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+<div class="subTitle">org.apache.commons.math3.util</div>
+<h2 title="Class MathUtils" class="title">Class MathUtils</h2>
+</div>
+<div class="contentContainer">
+<ul class="inheritance">
+<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
+<li>
+<ul class="inheritance">
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+<div class="description">
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+<pre>public final class <span class="strong">MathUtils</span>
+extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
+<div class="block">Miscellaneous utility functions.</div>
+<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/util/ArithmeticUtils.html" title="class in org.apache.commons.math3.util"><code>ArithmeticUtils</code></a>,
+<a href="../../../../../org/apache/commons/math3/util/Precision.html" title="class in org.apache.commons.math3.util"><code>Precision</code></a>,
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+<th class="colFirst" scope="col">Modifier and Type</th>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#PI_SQUARED">PI_SQUARED</a></strong></code>
+<div class="block">\(\pi^2\)</div>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#TWO_PI">TWO_PI</a></strong></code>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#checkFinite(double)">checkFinite</a></strong>(double&nbsp;x)</code>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#checkFinite(double[])">checkFinite</a></strong>(double[]&nbsp;val)</code>
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+<div class="block">Checks that an object is not null.</div>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#copySign(byte,%20byte)">copySign</a></strong>(byte&nbsp;magnitude,
+ byte&nbsp;sign)</code>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
+</td>
+</tr>
+<tr class="rowColor">
+<td class="colFirst"><code>static int</code></td>
+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#copySign(int,%20int)">copySign</a></strong>(int&nbsp;magnitude,
+ int&nbsp;sign)</code>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
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+<tr class="altColor">
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+ long&nbsp;sign)</code>
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+ double&nbsp;y)</code>
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+ T&nbsp;e2)</code>
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+</td>
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+<tr class="altColor">
+<td class="colFirst"><code>static &lt;T extends <a href="../../../../../org/apache/commons/math3/RealFieldElement.html" title="interface in org.apache.commons.math3">RealFieldElement</a>&lt;T&gt;&gt;&nbsp;<br>T</code></td>
+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#min(T,%20T)">min</a></strong>(T&nbsp;e1,
+ T&nbsp;e2)</code>
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+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#normalizeAngle(double,%20double)">normalizeAngle</a></strong>(double&nbsp;a,
+ double&nbsp;center)</code>
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+</td>
+</tr>
+<tr class="altColor">
+<td class="colFirst"><code>static double</code></td>
+<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/util/MathUtils.html#reduce(double,%20double,%20double)">reduce</a></strong>(double&nbsp;a,
+ double&nbsp;period,
+ double&nbsp;offset)</code>
+<div class="block">Reduce <code>|a - offset|</code> to the primary interval
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+<pre>public static final&nbsp;double TWO_PI</pre>
+<div class="block">\(2\pi\)</div>
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+ <dd>2.1</dd>
+<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.util.MathUtils.TWO_PI">Constant Field Values</a></dd></dl>
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+<pre>public static final&nbsp;double PI_SQUARED</pre>
+<div class="block">\(\pi^2\)</div>
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+ <dd>3.4</dd>
+<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.util.MathUtils.PI_SQUARED">Constant Field Values</a></dd></dl>
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+<dt><span class="strong">Returns:</span></dt><dd>the hash code</dd></dl>
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+<dt><span class="strong">Returns:</span></dt><dd><code>new Double(x).equals(new Double(y))</code></dd></dl>
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+<dt><span class="strong">Returns:</span></dt><dd>the hash code</dd><dt><span class="strong">Since:</span></dt>
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+<div class="block">Normalize an angle in a 2&pi; wide interval around a center value.
+ <p>This method has three main uses:</p>
+ <ul>
+ <li>normalize an angle between 0 and 2&pi;:<br/>
+ <code>a = MathUtils.normalizeAngle(a, FastMath.PI);</code></li>
+ <li>normalize an angle between -&pi; and +&pi;<br/>
+ <code>a = MathUtils.normalizeAngle(a, 0.0);</code></li>
+ <li>compute the angle between two defining angular positions:<br>
+ <code>angle = MathUtils.normalizeAngle(end, start) - start;</code></li>
+ </ul>
+ <p>Note that due to numerical accuracy and since &pi; cannot be represented
+ exactly, the result interval is <em>closed</em>, it cannot be half-closed
+ as would be more satisfactory in a purely mathematical view.</p></div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - angle to normalize</dd><dd><code>center</code> - center of the desired 2&pi; interval for the result</dd>
+<dt><span class="strong">Returns:</span></dt><dd>a-2k&pi; with integer k and center-&pi; &lt;= a-2k&pi; &lt;= center+&pi;</dd><dt><span class="strong">Since:</span></dt>
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+<div class="block">Find the maximum of two field elements.</div>
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+<div class="block">Find the minimum of two field elements.</div>
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+<dt><span class="strong">Returns:</span></dt><dd>min(a1, e2)</dd><dt><span class="strong">Since:</span></dt>
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+<h4>reduce</h4>
+<pre>public static&nbsp;double&nbsp;reduce(double&nbsp;a,
+ double&nbsp;period,
+ double&nbsp;offset)</pre>
