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<html>
<head>
<title>
MOC_DISPLAY - Estimate and plot the modulus of continuity function
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MOC_DISPLAY <br>
Estimate and plot the modulus of continuity function
</h1>
<hr>
<p>
<b>MOC_DISPLAY</b>
is a MATLAB library of functions which
estimate and plot the modulus of continuity function.
</p>
<p>
Given a function F(X) and an interval [A,B], the modulus of continuity
may be defined as
<blockquote>
MC(T) = max | F(X+DX) - F(X) |, for 0 <= DX <= T,
and X and X+DX in [A,B].
</blockquote>
The function MC(T) records the maximum change that can occur in
F(X) over an interval of length T or less. MC(T) is
a monotone increasing function.
</p>
<p>
For convenience, we define a related function
<blockquote>
MC1(DX) = max | F(X+DX) - F(X) |, for 0 <= DX,
and X and X+DX in [A,B].
</blockquote>
The function MC1(DX) records the maximum change that can occur in
F(X) over an interval of length exactly DX. MC1(DX) need
not be a strictly increasing function, particularly if F(X) is periodic.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>moc_display</b> ( <i>a</i>, <i>b</i>, <i>n</i>, <b>@</b><i>f</i> )
</blockquote>
where
<ul>
<li>
<i>a, b</i> are the endpoints of the interval;
</li>
<li>
<i>n</i> is the number of equally spaced sample points;
</li>
<li>
<b>@</b><i>f</i> is a handle to the function F(X).
</li>
</ul>
This command will evaluate F(X) at N points, estimate the modulus
of continuity function and displace F(X), MC1(DX) and MC(T).
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>MOC_DISPLAY</b> is available in
<a href = "../../m_src/moc_display/moc_display.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "moc.m">moc.m</a>
estimates MC(T).
</li>
<li>
<a href = "moc_display.m">moc_display.m</a>
estimates the modulus of continuity function, and displays
F(X), MC1(DX) and MC(T).
</li>
<li>
<a href = "moc1.m">moc1.m</a>
estimates MC1(DX).
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>F1</b> = cos ( 6 * pi * x ) .* exp ( - pi * x .* x );
<ul>
<li>
<a href = "f1.m">f1.m</a>,
evaluates the function.
</li>
<li>
<a href = "f1.png">f1.png</a>,
the plot created by MOC_DISPLAY.
</li>
</ul>
</p>
<p>
<b>F2</b> = cos ( 3 * pi * x );
<ul>
<li>
<a href = "f2.m">f2.m</a>,
evaluates the function.
</li>
<li>
<a href = "f2.png">f2.png</a>,
the plot created by MOC_DISPLAY.
</li>
</ul>
</p>
<p>
<b>F3</b> = x .* x + 0.5 * x - 2;
<ul>
<li>
<a href = "f3.m">f3.m</a>,
evaluates the function.
</li>
<li>
<a href = "f3.png">f3.png</a>,
the plot created by MOC_DISPLAY.
</li>
</ul>
</p>
<p>
<b>F4</b> = exp ( x ) + 3;
<ul>
<li>
<a href = "f4.m">f4.m</a>,
evaluates the function.
</li>
<li>
<a href = "f4.png">f4.png</a>,
the plot created by MOC_DISPLAY.
</li>
</ul>
</p>
<p>
<b>F5</b> = floor ( ( x - 1 ).^2 );
<ul>
<li>
<a href = "f5.m">f5.m</a>,
evaluates the function.
</li>
<li>
<a href = "f5.png">f5.png</a>,
the plot created by MOC_DISPLAY.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 04 October 2010.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>