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| <h2 title="Class Algebra" class="title">Class Algebra</h2> |
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| <li>org.apache.ignite.ml.math.Algebra</li> |
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| <pre>public class <span class="typeNameLabel">Algebra</span> |
| extends <a href="../../../../../org/apache/ignite/ml/math/Constants.html" title="class in org.apache.ignite.ml.math">Constants</a></pre> |
| <div class="block">Miscellaneous arithmetic and algebra functions. |
| Lifted from Apache Mahout.</div> |
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| <code><a href="../../../../../org/apache/ignite/ml/math/Constants.html#BIG">BIG</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#BIGINV">BIGINV</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#LOGPI">LOGPI</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#MACHEP">MACHEP</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#MAXGAM">MAXGAM</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#MAXLOG">MAXLOG</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#MINLOG">MINLOG</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#SQRTH">SQRTH</a>, <a href="../../../../../org/apache/ignite/ml/math/Constants.html#SQTPI">SQTPI</a></code></li> |
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| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#Algebra--">Algebra</a></span>()</code> </td> |
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| <tr> |
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| <th class="colLast" scope="col">Method and Description</th> |
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| <tr id="i0" class="altColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.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/ignite/ml/math/Algebra.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/ignite/ml/math/Algebra.html#ceil-double-">ceil</a></span>(double val)</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/ignite/ml/math/Algebra.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 double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#evalPoly-double-double:A-int-">evalPoly</a></span>(double x, |
| double[] coef, |
| int n)</code> |
| <div class="block">Evaluates the given polynomial of degree <code>N</code> at <code>x</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/ignite/ml/math/Algebra.html#evalPoly1-double-double:A-int-">evalPoly1</a></span>(double x, |
| double[] coef, |
| int n)</code> |
| <div class="block">Evaluates the given polynomial of degree <code>N</code> at <code>x</code>, assuming coefficient of N is 1.0.</div> |
| </td> |
| </tr> |
| <tr id="i6" class="altColor"> |
| <td class="colFirst"><code>static long</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#floor-double-">floor</a></span>(double val)</code> |
| <div class="block">Returns the largest <code>long <= value</code>.</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/ignite/ml/math/Algebra.html#hypot-double-double-">hypot</a></span>(double a, |
| double b)</code> |
| <div class="block">Gets <code>sqrt(a^2 + b^2)</code> without under/overflow.</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/ignite/ml/math/Algebra.html#log-double-double-">log</a></span>(double base, |
| double val)</code> |
| <div class="block">Returns <code>log<sub>base</sub>value</code>.</div> |
| </td> |
| </tr> |
| <tr id="i9" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#log10-double-">log10</a></span>(double val)</code> |
| <div class="block">Returns <code>log<sub>10</sub>value</code>.</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/ignite/ml/math/Algebra.html#log2-double-">log2</a></span>(double val)</code> |
| <div class="block">Returns <code>log<sub>2</sub>value</code>.</div> |
| </td> |
| </tr> |
| <tr id="i11" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#logFactorial-int-">logFactorial</a></span>(int k)</code> |
| <div class="block">Returns <code>log(k!)</code>.</div> |
| </td> |
| </tr> |
| <tr id="i12" class="altColor"> |
| <td class="colFirst"><code>static long</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#longFactorial-int-">longFactorial</a></span>(int k)</code> |
| <div class="block">Instantly returns the factorial <code>k!</code>.</div> |
| </td> |
| </tr> |
| <tr id="i13" class="rowColor"> |
| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/ignite/ml/math/Algebra.html#stirlingCorrection-int-">stirlingCorrection</a></span>(int k)</code> |
| <div class="block">Returns the StirlingCorrection.</div> |
| </td> |
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| <code><a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#clone--" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#equals-java.lang.Object-" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#finalize--" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#getClass--" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#hashCode--" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#notify--" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#notifyAll--" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#toString--" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait--" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait-long-" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait-long-int-" title="class or interface in java.lang">wait</a></code></li> |
| </ul> |
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| <h4>Algebra</h4> |
| <pre>public Algebra()</pre> |
| </li> |
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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 |
| <code>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</code>. |
| <ul> <li><code>k&lt;0</code>: <code>0</code>.</li> |
| <li><code>k==0</code>: <code>1</code>.</li> |
| <li><code>k==1</code>: <code>n</code>.</li> |
| <li>else: <code>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k)</code>.</li> |
| </ul></div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>n</code> - Size of set.</dd> |
| <dd><code>k</code> - Size of subset.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>Binomial coefficient.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="binomial-long-long-"> |
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| </a> |
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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><code>k&lt;0</code>: <code>0</code>. <li><code>k==0 || k==n</code>: <code>1</code>. <li><code>k==1 || k==n-1</code>: |