+<div class="block"><p>Reduce <code>|a - offset|</code> to the primary interval
+ <code>[0, |period|)</code>.</p>
+
+ <p>Specifically, the value returned is <br/>
+ <code>a - |period| * floor((a - offset) / |period|) - offset</code>.</p>
+
+ <p>If any of the parameters are <code>NaN</code> or infinite, the result is
+ <code>NaN</code>.</p></div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Value to reduce.</dd><dd><code>period</code> - Period.</dd><dd><code>offset</code> - Value that will be mapped to <code>0</code>.</dd>
+<dt><span class="strong">Returns:</span></dt><dd>the value, within the interval <code>[0 |period|)</code>,
+ that corresponds to <code>a</code>.</dd></dl>
+</li>
+</ul>
+<a name="copySign(byte, byte)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>copySign</h4>
+<pre>public static&nbsp;byte&nbsp;copySign(byte&nbsp;magnitude,
+ byte&nbsp;sign)
+ throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - Magnitude of the returned value.</dd><dd><code>sign</code> - Sign of the returned value.</dd>
+<dt><span class="strong">Returns:</span></dt><dd>a value with magnitude equal to <code>magnitude</code> and with the
+ same sign as the <code>sign</code> argument.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if <code>magnitude == Byte.MIN_VALUE</code>
+ and <code>sign &gt;= 0</code>.</dd></dl>
+</li>
+</ul>
+<a name="copySign(short, short)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>copySign</h4>
+<pre>public static&nbsp;short&nbsp;copySign(short&nbsp;magnitude,
+ short&nbsp;sign)
+ throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - Magnitude of the returned value.</dd><dd><code>sign</code> - Sign of the returned value.</dd>
+<dt><span class="strong">Returns:</span></dt><dd>a value with magnitude equal to <code>magnitude</code> and with the
+ same sign as the <code>sign</code> argument.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if <code>magnitude == Short.MIN_VALUE</code>
+ and <code>sign &gt;= 0</code>.</dd></dl>
+</li>
+</ul>
+<a name="copySign(int, int)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>copySign</h4>
+<pre>public static&nbsp;int&nbsp;copySign(int&nbsp;magnitude,
+ int&nbsp;sign)
+ throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - Magnitude of the returned value.</dd><dd><code>sign</code> - Sign of the returned value.</dd>
+<dt><span class="strong">Returns:</span></dt><dd>a value with magnitude equal to <code>magnitude</code> and with the
+ same sign as the <code>sign</code> argument.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if <code>magnitude == Integer.MIN_VALUE</code>
+ and <code>sign &gt;= 0</code>.</dd></dl>
+</li>
+</ul>
+<a name="copySign(long, long)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>copySign</h4>
+<pre>public static&nbsp;long&nbsp;copySign(long&nbsp;magnitude,
+ long&nbsp;sign)
+ throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre>
+<div class="block">Returns the first argument with the sign of the second argument.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>magnitude</code> - Magnitude of the returned value.</dd><dd><code>sign</code> - Sign of the returned value.</dd>
+<dt><span class="strong">Returns:</span></dt><dd>a value with magnitude equal to <code>magnitude</code> and with the
+ same sign as the <code>sign</code> argument.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if <code>magnitude == Long.MIN_VALUE</code>
+ and <code>sign &gt;= 0</code>.</dd></dl>
+</li>
+</ul>
+<a name="checkFinite(double)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>checkFinite</h4>
+<pre>public static&nbsp;void&nbsp;checkFinite(double&nbsp;x)
+ throws <a href="../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></pre>
+<div class="block">Check that the argument is a real number.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Argument.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></code> - if <code>x</code> is not a
+ finite real number.</dd></dl>
+</li>
+</ul>
+<a name="checkFinite(double[])">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>checkFinite</h4>
+<pre>public static&nbsp;void&nbsp;checkFinite(double[]&nbsp;val)
+ throws <a href="../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></pre>
+<div class="block">Check that all the elements are real numbers.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>val</code> - Arguments.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/NotFiniteNumberException.html" title="class in org.apache.commons.math3.exception">NotFiniteNumberException</a></code> - if any values of the array is not a
+ finite real number.</dd></dl>
+</li>
+</ul>
+<a name="checkNotNull(java.lang.Object, org.apache.commons.math3.exception.util.Localizable, java.lang.Object...)">
+<!-- -->
+</a>
+<ul class="blockList">
+<li class="blockList">
+<h4>checkNotNull</h4>
+<pre>public static&nbsp;void&nbsp;checkNotNull(<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;o,
+ <a href="../../../../../org/apache/commons/math3/exception/util/Localizable.html" title="interface in org.apache.commons.math3.exception.util">Localizable</a>&nbsp;pattern,
+ <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>...&nbsp;args)
+ throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
+<div class="block">Checks that an object is not null.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>o</code> - Object to be checked.</dd><dd><code>pattern</code> - Message pattern.</dd><dd><code>args</code> - Arguments to replace the placeholders in <code>pattern</code>.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>o</code> is <code>null</code>.</dd></dl>
+</li>
+</ul>
+<a name="checkNotNull(java.lang.Object)">
+<!-- -->
+</a>
+<ul class="blockListLast">
+<li class="blockList">
+<h4>checkNotNull</h4>
+<pre>public static&nbsp;void&nbsp;checkNotNull(<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;o)
+ throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
+<div class="block">Checks that an object is not null.</div>
+<dl><dt><span class="strong">Parameters:</span></dt><dd><code>o</code> - Object to be checked.</dd>
+<dt><span class="strong">Throws:</span></dt>
+<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>o</code> is <code>null</code>.</dd></dl>
+</li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+</div>
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