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Arithmetic (Colt 1.2.0 - API Specification)
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cern.jet.math
 
Class Arithmetic</H2>
<PRE>
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">java.lang.Object</A>
 <IMG SRC="../../../resources/inherit.gif" ALT="extended by"><A HREF="../../../cern/jet/math/Constants.html" title="class in cern.jet.math">cern.jet.math.Constants</A>
 <IMG SRC="../../../resources/inherit.gif" ALT="extended by">cern.jet.math.Arithmetic
</PRE>
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<DL>
<DT>public class Arithmetic<DT>extends <A HREF="../../../cern/jet/math/Constants.html" title="class in cern.jet.math">Constants</A></DL>

Arithmetic functions.

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Method Summary</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#binomial(double, long)">binomial</A>(double&nbsp;n,
 long&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#binomial(long, long)">binomial</A>(long&nbsp;n,
 long&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
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<CODE>static&nbsp;long</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#ceil(double)">ceil</A>(double&nbsp;value)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the smallest <code>long &gt;= value</code>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#chbevl(double, double[], int)">chbevl</A>(double&nbsp;x,
 double[]&nbsp;coef,
 int&nbsp;N)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Evaluates the series of Chebyshev polynomials Ti at argument x/2.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#factorial(int)">factorial</A>(int&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Instantly returns the factorial <tt>k!</tt>.</TD>
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<CODE>static&nbsp;long</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#floor(double)">floor</A>(double&nbsp;value)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the largest <code>long &lt;= value</code>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#log(double, double)">log</A>(double&nbsp;base,
 double&nbsp;value)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <tt>logbasevalue</tt>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#log10(double)">log10</A>(double&nbsp;value)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <tt>log10value</tt>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#log2(double)">log2</A>(double&nbsp;value)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <tt>log2value</tt>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#logFactorial(int)">logFactorial</A>(int&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <tt>log(k!)</tt>.</TD>
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<CODE>static&nbsp;long</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#longFactorial(int)">longFactorial</A>(int&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Instantly returns the factorial <tt>k!</tt>.</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/math/Arithmetic.html#stirlingCorrection(int)">stirlingCorrection</A>(int&nbsp;k)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the StirlingCorrection.</TD>
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<A NAME="binomial(double, long)"></A><H3>
binomial</H3>
<PRE>
public static double binomial(double&nbsp;n,
 long&nbsp;k)</PRE>
<DL>
<DD>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>k<0<tt>: <tt>0</tt>.
 <li>k==0<tt>: <tt>1</tt>.
 <li>k==1<tt>: <tt>n</tt>.
 <li>else: <tt>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</tt>.
 </ul>

<DD><DL>

<DT>Returns:<DD>the binomial coefficient.</DL>
</DD>
</DL>
<HR>

<A NAME="binomial(long, long)"></A><H3>
binomial</H3>
<PRE>
public static double binomial(long&nbsp;n,
 long&nbsp;k)</PRE>
<DL>
<DD>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>k<0<tt>: <tt>0</tt>.
 <li>k==0 || k==n<tt>: <tt>1</tt>.
 <li>k==1 || k==n-1<tt>: <tt>n</tt>.
 <li>else: <tt>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</tt>.
 </ul>

<DD><DL>

<DT>Returns:<DD>the binomial coefficient.</DL>
</DD>
</DL>
<HR>

<A NAME="ceil(double)"></A><H3>
ceil</H3>
<PRE>
public static long ceil(double&nbsp;value)</PRE>
<DL>
<DD>Returns the smallest <code>long &gt;= value</code>.
 <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.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="chbevl(double, double[], int)"></A><H3>
chbevl</H3>
<PRE>
public static double chbevl(double&nbsp;x,
 double[]&nbsp;coef,
 int&nbsp;N)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></PRE>
<DL>
<DD>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.
 
 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.
 
 If the coefficients are for the inverted interval, in
 which (a, b) is mapped to (1/b, 1/a), the transformation
 required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
 this becomes x -> 4a/x - 1.
 
 SPEED:
 
 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.

<DD><DL>
<DT>Parameters:<DD><CODE>x</CODE> - argument to the polynomial.<DD><CODE>coef</CODE> - the coefficients of the polynomial.<DD><CODE>N</CODE> - the number of coefficients.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/ArithmeticException.html" title="class or interface in java.lang">ArithmeticException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="factorial(int)"></A><H3>
factorial</H3>
<PRE>
public static double factorial(int&nbsp;k)</PRE>
<DL>
<DD>Instantly returns the factorial <tt>k!</tt>.

<DD><DL>
<DT>Parameters:<DD><CODE>k</CODE> - must hold <tt>k &gt;= 0</tt>.</DL>
</DD>
</DL>
<HR>

<A NAME="floor(double)"></A><H3>
floor</H3>
<PRE>
public static long floor(double&nbsp;value)</PRE>
<DL>
<DD>Returns the largest <code>long &lt;= value</code>.
 <dt>Examples: <code>
 1.0 -> 1, 1.2 -> 1, 1.9 -> 1 <dt>
 2.0 -> 2, 2.2 -> 2, 2.9 -> 2 </code><dt>
 This method is safer than using (long) Math.floor(value), because of possible rounding error.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="log(double, double)"></A><H3>
log</H3>
<PRE>
public static double log(double&nbsp;base,
 double&nbsp;value)</PRE>
<DL>
<DD>Returns <tt>logbasevalue</tt>.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="log10(double)"></A><H3>
log10</H3>
<PRE>
public static double log10(double&nbsp;value)</PRE>
<DL>
<DD>Returns <tt>log10value</tt>.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="log2(double)"></A><H3>
log2</H3>
<PRE>
public static double log2(double&nbsp;value)</PRE>
<DL>
<DD>Returns <tt>log2value</tt>.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="logFactorial(int)"></A><H3>
logFactorial</H3>
<PRE>
public static double logFactorial(int&nbsp;k)</PRE>
<DL>
<DD>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.

<DD><DL>
<DT>Parameters:<DD><CODE>k</CODE> - must hold <tt>k &gt;= 0</tt>.</DL>
</DD>
</DL>
<HR>

<A NAME="longFactorial(int)"></A><H3>
longFactorial</H3>
<PRE>
public static long longFactorial(int&nbsp;k)
 throws <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></PRE>
<DL>
<DD>Instantly returns the factorial <tt>k!</tt>.

<DD><DL>
<DT>Parameters:<DD><CODE>k</CODE> - must hold <tt>k &gt;= 0 && k &lt; 21</tt>.
<DT>Throws:
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE></DL>
</DD>
</DL>
<HR>

<A NAME="stirlingCorrection(int)"></A><H3>
stirlingCorrection</H3>
<PRE>
public static double stirlingCorrection(int&nbsp;k)</PRE>
<DL>
<DD>Returns the StirlingCorrection. 
 
 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. 
 
 <tt>
 log k! = (k + 1/2)log(k + 1) - (k + 1) + (1/2)log(2Pi) +
 stirlingCorrection(k + 1) 
 
 log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + 
 stirlingCorrection(k)
 </tt>

<DD><DL>
</DL>
</DD>
</DL>

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