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| <div class="subTitle">org.apache.mahout.math.decomposer.lanczos</div> |
| <h2 title="Class LanczosSolver" class="title">Class LanczosSolver</h2> |
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| <li>org.apache.mahout.math.decomposer.lanczos.LanczosSolver</li> |
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| <div class="block"><span class="deprecatedLabel">Deprecated.</span></div> |
| <br> |
| <pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> |
| public class <span class="typeNameLabel">LanczosSolver</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">Simple implementation of the <a href="http://en.wikipedia.org/wiki/Lanczos_algorithm">Lanczos algorithm</a> for |
| finding eigenvalues of a symmetric matrix, applied to non-symmetric matrices by applying Matrix.timesSquared(vector) |
| as the "matrix-multiplication" method.<p> |
| |
| See the SSVD code for a better option |
| <a href="../../../../../../org/apache/mahout/math/ssvd/SequentialBigSvd.html" title="class in org.apache.mahout.math.ssvd"><code>SequentialBigSvd</code></a> |
| See also the docs on |
| <a href=https://mahout.apache.org/users/dim-reduction/ssvd.html>stochastic |
| projection SVD</a> |
| <p> |
| To avoid floating point overflow problems which arise in power-methods like Lanczos, an initial pass is made |
| through the input matrix to |
| <ul> |
| <li>generate a good starting seed vector by summing all the rows of the input matrix, and</li> |
| <li>compute the trace(inputMatrix<sup>t</sup>*matrix) |
| </ul> |
| <p> |
| This latter value, being the sum of all of the singular values, is used to rescale the entire matrix, effectively |
| forcing the largest singular value to be strictly less than one, and transforming floating point <em>overflow</em> |
| problems into floating point <em>underflow</em> (ie, very small singular values will become invisible, as they |
| will appear to be zero and the algorithm will terminate). |
| <p>This implementation uses <a href="../../../../../../org/apache/mahout/math/solver/EigenDecomposition.html" title="class in org.apache.mahout.math.solver"><code>EigenDecomposition</code></a> to do the |
| eigenvalue extraction from the small (desiredRank x desiredRank) tridiagonal matrix. Numerical stability is |
| achieved via brute-force: re-orthogonalization against all previous eigenvectors is computed after every pass. |
| This can be made smarter if (when!) this proves to be a major bottleneck. Of course, this step can be parallelized |
| as well.</div> |
| <dl> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="../../../../../../org/apache/mahout/math/ssvd/SequentialBigSvd.html" title="class in org.apache.mahout.math.ssvd"><code>SequentialBigSvd</code></a></dd> |
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| <tr class="altColor"> |
| <td class="colFirst"><code>static class </code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.TimingSection.html" title="enum in org.apache.mahout.math.decomposer.lanczos">LanczosSolver.TimingSection</a></span></code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#SAFE_MAX">SAFE_MAX</a></span></code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
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| <td class="colOne"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#LanczosSolver--">LanczosSolver</a></span>()</code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
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| <tr id="i0" class="altColor"> |
| <td class="colFirst"><code>protected static double</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#calculateScaleFactor-org.apache.mahout.math.Vector-">calculateScaleFactor</a></span>(<a href="../../../../../../org/apache/mahout/math/Vector.html" title="interface in org.apache.mahout.math">Vector</a> nextVector)</code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code>protected static void</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#orthoganalizeAgainstAllButLast-org.apache.mahout.math.Vector-org.apache.mahout.math.decomposer.lanczos.LanczosState-">orthoganalizeAgainstAllButLast</a></span>(<a href="../../../../../../org/apache/mahout/math/Vector.html" title="interface in org.apache.mahout.math">Vector</a> nextVector, |
| <a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state)</code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#solve-org.apache.mahout.math.decomposer.lanczos.LanczosState-int-">solve</a></span>(<a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state, |
| int desiredRank)</code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code>void</code></td> |
| <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosSolver.html#solve-org.apache.mahout.math.decomposer.lanczos.LanczosState-int-boolean-">solve</a></span>(<a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state, |
| int desiredRank, |
| boolean isSymmetric)</code> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </td> |
| </tr> |
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| <h3>Methods inherited from class java.lang.<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></h3> |
| <code><a href="http://docs.oracle.com/javase/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/docs/api/java/lang/Object.html?is-external=true#wait-long-int-" title="class or interface in java.lang">wait</a></code></li> |
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| <h4>SAFE_MAX</h4> |
| <pre>public static final double SAFE_MAX</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| <dl> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="../../../../../../constant-values.html#org.apache.mahout.math.decomposer.lanczos.LanczosSolver.SAFE_MAX">Constant Field Values</a></dd> |
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| <a name="LanczosSolver--"> |
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| <ul class="blockListLast"> |
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| <h4>LanczosSolver</h4> |
| <pre>public LanczosSolver()</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </li> |
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| <a name="solve-org.apache.mahout.math.decomposer.lanczos.LanczosState-int-"> |
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| <h4>solve</h4> |
| <pre>public void solve(<a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state, |
| int desiredRank)</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </li> |
| </ul> |
| <a name="solve-org.apache.mahout.math.decomposer.lanczos.LanczosState-int-boolean-"> |
| <!-- --> |
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| <h4>solve</h4> |
| <pre>public void solve(<a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state, |
| int desiredRank, |
| boolean isSymmetric)</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </li> |
| </ul> |
| <a name="calculateScaleFactor-org.apache.mahout.math.Vector-"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
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| <h4>calculateScaleFactor</h4> |
| <pre>protected static double calculateScaleFactor(<a href="../../../../../../org/apache/mahout/math/Vector.html" title="interface in org.apache.mahout.math">Vector</a> nextVector)</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
| </li> |
| </ul> |
| <a name="orthoganalizeAgainstAllButLast-org.apache.mahout.math.Vector-org.apache.mahout.math.decomposer.lanczos.LanczosState-"> |
| <!-- --> |
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| <h4>orthoganalizeAgainstAllButLast</h4> |
| <pre>protected static void orthoganalizeAgainstAllButLast(<a href="../../../../../../org/apache/mahout/math/Vector.html" title="interface in org.apache.mahout.math">Vector</a> nextVector, |
| <a href="../../../../../../org/apache/mahout/math/decomposer/lanczos/LanczosState.html" title="class in org.apache.mahout.math.decomposer.lanczos">LanczosState</a> state)</pre> |
| <div class="block"><span class="deprecatedLabel">Deprecated.</span> </div> |
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