| <code>n</code>. <li>else: <code>(n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k )</code>. </ul></div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>n</code> - Size of set.</dd> |
| <dd><code>k</code> - Size of subset.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>Binomial coefficient.</dd> |
| </dl> |
| </li> |
| </ul> |
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| </a> |
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| <h4>ceil</h4> |
| <pre>public static long ceil(double val)</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> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>val</code> - Value for ceil.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>Ceil of the given value.</dd> |
| </dl> |
| </li> |
| </ul> |
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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 class="snippet"> |
| 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> |
| <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> |
| <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> - Coefficients of the polynomial.</dd> |
| <dd><code>N</code> - Number of coefficients.</dd> |
| </dl> |
| </li> |
| </ul> |
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| </a> |
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| <h4>floor</h4> |
| <pre>public static long floor(double val)</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> |
| <a name="log-double-double-"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>log</h4> |
| <pre>public static double log(double base, |
| double val)</pre> |
| <div class="block">Returns <code>log<sub>base</sub>value</code>.</div> |
| </li> |
| </ul> |
| <a name="log10-double-"> |
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| </a> |
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| <h4>log10</h4> |
| <pre>public static double log10(double val)</pre> |
| <div class="block">Returns <code>log<sub>10</sub>value</code>.</div> |
| </li> |
| </ul> |
| <a name="log2-double-"> |
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| <ul class="blockList"> |
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| <h4>log2</h4> |
| <pre>public static double log2(double val)</pre> |
| <div class="block">Returns <code>log<sub>2</sub>value</code>.</div> |
| </li> |
| </ul> |
| <a name="logFactorial-int-"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>logFactorial</h4> |
| <pre>public static double logFactorial(int k)</pre> |
| <div class="block">Returns <code>log(k!)</code>. Tries to avoid overflows. For <code>k&lt;30</code> simply looks up a table in O(1). |
| For <code>k&gt;=30</code> uses Stirling's approximation.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - must hold <code>k &gt;= 0</code>.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="longFactorial-int-"> |
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| </a> |
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| <li class="blockList"> |
| <h4>longFactorial</h4> |
| <pre>public static long longFactorial(int k)</pre> |
| <div class="block">Instantly returns the factorial <code>k!</code>.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>k</code> - must hold <code>k >= 0 && k < 21</code></dd> |
| </dl> |
| </li> |
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| <a name="stirlingCorrection-int-"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <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 <code>log(k!)</code> (series in |
| 1/k, or table values for small k) with int parameter k. <code>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) </code> </p></div> |
| </li> |
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| <a name="evalPoly1-double-double:A-int-"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>evalPoly1</h4> |
| <pre>public static double evalPoly1(double x, |
| double[] coef, |
| int n)</pre> |
| <div class="block">Evaluates the given polynomial of degree <code>N</code> at <code>x</code>, assuming coefficient of N is 1.0. Otherwise same |
| as <a href="../../../../../org/apache/ignite/ml/math/Algebra.html#evalPoly-double-double:A-int-"><code>evalPoly(double, double[], int)</code></a>. |
| <pre class="snippet"> |
| 2 N |
| y = C + C x + C x +...+ C x |
| 0 1 2 N |
| </pre> |
| where <pre class="snippet"> |
| C = 1 |
| N |
| </pre> |
| and hence is omitted from the array. |
| <p> |
| Coefficients are stored in reverse order:</p> |
| <pre class="snippet"> |
| coef[0] = C , ..., coef[N-1] = C . |
| N-1 0 |
| </pre> |
| Calling arguments are otherwise the same as <a href="../../../../../org/apache/ignite/ml/math/Algebra.html#evalPoly-double-double:A-int-"><code>evalPoly(double, double[], int)</code></a>. |
| <p> |
| In the interest of speed, there are no checks for out of bounds arithmetic.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>x</code> - Argument to the polynomial.</dd> |
| <dd><code>coef</code> - Coefficients of the polynomial.</dd> |
| <dd><code>n</code> - Degree of the polynomial.</dd> |
| </dl> |
| </li> |
| </ul> |
| <a name="evalPoly-double-double:A-int-"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
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| <h4>evalPoly</h4> |
| <pre>public static double evalPoly(double x, |
| double[] coef, |
| int n)</pre> |
| <div class="block">Evaluates the given polynomial of degree <code>N</code> at <code>x</code>. |
| <pre class="snippet"> |
| 2 N |
| y = C + C x + C x +...+ C x |
| 0 1 2 N |
| </pre> |
| <p> |
| Coefficients are stored in reverse order:</p> |
| <pre class="snippet"> |
| coef[0] = C , ..., coef[N] = C . |
| N 0 |
| </pre> |
| <p> |
| In the interest of speed, there are no checks for out of bounds arithmetic.</p></div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>x</code> - Argument to the polynomial.</dd> |
| <dd><code>coef</code> - Coefficients of the polynomial.</dd> |
| <dd><code>n</code> - Degree of the polynomial.</dd> |
| </dl> |
| </li> |
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| <h4>hypot</h4> |
| <pre>public static double hypot(double a, |
| double b)</pre> |
| <div class="block">Gets <code>sqrt(a^2 + b^2)</code> without under/overflow.</div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>a</code> - First side value.</dd> |
| <dd><code>b</code> - Second side value.</dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>Hypotenuse value.</dd> |
| </dl> |
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