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| <h2 title="Class Arithmetic" class="title">Class Arithmetic</h2> |
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| <li>org.apache.mahout.collections.Arithmetic</li> |
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| <pre>public final class <span class="typeNameLabel">Arithmetic</span> |
| extends <a href="../../../../org/apache/mahout/collections/Constants.html" title="class in org.apache.mahout.collections">Constants</a></pre> |
| <div class="block">Arithmetic functions.</div> |
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| <code><a href="../../../../org/apache/mahout/collections/Constants.html#BIG">BIG</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#BIGINV">BIGINV</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#LOGPI">LOGPI</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#MACHEP">MACHEP</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#MAXGAM">MAXGAM</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#MAXLOG">MAXLOG</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#MINLOG">MINLOG</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#SQRTH">SQRTH</a>, <a href="../../../../org/apache/mahout/collections/Constants.html#SQTPI">SQTPI</a></code></li> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#binomial-double-long-">binomial</a></span>(double n, |
| long k)</code> |
| <div class="block">Efficiently returns the binomial coefficient, often also referred to as |
| "n over k" or "n choose k".</div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#binomial-long-long-">binomial</a></span>(long n, |
| long k)</code> |
| <div class="block">Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".</div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code>static long</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#ceil-double-">ceil</a></span>(double value)</code> |
| <div class="block">Returns the smallest <code>long >= value</code>.</div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#chbevl-double-double:A-int-">chbevl</a></span>(double x, |
| double[] coef, |
| int N)</code> |
| <div class="block">Evaluates the series of Chebyshev polynomials Ti at argument x/2.</div> |
| </td> |
| </tr> |
| <tr id="i4" class="altColor"> |
| <td class="colFirst"><code>static long</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#floor-double-">floor</a></span>(double value)</code> |
| <div class="block">Returns the largest <code>long <= value</code>.</div> |
| </td> |
| </tr> |
| <tr id="i5" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#log-double-double-">log</a></span>(double base, |
| double value)</code> |
| <div class="block">Returns <tt>log<sub>base</sub>value</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i6" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#log10-double-">log10</a></span>(double value)</code> |
| <div class="block">Returns <tt>log<sub>10</sub>value</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i7" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#log2-double-">log2</a></span>(double value)</code> |
| <div class="block">Returns <tt>log<sub>2</sub>value</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i8" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#logFactorial-int-">logFactorial</a></span>(int k)</code> |
| <div class="block">Returns <tt>log(k!)</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i9" class="rowColor"> |
| <td class="colFirst"><code>static long</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#longFactorial-int-">longFactorial</a></span>(int k)</code> |
| <div class="block">Instantly returns the factorial <tt>k!</tt>.</div> |
| </td> |
| </tr> |
| <tr id="i10" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/apache/mahout/collections/Arithmetic.html#stirlingCorrection-int-">stirlingCorrection</a></span>(int k)</code> |
| <div class="block">Returns the StirlingCorrection.</div> |
| </td> |
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| <h4>binomial</h4> |
| <pre>public static double binomial(double n, |
| long k)</pre> |
| <div class="block">Efficiently returns the binomial coefficient, often also referred to as |
| "n over k" or "n choose k". The binomial coefficient is defined as |
| <tt>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</tt>. |
| <ul> <li><tt>k<0</tt>: <tt>0</tt>.</li> |
| <li><tt>k==0</tt>: <tt>1</tt>.</li> |
| <li><tt>k==1</tt>: <tt>n</tt>.</li> |
| <li>else: <tt>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k)</tt>.</li> |
| </ul></div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>n</code> - </dd> |
| <dd><code>k</code> - </dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the binomial coefficient.</dd> |
| </dl> |
