1</code>, <code>b > 0</code><dd>
<pre class="example"> r = b * randg (a)
</pre>
<br><dt><code>beta (a, b)</code> for <code>a > -1</code>, <code>b > -1</code><dd>
<pre class="example"> r1 = randg (a, 1)
r = r1 / (r1 + randg (b, 1))
</pre>
<br><dt><code>Erlang (a, n)</code><dd>
<pre class="example"> r = a * randg (n)
</pre>
<br><dt><code>chisq (df)</code> for <code>df > 0</code><dd>
<pre class="example"> r = 2 * randg (df / 2)
</pre>
<br><dt><code>t (df)</code> for <code>0 < df < inf</code> (use randn if df is infinite)<dd>
<pre class="example"> r = randn () / sqrt (2 * randg (df / 2) / df)
</pre>
<br><dt><code>F (n1, n2)</code> for <code>0 < n1</code>, <code>0 < n2</code><dd>
<pre class="example"> ## r1 equals 1 if n1 is infinite
r1 = 2 * randg (n1 / 2) / n1
## r2 equals 1 if n2 is infinite
r2 = 2 * randg (n2 / 2) / n2
r = r1 / r2
</pre>
<br><dt>negative <code>binomial (n, p)</code> for <code>n > 0</code>, <code>0 < p <= 1</code><dd>
<pre class="example"> r = randp ((1 - p) / p * randg (n))
</pre>
<br><dt>non-central <code>chisq (df, L)</code>, for <code>df >= 0</code> and <code>L > 0</code><dd>(use chisq if <code>L = 0</code>)
<pre class="example"> r = randp (L / 2)
r(r > 0) = 2 * randg (r(r > 0))
r(df > 0) += 2 * randg (df(df > 0)/2)
</pre>
<br><dt><code>Dirichlet (a1, ... ak)</code><dd>
<pre class="example"> r = (randg (a1), ..., randg (ak))
r = r / sum (r)
</pre>
</dl>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drand.html#doc_002drand">rand</a>, <a href="doc_002drandn.html#doc_002drandn">randn</a>, <a href="doc_002drande.html#doc_002drande">rande</a>, <a href="doc_002drandp.html#doc_002drandp">randp</a>.
</p></blockquote></div>
<p>The generators operate in the new or old style together, it is not
possible to mix the two. Initializing any generator with
<code>"state"</code> or <code>"seed"</code> causes the others to switch to the
same style for future calls.
<p>The state of each generator is independent and calls to different
generators can be interleaved without affecting the final result. For
example,
<pre class="example"> rand ("state", [11, 22, 33]);
randn ("state", [44, 55, 66]);
u = rand (100, 1);
n = randn (100, 1);
</pre>
<p class="noindent">and
<pre class="example"> rand ("state", [11, 22, 33]);
randn ("state", [44, 55, 66]);
u = zeros (100, 1);
n = zeros (100, 1);
for i = 1:100
u(i) = rand ();
n(i) = randn ();
end
</pre>
<p class="noindent">produce equivalent results. When the generators are initialized in
the old style with <code>"seed"</code> only <code>rand</code> and <code>randn</code> are
independent, because the old <code>rande</code>, <code>randg</code> and
<code>randp</code> generators make calls to <code>rand</code> and <code>randn</code>.
<p>The generators are initialized with random states at start-up, so
that the sequences of random numbers are not the same each time you run
Octave.<a rel="footnote" href="#fn-1" name="fnd-1"><sup>1</sup></a> If you really do
need to reproduce a sequence of numbers exactly, you can set the state
or seed to a specific value.
<p>If invoked without arguments, <code>rand</code> and <code>randn</code> return a
single element of a random sequence.
<p>The original <code>rand</code> and <code>randn</code> functions use Fortran code from
<span class="sc">ranlib</span>, a library of Fortran routines for random number generation,
compiled by Barry W. Brown and James Lovato of the Department of
Biomathematics at The University of Texas, M.D. Anderson Cancer Center,
Houston, TX 77030.
<!-- randperm src/DLD-FUNCTIONS/rand.cc -->
<p><a name="doc_002drandperm"></a>
<div class="defun">
— Loadable Function: <b>randperm</b> (<var>n</var>)<var><a name="index-randperm-1759"></a></var><br>
— Loadable Function: <b>randperm</b> (<var>n, m</var>)<var><a name="index-randperm-1760"></a></var><br>
<blockquote><p>Return a row vector containing a random permutation of <code>1:</code><var>n</var>.
If <var>m</var> is supplied, return <var>m</var> unique entries, sampled without
replacement from <code>1:</code><var>n</var>. The complexity is O(<var>n</var>) in
memory and O(<var>m</var>) in time, unless <var>m</var> < <var>n</var>/5, in which case
O(<var>m</var>) memory is used as well. The randomization is performed using
rand(). All permutations are equally likely.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dperms.html#doc_002dperms">perms</a>.
</p></blockquote></div>
<div class="footnote">
<hr>
<h4>Footnotes</h4><p class="footnote"><small>[<a name="fn-1" href="#fnd-1">1</a>]</small> The old versions of <code>rand</code> and <code>randn</code>
obtain their initial seeds from the system clock.</p>
<hr></div>
</body></html>