| </li> |
| </ul> |
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| <h4>binomial</h4> |
| <pre>public static double binomial(long n, |
| long k)</pre> |
| <div class="block">Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial |
| coefficient is defined as <ul> <li><tt>k<0</tt>: <tt>0</tt>. <li><tt>k==0 || k==n</tt>: <tt>1</tt>. <li><tt>k==1 || k==n-1</tt>: |
| <tt>n</tt>. <li>else: <tt>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</tt>. </ul></div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the binomial coefficient.</dd> |
| </dl> |
| </li> |
| </ul> |
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| <h4>ceil</h4> |
| <pre>public static long ceil(double value)</pre> |
| <div class="block">Returns the smallest <code>long >= value</code>. |
| <dl><dt>Examples: <code>1.0 -> 1, 1.2 -> 2, 1.9 -> 2</code>. This |
| method is safer than using (long) Math.ceil(value), because of possible rounding error.</dt></dl></div> |
| </li> |
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| <h4>chbevl</h4> |
| <pre>public static double chbevl(double x, |
| double[] coef, |
| int N)</pre> |
| <div class="block">Evaluates the series of Chebyshev polynomials Ti at argument x/2. The series is given by |
| <pre> |
| N-1 |
| - ' |
| y = > coef[i] T (x/2) |
| - i |
| i=0 |
| </pre> |
| Coefficients are stored in reverse order, i.e. the zero order term is last in the array. Note N is the number of |
| coefficients, not the order. <p> If coefficients are for the interval a to b, x must have been transformed to x -< |
| 2(2x - b - a)/(b-a) before entering the routine. This maps x from (a, b) to (-1, 1), over which the Chebyshev |
| polynomials are defined. <p> If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, |
| 1/a), the transformation required is <code>x -> 2(2ab/x - b - a)/(b-a)</code>. If b is infinity, this becomes <code>x -> 4a/x - 1</code>. |
| <p> SPEED: <p> Taking advantage of the recurrence properties of the Chebyshev polynomials, the routine requires one |
| more addition per loop than evaluating a nested polynomial of the same degree.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>x</code> - argument to the polynomial.</dd> |
| <dd><code>coef</code> - the coefficients of the polynomial.</dd> |
| <dd><code>N</code> - the number of coefficients.</dd> |
| </dl> |
| </li> |
| </ul> |
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| <h4>floor</h4> |
| <pre>public static long floor(double value)</pre> |
| <div class="block">Returns the largest <code>long <= value</code>. |
| <dl><dt>Examples: <code>1.0 -> 1, 1.2 -> 1, 1.9 -> 1 <dt> 2.0 -> 2, 2.2 -> 2, 2.9 -> 2</code></dt></dl> |
| This method is safer than using (long) Math.floor(value), because of possible rounding error.</div> |
| </li> |
| </ul> |
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| <h4>log</h4> |
| <pre>public static double log(double base, |
| double value)</pre> |
| <div class="block">Returns <tt>log<sub>base</sub>value</tt>.</div> |
| </li> |
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| <h4>log10</h4> |
| <pre>public static double log10(double value)</pre> |
| <div class="block">Returns <tt>log<sub>10</sub>value</tt>.</div> |
| </li> |
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| <h4>log2</h4> |
| <pre>public static double log2(double value)</pre> |
| <div class="block">Returns <tt>log<sub>2</sub>value</tt>.</div> |
| </li> |
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| <h4>logFactorial</h4> |
| <pre>public static double logFactorial(int k)</pre> |
| <div class="block">Returns <tt>log(k!)</tt>. Tries to avoid overflows. For <tt>k<30</tt> simply looks up a table in O(1). For |
| <tt>k>=30</tt> uses stirlings approximation.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - must hold <tt>k >= 0</tt>.</dd> |
| </dl> |
| </li> |
| </ul> |
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| <h4>longFactorial</h4> |
| <pre>public static long longFactorial(int k)</pre> |
| <div class="block">Instantly returns the factorial <tt>k!</tt>.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - must hold <code>k >= 0 && k < 21</code></dd> |
| </dl> |
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| <h4>stirlingCorrection</h4> |
| <pre>public static double stirlingCorrection(int k)</pre> |
| <div class="block">Returns the StirlingCorrection. <p> Correction term of the Stirling approximation for <tt>log(k!)</tt> (series in |
| 1/k, or table values for small k) with int parameter k. </p> <tt> log k! = (k + 1/2)log(k + 1) - (k + 1) + |
| (1/2)log(2Pi) + STIRLING_CORRECTION(k + 1) log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + |
| STIRLING_CORRECTION(k) </tt></div> |
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